TSTP Solution File: GRP010-4 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP010-4 : 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 01:13:33 EDT 2023
% Result : Unsatisfiable 0.21s 0.58s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP010-4 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.14 % Command : toma --casc %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 20:08:59 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 % SZS status Unsatisfiable
% 0.21/0.58 % SZS output start Proof
% 0.21/0.58 original problem:
% 0.21/0.58 axioms:
% 0.21/0.58 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.21/0.58 multiply(identity(), X) = X
% 0.21/0.58 multiply(inverse(X), X) = identity()
% 0.21/0.58 multiply(c(), b()) = identity()
% 0.21/0.58 goal:
% 0.21/0.58 multiply(b(), c()) != identity()
% 0.21/0.58 To show the unsatisfiability of the original goal,
% 0.21/0.58 it suffices to show that multiply(b(), c()) = identity() (skolemized goal) is valid under the axioms.
% 0.21/0.58 Here is an equational proof:
% 0.21/0.58 0: multiply(multiply(X0, X1), X2) = multiply(X0, multiply(X1, X2)).
% 0.21/0.58 Proof: Axiom.
% 0.21/0.58
% 0.21/0.58 1: multiply(identity(), X0) = X0.
% 0.21/0.58 Proof: Axiom.
% 0.21/0.58
% 0.21/0.58 2: multiply(inverse(X0), X0) = identity().
% 0.21/0.58 Proof: Axiom.
% 0.21/0.58
% 0.21/0.58 3: multiply(c(), b()) = identity().
% 0.21/0.58 Proof: Axiom.
% 0.21/0.58
% 0.21/0.58 5: multiply(inverse(X3), multiply(X3, X2)) = multiply(identity(), X2).
% 0.21/0.58 Proof: A critical pair between equations 0 and 2.
% 0.21/0.58
% 0.21/0.58 6: multiply(inverse(X3), multiply(X3, X2)) = X2.
% 0.21/0.58 Proof: Rewrite equation 5,
% 0.21/0.58 lhs with equations []
% 0.21/0.58 rhs with equations [1].
% 0.21/0.58
% 0.21/0.58 8: b() = multiply(inverse(c()), identity()).
% 0.21/0.58 Proof: A critical pair between equations 6 and 3.
% 0.21/0.58
% 0.21/0.58 10: X4 = multiply(inverse(inverse(X4)), identity()).
% 0.21/0.58 Proof: A critical pair between equations 6 and 2.
% 0.21/0.58
% 0.21/0.58 12: multiply(X4, X5) = multiply(inverse(inverse(X4)), X5).
% 0.21/0.58 Proof: A critical pair between equations 6 and 6.
% 0.21/0.58
% 0.21/0.58 14: X4 = multiply(X4, identity()).
% 0.21/0.58 Proof: Rewrite equation 10,
% 0.21/0.58 lhs with equations []
% 0.21/0.58 rhs with equations [12].
% 0.21/0.58
% 0.21/0.58 15: b() = inverse(c()).
% 0.21/0.58 Proof: Rewrite equation 8,
% 0.21/0.58 lhs with equations []
% 0.21/0.58 rhs with equations [14].
% 0.21/0.58
% 0.21/0.58 18: multiply(b(), c()) = identity().
% 0.21/0.58 Proof: Rewrite lhs with equations [15,2]
% 0.21/0.58 rhs with equations [].
% 0.21/0.58
% 0.21/0.58 % SZS output end Proof
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