type expr =
        Implication of (expr * expr) |
        Conjunction of (expr * expr) |
        Disjunction of (expr * expr) |
        Negation of expr |
        Forall of (string * expr) |
        Exists of (string * expr) |
        Predicate of (string * term list) |
        Equals of (term * term)
and term =
        Add of (term * term) |
        Multiply of (term * term) |
        Var of string |
        Increment of term |
        Zero |
        Function of (string * term list)
and document = Document of (expr list * expr * expr list);;

let take s ind = if String.length s <= ind || ind < 0 then None else Some (String.get s ind);;

let rec trim s =
        match take s 0 with
        | Some ' ' -> trim (String.sub s 1 (String.length s - 1))
        | _ -> s;;

let rec trim_end s =
        match take s (String.length s - 1) with
        | Some ' ' | Some '\n' | Some '\t' -> trim_end (String.sub s 0 (String.length s - 1))
        | _ -> s;;

let rec printTerm term =
        match term with
        | Add (a, b) -> "(" ^ (printTerm a) ^ "+" ^ (printTerm b) ^ ")"
        | Multiply (a, b) -> "(" ^ (printTerm a) ^ "*" ^ (printTerm b) ^ ")"
        | Var name -> name
        | Increment a -> (printTerm a) ^ "'"
        | Zero -> "0"
        | Function (name, terms) -> name ^ "(" ^ (String.concat "," (List.map printTerm terms)) ^ ")";;

let rec printExpr expr =
        match expr with
        | Implication (a, b) -> "(" ^ (printExpr a) ^ "->" ^ (printExpr b) ^ ")"
        | Conjunction (a, b) -> "(" ^ (printExpr a) ^ "&" ^ (printExpr b) ^ ")"
        | Disjunction (a, b) -> "(" ^ (printExpr a) ^ "|" ^ (printExpr b) ^ ")"
        | Negation a -> "!" ^ (printExpr a)
        | Forall (name, e) -> "(@" ^ name ^ "." ^ (printExpr e) ^ ")"
        | Exists (name, e) -> "(?" ^ name ^ "." ^ (printExpr e) ^ ")"
        | Predicate (name, es) -> name ^ "(" ^ (String.concat "," (List.map printTerm es)) ^ ")"
        | Equals (a, b) -> (printTerm a) ^ "=" ^ (printTerm b);;

let rec parseImplication s =
        match parseDisjunction s with
        | Some (dis, s) ->
                let s = trim s in
                (match (take s 0, take s 1) with
                | (Some '-', Some '>') ->
                        let s = String.sub s 2 (String.length s - 2) in
                        (match parseImplication s with
                        | Some (impl, s) -> Some (Implication (dis, impl), s)
                        | None -> None)
                | _ -> Some (dis, s))
        | None -> None
and parseDisjunction s =
        match parseConjunction s with
        | Some (conj, s) ->
                let rec func prev s =
                        let s = trim s in
                        match take s 0 with
                        | Some '|' ->
                                let s = String.sub s 1 (String.length s - 1) in
                                (match parseConjunction s with
                                | Some (conj, s) -> func (Disjunction (prev, conj)) s
                                | None -> None)
                        | _ -> Some (prev, s) in
                func conj s
        | None -> None
and parseConjunction s =
        match parseUnary s with
        | Some (unary, s) ->
                let rec func prev s =
                        let s = trim s in
                        match take s 0 with
                        | Some '&' ->
                                let s = String.sub s 1 (String.length s - 1) in
                                (match parseUnary s with
                                | Some (unary, s) -> func (Conjunction (prev, unary)) s
                                | None -> None)
                        | _ -> Some (prev, s) in
                func unary s
        | None -> None
and parseUnary s =
        let s = trim s in
        match take s 0 with
        | Some '(' ->
                (match parseImplication (String.sub s 1 (String.length s - 1)) with
                | Some (impl, s) ->
                        let s = trim s in
                        (match take s 0 with
                        | Some ')' -> Some (impl, String.sub s 1 (String.length s - 1))
                        | _ -> None)
                | None -> parsePredicate s)
        | Some '!' -> (match parseUnary (String.sub s 1 (String.length s - 1)) with
                | Some (unary, s) -> Some (Negation unary, s)
                | None -> None)
        | Some '@' | Some '?' ->
                let construct var expr = if take s 0 = Some '@' then Forall (var, expr) else Exists (var, expr) in
                (match parseVar (String.sub s 1 (String.length s - 1)) with
                | Some (Var var, s) ->
                        let s = trim s in
                        (match take s 0 with
                        | Some '.' ->
                                (match parseUnary (String.sub s 1 (String.length s - 1)) with
                                | Some (impl, s) -> Some (construct var impl, s)
                                | None -> None)
                        | _ -> None)
                | _ -> None)

        | _ ->
                parsePredicate s
and parseVar s =
        let s = trim s in
        match take s 0 with
        | Some a ->
                (match a with
                | 'a'..'z' ->
                        let rec func have s =
                                match take s 0 with
                                | Some a ->
                                        (match a with
                                        | '0'..'9' ->
                                                func (have ^ (Char.escaped a)) (String.sub s 1 (String.length s - 1))
                                        | _ -> (have, s))
                                | None -> (have, s) in
                        let (name, s) = func (Char.escaped a) (String.sub s 1 (String.length s - 1)) in
                        Some (Var name, s)
                | _ -> None)
        | None -> None
and parsePredicate s =
        let s = trim s in
        match take s 0 with
        | Some a ->
                (match a with
                | 'A'..'Z' ->
                        let rec func have s =
                                match take s 0 with
                                | Some a ->
                                        (match a with
                                        | '0'..'9' -> func (have ^ Char.escaped a) (String.sub s 1 (String.length s - 1))
                                        | _ -> (have, s))
                                | None -> (have, s) in
                        let (name, s) = func (Char.escaped a) (String.sub s 1 (String.length s - 1)) in
                        (match take s 0 with
                        | Some '(' ->
                                let s = String.sub s 1 (String.length s - 1) in
                                (match parseTerm s with
                                | Some (term, s) ->
                                        let rec func s =
                                                let s = trim s in
                                                match take s 0 with
                                                | Some ',' ->
                                                        (match parseTerm (String.sub s 1 (String.length s - 1)) with
                                                        | Some (term, s) ->
                                                                (match func s with
                                                                | Some (terms, s) ->
                                                                        Some (term :: terms, s)
                                                                | None -> None)
                                                        | None -> None)
                                                | _ -> Some ([], s) in
                                        (match func s with
                                        | Some (terms, s) ->
                                                let s = trim s in
                                                (match take s 0 with
                                                | Some ')' ->
                                                        Some (Predicate (name, term :: terms), String.sub s 1 (String.length s - 1))
                                                | _ -> None)
                                        | None -> None)
                                | None -> None)
                        | _ -> None)
                | _ ->
                        (match parseTerm s with
                        | Some (term, s) ->
                                let s = trim s in
                                (match take s 0 with
                                | Some '=' ->
                                        (match parseTerm (String.sub s 1 (String.length s - 1)) with
                                        | Some (term1, s) ->
                                                Some (Equals (term, term1), s)
                                        | None -> None)
                                | _ -> None)
                        | None -> None))
        | None -> None
and parseTerm s =
        match parseSummand s with
        | Some (summand, s) ->
                let rec func have s =
                        let s = trim s in
                        match take s 0 with
                        | Some '+' ->
                                let s = String.sub s 1 (String.length s - 1) in
                                (match parseSummand s with
                                | Some (summand, s) ->
                                        func (Add (have, summand)) s
                                | None -> None)
                        | _ -> Some (have, s) in
                func summand s
        | None -> None
and parseSummand s =
        match parseInc s with
        | Some (mul, s) ->
                let rec func have s =
                        let s = trim s in
                        match take s 0 with
                        | Some '*' ->
                                let s = String.sub s 1 (String.length s - 1) in
                                (match parseInc s with
                                | Some (mul, s) ->
                                        func (Multiply (have, mul)) s
                                | None -> None)
                        | _ -> Some (have, s) in
                func mul s
        | None -> None
and parseInc s =
        match parseMultiplying s with
        | Some (now, s) ->
                let rec func have s =
                        let s = trim s in
                        match take s 0 with
                        | Some '\'' ->
                                func (Increment have) (String.sub s 1 (String.length s - 1))
                        | _ -> (have, s) in
                let (now, s) = func now s in
                Some (now, s)
        | None -> None
and parseMultiplying s =
        let s = trim s in
        match take s 0 with
        | Some a ->
                (match a with
                | '0' -> Some (Zero, String.sub s 1 (String.length s - 1))
                | '(' ->
                        let s = String.sub s 1 (String.length s - 1) in
                        (match parseTerm s with
                        | Some (term, s) ->
                                let s = trim s in
                                (match take s 0 with
                                | Some ')' ->
                                        Some (term, String.sub s 1 (String.length s - 1))
                                | _ -> None)
                        | None -> None)
                | _ ->
                        (match parseVar s with
                        | Some (Var name, s) ->
                                (match take s 0 with
                                | Some '(' ->
                                        let s = String.sub s 1 (String.length s - 1) in
                                        (match parseTerm s with
                                        | Some (term, s) ->
                                                let rec func s =
                                                        let s = trim s in
                                                        match take s 0 with
                                                        | Some ',' ->
                                                                (match parseTerm (String.sub s 1 (String.length s - 1)) with
                                                                | Some (term, s) ->
                                                                        (match func s with
                                                                        | Some (terms, s) ->
                                                                                Some (term :: terms, s)
                                                                        | None -> None)
                                                                | None -> None)
                                                        | _ -> Some ([], s) in
                                                (match func s with
                                                | Some (terms, s) ->
                                                        let s = trim s in
                                                        (match take s 0 with
                                                        | Some ')' ->
                                                                Some (Function (name, term :: terms), String.sub s 1 (String.length s - 1))
                                                        | _ -> None)
                                                | None -> None)
                                        | None -> None)
                                | _ -> Some (Var name, s))
                        | _ -> None))
        | None -> None;;

let parse s =
        match parseImplication s with
        | Some (expr, s) ->
                let s = trim s in
                if String.length s = 0 then Some expr else None
        | None -> None;;

let find_barrier s =
        let rec find_barrier_int s ind =
                match take s 0 with
                | Some '|' ->
                        (match take s 1 with
                        | Some '-' ->
                                Some ind
                        | _ ->
                                find_barrier_int (String.sub s 1 (String.length s - 1)) (ind + 1))
                | Some a ->
                        find_barrier_int (String.sub s 1 (String.length s - 1)) (ind + 1)
                | None -> None in
        find_barrier_int s 0;;

let parseDocument s =
        let rec func c s =
                match parseImplication s with
                | Some (impl, s) ->
                        let s = trim s in
                        if take s 0 = Some c then
                                (match func c (String.sub s 1 (String.length s - 1)) with
                                | Some (last, s) ->
                                        Some (impl :: last, s)
                                | None -> None)
                        else if take s 0 = None then
                                Some (impl :: [], s)
                        else None
                | None -> None in
        match find_barrier s with
        | Some ind ->
                let s1 = trim (String.sub s 0 ind) in
                let s = trim_end (trim (String.sub s (ind + 2) (String.length s - ind - 2))) in
                (match ((if String.length s1 = 0 then Some ([], "") else func ',' s1), func '\n' s) with
                | (Some (d1, _) , Some (d2 :: d3, _)) ->
                        Some (Document (d1, d2, d3))
                | _ -> None)
        | None -> None;;

let printDocument (Document (d1, d2, d3)) = (String.concat "," (List.map printExpr d1)) ^ "|-" ^ (printExpr d2) ^ "\n" ^ (String.concat "\n" (List.map printExpr d3));;

let parse_bad s =
        match parse s with
        | Some x -> x
        | None -> failwith "Bad expression"
and parseDocument_bad s =
        match parseDocument s with
        | Some x -> x
        | None -> failwith "Bad document";;

let rawSchemes =
        ["A(0) -> B(0) -> A(0)";
        "(A(0) -> B(0)) -> (A(0) -> B(0) -> C(0)) -> (A(0) -> C(0))";
        "A(0) -> B(0) -> A(0) & B(0)";
        "A(0) & B(0) -> A(0)";
        "A(0) & B(0) -> B(0)";
        "A(0) -> A(0) | B(0)";
        "B(0) -> A(0) | B(0)";
        "(A(0) -> C(0)) -> (B(0) -> C(0)) -> (A(0) | B(0) -> C(0))";
        "(A(0) -> B(0)) -> (A(0) -> !B(0)) -> !A(0)";
        "!!A(0) -> A(0)"];;

let schemes = List.map parse_bad rawSchemes;;

let rawAxioms =
        ["a = b -> a' = b'";
        "a = b -> a = c -> b = c";
        "a' = b' -> a = b";
        "!a' = 0";
        "a + b' = (a + b)'";
        "a + 0 = a";
        "a * 0 = 0";
        "a * b' = a * b + a"];;

let axioms = List.map parse_bad rawAxioms;;

module StringMap = Map.Make(String);;
module ExprMap = Map.Make(struct type t = expr let compare = compare end);;
module ExprSet = Set.Make(struct type t = expr let compare = compare end);;
module StringSet = Set.Make(String);;

let rec freeVars e =
        match e with
        | Implication (a, b) | Conjunction (a, b) | Disjunction (a, b) ->
                StringSet.union (freeVars a) (freeVars b)
        | Negation a ->
                freeVars a
        | Exists (name, a) | Forall (name, a) ->
                StringSet.remove name (freeVars a)
        | Predicate (_, l) ->
                List.fold_left (fun m a -> StringSet.union m (freeVarsTerm a)) StringSet.empty l
        | Equals (a, b) ->
                StringSet.union (freeVarsTerm a) (freeVarsTerm b)
and freeVarsTerm t =
        match t with
        | Add (a, b) | Multiply (a, b) ->
                StringSet.union (freeVarsTerm a) (freeVarsTerm b)
        | Var name ->
                StringSet.singleton name
        | Increment a ->
                freeVarsTerm a
        | Zero ->
                StringSet.empty
        | Function (_, l) ->
                List.fold_left (fun m a -> StringSet.union m (freeVarsTerm a)) StringSet.empty l;;

let upperPred e name =
        let rec upperPredExpr e name =
                match e with
                | Implication (a, b) | Conjunction (a, b) | Disjunction (a, b) ->
                        (match (upperPredExpr a name, upperPredExpr b name) with
                        | (None, None) -> None
                        | (a, b) -> Some (StringSet.union (takeOr a) (takeOr b)))
                | Negation a ->
                        upperPredExpr a name
                | Exists (var, a) | Forall (var, a) ->
                        (match upperPredExpr a name with
                        | None -> None
                        | Some b -> Some (StringSet.add var b))
                | Predicate (_, l) ->
                        List.fold_left (fun m a ->
                                match m with
                                | None -> upperPredTerm a name
                                | Some b ->
                                        Some (StringSet.union b (takeOr (upperPredTerm a name)))) None l
                | Equals (a, b) ->
                        (match (upperPredTerm a name, upperPredTerm b name) with
                        | (None, None) -> None
                        | (a, b) -> Some (StringSet.union (takeOr a) (takeOr b)))
        and upperPredTerm t name =
                match t with
                | Add (a, b) | Multiply (a, b) ->
                        (match (upperPredTerm a name, upperPredTerm b name) with
                        | (None, None) -> None
                        | (a, b) -> Some (StringSet.union (takeOr a) (takeOr b)))
                | Var var ->
                        if var = name then Some StringSet.empty else None
                | Increment a ->
                        upperPredTerm a name
                | Zero ->
                        None
                | Function (_, l) ->
                        List.fold_left (fun m a ->
                                match m with
                                | None -> upperPredTerm a name
                                | Some b ->
                                        Some (StringSet.union b (takeOr (upperPredTerm a name)))) None l

        and takeOr a =
                match a with
                | Some b -> b
                | None -> StringSet.empty in
        takeOr (upperPredExpr e name);;

let println_string s = print_string (s ^ "\n");;

let rec transformTerm e was became =
        let rec transform t =
                if t = was then became else
                        match t with
                        | Add (a, b) ->
                                Add (transform a, transform b)
                        | Multiply (a, b) ->
                                Multiply (transform a, transform b)
                        | Var name ->
                                Var name
                        | Increment a ->
                                Increment (transform a)
                        | Zero ->
                                Zero
                        | Function (name, l) ->
                                Function (name, List.map transform l) in
        let rec func e =
                match e with
                | Implication (a, b) ->
                        Implication (func a, func b)
                | Conjunction (a, b) ->
                        Conjunction (func a, func b)
                | Disjunction (a, b) ->
                        Disjunction (func a, func b)
                | Negation a ->
                        Negation (func a)
                | Forall (var, a) ->
                        Forall (var, func a)
                | Exists (var, a) ->
                        Exists (var, func a)
                | Predicate (name, l) ->
                        Predicate (name, List.map (fun e -> transform e) l)
                | Equals (a, b) ->
                        Equals (transform a, transform b) in
        func e
and transformExpr e was became =
        let rec func e =
                if e = was then became else
                        match e with
                        | Implication (a, b) ->
                                Implication (func a, func b)
                        | Conjunction (a, b) ->
                                Conjunction (func a, func b)
                        | Disjunction (a, b) ->
                                Disjunction (func a, func b)
                        | Negation a ->
                                Negation (func a)
                        | Forall (var, a) ->
                                Forall (var, func a)
                        | Exists (var, a) ->
                                Exists (var, func a)
                        | Predicate (name, l) ->
                                Predicate (name, l)
                        | Equals (a, b) ->
                                Equals (a, b) in
        func e;;

let rec findTerm e1 e2 need =
        let rec find t1 t2 =
                if t1 = need then Some t2 else
                        match (t1, t2) with
                        | (Add (a1, b1), Add (a2, b2)) | (Multiply (a1, b1), Multiply (a2, b2)) ->
                                let res = find a1 a2 in
                                if res = None then find b1 b2 else res
                        | (Increment a1, Increment a2) ->
                                find a1 a2
                        | (Function (name1, l1), Function (name2, l2)) ->
                                if name1 = name2 then
                                        if List.length l1 = List.length l2 then
                                                List.fold_left (fun a (b1, b2) ->
                                                        match a with
                                                        | Some c -> Some c
                                                        | None -> find b1 b2) None (List.combine l1 l2)
                                        else None
                                else None
                        | (_, _) -> None in
        let rec func e1 e2 =
                match (e1, e2) with
                | (Implication (a1, b1), Implication (a2, b2))
                | (Conjunction (a1, b1), Conjunction (a2, b2))
                | (Disjunction (a1, b1), Disjunction (a2, b2)) ->
                        let res = func a1 a2 in
                        if res = None then func b1 b2 else res
                | (Negation a1, Negation a2) ->
                        func a1 a2
                | (Forall (var1, a1), Forall (var2, a2))
                | (Exists (var1, a1), Exists (var2, a2)) ->
                        if var1 = var2 then func a1 a2 else None
                | (Predicate (name1, l1), Predicate (name2, l2)) ->
                        if name1 = name2 then
                                if List.length l1 = List.length l2 then
                                        List.fold_left (fun a (b1, b2) ->
                                                match a with
                                                | Some c -> Some c
                                                | None -> find b1 b2) None (List.combine l1 l2)
                                else None
                        else None
                | (Equals (a1, b1), Equals (a2, b2)) ->
                        let res = find a1 a2 in
                        if res = None then find b1 b2 else res
                | (_, _) -> None in
        func e1 e2
and findExpr e1 e2 need =
        let rec func e1 e2 =
                if e1 = need then Some e2 else
                        match (e1, e2) with
                        | (Implication (a1, b1), Implication (a2, b2))
                        | (Conjunction (a1, b1), Conjunction (a2, b2))
                        | (Disjunction (a1, b1), Disjunction (a2, b2)) ->
                                let res = func a1 a2 in
                                if res = None then func b1 b2 else res
                        | (Negation a1, Negation a2) ->
                                func a1 a2
                        | (Forall (var1, a1), Forall (var2, a2))
                        | (Exists (var1, a1), Exists (var2, a2)) ->
                                if var1 = var2 then func a1 a2 else None
                        | (_, _) -> None in
        func e1 e2;;

let is_scheme_axiom e ax =
        let func e was became =
                match became with
                | None -> e
                | Some became -> transformExpr e was became in
        let a = findExpr ax e (Predicate ("A", [Zero])) in
        let b = findExpr ax e (Predicate ("B", [Zero])) in
        let c = findExpr ax e (Predicate ("C", [Zero])) in
        let za = func ax (Predicate ("A", [Zero])) a in
        let zb = func za (Predicate ("B", [Zero])) b in
        let zc = func zb (Predicate ("C", [Zero])) c in
        zc = e;;

let enumerate l =
        let rec func l a =
                match l with
                | [] -> []
                | x :: xs -> (x, a) :: (func xs (a + 1)) in
        func l 0;;

let which_scheme_axiom e =
        let eschemes = enumerate schemes in
        let axs = List.map (fun (a, num) -> if is_scheme_axiom e a then Some num else None) eschemes in
        List.fold_left (fun was now ->
                match was with
                | None -> now
                | Some a -> Some a) None axs;;

let print_scheme_number e =
        match which_scheme_axiom e with
        | None -> -1
        | Some a -> a;;

let check11 e =
        match e with
        | Implication (Forall (var, c), b) ->
                (match findTerm c b (Var var) with
                | Some expr ->
                        if StringSet.is_empty (StringSet.inter (freeVarsTerm expr) (upperPred c var)) then
                                transformTerm c (Var var) expr = b
                        else false
                | None -> false)
        | _ -> false;;

let check12 e =
        match e with
        | Implication (b, Exists (var, c)) ->
                (match findTerm c b (Var var) with
                | Some expr ->
                        if StringSet.is_empty (StringSet.inter (freeVarsTerm expr) (upperPred c var)) then
                                transformTerm c (Var var) expr = b
                        else false
                | None -> false)
        | _ -> false;;

let checkInduction e =
        match e with
        | Implication (Conjunction (s, Forall (var, bb)), res) ->
                s = (transformTerm res (Var var) Zero) && bb = (Implication (res, transformTerm res (Var var) (Increment (Var var))))
        | _ -> false;;

let checkAllAxioms e =
        match which_scheme_axiom e with
        | Some a -> Some ("Scheme " ^ (string_of_int (a + 1)))
        | None ->
                if check11 e then Some "Scheme 11" else
                if check12 e then Some "Scheme 12" else
                if checkInduction e then Some "Induction" else
                let eaxioms = enumerate axioms in
                match List.find_opt (fun (now, _) -> now = e) eaxioms with
                | Some (_, num) -> Some ("Axiom " ^ (string_of_int (num + 1)))
                | None -> None;;

let printAllAxioms e =
        match checkAllAxioms e with
        | None -> "Nothing"
        | Some a -> a;;

let rec checkProof (Document (was, need, proof)) =
        let wasExprs = List.fold_left (fun set x -> ExprSet.add x set) ExprSet.empty was in
        let func was needLeft needRight e =
                if match checkAllAxioms e with
                | Some _ -> true
                | None ->
                        match e with
                        | Implication (a, Forall (x, b)) ->
                                if (List.exists (fun v -> v = x) (StringSet.elements (freeVars a)) = false) && (ExprSet.mem (Implication (a, b)) was) then true
                                else (ExprSet.mem e wasExprs) || (ExprSet.mem e needRight)
                        | Implication (Exists (x, b), a) ->
                                if (List.exists (fun v -> v = x) (StringSet.elements (freeVars a)) = false) && (ExprSet.mem (Implication (b, a)) was) then true
                                else (ExprSet.mem e wasExprs) || (ExprSet.mem e needRight)
                        | _ ->
                                (ExprSet.mem e wasExprs) || (ExprSet.mem e needRight) then
                        let was = ExprSet.add e was in
                        let (needLeft, needRight) =
                                match ExprMap.find_opt e needLeft with
                                | Some l ->
                                        (ExprMap.remove e needLeft, List.fold_left (fun need x -> ExprSet.add x need) needRight l)
                                | None ->
                                        (needLeft, needRight) in
                        let (needLeft, needRight) =
                                match e with
                                | Implication (a, b) ->
                                        if ExprSet.mem a was then (needLeft, ExprSet.add b needRight)
                                        else (ExprMap.add a (b :: (match ExprMap.find_opt a needLeft with
                                        | Some a -> a
                                        | None -> [])) needLeft, needRight)
                                | _ ->
                                        (needLeft, needRight) in
                        Some (was, needLeft, needRight)
                else None in
        let rec repeat eproof was needLeft needRight =
                match eproof with
                | (x, num) :: xs ->
                        (match func was needLeft needRight x with
                        | Some (was, needLeft, needRight) ->
                                repeat xs was needLeft needRight
                        | None -> Some num)
                | [] -> None in
        match repeat (enumerate proof) ExprSet.empty ExprMap.empty ExprSet.empty with
        | Some num -> "Line " ^ (string_of_int (num + 1)) ^ " can't be obtained"
        | None -> if List.exists (fun v -> v = need) proof then "Proof is correct" else "Required hasn't been proven";;

let parseList l = parseDocument_bad ("|-" ^ (List.nth l (List.length l - 1)) ^ "\n" ^ (String.concat "\n" l));;
let rec parseL l =
        match l with
        | x :: xs ->
                (match parse x with
                | Some _ -> parseL xs
                | None -> "Error on " ^ x)
        | [] -> "No errors";;
let zeroEqZero =
        ["(a=b->a=c->b=c)->(0=0->0=0->0=0)->(a=b->a=c->b=c)";
         "a=b->a=c->b=c";
         "0=0->0=0->0=0";
         "(0=0->0=0->0=0)->(a=b->a=c->b=c)";
         "(0=0->0=0->0=0)->@c.(a=b->a=c->b=c)";
         "(0=0->0=0->0=0)->@b.@c.(a=b->a=c->b=c)";
         "(0=0->0=0->0=0)->@a.@b.@c.(a=b->a=c->b=c)";
         "@a.@b.@c.(a=b->a=c->b=c)";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(0+0=b->0+0=c->b=c)";
         "@b.@c.(0+0=b->0+0=c->b=c)";
         "@b.@c.(0+0=b->0+0=c->b=c)->@c.(0+0=0->0+0=c->0=c)";
         "@c.(0+0=0->0+0=c->0=c)";
         "@c.(0+0=0->0+0=c->0=c)->(0+0=0->0+0=0->0=0)";
         "0+0=0->0+0=0->0=0";
         "(a+0=a)->(0=0->0=0->0=0)->(a+0=a)";
         "a+0=a";
         "(0=0->0=0->0=0)->(a+0=a)";
         "(0=0->0=0->0=0)->@a.(a+0=a)";
         "@a.(a+0=a)";
         "@a.(a+0=a)->(0+0=0)";
         "0+0=0";
         "0+0=0->0=0";
         "0=0"];;
let equality = zeroEqZero @
        ["(0=0)&@a.(a=a->a'=a')->a=a";
         "(a=b->a'=b')->(0=0)->(a=b->a'=b')";
         "a=b->a'=b'";
         "(0=0)->(a=b->a'=b')";
         "(0=0)->@b.(a=b->a'=b')";
         "@b.(a=b->a'=b')";
         "(0=0)->@a.@b.(a=b->a'=b')";
         "@a.@b.(a=b->a'=b')";
         "@b.(a=b->a'=b')->(a=a->a'=a')";
         "a=a->a'=a'";
         "(a=a->a'=a')->0=0->(a=a->a'=a')";
         "0=0->(a=a->a'=a')";
         "0=0->@a.(a=a->a'=a')";
         "@a.(a=a->a'=a')";
         "(0=0)->@a.(a=a->a'=a')->(0=0)&@a.(a=a->a'=a')";
         "@a.(a=a->a'=a')->(0=0)&@a.(a=a->a'=a')";
         "(0=0)&@a.(a=a->a'=a')";
         "a=a";
         "a=a->0=0->a=a";
         "0=0->a=a";
         "0=0->@a.(a=a)";
         "@a.(a=a)"];;
let commutativity = equality @
        ["(a=b->a=c->b=c)->(0=0)->(a=b->a=c->b=c)";
         "a=b->a=c->b=c";
         "0=0->a=b->a=c->b=c";
         "0=0->@c.(a=b->a=c->b=c)";
         "@c.(a=b->a=c->b=c)";
         "@c.(a=b->a=c->b=c)->(a=b->a=a->b=a)";
         "a=b->a=a->b=a";
         "(a=b->a=a)->(a=b->a=a->b=a)->(a=b->b=a)";
         "a=a->a=b->a=a";
         "a=b->a=a";
         "(a=b->a=a->b=a)->(a=b->b=a)";
         "a=b->b=a";
         "(a=b->b=a)->0=0->(a=b->b=a)";
         "0=0->a=b->b=a";
         "0=0->@b.(a=b->b=a)";
         "0=0->@a.@b.(a=b->b=a)";
         "@a.@b.(a=b->b=a)"];;
let a'pbEqapb' = commutativity @
        ["a=b->a'=b'";
         "(a=b->a'=b')->0=0->a=b->a'=b'";
         "0=0->a=b->a'=b'";
         "0=0->@b.(a=b->a'=b')";
         "0=0->@a.@b.(a=b->a'=b')";
         "@a.@b.(a=b->a'=b')";
         "@a.@b.(a=b->a'=b')->@b.(a'+e=b->(a'+e)'=b')";
         "@b.(a'+e=b->(a'+e)'=b')";
         "@b.(a'+e=b->(a'+e)'=b')->(a'+e=(a+e)'->(a'+e)'=(a+e)'')";
         "a'+e=(a+e)'->(a'+e)'=(a+e)''";
         "a+b'=(a+b)'";
         "a+b'=(a+b)'->0=0->a+b'=(a+b)'";
         "0=0->a+b'=(a+b)'";
         "0=0->@b.(a+b'=(a+b)')";
         "0=0->@a.@b.(a+b'=(a+b)')";
         "@a.@b.(a+b'=(a+b)')";
         "@a.@b.(a+b'=(a+b)')->@b.(a'+b'=(a'+b)')";
         "@b.(a'+b'=(a'+b)')";
         "@b.(a'+b'=(a'+b)')->a'+e'=(a'+e)'";
         "a'+e'=(a'+e)'";
         "@a.@b.(a=b->b=a)->@b.(a'+e'=b->b=a'+e')";
         "@b.(a'+e'=b->b=a'+e')";
         "@b.(a'+e'=b->b=a'+e')->(a'+e'=(a'+e)'->(a'+e)'=a'+e')";
         "a'+e'=(a'+e)'->(a'+e)'=a'+e'";
         "(a'+e)'=a'+e'";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.((a'+e)'=b->(a'+e)'=c->b=c)";
         "@b.@c.((a'+e)'=b->(a'+e)'=c->b=c)";
         "@b.@c.((a'+e)'=b->(a'+e)'=c->b=c)->@c.((a'+e)'=a'+e'->(a'+e)'=c->a'+e'=c)";
         "@c.((a'+e)'=a'+e'->(a'+e)'=c->a'+e'=c)";
         "@c.((a'+e)'=a'+e'->(a'+e)'=c->a'+e'=c)->((a'+e)'=a'+e'->(a'+e)'=(a+e)''->a'+e'=(a+e)'')";
         "(a'+e)'=a'+e'->(a'+e)'=(a+e)''->a'+e'=(a+e)''";
         "(a'+e)'=(a+e)''->a'+e'=(a+e)''";
         "((a'+e)'=(a+e)''->a'+e'=(a+e)'')->(a'+e=(a+e)')->((a'+e)'=(a+e)''->a'+e'=(a+e)'')";
         "a'+e=(a+e)'->(a'+e)'=(a+e)''->a'+e'=(a+e)''";
         "(a'+e=(a+e)'->(a'+e)'=(a+e)'')->(a'+e=(a+e)'->(a'+e)'=(a+e)''->a'+e'=(a+e)'')->(a'+e=(a+e)'->a'+e'=(a+e)'')";
         "(a'+e=(a+e)'->(a'+e)'=(a+e)''->a'+e'=(a+e)'')->(a'+e=(a+e)'->a'+e'=(a+e)'')";
         "a'+e=(a+e)'->a'+e'=(a+e)''";
         "@a.@b.(a=b->b=a)->@b.(a'+e'=b->b=a'+e')";
         "@b.(a'+e'=b->b=a'+e')";
         "@b.(a'+e'=b->b=a'+e')->(a'+e'=(a+e)''->(a+e)''=a'+e')";
         "a'+e'=(a+e)''->(a+e)''=a'+e'";
         "(a'+e'=(a+e)''->(a+e)''=a'+e')->(a'+e=(a+e)')->(a'+e'=(a+e)''->(a+e)''=a'+e')";
         "a'+e=(a+e)'->a'+e'=(a+e)''->(a+e)''=a'+e'";
         "(a'+e=(a+e)'->a'+e'=(a+e)'')->(a'+e=(a+e)'->a'+e'=(a+e)''->(a+e)''=a'+e')->(a'+e=(a+e)'->(a+e)''=a'+e')";
         "(a'+e=(a+e)'->a'+e'=(a+e)''->(a+e)''=a'+e')->(a'+e=(a+e)'->(a+e)''=a'+e')";
         "a'+e=(a+e)'->(a+e)''=a'+e'";
         "@a.@b.(a+b'=(a+b)')";
         "@a.@b.(a+b'=(a+b)')->@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')->a+e'=(a+e)'";
         "a+e'=(a+e)'";
         "@a.@b.(a=b->a'=b')->@b.(a+e'=b->(a+e')'=b')";
         "@b.(a+e'=b->(a+e')'=b')";
         "@b.(a+e'=b->(a+e')'=b')->(a+e'=(a+e)'->(a+e')'=(a+e)'')";
         "a+e'=(a+e)'->(a+e')'=(a+e)''";
         "(a+e')'=(a+e)''";
         "@a.@b.(a=b->b=a)->@b.((a+e')'=b->b=(a+e')')";
         "@b.((a+e')'=b->b=(a+e')')";
         "@b.((a+e')'=b->b=(a+e')')->((a+e')'=(a+e)''->(a+e)''=(a+e')')";
         "(a+e')'=(a+e)''->(a+e)''=(a+e')'";
         "(a+e)''=(a+e')'";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.((a+e)''=b->(a+e)''=c->b=c)";
         "@b.@c.((a+e)''=b->(a+e)''=c->b=c)";
         "@b.@c.((a+e)''=b->(a+e)''=c->b=c)->@c.((a+e)''=a'+e'->(a+e)''=c->a'+e'=c)";
         "@c.((a+e)''=a'+e'->(a+e)''=c->a'+e'=c)";
         "@c.((a+e)''=a'+e'->(a+e)''=c->a'+e'=c)->((a+e)''=a'+e'->(a+e)''=(a+e')'->a'+e'=(a+e')')";
         "(a+e)''=a'+e'->(a+e)''=(a+e')'->a'+e'=(a+e')'";
         "((a+e)''=a'+e'->(a+e)''=(a+e')'->a'+e'=(a+e')')->(a'+e=(a+e)')->((a+e)''=a'+e'->(a+e)''=(a+e')'->a'+e'=(a+e')')";
         "(a'+e=(a+e)')->((a+e)''=a'+e'->(a+e)''=(a+e')'->a'+e'=(a+e')')";
         "a'+e=(a+e)'->(a+e)''=a'+e'->(a+e)''=(a+e')'->a'+e'=(a+e')'";
         "(a'+e=(a+e)'->(a+e)''=a'+e')->(a'+e=(a+e)'->(a+e)''=a'+e'->(a+e)''=(a+e')'->a'+e'=(a+e')')->(a'+e=(a+e)'->(a+e)''=(a+e')'->a'+e'=(a+e')')";
         "(a'+e=(a+e)'->(a+e)''=a'+e'->(a+e)''=(a+e')'->a'+e'=(a+e')')->(a'+e=(a+e)'->(a+e)''=(a+e')'->a'+e'=(a+e')')";
         "a'+e=(a+e)'->(a+e)''=(a+e')'->a'+e'=(a+e')'";
         "(a+e)''=(a+e')'->a'+e=(a+e)'->(a+e)''=(a+e')'";
         "a'+e=(a+e)'->(a+e)''=(a+e')'";
         "(a'+e=(a+e)'->(a+e)''=(a+e')')->(a'+e=(a+e)'->(a+e)''=(a+e')'->a'+e'=(a+e')')->(a'+e=(a+e)'->a'+e'=(a+e')')";
         "(a'+e=(a+e)'->(a+e)''=(a+e')'->a'+e'=(a+e')')->(a'+e=(a+e)'->a'+e'=(a+e')')";
         "a'+e=(a+e)'->a'+e'=(a+e')'";
         "(a'+e=(a+e)'->a'+e'=(a+e')')->0=0->(a'+e=(a+e)'->a'+e'=(a+e')')";
         "0=0->(a'+e=(a+e)'->a'+e'=(a+e')')";
         "0=0->@e.(a'+e=(a+e)'->a'+e'=(a+e')')";
         "@e.(a'+e=(a+e)'->a'+e'=(a+e')')";
         "a+0=a->0=0->a+0=a";
         "0=0->a+0=a";
         "0=0->@a.(a+0=a)";
         "@a.(a+0=a)";
         "@a.(a+0=a)->(a'+0=a')";
         "a'+0=a'";
         "@a.@b.(a=b->a'=b')->@b.(a+0=b->(a+0)'=b')";
         "@b.(a+0=b->(a+0)'=b')";
         "@b.(a+0=b->(a+0)'=b')->(a+0=a->(a+0)'=a')";
         "a+0=a->(a+0)'=a'";
         "(a+0)'=a'";
         "@a.@b.(a=b->b=a)->@b.(a'+0=b->b=a'+0)";
         "@b.(a'+0=b->b=a'+0)";
         "@b.(a'+0=b->b=a'+0)->(a'+0=a'->a'=a'+0)";
         "a'+0=a'->a'=a'+0";
         "a'=a'+0";
         "@a.@b.(a=b->b=a)->@b.((a+0)'=b->b=(a+0)')";
         "@b.((a+0)'=b->b=(a+0)')";
         "@b.((a+0)'=b->b=(a+0)')->((a+0)'=a'->a'=(a+0)')";
         "(a+0)'=a'->a'=(a+0)'";
         "a'=(a+0)'";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(a'=b->a'=c->b=c)";
         "@b.@c.(a'=b->a'=c->b=c)";
         "@b.@c.(a'=b->a'=c->b=c)->@c.(a'=a'+0->a'=c->a'+0=c)";
         "@c.(a'=a'+0->a'=c->a'+0=c)";
         "@c.(a'=a'+0->a'=c->a'+0=c)->(a'=a'+0->a'=(a+0)'->a'+0=(a+0)')";
         "a'=a'+0->a'=(a+0)'->a'+0=(a+0)'";
         "a'=(a+0)'->a'+0=(a+0)'";
         "a'+0=(a+0)'";
         "a'+0=(a+0)'->@e.(a'+e=(a+e)'->a'+e'=(a+e')')->a'+0=(a+0)'&@e.(a'+e=(a+e)'->a'+e'=(a+e')')";
         "@e.(a'+e=(a+e)'->a'+e'=(a+e')')->a'+0=(a+0)'&@e.(a'+e=(a+e)'->a'+e'=(a+e')')";
         "a'+0=(a+0)'&@e.(a'+e=(a+e)'->a'+e'=(a+e')')";
         "a'+0=(a+0)'&@e.(a'+e=(a+e)'->a'+e'=(a+e')')->(a'+e=(a+e)')";
         "a'+e=(a+e)'";
         "(a'+e=(a+e)')->0=0->(a'+e=(a+e)')";
         "0=0->(a'+e=(a+e)')";
         "0=0->@e.(a'+e=(a+e)')";
         "0=0->@a.@e.(a'+e=(a+e)')";
         "@a.@e.(a'+e=(a+e)')";
         "@a.@e.(a'+e=(a+e)')->@e.(a'+e=(a+e)')";
         "@e.(a'+e=(a+e)')";
         "@e.(a'+e=(a+e)')->(a'+b=(a+b)')";
         "a'+b=(a+b)'";
         "a'+b=(a+b)'->0=0->a'+b=(a+b)'";
         "0=0->a'+b=(a+b)'";
         "0=0->@b.(a'+b=(a+b)')";
         "0=0->@a.@b.(a'+b=(a+b)')";
         "@a.@b.(a'+b=(a+b)')"];;
let zeroPlusAEqA = a'pbEqapb' @
        ["@a.(a+0=a)->(0+0=0)";
         "0+0=0";
         "@a.@b.(a=b->a'=b')->@b.(0+a=b->(0+a)'=b')";
         "@b.(0+a=b->(0+a)'=b')";
         "@b.(0+a=b->(0+a)'=b')->(0+a=a->(0+a)'=a')";
         "0+a=a->(0+a)'=a'";
         "@a.@b.(a+b'=(a+b)')->@b.(0+b'=(0+b)')";
         "@b.(0+b'=(0+b)')";
         "@b.(0+b'=(0+b)')->(0+a'=(0+a)')";
         "0+a'=(0+a)'";
         "@a.@b.(a=b->b=a)->@b.(0+a'=b->b=0+a')";
         "@b.(0+a'=b->b=0+a')";
         "@b.(0+a'=b->b=0+a')->(0+a'=(0+a)'->(0+a)'=0+a')";
         "0+a'=(0+a)'->(0+a)'=0+a'";
         "(0+a)'=0+a'";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.((0+a)'=b->(0+a)'=c->b=c)";
         "@b.@c.((0+a)'=b->(0+a)'=c->b=c)";
         "@b.@c.((0+a)'=b->(0+a)'=c->b=c)->@c.((0+a)'=0+a'->(0+a)'=c->0+a'=c)";
         "@c.((0+a)'=0+a'->(0+a)'=c->0+a'=c)";
         "@c.((0+a)'=0+a'->(0+a)'=c->0+a'=c)->((0+a)'=0+a'->(0+a)'=a'->0+a'=a')";
         "(0+a)'=0+a'->(0+a)'=a'->0+a'=a'";
         "(0+a)'=a'->0+a'=a'";
         "((0+a)'=a'->0+a'=a')->0+a=a->((0+a)'=a'->0+a'=a')";
         "0+a=a->(0+a)'=a'->0+a'=a'";
         "(0+a=a->(0+a)'=a')->(0+a=a->(0+a)'=a'->0+a'=a')->(0+a=a->0+a'=a')";
         "(0+a=a->(0+a)'=a'->0+a'=a')->(0+a=a->0+a'=a')";
         "0+a=a->0+a'=a'";
         "(0+a=a->0+a'=a')->0=0->(0+a=a->0+a'=a')";
         "0=0->(0+a=a->0+a'=a')";
         "0=0->@a.(0+a=a->0+a'=a')";
         "@a.(0+a=a->0+a'=a')";
         "(0+0=0)->@a.(0+a=a->0+a'=a')->(0+0=0)&@a.(0+a=a->0+a'=a')";
         "@a.(0+a=a->0+a'=a')->(0+0=0)&@a.(0+a=a->0+a'=a')";
         "(0+0=0)&@a.(0+a=a->0+a'=a')";
         "(0+0=0)&@a.(0+a=a->0+a'=a')->0+a=a";
         "0+a=a";
         "0+a=a->0=0->0+a=a";
         "0=0->0+a=a";
         "0=0->@a.(0+a=a)";
         "@a.(0+a=a)"];;
let helpful = zeroPlusAEqA @
        ["(a=b->a=c->b=c)->b=a->a=b->a=c->b=c";
         "b=a->a=b->a=c->b=c";
         "@a.@b.(a=b->b=a)->@b.(d=b->b=d)";
         "@b.(d=b->b=d)";
         "@b.(d=b->b=d)->(d=e->e=d)";
         "d=e->e=d";
         "(d=e->e=d)->0=0->(d=e->e=d)";
         "0=0->(d=e->e=d)";
         "0=0->@e.(d=e->e=d)";
         "0=0->@d.@e.(d=e->e=d)";
         "@d.@e.(d=e->e=d)";
         "@d.@e.(d=e->e=d)->@e.(b=e->e=b)";
         "@e.(b=e->e=b)";
         "@e.(b=e->e=b)->(b=a->a=b)";
         "b=a->a=b";
         "(b=a->a=b)->(b=a->a=b->a=c->b=c)->(b=a->a=c->b=c)";
         "(b=a->a=b->a=c->b=c)->(b=a->a=c->b=c)";
         "b=a->a=c->b=c";
         "(b=a->a=c->b=c)->0=0->(b=a->a=c->b=c)";
         "0=0->(b=a->a=c->b=c)";
         "0=0->@c.(b=a->a=c->b=c)";
         "0=0->@b.@c.(b=a->a=c->b=c)";
         "0=0->@a.@b.@c.(b=a->a=c->b=c)";
         "@a.@b.@c.(b=a->a=c->b=c)";
         "@a.@b.(a=b->b=a)->@b.(c=b->b=c)";
         "@b.(c=b->b=c)";
         "@b.(c=b->b=c)->(c=a->a=c)";
         "c=a->a=c";
         "(a=c->b=c)->c=a->(a=c->b=c)";
         "((a=c->b=c)->c=a->(a=c->b=c))->b=a->((a=c->b=c)->c=a->(a=c->b=c))";
         "b=a->(a=c->b=c)->c=a->(a=c->b=c)";
         "(b=a->a=c->b=c)->(b=a->(a=c->b=c)->(c=a->a=c->b=c))->(b=a->c=a->a=c->b=c)";
         "(b=a->(a=c->b=c)->(c=a->a=c->b=c))->(b=a->c=a->a=c->b=c)";
         "b=a->c=a->a=c->b=c";
         "(c=a->a=c)->(c=a->a=c->b=c)->(c=a->b=c)";
         "((c=a->a=c)->(c=a->a=c->b=c)->(c=a->b=c))->b=a->((c=a->a=c)->(c=a->a=c->b=c)->(c=a->b=c))";
         "b=a->(c=a->a=c)->(c=a->a=c->b=c)->(c=a->b=c)";
         "(c=a->a=c)->b=a->(c=a->a=c)";
         "b=a->c=a->a=c";
         "(b=a->c=a->a=c)->(b=a->(c=a->a=c)->(c=a->a=c->b=c)->(c=a->b=c))->(b=a->(c=a->a=c->b=c)->(c=a->b=c))";
         "(b=a->(c=a->a=c)->(c=a->a=c->b=c)->(c=a->b=c))->(b=a->(c=a->a=c->b=c)->(c=a->b=c))";
         "b=a->(c=a->a=c->b=c)->(c=a->b=c)";
         "(b=a->c=a->a=c->b=c)->(b=a->(c=a->a=c->b=c)->(c=a->b=c))->(b=a->c=a->b=c)";
         "(b=a->(c=a->a=c->b=c)->(c=a->b=c))->(b=a->c=a->b=c)";
         "b=a->c=a->b=c";
         "(b=a->c=a->b=c)->0=0->(b=a->c=a->b=c)";
         "0=0->(b=a->c=a->b=c)";
         "0=0->@c.(b=a->c=a->b=c)";
         "0=0->@b.@c.(b=a->c=a->b=c)";
         "0=0->@a.@b.@c.(b=a->c=a->b=c)";
         "@a.@b.@c.(b=a->c=a->b=c)"];;
let commutativity2 = helpful @
        ["@a.@b.(a=b->b=a)->@b.(0+a=b->b=0+a)";
         "@b.(0+a=b->b=0+a)";
         "@b.(0+a=b->b=0+a)->(0+a=a->a=0+a)";
         "0+a=a->a=0+a";
         "a=0+a";
         "@a.@b.(a=b->b=a)->@b.(a+0=b->b=a+0)";
         "@b.(a+0=b->b=a+0)";
         "@b.(a+0=b->b=a+0)->(a+0=a->a=a+0)";
         "a+0=a->a=a+0";
         "a=a+0";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(a=b->a=c->b=c)";
         "@b.@c.(a=b->a=c->b=c)";
         "@b.@c.(a=b->a=c->b=c)->@c.(a=a+0->a=c->a+0=c)";
         "@c.(a=a+0->a=c->a+0=c)";
         "@c.(a=a+0->a=c->a+0=c)->(a=a+0->a=0+a->a+0=0+a)";
         "a=a+0->a=0+a->a+0=0+a";
         "a=0+a->a+0=0+a";
         "a+0=0+a";
         "@a.@b.(a=b->a'=b')->@b.(a+e=b->(a+e)'=b')";
         "@b.(a+e=b->(a+e)'=b')";
         "@b.(a+e=b->(a+e)'=b')->(a+e=e+a->(a+e)'=(e+a)')";
         "a+e=e+a->(a+e)'=(e+a)'";
         "@a.@b.(a=b->b=a)->@b.(a'+e=b->b=a'+e)";
         "@b.(a'+e=b->b=a'+e)";
         "@b.(a'+e=b->b=a'+e)->(a'+e=(a+e)'->(a+e)'=a'+e)";
         "a'+e=(a+e)'->(a+e)'=a'+e";
         "(a+e)'=a'+e";
         "((a+e)'=a'+e)->0=0->((a+e)'=a'+e)";
         "0=0->((a+e)'=a'+e)";
         "0=0->@e.((a+e)'=a'+e)";
         "0=0->@a.@e.((a+e)'=a'+e)";
         "@a.@e.((a+e)'=a'+e)";
         "@a.@e.((a+e)'=a'+e)->@e.((b+e)'=b'+e)";
         "@e.((b+e)'=b'+e)";
         "@e.((b+e)'=b'+e)->(b+a)'=b'+a";
         "(b+a)'=b'+a";
         "(b+a)'=b'+a->0=0->(b+a)'=b'+a";
         "0=0->(b+a)'=b'+a";
         "0=0->@b.((b+a)'=b'+a)";
         "@b.((b+a)'=b'+a)";
         "@b.((b+a)'=b'+a)->(e+a)'=e'+a";
         "(e+a)'=e'+a";
         "@a.@b.(a=b->b=a)->@b.(a+e'=b->b=a+e')";
         "@b.(a+e'=b->b=a+e')";
         "@b.(a+e'=b->b=a+e')->(a+e'=(a+e)'->(a+e)'=a+e')";
         "a+e'=(a+e)'->(a+e)'=a+e'";
         "@a.@b.(a+b'=(a+b)')->@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')->a+e'=(a+e)'";
         "a+e'=(a+e)'";
         "(a+e)'=a+e'";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.((a+e)'=b->(a+e)'=c->b=c)";
         "@b.@c.((a+e)'=b->(a+e)'=c->b=c)";
         "@b.@c.((a+e)'=b->(a+e)'=c->b=c)->@c.((a+e)'=a+e'->(a+e)'=c->a+e'=c)";
         "@c.((a+e)'=a+e'->(a+e)'=c->a+e'=c)";
         "@c.((a+e)'=a+e'->(a+e)'=c->a+e'=c)->((a+e)'=a+e'->(a+e)'=(e+a)'->a+e'=(e+a)')";
         "(a+e)'=a+e'->(a+e)'=(e+a)'->a+e'=(e+a)'";
         "(a+e)'=(e+a)'->a+e'=(e+a)'";
         "((a+e)'=(e+a)'->a+e'=(e+a)')->a+e=e+a->((a+e)'=(e+a)'->a+e'=(e+a)')";
         "a+e=e+a->(a+e)'=(e+a)'->a+e'=(e+a)'";
         "(a+e=e+a->(a+e)'=(e+a)')->(a+e=e+a->(a+e)'=(e+a)'->a+e'=(e+a)')->(a+e=e+a->a+e'=(e+a)')";
         "(a+e=e+a->(a+e)'=(e+a)'->a+e'=(e+a)')->(a+e=e+a->a+e'=(e+a)')";
         "a+e=e+a->a+e'=(e+a)'";
         "@a.@b.(a=b->b=a)->@b.(a+e'=b->b=a+e')";
         "@b.(a+e'=b->b=a+e')";
         "@b.(a+e'=b->b=a+e')->(a+e'=(e+a)'->(e+a)'=a+e')";
         "a+e'=(e+a)'->(e+a)'=a+e'";
         "(a+e'=(e+a)'->(e+a)'=a+e')->a+e=e+a->(a+e'=(e+a)'->(e+a)'=a+e')";
         "a+e=e+a->a+e'=(e+a)'->(e+a)'=a+e'";
         "(a+e=e+a->a+e'=(e+a)')->(a+e=e+a->a+e'=(e+a)'->(e+a)'=a+e')->(a+e=e+a->(e+a)'=a+e')";
         "(a+e=e+a->a+e'=(e+a)'->(e+a)'=a+e')->(a+e=e+a->(e+a)'=a+e')";
         "a+e=e+a->(e+a)'=a+e'";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.((e+a)'=b->(e+a)'=c->b=c)";
         "@b.@c.((e+a)'=b->(e+a)'=c->b=c)";
         "@b.@c.((e+a)'=b->(e+a)'=c->b=c)->@c.((e+a)'=a+e'->(e+a)'=c->a+e'=c)";
         "@c.((e+a)'=a+e'->(e+a)'=c->a+e'=c)";
         "@c.((e+a)'=a+e'->(e+a)'=c->a+e'=c)->((e+a)'=a+e'->(e+a)'=e'+a->a+e'=e'+a)";
         "(e+a)'=a+e'->(e+a)'=e'+a->a+e'=e'+a";
         "((e+a)'=a+e'->(e+a)'=e'+a->a+e'=e'+a)->(a+e=e+a)->((e+a)'=a+e'->(e+a)'=e'+a->a+e'=e'+a)";
         "a+e=e+a->(e+a)'=a+e'->(e+a)'=e'+a->a+e'=e'+a";
         "(a+e=e+a->(e+a)'=a+e')->(a+e=e+a->(e+a)'=a+e'->(e+a)'=e'+a->a+e'=e'+a)->(a+e=e+a->(e+a)'=e'+a->a+e'=e'+a)";
         "(a+e=e+a->(e+a)'=a+e'->(e+a)'=e'+a->a+e'=e'+a)->(a+e=e+a->(e+a)'=e'+a->a+e'=e'+a)";
         "a+e=e+a->(e+a)'=e'+a->a+e'=e'+a";
         "(e+a)'=e'+a->a+e=e+a->(e+a)'=e'+a";
         "a+e=e+a->(e+a)'=e'+a";
         "(a+e=e+a->(e+a)'=e'+a)->(a+e=e+a->(e+a)'=e'+a->a+e'=e'+a)->(a+e=e+a->a+e'=e'+a)";
         "(a+e=e+a->(e+a)'=e'+a->a+e'=e'+a)->(a+e=e+a->a+e'=e'+a)";
         "a+e=e+a->a+e'=e'+a";
         "(a+e=e+a->a+e'=e'+a)->0=0->(a+e=e+a->a+e'=e'+a)";
         "0=0->(a+e=e+a->a+e'=e'+a)";
         "0=0->@e.(a+e=e+a->a+e'=e'+a)";
         "@e.(a+e=e+a->a+e'=e'+a)";
         "a+0=0+a->@e.(a+e=e+a->a+e'=e'+a)->a+0=0+a&@e.(a+e=e+a->a+e'=e'+a)";
         "@e.(a+e=e+a->a+e'=e'+a)->a+0=0+a&@e.(a+e=e+a->a+e'=e'+a)";
         "a+0=0+a&@e.(a+e=e+a->a+e'=e'+a)";
         "a+0=0+a&@e.(a+e=e+a->a+e'=e'+a)->a+e=e+a";
         "a+e=e+a";
         "a+e=e+a->0=0->a+e=e+a";
         "0=0->a+e=e+a";
         "0=0->@e.(a+e=e+a)";
         "@e.(a+e=e+a)";
         "@e.(a+e=e+a)->a+b=b+a";
         "a+b=b+a";
         "a+b=b+a->0=0->a+b=b+a";
         "0=0->a+b=b+a";
         "0=0->@b.(a+b=b+a)";
         "0=0->@a.@b.(a+b=b+a)";
         "@a.@b.(a+b=b+a)";
         "0=0->@a.@e.(a+e=e+a)";
         "@a.@e.(a+e=e+a)"];;
let additionDoesntChangeEquality = commutativity2 @
        ["@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=a->a=c->b=c)";
         "@b.@c.(b=a->a=c->b=c)";
         "@b.@c.(b=a->a=c->b=c)->@c.(a+0=a->a=c->a+0=c)";
         "@c.(a+0=a->a=c->a+0=c)";
         "@c.(a+0=a->a=c->a+0=c)->(a+0=a->a=d->a+0=d)";
         "a+0=a->a=d->a+0=d";
         "a=d->a+0=d";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=d->c=d->b=c)";
         "@b.@c.(b=d->c=d->b=c)";
         "@b.@c.(b=d->c=d->b=c)->@c.(d+0=d->c=d->d+0=c)";
         "@c.(d+0=d->c=d->d+0=c)";
         "@c.(d+0=d->c=d->d+0=c)->(d+0=d->a+0=d->d+0=a+0)";
         "d+0=d->a+0=d->d+0=a+0";
         "@a.(a+0=a)->(d+0=d)";
         "d+0=d";
         "a+0=d->d+0=a+0";
         "(a+0=d->d+0=a+0)->a=d->(a+0=d->d+0=a+0)";
         "a=d->a+0=d->d+0=a+0";
         "(a=d->a+0=d)->(a=d->a+0=d->d+0=a+0)->(a=d->d+0=a+0)";
         "(a=d->a+0=d->d+0=a+0)->(a=d->d+0=a+0)";
         "a=d->d+0=a+0";
         "@a.@b.(a=b->b=a)->@b.(d+0=b->b=d+0)";
         "@b.(d+0=b->b=d+0)";
         "@b.(d+0=b->b=d+0)->(d+0=a+0->a+0=d+0)";
         "d+0=a+0->a+0=d+0";
         "(d+0=a+0->a+0=d+0)->a=d->(d+0=a+0->a+0=d+0)";
         "a=d->d+0=a+0->a+0=d+0";
         "(a=d->d+0=a+0)->(a=d->d+0=a+0->a+0=d+0)->(a=d->a+0=d+0)";
         "(a=d->d+0=a+0->a+0=d+0)->(a=d->a+0=d+0)";
         "a=d->a+0=d+0";
         "@a.@b.(a=b->a'=b')->@b.(a+e=b->(a+e)'=b')";
         "@b.(a+e=b->(a+e)'=b')";
         "@b.(a+e=b->(a+e)'=b')->(a+e=d+e->(a+e)'=(d+e)')";
         "a+e=d+e->(a+e)'=(d+e)'";
         "@a.@b.(a+b'=(a+b)')->@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')->a+e'=(a+e)'";
         "a+e'=(a+e)'";
         "@a.@b.(a+b'=(a+b)')->@b.(d+b'=(d+b)')";
         "@b.(d+b'=(d+b)')";
         "@b.(d+b'=(d+b)')->d+e'=(d+e)'";
         "d+e'=(d+e)'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(a+e)'->(a+e)'=c->b=c)";
         "@b.@c.(b=(a+e)'->(a+e)'=c->b=c)";
         "@b.@c.(b=(a+e)'->(a+e)'=c->b=c)->@c.(a+e'=(a+e)'->(a+e)'=c->a+e'=c)";
         "@c.(a+e'=(a+e)'->(a+e)'=c->a+e'=c)";
         "@c.(a+e'=(a+e)'->(a+e)'=c->a+e'=c)->(a+e'=(a+e)'->(a+e)'=(d+e)'->a+e'=(d+e)')";
         "a+e'=(a+e)'->(a+e)'=(d+e)'->a+e'=(d+e)'";
         "(a+e)'=(d+e)'->a+e'=(d+e)'";
         "((a+e)'=(d+e)'->a+e'=(d+e)')->a+e=d+e->((a+e)'=(d+e)'->a+e'=(d+e)')";
         "a+e=d+e->(a+e)'=(d+e)'->a+e'=(d+e)'";
         "(a+e=d+e->(a+e)'=(d+e)')->(a+e=d+e->(a+e)'=(d+e)'->a+e'=(d+e)')->(a+e=d+e->a+e'=(d+e)')";
         "(a+e=d+e->(a+e)'=(d+e)'->a+e'=(d+e)')->(a+e=d+e->a+e'=(d+e)')";
         "a+e=d+e->a+e'=(d+e)'";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=(d+e)'->c=(d+e)'->b=c)";
         "@b.@c.(b=(d+e)'->c=(d+e)'->b=c)";
         "@b.@c.(b=(d+e)'->c=(d+e)'->b=c)->@c.(d+e'=(d+e)'->c=(d+e)'->d+e'=c)";
         "@c.(d+e'=(d+e)'->c=(d+e)'->d+e'=c)";
         "@c.(d+e'=(d+e)'->c=(d+e)'->d+e'=c)->(d+e'=(d+e)'->a+e'=(d+e)'->d+e'=a+e')";
         "d+e'=(d+e)'->a+e'=(d+e)'->d+e'=a+e'";
         "a+e'=(d+e)'->d+e'=a+e'";
         "(a+e'=(d+e)'->d+e'=a+e')->a+e=d+e->(a+e'=(d+e)'->d+e'=a+e')";
         "a+e=d+e->a+e'=(d+e)'->d+e'=a+e'";
         "(a+e=d+e->a+e'=(d+e)')->(a+e=d+e->a+e'=(d+e)'->d+e'=a+e')->(a+e=d+e->d+e'=a+e')";
         "(a+e=d+e->a+e'=(d+e)'->d+e'=a+e')->(a+e=d+e->d+e'=a+e')";
         "a+e=d+e->d+e'=a+e'";
         "@a.@b.(a=b->b=a)->@b.(d+e'=b->b=d+e')";
         "@b.(d+e'=b->b=d+e')";
         "@b.(d+e'=b->b=d+e')->(d+e'=a+e'->a+e'=d+e')";
         "d+e'=a+e'->a+e'=d+e'";
         "(d+e'=a+e'->a+e'=d+e')->a+e=d+e->(d+e'=a+e'->a+e'=d+e')";
         "a+e=d+e->d+e'=a+e'->a+e'=d+e'";
         "(a+e=d+e->d+e'=a+e')->(a+e=d+e->d+e'=a+e'->a+e'=d+e')->(a+e=d+e->a+e'=d+e')";
         "(a+e=d+e->d+e'=a+e'->a+e'=d+e')->(a+e=d+e->a+e'=d+e')";
         "a+e=d+e->a+e'=d+e'";
         "(a+e=d+e->a+e'=d+e')->a=d->(a+e=d+e->a+e'=d+e')";
         "a=d->(a+e=d+e->a+e'=d+e')";
         "(a=d->(a+e=d+e->a+e'=d+e'))->(a=d->a+e=d+e)->(a=d->(a+e=d+e->a+e'=d+e'))";
         "(a=d->a+e=d+e)->(a=d->a+e=d+e->a+e'=d+e')";
         "(a=d->a+e=d+e)->(a=d->a+e=d+e->a+e'=d+e')->(a=d->a+e'=d+e')";
         "((a=d->a+e=d+e)->(a=d->a+e=d+e->a+e'=d+e'))->((a=d->a+e=d+e)->(a=d->a+e=d+e->a+e'=d+e')->(a=d->a+e'=d+e'))->((a=d->a+e=d+e)->(a=d->a+e'=d+e'))";
         "((a=d->a+e=d+e)->(a=d->a+e=d+e->a+e'=d+e')->(a=d->a+e'=d+e'))->((a=d->a+e=d+e)->(a=d->a+e'=d+e'))";
         "(a=d->a+e=d+e)->(a=d->a+e'=d+e')";
         "((a=d->a+e=d+e)->(a=d->a+e'=d+e'))->0=0->((a=d->a+e=d+e)->(a=d->a+e'=d+e'))";
         "0=0->((a=d->a+e=d+e)->(a=d->a+e'=d+e'))";
         "0=0->@e.((a=d->a+e=d+e)->(a=d->a+e'=d+e'))";
         "@e.((a=d->a+e=d+e)->(a=d->a+e'=d+e'))";
         "(a=d->a+0=d+0)->@e.((a=d->a+e=d+e)->(a=d->a+e'=d+e'))->(a=d->a+0=d+0)&@e.((a=d->a+e=d+e)->(a=d->a+e'=d+e'))";
         "@e.((a=d->a+e=d+e)->(a=d->a+e'=d+e'))->(a=d->a+0=d+0)&@e.((a=d->a+e=d+e)->(a=d->a+e'=d+e'))";
         "(a=d->a+0=d+0)&@e.((a=d->a+e=d+e)->(a=d->a+e'=d+e'))";
         "(a=d->a+0=d+0)&@e.((a=d->a+e=d+e)->(a=d->a+e'=d+e'))->a=d->a+e=d+e";
         "a=d->a+e=d+e";
         "(a=d->a+e=d+e)->0=0->(a=d->a+e=d+e)";
         "0=0->(a=d->a+e=d+e)";
         "0=0->@e.(a=d->a+e=d+e)";
         "0=0->@d.@e.(a=d->a+e=d+e)";
         "0=0->@a.@d.@e.(a=d->a+e=d+e)";
         "@a.@d.@e.(a=d->a+e=d+e)";
         "@a.@d.@e.(a=d->a+e=d+e)->@d.@e.(a=d->a+e=d+e)";
         "@d.@e.(a=d->a+e=d+e)";
         "@d.@e.(a=d->a+e=d+e)->@e.(a=b->a+e=b+e)";
         "@e.(a=b->a+e=b+e)";
         "@e.(a=b->a+e=b+e)->(a=b->a+c=b+c)";
         "a=b->a+c=b+c";
         "(a=b->a+c=b+c)->0=0->(a=b->a+c=b+c)";
         "0=0->(a=b->a+c=b+c)";
         "0=0->@c.(a=b->a+c=b+c)";
         "0=0->@b.@c.(a=b->a+c=b+c)";
         "0=0->@a.@b.@c.(a=b->a+c=b+c)";
         "@a.@b.@c.(a=b->a+c=b+c)";
         "@a.@e.(a+e=e+a)->@e.(d+e=e+d)";
         "@e.(d+e=e+d)";
         "@e.(d+e=e+d)->(d+e=e+d)";
         "d+e=e+d";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(a+e=b->a+e=c->b=c)";
         "@b.@c.(a+e=b->a+e=c->b=c)";
         "@b.@c.(a+e=b->a+e=c->b=c)->@c.(a+e=e+a->a+e=c->e+a=c)";
         "@c.(a+e=e+a->a+e=c->e+a=c)";
         "@c.(a+e=e+a->a+e=c->e+a=c)->(a+e=e+a->a+e=d+e->e+a=d+e)";
         "a+e=e+a->a+e=d+e->e+a=d+e";
         "a+e=d+e->e+a=d+e";
         "(a+e=d+e->e+a=d+e)->a=d->a+e=d+e->e+a=d+e";
         "a=d->a+e=d+e->e+a=d+e";
         "(a=d->a+e=d+e)->(a=d->a+e=d+e->e+a=d+e)->(a=d->e+a=d+e)";
         "(a=d->a+e=d+e->e+a=d+e)->(a=d->e+a=d+e)";
         "a=d->e+a=d+e";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=d+e->d+e=c->b=c)";
         "@b.@c.(b=d+e->d+e=c->b=c)";
         "@b.@c.(b=d+e->d+e=c->b=c)->@c.(e+a=d+e->d+e=c->e+a=c)";
         "@c.(e+a=d+e->d+e=c->e+a=c)";
         "@c.(e+a=d+e->d+e=c->e+a=c)->(e+a=d+e->d+e=e+d->e+a=e+d)";
         "e+a=d+e->d+e=e+d->e+a=e+d";
         "d+e=e+d->e+a=d+e->d+e=e+d";
         "e+a=d+e->d+e=e+d";
         "(e+a=d+e->d+e=e+d)->(e+a=d+e->d+e=e+d->e+a=e+d)->(e+a=d+e->e+a=e+d)";
         "(e+a=d+e->d+e=e+d->e+a=e+d)->(e+a=d+e->e+a=e+d)";
         "e+a=d+e->e+a=e+d";
         "(e+a=d+e->e+a=e+d)->a=d->e+a=d+e->e+a=e+d";
         "a=d->e+a=d+e->e+a=e+d";
         "(a=d->e+a=d+e)->(a=d->e+a=d+e->e+a=e+d)->(a=d->e+a=e+d)";
         "(a=d->e+a=d+e->e+a=e+d)->(a=d->e+a=e+d)";
         "a=d->e+a=e+d";
         "(a=d->e+a=e+d)->0=0->(a=d->e+a=e+d)";
         "0=0->(a=d->e+a=e+d)";
         "0=0->@e.(a=d->e+a=e+d)";
         "0=0->@d.@e.(a=d->e+a=e+d)";
         "0=0->@a.@d.@e.(a=d->e+a=e+d)";
         "@a.@d.@e.(a=d->e+a=e+d)";
         "@a.@d.@e.(a=d->e+a=e+d)->@d.@e.(a=d->e+a=e+d)";
         "@d.@e.(a=d->e+a=e+d)";
         "@d.@e.(a=d->e+a=e+d)->@e.(a=b->e+a=e+b)";
         "@e.(a=b->e+a=e+b)";
         "@e.(a=b->e+a=e+b)->(a=b->c+a=c+b)";
         "a=b->c+a=c+b";
         "(a=b->c+a=c+b)->0=0->(a=b->c+a=c+b)";
         "0=0->(a=b->c+a=c+b)";
         "0=0->@c.(a=b->c+a=c+b)";
         "0=0->@b.@c.(a=b->c+a=c+b)";
         "0=0->@a.@b.@c.(a=b->c+a=c+b)";
         "@a.@b.@c.(a=b->c+a=c+b)"];;
let associativity = additionDoesntChangeEquality @
        ["@a.@b.(a+b'=(a+b)')->@b.((a+d)+b'=((a+d)+b)')";
         "@b.((a+d)+b'=((a+d)+b)')";
         "@b.((a+d)+b'=((a+d)+b)')->(a+d)+e'=((a+d)+e)'";
         "(a+d)+e'=((a+d)+e)'";
         "@a.@b.(a+b'=(a+b)')->@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')->a+(d+e)'=(a+(d+e))'";
         "a+(d+e)'=(a+(d+e))'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=((a+d)+e)'->((a+d)+e)'=c->b=c)";
         "@b.@c.(b=((a+d)+e)'->((a+d)+e)'=c->b=c)";
         "@b.@c.(b=((a+d)+e)'->((a+d)+e)'=c->b=c)->@c.((a+d)+e'=((a+d)+e)'->((a+d)+e)'=c->(a+d)+e'=c)";
         "@c.((a+d)+e'=((a+d)+e)'->((a+d)+e)'=c->(a+d)+e'=c)";
         "@c.((a+d)+e'=((a+d)+e)'->((a+d)+e)'=c->(a+d)+e'=c)->((a+d)+e'=((a+d)+e)'->((a+d)+e)'=(a+(d+e))'->(a+d)+e'=(a+(d+e))')";
         "(a+d)+e'=((a+d)+e)'->((a+d)+e)'=(a+(d+e))'->(a+d)+e'=(a+(d+e))'";
         "((a+d)+e)'=(a+(d+e))'->(a+d)+e'=(a+(d+e))'";
         "@a.@b.(a+b'=(a+b)')->@b.(d+b'=(d+b)')";
         "@b.(d+b'=(d+b)')";
         "@b.(d+b'=(d+b)')->(d+e'=(d+e)')";
         "d+e'=(d+e)'";
         "@a.@b.@c.(a=b->c+a=c+b)->@b.@c.(d+e'=b->c+(d+e')=c+b)";
         "@b.@c.(d+e'=b->c+(d+e')=c+b)";
         "@b.@c.(d+e'=b->c+(d+e')=c+b)->@c.(d+e'=(d+e)'->c+(d+e')=c+(d+e)')";
         "@c.(d+e'=(d+e)'->c+(d+e')=c+(d+e)')";
         "@c.(d+e'=(d+e)'->c+(d+e')=c+(d+e)')->(d+e'=(d+e)'->a+(d+e')=a+(d+e)')";
         "d+e'=(d+e)'->a+(d+e')=a+(d+e)'";
         "a+(d+e')=a+(d+e)'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=a+(d+e)'->a+(d+e)'=c->b=c)";
         "@b.@c.(b=a+(d+e)'->a+(d+e)'=c->b=c)";
         "@b.@c.(b=a+(d+e)'->a+(d+e)'=c->b=c)->@c.(a+(d+e')=a+(d+e)'->a+(d+e)'=c->a+(d+e')=c)";
         "@c.(a+(d+e')=a+(d+e)'->a+(d+e)'=c->a+(d+e')=c)";
         "@c.(a+(d+e')=a+(d+e)'->a+(d+e)'=c->a+(d+e')=c)->(a+(d+e')=a+(d+e)'->a+(d+e)'=(a+(d+e))'->a+(d+e')=(a+(d+e))')";
         "a+(d+e')=a+(d+e)'->a+(d+e)'=(a+(d+e))'->a+(d+e')=(a+(d+e))'";
         "a+(d+e)'=(a+(d+e))'->a+(d+e')=(a+(d+e))'";
         "a+(d+e')=(a+(d+e))'";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=(a+(d+e))'->c=(a+(d+e))'->b=c)";
         "@b.@c.(b=(a+(d+e))'->c=(a+(d+e))'->b=c)";
         "@b.@c.(b=(a+(d+e))'->c=(a+(d+e))'->b=c)->@c.((a+d)+e'=(a+(d+e))'->c=(a+(d+e))'->(a+d)+e'=c)";
         "@c.((a+d)+e'=(a+(d+e))'->c=(a+(d+e))'->(a+d)+e'=c)";
         "@c.((a+d)+e'=(a+(d+e))'->c=(a+(d+e))'->(a+d)+e'=c)->((a+d)+e'=(a+(d+e))'->a+(d+e')=(a+(d+e))'->(a+d)+e'=a+(d+e'))";
         "(a+d)+e'=(a+(d+e))'->a+(d+e')=(a+(d+e))'->(a+d)+e'=a+(d+e')";
         "a+(d+e')=(a+(d+e))'->(a+d)+e'=(a+(d+e))'->a+(d+e')=(a+(d+e))'";
         "(a+d)+e'=(a+(d+e))'->a+(d+e')=(a+(d+e))'";
         "((a+d)+e'=(a+(d+e))'->a+(d+e')=(a+(d+e))')->((a+d)+e'=(a+(d+e))'->a+(d+e')=(a+(d+e))'->(a+d)+e'=a+(d+e'))->((a+d)+e'=(a+(d+e))'->(a+d)+e'=a+(d+e'))";
         "((a+d)+e'=(a+(d+e))'->a+(d+e')=(a+(d+e))'->(a+d)+e'=a+(d+e'))->((a+d)+e'=(a+(d+e))'->(a+d)+e'=a+(d+e'))";
         "(a+d)+e'=(a+(d+e))'->(a+d)+e'=a+(d+e')";
         "((a+d)+e'=(a+(d+e))'->(a+d)+e'=a+(d+e'))->((a+d)+e)'=(a+(d+e))'->((a+d)+e'=(a+(d+e))'->(a+d)+e'=a+(d+e'))";
         "((a+d)+e)'=(a+(d+e))'->(a+d)+e'=(a+(d+e))'->(a+d)+e'=a+(d+e')";
         "(((a+d)+e)'=(a+(d+e))'->(a+d)+e'=(a+(d+e))')->(((a+d)+e)'=(a+(d+e))'->(a+d)+e'=(a+(d+e))'->(a+d)+e'=a+(d+e'))->(((a+d)+e)'=(a+(d+e))'->(a+d)+e'=a+(d+e'))";
         "(((a+d)+e)'=(a+(d+e))'->(a+d)+e'=(a+(d+e))'->(a+d)+e'=a+(d+e'))->(((a+d)+e)'=(a+(d+e))'->(a+d)+e'=a+(d+e'))";
         "((a+d)+e)'=(a+(d+e))'->(a+d)+e'=a+(d+e')";
         "(((a+d)+e)'=(a+(d+e))'->(a+d)+e'=a+(d+e'))->((a+d)+e=a+(d+e))->(((a+d)+e)'=(a+(d+e))'->(a+d)+e'=a+(d+e'))";
         "(a+d)+e=a+(d+e)->((a+d)+e)'=(a+(d+e))'->(a+d)+e'=a+(d+e')";
         "@a.@b.(a=b->a'=b')->@b.((a+d)+e=b->((a+d)+e)'=b')";
         "@b.((a+d)+e=b->((a+d)+e)'=b')";
         "@b.((a+d)+e=b->((a+d)+e)'=b')->((a+d)+e=a+(d+e)->((a+d)+e)'=(a+(d+e))')";
         "(a+d)+e=a+(d+e)->((a+d)+e)'=(a+(d+e))'";
         "((a+d)+e=a+(d+e)->((a+d)+e)'=(a+(d+e))')->((a+d)+e=a+(d+e)->((a+d)+e)'=(a+(d+e))'->(a+d)+e'=a+(d+e'))->((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))";
         "((a+d)+e=a+(d+e)->((a+d)+e)'=(a+(d+e))'->(a+d)+e'=a+(d+e'))->((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))";
         "(a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e')";
         "((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))->0=0->((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))";
         "0=0->((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))";
         "0=0->@e.((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))";
         "@e.((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))";
         "@a.(a+0=a)->((a+d)+0=a+d)";
         "(a+d)+0=a+d";
         "@a.(a+0=a)->(d+0=d)";
         "d+0=d";
         "@a.@b.@c.(a=b->c+a=c+b)->@b.@c.(d+0=b->c+(d+0)=c+b)";
         "@b.@c.(d+0=b->c+(d+0)=c+b)";
         "@b.@c.(d+0=b->c+(d+0)=c+b)->@c.(d+0=d->c+(d+0)=c+d)";
         "@c.(d+0=d->c+(d+0)=c+d)";
         "@c.(d+0=d->c+(d+0)=c+d)->(d+0=d->a+(d+0)=a+d)";
         "d+0=d->a+(d+0)=a+d";
         "a+(d+0)=a+d";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=a+d->c=a+d->b=c)";
         "@b.@c.(b=a+d->c=a+d->b=c)";
         "@b.@c.(b=a+d->c=a+d->b=c)->@c.((a+d)+0=a+d->c=a+d->(a+d)+0=c)";
         "@c.((a+d)+0=a+d->c=a+d->(a+d)+0=c)";
         "@c.((a+d)+0=a+d->c=a+d->(a+d)+0=c)->((a+d)+0=a+d->a+(d+0)=a+d->(a+d)+0=a+(d+0))";
         "(a+d)+0=a+d->a+(d+0)=a+d->(a+d)+0=a+(d+0)";
         "a+(d+0)=a+d->(a+d)+0=a+(d+0)";
         "(a+d)+0=a+(d+0)";
         "(a+d)+0=a+(d+0)->@e.((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))->(a+d)+0=a+(d+0)&@e.((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))";
         "@e.((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))->(a+d)+0=a+(d+0)&@e.((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))";
         "(a+d)+0=a+(d+0)&@e.((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))";
         "(a+d)+0=a+(d+0)&@e.((a+d)+e=a+(d+e)->(a+d)+e'=a+(d+e'))->(a+d)+e=a+(d+e)";
         "(a+d)+e=a+(d+e)";
         "(a+d)+e=a+(d+e)->0=0->(a+d)+e=a+(d+e)";
         "0=0->(a+d)+e=a+(d+e)";
         "0=0->@e.((a+d)+e=a+(d+e))";
         "0=0->@d.@e.((a+d)+e=a+(d+e))";
         "0=0->@a.@d.@e.((a+d)+e=a+(d+e))";
         "@a.@d.@e.((a+d)+e=a+(d+e))";
         "@a.@d.@e.((a+d)+e=a+(d+e))";
         "@a.@d.@e.((a+d)+e=a+(d+e))->@d.@e.((a+d)+e=a+(d+e))";
         "@d.@e.((a+d)+e=a+(d+e))";
         "@d.@e.((a+d)+e=a+(d+e))->@e.((a+b)+e=a+(b+e))";
         "@e.((a+b)+e=a+(b+e))";
         "@e.((a+b)+e=a+(b+e))->((a+b)+c=a+(b+c))";
         "(a+b)+c=a+(b+c)";
         "(a+b)+c=a+(b+c)->0=0->(a+b)+c=a+(b+c)";
         "0=0->(a+b)+c=a+(b+c)";
         "0=0->@c.((a+b)+c=a+(b+c))";
         "0=0->@b.@c.((a+b)+c=a+(b+c))";
         "0=0->@a.@b.@c.((a+b)+c=a+(b+c))";
         "@a.@b.@c.((a+b)+c=a+(b+c))"];;
let e'aEqeaPa = associativity @
        ["a*b'=a*b+a";
         "a*b'=a*b+a->0=0->a*b'=a*b+a";
         "0=0->a*b'=a*b+a";
         "0=0->@b.(a*b'=a*b+a)";
         "0=0->@a.@b.(a*b'=a*b+a)";
         "@a.@b.(a*b'=a*b+a)";
         "@a.@b.(a*b'=a*b+a)->@b.(e*b'=e*b+e)";
         "@b.(e*b'=e*b+e)";
         "@b.(e*b'=e*b+e)->(e*a'=e*a+e)";
         "e*a'=e*a+e";
         "@a.@b.@c.(a=b->a+c=b+c)->@b.@c.(e*a'=b->e*a'+c=b+c)";
         "@b.@c.(e*a'=b->e*a'+c=b+c)";
         "@b.@c.(e*a'=b->e*a'+c=b+c)->@c.(e*a'=e*a+e->e*a'+c=(e*a+e)+c)";
         "@c.(e*a'=e*a+e->e*a'+c=(e*a+e)+c)";
         "@c.(e*a'=e*a+e->e*a'+c=(e*a+e)+c)->(e*a'=e*a+e->e*a'+a'=(e*a+e)+a')";
         "e*a'=e*a+e->e*a'+a'=(e*a+e)+a'";
         "e*a'+a'=(e*a+e)+a'";
         "@a.@b.@c.((a+b)+c=a+(b+c))->@b.@c.((e*a+b)+c=e*a+(b+c))";
         "@b.@c.((e*a+b)+c=e*a+(b+c))";
         "@b.@c.((e*a+b)+c=e*a+(b+c))->@c.((e*a+e)+c=e*a+(e+c))";
         "@c.((e*a+e)+c=e*a+(e+c))";
         "@c.((e*a+e)+c=e*a+(e+c))->(e*a+e)+a'=e*a+(e+a')";
         "(e*a+e)+a'=e*a+(e+a')";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(e*a+e)+a'->(e*a+e)+a'=c->b=c)";
         "@b.@c.(b=(e*a+e)+a'->(e*a+e)+a'=c->b=c)";
         "@b.@c.(b=(e*a+e)+a'->(e*a+e)+a'=c->b=c)->@c.(e*a'+a'=(e*a+e)+a'->(e*a+e)+a'=c->e*a'+a'=c)";
         "@c.(e*a'+a'=(e*a+e)+a'->(e*a+e)+a'=c->e*a'+a'=c)";
         "@c.(e*a'+a'=(e*a+e)+a'->(e*a+e)+a'=c->e*a'+a'=c)->(e*a'+a'=(e*a+e)+a'->(e*a+e)+a'=e*a+(e+a')->e*a'+a'=e*a+(e+a'))";
         "e*a'+a'=(e*a+e)+a'->(e*a+e)+a'=e*a+(e+a')->e*a'+a'=e*a+(e+a')";
         "(e*a+e)+a'=e*a+(e+a')->e*a'+a'=e*a+(e+a')";
         "e*a'+a'=e*a+(e+a')";
         "@a.@b.(a+b'=(a+b)')->@b.(e+b'=(e+b)')";
         "@b.(e+b'=(e+b)')";
         "@b.(e+b'=(e+b)')->(e+a'=(e+a)')";
         "e+a'=(e+a)'";
         "@a.@b.(a'+b=(a+b)')->@b.(e'+b=(e+b)')";
         "@b.(e'+b=(e+b)')";
         "@b.(e'+b=(e+b)')->(e'+a=(e+a)')";
         "e'+a=(e+a)'";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=(e+a)'->c=(e+a)'->b=c)";
         "@b.@c.(b=(e+a)'->c=(e+a)'->b=c)";
         "@b.@c.(b=(e+a)'->c=(e+a)'->b=c)->@c.(e+a'=(e+a)'->c=(e+a)'->e+a'=c)";
         "@c.(e+a'=(e+a)'->c=(e+a)'->e+a'=c)";
         "@c.(e+a'=(e+a)'->c=(e+a)'->e+a'=c)->(e+a'=(e+a)'->e'+a=(e+a)'->e+a'=e'+a)";
         "e+a'=(e+a)'->e'+a=(e+a)'->e+a'=e'+a";
         "e'+a=(e+a)'->e+a'=e'+a";
         "e+a'=e'+a";
         "@a.@b.@c.(a=b->c+a=c+b)->@b.@c.(e+a'=b->c+(e+a')=c+b)";
         "@b.@c.(e+a'=b->c+(e+a')=c+b)";
         "@b.@c.(e+a'=b->c+(e+a')=c+b)->@c.(e+a'=e'+a->c+(e+a')=c+(e'+a))";
         "@c.(e+a'=e'+a->c+(e+a')=c+(e'+a))";
         "@c.(e+a'=e'+a->c+(e+a')=c+(e'+a))->(e+a'=e'+a->e*a+(e+a')=e*a+(e'+a))";
         "e+a'=e'+a->e*a+(e+a')=e*a+(e'+a)";
         "e*a+(e+a')=e*a+(e'+a)";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=e*a+(e+a')->e*a+(e+a')=c->b=c)";
         "@b.@c.(b=e*a+(e+a')->e*a+(e+a')=c->b=c)";
         "@b.@c.(b=e*a+(e+a')->e*a+(e+a')=c->b=c)->@c.(e*a'+a'=e*a+(e+a')->e*a+(e+a')=c->e*a'+a'=c)";
         "@c.(e*a'+a'=e*a+(e+a')->e*a+(e+a')=c->e*a'+a'=c)";
         "@c.(e*a'+a'=e*a+(e+a')->e*a+(e+a')=c->e*a'+a'=c)->(e*a'+a'=e*a+(e+a')->e*a+(e+a')=e*a+(e'+a)->e*a'+a'=e*a+(e'+a))";
         "e*a'+a'=e*a+(e+a')->e*a+(e+a')=e*a+(e'+a)->e*a'+a'=e*a+(e'+a)";
         "e*a+(e+a')=e*a+(e'+a)->e*a'+a'=e*a+(e'+a)";
         "e*a'+a'=e*a+(e'+a)";
         "@a.@b.(a+b=b+a)->@b.(e'+b=b+e')";
         "@b.(e'+b=b+e')";
         "@b.(e'+b=b+e')->(e'+a=a+e')";
         "e'+a=a+e'";
         "@a.@b.@c.(a=b->c+a=c+b)->@b.@c.(e'+a=b->c+(e'+a)=c+b)";
         "@b.@c.(e'+a=b->c+(e'+a)=c+b)";
         "@b.@c.(e'+a=b->c+(e'+a)=c+b)->@c.(e'+a=a+e'->c+(e'+a)=c+(a+e'))";
         "@c.(e'+a=a+e'->c+(e'+a)=c+(a+e'))";
         "@c.(e'+a=a+e'->c+(e'+a)=c+(a+e'))->(e'+a=a+e'->e*a+(e'+a)=e*a+(a+e'))";
         "e'+a=a+e'->e*a+(e'+a)=e*a+(a+e')";
         "e*a+(e'+a)=e*a+(a+e')";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=e*a+(e'+a)->e*a+(e'+a)=c->b=c)";
         "@b.@c.(b=e*a+(e'+a)->e*a+(e'+a)=c->b=c)";
         "@b.@c.(b=e*a+(e'+a)->e*a+(e'+a)=c->b=c)->@c.(e*a'+a'=e*a+(e'+a)->e*a+(e'+a)=c->e*a'+a'=c)";
         "@c.(e*a'+a'=e*a+(e'+a)->e*a+(e'+a)=c->e*a'+a'=c)";
         "@c.(e*a'+a'=e*a+(e'+a)->e*a+(e'+a)=c->e*a'+a'=c)->(e*a'+a'=e*a+(e'+a)->e*a+(e'+a)=e*a+(a+e')->e*a'+a'=e*a+(a+e'))";
         "e*a'+a'=e*a+(e'+a)->e*a+(e'+a)=e*a+(a+e')->e*a'+a'=e*a+(a+e')";
         "e*a+(e'+a)=e*a+(a+e')->e*a'+a'=e*a+(a+e')";
         "e*a'+a'=e*a+(a+e')";
         "@a.@b.@c.((a+b)+c=a+(b+c))->@b.@c.((e*a+b)+c=e*a+(b+c))";
         "@b.@c.((e*a+b)+c=e*a+(b+c))";
         "@b.@c.((e*a+b)+c=e*a+(b+c))->@c.((e*a+a)+c=e*a+(a+c))";
         "@c.((e*a+a)+c=e*a+(a+c))";
         "@c.((e*a+a)+c=e*a+(a+c))->((e*a+a)+e'=e*a+(a+e'))";
         "(e*a+a)+e'=e*a+(a+e')";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=e*a+(a+e')->c=e*a+(a+e')->b=c)";
         "@b.@c.(b=e*a+(a+e')->c=e*a+(a+e')->b=c)";
         "@b.@c.(b=e*a+(a+e')->c=e*a+(a+e')->b=c)->@c.(e*a'+a'=e*a+(a+e')->c=e*a+(a+e')->e*a'+a'=c)";
         "@c.(e*a'+a'=e*a+(a+e')->c=e*a+(a+e')->e*a'+a'=c)";
         "@c.(e*a'+a'=e*a+(a+e')->c=e*a+(a+e')->e*a'+a'=c)->(e*a'+a'=e*a+(a+e')->(e*a+a)+e'=e*a+(a+e')->e*a'+a'=(e*a+a)+e')";
         "e*a'+a'=e*a+(a+e')->(e*a+a)+e'=e*a+(a+e')->e*a'+a'=(e*a+a)+e'";
         "(e*a+a)+e'=e*a+(a+e')->e*a'+a'=(e*a+a)+e'";
         "e*a'+a'=(e*a+a)+e'";
         "@a.@b.@c.(a=b->a+c=b+c)->@b.@c.(e*a+a=b->(e*a+a)+c=b+c)";
         "@b.@c.(e*a+a=b->(e*a+a)+c=b+c)";
         "@b.@c.(e*a+a=b->(e*a+a)+c=b+c)->@c.(e*a+a=e'*a->(e*a+a)+c=e'*a+c)";
         "@c.(e*a+a=e'*a->(e*a+a)+c=e'*a+c)";
         "@c.(e*a+a=e'*a->(e*a+a)+c=e'*a+c)->(e*a+a=e'*a->(e*a+a)+e'=e'*a+e')";
         "e*a+a=e'*a->(e*a+a)+e'=e'*a+e'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(e*a+a)+e'->(e*a+a)+e'=c->b=c)";
         "@b.@c.(b=(e*a+a)+e'->(e*a+a)+e'=c->b=c)";
         "@b.@c.(b=(e*a+a)+e'->(e*a+a)+e'=c->b=c)->@c.(e*a'+a'=(e*a+a)+e'->(e*a+a)+e'=c->e*a'+a'=c)";
         "@c.(e*a'+a'=(e*a+a)+e'->(e*a+a)+e'=c->e*a'+a'=c)";
         "@c.(e*a'+a'=(e*a+a)+e'->(e*a+a)+e'=c->e*a'+a'=c)->(e*a'+a'=(e*a+a)+e'->(e*a+a)+e'=e'*a+e'->e*a'+a'=e'*a+e')";
         "e*a'+a'=(e*a+a)+e'->(e*a+a)+e'=e'*a+e'->e*a'+a'=e'*a+e'";
         "(e*a+a)+e'=e'*a+e'->e*a'+a'=e'*a+e'";
         "((e*a+a)+e'=e'*a+e'->e*a'+a'=e'*a+e')->e*a+a=e'*a->((e*a+a)+e'=e'*a+e'->e*a'+a'=e'*a+e')";
         "e*a+a=e'*a->(e*a+a)+e'=e'*a+e'->e*a'+a'=e'*a+e'";
         "(e*a+a=e'*a->(e*a+a)+e'=e'*a+e')->(e*a+a=e'*a->(e*a+a)+e'=e'*a+e'->e*a'+a'=e'*a+e')->(e*a+a=e'*a->e*a'+a'=e'*a+e')";
         "(e*a+a=e'*a->(e*a+a)+e'=e'*a+e'->e*a'+a'=e'*a+e')->(e*a+a=e'*a->e*a'+a'=e'*a+e')";
         "e*a+a=e'*a->e*a'+a'=e'*a+e'";
         "@a.@b.(a*b'=a*b+a)->@b.(e'*b'=e'*b+e')";
         "@b.(e'*b'=e'*b+e')";
         "@b.(e'*b'=e'*b+e')->(e'*a'=e'*a+e')";
         "e'*a'=e'*a+e'";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=e'*a+e'->c=e'*a+e'->b=c)";
         "@b.@c.(b=e'*a+e'->c=e'*a+e'->b=c)";
         "@b.@c.(b=e'*a+e'->c=e'*a+e'->b=c)->@c.(e*a'+a'=e'*a+e'->c=e'*a+e'->e*a'+a'=c)";
         "@c.(e*a'+a'=e'*a+e'->c=e'*a+e'->e*a'+a'=c)";
         "@c.(e*a'+a'=e'*a+e'->c=e'*a+e'->e*a'+a'=c)->(e*a'+a'=e'*a+e'->e'*a'=e'*a+e'->e*a'+a'=e'*a')";
         "e*a'+a'=e'*a+e'->e'*a'=e'*a+e'->e*a'+a'=e'*a'";
         "(e*a'+a'=e'*a+e'->e'*a'=e'*a+e'->e*a'+a'=e'*a')->e*a+a=e'*a->(e*a'+a'=e'*a+e'->e'*a'=e'*a+e'->e*a'+a'=e'*a')";
         "e*a+a=e'*a->e*a'+a'=e'*a+e'->e'*a'=e'*a+e'->e*a'+a'=e'*a'";
         "(e*a+a=e'*a->e*a'+a'=e'*a+e')->(e*a+a=e'*a->e*a'+a'=e'*a+e'->e'*a'=e'*a+e'->e*a'+a'=e'*a')->(e*a+a=e'*a->e'*a'=e'*a+e'->e*a'+a'=e'*a')";
         "(e*a+a=e'*a->e*a'+a'=e'*a+e'->e'*a'=e'*a+e'->e*a'+a'=e'*a')->(e*a+a=e'*a->e'*a'=e'*a+e'->e*a'+a'=e'*a')";
         "e*a+a=e'*a->e'*a'=e'*a+e'->e*a'+a'=e'*a'";
         "e'*a'=e'*a+e'->e*a+a=e'*a->e'*a'=e'*a+e'";
         "e*a+a=e'*a->e'*a'=e'*a+e'";
         "(e*a+a=e'*a->e'*a'=e'*a+e')->(e*a+a=e'*a->e'*a'=e'*a+e'->e*a'+a'=e'*a')->(e*a+a=e'*a->e*a'+a'=e'*a')";
         "(e*a+a=e'*a->e'*a'=e'*a+e'->e*a'+a'=e'*a')->(e*a+a=e'*a->e*a'+a'=e'*a')";
         "e*a+a=e'*a->e*a'+a'=e'*a'";
         "(e*a+a=e'*a->e*a'+a'=e'*a')->0=0->(e*a+a=e'*a->e*a'+a'=e'*a')";
         "0=0->(e*a+a=e'*a->e*a'+a'=e'*a')";
         "0=0->@a.(e*a+a=e'*a->e*a'+a'=e'*a')";
         "@a.(e*a+a=e'*a->e*a'+a'=e'*a')";
         "@a.(a+0=a)->(e*0+0=e*0)";
         "e*0+0=e*0";
         "a*0=0";
         "a*0=0->0=0->a*0=0";
         "0=0->a*0=0";
         "0=0->@a.(a*0=0)";
         "@a.(a*0=0)";
         "@a.(a*0=0)->(e*0=0)";
         "e*0=0";
         "@a.(a*0=0)->(e'*0=0)";
         "e'*0=0";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=e*0->e*0=c->b=c)";
         "@b.@c.(b=e*0->e*0=c->b=c)";
         "@b.@c.(b=e*0->e*0=c->b=c)->@c.(e*0+0=e*0->e*0=c->e*0+0=c)";
         "@c.(e*0+0=e*0->e*0=c->e*0+0=c)";
         "@c.(e*0+0=e*0->e*0=c->e*0+0=c)->(e*0+0=e*0->e*0=0->e*0+0=0)";
         "e*0+0=e*0->e*0=0->e*0+0=0";
         "e*0=0->e*0+0=0";
         "e*0+0=0";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=0->c=0->b=c)";
         "@b.@c.(b=0->c=0->b=c)";
         "@b.@c.(b=0->c=0->b=c)->@c.(e*0+0=0->c=0->e*0+0=c)";
         "@c.(e*0+0=0->c=0->e*0+0=c)";
         "@c.(e*0+0=0->c=0->e*0+0=c)->(e*0+0=0->e'*0=0->e*0+0=e'*0)";
         "e*0+0=0->e'*0=0->e*0+0=e'*0";
         "e'*0=0->e*0+0=e'*0";
         "e*0+0=e'*0";
         "e*0+0=e'*0->@a.(e*a+a=e'*a->e*a'+a'=e'*a')->e*0+0=e'*0&@a.(e*a+a=e'*a->e*a'+a'=e'*a')";
         "@a.(e*a+a=e'*a->e*a'+a'=e'*a')->e*0+0=e'*0&@a.(e*a+a=e'*a->e*a'+a'=e'*a')";
         "e*0+0=e'*0&@a.(e*a+a=e'*a->e*a'+a'=e'*a')";
         "e*0+0=e'*0&@a.(e*a+a=e'*a->e*a'+a'=e'*a')->e*a+a=e'*a";
         "e*a+a=e'*a";
         "e*a+a=e'*a->0=0->e*a+a=e'*a";
         "0=0->e*a+a=e'*a";
         "0=0->@e.(e*a+a=e'*a)";
         "0=0->@a.@e.(e*a+a=e'*a)";
         "@a.@e.(e*a+a=e'*a)";
         "@a.@e.(e*a+a=e'*a)->@e.(e*b+b=e'*b)";
         "@e.(e*b+b=e'*b)";
         "@e.(e*b+b=e'*b)->(a*b+b=a'*b)";
         "a*b+b=a'*b";
         "a*b+b=a'*b->0=0->a*b+b=a'*b";
         "0=0->a*b+b=a'*b";
         "0=0->@b.(a*b+b=a'*b)";
         "0=0->@a.@b.(a*b+b=a'*b)";
         "@a.@b.(a*b+b=a'*b)"];;
let zeroMulAEqZero = e'aEqeaPa @
        ["@a.@b.(a*b'=a*b+a)->@b.(0*b'=0*b+0)";
         "@b.(0*b'=0*b+0)";
         "@b.(0*b'=0*b+0)->(0*a'=0*a+0)";
         "0*a'=0*a+0";
         "@a.(a+0=a)->(0*a+0=0*a)";
         "0*a+0=0*a";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=0*a+0->0*a+0=c->b=c)";
         "@b.@c.(b=0*a+0->0*a+0=c->b=c)";
         "@b.@c.(b=0*a+0->0*a+0=c->b=c)->@c.(0*a'=0*a+0->0*a+0=c->0*a'=c)";
         "@c.(0*a'=0*a+0->0*a+0=c->0*a'=c)";
         "@c.(0*a'=0*a+0->0*a+0=c->0*a'=c)->(0*a'=0*a+0->0*a+0=0*a->0*a'=0*a)";
         "0*a'=0*a+0->0*a+0=0*a->0*a'=0*a";
         "0*a+0=0*a->0*a'=0*a";
         "0*a'=0*a";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=0*a->0*a=c->b=c)";
         "@b.@c.(b=0*a->0*a=c->b=c)";
         "@b.@c.(b=0*a->0*a=c->b=c)->@c.(0*a'=0*a->0*a=c->0*a'=c)";
         "@c.(0*a'=0*a->0*a=c->0*a'=c)";
         "@c.(0*a'=0*a->0*a=c->0*a'=c)->(0*a'=0*a->0*a=0->0*a'=0)";
         "0*a'=0*a->0*a=0->0*a'=0";
         "0*a=0->0*a'=0";
         "(0*a=0->0*a'=0)->0=0->(0*a=0->0*a'=0)";
         "0=0->(0*a=0->0*a'=0)";
         "0=0->@a.(0*a=0->0*a'=0)";
         "@a.(0*a=0->0*a'=0)";
         "@a.(a*0=0)->0*0=0";
         "0*0=0";
         "0*0=0->@a.(0*a=0->0*a'=0)->0*0=0&@a.(0*a=0->0*a'=0)";
         "@a.(0*a=0->0*a'=0)->0*0=0&@a.(0*a=0->0*a'=0)";
         "0*0=0&@a.(0*a=0->0*a'=0)";
         "0*0=0&@a.(0*a=0->0*a'=0)->0*a=0";
         "0*a=0";
         "(0*a=0)->0=0->(0*a=0)";
         "0=0->0*a=0";
         "0=0->@a.(0*a=0)";
         "@a.(0*a=0)"];;
let multiplicationDoesntChangeEquality = zeroMulAEqZero @
        ["@a.@b.(a*b+b=a'*b)->@b.(e*b+b=e'*b)";
         "@b.(e*b+b=e'*b)";
         "@b.(e*b+b=e'*b)->(e*d+d=e'*d)";
         "e*d+d=e'*d";
         "@a.@b.(a*b+b=a'*b)->@b.(e*b+b=e'*b)";
         "@b.(e*b+b=e'*b)";
         "@b.(e*b+b=e'*b)->(e*a+a=e'*a)";
         "e*a+a=e'*a";
         "@a.@b.@c.(a=b->a+c=b+c)->@b.@c.(e*a=b->e*a+c=b+c)";
         "@b.@c.(e*a=b->e*a+c=b+c)";
         "@b.@c.(e*a=b->e*a+c=b+c)->@c.(e*a=e*d->e*a+c=e*d+c)";
         "@c.(e*a=e*d->e*a+c=e*d+c)";
         "@c.(e*a=e*d->e*a+c=e*d+c)->(e*a=e*d->e*a+a=e*d+a)";
         "e*a=e*d->e*a+a=e*d+a";
         "(e*a=e*d->e*a+a=e*d+a)->a=d->(e*a=e*d->e*a+a=e*d+a)";
         "a=d->e*a=e*d->e*a+a=e*d+a";
         "(a=d->e*a=e*d)->(a=d->e*a=e*d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+a)";
         "(a=d->e*a=e*d->e*a+a=e*d+a)->(a=d->e*a=e*d)->(a=d->e*a=e*d->e*a+a=e*d+a)";
         "(a=d->e*a=e*d)->(a=d->e*a=e*d->e*a+a=e*d+a)";
         "((a=d->e*a=e*d)->(a=d->e*a=e*d->e*a+a=e*d+a))->((a=d->e*a=e*d)->(a=d->e*a=e*d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+a))->((a=d->e*a=e*d)->(a=d->e*a+a=e*d+a))";
         "((a=d->e*a=e*d)->(a=d->e*a=e*d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+a))->((a=d->e*a=e*d)->(a=d->e*a+a=e*d+a))";
         "(a=d->e*a=e*d)->(a=d->e*a+a=e*d+a)";
         "@a.@b.@c.(a=b->c+a=c+b)->@b.@c.(a=b->c+a=c+b)";
         "@b.@c.(a=b->c+a=c+b)";
         "@b.@c.(a=b->c+a=c+b)->@c.(a=d->c+a=c+d)";
         "@c.(a=d->c+a=c+d)";
         "@c.(a=d->c+a=c+d)->(a=d->e*d+a=e*d+d)";
         "a=d->e*d+a=e*d+d";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=e*d+a->e*d+a=c->b=c)";
         "@b.@c.(b=e*d+a->e*d+a=c->b=c)";
         "@b.@c.(b=e*d+a->e*d+a=c->b=c)->@c.(e*a+a=e*d+a->e*d+a=c->e*a+a=c)";
         "@c.(e*a+a=e*d+a->e*d+a=c->e*a+a=c)";
         "@c.(e*a+a=e*d+a->e*d+a=c->e*a+a=c)->(e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d)";
         "e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d";
         "(e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d)->a=d->(e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d)";
         "a=d->e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d";
         "(a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d)->(a=d->e*d+a=e*d+d->e*a+a=e*d+d)";
         "(a=d->e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d)";
         "(a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d)";
         "((a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d))->((a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d)->(a=d->e*d+a=e*d+d->e*a+a=e*d+d))->((a=d->e*a+a=e*d+a)->(a=d->e*d+a=e*d+d->e*a+a=e*d+d))";
         "((a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+a->e*d+a=e*d+d->e*a+a=e*d+d)->(a=d->e*d+a=e*d+d->e*a+a=e*d+d))->((a=d->e*a+a=e*d+a)->(a=d->e*d+a=e*d+d->e*a+a=e*d+d))";
         "(a=d->e*a+a=e*d+a)->(a=d->e*d+a=e*d+d->e*a+a=e*d+d)";
         "(a=d->e*d+a=e*d+d)->(a=d->e*d+a=e*d+d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d)";
         "(a=d->e*d+a=e*d+d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d)";
         "((a=d->e*d+a=e*d+d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d))->(a=d->e*a+a=e*d+a)->((a=d->e*d+a=e*d+d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d))";
         "(a=d->e*a+a=e*d+a)->(a=d->e*d+a=e*d+d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d)";
         "((a=d->e*a+a=e*d+a)->(a=d->e*d+a=e*d+d->e*a+a=e*d+d))->((a=d->e*a+a=e*d+a)->(a=d->e*d+a=e*d+d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d))->((a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+d))";
         "((a=d->e*a+a=e*d+a)->(a=d->e*d+a=e*d+d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d))->((a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+d))";
         "(a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+d)";
         "((a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+d))->(a=d->e*a=e*d)->((a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+d))";
         "(a=d->e*a=e*d)->(a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+d)";
         "((a=d->e*a=e*d)->(a=d->e*a+a=e*d+a))->((a=d->e*a=e*d)->(a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+d))->((a=d->e*a=e*d)->(a=d->e*a+a=e*d+d))";
         "((a=d->e*a=e*d)->(a=d->e*a+a=e*d+a)->(a=d->e*a+a=e*d+d))->((a=d->e*a=e*d)->(a=d->e*a+a=e*d+d))";
         "(a=d->e*a=e*d)->(a=d->e*a+a=e*d+d)";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(e*a+a=b->e*a+a=c->b=c)";
         "@b.@c.(e*a+a=b->e*a+a=c->b=c)";
         "@b.@c.(e*a+a=b->e*a+a=c->b=c)->@c.(e*a+a=e'*a->e*a+a=c->e'*a=c)";
         "@c.(e*a+a=e'*a->e*a+a=c->e'*a=c)";
         "@c.(e*a+a=e'*a->e*a+a=c->e'*a=c)->(e*a+a=e'*a->e*a+a=e*d+d->e'*a=e*d+d)";
         "e*a+a=e'*a->e*a+a=e*d+d->e'*a=e*d+d";
         "e*a+a=e*d+d->e'*a=e*d+d";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=e*d+d->e*d+d=c->b=c)";
         "@b.@c.(b=e*d+d->e*d+d=c->b=c)";
         "@b.@c.(b=e*d+d->e*d+d=c->b=c)->@c.(e'*a=e*d+d->e*d+d=c->e'*a=c)";
         "@c.(e'*a=e*d+d->e*d+d=c->e'*a=c)";
         "@c.(e'*a=e*d+d->e*d+d=c->e'*a=c)->(e'*a=e*d+d->e*d+d=e'*d->e'*a=e'*d)";
         "e'*a=e*d+d->e*d+d=e'*d->e'*a=e'*d";
         "(e'*a=e*d+d->e*d+d=e'*d->e'*a=e'*d)->e*a+a=e*d+d->(e'*a=e*d+d->e*d+d=e'*d->e'*a=e'*d)";
         "e*a+a=e*d+d->e'*a=e*d+d->e*d+d=e'*d->e'*a=e'*d";
         "(e*a+a=e*d+d->e'*a=e*d+d)->(e*a+a=e*d+d->e'*a=e*d+d->e*d+d=e'*d->e'*a=e'*d)->(e*a+a=e*d+d->e*d+d=e'*d->e'*a=e'*d)";
         "(e*a+a=e*d+d->e'*a=e*d+d->e*d+d=e'*d->e'*a=e'*d)->(e*a+a=e*d+d->e*d+d=e'*d->e'*a=e'*d)";
         "e*a+a=e*d+d->e*d+d=e'*d->e'*a=e'*d";
         "(e*d+d=e'*d)->(e*a+a=e*d+d)->(e*d+d=e'*d)";
         "e*a+a=e*d+d->e*d+d=e'*d";
         "(e*a+a=e*d+d->e*d+d=e'*d)->(e*a+a=e*d+d->e*d+d=e'*d->e'*a=e'*d)->(e*a+a=e*d+d->e'*a=e'*d)";
         "(e*a+a=e*d+d->e*d+d=e'*d->e'*a=e'*d)->(e*a+a=e*d+d->e'*a=e'*d)";
         "e*a+a=e*d+d->e'*a=e'*d";
         "(e*a+a=e*d+d->e'*a=e'*d)->a=d->(e*a+a=e*d+d->e'*a=e'*d)";
         "a=d->e*a+a=e*d+d->e'*a=e'*d";
         "(a=d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e'*a=e'*d)";
         "((a=d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e'*a=e'*d))->(a=d->e*a=e*d)->((a=d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e'*a=e'*d))";
         "(a=d->e*a=e*d)->(a=d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e'*a=e'*d)";
         "((a=d->e*a=e*d)->(a=d->e*a+a=e*d+d))->((a=d->e*a=e*d)->(a=d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e'*a=e'*d))->((a=d->e*a=e*d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e'*a=e'*d))";
         "((a=d->e*a=e*d)->(a=d->e*a+a=e*d+d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e'*a=e'*d))->((a=d->e*a=e*d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e'*a=e'*d))";
         "(a=d->e*a=e*d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e'*a=e'*d)";
         "(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e*a=e*d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)";
         "(a=d->e*a=e*d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)";
         "((a=d->e*a=e*d)->(a=d->e*a+a=e*d+d->e'*a=e'*d))->((a=d->e*a=e*d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e'*a=e'*d))->((a=d->e*a=e*d)->(a=d->e'*a=e'*d))";
         "((a=d->e*a=e*d)->(a=d->e*a+a=e*d+d->e'*a=e'*d)->(a=d->e'*a=e'*d))->((a=d->e*a=e*d)->(a=d->e'*a=e'*d))";
         "(a=d->e*a=e*d)->(a=d->e'*a=e'*d)";
         "((a=d->e*a=e*d)->(a=d->e'*a=e'*d))->0=0->((a=d->e*a=e*d)->(a=d->e'*a=e'*d))";
         "0=0->((a=d->e*a=e*d)->(a=d->e'*a=e'*d))";
         "0=0->@e.((a=d->e*a=e*d)->(a=d->e'*a=e'*d))";
         "@e.((a=d->e*a=e*d)->(a=d->e'*a=e'*d))";
         "@a.(0*a=0)->(0*a=0)";
         "0*a=0";
         "@a.(0*a=0)->(0*d=0)";
         "0*d=0";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=0->c=0->b=c)";
         "@b.@c.(b=0->c=0->b=c)";
         "@b.@c.(b=0->c=0->b=c)->@c.(0*a=0->c=0->0*a=c)";
         "@c.(0*a=0->c=0->0*a=c)";
         "@c.(0*a=0->c=0->0*a=c)->(0*a=0->0*d=0->0*a=0*d)";
         "0*a=0->0*d=0->0*a=0*d";
         "0*d=0->0*a=0*d";
         "0*a=0*d";
         "0*a=0*d->a=d->0*a=0*d";
         "a=d->0*a=0*d";
         "(a=d->0*a=0*d)->@e.((a=d->e*a=e*d)->(a=d->e'*a=e'*d))->(a=d->0*a=0*d)&@e.((a=d->e*a=e*d)->(a=d->e'*a=e'*d))";
         "@e.((a=d->e*a=e*d)->(a=d->e'*a=e'*d))->(a=d->0*a=0*d)&@e.((a=d->e*a=e*d)->(a=d->e'*a=e'*d))";
         "(a=d->0*a=0*d)&@e.((a=d->e*a=e*d)->(a=d->e'*a=e'*d))";
         "(a=d->0*a=0*d)&@e.((a=d->e*a=e*d)->(a=d->e'*a=e'*d))->(a=d->e*a=e*d)";
         "a=d->e*a=e*d";
         "(a=d->e*a=e*d)->0=0->(a=d->e*a=e*d)";
         "0=0->(a=d->e*a=e*d)";
         "0=0->@e.(a=d->e*a=e*d)";
         "0=0->@d.@e.(a=d->e*a=e*d)";
         "@d.@e.(a=d->e*a=e*d)";
         "@d.@e.(a=d->e*a=e*d)->@e.(a=b->e*a=e*b)";
         "@e.(a=b->e*a=e*b)";
         "@e.(a=b->e*a=e*b)->(a=b->c*a=c*b)";
         "a=b->c*a=c*b";
         "(a=b->c*a=c*b)->0=0->(a=b->c*a=c*b)";
         "0=0->(a=b->c*a=c*b)";
         "0=0->@c.(a=b->c*a=c*b)";
         "0=0->@b.@c.(a=b->c*a=c*b)";
         "0=0->@a.@b.@c.(a=b->c*a=c*b)";
         "@a.@b.@c.(a=b->c*a=c*b)"];;
let distributivity = multiplicationDoesntChangeEquality @
        ["@a.@b.(a+b'=(a+b)')->@b.(d+b'=(d+b)')";
         "@b.(d+b'=(d+b)')";
         "@b.(d+b'=(d+b)')->(d+e'=(d+e)')";
         "d+e'=(d+e)'";
         "@a.@b.@c.(a=b->c*a=c*b)->@b.@c.(d+e'=b->c*(d+e')=c*b)";
         "@b.@c.(d+e'=b->c*(d+e')=c*b)";
         "@b.@c.(d+e'=b->c*(d+e')=c*b)->@c.(d+e'=(d+e)'->c*(d+e')=c*(d+e)')";
         "@c.(d+e'=(d+e)'->c*(d+e')=c*(d+e)')";
         "@c.(d+e'=(d+e)'->c*(d+e')=c*(d+e)')->(d+e'=(d+e)'->a*(d+e')=a*(d+e)')";
         "d+e'=(d+e)'->a*(d+e')=a*(d+e)'";
         "a*(d+e')=a*(d+e)'";
         "@a.@b.(a*b'=a*b+a)->@b.(a*b'=a*b+a)";
         "@b.(a*b'=a*b+a)";
         "@b.(a*b'=a*b+a)->(a*(d+e)'=a*(d+e)+a)";
         "a*(d+e)'=a*(d+e)+a";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=a*(d+e)'->a*(d+e)'=c->b=c)";
         "@b.@c.(b=a*(d+e)'->a*(d+e)'=c->b=c)";
         "@b.@c.(b=a*(d+e)'->a*(d+e)'=c->b=c)->@c.(a*(d+e')=a*(d+e)'->a*(d+e)'=c->a*(d+e')=c)";
         "@c.(a*(d+e')=a*(d+e)'->a*(d+e)'=c->a*(d+e')=c)";
         "@c.(a*(d+e')=a*(d+e)'->a*(d+e)'=c->a*(d+e')=c)->(a*(d+e')=a*(d+e)'->a*(d+e)'=a*(d+e)+a->a*(d+e')=a*(d+e)+a)";
         "a*(d+e')=a*(d+e)'->a*(d+e)'=a*(d+e)+a->a*(d+e')=a*(d+e)+a";
         "a*(d+e)'=a*(d+e)+a->a*(d+e')=a*(d+e)+a";
         "a*(d+e')=a*(d+e)+a";
         "@a.@b.(a*b'=a*b+a)->@b.(a*b'=a*b+a)";
         "@b.(a*b'=a*b+a)";
         "@b.(a*b'=a*b+a)->(a*e'=a*e+a)";
         "a*e'=a*e+a";
         "@a.@b.@c.(a=b->c+a=c+b)->@b.@c.(a*e'=b->c+a*e'=c+b)";
         "@b.@c.(a*e'=b->c+a*e'=c+b)";
         "@b.@c.(a*e'=b->c+a*e'=c+b)->@c.(a*e'=a*e+a->c+a*e'=c+(a*e+a))";
         "@c.(a*e'=a*e+a->c+a*e'=c+(a*e+a))";
         "@c.(a*e'=a*e+a->c+a*e'=c+(a*e+a))->(a*e'=a*e+a->a*d+a*e'=a*d+(a*e+a))";
         "a*e'=a*e+a->a*d+a*e'=a*d+(a*e+a)";
         "a*d+a*e'=a*d+(a*e+a)";
         "@a.@b.@c.((a+b)+c=a+(b+c))->@b.@c.((a*d+b)+c=a*d+(b+c))";
         "@b.@c.((a*d+b)+c=a*d+(b+c))";
         "@b.@c.((a*d+b)+c=a*d+(b+c))->@c.((a*d+a*e)+c=a*d+(a*e+c))";
         "@c.((a*d+a*e)+c=a*d+(a*e+c))";
         "@c.((a*d+a*e)+c=a*d+(a*e+c))->((a*d+a*e)+a=a*d+(a*e+a))";
         "(a*d+a*e)+a=a*d+(a*e+a)";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=a*d+(a*e+a)->c=a*d+(a*e+a)->b=c)";
         "@b.@c.(b=a*d+(a*e+a)->c=a*d+(a*e+a)->b=c)";
         "@b.@c.(b=a*d+(a*e+a)->c=a*d+(a*e+a)->b=c)->@c.(a*d+a*e'=a*d+(a*e+a)->c=a*d+(a*e+a)->a*d+a*e'=c)";
         "@c.(a*d+a*e'=a*d+(a*e+a)->c=a*d+(a*e+a)->a*d+a*e'=c)";
         "@c.(a*d+a*e'=a*d+(a*e+a)->c=a*d+(a*e+a)->a*d+a*e'=c)->(a*d+a*e'=a*d+(a*e+a)->(a*d+a*e)+a=a*d+(a*e+a)->a*d+a*e'=(a*d+a*e)+a)";
         "a*d+a*e'=a*d+(a*e+a)->(a*d+a*e)+a=a*d+(a*e+a)->a*d+a*e'=(a*d+a*e)+a";
         "(a*d+a*e)+a=a*d+(a*e+a)->a*d+a*e'=(a*d+a*e)+a";
         "a*d+a*e'=(a*d+a*e)+a";
         "@a.@b.@c.(a=b->a+c=b+c)->@b.@c.(a*(d+e)=b->a*(d+e)+c=b+c)";
         "@b.@c.(a*(d+e)=b->a*(d+e)+c=b+c)";
         "@b.@c.(a*(d+e)=b->a*(d+e)+c=b+c)->@c.(a*(d+e)=a*d+a*e->a*(d+e)+c=(a*d+a*e)+c)";
         "@c.(a*(d+e)=a*d+a*e->a*(d+e)+c=(a*d+a*e)+c)";
         "@c.(a*(d+e)=a*d+a*e->a*(d+e)+c=(a*d+a*e)+c)->(a*(d+e)=a*d+a*e->a*(d+e)+a=(a*d+a*e)+a)";
         "a*(d+e)=a*d+a*e->a*(d+e)+a=(a*d+a*e)+a";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=(a*d+a*e)+a->c=(a*d+a*e)+a->b=c)";
         "@b.@c.(b=(a*d+a*e)+a->c=(a*d+a*e)+a->b=c)";
         "@b.@c.(b=(a*d+a*e)+a->c=(a*d+a*e)+a->b=c)->@c.(a*(d+e)+a=(a*d+a*e)+a->c=(a*d+a*e)+a->a*(d+e)+a=c)";
         "@c.(a*(d+e)+a=(a*d+a*e)+a->c=(a*d+a*e)+a->a*(d+e)+a=c)";
         "@c.(a*(d+e)+a=(a*d+a*e)+a->c=(a*d+a*e)+a->a*(d+e)+a=c)->(a*(d+e)+a=(a*d+a*e)+a->a*d+a*e'=(a*d+a*e)+a->a*(d+e)+a=a*d+a*e')";
         "a*(d+e)+a=(a*d+a*e)+a->a*d+a*e'=(a*d+a*e)+a->a*(d+e)+a=a*d+a*e'";
         "a*d+a*e'=(a*d+a*e)+a->a*(d+e)+a=(a*d+a*e)+a->a*d+a*e'=(a*d+a*e)+a";
         "a*(d+e)+a=(a*d+a*e)+a->a*d+a*e'=(a*d+a*e)+a";
         "(a*(d+e)+a=(a*d+a*e)+a->a*d+a*e'=(a*d+a*e)+a)->(a*(d+e)+a=(a*d+a*e)+a->a*d+a*e'=(a*d+a*e)+a->a*(d+e)+a=a*d+a*e')->(a*(d+e)+a=(a*d+a*e)+a->a*(d+e)+a=a*d+a*e')";
         "(a*(d+e)+a=(a*d+a*e)+a->a*d+a*e'=(a*d+a*e)+a->a*(d+e)+a=a*d+a*e')->(a*(d+e)+a=(a*d+a*e)+a->a*(d+e)+a=a*d+a*e')";
         "a*(d+e)+a=(a*d+a*e)+a->a*(d+e)+a=a*d+a*e'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=a*(d+e)+a->a*(d+e)+a=c->b=c)";
         "@b.@c.(b=a*(d+e)+a->a*(d+e)+a=c->b=c)";
         "@b.@c.(b=a*(d+e)+a->a*(d+e)+a=c->b=c)->@c.(a*(d+e')=a*(d+e)+a->a*(d+e)+a=c->a*(d+e')=c)";
         "@c.(a*(d+e')=a*(d+e)+a->a*(d+e)+a=c->a*(d+e')=c)";
         "@c.(a*(d+e')=a*(d+e)+a->a*(d+e)+a=c->a*(d+e')=c)->(a*(d+e')=a*(d+e)+a->a*(d+e)+a=a*d+a*e'->a*(d+e')=a*d+a*e')";
         "a*(d+e')=a*(d+e)+a->a*(d+e)+a=a*d+a*e'->a*(d+e')=a*d+a*e'";
         "a*(d+e)+a=a*d+a*e'->a*(d+e')=a*d+a*e'";
         "(a*(d+e)+a=a*d+a*e'->a*(d+e')=a*d+a*e')->a*(d+e)+a=(a*d+a*e)+a->(a*(d+e)+a=a*d+a*e'->a*(d+e')=a*d+a*e')";
         "a*(d+e)+a=(a*d+a*e)+a->a*(d+e)+a=a*d+a*e'->a*(d+e')=a*d+a*e'";
         "(a*(d+e)+a=(a*d+a*e)+a->a*(d+e)+a=a*d+a*e')->(a*(d+e)+a=(a*d+a*e)+a->a*(d+e)+a=a*d+a*e'->a*(d+e')=a*d+a*e')->(a*(d+e)+a=(a*d+a*e)+a->a*(d+e')=a*d+a*e')";
         "(a*(d+e)+a=(a*d+a*e)+a->a*(d+e)+a=a*d+a*e'->a*(d+e')=a*d+a*e')->(a*(d+e)+a=(a*d+a*e)+a->a*(d+e')=a*d+a*e')";
         "a*(d+e)+a=(a*d+a*e)+a->a*(d+e')=a*d+a*e'";
         "(a*(d+e)+a=(a*d+a*e)+a->a*(d+e')=a*d+a*e')->a*(d+e)=a*d+a*e->(a*(d+e)+a=(a*d+a*e)+a->a*(d+e')=a*d+a*e')";
         "a*(d+e)=a*d+a*e->a*(d+e)+a=(a*d+a*e)+a->a*(d+e')=a*d+a*e'";
         "(a*(d+e)=a*d+a*e->a*(d+e)+a=(a*d+a*e)+a)->(a*(d+e)=a*d+a*e->a*(d+e)+a=(a*d+a*e)+a->a*(d+e')=a*d+a*e')->(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')";
         "(a*(d+e)=a*d+a*e->a*(d+e)+a=(a*d+a*e)+a->a*(d+e')=a*d+a*e')->(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')";
         "a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e'";
         "(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')->0=0->(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')";
         "0=0->(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')";
         "0=0->@e.(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')";
         "@e.(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')";
         "@a.(a+0=a)->(d+0=d)";
         "d+0=d";
         "@a.@b.@c.(a=b->c*a=c*b)->@b.@c.(d+0=b->c*(d+0)=c*b)";
         "@b.@c.(d+0=b->c*(d+0)=c*b)";
         "@b.@c.(d+0=b->c*(d+0)=c*b)->@c.(d+0=d->c*(d+0)=c*d)";
         "@c.(d+0=d->c*(d+0)=c*d)";
         "@c.(d+0=d->c*(d+0)=c*d)->(d+0=d->a*(d+0)=a*d)";
         "d+0=d->a*(d+0)=a*d";
         "a*(d+0)=a*d";
         "a*0=0";
         "@a.@b.@c.(a=b->c+a=c+b)->@b.@c.(a*0=b->c+a*0=c+b)";
         "@b.@c.(a*0=b->c+a*0=c+b)";
         "@b.@c.(a*0=b->c+a*0=c+b)->@c.(a*0=0->c+a*0=c+0)";
         "@c.(a*0=0->c+a*0=c+0)";
         "@c.(a*0=0->c+a*0=c+0)->(a*0=0->a*d+a*0=a*d+0)";
         "a*0=0->a*d+a*0=a*d+0";
         "a*d+a*0=a*d+0";
         "@a.(a+0=a)->(a*d+0=a*d)";
         "a*d+0=a*d";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=a*d+0->a*d+0=c->b=c)";
         "@b.@c.(b=a*d+0->a*d+0=c->b=c)";
         "@b.@c.(b=a*d+0->a*d+0=c->b=c)->@c.(a*d+a*0=a*d+0->a*d+0=c->a*d+a*0=c)";
         "@c.(a*d+a*0=a*d+0->a*d+0=c->a*d+a*0=c)";
         "@c.(a*d+a*0=a*d+0->a*d+0=c->a*d+a*0=c)->(a*d+a*0=a*d+0->a*d+0=a*d->a*d+a*0=a*d)";
         "a*d+a*0=a*d+0->a*d+0=a*d->a*d+a*0=a*d";
         "a*d+0=a*d->a*d+a*0=a*d";
         "a*d+a*0=a*d";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=a*d->c=a*d->b=c)";
         "@b.@c.(b=a*d->c=a*d->b=c)";
         "@b.@c.(b=a*d->c=a*d->b=c)->@c.(a*(d+0)=a*d->c=a*d->a*(d+0)=c)";
         "@c.(a*(d+0)=a*d->c=a*d->a*(d+0)=c)";
         "@c.(a*(d+0)=a*d->c=a*d->a*(d+0)=c)->(a*(d+0)=a*d->a*d+a*0=a*d->a*(d+0)=a*d+a*0)";
         "a*(d+0)=a*d->a*d+a*0=a*d->a*(d+0)=a*d+a*0";
         "a*d+a*0=a*d->a*(d+0)=a*d+a*0";
         "a*(d+0)=a*d+a*0";
         "a*(d+0)=a*d+a*0->@e.(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')->a*(d+0)=a*d+a*0&@e.(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')";
         "@e.(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')->a*(d+0)=a*d+a*0&@e.(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')";
         "a*(d+0)=a*d+a*0&@e.(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')";
         "a*(d+0)=a*d+a*0&@e.(a*(d+e)=a*d+a*e->a*(d+e')=a*d+a*e')->a*(d+e)=a*d+a*e";
         "a*(d+e)=a*d+a*e";
         "a*(d+e)=a*d+a*e->0=0->a*(d+e)=a*d+a*e";
         "0=0->a*(d+e)=a*d+a*e";
         "0=0->@e.(a*(d+e)=a*d+a*e)";
         "0=0->@d.@e.(a*(d+e)=a*d+a*e)";
         "@d.@e.(a*(d+e)=a*d+a*e)";
         "@d.@e.(a*(d+e)=a*d+a*e)->@e.(a*(b+e)=a*b+a*e)";
         "@e.(a*(b+e)=a*b+a*e)";
         "@e.(a*(b+e)=a*b+a*e)->(a*(b+c)=a*b+a*c)";
         "a*(b+c)=a*b+a*c";
         "a*(b+c)=a*b+a*c->0=0->a*(b+c)=a*b+a*c";
         "0=0->a*(b+c)=a*b+a*c";
         "0=0->@c.(a*(b+c)=a*b+a*c)";
         "0=0->@b.@c.(a*(b+c)=a*b+a*c)";
         "0=0->@a.@b.@c.(a*(b+c)=a*b+a*c)";
         "@a.@b.@c.(a*(b+c)=a*b+a*c)"];;
let substractDoesntMatter = distributivity @
        ["a'=b'->a=b";
         "(a'=b'->a=b)->0=0->(a'=b'->a=b)";
         "0=0->(a'=b'->a=b)";
         "0=0->@b.(a'=b'->a=b)";
         "0=0->@a.@b.(a'=b'->a=b)";
         "@a.@b.(a'=b'->a=b)";
         "@a.@b.(a'=b'->a=b)->@b.((a+e)'=b'->a+e=b)";
         "@b.((a+e)'=b'->a+e=b)";
         "@b.((a+e)'=b'->a+e=b)->((a+e)'=(d+e)'->a+e=d+e)";
         "(a+e)'=(d+e)'->a+e=d+e";
         "@a.@b.(a+b'=(a+b)')->@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')->(a+e'=(a+e)')";
         "a+e'=(a+e)'";
         "@a.@b.(a+b'=(a+b)')->@b.(d+b'=(d+b)')";
         "@b.(d+b'=(d+b)')";
         "@b.(d+b'=(d+b)')->(d+e'=(d+e)')";
         "d+e'=(d+e)'";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(a+e'=b->a+e'=c->b=c)";
         "@b.@c.(a+e'=b->a+e'=c->b=c)";
         "@b.@c.(a+e'=b->a+e'=c->b=c)->@c.(a+e'=(a+e)'->a+e'=c->(a+e)'=c)";
         "@c.(a+e'=(a+e)'->a+e'=c->(a+e)'=c)";
         "@c.(a+e'=(a+e)'->a+e'=c->(a+e)'=c)->(a+e'=(a+e)'->a+e'=d+e'->(a+e)'=d+e')";
         "a+e'=(a+e)'->a+e'=d+e'->(a+e)'=d+e'";
         "a+e'=d+e'->(a+e)'=d+e'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=d+e'->d+e'=c->b=c)";
         "@b.@c.(b=d+e'->d+e'=c->b=c)";
         "@b.@c.(b=d+e'->d+e'=c->b=c)->@c.((a+e)'=d+e'->d+e'=c->(a+e)'=c)";
         "@c.((a+e)'=d+e'->d+e'=c->(a+e)'=c)";
         "@c.((a+e)'=d+e'->d+e'=c->(a+e)'=c)->((a+e)'=d+e'->d+e'=(d+e)'->(a+e)'=(d+e)')";
         "(a+e)'=d+e'->d+e'=(d+e)'->(a+e)'=(d+e)'";
         "d+e'=(d+e)'->(a+e)'=d+e'->d+e'=(d+e)'";
         "(a+e)'=d+e'->d+e'=(d+e)'";
         "((a+e)'=d+e'->d+e'=(d+e)')->((a+e)'=d+e'->d+e'=(d+e)'->(a+e)'=(d+e)')->((a+e)'=d+e'->(a+e)'=(d+e)')";
         "((a+e)'=d+e'->d+e'=(d+e)'->(a+e)'=(d+e)')->((a+e)'=d+e'->(a+e)'=(d+e)')";
         "(a+e)'=d+e'->(a+e)'=(d+e)'";
         "((a+e)'=d+e'->(a+e)'=(d+e)')->a+e'=d+e'->((a+e)'=d+e'->(a+e)'=(d+e)')";
         "a+e'=d+e'->(a+e)'=d+e'->(a+e)'=(d+e)'";
         "(a+e'=d+e'->(a+e)'=d+e')->(a+e'=d+e'->(a+e)'=d+e'->(a+e)'=(d+e)')->(a+e'=d+e'->(a+e)'=(d+e)')";
         "(a+e'=d+e'->(a+e)'=d+e'->(a+e)'=(d+e)')->(a+e'=d+e'->(a+e)'=(d+e)')";
         "a+e'=d+e'->(a+e)'=(d+e)'";
         "((a+e)'=(d+e)'->a+e=d+e)->a+e'=d+e'->((a+e)'=(d+e)'->a+e=d+e)";
         "a+e'=d+e'->(a+e)'=(d+e)'->a+e=d+e";
         "(a+e'=d+e'->(a+e)'=(d+e)')->(a+e'=d+e'->(a+e)'=(d+e)'->a+e=d+e)->(a+e'=d+e'->a+e=d+e)";
         "(a+e'=d+e'->(a+e)'=(d+e)'->a+e=d+e)->(a+e'=d+e'->a+e=d+e)";
         "a+e'=d+e'->a+e=d+e";
         "((a+e'=d+e'->a+e=d+e)->(a+e'=d+e'->a+e=d+e->a=d)->(a+e'=d+e'->a=d))->(a+e=d+e->a=d)->((a+e'=d+e'->a+e=d+e)->(a+e'=d+e'->a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "(a+e'=d+e'->a+e=d+e)->(a+e'=d+e'->a+e=d+e->a=d)->(a+e'=d+e'->a=d)";
         "(a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e)->(a+e'=d+e'->a+e=d+e->a=d)->(a+e'=d+e'->a=d)";
         "(a+e'=d+e'->a+e=d+e)->(a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e)";
         "(a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e)";
         "((a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e))->((a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e)->(a+e'=d+e'->a+e=d+e->a=d)->(a+e'=d+e'->a=d))->((a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "((a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e)->(a+e'=d+e'->a+e=d+e->a=d)->(a+e'=d+e'->a=d))->((a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "(a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e->a=d)->(a+e'=d+e'->a=d)";
         "(a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e->a=d)";
         "((a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e->a=d))->((a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e->a=d)->(a+e'=d+e'->a=d))->((a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "((a+e=d+e->a=d)->(a+e'=d+e'->a+e=d+e->a=d)->(a+e'=d+e'->a=d))->((a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "(a+e=d+e->a=d)->(a+e'=d+e'->a=d)";
         "((a+e=d+e->a=d)->(a+e'=d+e'->a=d))->0=0->((a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "0=0->((a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "0=0->@e.((a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "@e.((a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "@a.(a+0=a)->(d+0=d)";
         "d+0=d";
         "a+0=a";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(a+0=b->a+0=c->b=c)";
         "@b.@c.(a+0=b->a+0=c->b=c)";
         "@b.@c.(a+0=b->a+0=c->b=c)->@c.(a+0=a->a+0=c->a=c)";
         "@c.(a+0=a->a+0=c->a=c)";
         "@c.(a+0=a->a+0=c->a=c)->(a+0=a->a+0=d+0->a=d+0)";
         "a+0=a->a+0=d+0->a=d+0";
         "a+0=d+0->a=d+0";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=d+0->d+0=c->b=c)";
         "@b.@c.(b=d+0->d+0=c->b=c)";
         "@b.@c.(b=d+0->d+0=c->b=c)->@c.(a=d+0->d+0=c->a=c)";
         "@c.(a=d+0->d+0=c->a=c)";
         "@c.(a=d+0->d+0=c->a=c)->(a=d+0->d+0=d->a=d)";
         "a=d+0->d+0=d->a=d";
         "d+0=d->a=d+0->d+0=d";
         "a=d+0->d+0=d";
         "(a=d+0->d+0=d)->(a=d+0->d+0=d->a=d)->(a=d+0->a=d)";
         "(a=d+0->d+0=d->a=d)->(a=d+0->a=d)";
         "a=d+0->a=d";
         "(a=d+0->a=d)->a+0=d+0->(a=d+0->a=d)";
         "a+0=d+0->a=d+0->a=d";
         "(a+0=d+0->a=d+0)->(a+0=d+0->a=d+0->a=d)->(a+0=d+0->a=d)";
         "(a+0=d+0->a=d+0->a=d)->(a+0=d+0->a=d)";
         "a+0=d+0->a=d";
         "(a+0=d+0->a=d)->@e.((a+e=d+e->a=d)->(a+e'=d+e'->a=d))->(a+0=d+0->a=d)&@e.((a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "@e.((a+e=d+e->a=d)->(a+e'=d+e'->a=d))->(a+0=d+0->a=d)&@e.((a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "(a+0=d+0->a=d)&@e.((a+e=d+e->a=d)->(a+e'=d+e'->a=d))";
         "(a+0=d+0->a=d)&@e.((a+e=d+e->a=d)->(a+e'=d+e'->a=d))->(a+e=d+e->a=d)";
         "a+e=d+e->a=d";
         "(a+e=d+e->a=d)->0=0->(a+e=d+e->a=d)";
         "0=0->(a+e=d+e->a=d)";
         "0=0->@e.(a+e=d+e->a=d)";
         "0=0->@d.@e.(a+e=d+e->a=d)";
         "@d.@e.(a+e=d+e->a=d)";
         "@d.@e.(a+e=d+e->a=d)->@e.(a+e=b+e->a=b)";
         "@e.(a+e=b+e->a=b)";
         "@e.(a+e=b+e->a=b)->(a+c=b+c->a=b)";
         "a+c=b+c->a=b";
         "(a+c=b+c->a=b)->0=0->(a+c=b+c->a=b)";
         "0=0->(a+c=b+c->a=b)";
         "0=0->@c.(a+c=b+c->a=b)";
         "0=0->@b.@c.(a+c=b+c->a=b)";
         "0=0->@a.@b.@c.(a+c=b+c->a=b)";
         "@a.@b.@c.(a+c=b+c->a=b)";
         "@a.@b.(a+b=b+a)->@b.(a+b=b+a)";
         "@b.(a+b=b+a)";
         "@b.(a+b=b+a)->(a+e=e+a)";
         "a+e=e+a";
         "@a.@b.(a+b=b+a)->@b.(d+b=b+d)";
         "@b.(d+b=b+d)";
         "@b.(d+b=b+d)->(d+e=e+d)";
         "d+e=e+d";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=e+a->e+a=c->b=c)";
         "@b.@c.(b=e+a->e+a=c->b=c)";
         "@b.@c.(b=e+a->e+a=c->b=c)->@c.(a+e=e+a->e+a=c->a+e=c)";
         "@c.(a+e=e+a->e+a=c->a+e=c)";
         "@c.(a+e=e+a->e+a=c->a+e=c)->(a+e=e+a->e+a=e+d->a+e=e+d)";
         "a+e=e+a->e+a=e+d->a+e=e+d";
         "e+a=e+d->a+e=e+d";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=e+d->c=e+d->b=c)";
         "@b.@c.(b=e+d->c=e+d->b=c)";
         "@b.@c.(b=e+d->c=e+d->b=c)->@c.(a+e=e+d->c=e+d->a+e=c)";
         "@c.(a+e=e+d->c=e+d->a+e=c)";
         "@c.(a+e=e+d->c=e+d->a+e=c)->(a+e=e+d->d+e=e+d->a+e=d+e)";
         "a+e=e+d->d+e=e+d->a+e=d+e";
         "d+e=e+d->a+e=e+d->d+e=e+d";
         "a+e=e+d->d+e=e+d";
         "(a+e=e+d->d+e=e+d)->(a+e=e+d->d+e=e+d->a+e=d+e)->(a+e=e+d->a+e=d+e)";
         "(a+e=e+d->d+e=e+d->a+e=d+e)->(a+e=e+d->a+e=d+e)";
         "a+e=e+d->a+e=d+e";
         "(a+e=e+d->a+e=d+e)->e+a=e+d->(a+e=e+d->a+e=d+e)";
         "e+a=e+d->a+e=e+d->a+e=d+e";
         "(e+a=e+d->a+e=e+d)->(e+a=e+d->a+e=e+d->a+e=d+e)->(e+a=e+d->a+e=d+e)";
         "(e+a=e+d->a+e=e+d->a+e=d+e)->(e+a=e+d->a+e=d+e)";
         "e+a=e+d->a+e=d+e";
         "(a+e=d+e->a=d)->e+a=e+d->(a+e=d+e->a=d)";
         "e+a=e+d->a+e=d+e->a=d";
         "(e+a=e+d->a+e=d+e)->(e+a=e+d->a+e=d+e->a=d)->(e+a=e+d->a=d)";
         "(e+a=e+d->a+e=d+e->a=d)->(e+a=e+d->a=d)";
         "e+a=e+d->a=d";
         "(e+a=e+d->a=d)->0=0->(e+a=e+d->a=d)";
         "0=0->(e+a=e+d->a=d)";
         "0=0->@e.(e+a=e+d->a=d)";
         "0=0->@d.@e.(e+a=e+d->a=d)";
         "@d.@e.(e+a=e+d->a=d)";
         "@d.@e.(e+a=e+d->a=d)->@e.(e+a=e+b->a=b)";
         "@e.(e+a=e+b->a=b)";
         "@e.(e+a=e+b->a=b)->(c+a=c+b->a=b)";
         "c+a=c+b->a=b";
         "(c+a=c+b->a=b)->0=0->(c+a=c+b->a=b)";
         "0=0->(c+a=c+b->a=b)";
         "0=0->@c.(c+a=c+b->a=b)";
         "0=0->@b.@c.(c+a=c+b->a=b)";
         "0=0->@a.@b.@c.(c+a=c+b->a=b)";
         "@a.@b.@c.(c+a=c+b->a=b)"];;
let biggerFirstOrSecond = substractDoesntMatter @
        ["(0=0->a=e+d)->(0=0->!a=e+d)->!(0=0)";
         "((0=0->a=e+d)->(0=0->!a=e+d)->!(0=0))->a=e+d->((0=0->a=e+d)->(0=0->!a=e+d)->!(0=0))";
         "a=e+d->(0=0->a=e+d)->(0=0->!a=e+d)->!(0=0)";
         "a=e+d->0=0->a=e+d";
         "(a=e+d->0=0->a=e+d)->(a=e+d->(0=0->a=e+d)->(0=0->!a=e+d)->!(0=0))->(a=e+d->(0=0->!a=e+d)->!(0=0))";
         "(a=e+d->(0=0->a=e+d)->(0=0->!a=e+d)->!(0=0))->(a=e+d->(0=0->!a=e+d)->!(0=0))";
         "a=e+d->(0=0->!a=e+d)->!(0=0)";
         "(a=e+d->(0=0->!a=e+d)->!(0=0))->@e.!a=e+d->(a=e+d->(0=0->!a=e+d)->!(0=0))";
         "@e.!a=e+d->a=e+d->(0=0->!a=e+d)->!(0=0)";
         "@e.!a=e+d->!a=e+d";
         "!a=e+d->0=0->!a=e+d";
         "(!a=e+d->0=0->!a=e+d)->@e.!a=e+d->(!a=e+d->0=0->!a=e+d)";
         "@e.!a=e+d->!a=e+d->0=0->!a=e+d";
         "(@e.!a=e+d->!a=e+d)->(@e.!a=e+d->!a=e+d->0=0->!a=e+d)->(@e.!a=e+d->0=0->!a=e+d)";
         "(@e.!a=e+d->!a=e+d->0=0->!a=e+d)->(@e.!a=e+d->0=0->!a=e+d)";
         "@e.!a=e+d->0=0->!a=e+d";
         "(0=0->!a=e+d)->a=e+d->(0=0->!a=e+d)";
         "((0=0->!a=e+d)->a=e+d->(0=0->!a=e+d))->@e.!a=e+d->((0=0->!a=e+d)->a=e+d->(0=0->!a=e+d))";
         "@e.!a=e+d->(0=0->!a=e+d)->a=e+d->(0=0->!a=e+d)";
         "(@e.!a=e+d->0=0->!a=e+d)->(@e.!a=e+d->(0=0->!a=e+d)->a=e+d->(0=0->!a=e+d))->(@e.!a=e+d->a=e+d->(0=0->!a=e+d))";
         "(@e.!a=e+d->(0=0->!a=e+d)->a=e+d->(0=0->!a=e+d))->(@e.!a=e+d->a=e+d->(0=0->!a=e+d))";
         "@e.!a=e+d->a=e+d->0=0->!a=e+d";
         "(a=e+d->0=0->!a=e+d)->(a=e+d->(0=0->!a=e+d)->!(0=0))->(a=e+d->!(0=0))";
         "((a=e+d->0=0->!a=e+d)->(a=e+d->(0=0->!a=e+d)->!(0=0))->(a=e+d->!(0=0)))->@e.!a=e+d->((a=e+d->0=0->!a=e+d)->(a=e+d->(0=0->!a=e+d)->!(0=0))->(a=e+d->!(0=0)))";
         "@e.!a=e+d->(a=e+d->0=0->!a=e+d)->(a=e+d->(0=0->!a=e+d)->!(0=0))->(a=e+d->!(0=0))";
         "(@e.!a=e+d->a=e+d->0=0->!a=e+d)->(@e.!a=e+d->(a=e+d->0=0->!a=e+d)->(a=e+d->(0=0->!a=e+d)->!(0=0))->(a=e+d->!(0=0)))->(@e.!a=e+d->(a=e+d->(0=0->!a=e+d)->!(0=0))->(a=e+d->!(0=0)))";
         "(@e.!a=e+d->(a=e+d->0=0->!a=e+d)->(a=e+d->(0=0->!a=e+d)->!(0=0))->(a=e+d->!(0=0)))->(@e.!a=e+d->(a=e+d->(0=0->!a=e+d)->!(0=0))->(a=e+d->!(0=0)))";
         "@e.!a=e+d->(a=e+d->(0=0->!a=e+d)->!(0=0))->(a=e+d->!(0=0))";
         "(@e.!a=e+d->a=e+d->(0=0->!a=e+d)->!(0=0))->(@e.!a=e+d->(a=e+d->(0=0->!a=e+d)->!(0=0))->(a=e+d->!(0=0)))->(@e.!a=e+d->(a=e+d->!(0=0)))";
         "(@e.!a=e+d->(a=e+d->(0=0->!a=e+d)->!(0=0))->(a=e+d->!(0=0)))->(@e.!a=e+d->(a=e+d->!(0=0)))";
         "@e.!a=e+d->a=e+d->!(0=0)";
         "(@e.!a=e+d->a=e+d->!(0=0))->a=e+d->(@e.!a=e+d->a=e+d->!(0=0))";
         "a=e+d->@e.!a=e+d->a=e+d->!(0=0)";
         "a=e+d->@e.!a=e+d->a=e+d";
         "(@e.!a=e+d->a=e+d)->(@e.!a=e+d->a=e+d->!(0=0))->(@e.!a=e+d->!(0=0))";
         "((@e.!a=e+d->a=e+d)->(@e.!a=e+d->a=e+d->!(0=0))->(@e.!a=e+d->!(0=0)))->a=e+d->((@e.!a=e+d->a=e+d)->(@e.!a=e+d->a=e+d->!(0=0))->(@e.!a=e+d->!(0=0)))";
         "a=e+d->(@e.!a=e+d->a=e+d)->(@e.!a=e+d->a=e+d->!(0=0))->(@e.!a=e+d->!(0=0))";
         "(a=e+d->@e.!a=e+d->a=e+d)->(a=e+d->(@e.!a=e+d->a=e+d)->(@e.!a=e+d->a=e+d->!(0=0))->(@e.!a=e+d->!(0=0)))->(a=e+d->(@e.!a=e+d->a=e+d->!(0=0))->(@e.!a=e+d->!(0=0)))";
         "(a=e+d->(@e.!a=e+d->a=e+d)->(@e.!a=e+d->a=e+d->!(0=0))->(@e.!a=e+d->!(0=0)))->(a=e+d->(@e.!a=e+d->a=e+d->!(0=0))->(@e.!a=e+d->!(0=0)))";
         "a=e+d->(@e.!a=e+d->a=e+d->!(0=0))->(@e.!a=e+d->!(0=0))";
         "(a=e+d->@e.!a=e+d->a=e+d->!(0=0))->(a=e+d->(@e.!a=e+d->a=e+d->!(0=0))->(@e.!a=e+d->!(0=0)))->(a=e+d->(@e.!a=e+d->!(0=0)))";
         "(a=e+d->(@e.!a=e+d->a=e+d->!(0=0))->(@e.!a=e+d->!(0=0)))->(a=e+d->(@e.!a=e+d->!(0=0)))";
         "a=e+d->@e.!a=e+d->!(0=0)";
         "?e.a=e+d->@e.!a=e+d->!(0=0)";
         "(?e.a=e+d->@e.!a=e+d->!(0=0))->@e.!a=e+d->(?e.a=e+d->@e.!a=e+d->!(0=0))";
         "@e.!a=e+d->?e.a=e+d->@e.!a=e+d->!(0=0)";
         "@e.!a=e+d->?e.a=e+d->@e.!a=e+d";
         "(?e.a=e+d->@e.!a=e+d)->(?e.a=e+d->@e.!a=e+d->!(0=0))->(?e.a=e+d->!(0=0))";
         "((?e.a=e+d->@e.!a=e+d)->(?e.a=e+d->@e.!a=e+d->!(0=0))->(?e.a=e+d->!(0=0)))->@e.!a=e+d->((?e.a=e+d->@e.!a=e+d)->(?e.a=e+d->@e.!a=e+d->!(0=0))->(?e.a=e+d->!(0=0)))";
         "@e.!a=e+d->(?e.a=e+d->@e.!a=e+d)->(?e.a=e+d->@e.!a=e+d->!(0=0))->(?e.a=e+d->!(0=0))";
         "(@e.!a=e+d->?e.a=e+d->@e.!a=e+d)->(@e.!a=e+d->(?e.a=e+d->@e.!a=e+d)->(?e.a=e+d->@e.!a=e+d->!(0=0))->(?e.a=e+d->!(0=0)))->(@e.!a=e+d->(?e.a=e+d->@e.!a=e+d->!(0=0))->(?e.a=e+d->!(0=0)))";
         "(@e.!a=e+d->(?e.a=e+d->@e.!a=e+d)->(?e.a=e+d->@e.!a=e+d->!(0=0))->(?e.a=e+d->!(0=0)))->(@e.!a=e+d->(?e.a=e+d->@e.!a=e+d->!(0=0))->(?e.a=e+d->!(0=0)))";
         "@e.!a=e+d->(?e.a=e+d->@e.!a=e+d->!(0=0))->(?e.a=e+d->!(0=0))";
         "(@e.!a=e+d->?e.a=e+d->@e.!a=e+d->!(0=0))->(@e.!a=e+d->(?e.a=e+d->@e.!a=e+d->!(0=0))->(?e.a=e+d->!(0=0)))->(@e.!a=e+d->(?e.a=e+d->!(0=0)))";
         "(@e.!a=e+d->(?e.a=e+d->@e.!a=e+d->!(0=0))->(?e.a=e+d->!(0=0)))->(@e.!a=e+d->(?e.a=e+d->!(0=0)))";
         "@e.!a=e+d->?e.a=e+d->!(0=0)";
         "0=0->?e.a=e+d->0=0";
         "?e.a=e+d->0=0";
         "(?e.a=e+d->0=0)->(?e.a=e+d->!(0=0))->!?e.a=e+d";
         "(?e.a=e+d->!(0=0))->!?e.a=e+d";
         "((?e.a=e+d->!(0=0))->!?e.a=e+d)->@e.!a=e+d->((?e.a=e+d->!(0=0))->!?e.a=e+d)";
         "@e.!a=e+d->(?e.a=e+d->!(0=0))->!?e.a=e+d";
         "(@e.!a=e+d->?e.a=e+d->!(0=0))->(@e.!a=e+d->(?e.a=e+d->!(0=0))->!?e.a=e+d)->(@e.!a=e+d->!?e.a=e+d)";
         "(@e.!a=e+d->(?e.a=e+d->!(0=0))->!?e.a=e+d)->(@e.!a=e+d->!?e.a=e+d)";
         "@e.!a=e+d->!?e.a=e+d";
         "@a.@b.(a'+b=(a+b)')->@b.(e'+b=(e+b)')";
         "@b.(e'+b=(e+b)')";
         "@b.(e'+b=(e+b)')->(e'+d=(e+d)')";
         "e'+d=(e+d)'";
         "@a.@b.(a+b'=(a+b)')->@b.(e+b'=(e+b)')";
         "@b.(e+b'=(e+b)')";
         "@b.(e+b'=(e+b)')->(e+d'=(e+d)')";
         "e+d'=(e+d)'";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=(e+d)'->c=(e+d)'->b=c)";
         "@b.@c.(b=(e+d)'->c=(e+d)'->b=c)";
         "@b.@c.(b=(e+d)'->c=(e+d)'->b=c)->@c.(e'+d=(e+d)'->c=(e+d)'->e'+d=c)";
         "@c.(e'+d=(e+d)'->c=(e+d)'->e'+d=c)";
         "@c.(e'+d=(e+d)'->c=(e+d)'->e'+d=c)->(e'+d=(e+d)'->e+d'=(e+d)'->e'+d=e+d')";
         "e'+d=(e+d)'->e+d'=(e+d)'->e'+d=e+d'";
         "e+d'=(e+d)'->e'+d=e+d'";
         "e'+d=e+d'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=e'+d->e'+d=c->b=c)";
         "@b.@c.(b=e'+d->e'+d=c->b=c)";
         "@b.@c.(b=e'+d->e'+d=c->b=c)->@c.(a=e'+d->e'+d=c->a=c)";
         "@c.(a=e'+d->e'+d=c->a=c)";
         "@c.(a=e'+d->e'+d=c->a=c)->(a=e'+d->e'+d=e+d'->a=e+d')";
         "a=e'+d->e'+d=e+d'->a=e+d'";
         "e'+d=e+d'->a=e'+d->e'+d=e+d'";
         "a=e'+d->e'+d=e+d'";
         "(a=e'+d->e'+d=e+d')->(a=e'+d->e'+d=e+d'->a=e+d')->(a=e'+d->a=e+d')";
         "(a=e'+d->e'+d=e+d'->a=e+d')->(a=e'+d->a=e+d')";
         "a=e'+d->a=e+d'";
         "a=e+d'->?e.(a=e+d')";
         "(a=e+d'->?e.(a=e+d'))->a=e'+d->(a=e+d'->?e.(a=e+d'))";
         "a=e'+d->a=e+d'->?e.(a=e+d')";
         "(a=e'+d->a=e+d')->(a=e'+d->a=e+d'->?e.(a=e+d'))->(a=e'+d->?e.(a=e+d'))";
         "(a=e'+d->a=e+d'->?e.(a=e+d'))->(a=e'+d->?e.(a=e+d'))";
         "a=e'+d->?e.(a=e+d')";
         "!?e.(a=e+d')->a=e'+d->!?e.(a=e+d')";
         "(a=e'+d->?e.(a=e+d'))->!?e.(a=e+d')->(a=e'+d->?e.(a=e+d'))";
         "!?e.(a=e+d')->a=e'+d->?e.(a=e+d')";
         "(a=e'+d->?e.(a=e+d'))->(a=e'+d->!?e.(a=e+d'))->!a=e'+d";
         "((a=e'+d->?e.(a=e+d'))->(a=e'+d->!?e.(a=e+d'))->!a=e'+d)->!?e.(a=e+d')->((a=e'+d->?e.(a=e+d'))->(a=e'+d->!?e.(a=e+d'))->!a=e'+d)";
         "!?e.(a=e+d')->(a=e'+d->?e.(a=e+d'))->(a=e'+d->!?e.(a=e+d'))->!a=e'+d";
         "(!?e.(a=e+d')->a=e'+d->?e.(a=e+d'))->(!?e.(a=e+d')->(a=e'+d->?e.(a=e+d'))->(a=e'+d->!?e.(a=e+d'))->!a=e'+d)->(!?e.(a=e+d')->(a=e'+d->!?e.(a=e+d'))->!a=e'+d)";
         "(!?e.(a=e+d')->(a=e'+d->?e.(a=e+d'))->(a=e'+d->!?e.(a=e+d'))->!a=e'+d)->(!?e.(a=e+d')->(a=e'+d->!?e.(a=e+d'))->!a=e'+d)";
         "!?e.(a=e+d')->(a=e'+d->!?e.(a=e+d'))->!a=e'+d";
         "(!?e.(a=e+d')->a=e'+d->!?e.(a=e+d'))->(!?e.(a=e+d')->(a=e'+d->!?e.(a=e+d'))->!a=e'+d)->(!?e.(a=e+d')->!a=e'+d)";
         "(!?e.(a=e+d')->(a=e'+d->!?e.(a=e+d'))->!a=e'+d)->(!?e.(a=e+d')->!a=e'+d)";
         "!?e.(a=e+d')->!a=e'+d";
         "(!a=e'+d->!a=e+d->!a=e'+d)->!?e.(a=e+d')->(!a=e'+d->!a=e+d->!a=e'+d)";
         "!a=e'+d->!a=e+d->!a=e'+d";
         "!?e.(a=e+d')->!a=e'+d->!a=e+d->!a=e'+d";
         "(!?e.(a=e+d')->!a=e'+d)->(!?e.(a=e+d')->!a=e'+d->!a=e+d->!a=e'+d)->(!?e.(a=e+d')->!a=e+d->!a=e'+d)";
         "(!?e.(a=e+d')->!a=e'+d->!a=e+d->!a=e'+d)->(!?e.(a=e+d')->!a=e+d->!a=e'+d)";
         "!?e.(a=e+d')->!a=e+d->!a=e'+d";
         "!?e.(a=e+d')->@e.(!a=e+d->!a=e'+d)";
         "!a=0+d->@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)";
         "!a=0+d&@e.(!a=e+d->!a=e'+d)->!a=e+d";
         "!a=0+d&@e.(!a=e+d->!a=e'+d)->@e.!a=e+d";
         "(@e.!a=e+d->!?e.a=e+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->(@e.!a=e+d->!?e.a=e+d)";
         "!a=0+d&@e.(!a=e+d->!a=e'+d)->@e.!a=e+d->!?e.a=e+d";
         "(!a=0+d&@e.(!a=e+d->!a=e'+d)->@e.!a=e+d)->(!a=0+d&@e.(!a=e+d->!a=e'+d)->@e.!a=e+d->!?e.a=e+d)->(!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)";
         "(!a=0+d&@e.(!a=e+d->!a=e'+d)->@e.!a=e+d->!?e.a=e+d)->(!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)";
         "!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d";
         "(!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->@e.(!a=e+d->!a=e'+d)->(!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)";
         "@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d";
         "(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->!a=0+d->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)";
         "!a=0+d->@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d";
         "(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d))->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)";
         "((@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d))->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d))->!a=0+d->((@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d))->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d))";
         "!a=0+d->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d))->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)";
         "(!a=0+d->@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d))->(!a=0+d->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d))->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d))->(!a=0+d->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d))";
         "(!a=0+d->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d))->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d))->(!a=0+d->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d))";
         "!a=0+d->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)";
         "(!a=0+d->@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d))->(!a=0+d->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d))";
         "(!a=0+d->(@e.(!a=e+d->!a=e'+d)->!a=0+d&@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d))->(!a=0+d->(@e.(!a=e+d->!a=e'+d)->!?e.a=e+d))";
         "!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d";
         "(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->@e.(!a=e+d->!a=e'+d)->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)";
         "@e.(!a=e+d->!a=e'+d)->!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d";
         "@e.(!a=e+d->!a=e'+d)->!a=0+d->@e.(!a=e+d->!a=e'+d)";
         "(!a=0+d->@e.(!a=e+d->!a=e'+d))->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->!?e.a=e+d)";
         "((!a=0+d->@e.(!a=e+d->!a=e'+d))->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->!?e.a=e+d))->@e.(!a=e+d->!a=e'+d)->((!a=0+d->@e.(!a=e+d->!a=e'+d))->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->!?e.a=e+d))";
         "@e.(!a=e+d->!a=e'+d)->(!a=0+d->@e.(!a=e+d->!a=e'+d))->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->!?e.a=e+d)";
         "(@e.(!a=e+d->!a=e'+d)->!a=0+d->@e.(!a=e+d->!a=e'+d))->(@e.(!a=e+d->!a=e'+d)->(!a=0+d->@e.(!a=e+d->!a=e'+d))->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->!?e.a=e+d))->(@e.(!a=e+d->!a=e'+d)->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->!?e.a=e+d))";
         "(@e.(!a=e+d->!a=e'+d)->(!a=0+d->@e.(!a=e+d->!a=e'+d))->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->!?e.a=e+d))->(@e.(!a=e+d->!a=e'+d)->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->!?e.a=e+d))";
         "@e.(!a=e+d->!a=e'+d)->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->!?e.a=e+d)";
         "(@e.(!a=e+d->!a=e'+d)->!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(@e.(!a=e+d->!a=e'+d)->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->!?e.a=e+d))->(@e.(!a=e+d->!a=e'+d)->(!a=0+d->!?e.a=e+d))";
         "(@e.(!a=e+d->!a=e'+d)->(!a=0+d->@e.(!a=e+d->!a=e'+d)->!?e.a=e+d)->(!a=0+d->!?e.a=e+d))->(@e.(!a=e+d->!a=e'+d)->(!a=0+d->!?e.a=e+d))";
         "@e.(!a=e+d->!a=e'+d)->!a=0+d->!?e.a=e+d";
         "(@e.(!a=e+d->!a=e'+d)->!a=0+d->!?e.a=e+d)->!?e.(a=e+d')->(@e.(!a=e+d->!a=e'+d)->!a=0+d->!?e.a=e+d)";
         "!?e.(a=e+d')->@e.(!a=e+d->!a=e'+d)->!a=0+d->!?e.a=e+d";
         "(!?e.(a=e+d')->@e.(!a=e+d->!a=e'+d))->(!?e.(a=e+d')->@e.(!a=e+d->!a=e'+d)->!a=0+d->!?e.a=e+d)->(!?e.(a=e+d')->!a=0+d->!?e.a=e+d)";
         "(!?e.(a=e+d')->@e.(!a=e+d->!a=e'+d)->!a=0+d->!?e.a=e+d)->(!?e.(a=e+d')->!a=0+d->!?e.a=e+d)";
         "!?e.(a=e+d')->!a=0+d->!?e.a=e+d";
         "(!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d";
         "((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->(!a=0+d->!?e.a=e+d)->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)";
         "(!a=0+d->!?e.a=e+d)->(!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d";
         "(!a=0+d->!?e.a=e+d)->(!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)";
         "((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d))->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->!!a=0+d)";
         "(((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d))->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->!!a=0+d))->(!a=0+d->!?e.a=e+d)->(((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d))->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->!!a=0+d))";
         "(!a=0+d->!?e.a=e+d)->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d))->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->!!a=0+d)";
         "((!a=0+d->!?e.a=e+d)->(!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d))->((!a=0+d->!?e.a=e+d)->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d))->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->!!a=0+d))->((!a=0+d->!?e.a=e+d)->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->!!a=0+d))";
         "((!a=0+d->!?e.a=e+d)->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d))->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->!!a=0+d))->((!a=0+d->!?e.a=e+d)->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->!!a=0+d))";
         "(!a=0+d->!?e.a=e+d)->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->!!a=0+d)";
         "((!a=0+d->!?e.a=e+d)->(!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->!?e.a=e+d)->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->!!a=0+d))->((!a=0+d->!?e.a=e+d)->((!a=0+d->?e.a=e+d)->!!a=0+d))";
         "((!a=0+d->!?e.a=e+d)->((!a=0+d->?e.a=e+d)->(!a=0+d->!?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->!!a=0+d))->((!a=0+d->!?e.a=e+d)->((!a=0+d->?e.a=e+d)->!!a=0+d))";
         "(!a=0+d->!?e.a=e+d)->(!a=0+d->?e.a=e+d)->!!a=0+d";
         "((!a=0+d->!?e.a=e+d)->(!a=0+d->?e.a=e+d)->!!a=0+d)->!?e.(a=e+d')->((!a=0+d->!?e.a=e+d)->(!a=0+d->?e.a=e+d)->!!a=0+d)";
         "!?e.(a=e+d')->(!a=0+d->!?e.a=e+d)->(!a=0+d->?e.a=e+d)->!!a=0+d";
         "(!?e.(a=e+d')->!a=0+d->!?e.a=e+d)->(!?e.(a=e+d')->(!a=0+d->!?e.a=e+d)->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)";
         "(!?e.(a=e+d')->(!a=0+d->!?e.a=e+d)->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)";
         "!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d";
         "(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)";
         "(!a=0+d->?e.a=e+d)->!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d";
         "(!a=0+d->?e.a=e+d)->!?e.(a=e+d')->(!a=0+d->?e.a=e+d)";
         "(!?e.(a=e+d')->(!a=0+d->?e.a=e+d))->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d)";
         "((!?e.(a=e+d')->(!a=0+d->?e.a=e+d))->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d))->(!a=0+d->?e.a=e+d)->((!?e.(a=e+d')->(!a=0+d->?e.a=e+d))->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d))";
         "(!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d))->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d)";
         "((!a=0+d->?e.a=e+d)->!?e.(a=e+d')->(!a=0+d->?e.a=e+d))->((!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d))->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d))->((!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d))";
         "((!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d))->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d))->((!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d))";
         "(!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d)";
         "((!a=0+d->?e.a=e+d)->!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->((!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d))->((!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->!!a=0+d))";
         "((!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->(!a=0+d->?e.a=e+d)->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d))->((!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->!!a=0+d))";
         "(!a=0+d->?e.a=e+d)->!?e.(a=e+d')->!!a=0+d";
         "((!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->!!a=0+d))->?e.a=e+d->((!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->!!a=0+d))";
         "?e.a=e+d->(!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->!!a=0+d)";
         "?e.a=e+d->!a=0+d->?e.a=e+d";
         "(?e.a=e+d->!a=0+d->?e.a=e+d)->(?e.a=e+d->(!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->!!a=0+d))->(?e.a=e+d->(!?e.(a=e+d')->!!a=0+d))";
         "(?e.a=e+d->(!a=0+d->?e.a=e+d)->(!?e.(a=e+d')->!!a=0+d))->(?e.a=e+d->(!?e.(a=e+d')->!!a=0+d))";
         "?e.a=e+d->!?e.(a=e+d')->!!a=0+d";
         "!!a=0+d->a=0+d";
         "@a.(0+a=a)->0+d=d";
         "0+d=d";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=0+d->0+d=c->b=c)";
         "@b.@c.(b=0+d->0+d=c->b=c)";
         "@b.@c.(b=0+d->0+d=c->b=c)->@c.(a=0+d->0+d=c->a=c)";
         "@c.(a=0+d->0+d=c->a=c)";
         "@c.(a=0+d->0+d=c->a=c)->(a=0+d->0+d=d->a=d)";
         "a=0+d->0+d=d->a=d";
         "0+d=d->a=0+d->0+d=d";
         "a=0+d->0+d=d";
         "(a=0+d->0+d=d)->(a=0+d->0+d=d->a=d)->(a=0+d->a=d)";
         "(a=0+d->0+d=d->a=d)->(a=0+d->a=d)";
         "a=0+d->a=d";
         "(a=0+d->a=d)->!!a=0+d->(a=0+d->a=d)";
         "!!a=0+d->a=0+d->a=d";
         "(!!a=0+d->a=0+d)->(!!a=0+d->a=0+d->a=d)->(!!a=0+d->a=d)";
         "(!!a=0+d->a=0+d->a=d)->(!!a=0+d->a=d)";
         "!!a=0+d->a=d";
         "@a.@b.(a=b->a'=b')->@b.(a=b->a'=b')";
         "@b.(a=b->a'=b')";
         "@b.(a=b->a'=b')->(a=d->a'=d')";
         "a=d->a'=d'";
         "(a=d->a'=d')->!!a=0+d->(a=d->a'=d')";
         "!!a=0+d->a=d->a'=d'";
         "(!!a=0+d->a=d)->(!!a=0+d->a=d->a'=d')->(!!a=0+d->a'=d')";
         "(!!a=0+d->a=d->a'=d')->(!!a=0+d->a'=d')";
         "!!a=0+d->a'=d'";
         "a+0=a";
         "@a.@b.(a=b->a'=b')->@b.(a+0=b->(a+0)'=b')";
         "@b.(a+0=b->(a+0)'=b')";
         "@b.(a+0=b->(a+0)'=b')->(a+0=a->(a+0)'=a')";
         "a+0=a->(a+0)'=a'";
         "(a+0)'=a'";
         "@a.@b.(a+b'=(a+b)')->@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')->(a+0'=(a+0)')";
         "a+0'=(a+0)'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(a+0)'->(a+0)'=c->b=c)";
         "@b.@c.(b=(a+0)'->(a+0)'=c->b=c)";
         "@b.@c.(b=(a+0)'->(a+0)'=c->b=c)->@c.(a+0'=(a+0)'->(a+0)'=c->a+0'=c)";
         "@c.(a+0'=(a+0)'->(a+0)'=c->a+0'=c)";
         "@c.(a+0'=(a+0)'->(a+0)'=c->a+0'=c)->(a+0'=(a+0)'->(a+0)'=a'->a+0'=a')";
         "a+0'=(a+0)'->(a+0)'=a'->a+0'=a'";
         "(a+0)'=a'->a+0'=a'";
         "a+0'=a'";
         "a+0'=a'->0=0->a+0'=a'";
         "0=0->(a+0'=a')";
         "0=0->@a.(a+0'=a')";
         "@a.(a+0'=a')";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=a'->a'=c->b=c)";
         "@b.@c.(b=a'->a'=c->b=c)";
         "@b.@c.(b=a'->a'=c->b=c)->@c.(a+0'=a'->a'=c->a+0'=c)";
         "@c.(a+0'=a'->a'=c->a+0'=c)";
         "@c.(a+0'=a'->a'=c->a+0'=c)->(a+0'=a'->a'=d'->a+0'=d')";
         "a+0'=a'->a'=d'->a+0'=d'";
         "a'=d'->a+0'=d'";
         "(a'=d'->a+0'=d')->!!a=0+d->(a'=d'->a+0'=d')";
         "!!a=0+d->a'=d'->a+0'=d'";
         "(!!a=0+d->a'=d')->(!!a=0+d->a'=d'->a+0'=d')->(!!a=0+d->a+0'=d')";
         "(!!a=0+d->a'=d'->a+0'=d')->(!!a=0+d->a+0'=d')";
         "!!a=0+d->a+0'=d'";
         "a+0'=d'->?e.a+e=d'";
         "(a+0'=d'->?e.a+e=d')->!!a=0+d->(a+0'=d'->?e.a+e=d')";
         "!!a=0+d->a+0'=d'->?e.a+e=d'";
         "(!!a=0+d->a+0'=d')->(!!a=0+d->a+0'=d'->?e.a+e=d')->(!!a=0+d->?e.a+e=d')";
         "(!!a=0+d->a+0'=d'->?e.a+e=d')->(!!a=0+d->?e.a+e=d')";
         "!!a=0+d->?e.a+e=d'";
         "?e.a+e=d'->?e.a=e+d'|?e.a+e=d'";
         "(?e.a+e=d'->?e.a=e+d'|?e.a+e=d')->!!a=0+d->(?e.a+e=d'->?e.a=e+d'|?e.a+e=d')";
         "!!a=0+d->?e.a+e=d'->?e.a=e+d'|?e.a+e=d'";
         "(!!a=0+d->?e.a+e=d')->(!!a=0+d->?e.a+e=d'->?e.a=e+d'|?e.a+e=d')->(!!a=0+d->?e.a=e+d'|?e.a+e=d')";
         "(!!a=0+d->?e.a+e=d'->?e.a=e+d'|?e.a+e=d')->(!!a=0+d->?e.a=e+d'|?e.a+e=d')";
         "!!a=0+d->?e.a=e+d'|?e.a+e=d'";
         "(!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->!?e.(a=e+d')->(!!a=0+d->(?e.a=e+d'|?e.a+e=d'))";
         "!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d')";
         "(!?e.(a=e+d')->(!!a=0+d->(?e.a=e+d'|?e.a+e=d')))->?e.a=e+d->(!?e.(a=e+d')->(!!a=0+d->(?e.a=e+d'|?e.a+e=d')))";
         "?e.a=e+d->!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d')";
         "(!?e.(a=e+d')->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d'))";
         "((!?e.(a=e+d')->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d')))->?e.a=e+d->((!?e.(a=e+d')->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d')))";
         "?e.a=e+d->(!?e.(a=e+d')->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d'))";
         "(?e.a=e+d->!?e.(a=e+d')->!!a=0+d)->(?e.a=e+d->(!?e.(a=e+d')->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d')))->(?e.a=e+d->(!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d')))";
         "(?e.a=e+d->(!?e.(a=e+d')->!!a=0+d)->(!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d')))->(?e.a=e+d->(!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d')))";
         "?e.a=e+d->(!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d'))";
         "(?e.a=e+d->!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(?e.a=e+d->(!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d')))->(?e.a=e+d->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d')))";
         "(?e.a=e+d->(!?e.(a=e+d')->!!a=0+d->(?e.a=e+d'|?e.a+e=d'))->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d')))->(?e.a=e+d->(!?e.(a=e+d')->(?e.a=e+d'|?e.a+e=d')))";
         "?e.a=e+d->!?e.a=e+d'->?e.a=e+d'|?e.a+e=d'";
         "@a.@b.(a=b->a'=b')->@b.(a+e=b->(a+e)'=b')";
         "@b.(a+e=b->(a+e)'=b')";
         "@b.(a+e=b->(a+e)'=b')->(a+e=d->(a+e)'=d')";
         "a+e=d->(a+e)'=d'";
         "@a.@b.(a+b'=(a+b)')->@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')";
         "@b.(a+b'=(a+b)')->(a+e'=(a+e)')";
         "a+e'=(a+e)'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(a+e)'->(a+e)'=c->b=c)";
         "@b.@c.(b=(a+e)'->(a+e)'=c->b=c)";
         "@b.@c.(b=(a+e)'->(a+e)'=c->b=c)->@c.(a+e'=(a+e)'->(a+e)'=c->a+e'=c)";
         "@c.(a+e'=(a+e)'->(a+e)'=c->a+e'=c)";
         "@c.(a+e'=(a+e)'->(a+e)'=c->a+e'=c)->(a+e'=(a+e)'->(a+e)'=d'->a+e'=d')";
         "a+e'=(a+e)'->(a+e)'=d'->a+e'=d'";
         "(a+e)'=d'->a+e'=d'";
         "((a+e)'=d'->a+e'=d')->a+e=d->((a+e)'=d'->a+e'=d')";
         "a+e=d->(a+e)'=d'->a+e'=d'";
         "(a+e=d->(a+e)'=d')->(a+e=d->(a+e)'=d'->a+e'=d')->(a+e=d->a+e'=d')";
         "(a+e=d->(a+e)'=d'->a+e'=d')->(a+e=d->a+e'=d')";
         "a+e=d->a+e'=d'";
         "a+e'=d'->?e.(a+e=d')";
         "(a+e'=d'->?e.(a+e=d'))->a+e=d->(a+e'=d'->?e.(a+e=d'))";
         "a+e=d->a+e'=d'->?e.(a+e=d')";
         "(a+e=d->a+e'=d')->(a+e=d->a+e'=d'->?e.(a+e=d'))->(a+e=d->?e.(a+e=d'))";
         "(a+e=d->a+e'=d'->?e.(a+e=d'))->(a+e=d->?e.(a+e=d'))";
         "a+e=d->?e.(a+e=d')";
         "?e.a+e=d->?e.a+e=d'";
         "?e.a=e+d'->?e.a=e+d'|?e.a+e=d'";
         "?e.a=e+d'->?e.a=e+d'|!?e.a=e+d'";
         "(?e.a=e+d'->?e.a=e+d'|!?e.a=e+d')->(?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!?e.a=e+d'";
         "(?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!?e.a=e+d'";
         "((?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!?e.a=e+d')->!(?e.a=e+d'|!?e.a=e+d')->((?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!?e.a=e+d')";
         "!(?e.a=e+d'|!?e.a=e+d')->(?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!?e.a=e+d'";
         "!(?e.a=e+d'|!?e.a=e+d')->?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d')";
         "(!(?e.a=e+d'|!?e.a=e+d')->?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->(!(?e.a=e+d'|!?e.a=e+d')->(?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!?e.a=e+d')->(!(?e.a=e+d'|!?e.a=e+d')->!?e.a=e+d')";
         "(!(?e.a=e+d'|!?e.a=e+d')->(?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!?e.a=e+d')->(!(?e.a=e+d'|!?e.a=e+d')->!?e.a=e+d')";
         "!(?e.a=e+d'|!?e.a=e+d')->!?e.a=e+d'";
         "!?e.a=e+d'->?e.a=e+d'|!?e.a=e+d'";
         "(!?e.a=e+d'->?e.a=e+d'|!?e.a=e+d')->(!?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!!?e.a=e+d'";
         "(!?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!!?e.a=e+d'";
         "((!?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!!?e.a=e+d')->!(?e.a=e+d'|!?e.a=e+d')->((!?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!!?e.a=e+d')";
         "!(?e.a=e+d'|!?e.a=e+d')->(!?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!!?e.a=e+d'";
         "!(?e.a=e+d'|!?e.a=e+d')->!?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d')";
         "(!(?e.a=e+d'|!?e.a=e+d')->!?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->(!(?e.a=e+d'|!?e.a=e+d')->(!?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!!?e.a=e+d')->(!(?e.a=e+d'|!?e.a=e+d')->!!?e.a=e+d')";
         "(!(?e.a=e+d'|!?e.a=e+d')->(!?e.a=e+d'->!(?e.a=e+d'|!?e.a=e+d'))->!!?e.a=e+d')->(!(?e.a=e+d'|!?e.a=e+d')->!!?e.a=e+d')";
         "!(?e.a=e+d'|!?e.a=e+d')->!!?e.a=e+d'";
         "(!(?e.a=e+d'|!?e.a=e+d')->!?e.a=e+d')->(!(?e.a=e+d'|!?e.a=e+d')->!!?e.a=e+d')->!!(?e.a=e+d'|!?e.a=e+d')";
         "(!(?e.a=e+d'|!?e.a=e+d')->!!?e.a=e+d')->!!(?e.a=e+d'|!?e.a=e+d')";
         "!!(?e.a=e+d'|!?e.a=e+d')";
         "!!(?e.a=e+d'|!?e.a=e+d')->?e.a=e+d'|!?e.a=e+d'";
         "?e.a=e+d'|!?e.a=e+d'";
         "(?e.a=e+d'->?e.a=e+d'|?e.a+e=d')->(!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')";
         "(!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')";
         "((!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d'))->?e.a=e+d->((!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d'))";
         "?e.a=e+d->(!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')";
         "(?e.a=e+d->!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d->(!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d'))->(?e.a=e+d->(?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d'))";
         "(?e.a=e+d->(!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d'))->(?e.a=e+d->(?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d'))";
         "?e.a=e+d->?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d'";
         "?e.a=e+d'|!?e.a=e+d'->?e.a=e+d->?e.a=e+d'|!?e.a=e+d'";
         "?e.a=e+d->?e.a=e+d'|!?e.a=e+d'";
         "(?e.a=e+d->?e.a=e+d'|!?e.a=e+d')->(?e.a=e+d->?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d->?e.a=e+d'|?e.a+e=d')";
         "(?e.a=e+d->?e.a=e+d'|!?e.a=e+d'->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d->?e.a=e+d'|?e.a+e=d')";
         "?e.a=e+d->?e.a=e+d'|?e.a+e=d'";
         "?e.a+e=d'->?e.a=e+d'|?e.a+e=d'";
         "(?e.a+e=d'->?e.a=e+d'|?e.a+e=d')->?e.a+e=d->(?e.a+e=d'->?e.a=e+d'|?e.a+e=d')";
         "?e.a+e=d->?e.a+e=d'->?e.a=e+d'|?e.a+e=d'";
         "(?e.a+e=d->?e.a+e=d')->(?e.a+e=d->?e.a+e=d'->?e.a=e+d'|?e.a+e=d')->(?e.a+e=d->?e.a=e+d'|?e.a+e=d')";
         "(?e.a+e=d->?e.a+e=d'->?e.a=e+d'|?e.a+e=d')->(?e.a+e=d->?e.a=e+d'|?e.a+e=d')";
         "?e.a+e=d->?e.a=e+d'|?e.a+e=d'";
         "(?e.a=e+d->?e.a=e+d'|?e.a+e=d')->(?e.a+e=d->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')";
         "(?e.a+e=d->?e.a=e+d'|?e.a+e=d')->(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')";
         "?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d'";
         "(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')->0=0->(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')";
         "0=0->(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')";
         "0=0->@d.(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')";
         "@d.(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')";
         "@a.@b.(a=b->b=a)->@b.(a+0=b->b=a+0)";
         "@b.(a+0=b->b=a+0)";
         "@b.(a+0=b->b=a+0)->(a+0=a->a=a+0)";
         "a+0=a->a=a+0";
         "a=a+0";
         "a=a+0->?e.a=e+0";
         "?e.a=e+0";
         "?e.a=e+0->?e.a=e+0|?e.a+e=0";
         "?e.a=e+0|?e.a+e=0";
         "?e.a=e+0|?e.a+e=0->@d.(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')->(?e.a=e+0|?e.a+e=0)&@d.(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')";
         "@d.(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')->(?e.a=e+0|?e.a+e=0)&@d.(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')";
         "(?e.a=e+0|?e.a+e=0)&@d.(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')";
         "(?e.a=e+0|?e.a+e=0)&@d.(?e.a=e+d|?e.a+e=d->?e.a=e+d'|?e.a+e=d')->?e.a=e+d|?e.a+e=d";
         "?e.a=e+d|?e.a+e=d";
         "(?e.a=e+d|?e.a+e=d)->0=0->(?e.a=e+d|?e.a+e=d)";
         "0=0->(?e.a=e+d|?e.a+e=d)";
         "0=0->@d.(?e.a=e+d|?e.a+e=d)";
         "@d.(?e.a=e+d|?e.a+e=d)";
         "@d.(?e.a=e+d|?e.a+e=d)->(?e.a=e+b|?e.a+e=b)";
         "?e.a=e+b|?e.a+e=b";
         "(?e.a=e+b|?e.a+e=b)->0=0->(?e.a=e+b|?e.a+e=b)";
         "0=0->(?e.a=e+b|?e.a+e=b)";
         "0=0->@b.(?e.a=e+b|?e.a+e=b)";
         "0=0->@a.@b.(?e.a=e+b|?e.a+e=b)";
         "@a.@b.(?e.a=e+b|?e.a+e=b)"];;
let twoMulANeqOne = biggerFirstOrSecond @
        ["@a.@b.(a*b'=a*b+a)->@b.(0''*b'=0''*b+0'')";
         "@b.(0''*b'=0''*b+0'')";
         "@b.(0''*b'=0''*b+0'')->(0''*a'=0''*a+0'')";
         "0''*a'=0''*a+0''";
         "@a.@b.(a+b'=(a+b)')->@b.(0''*a+b'=(0''*a+b)')";
         "@b.(0''*a+b'=(0''*a+b)')";
         "@b.(0''*a+b'=(0''*a+b)')->(0''*a+0''=(0''*a+0')')";
         "0''*a+0''=(0''*a+0')'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=0''*a+0''->0''*a+0''=c->b=c)";
         "@b.@c.(b=0''*a+0''->0''*a+0''=c->b=c)";
         "@b.@c.(b=0''*a+0''->0''*a+0''=c->b=c)->@c.(0''*a'=0''*a+0''->0''*a+0''=c->0''*a'=c)";
         "@c.(0''*a'=0''*a+0''->0''*a+0''=c->0''*a'=c)";
         "@c.(0''*a'=0''*a+0''->0''*a+0''=c->0''*a'=c)->(0''*a'=0''*a+0''->0''*a+0''=(0''*a+0')'->0''*a'=(0''*a+0')')";
         "0''*a'=0''*a+0''->0''*a+0''=(0''*a+0')'->0''*a'=(0''*a+0')'";
         "0''*a+0''=(0''*a+0')'->0''*a'=(0''*a+0')'";
         "0''*a'=(0''*a+0')'";
         "@a.@b.(a+b'=(a+b)')->@b.(0''*a+b'=(0''*a+b)')";
         "@b.(0''*a+b'=(0''*a+b)')";
         "@b.(0''*a+b'=(0''*a+b)')->(0''*a+0'=(0''*a+0)')";
         "0''*a+0'=(0''*a+0)'";
         "@a.@b.(a=b->a'=b')->@b.(0''*a+0'=b->(0''*a+0')'=b')";
         "@b.(0''*a+0'=b->(0''*a+0')'=b')";
         "@b.(0''*a+0'=b->(0''*a+0')'=b')->(0''*a+0'=(0''*a+0)'->(0''*a+0')'=(0''*a+0)'')";
         "0''*a+0'=(0''*a+0)'->(0''*a+0')'=(0''*a+0)''";
         "(0''*a+0')'=(0''*a+0)''";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(0''*a+0')'->(0''*a+0')'=c->b=c)";
         "@b.@c.(b=(0''*a+0')'->(0''*a+0')'=c->b=c)";
         "@b.@c.(b=(0''*a+0')'->(0''*a+0')'=c->b=c)->@c.(0''*a'=(0''*a+0')'->(0''*a+0')'=c->0''*a'=c)";
         "@c.(0''*a'=(0''*a+0')'->(0''*a+0')'=c->0''*a'=c)";
         "@c.(0''*a'=(0''*a+0')'->(0''*a+0')'=c->0''*a'=c)->(0''*a'=(0''*a+0')'->(0''*a+0')'=(0''*a+0)''->0''*a'=(0''*a+0)'')";
         "0''*a'=(0''*a+0')'->(0''*a+0')'=(0''*a+0)''->0''*a'=(0''*a+0)''";
         "(0''*a+0')'=(0''*a+0)''->0''*a'=(0''*a+0)''";
         "0''*a'=(0''*a+0)''";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(0''*a'=b->0''*a'=c->b=c)";
         "@b.@c.(0''*a'=b->0''*a'=c->b=c)";
         "@b.@c.(0''*a'=b->0''*a'=c->b=c)->@c.(0''*a'=(0''*a+0)''->0''*a'=c->(0''*a+0)''=c)";
         "@c.(0''*a'=(0''*a+0)''->0''*a'=c->(0''*a+0)''=c)";
         "@c.(0''*a'=(0''*a+0)''->0''*a'=c->(0''*a+0)''=c)->(0''*a'=(0''*a+0)''->0''*a'=0'->(0''*a+0)''=0')";
         "0''*a'=(0''*a+0)''->0''*a'=0'->(0''*a+0)''=0'";
         "0''*a'=0'->(0''*a+0)''=0'";
         "@a.@b.(a'=b'->a=b)->@b.((0''*a+0)''=b'->(0''*a+0)'=b)";
         "@b.((0''*a+0)''=b'->(0''*a+0)'=b)";
         "@b.((0''*a+0)''=b'->(0''*a+0)'=b)->((0''*a+0)''=0'->(0''*a+0)'=0)";
         "(0''*a+0)''=0'->(0''*a+0)'=0";
         "((0''*a+0)''=0'->(0''*a+0)'=0)->0''*a'=0'->((0''*a+0)''=0'->(0''*a+0)'=0)";
         "0''*a'=0'->(0''*a+0)''=0'->(0''*a+0)'=0";
         "(0''*a'=0'->(0''*a+0)''=0')->(0''*a'=0'->(0''*a+0)''=0'->(0''*a+0)'=0)->(0''*a'=0'->(0''*a+0)'=0)";
         "(0''*a'=0'->(0''*a+0)''=0'->(0''*a+0)'=0)->(0''*a'=0'->(0''*a+0)'=0)";
         "0''*a'=0'->(0''*a+0)'=0";
         "!(a'=0)";
         "!(a'=0)->0=0->!(a'=0)";
         "0=0->!(a'=0)";
         "0=0->@a.!(a'=0)";
         "@a.!(a'=0)";
         "@a.!(a'=0)->!((0''*a+0)'=0)";
         "!((0''*a+0)'=0)";
         "!((0''*a+0)'=0)->0''*a'=0'->!((0''*a+0)'=0)";
         "0''*a'=0'->!((0''*a+0)'=0)";
         "(0''*a'=0'->(0''*a+0)'=0)->(0''*a'=0'->!(0''*a+0)'=0)->!0''*a'=0'";
         "(0''*a'=0'->!(0''*a+0)'=0)->!0''*a'=0'";
         "!0''*a'=0'";
         "!0''*a'=0'->!0''*a=0'->!0''*a'=0'";
         "!0''*a=0'->!0''*a'=0'";
         "(!0''*a=0'->!0''*a'=0')->0=0->(!0''*a=0'->!0''*a'=0')";
         "0=0->(!0''*a=0'->!0''*a'=0')";
         "0=0->@a.(!0''*a=0'->!0''*a'=0')";
         "@a.(!0''*a=0'->!0''*a'=0')";
         "@a.(a*0=0)->0''*0=0";
         "0''*0=0";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(0''*0=b->0''*0=c->b=c)";
         "@b.@c.(0''*0=b->0''*0=c->b=c)";
         "@b.@c.(0''*0=b->0''*0=c->b=c)->@c.(0''*0=0'->0''*0=c->0'=c)";
         "@c.(0''*0=0'->0''*0=c->0'=c)";
         "@c.(0''*0=0'->0''*0=c->0'=c)->(0''*0=0'->0''*0=0->0'=0)";
         "0''*0=0'->0''*0=0->0'=0";
         "0''*0=0->0''*0=0'->0''*0=0";
         "0''*0=0'->0''*0=0";
         "(0''*0=0'->0''*0=0)->(0''*0=0'->0''*0=0->0'=0)->(0''*0=0'->0'=0)";
         "(0''*0=0'->0''*0=0->0'=0)->(0''*0=0'->0'=0)";
         "0''*0=0'->0'=0";
         "@a.!a'=0->!0'=0";
         "!0'=0";
         "!0'=0->0''*0=0'->!0'=0";
         "0''*0=0'->!0'=0";
         "(0''*0=0'->0'=0)->(0''*0=0'->!0'=0)->!0''*0=0'";
         "(0''*0=0'->!0'=0)->!0''*0=0'";
         "!0''*0=0'";
         "!0''*0=0'->@a.(!0''*a=0'->!0''*a'=0')->!0''*0=0'&@a.(!0''*a=0'->!0''*a'=0')";
         "@a.(!0''*a=0'->!0''*a'=0')->!0''*0=0'&@a.(!0''*a=0'->!0''*a'=0')";
         "!0''*0=0'&@a.(!0''*a=0'->!0''*a'=0')";
         "!0''*0=0'&@a.(!0''*a=0'->!0''*a'=0')->!0''*a=0'";
         "!0''*a=0'";
         "!0''*a=0'->0=0->!0''*a=0'";
         "0=0->!0''*a=0'";
         "0=0->@a.!0''*a=0'";
         "@a.!0''*a=0'"];;
let evenNeqOdd = twoMulANeqOne @
        ["@a.@b.@c.(a=b->c*a=c*b)->@b.@c.(a=b->c*a=c*b)";
         "@b.@c.(a=b->c*a=c*b)";
         "@b.@c.(a=b->c*a=c*b)->@c.(a=e+d->c*a=c*(e+d))";
         "@c.(a=e+d->c*a=c*(e+d))";
         "@c.(a=e+d->c*a=c*(e+d))->(a=e+d->0''*a=0''*(e+d))";
         "a=e+d->0''*a=0''*(e+d)";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(0''*a=b->0''*a=c->b=c)";
         "@b.@c.(0''*a=b->0''*a=c->b=c)";
         "@b.@c.(0''*a=b->0''*a=c->b=c)->@c.(0''*a=0''*(e+d)->0''*a=c->0''*(e+d)=c)";
         "@c.(0''*a=0''*(e+d)->0''*a=c->0''*(e+d)=c)";
         "@c.(0''*a=0''*(e+d)->0''*a=c->0''*(e+d)=c)->(0''*a=0''*(e+d)->0''*a=(0''*d)'->0''*(e+d)=(0''*d)')";
         "0''*a=0''*(e+d)->0''*a=(0''*d)'->0''*(e+d)=(0''*d)'";
         "(0''*a=0''*(e+d)->0''*a=(0''*d)'->0''*(e+d)=(0''*d)')->a=e+d->(0''*a=0''*(e+d)->0''*a=(0''*d)'->0''*(e+d)=(0''*d)')";
         "a=e+d->0''*a=0''*(e+d)->0''*a=(0''*d)'->0''*(e+d)=(0''*d)'";
         "(a=e+d->0''*a=0''*(e+d))->(a=e+d->0''*a=0''*(e+d)->0''*a=(0''*d)'->0''*(e+d)=(0''*d)')->(a=e+d->0''*a=(0''*d)'->0''*(e+d)=(0''*d)')";
         "(a=e+d->0''*a=0''*(e+d)->0''*a=(0''*d)'->0''*(e+d)=(0''*d)')->(a=e+d->0''*a=(0''*d)'->0''*(e+d)=(0''*d)')";
         "a=e+d->0''*a=(0''*d)'->0''*(e+d)=(0''*d)'";
         "@a.@b.@c.(a*(b+c)=a*b+a*c)->@b.@c.(0''*(b+c)=0''*b+0''*c)";
         "@b.@c.(0''*(b+c)=0''*b+0''*c)";
         "@b.@c.(0''*(b+c)=0''*b+0''*c)->@c.(0''*(e+c)=0''*e+0''*c)";
         "@c.(0''*(e+c)=0''*e+0''*c)";
         "@c.(0''*(e+c)=0''*e+0''*c)->(0''*(e+d)=0''*e+0''*d)";
         "0''*(e+d)=0''*e+0''*d";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(0''*(e+d)=b->0''*(e+d)=c->b=c)";
         "@b.@c.(0''*(e+d)=b->0''*(e+d)=c->b=c)";
         "@b.@c.(0''*(e+d)=b->0''*(e+d)=c->b=c)->@c.(0''*(e+d)=0''*e+0''*d->0''*(e+d)=c->0''*e+0''*d=c)";
         "@c.(0''*(e+d)=0''*e+0''*d->0''*(e+d)=c->0''*e+0''*d=c)";
         "@c.(0''*(e+d)=0''*e+0''*d->0''*(e+d)=c->0''*e+0''*d=c)->(0''*(e+d)=0''*e+0''*d->0''*(e+d)=(0''*d)'->0''*e+0''*d=(0''*d)')";
         "0''*(e+d)=0''*e+0''*d->0''*(e+d)=(0''*d)'->0''*e+0''*d=(0''*d)'";
         "0''*(e+d)=(0''*d)'->0''*e+0''*d=(0''*d)'";
         "@a.(0+a=a)->0+0''*d=0''*d";
         "0+0''*d=0''*d";
         "@a.@b.(a=b->a'=b')->@b.(0+0''*d=b->(0+0''*d)'=b')";
         "@b.(0+0''*d=b->(0+0''*d)'=b')";
         "@b.(0+0''*d=b->(0+0''*d)'=b')->(0+0''*d=0''*d->(0+0''*d)'=(0''*d)')";
         "0+0''*d=0''*d->(0+0''*d)'=(0''*d)'";
         "(0+0''*d)'=(0''*d)'";
         "@a.@b.(a'+b=(a+b)')->@b.(0'+b=(0+b)')";
         "@b.(0'+b=(0+b)')";
         "@b.(0'+b=(0+b)')->(0'+0''*d=(0+0''*d)')";
         "0'+0''*d=(0+0''*d)'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(0+0''*d)'->(0+0''*d)'=c->b=c)";
         "@b.@c.(b=(0+0''*d)'->(0+0''*d)'=c->b=c)";
         "@b.@c.(b=(0+0''*d)'->(0+0''*d)'=c->b=c)->@c.(0'+0''*d=(0+0''*d)'->(0+0''*d)'=c->0'+0''*d=c)";
         "@c.(0'+0''*d=(0+0''*d)'->(0+0''*d)'=c->0'+0''*d=c)";
         "@c.(0'+0''*d=(0+0''*d)'->(0+0''*d)'=c->0'+0''*d=c)->(0'+0''*d=(0+0''*d)'->(0+0''*d)'=(0''*d)'->0'+0''*d=(0''*d)')";
         "0'+0''*d=(0+0''*d)'->(0+0''*d)'=(0''*d)'->0'+0''*d=(0''*d)'";
         "(0+0''*d)'=(0''*d)'->0'+0''*d=(0''*d)'";
         "0'+0''*d=(0''*d)'";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=(0''*d)'->c=(0''*d)'->b=c)";
         "@b.@c.(b=(0''*d)'->c=(0''*d)'->b=c)";
         "@b.@c.(b=(0''*d)'->c=(0''*d)'->b=c)->@c.(0''*e+0''*d=(0''*d)'->c=(0''*d)'->0''*e+0''*d=c)";
         "@c.(0''*e+0''*d=(0''*d)'->c=(0''*d)'->0''*e+0''*d=c)";
         "@c.(0''*e+0''*d=(0''*d)'->c=(0''*d)'->0''*e+0''*d=c)->(0''*e+0''*d=(0''*d)'->0'+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d)";
         "0''*e+0''*d=(0''*d)'->0'+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d";
         "0'+0''*d=(0''*d)'->0''*e+0''*d=(0''*d)'->0'+0''*d=(0''*d)'";
         "0''*e+0''*d=(0''*d)'->0'+0''*d=(0''*d)'";
         "(0''*e+0''*d=(0''*d)'->0'+0''*d=(0''*d)')->(0''*e+0''*d=(0''*d)'->0'+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d)->(0''*e+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d)";
         "(0''*e+0''*d=(0''*d)'->0'+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d)->(0''*e+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d)";
         "0''*e+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d";
         "(0''*e+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d)->0''*(e+d)=(0''*d)'->(0''*e+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d)";
         "0''*(e+d)=(0''*d)'->0''*e+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d";
         "(0''*(e+d)=(0''*d)'->0''*e+0''*d=(0''*d)')->(0''*(e+d)=(0''*d)'->0''*e+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d)->(0''*(e+d)=(0''*d)'->0''*e+0''*d=0'+0''*d)";
         "(0''*(e+d)=(0''*d)'->0''*e+0''*d=(0''*d)'->0''*e+0''*d=0'+0''*d)->(0''*(e+d)=(0''*d)'->0''*e+0''*d=0'+0''*d)";
         "0''*(e+d)=(0''*d)'->0''*e+0''*d=0'+0''*d";
         "@a.@b.@c.(a+c=b+c->a=b)->@b.@c.(0''*e+c=b+c->0''*e=b)";
         "@b.@c.(0''*e+c=b+c->0''*e=b)";
         "@b.@c.(0''*e+c=b+c->0''*e=b)->@c.(0''*e+c=0'+c->0''*e=0')";
         "@c.(0''*e+c=0'+c->0''*e=0')";
         "@c.(0''*e+c=0'+c->0''*e=0')->(0''*e+0''*d=0'+0''*d->0''*e=0')";
         "0''*e+0''*d=0'+0''*d->0''*e=0'";
         "(0''*e+0''*d=0'+0''*d->0''*e=0')->0''*(e+d)=(0''*d)'->(0''*e+0''*d=0'+0''*d->0''*e=0')";
         "0''*(e+d)=(0''*d)'->0''*e+0''*d=0'+0''*d->0''*e=0'";
         "(0''*(e+d)=(0''*d)'->0''*e+0''*d=0'+0''*d)->(0''*(e+d)=(0''*d)'->0''*e+0''*d=0'+0''*d->0''*e=0')->(0''*(e+d)=(0''*d)'->0''*e=0')";
         "(0''*(e+d)=(0''*d)'->0''*e+0''*d=0'+0''*d->0''*e=0')->(0''*(e+d)=(0''*d)'->0''*e=0')";
         "0''*(e+d)=(0''*d)'->0''*e=0'";
         "@a.!0''*a=0'->!0''*e=0'";
         "!0''*e=0'";
         "!0''*e=0'->0''*(e+d)=(0''*d)'->!0''*e=0'";
         "0''*(e+d)=(0''*d)'->!0''*e=0'";
         "(0''*(e+d)=(0''*d)'->0''*e=0')->(0''*(e+d)=(0''*d)'->!0''*e=0')->!0''*(e+d)=(0''*d)'";
         "(0''*(e+d)=(0''*d)'->!0''*e=0')->!0''*(e+d)=(0''*d)'";
         "!0''*(e+d)=(0''*d)'";
         "!0''*(e+d)=(0''*d)'->0''*a=(0''*d)'->!0''*(e+d)=(0''*d)'";
         "0''*a=(0''*d)'->!0''*(e+d)=(0''*d)'";
         "(0''*a=(0''*d)'->0''*(e+d)=(0''*d)')->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->!0''*a=(0''*d)'";
         "((0''*a=(0''*d)'->0''*(e+d)=(0''*d)')->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->!0''*a=(0''*d)')->a=e+d->((0''*a=(0''*d)'->0''*(e+d)=(0''*d)')->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->!0''*a=(0''*d)')";
         "a=e+d->(0''*a=(0''*d)'->0''*(e+d)=(0''*d)')->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->!0''*a=(0''*d)'";
         "(a=e+d->0''*a=(0''*d)'->0''*(e+d)=(0''*d)')->(a=e+d->(0''*a=(0''*d)'->0''*(e+d)=(0''*d)')->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->!0''*a=(0''*d)')->(a=e+d->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->!0''*a=(0''*d)')";
         "(a=e+d->(0''*a=(0''*d)'->0''*(e+d)=(0''*d)')->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->!0''*a=(0''*d)')->(a=e+d->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->!0''*a=(0''*d)')";
         "a=e+d->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->!0''*a=(0''*d)'";
         "(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->a=e+d->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')";
         "a=e+d->0''*a=(0''*d)'->!0''*(e+d)=(0''*d)'";
         "(a=e+d->0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->(a=e+d->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->!0''*a=(0''*d)')->(a=e+d->!0''*a=(0''*d)')";
         "(a=e+d->(0''*a=(0''*d)'->!0''*(e+d)=(0''*d)')->!0''*a=(0''*d)')->(a=e+d->!0''*a=(0''*d)')";
         "a=e+d->!0''*a=(0''*d)'";
         "?e.a=e+d->!0''*a=(0''*d)'";
         "@a.@b.@c.(a=b->c*a=c*b)->@b.@c.(a+e=b->c*(a+e)=c*b)";
         "@b.@c.(a+e=b->c*(a+e)=c*b)";
         "@b.@c.(a+e=b->c*(a+e)=c*b)->@c.(a+e=d->c*(a+e)=c*d)";
         "@c.(a+e=d->c*(a+e)=c*d)";
         "@c.(a+e=d->c*(a+e)=c*d)->(a+e=d->0''*(a+e)=0''*d)";
         "a+e=d->0''*(a+e)=0''*d";
         "@a.@b.@c.(a*(b+c)=a*b+a*c)->@b.@c.(0''*(b+c)=0''*b+0''*c)";
         "@b.@c.(0''*(b+c)=0''*b+0''*c)";
         "@b.@c.(0''*(b+c)=0''*b+0''*c)->@c.(0''*(a+c)=0''*a+0''*c)";
         "@c.(0''*(a+c)=0''*a+0''*c)";
         "@c.(0''*(a+c)=0''*a+0''*c)->(0''*(a+e)=0''*a+0''*e)";
         "0''*(a+e)=0''*a+0''*e";
         "@a.@b.@c.(a=b->a=c->b=c)->@b.@c.(0''*(a+e)=b->0''*(a+e)=c->b=c)";
         "@b.@c.(0''*(a+e)=b->0''*(a+e)=c->b=c)";
         "@b.@c.(0''*(a+e)=b->0''*(a+e)=c->b=c)->@c.(0''*(a+e)=0''*a+0''*e->0''*(a+e)=c->0''*a+0''*e=c)";
         "@c.(0''*(a+e)=0''*a+0''*e->0''*(a+e)=c->0''*a+0''*e=c)";
         "@c.(0''*(a+e)=0''*a+0''*e->0''*(a+e)=c->0''*a+0''*e=c)->(0''*(a+e)=0''*a+0''*e->0''*(a+e)=0''*d->0''*a+0''*e=0''*d)";
         "0''*(a+e)=0''*a+0''*e->0''*(a+e)=0''*d->0''*a+0''*e=0''*d";
         "0''*(a+e)=0''*d->0''*a+0''*e=0''*d";
         "0''*(a+e)=0''*d->0''*a+0''*e=0''*d";
         "(0''*(a+e)=0''*d->0''*a+0''*e=0''*d)->a+e=d->(0''*(a+e)=0''*d->0''*a+0''*e=0''*d)";
         "a+e=d->0''*(a+e)=0''*d->0''*a+0''*e=0''*d";
         "(a+e=d->0''*(a+e)=0''*d)->(a+e=d->0''*(a+e)=0''*d->0''*a+0''*e=0''*d)->(a+e=d->0''*a+0''*e=0''*d)";
         "(a+e=d->0''*(a+e)=0''*d->0''*a+0''*e=0''*d)->(a+e=d->0''*a+0''*e=0''*d)";
         "a+e=d->0''*a+0''*e=0''*d";
         "@a.@b.(a=b->a'=b')->@b.(0''*a+0''*e=b->(0''*a+0''*e)'=b')";
         "@b.(0''*a+0''*e=b->(0''*a+0''*e)'=b')";
         "@b.(0''*a+0''*e=b->(0''*a+0''*e)'=b')->(0''*a+0''*e=0''*d->(0''*a+0''*e)'=(0''*d)')";
         "0''*a+0''*e=0''*d->(0''*a+0''*e)'=(0''*d)'";
         "(0''*a+0''*e=0''*d->(0''*a+0''*e)'=(0''*d)')->a+e=d->(0''*a+0''*e=0''*d->(0''*a+0''*e)'=(0''*d)')";
         "a+e=d->0''*a+0''*e=0''*d->(0''*a+0''*e)'=(0''*d)'";
         "(a+e=d->0''*a+0''*e=0''*d)->(a+e=d->0''*a+0''*e=0''*d->(0''*a+0''*e)'=(0''*d)')->(a+e=d->(0''*a+0''*e)'=(0''*d)')";
         "(a+e=d->0''*a+0''*e=0''*d->(0''*a+0''*e)'=(0''*d)')->(a+e=d->(0''*a+0''*e)'=(0''*d)')";
         "a+e=d->(0''*a+0''*e)'=(0''*d)'";
         "@a.@b.(a+b'=(a+b)')->@b.(0''*a+b'=(0''*a+b)')";
         "@b.(0''*a+b'=(0''*a+b)')";
         "@b.(0''*a+b'=(0''*a+b)')->(0''*a+(0''*e)'=(0''*a+0''*e)')";
         "0''*a+(0''*e)'=(0''*a+0''*e)'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(0''*a+0''*e)'->(0''*a+0''*e)'=c->b=c)";
         "@b.@c.(b=(0''*a+0''*e)'->(0''*a+0''*e)'=c->b=c)";
         "@b.@c.(b=(0''*a+0''*e)'->(0''*a+0''*e)'=c->b=c)->@c.(0''*a+(0''*e)'=(0''*a+0''*e)'->(0''*a+0''*e)'=c->0''*a+(0''*e)'=c)";
         "@c.(0''*a+(0''*e)'=(0''*a+0''*e)'->(0''*a+0''*e)'=c->0''*a+(0''*e)'=c)";
         "@c.(0''*a+(0''*e)'=(0''*a+0''*e)'->(0''*a+0''*e)'=c->0''*a+(0''*e)'=c)->(0''*a+(0''*e)'=(0''*a+0''*e)'->(0''*a+0''*e)'=(0''*d)'->0''*a+(0''*e)'=(0''*d)')";
         "0''*a+(0''*e)'=(0''*a+0''*e)'->(0''*a+0''*e)'=(0''*d)'->0''*a+(0''*e)'=(0''*d)'";
         "(0''*a+0''*e)'=(0''*d)'->0''*a+(0''*e)'=(0''*d)'";
         "((0''*a+0''*e)'=(0''*d)'->0''*a+(0''*e)'=(0''*d)')->a+e=d->((0''*a+0''*e)'=(0''*d)'->0''*a+(0''*e)'=(0''*d)')";
         "a+e=d->(0''*a+0''*e)'=(0''*d)'->0''*a+(0''*e)'=(0''*d)'";
         "(a+e=d->(0''*a+0''*e)'=(0''*d)')->(a+e=d->(0''*a+0''*e)'=(0''*d)'->0''*a+(0''*e)'=(0''*d)')->(a+e=d->0''*a+(0''*e)'=(0''*d)')";
         "(a+e=d->(0''*a+0''*e)'=(0''*d)'->0''*a+(0''*e)'=(0''*d)')->(a+e=d->0''*a+(0''*e)'=(0''*d)')";
         "a+e=d->0''*a+(0''*e)'=(0''*d)'";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=(0''*d)'->c=(0''*d)'->b=c)";
         "@b.@c.(b=(0''*d)'->c=(0''*d)'->b=c)";
         "@b.@c.(b=(0''*d)'->c=(0''*d)'->b=c)->@c.(0''*a+(0''*e)'=(0''*d)'->c=(0''*d)'->0''*a+(0''*e)'=c)";
         "@c.(0''*a+(0''*e)'=(0''*d)'->c=(0''*d)'->0''*a+(0''*e)'=c)";
         "@c.(0''*a+(0''*e)'=(0''*d)'->c=(0''*d)'->0''*a+(0''*e)'=c)->(0''*a+(0''*e)'=(0''*d)'->0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)";
         "0''*a+(0''*e)'=(0''*d)'->0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a";
         "(0''*a+(0''*e)'=(0''*d)'->0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)->a+e=d->(0''*a+(0''*e)'=(0''*d)'->0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)";
         "a+e=d->0''*a+(0''*e)'=(0''*d)'->0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a";
         "(a+e=d->0''*a+(0''*e)'=(0''*d)')->(a+e=d->0''*a+(0''*e)'=(0''*d)'->0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)->(a+e=d->0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)";
         "(a+e=d->0''*a+(0''*e)'=(0''*d)'->0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)->(a+e=d->0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)";
         "a+e=d->0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a";
         "@a.(a+0=a)->0''*a+0=0''*a";
         "0''*a+0=0''*a";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=0''*a->c=0''*a->b=c)";
         "@b.@c.(b=0''*a->c=0''*a->b=c)";
         "@b.@c.(b=0''*a->c=0''*a->b=c)->@c.(0''*a+(0''*e)'=0''*a->c=0''*a->0''*a+(0''*e)'=c)";
         "@c.(0''*a+(0''*e)'=0''*a->c=0''*a->0''*a+(0''*e)'=c)";
         "@c.(0''*a+(0''*e)'=0''*a->c=0''*a->0''*a+(0''*e)'=c)->(0''*a+(0''*e)'=0''*a->0''*a+0=0''*a->0''*a+(0''*e)'=0''*a+0)";
         "0''*a+(0''*e)'=0''*a->0''*a+0=0''*a->0''*a+(0''*e)'=0''*a+0";
         "0''*a+0=0''*a->0''*a+(0''*e)'=0''*a->0''*a+0=0''*a";
         "0''*a+(0''*e)'=0''*a->0''*a+0=0''*a";
         "(0''*a+(0''*e)'=0''*a->0''*a+0=0''*a)->(0''*a+(0''*e)'=0''*a->0''*a+0=0''*a->0''*a+(0''*e)'=0''*a+0)->(0''*a+(0''*e)'=0''*a->0''*a+(0''*e)'=0''*a+0)";
         "(0''*a+(0''*e)'=0''*a->0''*a+0=0''*a->0''*a+(0''*e)'=0''*a+0)->(0''*a+(0''*e)'=0''*a->0''*a+(0''*e)'=0''*a+0)";
         "0''*a+(0''*e)'=0''*a->0''*a+(0''*e)'=0''*a+0";
         "@a.@b.@c.(c+a=c+b->a=b)->@b.@c.(c+(0''*e)'=c+b->(0''*e)'=b)";
         "@b.@c.(c+(0''*e)'=c+b->(0''*e)'=b)";
         "@b.@c.(c+(0''*e)'=c+b->(0''*e)'=b)->@c.(c+(0''*e)'=c+0->(0''*e)'=0)";
         "@c.(c+(0''*e)'=c+0->(0''*e)'=0)";
         "@c.(c+(0''*e)'=c+0->(0''*e)'=0)->(0''*a+(0''*e)'=0''*a+0->(0''*e)'=0)";
         "0''*a+(0''*e)'=0''*a+0->(0''*e)'=0";
         "(0''*a+(0''*e)'=0''*a+0->(0''*e)'=0)->0''*a+(0''*e)'=0''*a->(0''*a+(0''*e)'=0''*a+0->(0''*e)'=0)";
         "0''*a+(0''*e)'=0''*a->0''*a+(0''*e)'=0''*a+0->(0''*e)'=0";
         "(0''*a+(0''*e)'=0''*a->0''*a+(0''*e)'=0''*a+0)->(0''*a+(0''*e)'=0''*a->0''*a+(0''*e)'=0''*a+0->(0''*e)'=0)->(0''*a+(0''*e)'=0''*a->(0''*e)'=0)";
         "(0''*a+(0''*e)'=0''*a->0''*a+(0''*e)'=0''*a+0->(0''*e)'=0)->(0''*a+(0''*e)'=0''*a->(0''*e)'=0)";
         "0''*a+(0''*e)'=0''*a->(0''*e)'=0";
         "@a.!a'=0->!(0''*e)'=0";
         "!(0''*e)'=0";
         "!(0''*e)'=0->0''*a+(0''*e)'=0''*a->!(0''*e)'=0";
         "0''*a+(0''*e)'=0''*a->!(0''*e)'=0";
         "(0''*a+(0''*e)'=0''*a->(0''*e)'=0)->(0''*a+(0''*e)'=0''*a->!(0''*e)'=0)->!0''*a+(0''*e)'=0''*a";
         "(0''*a+(0''*e)'=0''*a->!(0''*e)'=0)->!0''*a+(0''*e)'=0''*a";
         "!0''*a+(0''*e)'=0''*a";
         "!0''*a+(0''*e)'=0''*a->0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a";
         "0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a";
         "(0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->!0''*a=(0''*d)'";
         "((0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->!0''*a=(0''*d)')->a+e=d->((0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->!0''*a=(0''*d)')";
         "a+e=d->(0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->!0''*a=(0''*d)'";
         "(a+e=d->0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)->(a+e=d->(0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->!0''*a=(0''*d)')->(a+e=d->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->!0''*a=(0''*d)')";
         "(a+e=d->(0''*a=(0''*d)'->0''*a+(0''*e)'=0''*a)->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->!0''*a=(0''*d)')->(a+e=d->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->!0''*a=(0''*d)')";
         "a+e=d->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->!0''*a=(0''*d)'";
         "(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->a+e=d->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)";
         "a+e=d->0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a";
         "(a+e=d->0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->(a+e=d->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->!0''*a=(0''*d)')->(a+e=d->!0''*a=(0''*d)')";
         "(a+e=d->(0''*a=(0''*d)'->!0''*a+(0''*e)'=0''*a)->!0''*a=(0''*d)')->(a+e=d->!0''*a=(0''*d)')";
         "a+e=d->!0''*a=(0''*d)'";
         "?e.a+e=d->!0''*a=(0''*d)'";
         "(?e.a=e+d->!0''*a=(0''*d)')->(?e.a+e=d->!0''*a=(0''*d)')->(?e.a=e+d|?e.a+e=d->!0''*a=(0''*d)')";
         "(?e.a+e=d->!0''*a=(0''*d)')->(?e.a=e+d|?e.a+e=d->!0''*a=(0''*d)')";
         "?e.a=e+d|?e.a+e=d->!0''*a=(0''*d)'";
         "!0''*a=(0''*d)'";
         "!0''*a=(0''*d)'->0=0->!0''*a=(0''*d)'";
         "0=0->!0''*a=(0''*d)'";
         "0=0->@d.!0''*a=(0''*d)'";
         "@d.!0''*a=(0''*d)'";
         "@d.!0''*a=(0''*d)'->!0''*a=(0''*b)'";
         "!0''*a=(0''*b)'";
         "!0''*a=(0''*b)'->0=0->!0''*a=(0''*b)'";
         "0=0->!0''*a=(0''*b)'";
         "0=0->@b.!0''*a=(0''*b)'";
         "0=0->@a.@b.!0''*a=(0''*b)'";
         "@a.@b.!0''*a=(0''*b)'";
         "@a.(a+0=a)->0''*d+0=0''*d";
         "0''*d+0=0''*d";
         "@a.@b.(a=b->a'=b')->@b.(0''*d+0=b->(0''*d+0)'=b')";
         "@b.(0''*d+0=b->(0''*d+0)'=b')";
         "@b.(0''*d+0=b->(0''*d+0)'=b')->(0''*d+0=0''*d->(0''*d+0)'=(0''*d)')";
         "0''*d+0=0''*d->(0''*d+0)'=(0''*d)'";
         "(0''*d+0)'=(0''*d)'";
         "@a.@b.(a+b'=(a+b)')->@b.(0''*d+b'=(0''*d+b)')";
         "@b.(0''*d+b'=(0''*d+b)')";
         "@b.(0''*d+b'=(0''*d+b)')->(0''*d+0'=(0''*d+0)')";
         "0''*d+0'=(0''*d+0)'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(0''*d+0)'->(0''*d+0)'=c->b=c)";
         "@b.@c.(b=(0''*d+0)'->(0''*d+0)'=c->b=c)";
         "@b.@c.(b=(0''*d+0)'->(0''*d+0)'=c->b=c)->@c.(0''*d+0'=(0''*d+0)'->(0''*d+0)'=c->0''*d+0'=c)";
         "@c.(0''*d+0'=(0''*d+0)'->(0''*d+0)'=c->0''*d+0'=c)";
         "@c.(0''*d+0'=(0''*d+0)'->(0''*d+0)'=c->0''*d+0'=c)->(0''*d+0'=(0''*d+0)'->(0''*d+0)'=(0''*d)'->0''*d+0'=(0''*d)')";
         "0''*d+0'=(0''*d+0)'->(0''*d+0)'=(0''*d)'->0''*d+0'=(0''*d)'";
         "(0''*d+0)'=(0''*d)'->0''*d+0'=(0''*d)'";
         "0''*d+0'=(0''*d)'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=0''*d+0'->0''*d+0'=c->b=c)";
         "@b.@c.(b=0''*d+0'->0''*d+0'=c->b=c)";
         "@b.@c.(b=0''*d+0'->0''*d+0'=c->b=c)->@c.(0''*a=0''*d+0'->0''*d+0'=c->0''*a=c)";
         "@c.(0''*a=0''*d+0'->0''*d+0'=c->0''*a=c)";
         "@c.(0''*a=0''*d+0'->0''*d+0'=c->0''*a=c)->(0''*a=0''*d+0'->0''*d+0'=(0''*d)'->0''*a=(0''*d)')";
         "0''*a=0''*d+0'->0''*d+0'=(0''*d)'->0''*a=(0''*d)'";
         "0''*d+0'=(0''*d)'->0''*a=0''*d+0'->0''*d+0'=(0''*d)'";
         "0''*a=0''*d+0'->0''*d+0'=(0''*d)'";
         "(0''*a=0''*d+0'->0''*d+0'=(0''*d)')->(0''*a=0''*d+0'->0''*d+0'=(0''*d)'->0''*a=(0''*d)')->(0''*a=0''*d+0'->0''*a=(0''*d)')";
         "(0''*a=0''*d+0'->0''*d+0'=(0''*d)'->0''*a=(0''*d)')->(0''*a=0''*d+0'->0''*a=(0''*d)')";
         "0''*a=0''*d+0'->0''*a=(0''*d)'";
         "!0''*a=(0''*d)'->0''*a=0''*d+0'->!0''*a=(0''*d)'";
         "0''*a=0''*d+0'->!0''*a=(0''*d)'";
         "(0''*a=0''*d+0'->0''*a=(0''*d)')->(0''*a=0''*d+0'->!0''*a=(0''*d)')->!0''*a=0''*d+0'";
         "(0''*a=0''*d+0'->!0''*a=(0''*d)')->!0''*a=0''*d+0'";
         "!0''*a=0''*d+0'";
         "!0''*a=0''*d+0'->0=0->!0''*a=0''*d+0'";
         "0=0->!0''*a=0''*d+0'";
         "0=0->@d.!0''*a=0''*d+0'";
         "@d.!0''*a=0''*d+0'";
         "@d.!0''*a=0''*d+0'->!0''*a=0''*b+0'";
         "!0''*a=0''*b+0'";
         "!0''*a=0''*b+0'->0=0->!0''*a=0''*b+0'";
         "0=0->!0''*a=0''*b+0'";
         "0=0->@b.!0''*a=0''*b+0'";
         "0=0->@a.@b.!0''*a=0''*b+0'";
         "@a.@b.!0''*a=0''*b+0'"];;
let constructTheorem = evenNeqOdd @
        ["@a.(a*0=0)->0''*0=0";
         "0''*0=0";
         "@a.@b.(a=b->a'=b')->@b.(0''*a=b->(0''*a)'=b')";
         "@b.(0''*a=b->(0''*a)'=b')";
         "@b.(0''*a=b->(0''*a)'=b')->(0''*a=d->(0''*a)'=d')";
         "0''*a=d->(0''*a)'=d'";
         "@a.@b.(a=b->a'=b')->@b.((0''*a)'=b->(0''*a)''=b')";
         "@b.((0''*a)'=b->(0''*a)''=b')";
         "@b.((0''*a)'=b->(0''*a)''=b')->((0''*a)'=d'->(0''*a)''=d'')";
         "(0''*a)'=d'->(0''*a)''=d''";
         "((0''*a)'=d'->(0''*a)''=d'')->0''*a=d->((0''*a)'=d'->(0''*a)''=d'')";
         "0''*a=d->(0''*a)'=d'->(0''*a)''=d''";
         "(0''*a=d->(0''*a)'=d')->(0''*a=d->(0''*a)'=d'->(0''*a)''=d'')->(0''*a=d->(0''*a)''=d'')";
         "(0''*a=d->(0''*a)'=d'->(0''*a)''=d'')->(0''*a=d->(0''*a)''=d'')";
         "0''*a=d->(0''*a)''=d''";
         "@a.(a+0=a)->(0''*a+0=0''*a)";
         "0''*a+0=0''*a";
         "@a.@b.(a=b->a'=b')->@b.(0''*a+0=b->(0''*a+0)'=b')";
         "@b.(0''*a+0=b->(0''*a+0)'=b')";
         "@b.(0''*a+0=b->(0''*a+0)'=b')->(0''*a+0=0''*a->(0''*a+0)'=(0''*a)')";
         "0''*a+0=0''*a->(0''*a+0)'=(0''*a)'";
         "(0''*a+0)'=(0''*a)'";
         "@a.@b.(a=b->a'=b')->@b.((0''*a+0)'=b->(0''*a+0)''=b')";
         "@b.((0''*a+0)'=b->(0''*a+0)''=b')";
         "@b.((0''*a+0)'=b->(0''*a+0)''=b')->((0''*a+0)'=(0''*a)'->(0''*a+0)''=(0''*a)'')";
         "(0''*a+0)'=(0''*a)'->(0''*a+0)''=(0''*a)''";
         "(0''*a+0)''=(0''*a)''";
         "@a.@b.(a+b'=(a+b)')->@b.(0''*a+b'=(0''*a+b)')";
         "@b.(0''*a+b'=(0''*a+b)')";
         "@b.(0''*a+b'=(0''*a+b)')->(0''*a+0'=(0''*a+0)')";
         "0''*a+0'=(0''*a+0)'";
         "@a.@b.(a=b->a'=b')->@b.(0''*a+0'=b->(0''*a+0')'=b')";
         "@b.(0''*a+0'=b->(0''*a+0')'=b')";
         "@b.(0''*a+0'=b->(0''*a+0')'=b')->(0''*a+0'=(0''*a+0)'->(0''*a+0')'=(0''*a+0)'')";
         "0''*a+0'=(0''*a+0)'->(0''*a+0')'=(0''*a+0)''";
         "(0''*a+0')'=(0''*a+0)''";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(0''*a+0)''->(0''*a+0)''=c->b=c)";
         "@b.@c.(b=(0''*a+0)''->(0''*a+0)''=c->b=c)";
         "@b.@c.(b=(0''*a+0)''->(0''*a+0)''=c->b=c)->@c.((0''*a+0')'=(0''*a+0)''->(0''*a+0)''=c->(0''*a+0')'=c)";
         "@c.((0''*a+0')'=(0''*a+0)''->(0''*a+0)''=c->(0''*a+0')'=c)";
         "@c.((0''*a+0')'=(0''*a+0)''->(0''*a+0)''=c->(0''*a+0')'=c)->((0''*a+0')'=(0''*a+0)''->(0''*a+0)''=(0''*a)''->(0''*a+0')'=(0''*a)'')";
         "(0''*a+0')'=(0''*a+0)''->(0''*a+0)''=(0''*a)''->(0''*a+0')'=(0''*a)''";
         "(0''*a+0)''=(0''*a)''->(0''*a+0')'=(0''*a)''";
         "(0''*a+0')'=(0''*a)''";
         "@a.@b.(a+b'=(a+b)')->@b.(0''*a+b'=(0''*a+b)')";
         "@b.(0''*a+b'=(0''*a+b)')";
         "@b.(0''*a+b'=(0''*a+b)')->(0''*a+0''=(0''*a+0')')";
         "0''*a+0''=(0''*a+0')'";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(0''*a+0')'->(0''*a+0')'=c->b=c)";
         "@b.@c.(b=(0''*a+0')'->(0''*a+0')'=c->b=c)";
         "@b.@c.(b=(0''*a+0')'->(0''*a+0')'=c->b=c)->@c.(0''*a+0''=(0''*a+0')'->(0''*a+0')'=c->0''*a+0''=c)";
         "@c.(0''*a+0''=(0''*a+0')'->(0''*a+0')'=c->0''*a+0''=c)";
         "@c.(0''*a+0''=(0''*a+0')'->(0''*a+0')'=c->0''*a+0''=c)->(0''*a+0''=(0''*a+0')'->(0''*a+0')'=(0''*a)''->0''*a+0''=(0''*a)'')";
         "0''*a+0''=(0''*a+0')'->(0''*a+0')'=(0''*a)''->0''*a+0''=(0''*a)''";
         "(0''*a+0')'=(0''*a)''->0''*a+0''=(0''*a)''";
         "0''*a+0''=(0''*a)''";
         "@a.@b.(a*b'=a*b+a)->@b.(0''*b'=0''*b+0'')";
         "@b.(0''*b'=0''*b+0'')";
         "@b.(0''*b'=0''*b+0'')->(0''*a'=0''*a+0'')";
         "0''*a'=0''*a+0''";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=0''*a+0''->0''*a+0''=c->b=c)";
         "@b.@c.(b=0''*a+0''->0''*a+0''=c->b=c)";
         "@b.@c.(b=0''*a+0''->0''*a+0''=c->b=c)->@c.(0''*a'=0''*a+0''->0''*a+0''=c->0''*a'=c)";
         "@c.(0''*a'=0''*a+0''->0''*a+0''=c->0''*a'=c)";
         "@c.(0''*a'=0''*a+0''->0''*a+0''=c->0''*a'=c)->(0''*a'=0''*a+0''->0''*a+0''=(0''*a)''->0''*a'=(0''*a)'')";
         "0''*a'=0''*a+0''->0''*a+0''=(0''*a)''->0''*a'=(0''*a)''";
         "0''*a+0''=(0''*a)''->0''*a'=(0''*a)''";
         "0''*a'=(0''*a)''";
         "@a.@b.@c.(b=a->a=c->b=c)->@b.@c.(b=(0''*a)''->(0''*a)''=c->b=c)";
         "@b.@c.(b=(0''*a)''->(0''*a)''=c->b=c)";
         "@b.@c.(b=(0''*a)''->(0''*a)''=c->b=c)->@c.(0''*a'=(0''*a)''->(0''*a)''=c->0''*a'=c)";
         "@c.(0''*a'=(0''*a)''->(0''*a)''=c->0''*a'=c)";
         "@c.(0''*a'=(0''*a)''->(0''*a)''=c->0''*a'=c)->(0''*a'=(0''*a)''->(0''*a)''=d''->0''*a'=d'')";
         "0''*a'=(0''*a)''->(0''*a)''=d''->0''*a'=d''";
         "(0''*a)''=d''->0''*a'=d''";
         "((0''*a)''=d''->0''*a'=d'')->0''*a=d->((0''*a)''=d''->0''*a'=d'')";
         "0''*a=d->(0''*a)''=d''->0''*a'=d''";
         "(0''*a=d->(0''*a)''=d'')->(0''*a=d->(0''*a)''=d''->0''*a'=d'')->(0''*a=d->0''*a'=d'')";
         "(0''*a=d->(0''*a)''=d''->0''*a'=d'')->(0''*a=d->0''*a'=d'')";
         "0''*a=d->0''*a'=d''";
         "(0''*a=d->0''*a'=d'')->0=0->(0''*a=d->0''*a'=d'')";
         "0=0->(0''*a=d->0''*a'=d'')";
         "0=0->@d.(0''*a=d->0''*a'=d'')";
         "@d.(0''*a=d->0''*a'=d'')";
         "@d.(0''*a=d->0''*a'=d'')->(0''*a=b->0''*a'=b'')";
         "0''*a=b->0''*a'=b''";
         "(0''*a=b->0''*a'=b'')->0=0->(0''*a=b->0''*a'=b'')";
         "0=0->(0''*a=b->0''*a'=b'')";
         "0=0->@b.(0''*a=b->0''*a'=b'')";
         "0=0->@a.@b.(0''*a=b->0''*a'=b'')";
         "@a.@b.(0''*a=b->0''*a'=b'')";
        ];;
let lastOneForNeg =
        ["(0''*f)'=x";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=x->c=x->b=c)";
         "@b.@c.(b=x->c=x->b=c)";
         "@b.@c.(b=x->c=x->b=c)->@c.(0''*p=x->c=x->0''*p=c)";
         "@c.(0''*p=x->c=x->0''*p=c)";
         "@c.(0''*p=x->c=x->0''*p=c)->(0''*p=x->(0''*f)'=x->0''*p=(0''*f)')";
         "0''*p=x->(0''*f)'=x->0''*p=(0''*f)'";
         "(0''*f)'=x->0''*p=x->(0''*f)'=x";
         "0''*p=x->(0''*f)'=x";
         "(0''*p=x->(0''*f)'=x)->(0''*p=x->(0''*f)'=x->0''*p=(0''*f)')->(0''*p=x->0''*p=(0''*f)')";
         "(0''*p=x->(0''*f)'=x->0''*p=(0''*f)')->(0''*p=x->0''*p=(0''*f)')";
         "0''*p=x->0''*p=(0''*f)'";
         "@a.@b.!0''*a=(0''*b)'->@b.!0''*p=(0''*b)'";
         "@b.!0''*p=(0''*b)'";
         "@b.!0''*p=(0''*b)'->!0''*p=(0''*f)'";
         "!0''*p=(0''*f)'";
         "!0''*p=(0''*f)'->0''*p=x->!0''*p=(0''*f)'";
         "0''*p=x->!0''*p=(0''*f)'";
         "(0''*p=x->0''*p=(0''*f)')->(0''*p=x->!0''*p=(0''*f)')->!0''*p=x";
         "(0''*p=x->!0''*p=(0''*f)')->!0''*p=x";
         "!0''*p=x";
         "!0''*p=x->0''*p=x&0''*q=y->!0''*p=x";
         "0''*p=x&0''*q=y->!0''*p=x";
         "0''*p=x&0''*q=y->0''*p=x";
         "(0''*p=x&0''*q=y->0''*p=x)->(0''*p=x&0''*q=y->!0''*p=x)->!(0''*p=x&0''*q=y)";
         "(0''*p=x&0''*q=y->!0''*p=x)->!(0''*p=x&0''*q=y)";
         "!(0''*p=x&0''*q=y)";
         "!0''*p=x->0''*q=y&0''*p=x->!0''*p=x";
         "0''*q=y&0''*p=x->!0''*p=x";
         "0''*q=y&0''*p=x->0''*p=x";
         "(0''*q=y&0''*p=x->0''*p=x)->(0''*q=y&0''*p=x->!0''*p=x)->!(0''*q=y&0''*p=x)";
         "(0''*q=y&0''*p=x->!0''*p=x)->!(0''*q=y&0''*p=x)";
         "!(0''*q=y&0''*p=x)";
         "0''*g=y";
         "@a.@b.@c.(a=b->a+c=b+c)->@b.@c.(0''*g=b->0''*g+c=b+c)";
         "@b.@c.(0''*g=b->0''*g+c=b+c)";
         "@b.@c.(0''*g=b->0''*g+c=b+c)->@c.(0''*g=y->0''*g+c=y+c)";
         "@c.(0''*g=y->0''*g+c=y+c)";
         "@c.(0''*g=y->0''*g+c=y+c)->(0''*g=y->0''*g+0'=y+0')";
         "0''*g=y->0''*g+0'=y+0'";
         "0''*g+0'=y+0'";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=y+0'->c=y+0'->b=c)";
         "@b.@c.(b=y+0'->c=y+0'->b=c)";
         "@b.@c.(b=y+0'->c=y+0'->b=c)->@c.(0''*q=y+0'->c=y+0'->0''*q=c)";
         "@c.(0''*q=y+0'->c=y+0'->0''*q=c)";
         "@c.(0''*q=y+0'->c=y+0'->0''*q=c)->(0''*q=y+0'->0''*g+0'=y+0'->0''*q=0''*g+0')";
         "0''*q=y+0'->0''*g+0'=y+0'->0''*q=0''*g+0'";
         "0''*g+0'=y+0'->0''*q=y+0'->0''*g+0'=y+0'";
         "0''*q=y+0'->0''*g+0'=y+0'";
         "(0''*q=y+0'->0''*g+0'=y+0')->(0''*q=y+0'->0''*g+0'=y+0'->0''*q=0''*g+0')->(0''*q=y+0'->0''*q=0''*g+0')";
         "(0''*q=y+0'->0''*g+0'=y+0'->0''*q=0''*g+0')->(0''*q=y+0'->0''*q=0''*g+0')";
         "0''*q=y+0'->0''*q=0''*g+0'";
         "@a.@b.!0''*a=0''*b+0'->@b.!0''*q=0''*b+0'";
         "@b.!0''*q=0''*b+0'";
         "@b.!0''*q=0''*b+0'->!0''*q=0''*g+0'";
         "!0''*q=0''*g+0'";
         "!0''*q=0''*g+0'->0''*q=y+0'->!0''*q=0''*g+0'";
         "0''*q=y+0'->!0''*q=0''*g+0'";
         "(0''*q=y+0'->0''*q=0''*g+0')->(0''*q=y+0'->!0''*q=0''*g+0')->!0''*q=y+0'";
         "(0''*q=y+0'->!0''*q=0''*g+0')->!0''*q=y+0'";
         "!0''*q=y+0'";
         "!0''*q=y+0'->0''*q=y+0'&0''*p=x+0'->!0''*q=y+0'";
         "0''*q=y+0'&0''*p=x+0'->!0''*q=y+0'";
         "0''*q=y+0'&0''*p=x+0'->0''*q=y+0'";
         "(0''*q=y+0'&0''*p=x+0'->0''*q=y+0')->(0''*q=y+0'&0''*p=x+0'->!0''*q=y+0')->!(0''*q=y+0'&0''*p=x+0')";
         "(0''*q=y+0'&0''*p=x+0'->!0''*q=y+0')->!(0''*q=y+0'&0''*p=x+0')";
         "!(0''*q=y+0'&0''*p=x+0')";
         "!0''*q=y+0'->0''*p=x+0'&0''*q=y+0'->!0''*q=y+0'";
         "0''*p=x+0'&0''*q=y+0'->!0''*q=y+0'";
         "0''*p=x+0'&0''*q=y+0'->0''*q=y+0'";
         "(0''*p=x+0'&0''*q=y+0'->0''*q=y+0')->(0''*p=x+0'&0''*q=y+0'->!0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0')";
         "(0''*p=x+0'&0''*q=y+0'->!0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0')";
         "!(0''*p=x+0'&0''*q=y+0')";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(0''*p=x&0''*q=y)->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "(0''*p=x&0''*q=y)->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(0''*p=x&0''*q=y)->(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y)";
         "((0''*p=x&0''*q=y)->(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y))->((0''*p=x&0''*q=y)->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x&0''*q=y)->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "((0''*p=x&0''*q=y)->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x&0''*q=y)->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "(0''*p=x&0''*q=y)->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "!(0''*p=x&0''*q=y)->(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y)";
         "(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y)";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->(0''*p=x&0''*q=y)->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))";
         "(0''*p=x&0''*q=y)->(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y)";
         "((0''*p=x&0''*q=y)->(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->((0''*p=x&0''*q=y)->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x&0''*q=y)->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "((0''*p=x&0''*q=y)->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x&0''*q=y))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x&0''*q=y)->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "(0''*p=x&0''*q=y)->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(0''*p=x+0'&0''*q=y+0')->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "(0''*p=x+0'&0''*q=y+0')->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x+0'&0''*q=y+0')";
         "((0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x+0'&0''*q=y+0'))->((0''*p=x+0'&0''*q=y+0')->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x+0'&0''*q=y+0')->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "((0''*p=x+0'&0''*q=y+0')->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x+0'&0''*q=y+0')->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "(0''*p=x+0'&0''*q=y+0')->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "!(0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0')";
         "(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0')";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->(0''*p=x+0'&0''*q=y+0')->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))";
         "(0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0')";
         "((0''*p=x+0'&0''*q=y+0')->(0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->((0''*p=x+0'&0''*q=y+0')->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x+0'&0''*q=y+0')->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "((0''*p=x+0'&0''*q=y+0')->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')->!(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x+0'&0''*q=y+0')->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "(0''*p=x+0'&0''*q=y+0')->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "((0''*p=x&0''*q=y)->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x+0'&0''*q=y+0')->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "((0''*p=x+0'&0''*q=y+0')->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->(0''*q=y&0''*p=x)->(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "(0''*q=y&0''*p=x)->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "(0''*q=y&0''*p=x)->(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x)";
         "((0''*q=y&0''*p=x)->(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x))->((0''*q=y&0''*p=x)->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y&0''*p=x)->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "((0''*q=y&0''*p=x)->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y&0''*p=x)->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "(0''*q=y&0''*p=x)->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "!(0''*q=y&0''*p=x)->(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x)";
         "(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x)";
         "((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->(0''*q=y&0''*p=x)->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))";
         "(0''*q=y&0''*p=x)->(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x)";
         "((0''*q=y&0''*p=x)->(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->((0''*q=y&0''*p=x)->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y&0''*p=x)->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "((0''*q=y&0''*p=x)->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y&0''*p=x))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y&0''*p=x)->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "(0''*q=y&0''*p=x)->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->(0''*q=y+0'&0''*p=x+0')->(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "(0''*q=y+0'&0''*p=x+0')->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "(0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y+0'&0''*p=x+0')";
         "((0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y+0'&0''*p=x+0'))->((0''*q=y+0'&0''*p=x+0')->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y+0'&0''*p=x+0')->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "((0''*q=y+0'&0''*p=x+0')->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y+0'&0''*p=x+0')->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "(0''*q=y+0'&0''*p=x+0')->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "!(0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0')";
         "(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0')";
         "((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->(0''*q=y+0'&0''*p=x+0')->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))";
         "(0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0')";
         "((0''*q=y+0'&0''*p=x+0')->(0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->((0''*q=y+0'&0''*p=x+0')->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y+0'&0''*p=x+0')->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "((0''*q=y+0'&0''*p=x+0')->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')->!(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y+0'&0''*p=x+0')->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "(0''*q=y+0'&0''*p=x+0')->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "((0''*q=y&0''*p=x)->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y+0'&0''*p=x+0')->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "((0''*q=y+0'&0''*p=x+0')->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))";
         "((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "(((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0')))->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->0=0->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "0=0->!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "0=0->@q.!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "@q.!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))";
         "@q.!((0''*q=y&0''*p=x)|(0''*q=y+0'&0''*p=x+0'))->!((0''*w=y&0''*p=x)|(0''*w=y+0'&0''*p=x+0'))";
         "!((0''*w=y&0''*p=x)|(0''*w=y+0'&0''*p=x+0'))";
         "!((0''*w=y&0''*p=x)|(0''*w=y+0'&0''*p=x+0'))->0=0->!((0''*w=y&0''*p=x)|(0''*w=y+0'&0''*p=x+0'))";
         "0=0->!((0''*w=y&0''*p=x)|(0''*w=y+0'&0''*p=x+0'))";
         "0=0->@w.!((0''*w=y&0''*p=x)|(0''*w=y+0'&0''*p=x+0'))";
         "0=0->@p.@w.!((0''*w=y&0''*p=x)|(0''*w=y+0'&0''*p=x+0'))";
         "@p.@w.!((0''*w=y&0''*p=x)|(0''*w=y+0'&0''*p=x+0'))";
         "@p.@w.!((0''*w=y&0''*p=x)|(0''*w=y+0'&0''*p=x+0'))->@w.!((0''*w=y&0''*q=x)|(0''*w=y+0'&0''*q=x+0'))";
         "@w.!((0''*w=y&0''*q=x)|(0''*w=y+0'&0''*q=x+0'))";
         "@w.!((0''*w=y&0''*q=x)|(0''*w=y+0'&0''*q=x+0'))->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))";
         "!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))";
         "!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(0=0->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!0=0";
         "((0=0->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!0=0)->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->((0=0->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!0=0)";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(0=0->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!0=0";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->0=0->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->0=0->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(0=0->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!0=0)->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!0=0)";
         "(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(0=0->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!0=0)->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!0=0)";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!0=0";
         "!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!0=0)->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!0=0)";
         "(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->(0=0->!((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0')))->!0=0)->(((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!0=0)";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!0=0";
         "0=0->((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->0=0";
         "((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->0=0";
         "?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!0=0";
         "?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!0=0";
         "?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->0=0";
         "?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->0=0";
         "(?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->0=0)->(?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!0=0)->!?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))->!0=0)->!?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "!?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "(0=0->((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->!0=0";
         "((0=0->((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->!0=0)->((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->((0=0->((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->!0=0)";
         "((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->(0=0->((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->!0=0";
         "((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->0=0->((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))";
         "(((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->0=0->((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->(((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->(0=0->((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->!0=0)->(((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->!0=0)";
         "(((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->(0=0->((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->!0=0)->(((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->!0=0)";
         "((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->!0=0";
         "!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))";
         "0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))";
         "(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))";
         "((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))";
         "(((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->(((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->!0=0)->(((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->!0=0)";
         "(((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->(0=0->!((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0')))->!0=0)->(((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->!0=0)";
         "((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->!0=0";
         "0=0->((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->0=0";
         "((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->0=0";
         "?q.((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->!0=0";
         "?p.?q.((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->!0=0";
         "?q.((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->0=0";
         "?p.?q.((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->0=0";
         "(?p.?q.((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->0=0)->(?p.?q.((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->!0=0)->!?p.?q.((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))";
         "(?p.?q.((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))->!0=0)->!?p.?q.((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))";
         "!?p.?q.((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))";
         "!?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
        ];;
let evenProve =
        ["0''*f=x";
         "0''*g=y";
         "0''*f=x->0''*g=y->0''*f=x&0''*g=y";
         "0''*g=y->0''*f=x&0''*g=y";
         "0''*f=x&0''*g=y";
         "0''*f=x&0''*g=y->(0''*f=x&0''*g=y)|(0''*f=x+0'&0''*g=y+0')";
         "(0''*f=x&0''*g=y)|(0''*f=x+0'&0''*g=y+0')";
         "(0''*f=x&0''*g=y)|(0''*f=x+0'&0''*g=y+0')->?q.((0''*f=x&0''*q=y)|(0''*f=x+0'&0''*q=y+0'))";
         "?q.((0''*f=x&0''*q=y)|(0''*f=x+0'&0''*q=y+0'))";
         "?q.((0''*f=x&0''*q=y)|(0''*f=x+0'&0''*q=y+0'))->?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
        ];;
let oddProve =
        ["0''*f=x'";
         "0''*g=y'";
         "@a.(a+0'=a')->(x+0'=x')";
         "x+0'=x'";
         "@a.(a+0'=a')->(y+0'=y')";
         "y+0'=y'";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=x'->c=x'->b=c)";
         "@b.@c.(b=x'->c=x'->b=c)";
         "@b.@c.(b=x'->c=x'->b=c)->@c.(0''*f=x'->c=x'->0''*f=c)";
         "@c.(0''*f=x'->c=x'->0''*f=c)";
         "@c.(0''*f=x'->c=x'->0''*f=c)->(0''*f=x'->x+0'=x'->0''*f=x+0')";
         "0''*f=x'->x+0'=x'->0''*f=x+0'";
         "x+0'=x'->0''*f=x+0'";
         "0''*f=x+0'";
         "@a.@b.@c.(b=a->c=a->b=c)->@b.@c.(b=y'->c=y'->b=c)";
         "@b.@c.(b=y'->c=y'->b=c)";
         "@b.@c.(b=y'->c=y'->b=c)->@c.(0''*g=y'->c=y'->0''*g=c)";
         "@c.(0''*g=y'->c=y'->0''*g=c)";
         "@c.(0''*g=y'->c=y'->0''*g=c)->(0''*g=y'->y+0'=y'->0''*g=y+0')";
         "0''*g=y'->y+0'=y'->0''*g=y+0'";
         "y+0'=y'->0''*g=y+0'";
         "0''*g=y+0'";
         "0''*f=x+0'->0''*g=y+0'->0''*f=x+0'&0''*g=y+0'";
         "0''*g=y+0'->0''*f=x+0'&0''*g=y+0'";
         "0''*f=x+0'&0''*g=y+0'";
         "0''*f=x+0'&0''*g=y+0'->(0''*f=x&0''*g=y)|(0''*f=x+0'&0''*g=y+0')";
         "(0''*f=x&0''*g=y)|(0''*f=x+0'&0''*g=y+0')";
         "(0''*f=x&0''*g=y)|(0''*f=x+0'&0''*g=y+0')->?q.((0''*f=x&0''*q=y)|(0''*f=x+0'&0''*q=y+0'))";
         "?q.((0''*f=x&0''*q=y)|(0''*f=x+0'&0''*q=y+0'))";
         "?q.((0''*f=x&0''*q=y)|(0''*f=x+0'&0''*q=y+0'))->?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         "?p.?q.((0''*p=x&0''*q=y)|(0''*p=x+0'&0''*q=y+0'))";
         ];;

let buildProve a b =
        let rec number a =
                if a = 0 then "0" else (number (a - 1)) ^ "'" in
        let rec numberTerm a =
                if a = 0 then Zero else Increment (numberTerm (a - 1))  in
        let rec build c a b =
                if c = 0 then [] else
                        ("@a.@b.(0''*a=b->0''*a'=b'')->@b.(0''*" ^ a ^ "=b->0''*" ^ a ^ "'=b'')") ::
                        ("@b.(0''*" ^ a ^ "=b->0''*" ^ a ^ "'=b'')") ::
                        ("@b.(0''*" ^ a ^ "=b->0''*" ^ a ^ "'=b'')->(0''*" ^ a ^ "=" ^ b ^ "->0''*" ^ a ^ "'=" ^ b ^ "'')") ::
                        ("0''*" ^ a ^ "=" ^ b ^ "->0''*" ^ a ^ "'=" ^ b ^ "''") ::
                        ("0''*" ^ a ^ "'=" ^ b ^ "''") :: (build (c - 1) (a ^ "'") (b ^ "''")) in
        let substitute e f x g y =
                let e = (transformTerm e (Var "x") (numberTerm x)) in
                let e = (transformTerm e (Var "y") (numberTerm y)) in
                let e = (transformTerm e (Var "f") (numberTerm f)) in
                let e = (transformTerm e (Var "g") (numberTerm g)) in
                e in
        let neg a b =
                let ra = number (a - 1) in
                let da = number (a / 2) in
                constructTheorem @ (build (b / 2) "0" "0") @ (build (a / 2) "0" "0") @
                        (("@a.@b.(a=b->a'=b')->@b.(0''*" ^ da ^ "=b->(0''*" ^ da ^ ")'=b')") ::
                        ("@b.(0''*" ^ da ^ "=b->(0''*" ^ da ^ ")'=b')") ::
                        ("@b.(0''*" ^ da ^ "=b->(0''*" ^ da ^ ")'=b')->(0''*" ^ da ^ "=" ^ ra ^ "->(0''*" ^ da ^ ")'=" ^ ra ^ "')") ::
                        ("0''*" ^ da ^ "=" ^ ra ^ "->(0''*" ^ da ^ ")'=" ^ ra ^ "'") ::
                        ("(0''*" ^ da ^ ")'=" ^ ra ^ "'") :: (List.map (fun x -> printExpr (substitute (parse_bad x) (a / 2) a (b / 2) b)) lastOneForNeg)) in
        let result =
                if a - 2 * (a / 2) = 1 && b - 2 * (b / 2) = 0 then
                        neg a b
                else if a - 2 * (a / 2) = 0 && b - 2 * (b / 2) = 1 then
                        (neg b a) @ [printExpr (substitute (parse_bad "!?p.?q.((0''*p=y&0''*q=x)|(0''*p=y+0'&0''*q=x+0'))") (b / 2) b (a / 2) a)]
                else if a - 2 * (a / 2) = 0 && b - 2 * (b / 2) = 0 then
                        constructTheorem @ (build (b / 2) "0" "0") @ (build (a / 2) "0" "0") @
                                (List.map (fun x -> printExpr (substitute (parse_bad x) (a / 2) a (b / 2) b)) evenProve)
                else
                        let a = a + 1 in
                        let b = b + 1 in
                        constructTheorem @ (build (b / 2) "0" "0") @ (build (a / 2) "0" "0") @
                                (List.map (fun x -> printExpr (substitute (parse_bad x) (a / 2) (a - 1) (b / 2) (b - 1))) oddProve) in
        result;;

println_string (let doc = parseList (buildProve (read_int ()) (read_int ())) in (printDocument doc)(* ^ "\n" ^ (checkProof doc)*));;