TSTP Solution File: GRP440-1 by Twee---2.5.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : GRP440-1 : TPTP v8.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n026.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 : Mon Jun 24 07:12:22 EDT 2024
% Result : Unsatisfiable 2.66s 0.72s
% Output : Proof 3.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP440-1 : TPTP v8.2.0. Released v2.6.0.
% 0.07/0.12 % Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 20 08:05:09 EDT 2024
% 0.13/0.33 % CPUTime :
% 2.66/0.72 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 2.66/0.72
% 2.66/0.72 % SZS status Unsatisfiable
% 2.66/0.72
% 3.27/0.80 % SZS output start Proof
% 3.27/0.80 Axiom 1 (single_axiom): inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(W, multiply(X, Z))))))) = W.
% 3.27/0.80
% 3.27/0.80 Lemma 2: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), W)))) = V.
% 3.27/0.80 Proof:
% 3.27/0.80 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), W))))
% 3.27/0.80 = { by axiom 1 (single_axiom) R->L }
% 3.27/0.80 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), inverse(multiply(V, multiply(X, multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z)))))))))))
% 3.27/0.80 = { by axiom 1 (single_axiom) }
% 3.27/0.80 V
% 3.27/0.80
% 3.27/0.80 Lemma 3: inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(V, U), inverse(multiply(T, multiply(X, U))))))) = T.
% 3.27/0.80 Proof:
% 3.27/0.80 inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(V, U), inverse(multiply(T, multiply(X, U)))))))
% 3.27/0.80 = { by axiom 1 (single_axiom) R->L }
% 3.27/0.80 inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W))))))), U), inverse(multiply(T, multiply(X, U)))))))
% 3.27/0.80 = { by axiom 1 (single_axiom) }
% 3.27/0.80 T
% 3.27/0.80
% 3.27/0.80 Lemma 4: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(U, W))))), V)), U)))) = Z.
% 3.27/0.80 Proof:
% 3.27/0.80 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(U, W))))), V)), U))))
% 3.27/0.80 = { by lemma 2 R->L }
% 3.27/0.80 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(U, W))))), V)), inverse(multiply(Z, multiply(X, multiply(multiply(inverse(X), multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(U, W))))), V))))))))
% 3.27/0.80 = { by axiom 1 (single_axiom) }
% 3.27/0.80 Z
% 3.27/0.80
% 3.27/0.80 Lemma 5: multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z)))))) = W.
% 3.27/0.80 Proof:
% 3.27/0.80 multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z))))))
% 3.27/0.80 = { by lemma 2 R->L }
% 3.27/0.80 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), inverse(multiply(X2, multiply(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z)))))), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))))))), X2))))
% 3.27/0.80 = { by lemma 3 }
% 3.27/0.80 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 3.27/0.80 = { by lemma 4 }
% 3.27/0.80 W
% 3.27/0.80
% 3.27/0.80 Lemma 6: inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y)))))) = Z.
% 3.27/0.80 Proof:
% 3.27/0.80 inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y))))))
% 3.27/0.80 = { by lemma 5 R->L }
% 3.27/0.80 inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, multiply(inverse(X), multiply(W, multiply(multiply(inverse(W), V), inverse(multiply(inverse(Y), multiply(inverse(X), V))))))))))))
% 3.27/0.80 = { by lemma 5 R->L }
% 3.27/0.80 inverse(multiply(inverse(X), multiply(X, multiply(multiply(inverse(X), multiply(W, multiply(multiply(inverse(W), V), inverse(multiply(inverse(Y), multiply(inverse(X), V)))))), inverse(multiply(Z, multiply(inverse(X), multiply(W, multiply(multiply(inverse(W), V), inverse(multiply(inverse(Y), multiply(inverse(X), V))))))))))))
% 3.27/0.80 = { by axiom 1 (single_axiom) }
% 3.27/0.80 Z
% 3.27/0.80
% 3.27/0.80 Lemma 7: multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W))) = X.
% 3.27/0.80 Proof:
% 3.27/0.80 multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W)))
% 3.27/0.81 = { by lemma 6 R->L }
% 3.62/0.81 multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), inverse(multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(W, Z)))))))))
% 3.62/0.81 = { by lemma 2 R->L }
% 3.62/0.81 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(X), T), inverse(multiply(S, multiply(X2, T))))), inverse(multiply(X2, multiply(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), inverse(multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(W, Z))))))))), multiply(multiply(inverse(X), T), inverse(multiply(S, multiply(X2, T))))))))), X2))))
% 3.62/0.81 = { by lemma 3 }
% 3.62/0.81 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(X), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 3.62/0.81 = { by lemma 3 R->L }
% 3.62/0.81 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(X), T), inverse(multiply(S, multiply(X2, T))))), inverse(multiply(X2, multiply(multiply(Y2, multiply(Z2, multiply(multiply(inverse(Z2), W2), inverse(multiply(inverse(X), multiply(Y2, W2)))))), multiply(multiply(inverse(X), T), inverse(multiply(S, multiply(X2, T))))))))), X2))))
% 3.62/0.81 = { by lemma 2 }
% 3.62/0.81 multiply(Y2, multiply(Z2, multiply(multiply(inverse(Z2), W2), inverse(multiply(inverse(X), multiply(Y2, W2))))))
% 3.62/0.81 = { by lemma 5 }
% 3.62/0.81 X
% 3.62/0.81
% 3.62/0.81 Lemma 8: inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, X)))))) = Z.
% 3.62/0.81 Proof:
% 3.62/0.81 inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, X))))))
% 3.62/0.81 = { by lemma 7 R->L }
% 3.62/0.81 inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, multiply(multiply(inverse(W), multiply(V, inverse(multiply(U, V)))), U)))))))))
% 3.62/0.81 = { by lemma 7 R->L }
% 3.62/0.81 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(W, multiply(multiply(inverse(W), multiply(V, inverse(multiply(U, V)))), U))), inverse(multiply(Z, multiply(X, multiply(W, multiply(multiply(inverse(W), multiply(V, inverse(multiply(U, V)))), U)))))))))
% 3.62/0.81 = { by axiom 1 (single_axiom) }
% 3.62/0.81 Z
% 3.62/0.81
% 3.62/0.81 Lemma 9: inverse(multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z)))) = inverse(X).
% 3.62/0.81 Proof:
% 3.62/0.81 inverse(multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z))))
% 3.62/0.81 = { by lemma 6 R->L }
% 3.62/0.81 inverse(multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y))))))))))
% 3.62/0.81 = { by lemma 8 }
% 3.62/0.81 inverse(X)
% 3.62/0.81
% 3.62/0.81 Lemma 10: inverse(multiply(multiply(X, multiply(inverse(X), Y)), multiply(Z, multiply(inverse(Z), inverse(W))))) = multiply(W, multiply(V, inverse(multiply(Y, V)))).
% 3.62/0.81 Proof:
% 3.62/0.81 inverse(multiply(multiply(X, multiply(inverse(X), Y)), multiply(Z, multiply(inverse(Z), inverse(W)))))
% 3.62/0.81 = { by lemma 9 R->L }
% 3.62/0.81 inverse(multiply(multiply(X, multiply(inverse(X), Y)), multiply(Z, multiply(inverse(Z), inverse(multiply(multiply(W, multiply(V, inverse(multiply(Y, V)))), multiply(X, multiply(inverse(X), Y))))))))
% 3.62/0.81 = { by lemma 8 }
% 3.62/0.81 multiply(W, multiply(V, inverse(multiply(Y, V))))
% 3.62/0.81
% 3.62/0.81 Lemma 11: multiply(multiply(X, multiply(Y, multiply(inverse(Y), Z))), multiply(W, inverse(multiply(Z, W)))) = X.
% 3.62/0.81 Proof:
% 3.62/0.81 multiply(multiply(X, multiply(Y, multiply(inverse(Y), Z))), multiply(W, inverse(multiply(Z, W))))
% 3.62/0.81 = { by lemma 2 R->L }
% 3.62/0.81 multiply(multiply(X, inverse(multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(X2, multiply(multiply(inverse(X2), multiply(multiply(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T))))))), multiply(Y2, multiply(multiply(inverse(Y2), Z2), inverse(multiply(inverse(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))))), multiply(S, Z2)))))), inverse(multiply(W2, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(Y2, multiply(multiply(inverse(Y2), Z2), inverse(multiply(inverse(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))))), multiply(S, Z2)))))))))), W2))))), multiply(W, inverse(multiply(Z, W))))
% 3.62/0.81 = { by axiom 1 (single_axiom) }
% 3.62/0.81 multiply(multiply(X, inverse(multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(X2, multiply(multiply(inverse(X2), multiply(multiply(S, multiply(Y2, multiply(multiply(inverse(Y2), Z2), inverse(multiply(inverse(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))))), multiply(S, Z2)))))), inverse(multiply(W2, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(Y2, multiply(multiply(inverse(Y2), Z2), inverse(multiply(inverse(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))))), multiply(S, Z2)))))))))), W2))))), multiply(W, inverse(multiply(Z, W))))
% 3.62/0.81 = { by lemma 5 }
% 3.62/0.81 multiply(multiply(X, inverse(multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(X2, multiply(multiply(inverse(X2), multiply(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T))))))), inverse(multiply(W2, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(Y2, multiply(multiply(inverse(Y2), Z2), inverse(multiply(inverse(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))))), multiply(S, Z2)))))))))), W2))))), multiply(W, inverse(multiply(Z, W))))
% 3.62/0.81 = { by lemma 7 R->L }
% 3.62/0.81 multiply(multiply(X, inverse(multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(X2, multiply(multiply(inverse(X2), multiply(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T))))))), inverse(multiply(W2, multiply(multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(Y2, multiply(multiply(inverse(Y2), Z2), inverse(multiply(inverse(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))))), multiply(S, Z2)))))), multiply(V2, multiply(multiply(inverse(V2), multiply(U2, inverse(multiply(T2, U2)))), T2))))))), W2))))), multiply(W, inverse(multiply(Z, W))))
% 3.62/0.81 = { by lemma 7 R->L }
% 3.62/0.81 multiply(multiply(X, inverse(multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(X2, multiply(multiply(inverse(X2), multiply(multiply(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T))))))), multiply(V2, multiply(multiply(inverse(V2), multiply(U2, inverse(multiply(T2, U2)))), T2))), inverse(multiply(W2, multiply(multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(Y2, multiply(multiply(inverse(Y2), Z2), inverse(multiply(inverse(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))))), multiply(S, Z2)))))), multiply(V2, multiply(multiply(inverse(V2), multiply(U2, inverse(multiply(T2, U2)))), T2))))))), W2))))), multiply(W, inverse(multiply(Z, W))))
% 3.62/0.81 = { by lemma 2 }
% 3.62/0.81 multiply(multiply(X, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(Y2, multiply(multiply(inverse(Y2), Z2), inverse(multiply(inverse(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))))), multiply(S, Z2))))))), multiply(W, inverse(multiply(Z, W))))
% 3.62/0.81 = { by lemma 10 R->L }
% 3.62/0.81 inverse(multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T))))))), inverse(multiply(X, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(Y2, multiply(multiply(inverse(Y2), Z2), inverse(multiply(inverse(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))))), multiply(S, Z2))))))))))))
% 3.62/0.81 = { by lemma 5 R->L }
% 3.62/0.81 inverse(multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(multiply(S, multiply(Y2, multiply(multiply(inverse(Y2), Z2), inverse(multiply(inverse(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))))), multiply(S, Z2)))))), inverse(multiply(X, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(Y2, multiply(multiply(inverse(Y2), Z2), inverse(multiply(inverse(inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))))), multiply(S, Z2))))))))))))
% 3.62/0.81 = { by lemma 3 }
% 3.62/0.81 X
% 3.62/0.81
% 3.62/0.81 Lemma 12: inverse(multiply(multiply(X, multiply(inverse(X), inverse(multiply(Y, Z)))), multiply(W, multiply(inverse(W), Y)))) = Z.
% 3.62/0.81 Proof:
% 3.62/0.81 inverse(multiply(multiply(X, multiply(inverse(X), inverse(multiply(Y, Z)))), multiply(W, multiply(inverse(W), Y))))
% 3.62/0.81 = { by lemma 8 R->L }
% 3.62/0.81 inverse(multiply(multiply(X, multiply(inverse(X), inverse(multiply(Y, Z)))), multiply(W, multiply(inverse(W), inverse(multiply(Z, multiply(X, multiply(inverse(X), inverse(multiply(Y, Z))))))))))
% 3.62/0.81 = { by lemma 8 }
% 3.62/0.81 Z
% 3.62/0.81
% 3.62/0.81 Lemma 13: multiply(X, multiply(Y, inverse(multiply(inverse(multiply(inverse(X), Z)), Y)))) = Z.
% 3.62/0.81 Proof:
% 3.62/0.81 multiply(X, multiply(Y, inverse(multiply(inverse(multiply(inverse(X), Z)), Y))))
% 3.62/0.81 = { by lemma 10 R->L }
% 3.62/0.81 inverse(multiply(multiply(W, multiply(inverse(W), inverse(multiply(inverse(X), Z)))), multiply(V, multiply(inverse(V), inverse(X)))))
% 3.62/0.81 = { by lemma 12 }
% 3.62/0.82 Z
% 3.62/0.82
% 3.62/0.82 Lemma 14: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(Y, inverse(Y))
% 3.62/0.82 = { by lemma 7 R->L }
% 3.62/0.82 multiply(Y, multiply(inverse(Y), multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V))))
% 3.62/0.82 = { by lemma 6 R->L }
% 3.62/0.82 multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(Y), multiply(X, multiply(inverse(X), multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V)))))), multiply(multiply(inverse(Y), multiply(X, multiply(inverse(X), multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V))))), multiply(U, inverse(multiply(multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V)), U))))))))
% 3.62/0.82 = { by lemma 11 }
% 3.62/0.82 multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(Y), multiply(X, multiply(inverse(X), multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V)))))), inverse(Y)))))
% 3.62/0.82 = { by lemma 13 }
% 3.62/0.82 multiply(X, multiply(inverse(X), multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V))))
% 3.62/0.82 = { by lemma 7 }
% 3.62/0.82 multiply(X, inverse(X))
% 3.62/0.82
% 3.62/0.82 Lemma 15: multiply(inverse(X), multiply(X, multiply(multiply(Y, multiply(Z, inverse(multiply(W, Z)))), W))) = Y.
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(inverse(X), multiply(X, multiply(multiply(Y, multiply(Z, inverse(multiply(W, Z)))), W)))
% 3.62/0.82 = { by lemma 4 R->L }
% 3.62/0.82 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(multiply(inverse(X), multiply(X, multiply(multiply(Y, multiply(Z, inverse(multiply(W, Z)))), W)))), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 3.62/0.82 = { by lemma 6 R->L }
% 3.62/0.82 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(multiply(inverse(X), multiply(X, multiply(multiply(Y, multiply(Z, inverse(multiply(W, Z)))), inverse(multiply(inverse(Y), multiply(Y, multiply(Z, inverse(multiply(W, Z)))))))))), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 3.62/0.82 = { by lemma 6 }
% 3.62/0.82 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(Y), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 3.62/0.82 = { by lemma 4 }
% 3.62/0.82 Y
% 3.62/0.82
% 3.62/0.82 Lemma 16: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(inverse(Y), Y)
% 3.62/0.82 = { by lemma 7 R->L }
% 3.62/0.82 multiply(inverse(Y), multiply(Y, multiply(inverse(Y), multiply(multiply(inverse(inverse(Y)), multiply(Z, inverse(multiply(W, Z)))), W))))
% 3.62/0.82 = { by lemma 15 R->L }
% 3.62/0.82 multiply(inverse(X), multiply(X, multiply(multiply(multiply(inverse(Y), multiply(Y, multiply(inverse(Y), multiply(multiply(inverse(inverse(Y)), multiply(Z, inverse(multiply(W, Z)))), W)))), multiply(V, inverse(multiply(multiply(multiply(inverse(inverse(Y)), multiply(Z, inverse(multiply(W, Z)))), W), V)))), multiply(multiply(inverse(inverse(Y)), multiply(Z, inverse(multiply(W, Z)))), W))))
% 3.62/0.82 = { by lemma 11 }
% 3.62/0.82 multiply(inverse(X), multiply(X, multiply(inverse(Y), multiply(multiply(inverse(inverse(Y)), multiply(Z, inverse(multiply(W, Z)))), W))))
% 3.62/0.82 = { by lemma 7 }
% 3.62/0.82 multiply(inverse(X), X)
% 3.62/0.82
% 3.62/0.82 Lemma 17: multiply(inverse(W), multiply(W, multiply(X, Z))) = multiply(X, multiply(Y, multiply(inverse(Y), Z))).
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(inverse(W), multiply(W, multiply(X, Z)))
% 3.62/0.82 = { by lemma 11 R->L }
% 3.62/0.82 multiply(inverse(W), multiply(W, multiply(multiply(multiply(X, multiply(Y, multiply(inverse(Y), Z))), multiply(V, inverse(multiply(Z, V)))), Z)))
% 3.62/0.82 = { by lemma 15 }
% 3.62/0.82 multiply(X, multiply(Y, multiply(inverse(Y), Z)))
% 3.62/0.82
% 3.62/0.82 Lemma 18: multiply(X, multiply(Y, inverse(Y))) = X.
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(X, multiply(Y, inverse(Y)))
% 3.62/0.82 = { by lemma 12 R->L }
% 3.62/0.82 inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(W, multiply(X, multiply(Y, inverse(Y))))))), multiply(V, multiply(inverse(V), W))))
% 3.62/0.82 = { by lemma 14 }
% 3.62/0.82 inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(W, multiply(X, multiply(multiply(inverse(X), X), inverse(multiply(inverse(X), X)))))))), multiply(V, multiply(inverse(V), W))))
% 3.62/0.82 = { by lemma 16 }
% 3.62/0.82 inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(W, multiply(X, multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(W, X)), multiply(W, X))))))))), multiply(V, multiply(inverse(V), W))))
% 3.62/0.82 = { by lemma 5 }
% 3.62/0.82 inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(W, X)))), multiply(V, multiply(inverse(V), W))))
% 3.62/0.82 = { by lemma 17 R->L }
% 3.62/0.82 inverse(multiply(inverse(U), multiply(U, multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(W, X)))), W))))
% 3.62/0.82 = { by lemma 8 R->L }
% 3.62/0.82 inverse(multiply(inverse(U), multiply(U, multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(W, X)))), inverse(multiply(X, multiply(Z, multiply(inverse(Z), inverse(multiply(W, X))))))))))
% 3.62/0.82 = { by lemma 6 }
% 3.62/0.82 X
% 3.62/0.82
% 3.62/0.82 Lemma 19: multiply(X, multiply(inverse(X), inverse(multiply(Y, inverse(Z))))) = multiply(Z, multiply(W, inverse(multiply(Y, W)))).
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(X, multiply(inverse(X), inverse(multiply(Y, inverse(Z)))))
% 3.62/0.82 = { by lemma 13 R->L }
% 3.62/0.82 multiply(Z, multiply(W, inverse(multiply(inverse(multiply(inverse(Z), multiply(X, multiply(inverse(X), inverse(multiply(Y, inverse(Z))))))), W))))
% 3.62/0.82 = { by lemma 8 }
% 3.62/0.82 multiply(Z, multiply(W, inverse(multiply(Y, W))))
% 3.62/0.82
% 3.62/0.82 Lemma 20: multiply(Z, multiply(W, inverse(multiply(Z, W)))) = multiply(X, multiply(Y, inverse(multiply(X, Y)))).
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(Z, multiply(W, inverse(multiply(Z, W))))
% 3.62/0.82 = { by lemma 19 R->L }
% 3.62/0.82 multiply(V, multiply(inverse(V), inverse(multiply(Z, inverse(Z)))))
% 3.62/0.82 = { by lemma 14 }
% 3.62/0.82 multiply(V, multiply(inverse(V), inverse(multiply(X, inverse(X)))))
% 3.62/0.82 = { by lemma 19 }
% 3.62/0.82 multiply(X, multiply(Y, inverse(multiply(X, Y))))
% 3.62/0.82
% 3.62/0.82 Lemma 21: multiply(X, multiply(Y, inverse(multiply(X, Y)))) = inverse(multiply(inverse(Z), Z)).
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(X, multiply(Y, inverse(multiply(X, Y))))
% 3.62/0.82 = { by lemma 20 }
% 3.62/0.82 multiply(inverse(multiply(inverse(Z), Z)), multiply(W, inverse(multiply(inverse(multiply(inverse(Z), Z)), W))))
% 3.62/0.82 = { by lemma 10 R->L }
% 3.62/0.82 inverse(multiply(multiply(V, multiply(inverse(V), inverse(multiply(inverse(Z), Z)))), multiply(U, multiply(inverse(U), inverse(inverse(multiply(inverse(Z), Z)))))))
% 3.62/0.82 = { by lemma 16 }
% 3.62/0.82 inverse(multiply(multiply(V, multiply(inverse(V), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))), multiply(U, multiply(inverse(U), inverse(inverse(multiply(inverse(Z), Z)))))))
% 3.62/0.82 = { by lemma 12 }
% 3.62/0.82 inverse(multiply(inverse(Z), Z))
% 3.62/0.82
% 3.62/0.82 Lemma 22: multiply(inverse(X), multiply(X, Y)) = multiply(Y, multiply(Z, inverse(Z))).
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(inverse(X), multiply(X, Y))
% 3.62/0.82 = { by lemma 7 R->L }
% 3.62/0.82 multiply(inverse(X), multiply(X, multiply(Y, multiply(W, multiply(multiply(inverse(W), multiply(V, inverse(multiply(U, V)))), U)))))
% 3.62/0.82 = { by lemma 17 }
% 3.62/0.82 multiply(Y, multiply(Z, multiply(inverse(Z), multiply(W, multiply(multiply(inverse(W), multiply(V, inverse(multiply(U, V)))), U)))))
% 3.62/0.82 = { by lemma 7 }
% 3.62/0.82 multiply(Y, multiply(Z, inverse(Z)))
% 3.62/0.82
% 3.62/0.82 Lemma 23: multiply(X, inverse(multiply(inverse(Y), Y))) = X.
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(X, inverse(multiply(inverse(Y), Y)))
% 3.62/0.82 = { by lemma 21 R->L }
% 3.62/0.82 multiply(X, multiply(Z, multiply(inverse(Z), inverse(multiply(Z, inverse(Z))))))
% 3.62/0.82 = { by lemma 17 R->L }
% 3.62/0.82 multiply(inverse(W), multiply(W, multiply(X, inverse(multiply(Z, inverse(Z))))))
% 3.62/0.82 = { by lemma 12 R->L }
% 3.62/0.82 multiply(inverse(W), multiply(W, inverse(multiply(multiply(V, multiply(inverse(V), inverse(multiply(inverse(X), multiply(X, inverse(multiply(Z, inverse(Z)))))))), multiply(U, multiply(inverse(U), inverse(X)))))))
% 3.62/0.82 = { by lemma 22 }
% 3.62/0.82 multiply(inverse(W), multiply(W, inverse(multiply(multiply(V, multiply(inverse(V), inverse(multiply(inverse(multiply(Z, inverse(Z))), multiply(Z, inverse(Z)))))), multiply(U, multiply(inverse(U), inverse(X)))))))
% 3.62/0.82 = { by lemma 16 R->L }
% 3.62/0.82 multiply(inverse(W), multiply(W, inverse(multiply(multiply(V, multiply(inverse(V), inverse(multiply(inverse(X), X)))), multiply(U, multiply(inverse(U), inverse(X)))))))
% 3.62/0.82 = { by lemma 12 }
% 3.62/0.82 multiply(inverse(W), multiply(W, X))
% 3.62/0.82 = { by lemma 22 }
% 3.62/0.82 multiply(X, multiply(T, inverse(T)))
% 3.62/0.82 = { by lemma 18 }
% 3.62/0.82 X
% 3.62/0.82
% 3.62/0.82 Lemma 24: inverse(multiply(inverse(X), inverse(Y))) = multiply(Y, X).
% 3.62/0.82 Proof:
% 3.62/0.82 inverse(multiply(inverse(X), inverse(Y)))
% 3.62/0.82 = { by lemma 13 R->L }
% 3.62/0.82 multiply(Y, multiply(X, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(X), inverse(Y))))), X))))
% 3.62/0.82 = { by lemma 12 R->L }
% 3.62/0.82 multiply(Y, multiply(X, inverse(multiply(inverse(inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(W, multiply(inverse(Y), inverse(multiply(inverse(X), inverse(Y)))))))), multiply(V, multiply(inverse(V), W))))), X))))
% 3.62/0.82 = { by lemma 8 R->L }
% 3.62/0.82 multiply(Y, multiply(X, inverse(multiply(inverse(inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(X))), multiply(T, multiply(inverse(T), inverse(multiply(multiply(W, multiply(inverse(Y), inverse(multiply(inverse(X), inverse(Y))))), multiply(U, multiply(inverse(U), inverse(X)))))))))))), multiply(V, multiply(inverse(V), W))))), X))))
% 3.62/0.82 = { by lemma 9 }
% 3.62/0.82 multiply(Y, multiply(X, inverse(multiply(inverse(inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(X))), multiply(T, multiply(inverse(T), inverse(W)))))))), multiply(V, multiply(inverse(V), W))))), X))))
% 3.62/0.82 = { by lemma 9 R->L }
% 3.62/0.82 multiply(Y, multiply(X, inverse(multiply(inverse(inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(X))), multiply(T, multiply(inverse(T), inverse(multiply(multiply(W, multiply(X, inverse(multiply(inverse(X), X)))), multiply(U, multiply(inverse(U), inverse(X)))))))))))), multiply(V, multiply(inverse(V), W))))), X))))
% 3.62/0.82 = { by lemma 8 }
% 3.62/0.82 multiply(Y, multiply(X, inverse(multiply(inverse(inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(W, multiply(X, inverse(multiply(inverse(X), X))))))), multiply(V, multiply(inverse(V), W))))), X))))
% 3.62/0.82 = { by lemma 12 }
% 3.62/0.82 multiply(Y, multiply(X, inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(X), X)))), X))))
% 3.62/0.82 = { by lemma 23 }
% 3.62/0.82 multiply(Y, multiply(X, inverse(multiply(inverse(X), X))))
% 3.62/0.82 = { by lemma 23 }
% 3.62/0.82 multiply(Y, X)
% 3.62/0.82
% 3.62/0.82 Lemma 25: multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(Z), Y))))) = Z.
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(Z), Y)))))
% 3.62/0.82 = { by lemma 13 R->L }
% 3.62/0.82 multiply(inverse(X), multiply(X, multiply(multiply(Z, multiply(W, inverse(multiply(inverse(multiply(inverse(Z), Y)), W)))), inverse(multiply(inverse(Z), Y)))))
% 3.62/0.82 = { by lemma 15 }
% 3.62/0.82 Z
% 3.62/0.82
% 3.62/0.82 Lemma 26: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 3.62/0.82 Proof:
% 3.62/0.82 multiply(inverse(X), X)
% 3.62/0.83 = { by lemma 18 R->L }
% 3.62/0.83 multiply(inverse(X), multiply(X, multiply(Z, inverse(Z))))
% 3.62/0.83 = { by lemma 6 R->L }
% 3.62/0.83 multiply(inverse(X), multiply(X, multiply(Z, inverse(inverse(multiply(inverse(Z), multiply(Z, multiply(W, inverse(multiply(Z, W))))))))))
% 3.62/0.83 = { by lemma 21 }
% 3.62/0.83 multiply(inverse(X), multiply(X, multiply(Z, inverse(inverse(multiply(inverse(Z), inverse(multiply(inverse(V), V))))))))
% 3.62/0.83 = { by lemma 24 }
% 3.62/0.83 multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(multiply(inverse(V), V), Z)))))
% 3.62/0.83 = { by lemma 24 R->L }
% 3.62/0.83 multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(inverse(multiply(inverse(V), inverse(inverse(V)))), Z)))))
% 3.62/0.83 = { by lemma 14 R->L }
% 3.62/0.83 multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(inverse(multiply(Y, inverse(Y))), Z)))))
% 3.62/0.83 = { by lemma 25 }
% 3.62/0.83 multiply(Y, inverse(Y))
% 3.62/0.83
% 3.62/0.83 Lemma 27: multiply(inverse(X), multiply(X, Y)) = Y.
% 3.62/0.83 Proof:
% 3.62/0.83 multiply(inverse(X), multiply(X, Y))
% 3.62/0.83 = { by lemma 18 R->L }
% 3.62/0.83 multiply(inverse(X), multiply(X, multiply(Y, multiply(Z, inverse(Z)))))
% 3.62/0.83 = { by lemma 17 }
% 3.62/0.83 multiply(Y, multiply(W, multiply(inverse(W), multiply(Z, inverse(Z)))))
% 3.62/0.83 = { by lemma 18 }
% 3.62/0.83 multiply(Y, multiply(W, inverse(W)))
% 3.62/0.83 = { by lemma 18 }
% 3.62/0.83 Y
% 3.62/0.83
% 3.62/0.83 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 3.62/0.83 Proof:
% 3.62/0.83 multiply(multiply(inverse(b2), b2), a2)
% 3.62/0.83 = { by lemma 26 }
% 3.62/0.83 multiply(multiply(X, inverse(X)), a2)
% 3.62/0.83 = { by axiom 1 (single_axiom) R->L }
% 3.62/0.83 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))))))
% 3.62/0.83 = { by lemma 27 }
% 3.62/0.83 multiply(multiply(X, inverse(X)), inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))))
% 3.62/0.83 = { by lemma 26 R->L }
% 3.62/0.83 multiply(multiply(inverse(W), W), inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))))
% 3.62/0.83 = { by lemma 23 R->L }
% 3.62/0.83 multiply(multiply(inverse(W), multiply(W, inverse(multiply(inverse(W), W)))), inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))))
% 3.62/0.83 = { by lemma 20 R->L }
% 3.62/0.83 multiply(multiply(a2, multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))), inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))))
% 3.62/0.83 = { by lemma 24 R->L }
% 3.62/0.83 multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))), inverse(a2))), inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))))
% 3.62/0.83 = { by lemma 27 R->L }
% 3.62/0.83 multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))), multiply(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z)))), multiply(inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))), inverse(a2))))), inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))))
% 3.62/0.83 = { by lemma 11 R->L }
% 3.62/0.83 multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))), multiply(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z)))), multiply(inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))), inverse(a2))))), multiply(multiply(inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))), multiply(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z)))), multiply(inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(a2, multiply(inverse(Y), Z))))), inverse(a2)))), multiply(V, inverse(multiply(inverse(a2), V)))))
% 3.62/0.83 = { by lemma 25 }
% 3.62/0.83 a2
% 3.62/0.83 % SZS output end Proof
% 3.62/0.83
% 3.62/0.83 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------