TSTP Solution File: GRP441-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP441-1 : 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 : n005.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 01:18:26 EDT 2023
% Result : Unsatisfiable 2.93s 0.78s
% Output : Proof 4.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP441-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % 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 : n005.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 01:03:53 EDT 2023
% 0.14/0.34 % CPUTime :
% 2.93/0.78 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 2.93/0.78
% 2.93/0.78 % SZS status Unsatisfiable
% 2.93/0.78
% 3.67/0.87 % SZS output start Proof
% 3.67/0.87 Axiom 1 (single_axiom): inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(W, multiply(X, Z))))))) = W.
% 3.67/0.87
% 3.67/0.87 Lemma 2: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), W)))) = V.
% 3.67/0.87 Proof:
% 3.67/0.87 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), W))))
% 3.67/0.87 = { by axiom 1 (single_axiom) R->L }
% 3.67/0.87 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)))))))))))
% 3.67/0.87 = { by axiom 1 (single_axiom) }
% 3.67/0.87 V
% 3.67/0.87
% 3.67/0.87 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.
% 3.67/0.87 Proof:
% 3.67/0.87 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)))))))
% 3.67/0.87 = { by axiom 1 (single_axiom) R->L }
% 3.67/0.87 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)))))))
% 3.67/0.87 = { by axiom 1 (single_axiom) }
% 3.67/0.87 T
% 3.67/0.87
% 3.67/0.87 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.
% 3.67/0.87 Proof:
% 3.67/0.87 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))))
% 3.67/0.87 = { by lemma 2 R->L }
% 3.67/0.87 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))))))))
% 3.67/0.87 = { by axiom 1 (single_axiom) }
% 3.67/0.87 Z
% 3.67/0.87
% 3.67/0.87 Lemma 5: multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z)))))) = W.
% 3.67/0.87 Proof:
% 3.67/0.87 multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z))))))
% 3.67/0.87 = { by lemma 2 R->L }
% 3.67/0.87 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))))
% 3.67/0.87 = { by lemma 3 }
% 3.67/0.87 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))))
% 3.67/0.87 = { by lemma 4 }
% 3.67/0.87 W
% 3.67/0.87
% 3.67/0.87 Lemma 6: inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y)))))) = Z.
% 3.67/0.87 Proof:
% 3.67/0.87 inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y))))))
% 3.67/0.87 = { by lemma 5 R->L }
% 3.67/0.87 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))))))))))))
% 3.67/0.87 = { by lemma 5 R->L }
% 3.67/0.87 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))))))))))))
% 3.67/0.87 = { by axiom 1 (single_axiom) }
% 3.67/0.87 Z
% 3.67/0.87
% 3.67/0.87 Lemma 7: multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W))) = X.
% 3.67/0.87 Proof:
% 3.67/0.87 multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W)))
% 3.67/0.87 = { by lemma 6 R->L }
% 3.67/0.87 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)))))))))
% 3.67/0.87 = { by lemma 2 R->L }
% 3.67/0.87 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))))
% 3.67/0.87 = { by lemma 3 }
% 3.67/0.87 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))))
% 3.67/0.87 = { by lemma 3 R->L }
% 3.67/0.87 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))))
% 3.67/0.87 = { by lemma 2 }
% 3.67/0.87 multiply(Y2, multiply(Z2, multiply(multiply(inverse(Z2), W2), inverse(multiply(inverse(X), multiply(Y2, W2))))))
% 3.67/0.87 = { by lemma 5 }
% 3.67/0.87 X
% 3.67/0.87
% 3.67/0.87 Lemma 8: inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, X)))))) = Z.
% 3.67/0.87 Proof:
% 3.67/0.87 inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, X))))))
% 3.67/0.87 = { by lemma 7 R->L }
% 3.67/0.87 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)))))))))
% 3.67/0.87 = { by lemma 7 R->L }
% 3.67/0.87 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)))))))))
% 3.67/0.87 = { by axiom 1 (single_axiom) }
% 3.67/0.87 Z
% 3.67/0.87
% 3.67/0.87 Lemma 9: inverse(multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z)))) = inverse(X).
% 3.67/0.87 Proof:
% 3.67/0.87 inverse(multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z))))
% 3.67/0.87 = { by lemma 6 R->L }
% 3.67/0.87 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))))))))))
% 3.67/0.87 = { by lemma 8 }
% 3.67/0.87 inverse(X)
% 3.67/0.87
% 3.67/0.87 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)))).
% 3.67/0.87 Proof:
% 3.67/0.87 inverse(multiply(multiply(X, multiply(inverse(X), Y)), multiply(Z, multiply(inverse(Z), inverse(W)))))
% 3.67/0.87 = { by lemma 9 R->L }
% 3.67/0.87 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))))))))
% 3.67/0.87 = { by lemma 8 }
% 3.67/0.87 multiply(W, multiply(V, inverse(multiply(Y, V))))
% 3.67/0.87
% 3.67/0.87 Lemma 11: inverse(multiply(multiply(X, multiply(inverse(X), inverse(multiply(Y, Z)))), multiply(W, multiply(inverse(W), Y)))) = Z.
% 3.67/0.87 Proof:
% 3.67/0.87 inverse(multiply(multiply(X, multiply(inverse(X), inverse(multiply(Y, Z)))), multiply(W, multiply(inverse(W), Y))))
% 3.67/0.87 = { by lemma 8 R->L }
% 3.67/0.87 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))))))))))
% 3.67/0.87 = { by lemma 8 }
% 3.67/0.87 Z
% 3.67/0.87
% 3.67/0.87 Lemma 12: multiply(X, multiply(Y, inverse(multiply(inverse(multiply(inverse(X), Z)), Y)))) = Z.
% 3.67/0.87 Proof:
% 3.67/0.87 multiply(X, multiply(Y, inverse(multiply(inverse(multiply(inverse(X), Z)), Y))))
% 3.67/0.87 = { by lemma 10 R->L }
% 3.67/0.87 inverse(multiply(multiply(W, multiply(inverse(W), inverse(multiply(inverse(X), Z)))), multiply(V, multiply(inverse(V), inverse(X)))))
% 3.67/0.87 = { by lemma 11 }
% 3.67/0.87 Z
% 3.67/0.87
% 3.67/0.87 Lemma 13: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(inverse(X), inverse(multiply(Z, W)))), Z)))) = W.
% 3.67/0.87 Proof:
% 3.67/0.87 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(inverse(X), inverse(multiply(Z, W)))), Z))))
% 3.67/0.87 = { by lemma 7 R->L }
% 3.67/0.87 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(inverse(X), inverse(multiply(Z, multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T))))))), Z))))
% 3.67/0.87 = { by lemma 7 R->L }
% 3.67/0.87 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T))), inverse(multiply(Z, multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T))))))), Z))))
% 3.67/0.87 = { by lemma 2 }
% 3.67/0.88 W
% 3.67/0.88
% 3.67/0.88 Lemma 14: inverse(multiply(inverse(multiply(X, multiply(Y, multiply(inverse(Y), Z)))), X)) = Z.
% 3.67/0.88 Proof:
% 3.67/0.88 inverse(multiply(inverse(multiply(X, multiply(Y, multiply(inverse(Y), Z)))), X))
% 3.67/0.88 = { by lemma 3 R->L }
% 3.67/0.88 inverse(multiply(inverse(multiply(X, multiply(Y, multiply(inverse(Y), Z)))), inverse(multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(S, multiply(multiply(inverse(S), X2), inverse(multiply(inverse(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))))), multiply(T, X2)))))), inverse(multiply(X, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(S, multiply(multiply(inverse(S), X2), inverse(multiply(inverse(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))))), multiply(T, X2))))))))))))))
% 3.67/0.88 = { by lemma 5 }
% 3.67/0.88 inverse(multiply(inverse(multiply(X, multiply(Y, multiply(inverse(Y), Z)))), inverse(multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U))))))), inverse(multiply(X, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(S, multiply(multiply(inverse(S), X2), inverse(multiply(inverse(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))))), multiply(T, X2))))))))))))))
% 3.67/0.88 = { by lemma 10 }
% 3.67/0.88 inverse(multiply(inverse(multiply(X, multiply(Y, multiply(inverse(Y), Z)))), multiply(multiply(X, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(S, multiply(multiply(inverse(S), X2), inverse(multiply(inverse(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))))), multiply(T, X2))))))), multiply(Y2, inverse(multiply(Z, Y2))))))
% 3.67/0.88 = { by lemma 13 R->L }
% 3.67/0.88 inverse(multiply(inverse(multiply(X, multiply(Y, multiply(inverse(Y), Z)))), multiply(multiply(X, inverse(multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(Z2, multiply(multiply(inverse(Z2), multiply(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U))))))), inverse(multiply(W2, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(S, multiply(multiply(inverse(S), X2), inverse(multiply(inverse(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))))), multiply(T, X2)))))))))), W2))))), multiply(Y2, inverse(multiply(Z, Y2))))))
% 3.67/0.88 = { by lemma 5 R->L }
% 3.67/0.88 inverse(multiply(inverse(multiply(X, multiply(Y, multiply(inverse(Y), Z)))), multiply(multiply(X, inverse(multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(Z2, multiply(multiply(inverse(Z2), multiply(multiply(T, multiply(S, multiply(multiply(inverse(S), X2), inverse(multiply(inverse(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))))), multiply(T, X2)))))), inverse(multiply(W2, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(S, multiply(multiply(inverse(S), X2), inverse(multiply(inverse(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))))), multiply(T, X2)))))))))), W2))))), multiply(Y2, inverse(multiply(Z, Y2))))))
% 3.67/0.88 = { by axiom 1 (single_axiom) R->L }
% 3.67/0.88 inverse(multiply(inverse(multiply(X, multiply(Y, multiply(inverse(Y), Z)))), multiply(multiply(X, inverse(multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(Z2, multiply(multiply(inverse(Z2), multiply(multiply(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U))))))), multiply(S, multiply(multiply(inverse(S), X2), inverse(multiply(inverse(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))))), multiply(T, X2)))))), inverse(multiply(W2, multiply(multiply(Y, multiply(inverse(Y), Z)), multiply(S, multiply(multiply(inverse(S), X2), inverse(multiply(inverse(inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))))), multiply(T, X2)))))))))), W2))))), multiply(Y2, inverse(multiply(Z, Y2))))))
% 3.67/0.88 = { by lemma 2 }
% 3.67/0.88 inverse(multiply(inverse(multiply(X, multiply(Y, multiply(inverse(Y), Z)))), multiply(multiply(X, multiply(Y, multiply(inverse(Y), Z))), multiply(Y2, inverse(multiply(Z, Y2))))))
% 3.67/0.88 = { by lemma 6 }
% 3.67/0.88 Z
% 3.67/0.88
% 3.67/0.88 Lemma 15: multiply(X, multiply(inverse(X), Y)) = multiply(Z, multiply(inverse(Z), Y)).
% 3.67/0.88 Proof:
% 3.67/0.88 multiply(X, multiply(inverse(X), Y))
% 3.67/0.88 = { by lemma 12 R->L }
% 3.67/0.88 multiply(Z, multiply(inverse(Z), inverse(multiply(inverse(multiply(inverse(Z), multiply(X, multiply(inverse(X), Y)))), inverse(Z)))))
% 3.67/0.88 = { by lemma 14 }
% 3.67/0.88 multiply(Z, multiply(inverse(Z), Y))
% 3.67/0.88
% 3.67/0.88 Lemma 16: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 3.67/0.88 Proof:
% 3.67/0.88 multiply(Y, inverse(Y))
% 3.67/0.88 = { by lemma 7 R->L }
% 3.67/0.88 multiply(Y, multiply(inverse(Y), multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V))))
% 3.67/0.88 = { by lemma 15 R->L }
% 3.67/0.88 multiply(X, multiply(inverse(X), multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V))))
% 3.67/0.88 = { by lemma 7 }
% 3.67/0.88 multiply(X, inverse(X))
% 3.67/0.88
% 3.67/0.88 Lemma 17: multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z))) = X.
% 3.67/0.88 Proof:
% 3.67/0.88 multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z)))
% 3.67/0.88 = { by lemma 4 R->L }
% 3.67/0.88 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z)))), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 3.67/0.88 = { by lemma 9 }
% 3.67/0.88 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))))
% 3.67/0.88 = { by lemma 4 }
% 3.67/0.88 X
% 3.67/0.88
% 3.67/0.88 Lemma 18: multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(Z), X))))) = Z.
% 3.67/0.88 Proof:
% 3.67/0.88 multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(Z), X)))))
% 3.67/0.88 = { by lemma 12 R->L }
% 3.67/0.88 multiply(multiply(Z, multiply(W, inverse(multiply(inverse(multiply(inverse(Z), X)), W)))), multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(Z), X)))))
% 3.67/0.88 = { by lemma 17 }
% 3.67/0.88 Z
% 3.67/0.88
% 3.67/0.88 Lemma 19: multiply(inverse(multiply(Z, Y)), Z) = multiply(inverse(multiply(X, Y)), X).
% 3.67/0.88 Proof:
% 3.67/0.88 multiply(inverse(multiply(Z, Y)), Z)
% 3.67/0.88 = { by lemma 4 R->L }
% 3.67/0.88 inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(multiply(inverse(W), multiply(multiply(inverse(multiply(inverse(multiply(Z, Y)), Z)), U), inverse(multiply(T, multiply(S, U))))), T)), S))))
% 3.67/0.88 = { by lemma 18 R->L }
% 3.67/0.88 inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(multiply(inverse(W), multiply(multiply(inverse(multiply(inverse(multiply(Z, multiply(X2, multiply(inverse(X2), multiply(inverse(inverse(X2)), inverse(multiply(inverse(Y), X2))))))), Z)), U), inverse(multiply(T, multiply(S, U))))), T)), S))))
% 3.67/0.88 = { by lemma 14 }
% 3.67/0.88 inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(multiply(inverse(W), multiply(multiply(multiply(inverse(inverse(X2)), inverse(multiply(inverse(Y), X2))), U), inverse(multiply(T, multiply(S, U))))), T)), S))))
% 3.67/0.88 = { by lemma 14 R->L }
% 3.67/0.88 inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(multiply(inverse(W), multiply(multiply(inverse(multiply(inverse(multiply(X, multiply(X2, multiply(inverse(X2), multiply(inverse(inverse(X2)), inverse(multiply(inverse(Y), X2))))))), X)), U), inverse(multiply(T, multiply(S, U))))), T)), S))))
% 3.67/0.88 = { by lemma 18 }
% 3.67/0.88 inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(multiply(inverse(W), multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), X)), U), inverse(multiply(T, multiply(S, U))))), T)), S))))
% 3.67/0.88 = { by lemma 4 }
% 3.67/0.88 multiply(inverse(multiply(X, Y)), X)
% 3.67/0.88
% 3.67/0.88 Lemma 20: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 3.67/0.88 Proof:
% 3.67/0.88 multiply(inverse(Y), Y)
% 3.67/0.88 = { by lemma 7 R->L }
% 3.67/0.88 multiply(inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V)))), Y)
% 3.67/0.88 = { by lemma 19 }
% 3.67/0.88 multiply(inverse(multiply(X, multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V)))), X)
% 3.67/0.88 = { by lemma 7 }
% 3.67/0.88 multiply(inverse(X), X)
% 3.67/0.88
% 3.67/0.88 Lemma 21: inverse(multiply(inverse(X), multiply(Y, multiply(Z, inverse(multiply(Y, Z)))))) = X.
% 3.67/0.88 Proof:
% 3.67/0.88 inverse(multiply(inverse(X), multiply(Y, multiply(Z, inverse(multiply(Y, Z))))))
% 3.67/0.88 = { by lemma 8 R->L }
% 3.67/0.88 inverse(multiply(inverse(X), multiply(Y, multiply(Z, inverse(multiply(inverse(multiply(inverse(Y), multiply(W, multiply(inverse(W), inverse(multiply(Y, inverse(Y))))))), Z))))))
% 3.67/0.88 = { by lemma 12 }
% 3.67/0.88 inverse(multiply(inverse(X), multiply(W, multiply(inverse(W), inverse(multiply(Y, inverse(Y)))))))
% 3.67/0.88 = { by lemma 16 }
% 3.67/0.88 inverse(multiply(inverse(X), multiply(W, multiply(inverse(W), inverse(multiply(X, inverse(X)))))))
% 3.67/0.88 = { by lemma 8 }
% 3.67/0.88 X
% 3.67/0.88
% 3.67/0.88 Lemma 22: multiply(X, multiply(Y, inverse(multiply(X, Y)))) = inverse(multiply(inverse(Z), Z)).
% 3.67/0.88 Proof:
% 3.67/0.88 multiply(X, multiply(Y, inverse(multiply(X, Y))))
% 3.67/0.88 = { by lemma 21 R->L }
% 3.67/0.88 inverse(multiply(inverse(multiply(X, multiply(Y, inverse(multiply(X, Y))))), multiply(X, multiply(Y, inverse(multiply(X, Y))))))
% 3.67/0.88 = { by lemma 20 R->L }
% 3.67/0.88 inverse(multiply(inverse(Z), Z))
% 3.67/0.88
% 3.67/0.88 Lemma 23: inverse(multiply(inverse(X), X)) = multiply(Y, inverse(Y)).
% 3.67/0.88 Proof:
% 3.67/0.88 inverse(multiply(inverse(X), X))
% 3.67/0.88 = { by lemma 22 R->L }
% 3.67/0.88 multiply(multiply(inverse(Z), Z), multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(Z), Z))))))
% 3.67/0.88 = { by lemma 15 R->L }
% 3.67/0.88 multiply(inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(Z), Z)))), multiply(inverse(inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(Z), Z))))), inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(Z), Z))))))
% 3.67/0.88 = { by lemma 20 R->L }
% 3.67/0.88 multiply(inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(Z), Z)))), multiply(inverse(Z), Z))
% 3.67/0.88 = { by lemma 19 }
% 3.67/0.88 multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))), inverse(Y))
% 3.67/0.88 = { by lemma 22 R->L }
% 3.67/0.88 multiply(inverse(multiply(inverse(Y), multiply(W, multiply(V, inverse(multiply(W, V)))))), inverse(Y))
% 3.67/0.88 = { by lemma 21 }
% 3.67/0.89 multiply(Y, inverse(Y))
% 3.67/0.89
% 3.67/0.89 Lemma 24: multiply(Z, inverse(multiply(Y, Z))) = multiply(X, inverse(multiply(Y, X))).
% 3.67/0.89 Proof:
% 3.67/0.89 multiply(Z, inverse(multiply(Y, Z)))
% 3.67/0.89 = { by lemma 11 R->L }
% 3.67/0.89 inverse(multiply(multiply(W, multiply(inverse(W), inverse(multiply(V, multiply(Z, inverse(multiply(Y, Z))))))), multiply(U, multiply(inverse(U), V))))
% 3.67/0.89 = { by lemma 8 R->L }
% 3.67/0.89 inverse(multiply(multiply(W, multiply(inverse(W), inverse(inverse(multiply(multiply(T, multiply(inverse(T), Y)), multiply(S, multiply(inverse(S), inverse(multiply(multiply(V, multiply(Z, inverse(multiply(Y, Z)))), multiply(T, multiply(inverse(T), Y))))))))))), multiply(U, multiply(inverse(U), V))))
% 3.67/0.89 = { by lemma 9 }
% 3.67/0.89 inverse(multiply(multiply(W, multiply(inverse(W), inverse(inverse(multiply(multiply(T, multiply(inverse(T), Y)), multiply(S, multiply(inverse(S), inverse(V)))))))), multiply(U, multiply(inverse(U), V))))
% 3.67/0.89 = { by lemma 9 R->L }
% 3.67/0.89 inverse(multiply(multiply(W, multiply(inverse(W), inverse(inverse(multiply(multiply(T, multiply(inverse(T), Y)), multiply(S, multiply(inverse(S), inverse(multiply(multiply(V, multiply(X, inverse(multiply(Y, X)))), multiply(T, multiply(inverse(T), Y))))))))))), multiply(U, multiply(inverse(U), V))))
% 3.67/0.89 = { by lemma 8 }
% 3.67/0.89 inverse(multiply(multiply(W, multiply(inverse(W), inverse(multiply(V, multiply(X, inverse(multiply(Y, X))))))), multiply(U, multiply(inverse(U), V))))
% 3.67/0.89 = { by lemma 11 }
% 3.67/0.89 multiply(X, inverse(multiply(Y, X)))
% 3.67/0.89
% 3.67/0.89 Lemma 25: multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), Z) = multiply(W, inverse(multiply(inverse(X), W))).
% 3.67/0.89 Proof:
% 3.67/0.89 multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), Z)
% 3.67/0.89 = { by lemma 6 R->L }
% 3.67/0.89 multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y)))))))
% 3.67/0.89 = { by lemma 24 R->L }
% 3.67/0.89 multiply(W, inverse(multiply(inverse(X), W)))
% 3.67/0.89
% 3.67/0.89 Lemma 26: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 3.67/0.89 Proof:
% 3.67/0.89 multiply(X, inverse(multiply(Y, X)))
% 3.67/0.89 = { by lemma 24 }
% 3.67/0.89 multiply(inverse(Y), inverse(multiply(Y, inverse(Y))))
% 3.67/0.89 = { by lemma 16 R->L }
% 3.67/0.89 multiply(inverse(Y), inverse(multiply(Z, inverse(Z))))
% 3.67/0.89 = { by lemma 23 R->L }
% 3.67/0.89 multiply(inverse(Y), inverse(inverse(multiply(inverse(W), W))))
% 3.67/0.89 = { by lemma 12 R->L }
% 3.67/0.89 multiply(inverse(Y), multiply(multiply(inverse(W), W), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), W)), inverse(inverse(multiply(inverse(W), W))))), V)))))
% 3.67/0.89 = { by lemma 25 R->L }
% 3.67/0.89 multiply(inverse(Y), multiply(multiply(inverse(W), W), multiply(multiply(multiply(inverse(multiply(inverse(W), W)), inverse(inverse(multiply(inverse(W), W)))), multiply(U, inverse(multiply(T, U)))), T)))
% 3.67/0.89 = { by lemma 23 R->L }
% 3.67/0.89 multiply(inverse(Y), multiply(multiply(inverse(W), W), multiply(multiply(inverse(multiply(inverse(W), W)), multiply(U, inverse(multiply(T, U)))), T)))
% 3.67/0.89 = { by lemma 7 }
% 3.67/0.89 inverse(Y)
% 3.67/0.89
% 3.67/0.89 Lemma 27: multiply(X, multiply(Y, inverse(Y))) = X.
% 3.67/0.89 Proof:
% 3.67/0.89 multiply(X, multiply(Y, inverse(Y)))
% 3.67/0.89 = { by lemma 13 R->L }
% 3.67/0.89 inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), multiply(inverse(Z), inverse(multiply(V, multiply(X, multiply(Y, inverse(Y))))))), V))))
% 3.67/0.89 = { by lemma 16 }
% 3.67/0.89 inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), multiply(inverse(Z), inverse(multiply(V, multiply(X, multiply(multiply(inverse(X), X), inverse(multiply(inverse(X), X)))))))), V))))
% 3.67/0.89 = { by lemma 20 }
% 3.67/0.89 inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), multiply(inverse(Z), inverse(multiply(V, multiply(X, multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(V, X)), multiply(V, X))))))))), V))))
% 3.67/0.89 = { by lemma 5 }
% 3.67/0.89 inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), multiply(inverse(Z), inverse(multiply(V, X)))), V))))
% 3.67/0.89 = { by lemma 13 }
% 3.67/0.89 X
% 3.67/0.89
% 3.67/0.89 Lemma 28: multiply(inverse(X), multiply(X, Y)) = Y.
% 3.67/0.89 Proof:
% 3.67/0.89 multiply(inverse(X), multiply(X, Y))
% 3.67/0.89 = { by lemma 27 R->L }
% 3.67/0.89 multiply(inverse(X), multiply(X, multiply(Y, multiply(Z, inverse(Z)))))
% 3.67/0.89 = { by lemma 23 R->L }
% 3.67/0.89 multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(Y), Y)))))
% 4.19/0.89 = { by lemma 12 R->L }
% 4.19/0.89 multiply(inverse(X), multiply(X, multiply(multiply(Y, multiply(W, inverse(multiply(inverse(multiply(inverse(Y), Y)), W)))), inverse(multiply(inverse(Y), Y)))))
% 4.19/0.89 = { by lemma 4 R->L }
% 4.19/0.89 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(W, inverse(multiply(inverse(multiply(inverse(Y), Y)), W)))), inverse(multiply(inverse(Y), Y)))))), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 4.19/0.89 = { by lemma 6 R->L }
% 4.19/0.89 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(W, inverse(multiply(inverse(multiply(inverse(Y), Y)), W)))), inverse(multiply(inverse(Y), multiply(Y, multiply(W, inverse(multiply(inverse(multiply(inverse(Y), Y)), W)))))))))), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 4.19/0.89 = { by lemma 6 }
% 4.19/0.89 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))))
% 4.19/0.89 = { by lemma 4 }
% 4.19/0.89 Y
% 4.19/0.89
% 4.19/0.89 Lemma 29: multiply(X, multiply(inverse(X), Y)) = Y.
% 4.19/0.89 Proof:
% 4.19/0.89 multiply(X, multiply(inverse(X), Y))
% 4.19/0.89 = { by lemma 26 R->L }
% 4.19/0.89 multiply(X, multiply(multiply(Z, inverse(multiply(X, Z))), Y))
% 4.19/0.89 = { by lemma 28 R->L }
% 4.19/0.89 multiply(X, multiply(multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(X, Z))))), Y))
% 4.19/0.89 = { by lemma 21 R->L }
% 4.19/0.89 multiply(inverse(multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(X, Z)))))), multiply(multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(X, Z))))), Y))
% 4.19/0.89 = { by lemma 28 }
% 4.19/0.89 Y
% 4.19/0.89
% 4.19/0.89 Lemma 30: multiply(multiply(X, inverse(X)), Y) = Y.
% 4.19/0.89 Proof:
% 4.19/0.89 multiply(multiply(X, inverse(X)), Y)
% 4.19/0.89 = { by lemma 27 R->L }
% 4.19/0.89 multiply(multiply(X, inverse(X)), multiply(Y, multiply(inverse(Y), inverse(inverse(Y)))))
% 4.19/0.89 = { by lemma 15 }
% 4.19/0.89 multiply(multiply(X, inverse(X)), multiply(Z, multiply(inverse(Z), inverse(inverse(Y)))))
% 4.19/0.89 = { by lemma 27 R->L }
% 4.19/0.89 multiply(multiply(X, inverse(X)), multiply(Z, multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(X, inverse(X)))))))
% 4.19/0.89 = { by lemma 18 }
% 4.19/0.89 Y
% 4.19/0.89
% 4.19/0.89 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 4.19/0.89 Proof:
% 4.19/0.89 multiply(multiply(a3, b3), c3)
% 4.19/0.89 = { by lemma 11 R->L }
% 4.19/0.89 multiply(multiply(a3, b3), inverse(multiply(multiply(X, multiply(inverse(X), inverse(multiply(multiply(Y, Z), c3)))), multiply(Y, multiply(inverse(Y), multiply(Y, Z))))))
% 4.19/0.89 = { by lemma 28 }
% 4.19/0.89 multiply(multiply(a3, b3), inverse(multiply(multiply(X, multiply(inverse(X), inverse(multiply(multiply(Y, Z), c3)))), multiply(Y, Z))))
% 4.19/0.89 = { by lemma 8 R->L }
% 4.19/0.89 multiply(multiply(a3, b3), inverse(multiply(multiply(X, multiply(inverse(X), inverse(multiply(multiply(Y, Z), c3)))), inverse(multiply(c3, multiply(X, multiply(inverse(X), inverse(multiply(multiply(Y, Z), c3)))))))))
% 4.19/0.89 = { by lemma 24 R->L }
% 4.19/0.89 multiply(multiply(a3, b3), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.89 = { by lemma 14 R->L }
% 4.19/0.89 multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, b3)), multiply(multiply(a3, b3), multiply(inverse(multiply(a3, b3)), multiply(a3, b3))))), inverse(multiply(a3, b3)))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.89 = { by lemma 28 }
% 4.19/0.89 multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, b3)), multiply(a3, b3))), inverse(multiply(a3, b3)))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.89 = { by lemma 27 R->L }
% 4.19/0.89 multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, b3)), multiply(a3, b3))), inverse(multiply(multiply(a3, b3), multiply(W, inverse(W)))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.89 = { by lemma 23 R->L }
% 4.19/0.89 multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, b3)), multiply(a3, b3))), inverse(multiply(multiply(a3, b3), inverse(multiply(inverse(multiply(a3, b3)), multiply(a3, b3))))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 26 }
% 4.19/0.90 multiply(inverse(inverse(multiply(a3, b3))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 29 R->L }
% 4.19/0.90 multiply(inverse(inverse(multiply(a3, multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 29 R->L }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), a3)), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 3 R->L }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(multiply(b3, multiply(multiply(T, multiply(S, multiply(multiply(inverse(S), S), inverse(multiply(multiply(X2, inverse(X2)), multiply(T, S)))))), multiply(multiply(multiply(X2, inverse(X2)), c3), inverse(multiply(a3, multiply(b3, c3))))))))), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 30 }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(multiply(b3, multiply(multiply(T, multiply(S, multiply(multiply(inverse(S), S), inverse(multiply(multiply(X2, inverse(X2)), multiply(T, S)))))), multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 27 R->L }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(multiply(b3, multiply(multiply(T, multiply(S, multiply(multiply(inverse(S), multiply(S, multiply(Y2, inverse(Y2)))), inverse(multiply(multiply(X2, inverse(X2)), multiply(T, S)))))), multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 23 R->L }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(multiply(b3, multiply(multiply(T, multiply(S, multiply(multiply(inverse(S), multiply(S, inverse(multiply(inverse(S), S)))), inverse(multiply(multiply(X2, inverse(X2)), multiply(T, S)))))), multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 22 }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(multiply(b3, multiply(multiply(T, multiply(S, multiply(inverse(multiply(inverse(Z2), Z2)), inverse(multiply(multiply(X2, inverse(X2)), multiply(T, S)))))), multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 23 }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(multiply(b3, multiply(multiply(T, multiply(S, multiply(multiply(W2, inverse(W2)), inverse(multiply(multiply(X2, inverse(X2)), multiply(T, S)))))), multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 30 }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(multiply(b3, multiply(multiply(T, multiply(S, inverse(multiply(multiply(X2, inverse(X2)), multiply(T, S))))), multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 30 }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(multiply(b3, multiply(multiply(T, multiply(S, inverse(multiply(T, S)))), multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 22 }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(multiply(b3, multiply(inverse(multiply(inverse(V2), V2)), multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 23 }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(multiply(b3, multiply(multiply(U2, inverse(U2)), multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 30 }
% 4.19/0.90 multiply(inverse(inverse(multiply(multiply(U, multiply(inverse(U), inverse(multiply(b3, multiply(c3, inverse(multiply(a3, multiply(b3, c3)))))))), multiply(V, multiply(inverse(V), b3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 11 }
% 4.19/0.90 multiply(inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))), inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))
% 4.19/0.90 = { by lemma 25 R->L }
% 4.19/0.90 multiply(multiply(multiply(a3, multiply(b3, c3)), multiply(T2, inverse(multiply(multiply(S2, X3), T2)))), multiply(S2, X3))
% 4.19/0.90 = { by lemma 28 R->L }
% 4.19/0.90 multiply(multiply(multiply(a3, multiply(b3, c3)), multiply(T2, inverse(multiply(multiply(S2, X3), T2)))), multiply(S2, multiply(inverse(S2), multiply(S2, X3))))
% 4.19/0.90 = { by lemma 17 }
% 4.19/0.90 multiply(a3, multiply(b3, c3))
% 4.19/0.90 % SZS output end Proof
% 4.19/0.90
% 4.19/0.90 RESULT: Unsatisfiable (the axioms are contradictory).
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