TSTP Solution File: GRP416-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP416-1 : 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 : n028.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 01:18:20 EDT 2023
% Result : Unsatisfiable 2.54s 0.78s
% Output : Proof 4.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP416-1 : 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
% 0.13/0.33 % Computer : n028.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
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 02:48:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 2.54/0.78 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.54/0.78
% 2.54/0.78 % SZS status Unsatisfiable
% 2.54/0.78
% 4.34/0.91 % SZS output start Proof
% 4.34/0.91 Axiom 1 (single_axiom): inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X)))))) = Z.
% 4.34/0.91
% 4.34/0.91 Lemma 2: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X))))) = inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, Z))), inverse(multiply(inverse(W), W)))))).
% 4.34/0.91 Proof:
% 4.34/0.91 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X)))))
% 4.34/0.91 = { by axiom 1 (single_axiom) R->L }
% 4.34/0.91 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X))))))))), inverse(multiply(inverse(W), W))))))
% 4.34/0.91 = { by axiom 1 (single_axiom) }
% 4.34/0.91 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, Z))), inverse(multiply(inverse(W), W))))))
% 4.34/0.91
% 4.34/0.91 Lemma 3: inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(W, Z)), multiply(W, V))), inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(X), X)))))) = multiply(inverse(multiply(inverse(multiply(U, Y)), multiply(U, inverse(V)))), inverse(multiply(inverse(Y), Y))).
% 4.34/0.91 Proof:
% 4.34/0.91 inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(W, Z)), multiply(W, V))), inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(X), X))))))
% 4.34/0.91 = { by lemma 2 R->L }
% 4.34/0.91 inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(U, Y)), multiply(U, inverse(V)))), inverse(multiply(inverse(Y), Y))))))), inverse(multiply(inverse(X), X))))))
% 4.34/0.91 = { by axiom 1 (single_axiom) }
% 4.34/0.91 multiply(inverse(multiply(inverse(multiply(U, Y)), multiply(U, inverse(V)))), inverse(multiply(inverse(Y), Y)))
% 4.34/0.91
% 4.34/0.91 Lemma 4: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(Y), Y))) = inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), Z)), inverse(multiply(inverse(W), W)))))).
% 4.34/0.91 Proof:
% 4.34/0.91 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(Y), Y)))
% 4.34/0.91 = { by lemma 3 R->L }
% 4.34/0.91 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(Z)))), inverse(multiply(inverse(V), V)))))))), inverse(multiply(inverse(W), W))))))
% 4.34/0.91 = { by axiom 1 (single_axiom) }
% 4.34/0.91 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), Z)), inverse(multiply(inverse(W), W))))))
% 4.34/0.91
% 4.34/0.91 Lemma 5: multiply(X, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), inverse(multiply(inverse(Y), Y)))))))) = Z.
% 4.34/0.91 Proof:
% 4.34/0.91 multiply(X, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), inverse(multiply(inverse(Y), Y))))))))
% 4.34/0.91 = { by lemma 4 R->L }
% 4.34/0.91 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(W, X)), multiply(W, inverse(inverse(Z))))), inverse(multiply(inverse(X), X)))))
% 4.34/0.91 = { by lemma 2 }
% 4.34/0.91 inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(Z)))), inverse(multiply(inverse(V), V))))))
% 4.34/0.91 = { by axiom 1 (single_axiom) }
% 4.34/0.91 Z
% 4.34/0.91
% 4.34/0.91 Lemma 6: inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(W)))), inverse(multiply(inverse(inverse(multiply(Y, Z))), inverse(multiply(Y, Z)))))) = multiply(Y, inverse(inverse(multiply(Z, inverse(multiply(W, inverse(multiply(inverse(Z), Z)))))))).
% 4.34/0.91 Proof:
% 4.34/0.91 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(W)))), inverse(multiply(inverse(inverse(multiply(Y, Z))), inverse(multiply(Y, Z))))))
% 4.34/0.91 = { by lemma 5 R->L }
% 4.34/0.91 multiply(Y, inverse(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(W)))), inverse(multiply(inverse(inverse(multiply(Y, Z))), inverse(multiply(Y, Z)))))))), inverse(multiply(inverse(Z), Z))))))))
% 4.34/0.91 = { by axiom 1 (single_axiom) }
% 4.34/0.91 multiply(Y, inverse(inverse(multiply(Z, inverse(multiply(W, inverse(multiply(inverse(Z), Z))))))))
% 4.34/0.91
% 4.34/0.91 Lemma 7: multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y))))))))) = inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, Z))), inverse(multiply(inverse(W), W)))))).
% 4.34/0.91 Proof:
% 4.34/0.91 multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y)))))))))
% 4.34/0.91 = { by lemma 6 R->L }
% 4.34/0.91 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(X, Y)))), multiply(U, inverse(Z)))), inverse(multiply(inverse(inverse(multiply(X, Y))), inverse(multiply(X, Y)))))))
% 4.34/0.91 = { by lemma 2 }
% 4.34/0.91 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, Z))), inverse(multiply(inverse(W), W))))))
% 4.34/0.91
% 4.34/0.91 Lemma 8: inverse(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, Z))), inverse(multiply(inverse(X), X))))))) = Z.
% 4.34/0.91 Proof:
% 4.34/0.91 inverse(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, Z))), inverse(multiply(inverse(X), X)))))))
% 4.34/0.91 = { by lemma 2 R->L }
% 4.34/0.91 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W))))))
% 4.34/0.91 = { by axiom 1 (single_axiom) }
% 4.34/0.91 Z
% 4.34/0.91
% 4.34/0.91 Lemma 9: inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y)))))))))) = Z.
% 4.34/0.91 Proof:
% 4.34/0.91 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y))))))))))
% 4.34/0.91 = { by lemma 6 R->L }
% 4.34/0.91 inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(X, Y)))), multiply(W, inverse(Z)))), inverse(multiply(inverse(inverse(multiply(X, Y))), inverse(multiply(X, Y))))))))
% 4.34/0.91 = { by axiom 1 (single_axiom) }
% 4.34/0.91 Z
% 4.34/0.91
% 4.34/0.91 Lemma 10: inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z))) = inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))).
% 4.34/0.91 Proof:
% 4.34/0.91 inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z)))
% 4.34/0.91 = { by lemma 9 R->L }
% 4.34/0.91 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z))), inverse(multiply(inverse(Y), Y))))))))))
% 4.34/0.91 = { by axiom 1 (single_axiom) R->L }
% 4.34/0.91 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(inverse(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z))), inverse(multiply(inverse(Y), Y))))))))), inverse(multiply(inverse(S), S)))))))))))
% 4.34/0.91 = { by lemma 2 R->L }
% 4.34/0.92 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(inverse(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(T, U)), multiply(T, inverse(Z)))), inverse(multiply(inverse(U), U)))))))), inverse(multiply(inverse(S), S)))))))))))
% 4.34/0.92 = { by lemma 2 R->L }
% 4.34/0.92 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(T, U)), multiply(T, inverse(Z)))), inverse(multiply(inverse(U), U))))))))), inverse(multiply(inverse(Y), Y))))))))))
% 4.34/0.92 = { by axiom 1 (single_axiom) }
% 4.34/0.92 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), inverse(multiply(inverse(Y), Y))))))))))
% 4.34/0.92 = { by lemma 9 }
% 4.34/0.92 inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))
% 4.34/0.92
% 4.34/0.92 Lemma 11: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 4.34/0.92 Proof:
% 4.34/0.92 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 4.34/0.92 = { by axiom 1 (single_axiom) R->L }
% 4.34/0.92 inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z)))))), inverse(multiply(inverse(V), V))))))
% 4.34/0.92 = { by lemma 10 }
% 4.34/0.92 inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))))), inverse(multiply(inverse(V), V))))))
% 4.34/0.92 = { by axiom 1 (single_axiom) }
% 4.34/0.92 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 4.34/0.92
% 4.34/0.92 Lemma 12: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(Z))))))), inverse(multiply(inverse(Y), Y))) = Z.
% 4.34/0.92 Proof:
% 4.34/0.92 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(Z))))))), inverse(multiply(inverse(Y), Y)))
% 4.34/0.92 = { by lemma 4 }
% 4.34/0.92 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(W), W))))))
% 4.34/0.92 = { by axiom 1 (single_axiom) }
% 4.34/0.92 Z
% 4.34/0.92
% 4.34/0.92 Lemma 13: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 4.34/0.92 Proof:
% 4.34/0.92 multiply(inverse(Y), Y)
% 4.34/0.92 = { by axiom 1 (single_axiom) R->L }
% 4.34/0.92 inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(multiply(Y3, X3)), multiply(Y3, inverse(multiply(inverse(Y), Y))))), inverse(multiply(inverse(X3), X3))))))
% 4.34/0.92 = { by lemma 7 R->L }
% 4.34/0.92 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(U), U)))))))))
% 4.34/0.92 = { by lemma 8 R->L }
% 4.34/0.92 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), T)), multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.92 = { by lemma 11 R->L }
% 4.34/0.92 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), T)), multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.92 = { by axiom 1 (single_axiom) R->L }
% 4.34/0.92 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(inverse(multiply(T2, inverse(multiply(inverse(multiply(inverse(multiply(S2, T2)), multiply(S2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), T))))), inverse(multiply(inverse(T2), T2))))))), multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.92 = { by lemma 7 R->L }
% 4.34/0.92 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), T)), inverse(multiply(inverse(W2), W2)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.92 = { by lemma 12 R->L }
% 4.34/0.93 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, S)), multiply(U2, inverse(inverse(multiply(S, inverse(Y))))))), inverse(multiply(inverse(S), S)))), Y)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), T)), inverse(multiply(inverse(W2), W2)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.93 = { by lemma 12 R->L }
% 4.34/0.93 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, S)), multiply(U2, inverse(inverse(multiply(S, inverse(Y))))))), inverse(multiply(inverse(S), S)))), multiply(inverse(multiply(inverse(multiply(U2, S)), multiply(U2, inverse(inverse(multiply(S, inverse(Y))))))), inverse(multiply(inverse(S), S))))), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), T)), inverse(multiply(inverse(W2), W2)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.93 = { by lemma 6 }
% 4.34/0.93 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(multiply(inverse(S), inverse(inverse(multiply(S, inverse(multiply(multiply(inverse(S), S), inverse(multiply(inverse(S), S)))))))), T)), inverse(multiply(inverse(W2), W2)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.93 = { by lemma 6 R->L }
% 4.34/0.93 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, S)), multiply(V2, inverse(inverse(multiply(S, inverse(X))))))), inverse(multiply(inverse(S), S)))), multiply(inverse(multiply(inverse(multiply(V2, S)), multiply(V2, inverse(inverse(multiply(S, inverse(X))))))), inverse(multiply(inverse(S), S))))), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), T)), inverse(multiply(inverse(W2), W2)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.93 = { by lemma 12 }
% 4.34/0.93 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, S)), multiply(V2, inverse(inverse(multiply(S, inverse(X))))))), inverse(multiply(inverse(S), S)))), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), T)), inverse(multiply(inverse(W2), W2)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.93 = { by lemma 12 }
% 4.34/0.93 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), T)), inverse(multiply(inverse(W2), W2)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.93 = { by lemma 7 }
% 4.34/0.93 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(Y2, X2)), multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), T))))), inverse(multiply(inverse(X2), X2))))))), multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.93 = { by axiom 1 (single_axiom) }
% 4.34/0.93 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(inverse(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), T)), multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(T), T)))))))))))))
% 4.34/0.93 = { by lemma 8 }
% 4.34/0.93 multiply(inverse(multiply(V, U)), multiply(V, inverse(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(U), U)))))))))
% 4.34/0.93 = { by lemma 7 }
% 4.34/0.93 inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(W, Z)), multiply(W, inverse(multiply(inverse(X), X))))), inverse(multiply(inverse(Z), Z))))))
% 4.34/0.93 = { by axiom 1 (single_axiom) }
% 4.34/0.93 multiply(inverse(X), X)
% 4.34/0.93
% 4.34/0.93 Lemma 14: inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(Z), Z)))))) = X.
% 4.34/0.93 Proof:
% 4.34/0.93 inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(Z), Z))))))
% 4.34/0.93 = { by lemma 13 }
% 4.34/0.93 inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(inverse(X)), inverse(X)))))))
% 4.34/0.93 = { by lemma 13 }
% 4.34/0.93 inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(X))), multiply(W, inverse(X)))), inverse(multiply(inverse(inverse(X)), inverse(X)))))))
% 4.34/0.93 = { by axiom 1 (single_axiom) }
% 4.34/0.93 X
% 4.34/0.93
% 4.34/0.93 Lemma 15: inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y)))) = inverse(multiply(inverse(Z), Z)).
% 4.34/0.93 Proof:
% 4.34/0.93 inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))))
% 4.34/0.93 = { by lemma 14 R->L }
% 4.34/0.93 inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))))), inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))))))
% 4.34/0.93 = { by lemma 13 R->L }
% 4.34/0.93 inverse(multiply(inverse(Z), Z))
% 4.34/0.93
% 4.34/0.93 Lemma 16: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 4.34/0.93 Proof:
% 4.34/0.93 inverse(multiply(inverse(X), X))
% 4.34/0.93 = { by lemma 5 R->L }
% 4.34/0.93 multiply(inverse(Y), inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(X), X)))), inverse(multiply(inverse(Y), Y))))))))
% 4.34/0.93 = { by lemma 15 }
% 4.34/0.93 multiply(inverse(Y), inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, Y))), inverse(multiply(inverse(Y), Y))))))))
% 4.34/0.93 = { by lemma 2 R->L }
% 4.34/0.93 multiply(inverse(Y), inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(Y)))), inverse(multiply(inverse(inverse(Y)), inverse(Y))))))))
% 4.34/0.93 = { by lemma 14 }
% 4.34/0.93 multiply(inverse(Y), Y)
% 4.34/0.93
% 4.34/0.93 Lemma 17: inverse(multiply(inverse(X), multiply(inverse(Y), Y))) = X.
% 4.34/0.93 Proof:
% 4.34/0.93 inverse(multiply(inverse(X), multiply(inverse(Y), Y)))
% 4.34/0.93 = { by lemma 16 R->L }
% 4.34/0.93 inverse(multiply(inverse(X), inverse(multiply(inverse(Z), Z))))
% 4.34/0.93 = { by lemma 15 R->L }
% 4.34/0.93 inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(V), V))))))
% 4.34/0.93 = { by lemma 14 }
% 4.34/0.93 X
% 4.34/0.93
% 4.34/0.93 Lemma 18: multiply(multiply(inverse(X), X), multiply(inverse(Y), Y)) = multiply(inverse(Z), Z).
% 4.34/0.93 Proof:
% 4.34/0.93 multiply(multiply(inverse(X), X), multiply(inverse(Y), Y))
% 4.34/0.93 = { by lemma 16 R->L }
% 4.34/0.93 multiply(inverse(multiply(inverse(W), W)), multiply(inverse(Y), Y))
% 4.34/0.93 = { by lemma 16 R->L }
% 4.34/0.93 multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(V), V)))
% 4.34/0.93 = { by lemma 16 }
% 4.34/0.93 multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W))
% 4.34/0.93 = { by lemma 13 R->L }
% 4.34/0.93 multiply(inverse(Z), Z)
% 4.34/0.93
% 4.34/0.93 Lemma 19: inverse(multiply(multiply(inverse(X), X), multiply(inverse(Y), Z))) = multiply(inverse(Z), Y).
% 4.34/0.93 Proof:
% 4.34/0.93 inverse(multiply(multiply(inverse(X), X), multiply(inverse(Y), Z)))
% 4.34/0.93 = { by lemma 16 R->L }
% 4.34/0.93 inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z)))
% 4.34/0.93 = { by lemma 11 }
% 4.34/0.93 inverse(multiply(inverse(multiply(inverse(Z), Y)), multiply(inverse(Z), Z)))
% 4.34/0.93 = { by lemma 13 R->L }
% 4.34/0.93 inverse(multiply(inverse(multiply(inverse(Z), Y)), multiply(inverse(W), W)))
% 4.34/0.93 = { by lemma 17 }
% 4.34/0.93 multiply(inverse(Z), Y)
% 4.34/0.93
% 4.34/0.93 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 4.34/0.93 Proof:
% 4.34/0.93 multiply(multiply(inverse(b2), b2), a2)
% 4.34/0.93 = { by lemma 9 R->L }
% 4.34/0.93 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(multiply(multiply(inverse(b2), b2), a2), inverse(multiply(inverse(Y), Y))))))))))
% 4.34/0.93 = { by lemma 16 R->L }
% 4.34/0.93 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(Z), Z)), a2), inverse(multiply(inverse(Y), Y))))))))))
% 4.34/0.93 = { by lemma 19 R->L }
% 4.34/0.93 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(a2), multiply(inverse(Z), Z)))), inverse(multiply(inverse(Y), Y))))))))))
% 4.34/0.93 = { by lemma 19 R->L }
% 4.34/0.93 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(multiply(inverse(V), V), multiply(inverse(inverse(multiply(inverse(Y), Y))), multiply(multiply(inverse(W), W), multiply(inverse(a2), multiply(inverse(Z), Z)))))))))))))
% 4.34/0.93 = { by lemma 16 R->L }
% 4.34/0.93 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(Y), Y))), inverse(multiply(inverse(Y), Y)))), multiply(inverse(inverse(multiply(inverse(Y), Y))), multiply(multiply(inverse(W), W), multiply(inverse(a2), multiply(inverse(Z), Z)))))))))))))
% 4.34/0.93 = { by lemma 10 }
% 4.34/0.93 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, multiply(multiply(inverse(W), W), multiply(inverse(a2), multiply(inverse(Z), Z)))))))))))))
% 4.34/0.94 = { by lemma 14 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(a2), multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(inverse(U), U)), inverse(multiply(inverse(T), T)))))))))))))))))
% 4.34/0.94 = { by lemma 17 }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, multiply(multiply(inverse(W), W), inverse(multiply(a2, inverse(multiply(inverse(multiply(inverse(U), U)), inverse(multiply(inverse(T), T)))))))))))))))))
% 4.34/0.94 = { by lemma 15 }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, multiply(multiply(inverse(W), W), inverse(multiply(a2, inverse(multiply(inverse(S), S)))))))))))))))
% 4.34/0.94 = { by lemma 16 }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, multiply(multiply(inverse(W), W), inverse(multiply(a2, multiply(inverse(X2), X2))))))))))))))
% 4.34/0.94 = { by lemma 18 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, multiply(multiply(inverse(W), W), inverse(multiply(a2, multiply(multiply(inverse(Y2), Y2), multiply(inverse(a2), a2)))))))))))))))
% 4.34/0.94 = { by lemma 17 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, multiply(multiply(inverse(W), W), inverse(multiply(a2, inverse(multiply(inverse(multiply(multiply(inverse(Y2), Y2), multiply(inverse(a2), a2))), multiply(inverse(Z2), Z2))))))))))))))))
% 4.34/0.94 = { by lemma 17 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, inverse(multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(a2, inverse(multiply(inverse(multiply(multiply(inverse(Y2), Y2), multiply(inverse(a2), a2))), multiply(inverse(Z2), Z2))))))), multiply(inverse(W2), W2)))))))))))))
% 4.34/0.94 = { by lemma 16 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(a2), a2)), inverse(multiply(a2, inverse(multiply(inverse(multiply(multiply(inverse(Y2), Y2), multiply(inverse(a2), a2))), multiply(inverse(Z2), Z2))))))), multiply(inverse(W2), W2)))))))))))))
% 4.34/0.94 = { by lemma 16 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(a2), a2)), inverse(multiply(a2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(a2), a2)), multiply(inverse(a2), a2))), multiply(inverse(Z2), Z2))))))), multiply(inverse(W2), W2)))))))))))))
% 4.34/0.94 = { by lemma 16 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(a2), a2)), inverse(multiply(a2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(a2), a2)), multiply(inverse(a2), a2))), inverse(multiply(inverse(a2), a2)))))))), multiply(inverse(W2), W2)))))))))))))
% 4.34/0.94 = { by lemma 16 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(a2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(a2), a2)), inverse(multiply(a2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(a2), a2)), multiply(inverse(a2), a2))), inverse(multiply(inverse(a2), a2)))))))), inverse(multiply(inverse(a2), a2))))))))))))))
% 4.34/0.94 = { by lemma 17 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(a2), a2)), inverse(multiply(a2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(a2), a2)), multiply(inverse(a2), a2))), inverse(multiply(inverse(a2), a2)))))))), inverse(multiply(inverse(a2), a2)))))), multiply(inverse(V2), V2))))))))))))
% 4.34/0.94 = { by lemma 3 }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), inverse(multiply(multiply(inverse(multiply(inverse(multiply(U2, inverse(a2))), multiply(U2, inverse(a2)))), inverse(multiply(inverse(inverse(a2)), inverse(a2)))), multiply(inverse(V2), V2))))))))))))
% 4.34/0.94 = { by lemma 16 }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), inverse(multiply(multiply(multiply(inverse(T2), T2), inverse(multiply(inverse(inverse(a2)), inverse(a2)))), multiply(inverse(V2), V2))))))))))))
% 4.34/0.94 = { by lemma 16 }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), inverse(multiply(multiply(multiply(inverse(T2), T2), multiply(inverse(S2), S2)), multiply(inverse(V2), V2))))))))))))
% 4.34/0.94 = { by lemma 18 }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), inverse(multiply(multiply(inverse(X3), X3), multiply(inverse(V2), V2))))))))))))
% 4.34/0.94 = { by lemma 16 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), inverse(multiply(inverse(multiply(inverse(Y3), Y3)), multiply(inverse(V2), V2))))))))))))
% 4.34/0.94 = { by lemma 16 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), inverse(multiply(inverse(multiply(inverse(Y3), Y3)), inverse(multiply(inverse(Z3), Z3)))))))))))))
% 4.34/0.94 = { by lemma 15 R->L }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), inverse(multiply(inverse(multiply(inverse(Y3), Y3)), inverse(multiply(inverse(multiply(inverse(W3), W3)), inverse(multiply(inverse(V3), V3)))))))))))))))
% 4.34/0.94 = { by lemma 14 }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(multiply(a2, inverse(multiply(inverse(Y), Y)))), multiply(inverse(Y3), Y3))))))))))
% 4.34/0.94 = { by lemma 17 }
% 4.34/0.94 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(a2, inverse(multiply(inverse(Y), Y))))))))))
% 4.34/0.94 = { by lemma 9 }
% 4.34/0.94 a2
% 4.34/0.94 % SZS output end Proof
% 4.34/0.94
% 4.34/0.94 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------