[PHP-CLI] Basic first-order logic on finite sets checker

<?php

function forall($x="@",$set=[],$statement) {
    $str = "true";
    for ($i = 0; $i < count($set); $i++) {
        $str .= " & (".str_replace($x,$set[$i],$statement).")";
    }
    return "($str)";
}
function exists($x="@",$set=[],$statement) {
    $str = "false";
    for ($i = 0; $i < count($set); $i++) {
        $str .= " || (".str_replace($x,$set[$i],$statement).")";
    }
    return "($str)";
}
function implies($statement1,$statement2) {
    $str = "(($statement1) || !($statement2))";
    return $str;
}
function verify($statement) {
    eval("\$st = ($statement);");
    return $st;
}

//Example
print verify(forall("x",[1,2,4,8,16],implies("(x+1)%2==0","x==1"))); //Checks that ∀ x ∈ {1,2,4,8,16} (x+1 ≡ 0 (mod 2) => x=1)

?>