TSTP Solution File: GRP515-1 by Twee---2.5.0
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%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : GRP515-1 : TPTP v8.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n020.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 07:12:38 EDT 2024
% Result : Unsatisfiable 0.12s 0.31s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GRP515-1 : TPTP v8.2.0. Released v2.6.0.
% 0.00/0.08 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.07/0.27 % Computer : n020.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Thu Jun 20 10:16:53 EDT 2024
% 0.07/0.27 % CPUTime :
% 0.12/0.31 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.12/0.31
% 0.12/0.31 % SZS status Unsatisfiable
% 0.12/0.31
% 0.12/0.32 % SZS output start Proof
% 0.12/0.32 Axiom 1 (single_axiom): multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))) = Y.
% 0.12/0.32
% 0.12/0.32 Lemma 2: multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z))))))) = W.
% 0.12/0.32 Proof:
% 0.12/0.32 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.12/0.32 = { by axiom 1 (single_axiom) R->L }
% 0.12/0.32 multiply(X, multiply(multiply(W, multiply(multiply(Y, Z), inverse(multiply(W, Z)))), inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.12/0.32 = { by axiom 1 (single_axiom) }
% 0.12/0.32 W
% 0.12/0.32
% 0.12/0.32 Lemma 3: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.12/0.32 Proof:
% 0.12/0.32 multiply(X, multiply(Y, inverse(Y)))
% 0.12/0.32 = { by axiom 1 (single_axiom) R->L }
% 0.12/0.32 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))))))
% 0.12/0.32 = { by lemma 2 }
% 0.12/0.32 X
% 0.12/0.32
% 0.12/0.32 Lemma 4: multiply(X, multiply(Y, inverse(X))) = Y.
% 0.12/0.32 Proof:
% 0.12/0.32 multiply(X, multiply(Y, inverse(X)))
% 0.12/0.32 = { by lemma 3 R->L }
% 0.12/0.32 multiply(X, multiply(Y, inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.12/0.32 = { by lemma 3 R->L }
% 0.12/0.32 multiply(X, multiply(multiply(Y, multiply(Z, inverse(Z))), inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.12/0.32 = { by axiom 1 (single_axiom) }
% 0.12/0.32 Y
% 0.12/0.32
% 0.12/0.32 Lemma 5: multiply(multiply(X, Y), multiply(Z, inverse(X))) = multiply(Z, Y).
% 0.12/0.32 Proof:
% 0.12/0.32 multiply(multiply(X, Y), multiply(Z, inverse(X)))
% 0.12/0.32 = { by lemma 2 R->L }
% 0.12/0.32 multiply(multiply(X, Y), multiply(Z, inverse(multiply(multiply(X, Y), multiply(multiply(Z, Y), inverse(multiply(multiply(X, Y), multiply(multiply(multiply(Z, Y), Y), inverse(multiply(X, Y))))))))))
% 0.12/0.32 = { by lemma 4 }
% 0.12/0.32 multiply(multiply(X, Y), multiply(Z, inverse(multiply(multiply(X, Y), multiply(multiply(Z, Y), inverse(multiply(multiply(Z, Y), Y)))))))
% 0.12/0.32 = { by lemma 2 }
% 0.12/0.32 multiply(Z, Y)
% 0.12/0.32
% 0.12/0.32 Lemma 6: multiply(multiply(X, Y), Z) = multiply(multiply(X, Z), Y).
% 0.12/0.32 Proof:
% 0.12/0.32 multiply(multiply(X, Y), Z)
% 0.12/0.32 = { by lemma 5 R->L }
% 0.12/0.32 multiply(multiply(X, Z), multiply(multiply(X, Y), inverse(X)))
% 0.12/0.32 = { by axiom 1 (single_axiom) R->L }
% 0.12/0.32 multiply(multiply(X, Z), multiply(multiply(X, Y), inverse(multiply(multiply(X, Z), multiply(multiply(X, Y), inverse(multiply(multiply(X, Z), Y)))))))
% 0.12/0.32 = { by lemma 3 R->L }
% 0.12/0.32 multiply(multiply(X, Z), multiply(multiply(X, Y), inverse(multiply(multiply(X, Z), multiply(multiply(X, Y), inverse(multiply(multiply(multiply(X, Z), Y), multiply(W, inverse(W)))))))))
% 0.12/0.32 = { by lemma 3 R->L }
% 0.12/0.32 multiply(multiply(X, Z), multiply(multiply(X, Y), inverse(multiply(multiply(X, Z), multiply(multiply(multiply(X, Y), multiply(W, inverse(W))), inverse(multiply(multiply(multiply(X, Z), Y), multiply(W, inverse(W)))))))))
% 0.12/0.32 = { by lemma 2 }
% 0.12/0.32 multiply(multiply(X, Z), Y)
% 0.12/0.32
% 0.12/0.32 Lemma 7: multiply(X, inverse(multiply(Y, inverse(Y)))) = X.
% 0.12/0.32 Proof:
% 0.12/0.32 multiply(X, inverse(multiply(Y, inverse(Y))))
% 0.12/0.32 = { by lemma 4 R->L }
% 0.12/0.32 multiply(Y, multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), inverse(Y)))
% 0.12/0.32 = { by lemma 6 }
% 0.12/0.32 multiply(Y, multiply(multiply(X, inverse(Y)), inverse(multiply(Y, inverse(Y)))))
% 0.12/0.32 = { by axiom 1 (single_axiom) }
% 0.12/0.32 X
% 0.12/0.32
% 0.12/0.32 Lemma 8: multiply(Y, X) = multiply(X, Y).
% 0.12/0.32 Proof:
% 0.12/0.32 multiply(Y, X)
% 0.12/0.32 = { by lemma 7 R->L }
% 0.12/0.32 multiply(Y, multiply(X, inverse(multiply(Z, inverse(Z)))))
% 0.12/0.32 = { by lemma 5 R->L }
% 0.12/0.32 multiply(multiply(multiply(Z, inverse(Z)), multiply(X, inverse(multiply(Z, inverse(Z))))), multiply(Y, inverse(multiply(Z, inverse(Z)))))
% 0.12/0.32 = { by lemma 4 }
% 0.12/0.32 multiply(X, multiply(Y, inverse(multiply(Z, inverse(Z)))))
% 0.12/0.32 = { by lemma 7 }
% 0.12/0.32 multiply(X, Y)
% 0.12/0.32
% 0.12/0.32 Lemma 9: multiply(X, multiply(Y, Z)) = multiply(Z, multiply(Y, X)).
% 0.12/0.32 Proof:
% 0.12/0.32 multiply(X, multiply(Y, Z))
% 0.12/0.32 = { by lemma 8 }
% 0.12/0.32 multiply(multiply(Y, Z), X)
% 0.12/0.32 = { by lemma 6 R->L }
% 0.12/0.32 multiply(multiply(Y, X), Z)
% 0.12/0.32 = { by lemma 8 R->L }
% 0.12/0.32 multiply(Z, multiply(Y, X))
% 0.12/0.32
% 0.12/0.32 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.12/0.32 Proof:
% 0.12/0.32 multiply(multiply(a3, b3), c3)
% 0.12/0.32 = { by lemma 8 R->L }
% 0.12/0.32 multiply(c3, multiply(a3, b3))
% 0.12/0.32 = { by lemma 9 }
% 0.12/0.32 multiply(b3, multiply(a3, c3))
% 0.12/0.32 = { by lemma 8 }
% 0.12/0.32 multiply(b3, multiply(c3, a3))
% 0.12/0.32 = { by lemma 9 }
% 0.12/0.32 multiply(a3, multiply(c3, b3))
% 0.12/0.32 = { by lemma 8 R->L }
% 0.12/0.32 multiply(a3, multiply(b3, c3))
% 0.12/0.32 % SZS output end Proof
% 0.12/0.32
% 0.12/0.32 RESULT: Unsatisfiable (the axioms are contradictory).
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