Given a formula f and a clause a in CNF(-f), PCNF computes a proof of s o a (see logic.at/ceres for the definition of o) Note about checking containment up to variables renaming: we compute the variable renaming from the lk proof to the resolution proof for a specific clause.
Given a formula f and a clause a in CNF(-f), PCNF computes a proof of s o a (see logic.at/ceres for the definition of o) Note about checking containment up to variables renaming: we compute the variable renaming from the lk proof to the resolution proof for a specific clause. We cannot apply it to the formula in s as it might be quantified over this variables so we apply it to the resulted lk proof. We must apply it as otherwise the substitution in the resolution to lk transformation will not be applied to these clauses. In the weakenings application at the end of this method we try to apply it to the formulas as well as if it is quantified over these variables, it will be also quantified in the proof so no damage done.
Eliminates the insantiate rule from a RobinsonResolutionProof
Created by marty on 9/9/14.
Sometimes, we have a resolution refutation R of a set of clauses C and want a refutation R' of a set C' such that C implies C'.
Sometimes, we have a resolution refutation R of a set of clauses C and want a refutation R' of a set C' such that C implies C'.
This algorithm tries to obtain R' by trying to replace clauses c from C in R by derivations of C from C' in the following way:
If none of this works, we issue a warning and keep the clause c. If no warning is issued and the algorithm terminates, the result is the desired R'.
In general, if R is a derivation of a clause c, the result R' of fixDerivation(R) is a derivation of a subclause of c.
Applies a function to each initial clause in a resolution proof, replacing the initial clause with a new proof.
Applies a function to each initial clause in a resolution proof, replacing the initial clause with a new proof. The resulting proof may prove a smaller clause than the original one.
Created by sebastian on 7/13/15.