TSTP Solution File: GRP433-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP433-1 : 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 : n003.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 01:18:24 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP433-1 : TPTP v8.1.2. Released v2.6.0.
% 0.03/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 21:56:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.39 Command-line arguments: --no-flatten-goal
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Axiom 1 (single_axiom): inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, Y), Z)), X), Y), multiply(W, inverse(W)))) = Z.
% 0.19/0.41
% 0.19/0.41 Lemma 2: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(Y, inverse(Y))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), V)), Z), W), multiply(Y, inverse(Y)))), multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 inverse(multiply(multiply(multiply(V, multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), V)), Z), W), multiply(X, inverse(X)))), multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 multiply(X, inverse(X))
% 0.19/0.41
% 0.19/0.41 Lemma 3: inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(X))), Y), Z), multiply(W, inverse(W)))) = inverse(multiply(Y, Z)).
% 0.19/0.41 Proof:
% 0.19/0.41 inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(X))), Y), Z), multiply(W, inverse(W))))
% 0.19/0.41 = { by lemma 2 }
% 0.19/0.41 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Y, Z), inverse(multiply(Y, Z)))), Y), Z), multiply(W, inverse(W))))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 inverse(multiply(Y, Z))
% 0.19/0.41
% 0.19/0.41 Lemma 4: inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(Z, inverse(Z)))) = inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), Y)).
% 0.19/0.41 Proof:
% 0.19/0.41 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(Z, inverse(Z))))
% 0.19/0.41 = { by lemma 2 }
% 0.19/0.41 inverse(multiply(multiply(multiply(inverse(multiply(W, inverse(W))), inverse(inverse(multiply(W, inverse(W))))), Y), multiply(Z, inverse(Z))))
% 0.19/0.41 = { by lemma 3 }
% 0.19/0.41 inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), Y))
% 0.19/0.41
% 0.19/0.41 Lemma 5: inverse(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X), Y)) = multiply(W, inverse(W)).
% 0.19/0.41 Proof:
% 0.19/0.41 inverse(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X), Y))
% 0.19/0.41 = { by lemma 3 R->L }
% 0.19/0.41 inverse(multiply(multiply(multiply(inverse(multiply(Z, inverse(Z))), multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X)), Y), multiply(V, inverse(V))))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X), Y), multiply(W, inverse(W)))), multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X)), Y), multiply(V, inverse(V))))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 multiply(W, inverse(W))
% 0.19/0.41
% 0.19/0.41 Lemma 6: inverse(multiply(multiply(inverse(multiply(X, inverse(X))), Y), inverse(Y))) = multiply(Z, inverse(Z)).
% 0.19/0.41 Proof:
% 0.19/0.41 inverse(multiply(multiply(inverse(multiply(X, inverse(X))), Y), inverse(Y)))
% 0.19/0.41 = { by lemma 2 }
% 0.19/0.41 inverse(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y))))), Y), inverse(Y)))
% 0.19/0.41 = { by lemma 5 }
% 0.19/0.41 multiply(Z, inverse(Z))
% 0.19/0.41
% 0.19/0.41 Lemma 7: inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), Y)) = inverse(Y).
% 0.19/0.41 Proof:
% 0.19/0.41 inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), Y))
% 0.19/0.41 = { by lemma 4 R->L }
% 0.19/0.41 inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))), Y), multiply(W, inverse(W))))
% 0.19/0.41 = { by lemma 6 R->L }
% 0.19/0.41 inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(Z, inverse(Z))), Y), inverse(Y))), inverse(multiply(Z, inverse(Z)))), Y), multiply(W, inverse(W))))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.42 inverse(Y)
% 0.19/0.42
% 0.19/0.42 Lemma 8: inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), inverse(multiply(Y, inverse(Y))))) = inverse(multiply(multiply(Z, inverse(Z)), multiply(W, inverse(W)))).
% 0.19/0.42 Proof:
% 0.19/0.42 inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), inverse(multiply(Y, inverse(Y)))))
% 0.19/0.42 = { by lemma 4 R->L }
% 0.19/0.42 inverse(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), multiply(W, inverse(W))))
% 0.19/0.42 = { by lemma 2 R->L }
% 0.19/0.42 inverse(multiply(multiply(Z, inverse(Z)), multiply(W, inverse(W))))
% 0.19/0.42
% 0.19/0.42 Lemma 9: inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y)))) = multiply(Z, inverse(Z)).
% 0.19/0.42 Proof:
% 0.19/0.42 inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))))
% 0.19/0.42 = { by lemma 8 R->L }
% 0.19/0.42 inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(multiply(V, inverse(V)))))
% 0.19/0.42 = { by lemma 4 R->L }
% 0.19/0.42 inverse(multiply(multiply(multiply(U, inverse(U)), inverse(multiply(V, inverse(V)))), multiply(T, inverse(T))))
% 0.19/0.42 = { by lemma 6 R->L }
% 0.19/0.42 inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(V, inverse(V))), multiply(T, inverse(T))), inverse(multiply(T, inverse(T))))), inverse(multiply(V, inverse(V)))), multiply(T, inverse(T))))
% 0.19/0.42 = { by lemma 5 }
% 0.19/0.42 multiply(Z, inverse(Z))
% 0.19/0.42
% 0.19/0.42 Lemma 10: inverse(inverse(multiply(X, inverse(X)))) = multiply(Y, inverse(Y)).
% 0.19/0.42 Proof:
% 0.19/0.42 inverse(inverse(multiply(X, inverse(X))))
% 0.19/0.42 = { by lemma 7 R->L }
% 0.19/0.42 inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), inverse(multiply(X, inverse(X)))))
% 0.19/0.42 = { by lemma 8 }
% 0.19/0.42 inverse(multiply(multiply(W, inverse(W)), multiply(V, inverse(V))))
% 0.19/0.42 = { by lemma 9 }
% 0.19/0.42 multiply(Y, inverse(Y))
% 0.19/0.42
% 0.19/0.42 Lemma 11: inverse(inverse(inverse(inverse(X)))) = X.
% 0.19/0.42 Proof:
% 0.19/0.42 inverse(inverse(inverse(inverse(X))))
% 0.19/0.42 = { by lemma 7 R->L }
% 0.19/0.42 inverse(multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(inverse(X)))))
% 0.19/0.42 = { by lemma 7 R->L }
% 0.19/0.42 inverse(multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), X))))))
% 0.19/0.42 = { by lemma 10 }
% 0.19/0.42 inverse(multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(inverse(multiply(multiply(W, inverse(W)), X))))))
% 0.19/0.42 = { by lemma 4 R->L }
% 0.19/0.42 inverse(multiply(multiply(multiply(inverse(multiply(multiply(W, inverse(W)), X)), inverse(inverse(multiply(multiply(W, inverse(W)), X)))), inverse(inverse(inverse(multiply(multiply(W, inverse(W)), X))))), multiply(V, inverse(V))))
% 0.19/0.42 = { by lemma 2 }
% 0.19/0.42 inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(inverse(multiply(multiply(W, inverse(W)), X))), inverse(inverse(inverse(multiply(multiply(W, inverse(W)), X))))), X)), inverse(inverse(multiply(multiply(W, inverse(W)), X)))), inverse(inverse(inverse(multiply(multiply(W, inverse(W)), X))))), multiply(V, inverse(V))))
% 0.19/0.42 = { by axiom 1 (single_axiom) }
% 0.19/0.42 X
% 0.19/0.42
% 0.19/0.42 Lemma 12: inverse(multiply(X, multiply(Y, inverse(Y)))) = inverse(X).
% 0.19/0.42 Proof:
% 0.19/0.42 inverse(multiply(X, multiply(Y, inverse(Y))))
% 0.19/0.42 = { by lemma 11 R->L }
% 0.19/0.42 inverse(multiply(inverse(inverse(inverse(inverse(X)))), multiply(Y, inverse(Y))))
% 0.19/0.42 = { by lemma 7 R->L }
% 0.19/0.42 inverse(multiply(inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), X))))), multiply(Y, inverse(Y))))
% 0.19/0.42 = { by lemma 11 }
% 0.19/0.42 inverse(multiply(multiply(inverse(inverse(multiply(Z, inverse(Z)))), X), multiply(Y, inverse(Y))))
% 0.19/0.42 = { by lemma 10 }
% 0.19/0.42 inverse(multiply(multiply(multiply(W, inverse(W)), X), multiply(Y, inverse(Y))))
% 0.19/0.42 = { by lemma 4 }
% 0.19/0.42 inverse(multiply(inverse(inverse(multiply(V, inverse(V)))), X))
% 0.19/0.42 = { by lemma 7 }
% 0.19/0.42 inverse(X)
% 0.19/0.42
% 0.19/0.42 Lemma 13: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 0.19/0.42 Proof:
% 0.19/0.42 inverse(multiply(X, inverse(X)))
% 0.19/0.42 = { by lemma 2 }
% 0.19/0.42 inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))))
% 0.19/0.42 = { by lemma 10 R->L }
% 0.19/0.42 inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(multiply(Z, inverse(Z)))))
% 0.19/0.42 = { by lemma 8 }
% 0.19/0.42 inverse(multiply(multiply(V, inverse(V)), multiply(U, inverse(U))))
% 0.19/0.42 = { by lemma 9 }
% 0.19/0.42 multiply(Y, inverse(Y))
% 0.19/0.42
% 0.19/0.42 Lemma 14: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(inverse(X), X)
% 0.19/0.42 = { by lemma 11 R->L }
% 0.19/0.42 inverse(inverse(inverse(inverse(multiply(inverse(X), X)))))
% 0.19/0.42 = { by lemma 12 R->L }
% 0.19/0.42 inverse(inverse(inverse(inverse(multiply(inverse(multiply(X, multiply(Z, inverse(Z)))), X)))))
% 0.19/0.42 = { by lemma 12 R->L }
% 0.19/0.42 inverse(inverse(inverse(inverse(multiply(inverse(multiply(multiply(X, multiply(Z, inverse(Z))), multiply(W, inverse(W)))), X)))))
% 0.19/0.42 = { by lemma 13 R->L }
% 0.19/0.42 inverse(inverse(inverse(inverse(multiply(inverse(multiply(multiply(X, multiply(Z, inverse(Z))), inverse(multiply(V, inverse(V))))), X)))))
% 0.19/0.42 = { by lemma 12 R->L }
% 0.19/0.42 inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(multiply(X, multiply(Z, inverse(Z))), inverse(multiply(V, inverse(V))))), X), multiply(Z, inverse(Z)))))))
% 0.19/0.42 = { by lemma 5 }
% 0.19/0.42 inverse(inverse(inverse(multiply(U, inverse(U)))))
% 0.19/0.42 = { by lemma 10 }
% 0.19/0.42 inverse(multiply(T, inverse(T)))
% 0.19/0.42 = { by lemma 13 }
% 0.19/0.42 multiply(Y, inverse(Y))
% 0.19/0.42
% 0.19/0.42 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(inverse(a1), a1)
% 0.19/0.42 = { by lemma 14 }
% 0.19/0.42 multiply(X, inverse(X))
% 0.19/0.42 = { by lemma 14 R->L }
% 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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