TSTP Solution File: GRP516-1 by Twee---2.5.0
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%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : GRP516-1 : TPTP v8.2.0. Bugfixed v2.7.0.
% 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 : n027.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 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP516-1 : TPTP v8.2.0. Bugfixed v2.7.0.
% 0.07/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 20 08:32:39 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.12/0.39
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Axiom 1 (single_axiom): multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))) = Y.
% 0.19/0.40
% 0.19/0.40 Lemma 2: multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z))))))) = W.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.19/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.40 multiply(X, multiply(multiply(W, multiply(multiply(Y, Z), inverse(multiply(W, Z)))), inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.19/0.40 = { by axiom 1 (single_axiom) }
% 0.19/0.40 W
% 0.19/0.40
% 0.19/0.40 Lemma 3: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, multiply(Y, inverse(Y)))
% 0.19/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.40 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))))))
% 0.19/0.40 = { by lemma 2 }
% 0.19/0.40 X
% 0.19/0.40
% 0.19/0.40 Lemma 4: multiply(X, multiply(Y, inverse(X))) = Y.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, multiply(Y, inverse(X)))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 multiply(X, multiply(Y, inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 multiply(X, multiply(multiply(Y, multiply(Z, inverse(Z))), inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.19/0.40 = { by axiom 1 (single_axiom) }
% 0.19/0.40 Y
% 0.19/0.40
% 0.19/0.40 Lemma 5: multiply(multiply(X, Y), multiply(Z, inverse(X))) = multiply(Z, Y).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(multiply(X, Y), multiply(Z, inverse(X)))
% 0.19/0.40 = { by lemma 2 R->L }
% 0.19/0.40 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))))))))))
% 0.19/0.40 = { by lemma 4 }
% 0.19/0.40 multiply(multiply(X, Y), multiply(Z, inverse(multiply(multiply(X, Y), multiply(multiply(Z, Y), inverse(multiply(multiply(Z, Y), Y)))))))
% 0.19/0.40 = { by lemma 2 }
% 0.19/0.40 multiply(Z, Y)
% 0.19/0.40
% 0.19/0.40 Lemma 6: multiply(X, inverse(multiply(Y, inverse(Y)))) = X.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, inverse(multiply(Y, inverse(Y))))
% 0.19/0.40 = { by lemma 4 R->L }
% 0.19/0.40 multiply(Y, multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), inverse(Y)))
% 0.19/0.40 = { by lemma 5 R->L }
% 0.19/0.40 multiply(Y, multiply(multiply(X, inverse(Y)), multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), inverse(X))))
% 0.19/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.40 multiply(Y, multiply(multiply(X, inverse(Y)), multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), inverse(multiply(multiply(X, inverse(Y)), multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), inverse(multiply(multiply(X, inverse(Y)), inverse(multiply(Y, inverse(Y)))))))))))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 multiply(Y, multiply(multiply(X, inverse(Y)), multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), inverse(multiply(multiply(X, inverse(Y)), multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), inverse(multiply(multiply(multiply(X, inverse(Y)), inverse(multiply(Y, inverse(Y)))), multiply(Z, inverse(Z))))))))))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 multiply(Y, multiply(multiply(X, inverse(Y)), multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), inverse(multiply(multiply(X, inverse(Y)), multiply(multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), multiply(Z, inverse(Z))), inverse(multiply(multiply(multiply(X, inverse(Y)), inverse(multiply(Y, inverse(Y)))), multiply(Z, inverse(Z))))))))))
% 0.19/0.40 = { by lemma 2 }
% 0.19/0.40 multiply(Y, multiply(multiply(X, inverse(Y)), inverse(multiply(Y, inverse(Y)))))
% 0.19/0.40 = { by axiom 1 (single_axiom) }
% 0.19/0.40 X
% 0.19/0.40
% 0.19/0.40 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(a, b)
% 0.19/0.40 = { by lemma 6 R->L }
% 0.19/0.40 multiply(a, multiply(b, inverse(multiply(X, inverse(X)))))
% 0.19/0.40 = { by lemma 5 R->L }
% 0.19/0.40 multiply(multiply(multiply(X, inverse(X)), multiply(b, inverse(multiply(X, inverse(X))))), multiply(a, inverse(multiply(X, inverse(X)))))
% 0.19/0.40 = { by lemma 4 }
% 0.19/0.40 multiply(b, multiply(a, inverse(multiply(X, inverse(X)))))
% 0.19/0.40 = { by lemma 6 }
% 0.19/0.40 multiply(b, a)
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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