TSTP Solution File: GRP430-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP430-1 : 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 : n019.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 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP430-1 : 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
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 01:58:28 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.41
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 Axiom 1 (single_axiom): multiply(X, inverse(multiply(Y, multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, Y))), X)))) = W.
% 0.20/0.43
% 0.20/0.43 Lemma 2: multiply(X, inverse(multiply(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V))), multiply(Z, X)))) = W.
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, inverse(multiply(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V))), multiply(Z, X))))
% 0.20/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.43 multiply(X, inverse(multiply(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V))), multiply(multiply(multiply(V, inverse(V)), inverse(multiply(W, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V)))))), X))))
% 0.20/0.43 = { by axiom 1 (single_axiom) }
% 0.20/0.43 W
% 0.20/0.43
% 0.20/0.43 Lemma 3: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(Y, inverse(Y))
% 0.20/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.43 multiply(Z, inverse(multiply(inverse(multiply(W, V)), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(W, V))))), Z))))
% 0.20/0.43 = { by lemma 2 R->L }
% 0.20/0.43 multiply(Z, inverse(multiply(inverse(multiply(W, V)), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(W, multiply(S, inverse(multiply(multiply(multiply(multiply(X, inverse(X)), inverse(multiply(W, V))), multiply(X2, inverse(X2))), multiply(W, S))))))))), Z))))
% 0.20/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.43 multiply(Z, inverse(multiply(inverse(multiply(W, V)), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(W, multiply(S, inverse(multiply(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(W, multiply(multiply(multiply(T, inverse(T)), inverse(multiply(multiply(multiply(X, inverse(X)), inverse(multiply(W, V))), W))), multiply(Y, inverse(Y)))))), multiply(X2, inverse(X2))), multiply(W, S))))))))), Z))))
% 0.20/0.43 = { by lemma 2 }
% 0.20/0.43 multiply(Z, inverse(multiply(inverse(multiply(W, V)), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(W, multiply(multiply(multiply(T, inverse(T)), inverse(multiply(multiply(multiply(X, inverse(X)), inverse(multiply(W, V))), W))), multiply(Y, inverse(Y)))))))), Z))))
% 0.20/0.43 = { by axiom 1 (single_axiom) }
% 0.20/0.43 multiply(Z, inverse(multiply(inverse(multiply(W, V)), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(multiply(X, inverse(X)), inverse(multiply(W, V))))), Z))))
% 0.20/0.43 = { by axiom 1 (single_axiom) }
% 0.20/0.43 multiply(X, inverse(X))
% 0.20/0.43
% 0.20/0.43 Lemma 4: multiply(X, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, X)))) = inverse(W).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, X))))
% 0.20/0.43 = { by lemma 3 }
% 0.20/0.43 multiply(X, inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(W, inverse(W)))), multiply(Z, inverse(Z))), multiply(W, X))))
% 0.20/0.43 = { by lemma 2 }
% 0.20/0.43 inverse(W)
% 0.20/0.43
% 0.20/0.43 Lemma 5: multiply(inverse(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z)))), inverse(multiply(Z, multiply(W, inverse(W))))) = Y.
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(inverse(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z)))), inverse(multiply(Z, multiply(W, inverse(W)))))
% 0.20/0.43 = { by lemma 3 }
% 0.20/0.43 multiply(inverse(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z)))), inverse(multiply(Z, multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), inverse(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))))))))
% 0.20/0.43 = { by axiom 1 (single_axiom) }
% 0.20/0.44 Y
% 0.20/0.44
% 0.20/0.44 Lemma 6: multiply(X, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, inverse(W))))) = X.
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(X, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, inverse(W)))))
% 0.20/0.44 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.44 multiply(multiply(V, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(X, multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z)))))), V)))), inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, inverse(W)))))
% 0.20/0.44 = { by lemma 4 }
% 0.20/0.44 multiply(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(X, multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))))))), inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, inverse(W)))))
% 0.20/0.44 = { by lemma 5 }
% 0.20/0.44 X
% 0.20/0.44
% 0.20/0.44 Lemma 7: inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y)))) = multiply(Z, inverse(Z)).
% 0.20/0.44 Proof:
% 0.20/0.44 inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))))
% 0.20/0.44 = { by lemma 4 R->L }
% 0.20/0.44 multiply(W, inverse(multiply(multiply(multiply(V, inverse(V)), multiply(U, inverse(U))), multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), W))))
% 0.20/0.44 = { by lemma 6 R->L }
% 0.20/0.44 multiply(W, inverse(multiply(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), multiply(Z, inverse(Z))))), multiply(U, inverse(U))), multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), W))))
% 0.20/0.44 = { by lemma 2 }
% 0.20/0.44 multiply(Z, inverse(Z))
% 0.20/0.44
% 0.20/0.44 Lemma 8: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(X, multiply(Y, inverse(Y)))
% 0.20/0.44 = { by lemma 7 R->L }
% 0.20/0.44 multiply(X, inverse(multiply(multiply(Z, inverse(Z)), multiply(W, inverse(W)))))
% 0.20/0.44 = { by lemma 5 R->L }
% 0.20/0.44 multiply(X, inverse(multiply(multiply(inverse(multiply(multiply(V, inverse(V)), inverse(multiply(multiply(Z, inverse(Z)), multiply(U, inverse(U)))))), inverse(multiply(multiply(U, inverse(U)), multiply(T, inverse(T))))), multiply(W, inverse(W)))))
% 0.20/0.44 = { by lemma 7 }
% 0.20/0.44 multiply(X, inverse(multiply(multiply(inverse(multiply(multiply(V, inverse(V)), multiply(S, inverse(S)))), inverse(multiply(multiply(U, inverse(U)), multiply(T, inverse(T))))), multiply(W, inverse(W)))))
% 0.20/0.44 = { by lemma 7 }
% 0.20/0.44 multiply(X, inverse(multiply(multiply(inverse(multiply(multiply(V, inverse(V)), multiply(S, inverse(S)))), multiply(X2, inverse(X2))), multiply(W, inverse(W)))))
% 0.20/0.44 = { by lemma 7 }
% 0.20/0.44 multiply(X, inverse(multiply(multiply(multiply(Y2, inverse(Y2)), multiply(X2, inverse(X2))), multiply(W, inverse(W)))))
% 0.20/0.44 = { by lemma 6 }
% 0.20/0.44 X
% 0.20/0.44
% 0.20/0.44 Lemma 9: inverse(multiply(multiply(X, inverse(X)), inverse(Y))) = Y.
% 0.20/0.44 Proof:
% 0.20/0.44 inverse(multiply(multiply(X, inverse(X)), inverse(Y)))
% 0.20/0.44 = { by lemma 8 R->L }
% 0.20/0.44 multiply(inverse(multiply(multiply(X, inverse(X)), inverse(Y))), multiply(Z, inverse(Z)))
% 0.20/0.44 = { by lemma 7 R->L }
% 0.20/0.44 multiply(inverse(multiply(multiply(X, inverse(X)), inverse(Y))), inverse(multiply(multiply(W, inverse(W)), multiply(V, inverse(V)))))
% 0.20/0.44 = { by lemma 8 R->L }
% 0.20/0.44 multiply(inverse(multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(W, inverse(W)))))), inverse(multiply(multiply(W, inverse(W)), multiply(V, inverse(V)))))
% 0.20/0.44 = { by lemma 5 }
% 0.20/0.44 Y
% 0.20/0.44
% 0.20/0.44 Lemma 10: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(inverse(X), X)
% 0.20/0.44 = { by lemma 9 R->L }
% 0.20/0.44 inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(X), X))))
% 0.20/0.44 = { by lemma 5 R->L }
% 0.20/0.44 multiply(inverse(multiply(multiply(W, inverse(W)), inverse(multiply(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(X), X)))), inverse(multiply(X, multiply(V, inverse(V)))))))), inverse(multiply(inverse(multiply(X, multiply(V, inverse(V)))), multiply(U, inverse(U)))))
% 0.20/0.44 = { by lemma 9 }
% 0.20/0.44 multiply(multiply(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(X), X)))), inverse(multiply(X, multiply(V, inverse(V))))), inverse(multiply(inverse(multiply(X, multiply(V, inverse(V)))), multiply(U, inverse(U)))))
% 0.20/0.44 = { by lemma 8 }
% 0.20/0.44 multiply(multiply(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(X), X)))), inverse(multiply(X, multiply(V, inverse(V))))), inverse(inverse(multiply(X, multiply(V, inverse(V))))))
% 0.20/0.44 = { by lemma 5 }
% 0.20/0.44 multiply(inverse(X), inverse(inverse(multiply(X, multiply(V, inverse(V))))))
% 0.20/0.44 = { by lemma 8 }
% 0.20/0.44 multiply(inverse(X), inverse(inverse(X)))
% 0.20/0.44 = { by lemma 3 R->L }
% 0.20/0.44 multiply(Y, inverse(Y))
% 0.20/0.44
% 0.20/0.44 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(inverse(a1), a1)
% 0.20/0.44 = { by lemma 10 }
% 0.20/0.44 multiply(X, inverse(X))
% 0.20/0.44 = { by lemma 10 R->L }
% 0.20/0.44 multiply(inverse(b1), b1)
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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