TSTP Solution File: GRP442-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP442-1 : 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 : n020.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 01:18:27 EDT 2023
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP442-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % 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 : n020.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 21:24:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.42 Command-line arguments: --no-flatten-goal
% 0.19/0.42
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 Axiom 1 (single_axiom): inverse(multiply(X, multiply(Y, multiply(multiply(Z, inverse(Z)), inverse(multiply(W, multiply(X, Y))))))) = W.
% 0.19/0.50
% 0.19/0.50 Lemma 2: inverse(multiply(X, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))), multiply(multiply(V, inverse(V)), Z)))) = W.
% 0.19/0.50 Proof:
% 0.19/0.50 inverse(multiply(X, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))), multiply(multiply(V, inverse(V)), Z))))
% 0.19/0.50 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.50 inverse(multiply(X, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))), multiply(multiply(V, inverse(V)), inverse(multiply(W, multiply(X, multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))))))))))
% 0.19/0.50 = { by axiom 1 (single_axiom) }
% 0.19/0.50 W
% 0.19/0.50
% 0.19/0.50 Lemma 3: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.19/0.50 Proof:
% 0.19/0.50 multiply(Y, inverse(Y))
% 0.19/0.50 = { by lemma 2 R->L }
% 0.19/0.50 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, V))))))), multiply(multiply(S, inverse(S)), T))))
% 0.19/0.50 = { by lemma 2 R->L }
% 0.19/0.50 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, inverse(multiply(multiply(multiply(X2, inverse(X2)), Z), multiply(multiply(multiply(Y2, inverse(Y2)), inverse(multiply(V, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, V)))), multiply(multiply(X2, inverse(X2)), Z))))), multiply(multiply(Z2, inverse(Z2)), V))))))), multiply(multiply(S, inverse(S)), T))))
% 0.19/0.50 = { by lemma 2 }
% 0.19/0.50 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, inverse(multiply(multiply(multiply(X2, inverse(X2)), Z), multiply(multiply(multiply(Y2, inverse(Y2)), W), multiply(multiply(Z2, inverse(Z2)), V))))))), multiply(multiply(S, inverse(S)), T))))
% 0.19/0.50 = { by lemma 2 R->L }
% 0.19/0.50 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, inverse(multiply(multiply(multiply(X2, inverse(X2)), Z), multiply(multiply(multiply(Y2, inverse(Y2)), inverse(multiply(V, multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Z, multiply(W, V)))), multiply(multiply(X2, inverse(X2)), Z))))), multiply(multiply(Z2, inverse(Z2)), V))))))), multiply(multiply(S, inverse(S)), T))))
% 0.19/0.50 = { by lemma 2 }
% 0.19/0.50 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, multiply(multiply(X, inverse(X)), inverse(multiply(Z, multiply(W, V))))))), multiply(multiply(S, inverse(S)), T))))
% 0.19/0.50 = { by lemma 2 }
% 0.19/0.50 multiply(X, inverse(X))
% 0.19/0.50
% 0.19/0.50 Lemma 4: inverse(multiply(inverse(X), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W))))), multiply(multiply(V, inverse(V)), Z)))) = X.
% 0.19/0.50 Proof:
% 0.19/0.50 inverse(multiply(inverse(X), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W))))), multiply(multiply(V, inverse(V)), Z))))
% 0.19/0.50 = { by lemma 3 }
% 0.19/0.50 inverse(multiply(inverse(X), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(X, inverse(X))))), multiply(multiply(V, inverse(V)), Z))))
% 0.19/0.50 = { by lemma 2 }
% 0.19/0.50 X
% 0.19/0.50
% 0.19/0.50 Lemma 5: inverse(multiply(inverse(X), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(inverse(multiply(Z, inverse(Z))), multiply(W, inverse(W))))), multiply(V, inverse(V))))) = X.
% 0.19/0.50 Proof:
% 0.19/0.50 inverse(multiply(inverse(X), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(inverse(multiply(Z, inverse(Z))), multiply(W, inverse(W))))), multiply(V, inverse(V)))))
% 0.19/0.50 = { by lemma 3 }
% 0.19/0.50 inverse(multiply(inverse(X), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(inverse(multiply(Z, inverse(Z))), multiply(W, inverse(W))))), multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))))))
% 0.19/0.50 = { by lemma 4 }
% 0.19/0.50 X
% 0.19/0.50
% 0.19/0.50 Lemma 6: inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(Z, inverse(Z)), W), multiply(multiply(V, inverse(V)), U)))) = multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(W, U)))).
% 0.19/0.50 Proof:
% 0.19/0.50 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(Z, inverse(Z)), W), multiply(multiply(V, inverse(V)), U))))
% 0.19/0.50 = { by lemma 2 R->L }
% 0.19/0.50 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(U, multiply(multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(W, U)))), multiply(multiply(X, inverse(X)), Y))))), multiply(multiply(V, inverse(V)), U))))
% 0.19/0.50 = { by lemma 2 }
% 0.19/0.50 multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(W, U))))
% 0.19/0.50
% 0.19/0.50 Lemma 7: inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(Z, inverse(Z)), multiply(multiply(W, inverse(W)), V)))) = multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(inverse(multiply(T, inverse(T))), V)))).
% 0.19/0.50 Proof:
% 0.19/0.50 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(Z, inverse(Z)), multiply(multiply(W, inverse(W)), V))))
% 0.19/0.50 = { by lemma 3 }
% 0.19/0.50 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(T, inverse(T)), inverse(multiply(T, inverse(T)))), multiply(multiply(W, inverse(W)), V))))
% 0.19/0.50 = { by lemma 6 }
% 0.19/0.51 multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(inverse(multiply(T, inverse(T))), V))))
% 0.19/0.51
% 0.19/0.51 Lemma 8: inverse(multiply(X, multiply(inverse(X), multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W)))))))) = Z.
% 0.19/0.51 Proof:
% 0.19/0.51 inverse(multiply(X, multiply(inverse(X), multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W))))))))
% 0.19/0.51 = { by lemma 3 }
% 0.19/0.51 inverse(multiply(X, multiply(inverse(X), multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(X, inverse(X))))))))
% 0.19/0.51 = { by axiom 1 (single_axiom) }
% 0.19/0.51 Z
% 0.19/0.51
% 0.19/0.51 Lemma 9: multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(Y, W)))) = inverse(W).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(Y, W))))
% 0.19/0.51 = { by lemma 6 R->L }
% 0.19/0.51 inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(Y, multiply(Z, inverse(Z))))), multiply(multiply(multiply(U, inverse(U)), Y), multiply(multiply(T, inverse(T)), W))))
% 0.19/0.51 = { by lemma 8 R->L }
% 0.19/0.51 inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(Y, multiply(Z, inverse(Z))))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(W, multiply(inverse(W), multiply(multiply(V, inverse(V)), inverse(multiply(Y, multiply(Z, inverse(Z))))))))), multiply(multiply(T, inverse(T)), W))))
% 0.19/0.51 = { by lemma 2 }
% 0.19/0.51 inverse(W)
% 0.19/0.51
% 0.19/0.51 Lemma 10: multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(W, inverse(W))))) = inverse(inverse(Y)).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(W, inverse(W)))))
% 0.19/0.51 = { by lemma 3 }
% 0.19/0.51 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(Y, inverse(Y)))))
% 0.19/0.51 = { by lemma 9 }
% 0.19/0.51 inverse(inverse(Y))
% 0.19/0.51
% 0.19/0.51 Lemma 11: multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(Y))), multiply(Z, inverse(Z))))) = inverse(multiply(W, inverse(W))).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(Y))), multiply(Z, inverse(Z)))))
% 0.19/0.51 = { by lemma 3 }
% 0.19/0.51 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(multiply(V, multiply(inverse(V), multiply(multiply(U, inverse(U)), inverse(multiply(multiply(W, inverse(W)), multiply(T, inverse(T))))))), inverse(multiply(V, multiply(inverse(V), multiply(multiply(U, inverse(U)), inverse(multiply(multiply(W, inverse(W)), multiply(T, inverse(T)))))))))), multiply(Z, inverse(Z)))))
% 0.19/0.51 = { by lemma 8 }
% 0.19/0.51 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(multiply(V, multiply(inverse(V), multiply(multiply(U, inverse(U)), inverse(multiply(multiply(W, inverse(W)), multiply(T, inverse(T))))))), multiply(W, inverse(W)))), multiply(Z, inverse(Z)))))
% 0.19/0.51 = { by lemma 10 }
% 0.19/0.51 inverse(inverse(multiply(V, multiply(inverse(V), multiply(multiply(U, inverse(U)), inverse(multiply(multiply(W, inverse(W)), multiply(T, inverse(T)))))))))
% 0.19/0.51 = { by lemma 8 }
% 0.19/0.51 inverse(multiply(W, inverse(W)))
% 0.19/0.51
% 0.19/0.51 Lemma 12: inverse(multiply(inverse(X), multiply(inverse(multiply(Y, inverse(Y))), multiply(Z, inverse(Z))))) = X.
% 0.19/0.51 Proof:
% 0.19/0.51 inverse(multiply(inverse(X), multiply(inverse(multiply(Y, inverse(Y))), multiply(Z, inverse(Z)))))
% 0.19/0.51 = { by lemma 3 }
% 0.19/0.51 inverse(multiply(inverse(X), multiply(inverse(multiply(Y, inverse(Y))), multiply(multiply(W, inverse(W)), inverse(multiply(W, inverse(W)))))))
% 0.19/0.51 = { by lemma 11 R->L }
% 0.19/0.51 inverse(multiply(inverse(X), multiply(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(multiply(W, inverse(W))), multiply(U, inverse(U))))), multiply(multiply(W, inverse(W)), inverse(multiply(W, inverse(W)))))))
% 0.19/0.51 = { by lemma 4 }
% 0.19/0.51 X
% 0.19/0.51
% 0.19/0.51 Lemma 13: inverse(multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), multiply(multiply(Z, inverse(Z)), multiply(W, inverse(W))))) = multiply(V, inverse(V)).
% 0.19/0.51 Proof:
% 0.19/0.51 inverse(multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), multiply(multiply(Z, inverse(Z)), multiply(W, inverse(W)))))
% 0.19/0.51 = { by lemma 3 }
% 0.19/0.51 inverse(multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), multiply(multiply(Z, inverse(Z)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))
% 0.19/0.51 = { by lemma 7 }
% 0.19/0.51 multiply(multiply(T, inverse(T)), inverse(multiply(multiply(Y, inverse(Y)), multiply(inverse(multiply(S, inverse(S))), inverse(multiply(U, inverse(U)))))))
% 0.19/0.51 = { by lemma 7 R->L }
% 0.19/0.51 inverse(multiply(multiply(multiply(X2, inverse(X2)), multiply(Y, inverse(Y))), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), multiply(multiply(Y2, inverse(Y2)), inverse(multiply(U, inverse(U)))))))
% 0.19/0.51 = { by lemma 12 R->L }
% 0.19/0.51 inverse(multiply(multiply(multiply(X2, inverse(X2)), multiply(Y, inverse(Y))), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), multiply(multiply(Y2, inverse(Y2)), inverse(inverse(multiply(inverse(multiply(U, inverse(U))), multiply(inverse(multiply(Z2, inverse(Z2))), multiply(W2, inverse(W2))))))))))
% 0.19/0.51 = { by lemma 11 R->L }
% 0.19/0.51 inverse(multiply(multiply(multiply(X2, inverse(X2)), multiply(Y, inverse(Y))), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), multiply(multiply(Y2, inverse(Y2)), inverse(inverse(multiply(multiply(multiply(V2, inverse(V2)), inverse(multiply(inverse(multiply(U2, inverse(U2))), multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y))))))), multiply(inverse(multiply(Z2, inverse(Z2))), multiply(W2, inverse(W2))))))))))
% 0.19/0.51 = { by lemma 6 R->L }
% 0.19/0.51 inverse(multiply(multiply(multiply(X2, inverse(X2)), multiply(Y, inverse(Y))), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), multiply(multiply(Y2, inverse(Y2)), inverse(inverse(multiply(inverse(multiply(multiply(multiply(U2, inverse(U2)), inverse(multiply(U2, inverse(U2)))), multiply(multiply(multiply(X2, inverse(X2)), multiply(Y, inverse(Y))), multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y))))))), multiply(inverse(multiply(Z2, inverse(Z2))), multiply(W2, inverse(W2))))))))))
% 0.19/0.51 = { by lemma 3 R->L }
% 0.19/0.51 inverse(multiply(multiply(multiply(X2, inverse(X2)), multiply(Y, inverse(Y))), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), multiply(multiply(Y2, inverse(Y2)), inverse(inverse(multiply(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(multiply(X2, inverse(X2)), multiply(Y, inverse(Y))), multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y))))))), multiply(inverse(multiply(Z2, inverse(Z2))), multiply(W2, inverse(W2))))))))))
% 0.19/0.51 = { by lemma 12 }
% 0.19/0.51 inverse(multiply(multiply(multiply(X2, inverse(X2)), multiply(Y, inverse(Y))), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), multiply(multiply(Y2, inverse(Y2)), inverse(multiply(multiply(V, inverse(V)), multiply(multiply(multiply(X2, inverse(X2)), multiply(Y, inverse(Y))), multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))))))))))
% 0.19/0.51 = { by axiom 1 (single_axiom) }
% 0.19/0.51 multiply(V, inverse(V))
% 0.19/0.51
% 0.19/0.51 Lemma 14: multiply(multiply(X, inverse(X)), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W))))), multiply(V, inverse(V)))) = inverse(multiply(multiply(U, inverse(U)), Z)).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(multiply(X, inverse(X)), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W))))), multiply(V, inverse(V))))
% 0.19/0.51 = { by lemma 4 R->L }
% 0.19/0.51 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W))))), multiply(V, inverse(V)))), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W))))), multiply(multiply(U, inverse(U)), Z)))))
% 0.19/0.51 = { by lemma 9 }
% 0.19/0.51 inverse(multiply(multiply(U, inverse(U)), Z))
% 0.19/0.51
% 0.19/0.51 Lemma 15: multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))) = multiply(Z, inverse(Z)).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y)))
% 0.19/0.51 = { by lemma 2 R->L }
% 0.19/0.51 inverse(multiply(multiply(multiply(W, inverse(W)), multiply(V, inverse(V))), multiply(multiply(multiply(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))), inverse(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))))), inverse(multiply(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))), multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), multiply(multiply(W, inverse(W)), multiply(V, inverse(V))))))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))), inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))))
% 0.19/0.51 = { by lemma 5 R->L }
% 0.19/0.51 inverse(multiply(multiply(multiply(W, inverse(W)), multiply(V, inverse(V))), multiply(multiply(multiply(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))), inverse(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))))), inverse(multiply(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))), inverse(multiply(inverse(multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), multiply(multiply(W, inverse(W)), multiply(V, inverse(V))))), multiply(multiply(multiply(T, inverse(T)), inverse(multiply(inverse(multiply(U, inverse(U))), multiply(S, inverse(S))))), multiply(X2, inverse(X2)))))))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))), inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))))
% 0.19/0.51 = { by lemma 13 }
% 0.19/0.51 inverse(multiply(multiply(multiply(W, inverse(W)), multiply(V, inverse(V))), multiply(multiply(multiply(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))), inverse(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))))), inverse(multiply(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))), inverse(multiply(multiply(Y2, inverse(Y2)), multiply(multiply(multiply(T, inverse(T)), inverse(multiply(inverse(multiply(U, inverse(U))), multiply(S, inverse(S))))), multiply(X2, inverse(X2)))))))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))), inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))))
% 0.19/0.51 = { by lemma 14 }
% 0.19/0.51 inverse(multiply(multiply(multiply(W, inverse(W)), multiply(V, inverse(V))), multiply(multiply(multiply(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))), inverse(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))))), inverse(multiply(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))), inverse(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))))))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))), inverse(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))))
% 0.19/0.51 = { by lemma 13 }
% 0.19/0.51 multiply(Z, inverse(Z))
% 0.19/0.51
% 0.19/0.51 Lemma 16: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 0.19/0.51 Proof:
% 0.19/0.51 inverse(multiply(X, inverse(X)))
% 0.19/0.51 = { by lemma 15 R->L }
% 0.19/0.51 inverse(multiply(multiply(Z, inverse(Z)), multiply(W, inverse(W))))
% 0.19/0.51 = { by lemma 14 R->L }
% 0.19/0.51 multiply(multiply(V, inverse(V)), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(multiply(W, inverse(W)), multiply(T, inverse(T))))), multiply(S, inverse(S))))
% 0.19/0.51 = { by lemma 15 }
% 0.19/0.51 multiply(multiply(V, inverse(V)), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))), multiply(S, inverse(S))))
% 0.19/0.51 = { by lemma 15 }
% 0.19/0.51 multiply(multiply(V, inverse(V)), multiply(X2, inverse(X2)))
% 0.19/0.51 = { by lemma 15 }
% 0.19/0.51 multiply(Y, inverse(Y))
% 0.19/0.51
% 0.19/0.51 Lemma 17: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(inverse(X), X)
% 0.19/0.51 = { by lemma 4 R->L }
% 0.19/0.51 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(multiply(W, inverse(W)), multiply(V, inverse(V))))), multiply(multiply(U, inverse(U)), multiply(W, inverse(W)))))))
% 0.19/0.51 = { by lemma 15 }
% 0.19/0.51 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))), multiply(multiply(U, inverse(U)), multiply(W, inverse(W)))))))
% 0.19/0.51 = { by lemma 15 }
% 0.19/0.51 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))), multiply(T, inverse(T))))))
% 0.19/0.51 = { by lemma 15 }
% 0.19/0.51 multiply(inverse(X), inverse(multiply(inverse(X), multiply(S, inverse(S)))))
% 0.19/0.51 = { by lemma 9 R->L }
% 0.19/0.51 multiply(inverse(X), multiply(multiply(X2, inverse(X2)), inverse(multiply(inverse(multiply(X, multiply(Y2, inverse(Y2)))), multiply(X, multiply(inverse(X), multiply(S, inverse(S))))))))
% 0.19/0.51 = { by lemma 5 R->L }
% 0.19/0.51 multiply(inverse(X), multiply(multiply(X2, inverse(X2)), inverse(multiply(inverse(multiply(X, multiply(Y2, inverse(Y2)))), inverse(multiply(inverse(multiply(X, multiply(inverse(X), multiply(S, inverse(S))))), multiply(multiply(multiply(Z2, inverse(Z2)), inverse(multiply(inverse(multiply(W2, inverse(W2))), multiply(V2, inverse(V2))))), multiply(U2, inverse(U2)))))))))
% 0.19/0.51 = { by lemma 16 R->L }
% 0.19/0.51 multiply(inverse(X), multiply(multiply(X2, inverse(X2)), inverse(multiply(inverse(multiply(X, multiply(Y2, inverse(Y2)))), inverse(multiply(inverse(multiply(X, multiply(inverse(X), inverse(multiply(T2, inverse(T2)))))), multiply(multiply(multiply(Z2, inverse(Z2)), inverse(multiply(inverse(multiply(W2, inverse(W2))), multiply(V2, inverse(V2))))), multiply(U2, inverse(U2)))))))))
% 0.19/0.51 = { by lemma 11 R->L }
% 0.19/0.51 multiply(inverse(X), multiply(multiply(X2, inverse(X2)), inverse(multiply(inverse(multiply(X, multiply(Y2, inverse(Y2)))), inverse(multiply(inverse(multiply(X, multiply(inverse(X), multiply(multiply(S2, inverse(S2)), inverse(multiply(inverse(multiply(X3, inverse(X3))), multiply(Y3, inverse(Y3)))))))), multiply(multiply(multiply(Z2, inverse(Z2)), inverse(multiply(inverse(multiply(W2, inverse(W2))), multiply(V2, inverse(V2))))), multiply(U2, inverse(U2)))))))))
% 0.19/0.52 = { by lemma 8 }
% 0.19/0.52 multiply(inverse(X), multiply(multiply(X2, inverse(X2)), inverse(multiply(inverse(multiply(X, multiply(Y2, inverse(Y2)))), inverse(multiply(inverse(multiply(X3, inverse(X3))), multiply(multiply(multiply(Z2, inverse(Z2)), inverse(multiply(inverse(multiply(W2, inverse(W2))), multiply(V2, inverse(V2))))), multiply(U2, inverse(U2)))))))))
% 0.19/0.52 = { by lemma 16 }
% 0.19/0.52 multiply(inverse(X), multiply(multiply(X2, inverse(X2)), inverse(multiply(inverse(multiply(X, multiply(Y2, inverse(Y2)))), inverse(multiply(multiply(Z3, inverse(Z3)), multiply(multiply(multiply(Z2, inverse(Z2)), inverse(multiply(inverse(multiply(W2, inverse(W2))), multiply(V2, inverse(V2))))), multiply(U2, inverse(U2)))))))))
% 0.19/0.52 = { by lemma 14 }
% 0.19/0.52 multiply(inverse(X), multiply(multiply(X2, inverse(X2)), inverse(multiply(inverse(multiply(X, multiply(Y2, inverse(Y2)))), inverse(inverse(multiply(multiply(W2, inverse(W2)), inverse(multiply(W2, inverse(W2))))))))))
% 0.19/0.52 = { by lemma 16 }
% 0.19/0.52 multiply(inverse(X), multiply(multiply(X2, inverse(X2)), inverse(multiply(inverse(multiply(X, multiply(Y2, inverse(Y2)))), inverse(multiply(W3, inverse(W3)))))))
% 0.19/0.52 = { by lemma 16 }
% 0.19/0.52 multiply(inverse(X), multiply(multiply(X2, inverse(X2)), inverse(multiply(inverse(multiply(X, multiply(Y2, inverse(Y2)))), multiply(V3, inverse(V3))))))
% 0.19/0.52 = { by lemma 10 }
% 0.19/0.52 multiply(inverse(X), inverse(inverse(X)))
% 0.19/0.52 = { by lemma 3 R->L }
% 0.19/0.52 multiply(Y, inverse(Y))
% 0.19/0.52
% 0.19/0.52 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.52 Proof:
% 0.19/0.52 multiply(inverse(a1), a1)
% 0.19/0.52 = { by lemma 17 }
% 0.19/0.52 multiply(X, inverse(X))
% 0.19/0.52 = { by lemma 17 R->L }
% 0.19/0.52 multiply(inverse(b1), b1)
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52
% 0.19/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
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