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- Premises:
- (tim --> cat).
- ((&&,($1 --> cat),($1 --> [orange])) ==> ($1 <-> garfield)).
- Rule:
- (S --> M), ((&&,($1 --> M),A_1..n) ==> B), substitute($1,S) |- ((&&,A_1..n) ==> B)
- Match Process:
- P:={}, Q:={}
- MATCH Step1:
- Unify (S --> M) with (tim --> cat) under P
- => P={S -> tim, M -> cat}
- MATCH Step2:
- Unify ((&&,($1 --> M),A_1..n) ==> B) with ((&&,($1 --> cat),($1 --> [orange])) ==> ($1 <-> garfield)) under P
- => P={S -> tim, M -> cat, A_1 -> ($1 --> [orange]), B -> ($1 <-> garfield)}
- MATCH Step3:
- Satisfy substitute($1,S) by applying the subsitutions in M to substitute($1,S) leading to substitute($1,tim),
- this described substitution is now added to the substitution set Q:
- => Q={$1 -> S}
- "Construction of Conclusion" Step4:
- The match process is finished, and was satisfyable, now lets build the conclusion
- by applying at first the substitutions in P to the conclusion ((&&,A_1..n) ==> B) specified by the rule
- leading to:
- (($1 --> [orange]) ==> ($1 <-> garfield))
- now finally we apply Q to this result and get:
- ((tim --> [orange]) ==> (tim <-> garfield))
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