TSTP Solution File: GRP414-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP414-1 : 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 : n010.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 01:18:19 EDT 2023
% Result : Unsatisfiable 0.22s 0.48s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP414-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 02:23:49 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.22/0.48 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.48
% 0.22/0.48 % SZS status Unsatisfiable
% 0.22/0.48
% 0.22/0.54 % SZS output start Proof
% 0.22/0.54 Axiom 1 (single_axiom): multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(X, inverse(Y))), Z))), Y))) = Z.
% 0.22/0.54
% 0.22/0.54 Lemma 2: inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X)) = multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(W)), Z))).
% 0.22/0.54 Proof:
% 0.22/0.54 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X))
% 0.22/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.54 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X))))), Z)))
% 0.22/0.54 = { by axiom 1 (single_axiom) }
% 0.22/0.54 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(W)), Z)))
% 0.22/0.54
% 0.22/0.54 Lemma 3: multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y)))) = Z.
% 0.22/0.54 Proof:
% 0.22/0.54 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y))))
% 0.22/0.54 = { by lemma 2 R->L }
% 0.22/0.54 multiply(inverse(multiply(X, inverse(Y))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(Y))), inverse(W))), Z))), W)))
% 0.22/0.54 = { by axiom 1 (single_axiom) }
% 0.22/0.54 Z
% 0.22/0.55
% 0.22/0.55 Lemma 4: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X) = multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(Z, Y)))).
% 0.22/0.55 Proof:
% 0.22/0.55 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X)
% 0.22/0.55 = { by lemma 3 R->L }
% 0.22/0.55 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X))), Y))))
% 0.22/0.55 = { by axiom 1 (single_axiom) }
% 0.22/0.55 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(Z, Y))))
% 0.22/0.55
% 0.22/0.55 Lemma 5: multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(Z, X)))))) = Z.
% 0.22/0.55 Proof:
% 0.22/0.55 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(Z, X))))))
% 0.22/0.55 = { by lemma 4 R->L }
% 0.22/0.55 multiply(multiply(inverse(X), X), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(multiply(inverse(X), X), inverse(W))), Z))), W)))
% 0.22/0.55 = { by axiom 1 (single_axiom) }
% 0.22/0.55 Z
% 0.22/0.55
% 0.22/0.55 Lemma 6: inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), multiply(inverse(multiply(Y, inverse(Z))), W)))), X)) = W.
% 0.22/0.55 Proof:
% 0.22/0.55 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), multiply(inverse(multiply(Y, inverse(Z))), W)))), X))
% 0.22/0.55 = { by lemma 2 }
% 0.22/0.55 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(Y, inverse(Z))), W))), Z)))
% 0.22/0.55 = { by axiom 1 (single_axiom) }
% 0.22/0.55 W
% 0.22/0.55
% 0.22/0.55 Lemma 7: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(V, W))))))) = multiply(inverse(multiply(multiply(inverse(W), W), Y)), V).
% 0.22/0.55 Proof:
% 0.22/0.55 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(V, W)))))))
% 0.22/0.55 = { by lemma 6 R->L }
% 0.22/0.55 multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), multiply(X, inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(V, W)))))))
% 0.22/0.55 = { by lemma 4 R->L }
% 0.22/0.55 multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), multiply(X, inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)), multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)), inverse(multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), V))), multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))))
% 0.22/0.55 = { by lemma 3 }
% 0.22/0.55 multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), V)
% 0.22/0.55 = { by lemma 6 }
% 0.22/0.55 multiply(inverse(multiply(multiply(inverse(W), W), Y)), V)
% 0.22/0.55
% 0.22/0.55 Lemma 8: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(Z))))), X) = Z.
% 0.22/0.55 Proof:
% 0.22/0.55 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(Z))))), X)
% 0.22/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.55 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(inverse(multiply(W, inverse(V))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(V))), inverse(U))), Z))), U)))))))), X)
% 0.22/0.55 = { by lemma 2 }
% 0.22/0.55 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(inverse(multiply(W, inverse(V))), multiply(W, inverse(multiply(multiply(multiply(inverse(V), V), inverse(Z)), V))))))))), X)
% 0.22/0.55 = { by lemma 7 }
% 0.22/0.55 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(X))), multiply(multiply(inverse(V), V), inverse(Z))))), X)
% 0.22/0.55 = { by lemma 4 }
% 0.22/0.55 multiply(inverse(multiply(T, inverse(V))), multiply(T, inverse(multiply(multiply(multiply(inverse(V), V), inverse(Z)), V))))
% 0.22/0.55 = { by lemma 3 }
% 0.22/0.55 Z
% 0.22/0.55
% 0.22/0.55 Lemma 9: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 0.22/0.55 Proof:
% 0.22/0.55 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.22/0.55 = { by lemma 6 R->L }
% 0.22/0.55 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))))
% 0.22/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.55 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(inverse(multiply(Z2, inverse(X2))), inverse(multiply(multiply(multiply(inverse(W2), W2), inverse(multiply(inverse(multiply(inverse(multiply(Z2, inverse(X2))), inverse(W2))), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V)))), W2))))))
% 0.22/0.55 = { by lemma 2 }
% 0.22/0.55 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(inverse(multiply(Z2, inverse(X2))), multiply(Z2, inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))), X2)))))))
% 0.22/0.55 = { by lemma 7 }
% 0.22/0.55 multiply(inverse(multiply(multiply(inverse(X2), X2), Y)), multiply(multiply(inverse(X2), X2), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))))
% 0.22/0.55 = { by lemma 7 R->L }
% 0.22/0.55 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(S, inverse(X2))), multiply(S, inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))), X2)))))))
% 0.22/0.55 = { by lemma 2 R->L }
% 0.22/0.55 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(S, inverse(X2))), inverse(multiply(multiply(multiply(inverse(Y2), Y2), inverse(multiply(inverse(multiply(inverse(multiply(S, inverse(X2))), inverse(Y2))), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V)))), Y2))))))
% 0.22/0.55 = { by axiom 1 (single_axiom) }
% 0.22/0.55 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))))
% 0.22/0.55 = { by lemma 6 }
% 0.22/0.55 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.22/0.55
% 0.22/0.55 Lemma 10: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.22/0.55 Proof:
% 0.22/0.55 multiply(inverse(Y), Y)
% 0.22/0.55 = { by lemma 5 R->L }
% 0.22/0.55 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, inverse(multiply(multiply(inverse(Y), Y), Z))))))
% 0.22/0.55 = { by lemma 5 R->L }
% 0.22/0.55 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(U, inverse(V))), multiply(U, inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), Z)), V))))))))))
% 0.22/0.55 = { by lemma 7 R->L }
% 0.22/0.55 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(U, inverse(V))), multiply(U, inverse(multiply(inverse(multiply(T, Z)), multiply(T, inverse(multiply(inverse(multiply(V2, inverse(Y))), multiply(V2, inverse(multiply(V, Y))))))))))))))))
% 0.22/0.56 = { by lemma 8 R->L }
% 0.22/0.56 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(U, inverse(V))), multiply(U, inverse(multiply(inverse(multiply(T, Z)), multiply(T, inverse(multiply(inverse(multiply(V2, inverse(Y))), multiply(V2, inverse(multiply(V, multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(W2, inverse(X2))), multiply(W2, inverse(Y))))), X2)))))))))))))))))
% 0.22/0.56 = { by lemma 8 R->L }
% 0.22/0.56 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(U, inverse(V))), multiply(U, inverse(multiply(inverse(multiply(T, Z)), multiply(T, inverse(multiply(inverse(multiply(V2, inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(W2, inverse(X2))), multiply(W2, inverse(Y))))), X2)))), multiply(V2, inverse(multiply(V, multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(W2, inverse(X2))), multiply(W2, inverse(Y))))), X2)))))))))))))))))
% 0.22/0.56 = { by lemma 4 R->L }
% 0.22/0.56 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(U, inverse(V))), multiply(U, inverse(multiply(inverse(multiply(T, Z)), multiply(T, inverse(multiply(multiply(multiply(inverse(Z2), Z2), inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(W2, inverse(X2))), multiply(W2, inverse(Y))))), X2)), multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(W2, inverse(X2))), multiply(W2, inverse(Y))))), X2)), inverse(Z2))), V))), Z2)))))))))))))
% 0.22/0.56 = { by lemma 9 }
% 0.22/0.56 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(U, inverse(V))), multiply(U, inverse(multiply(inverse(multiply(T, Z)), multiply(T, inverse(multiply(multiply(multiply(inverse(Z2), Z2), inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(Y2, inverse(X2))), multiply(Y2, inverse(X))))), X2)), multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(Y2, inverse(X2))), multiply(Y2, inverse(X))))), X2)), inverse(Z2))), V))), Z2)))))))))))))
% 0.22/0.56 = { by lemma 4 }
% 0.22/0.56 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(U, inverse(V))), multiply(U, inverse(multiply(inverse(multiply(T, Z)), multiply(T, inverse(multiply(inverse(multiply(S, inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(Y2, inverse(X2))), multiply(Y2, inverse(X))))), X2)))), multiply(S, inverse(multiply(V, multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(Y2, inverse(X2))), multiply(Y2, inverse(X))))), X2)))))))))))))))))
% 0.22/0.56 = { by lemma 8 }
% 0.22/0.56 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(U, inverse(V))), multiply(U, inverse(multiply(inverse(multiply(T, Z)), multiply(T, inverse(multiply(inverse(multiply(S, inverse(X))), multiply(S, inverse(multiply(V, multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(Y2, inverse(X2))), multiply(Y2, inverse(X))))), X2)))))))))))))))))
% 0.22/0.56 = { by lemma 8 }
% 0.22/0.56 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(U, inverse(V))), multiply(U, inverse(multiply(inverse(multiply(T, Z)), multiply(T, inverse(multiply(inverse(multiply(S, inverse(X))), multiply(S, inverse(multiply(V, X))))))))))))))))
% 0.22/0.56 = { by lemma 7 }
% 0.22/0.56 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(U, inverse(V))), multiply(U, inverse(multiply(inverse(multiply(multiply(inverse(X), X), Z)), V))))))))))
% 0.22/0.56 = { by lemma 5 }
% 0.22/0.56 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, inverse(multiply(multiply(inverse(X), X), Z))))))
% 0.22/0.56 = { by lemma 5 }
% 0.22/0.56 multiply(inverse(X), X)
% 0.22/0.56
% 0.22/0.56 Lemma 11: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))), Z) = Z.
% 0.22/0.56 Proof:
% 0.22/0.56 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))), Z)
% 0.22/0.56 = { by lemma 10 }
% 0.22/0.56 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(Y), Y))), Z)
% 0.22/0.56 = { by lemma 10 }
% 0.22/0.56 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, inverse(Z))))), Z)
% 0.22/0.56 = { by lemma 8 }
% 0.22/0.56 Z
% 0.22/0.56
% 0.22/0.56 Lemma 12: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(inverse(Y), Z).
% 0.22/0.56 Proof:
% 0.22/0.56 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.22/0.56 = { by lemma 9 }
% 0.22/0.56 multiply(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Y)), multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))
% 0.22/0.56 = { by lemma 11 }
% 0.22/0.56 multiply(inverse(Y), multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))
% 0.22/0.56 = { by lemma 11 }
% 0.22/0.56 multiply(inverse(Y), Z)
% 0.22/0.56
% 0.22/0.56 Lemma 13: multiply(multiply(inverse(X), X), inverse(multiply(inverse(inverse(Y)), inverse(multiply(inverse(Z), Z))))) = inverse(Y).
% 0.22/0.56 Proof:
% 0.22/0.56 multiply(multiply(inverse(X), X), inverse(multiply(inverse(inverse(Y)), inverse(multiply(inverse(Z), Z)))))
% 0.22/0.56 = { by lemma 10 }
% 0.22/0.56 multiply(multiply(inverse(X), X), inverse(multiply(inverse(inverse(Y)), inverse(multiply(inverse(Y), Y)))))
% 0.22/0.56 = { by lemma 10 }
% 0.22/0.56 multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(inverse(Y)), inverse(multiply(inverse(Y), Y)))))
% 0.22/0.56 = { by lemma 12 R->L }
% 0.22/0.56 multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(inverse(Y), Y))))))
% 0.22/0.56 = { by lemma 5 }
% 0.22/0.56 inverse(Y)
% 0.22/0.56
% 0.22/0.56 Lemma 14: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = inverse(multiply(inverse(Z), Z)).
% 0.22/0.56 Proof:
% 0.22/0.56 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 0.22/0.56 = { by lemma 10 }
% 0.22/0.56 multiply(multiply(inverse(X), X), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.22/0.56 = { by lemma 13 }
% 0.22/0.56 inverse(multiply(inverse(Z), Z))
% 0.22/0.56
% 0.22/0.56 Lemma 15: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.22/0.56 Proof:
% 0.22/0.56 inverse(multiply(inverse(X), X))
% 0.22/0.56 = { by lemma 14 R->L }
% 0.22/0.56 multiply(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(W, inverse(inverse(multiply(inverse(Z), Z))))), multiply(W, inverse(inverse(multiply(inverse(Z), Z)))))))
% 0.22/0.56 = { by lemma 14 R->L }
% 0.22/0.56 multiply(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(W, inverse(inverse(multiply(inverse(Z), Z))))), multiply(W, inverse(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Z), Z))))))))
% 0.22/0.56 = { by lemma 5 }
% 0.22/0.56 multiply(inverse(Y), Y)
% 0.22/0.56
% 0.22/0.56 Lemma 16: multiply(inverse(multiply(inverse(X), X)), Y) = Y.
% 0.22/0.56 Proof:
% 0.22/0.56 multiply(inverse(multiply(inverse(X), X)), Y)
% 0.22/0.56 = { by lemma 14 R->L }
% 0.22/0.56 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(W), W))), Y)
% 0.22/0.56 = { by lemma 11 }
% 0.22/0.56 Y
% 0.22/0.56
% 0.22/0.56 Lemma 17: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.22/0.56 Proof:
% 0.22/0.56 multiply(X, multiply(inverse(X), Y))
% 0.22/0.56 = { by lemma 6 R->L }
% 0.22/0.56 multiply(inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(V))), inverse(Z))), multiply(inverse(multiply(W, inverse(V))), X)))), Z)), multiply(inverse(X), Y))
% 0.22/0.56 = { by lemma 13 R->L }
% 0.22/0.56 multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(V))), inverse(Z))), multiply(inverse(multiply(W, inverse(V))), X)))), Z))), inverse(multiply(inverse(T), T))))), multiply(inverse(X), Y))
% 0.22/0.56 = { by lemma 6 }
% 0.22/0.56 multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(X), inverse(multiply(inverse(T), T))))), multiply(inverse(X), Y))
% 0.22/0.56 = { by lemma 15 R->L }
% 0.22/0.56 multiply(multiply(inverse(multiply(inverse(S), S)), inverse(multiply(inverse(X), inverse(multiply(inverse(T), T))))), multiply(inverse(X), Y))
% 0.22/0.56 = { by lemma 16 }
% 0.22/0.56 multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(T), T)))), multiply(inverse(X), Y))
% 0.22/0.56 = { by lemma 15 }
% 0.22/0.56 multiply(inverse(multiply(inverse(X), multiply(inverse(X2), X2))), multiply(inverse(X), Y))
% 0.22/0.56 = { by lemma 12 }
% 0.22/0.56 multiply(inverse(multiply(inverse(X2), X2)), Y)
% 0.22/0.56 = { by lemma 16 }
% 0.22/0.56 Y
% 0.22/0.56
% 0.22/0.56 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.22/0.56 Proof:
% 0.22/0.56 multiply(multiply(a3, b3), c3)
% 0.22/0.56 = { by lemma 16 R->L }
% 0.22/0.56 multiply(multiply(a3, b3), multiply(inverse(multiply(inverse(b3), b3)), c3))
% 0.22/0.56 = { by lemma 12 R->L }
% 0.22/0.56 multiply(multiply(a3, b3), multiply(inverse(multiply(b3, multiply(inverse(b3), b3))), multiply(b3, c3)))
% 0.22/0.56 = { by lemma 17 }
% 0.22/0.56 multiply(multiply(a3, b3), multiply(inverse(b3), multiply(b3, c3)))
% 0.22/0.56 = { by lemma 12 R->L }
% 0.22/0.56 multiply(multiply(a3, b3), multiply(inverse(multiply(a3, b3)), multiply(a3, multiply(b3, c3))))
% 0.22/0.56 = { by lemma 17 }
% 0.22/0.56 multiply(a3, multiply(b3, c3))
% 0.22/0.56 % SZS output end Proof
% 0.22/0.56
% 0.22/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------