TSTP Solution File: GRP404-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP404-1 : 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 : n015.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 01:18:17 EDT 2023
% Result : Unsatisfiable 0.21s 0.50s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP404-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 00:19:40 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.50 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.50
% 0.21/0.50 % SZS status Unsatisfiable
% 0.21/0.50
% 0.21/0.52 % SZS output start Proof
% 0.21/0.52 Axiom 1 (single_axiom): multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), inverse(multiply(Y, multiply(inverse(Y), Y)))))) = Z.
% 0.21/0.52
% 0.21/0.52 Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))) = multiply(X, inverse(multiply(inverse(W), inverse(multiply(Y, multiply(inverse(Y), Y)))))).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z)))))
% 0.21/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.53 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.53 = { by axiom 1 (single_axiom) }
% 0.21/0.53 multiply(X, inverse(multiply(inverse(W), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.53
% 0.21/0.53 Lemma 3: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), inverse(multiply(Z, multiply(inverse(Z), Z))))) = W.
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), inverse(multiply(Z, multiply(inverse(Z), Z)))))
% 0.21/0.53 = { by lemma 2 }
% 0.21/0.53 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.53 = { by axiom 1 (single_axiom) }
% 0.21/0.53 W
% 0.21/0.53
% 0.21/0.53 Lemma 4: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), inverse(multiply(Y, multiply(inverse(Y), Y))))) = Z.
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 0.21/0.53 = { by lemma 3 R->L }
% 0.21/0.53 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 0.21/0.53 = { by lemma 3 R->L }
% 0.21/0.53 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 Z
% 0.21/0.53
% 0.21/0.53 Lemma 5: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), inverse(multiply(Y, multiply(inverse(Y), Y))))))) = Z.
% 0.21/0.53 Proof:
% 0.21/0.53 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), inverse(multiply(Y, multiply(inverse(Y), Y)))))))
% 0.21/0.53 = { by lemma 2 R->L }
% 0.21/0.53 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z)), inverse(multiply(W, multiply(inverse(W), W))))))
% 0.21/0.53 = { by axiom 1 (single_axiom) }
% 0.21/0.53 Z
% 0.21/0.53
% 0.21/0.53 Lemma 6: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y)))) = Z.
% 0.21/0.53 Proof:
% 0.21/0.53 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y))))
% 0.21/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.53 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y))))), inverse(multiply(multiply(X, inverse(Z)), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))))))
% 0.21/0.53 = { by lemma 4 }
% 0.21/0.53 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(Z), inverse(multiply(multiply(X, inverse(Z)), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))))))
% 0.21/0.53 = { by lemma 5 }
% 0.21/0.53 Z
% 0.21/0.53
% 0.21/0.53 Lemma 7: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.21/0.53 Proof:
% 0.21/0.53 multiply(inverse(Y), Y)
% 0.21/0.53 = { by lemma 6 R->L }
% 0.21/0.53 multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), V)), multiply(inverse(multiply(U, T)), inverse(Y)))), inverse(multiply(V, multiply(inverse(V), V)))))
% 0.21/0.53 = { by lemma 3 R->L }
% 0.21/0.53 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), V)), multiply(inverse(multiply(U, T)), inverse(Y)))), inverse(multiply(V, multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), V)), multiply(inverse(multiply(U, T)), inverse(Y)))), inverse(multiply(V, multiply(inverse(V), V)))))
% 0.21/0.53 = { by lemma 4 R->L }
% 0.21/0.53 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), V)), multiply(inverse(multiply(U, T)), inverse(Y)))), inverse(multiply(V, multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), V)), multiply(inverse(multiply(U, T)), inverse(Y)))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), multiply(inverse(multiply(Z, W)), inverse(X)))), inverse(multiply(V, multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), multiply(inverse(multiply(Z, W)), inverse(X)))), inverse(multiply(V, multiply(inverse(V), V)))))), inverse(multiply(inverse(multiply(V, multiply(inverse(V), V))), multiply(inverse(inverse(multiply(V, multiply(inverse(V), V)))), inverse(multiply(V, multiply(inverse(V), V))))))))))
% 0.21/0.53 = { by lemma 5 }
% 0.21/0.53 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), multiply(inverse(multiply(Z, W)), inverse(X)))), inverse(multiply(V, multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), multiply(inverse(multiply(Z, W)), inverse(X)))), inverse(multiply(V, multiply(inverse(V), V)))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), multiply(inverse(multiply(Z, W)), inverse(X)))), inverse(multiply(V, multiply(inverse(V), V)))))
% 0.21/0.53 = { by lemma 6 }
% 0.21/0.53 multiply(inverse(X), X)
% 0.21/0.53
% 0.21/0.53 Lemma 8: inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(Y, multiply(inverse(Z), Z))))) = Y.
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(Y, multiply(inverse(Z), Z)))))
% 0.21/0.53 = { by lemma 7 }
% 0.21/0.53 inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 0.21/0.53 = { by lemma 7 }
% 0.21/0.53 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Y))), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 0.21/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.53 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Y))), inverse(multiply(Y, multiply(inverse(Y), Y))))))), inverse(multiply(V, multiply(inverse(V), V))))))
% 0.21/0.53 = { by axiom 1 (single_axiom) }
% 0.21/0.53 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), inverse(multiply(V, multiply(inverse(V), V))))))
% 0.21/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.53 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), Y))), inverse(multiply(U, multiply(inverse(U), U))))))), inverse(multiply(V, multiply(inverse(V), V))))))
% 0.21/0.53 = { by axiom 1 (single_axiom) }
% 0.21/0.53 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), Y))), inverse(multiply(U, multiply(inverse(U), U)))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 Y
% 0.21/0.53
% 0.21/0.53 Lemma 9: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(multiply(inverse(X), X))
% 0.21/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.53 multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(X), X)))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.53 = { by lemma 7 }
% 0.21/0.53 multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.53 = { by lemma 8 }
% 0.21/0.53 multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.53 = { by lemma 8 }
% 0.21/0.53 multiply(inverse(Y), Y)
% 0.21/0.53
% 0.21/0.53 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.21/0.53 Proof:
% 0.21/0.53 multiply(multiply(inverse(b2), b2), a2)
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 multiply(inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))), a2)
% 0.21/0.53 = { by lemma 9 }
% 0.21/0.53 multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), a2)
% 0.21/0.53 = { by lemma 8 R->L }
% 0.21/0.53 multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), a2)), multiply(inverse(W), W))))), multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), a2)), multiply(inverse(W), W)))))), inverse(multiply(a2, multiply(inverse(a2), a2))))))
% 0.21/0.54 = { by lemma 8 }
% 0.21/0.54 multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), a2)), multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), a2)), multiply(inverse(W), W)))))), inverse(multiply(a2, multiply(inverse(a2), a2))))))
% 0.21/0.54 = { by lemma 9 }
% 0.21/0.54 multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), a2)), multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), a2)), multiply(inverse(W), W)))))), inverse(multiply(a2, multiply(inverse(a2), a2))))))
% 0.21/0.54 = { by axiom 1 (single_axiom) }
% 0.21/0.54 multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), a2)), multiply(inverse(W), W))))
% 0.21/0.54 = { by lemma 9 R->L }
% 0.21/0.54 multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), a2)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)))))))
% 0.21/0.54 = { by lemma 9 }
% 0.21/0.54 multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), X))), a2)), inverse(multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)))))))
% 0.21/0.54 = { by axiom 1 (single_axiom) }
% 0.21/0.54 a2
% 0.21/0.54 % SZS output end Proof
% 0.21/0.54
% 0.21/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
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