TSTP Solution File: GRP511-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP511-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n004.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 01:18:43 EDT 2023
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP511-1 : TPTP v8.1.2. Released v2.6.0.
% 0.06/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 23:54:07 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.37 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.18/0.37
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 Axiom 1 (single_axiom): multiply(multiply(multiply(X, Y), Z), inverse(multiply(X, Z))) = Y.
% 0.18/0.38
% 0.18/0.38 Lemma 2: multiply(X, inverse(multiply(multiply(Y, X), inverse(multiply(Y, Z))))) = Z.
% 0.18/0.38 Proof:
% 0.18/0.38 multiply(X, inverse(multiply(multiply(Y, X), inverse(multiply(Y, Z)))))
% 0.18/0.38 = { by axiom 1 (single_axiom) R->L }
% 0.18/0.38 multiply(multiply(multiply(multiply(Y, X), Z), inverse(multiply(Y, Z))), inverse(multiply(multiply(Y, X), inverse(multiply(Y, Z)))))
% 0.18/0.38 = { by axiom 1 (single_axiom) }
% 0.18/0.38 Z
% 0.18/0.38
% 0.18/0.38 Lemma 3: inverse(multiply(multiply(X, Y), inverse(multiply(X, Z)))) = multiply(multiply(Z, W), inverse(multiply(Y, W))).
% 0.18/0.38 Proof:
% 0.18/0.38 inverse(multiply(multiply(X, Y), inverse(multiply(X, Z))))
% 0.18/0.38 = { by axiom 1 (single_axiom) R->L }
% 0.18/0.38 multiply(multiply(multiply(Y, inverse(multiply(multiply(X, Y), inverse(multiply(X, Z))))), W), inverse(multiply(Y, W)))
% 0.18/0.38 = { by lemma 2 }
% 0.18/0.38 multiply(multiply(Z, W), inverse(multiply(Y, W)))
% 0.18/0.38
% 0.18/0.38 Lemma 4: multiply(X, multiply(multiply(Y, Z), inverse(multiply(Y, Z)))) = X.
% 0.18/0.38 Proof:
% 0.18/0.38 multiply(X, multiply(multiply(Y, Z), inverse(multiply(Y, Z))))
% 0.18/0.38 = { by lemma 3 R->L }
% 0.18/0.38 multiply(X, inverse(multiply(multiply(W, Y), inverse(multiply(W, Y)))))
% 0.18/0.38 = { by lemma 2 R->L }
% 0.18/0.38 multiply(X, inverse(multiply(multiply(multiply(W, inverse(multiply(multiply(V, W), inverse(multiply(V, W))))), Y), inverse(multiply(W, Y)))))
% 0.18/0.38 = { by axiom 1 (single_axiom) }
% 0.18/0.38 multiply(X, inverse(inverse(multiply(multiply(V, W), inverse(multiply(V, W))))))
% 0.18/0.38 = { by axiom 1 (single_axiom) R->L }
% 0.18/0.38 multiply(X, inverse(multiply(multiply(multiply(W, inverse(multiply(multiply(V, W), inverse(multiply(V, W))))), X), inverse(multiply(W, X)))))
% 0.18/0.38 = { by lemma 2 }
% 0.18/0.38 multiply(X, inverse(multiply(multiply(W, X), inverse(multiply(W, X)))))
% 0.18/0.38 = { by lemma 2 }
% 0.18/0.38 X
% 0.18/0.38
% 0.18/0.38 Lemma 5: multiply(multiply(X, Y), inverse(X)) = Y.
% 0.18/0.38 Proof:
% 0.18/0.38 multiply(multiply(X, Y), inverse(X))
% 0.18/0.38 = { by lemma 4 R->L }
% 0.18/0.38 multiply(multiply(X, Y), inverse(multiply(X, multiply(multiply(Z, W), inverse(multiply(Z, W))))))
% 0.18/0.38 = { by lemma 4 R->L }
% 0.18/0.38 multiply(multiply(multiply(X, Y), multiply(multiply(Z, W), inverse(multiply(Z, W)))), inverse(multiply(X, multiply(multiply(Z, W), inverse(multiply(Z, W))))))
% 0.18/0.38 = { by axiom 1 (single_axiom) }
% 0.18/0.38 Y
% 0.18/0.38
% 0.18/0.38 Lemma 6: multiply(X, multiply(Y, inverse(X))) = Y.
% 0.18/0.38 Proof:
% 0.18/0.38 multiply(X, multiply(Y, inverse(X)))
% 0.18/0.38 = { by lemma 4 R->L }
% 0.18/0.38 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Z, W), inverse(multiply(Z, W)))))))
% 0.18/0.38 = { by lemma 4 R->L }
% 0.18/0.38 multiply(X, multiply(multiply(Y, multiply(multiply(Z, W), inverse(multiply(Z, W)))), inverse(multiply(X, multiply(multiply(Z, W), inverse(multiply(Z, W)))))))
% 0.18/0.38 = { by lemma 3 R->L }
% 0.18/0.38 multiply(X, inverse(multiply(multiply(V, X), inverse(multiply(V, Y)))))
% 0.18/0.38 = { by axiom 1 (single_axiom) R->L }
% 0.18/0.38 multiply(multiply(multiply(multiply(V, X), inverse(multiply(V, Y))), inverse(multiply(V, inverse(multiply(V, Y))))), inverse(multiply(multiply(V, X), inverse(multiply(V, Y)))))
% 0.18/0.38 = { by lemma 5 }
% 0.18/0.38 inverse(multiply(V, inverse(multiply(V, Y))))
% 0.18/0.38 = { by lemma 5 R->L }
% 0.18/0.38 multiply(multiply(multiply(multiply(V, inverse(multiply(V, Y))), inverse(multiply(V, Y))), inverse(multiply(V, inverse(multiply(V, Y))))), inverse(multiply(multiply(V, inverse(multiply(V, Y))), inverse(multiply(V, Y)))))
% 0.18/0.38 = { by lemma 5 }
% 0.18/0.38 multiply(inverse(multiply(V, Y)), inverse(multiply(multiply(V, inverse(multiply(V, Y))), inverse(multiply(V, Y)))))
% 0.18/0.38 = { by lemma 2 }
% 0.18/0.38 Y
% 0.18/0.38
% 0.18/0.38 Lemma 7: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.18/0.38 Proof:
% 0.18/0.38 multiply(multiply(X, inverse(X)), Y)
% 0.18/0.38 = { by axiom 1 (single_axiom) R->L }
% 0.18/0.38 multiply(multiply(multiply(X, multiply(multiply(X, inverse(X)), Y)), inverse(X)), inverse(multiply(X, inverse(X))))
% 0.18/0.38 = { by lemma 5 }
% 0.18/0.38 multiply(multiply(multiply(X, inverse(X)), Y), inverse(multiply(X, inverse(X))))
% 0.18/0.38 = { by lemma 5 }
% 0.18/0.38 Y
% 0.18/0.38
% 0.18/0.38 Lemma 8: multiply(X, Y) = multiply(Y, X).
% 0.18/0.38 Proof:
% 0.18/0.38 multiply(X, Y)
% 0.18/0.38 = { by lemma 6 R->L }
% 0.18/0.38 multiply(Y, multiply(multiply(X, Y), inverse(Y)))
% 0.18/0.38 = { by lemma 7 R->L }
% 0.18/0.38 multiply(Y, multiply(multiply(multiply(multiply(Z, inverse(Z)), X), Y), inverse(Y)))
% 0.18/0.38 = { by lemma 7 R->L }
% 0.18/0.38 multiply(Y, multiply(multiply(multiply(multiply(Z, inverse(Z)), X), Y), inverse(multiply(multiply(Z, inverse(Z)), Y))))
% 0.18/0.38 = { by axiom 1 (single_axiom) }
% 0.18/0.38 multiply(Y, X)
% 0.18/0.38
% 0.18/0.38 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.18/0.38 Proof:
% 0.18/0.38 multiply(multiply(a3, b3), c3)
% 0.18/0.38 = { by lemma 8 }
% 0.18/0.38 multiply(c3, multiply(a3, b3))
% 0.18/0.38 = { by lemma 8 R->L }
% 0.18/0.38 multiply(c3, multiply(b3, a3))
% 0.18/0.38 = { by lemma 8 R->L }
% 0.18/0.38 multiply(multiply(b3, a3), c3)
% 0.18/0.38 = { by lemma 6 R->L }
% 0.18/0.38 multiply(multiply(b3, c3), multiply(multiply(multiply(b3, a3), c3), inverse(multiply(b3, c3))))
% 0.18/0.38 = { by axiom 1 (single_axiom) }
% 0.18/0.38 multiply(multiply(b3, c3), a3)
% 0.18/0.38 = { by lemma 8 }
% 0.18/0.38 multiply(a3, multiply(b3, c3))
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38
% 0.18/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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