TSTP Solution File: GRP012-4 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP012-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:13:34 EDT 2023
% Result : Unsatisfiable 0.50s 0.77s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP012-4 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 02:45:59 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.50/0.77 % SZS status Unsatisfiable
% 0.50/0.77 % SZS output start Proof
% 0.50/0.77 original problem:
% 0.50/0.77 axioms:
% 0.50/0.77 multiply(identity(), X) = X
% 0.50/0.77 multiply(inverse(X), X) = identity()
% 0.50/0.77 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.50/0.77 multiply(X, identity()) = X
% 0.50/0.77 multiply(X, inverse(X)) = identity()
% 0.50/0.77 goal:
% 0.50/0.77 inverse(multiply(a(), b())) != multiply(inverse(b()), inverse(a()))
% 0.50/0.77 To show the unsatisfiability of the original goal,
% 0.50/0.77 it suffices to show that inverse(multiply(a(), b())) = multiply(inverse(b()), inverse(a())) (skolemized goal) is valid under the axioms.
% 0.50/0.77 Here is an equational proof:
% 0.50/0.77 0: multiply(identity(), X0) = X0.
% 0.50/0.77 Proof: Axiom.
% 0.50/0.77
% 0.50/0.77 1: multiply(inverse(X0), X0) = identity().
% 0.50/0.77 Proof: Axiom.
% 0.50/0.77
% 0.50/0.77 2: multiply(multiply(X0, X1), X2) = multiply(X0, multiply(X1, X2)).
% 0.50/0.77 Proof: Axiom.
% 0.50/0.77
% 0.50/0.77 3: multiply(X0, identity()) = X0.
% 0.50/0.77 Proof: Axiom.
% 0.50/0.77
% 0.50/0.77 4: multiply(X0, inverse(X0)) = identity().
% 0.50/0.77 Proof: Axiom.
% 0.50/0.77
% 0.50/0.77 6: multiply(inverse(X3), multiply(X3, X2)) = multiply(identity(), X2).
% 0.50/0.77 Proof: A critical pair between equations 2 and 1.
% 0.50/0.77
% 0.50/0.77 8: multiply(X0, multiply(X1, inverse(multiply(X0, X1)))) = identity().
% 0.50/0.77 Proof: A critical pair between equations 2 and 4.
% 0.50/0.77
% 0.50/0.77 10: multiply(inverse(X3), multiply(X3, X2)) = X2.
% 0.50/0.77 Proof: Rewrite equation 6,
% 0.50/0.77 lhs with equations []
% 0.50/0.77 rhs with equations [0].
% 0.50/0.77
% 0.50/0.77 15: multiply(X5, inverse(multiply(X4, X5))) = multiply(inverse(X4), identity()).
% 0.50/0.77 Proof: A critical pair between equations 10 and 8.
% 0.50/0.77
% 0.50/0.77 22: multiply(X5, inverse(multiply(X4, X5))) = inverse(X4).
% 0.50/0.77 Proof: Rewrite equation 15,
% 0.50/0.77 lhs with equations []
% 0.50/0.77 rhs with equations [3].
% 0.50/0.77
% 0.50/0.77 24: inverse(multiply(X7, X6)) = multiply(inverse(X6), inverse(X7)).
% 0.50/0.77 Proof: A critical pair between equations 10 and 22.
% 0.50/0.77
% 0.50/0.77 36: inverse(multiply(a(), b())) = multiply(inverse(b()), inverse(a())).
% 0.50/0.77 Proof: Rewrite lhs with equations [24]
% 0.50/0.77 rhs with equations [].
% 0.50/0.77
% 0.50/0.77 % SZS output end Proof
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