TSTP Solution File: GRP418-1 by Twee---2.5.0
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% File : Twee---2.5.0
% Problem : GRP418-1 : TPTP v8.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 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 : Mon Jun 24 07:12:17 EDT 2024
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP418-1 : TPTP v8.2.0. Released v2.6.0.
% 0.07/0.12 % Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 20 12:26:54 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.40 Command-line arguments: --no-flatten-goal
% 0.13/0.40
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Axiom 1 (single_axiom): inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))) = Y.
% 0.19/0.41
% 0.19/0.41 Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y)) = W.
% 0.19/0.41 Proof:
% 0.19/0.41 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(Y), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 W
% 0.19/0.41
% 0.19/0.41 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(inverse(a1), a1)
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))))), multiply(X, Y)))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(a1)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W))), a1)), inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))))), multiply(X, Y)))
% 0.19/0.42 = { by lemma 2 R->L }
% 0.19/0.42 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(a1)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(inverse(inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), inverse(multiply(inverse(multiply(Z, W)), inverse(multiply(multiply(V, U), inverse(multiply(inverse(multiply(V, U)), multiply(V, U))))))))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))))), a1)), inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))))), multiply(X, Y)))
% 0.19/0.42 = { by lemma 2 }
% 0.19/0.42 inverse(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(V, inverse(multiply(inverse(inverse(inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), inverse(multiply(inverse(multiply(Z, W)), inverse(multiply(multiply(V, U), inverse(multiply(inverse(multiply(V, U)), multiply(V, U)))))))), inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))))), multiply(X, Y)))
% 0.19/0.42 = { by lemma 2 R->L }
% 0.19/0.42 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(b1)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(inverse(inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), inverse(multiply(inverse(multiply(Z, W)), inverse(multiply(multiply(V, U), inverse(multiply(inverse(multiply(V, U)), multiply(V, U))))))))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))))), b1)), inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))))), multiply(X, Y)))
% 0.19/0.42 = { by lemma 2 }
% 0.19/0.42 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(b1)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W))), b1)), inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))))), multiply(X, Y)))
% 0.19/0.42 = { by axiom 1 (single_axiom) }
% 0.19/0.42 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))))), multiply(X, Y)))
% 0.19/0.42 = { by axiom 1 (single_axiom) }
% 0.19/0.42 multiply(inverse(b1), b1)
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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