TSTP Solution File: GRP001-4 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP001-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n001.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 01:13:30 EDT 2023
% Result : Unsatisfiable 0.20s 0.69s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP001-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 01:34:51 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.69 % SZS status Unsatisfiable
% 0.20/0.69 % SZS output start Proof
% 0.20/0.69 original problem:
% 0.20/0.69 axioms:
% 0.20/0.69 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.20/0.69 multiply(identity(), X) = X
% 0.20/0.69 multiply(X, X) = identity()
% 0.20/0.69 multiply(a(), b()) = c()
% 0.20/0.69 goal:
% 0.20/0.69 multiply(b(), a()) != c()
% 0.20/0.69 To show the unsatisfiability of the original goal,
% 0.20/0.69 it suffices to show that multiply(b(), a()) = c() (skolemized goal) is valid under the axioms.
% 0.20/0.69 Here is an equational proof:
% 0.20/0.69 0: multiply(multiply(X0, X1), X2) = multiply(X0, multiply(X1, X2)).
% 0.20/0.69 Proof: Axiom.
% 0.20/0.69
% 0.20/0.69 1: multiply(identity(), X0) = X0.
% 0.20/0.69 Proof: Axiom.
% 0.20/0.69
% 0.20/0.69 2: multiply(X0, X0) = identity().
% 0.20/0.69 Proof: Axiom.
% 0.20/0.69
% 0.20/0.69 3: multiply(a(), b()) = c().
% 0.20/0.69 Proof: Axiom.
% 0.20/0.69
% 0.20/0.69 4: multiply(X3, multiply(X3, X2)) = multiply(identity(), X2).
% 0.20/0.69 Proof: A critical pair between equations 0 and 2.
% 0.20/0.69
% 0.20/0.69 5: multiply(X0, multiply(X1, multiply(X0, X1))) = identity().
% 0.20/0.69 Proof: A critical pair between equations 0 and 2.
% 0.20/0.69
% 0.20/0.69 7: multiply(X3, multiply(X3, X2)) = X2.
% 0.20/0.69 Proof: Rewrite equation 4,
% 0.20/0.69 lhs with equations []
% 0.20/0.69 rhs with equations [1].
% 0.20/0.69
% 0.20/0.69 8: X4 = multiply(X4, identity()).
% 0.20/0.69 Proof: A critical pair between equations 7 and 2.
% 0.20/0.69
% 0.20/0.69 9: multiply(X5, multiply(X4, X5)) = multiply(X4, identity()).
% 0.20/0.69 Proof: A critical pair between equations 7 and 5.
% 0.20/0.69
% 0.20/0.69 18: multiply(X5, multiply(X4, X5)) = X4.
% 0.20/0.69 Proof: Rewrite equation 9,
% 0.20/0.69 lhs with equations []
% 0.20/0.69 rhs with equations [8].
% 0.20/0.69
% 0.20/0.69 19: b() = multiply(a(), c()).
% 0.20/0.69 Proof: A critical pair between equations 7 and 3.
% 0.20/0.69
% 0.20/0.69 21: multiply(X7, X6) = multiply(X6, X7).
% 0.20/0.69 Proof: A critical pair between equations 7 and 18.
% 0.20/0.69
% 0.20/0.69 31: b() = multiply(c(), a()).
% 0.20/0.69 Proof: Rewrite equation 19,
% 0.20/0.69 lhs with equations []
% 0.20/0.69 rhs with equations [21].
% 0.20/0.69
% 0.20/0.69 33: multiply(b(), a()) = c().
% 0.20/0.69 Proof: Rewrite lhs with equations [31,0,2,8]
% 0.20/0.69 rhs with equations [].
% 0.20/0.69
% 0.20/0.69 % SZS output end Proof
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