TSTP Solution File: GRP405-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP405-1 : 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 : n022.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 01:18:17 EDT 2023
% Result : Unsatisfiable 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP405-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.13 % 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 : n022.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 01:09:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.53 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.53
% 0.21/0.53 % SZS status Unsatisfiable
% 0.21/0.53
% 0.21/0.58 % SZS output start Proof
% 0.21/0.58 Axiom 1 (single_axiom): multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), inverse(multiply(Y, multiply(inverse(Y), Y)))))) = Z.
% 0.21/0.58
% 0.21/0.58 Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))) = multiply(X, inverse(multiply(inverse(W), inverse(multiply(Y, multiply(inverse(Y), Y)))))).
% 0.21/0.58 Proof:
% 0.21/0.58 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z)))))
% 0.21/0.58 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.58 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.58 = { by axiom 1 (single_axiom) }
% 0.21/0.58 multiply(X, inverse(multiply(inverse(W), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.58
% 0.21/0.58 Lemma 3: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), inverse(multiply(Y, multiply(inverse(Y), Y))))))) = Z.
% 0.21/0.58 Proof:
% 0.21/0.58 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), inverse(multiply(Y, multiply(inverse(Y), Y)))))))
% 0.21/0.58 = { by lemma 2 R->L }
% 0.21/0.58 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z)), inverse(multiply(W, multiply(inverse(W), W))))))
% 0.21/0.58 = { by axiom 1 (single_axiom) }
% 0.21/0.58 Z
% 0.21/0.58
% 0.21/0.58 Lemma 4: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), inverse(multiply(Z, multiply(inverse(Z), Z))))) = W.
% 0.21/0.58 Proof:
% 0.21/0.58 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), inverse(multiply(Z, multiply(inverse(Z), Z)))))
% 0.21/0.58 = { by lemma 2 }
% 0.21/0.58 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.58 = { by axiom 1 (single_axiom) }
% 0.21/0.58 W
% 0.21/0.58
% 0.21/0.58 Lemma 5: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), V)), W)), inverse(multiply(V, multiply(inverse(V), V))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))).
% 0.21/0.58 Proof:
% 0.21/0.58 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), V)), W)), inverse(multiply(V, multiply(inverse(V), V)))))
% 0.21/0.58 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.58 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), V)), W)), inverse(multiply(V, multiply(inverse(V), V))))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.58 = { by axiom 1 (single_axiom) }
% 0.21/0.58 multiply(X, inverse(multiply(inverse(W), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.58 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.58 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.58 = { by axiom 1 (single_axiom) }
% 0.21/0.58 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z)))))
% 0.21/0.58
% 0.21/0.58 Lemma 6: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), inverse(multiply(Y, multiply(inverse(Y), Y))))) = Z.
% 0.21/0.58 Proof:
% 0.21/0.58 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 0.21/0.58 = { by lemma 4 R->L }
% 0.21/0.58 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 0.21/0.58 = { by lemma 4 R->L }
% 0.21/0.58 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 0.21/0.58 = { by lemma 4 }
% 0.21/0.58 Z
% 0.21/0.58
% 0.21/0.58 Lemma 7: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(inverse(multiply(W, Y)), multiply(W, Z)).
% 0.21/0.58 Proof:
% 0.21/0.58 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.21/0.58 = { by lemma 3 R->L }
% 0.21/0.58 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))))
% 0.21/0.58 = { by lemma 4 R->L }
% 0.21/0.58 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), X))), inverse(multiply(T, multiply(inverse(T), T))))), Y)), multiply(X, Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))))
% 0.21/0.58 = { by lemma 5 R->L }
% 0.21/0.58 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), X))), inverse(multiply(T, multiply(inverse(T), T))))), S)), multiply(X, Z))), inverse(multiply(S, multiply(inverse(S), S)))))))
% 0.21/0.58 = { by lemma 4 }
% 0.21/0.58 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, S)), multiply(X, Z))), inverse(multiply(S, multiply(inverse(S), S)))))))
% 0.21/0.58 = { by lemma 6 }
% 0.21/0.58 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.21/0.58
% 0.21/0.58 Lemma 8: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y)))) = Z.
% 0.21/0.58 Proof:
% 0.21/0.58 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y))))
% 0.21/0.58 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.58 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y))))), inverse(multiply(multiply(X, inverse(Z)), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))))))
% 0.21/0.58 = { by lemma 6 }
% 0.21/0.58 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(Z), inverse(multiply(multiply(X, inverse(Z)), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))))))
% 0.21/0.58 = { by lemma 3 }
% 0.21/0.58 Z
% 0.21/0.58
% 0.21/0.58 Lemma 9: multiply(V, multiply(inverse(multiply(inverse(multiply(U, Z)), multiply(U, V))), W)) = multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, X))), W)).
% 0.21/0.58 Proof:
% 0.21/0.58 multiply(V, multiply(inverse(multiply(inverse(multiply(U, Z)), multiply(U, V))), W))
% 0.21/0.58 = { by lemma 7 R->L }
% 0.21/0.58 multiply(V, multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), W))
% 0.21/0.58 = { by lemma 4 R->L }
% 0.21/0.58 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), inverse(multiply(Z, multiply(inverse(Z), Z))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), W))
% 0.21/0.58 = { by lemma 7 }
% 0.21/0.58 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), inverse(multiply(Z, multiply(inverse(Z), Z))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), W))
% 0.21/0.59 = { by lemma 4 }
% 0.21/0.59 multiply(X, multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), W))
% 0.21/0.59 = { by lemma 7 }
% 0.21/0.59 multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, X))), W))
% 0.21/0.59
% 0.21/0.59 Lemma 10: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(inverse(Y), Y)
% 0.21/0.59 = { by lemma 8 R->L }
% 0.21/0.59 multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Y)))), inverse(multiply(W, multiply(inverse(W), W)))))
% 0.21/0.59 = { by lemma 9 R->L }
% 0.21/0.59 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(Z, inverse(X)))), inverse(multiply(W, multiply(inverse(W), W)))))
% 0.21/0.59 = { by lemma 8 }
% 0.21/0.59 multiply(inverse(X), X)
% 0.21/0.59
% 0.21/0.59 Lemma 11: inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(Y, multiply(inverse(Z), Z))))) = Y.
% 0.21/0.59 Proof:
% 0.21/0.59 inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(Y, multiply(inverse(Z), Z)))))
% 0.21/0.59 = { by lemma 10 }
% 0.21/0.59 inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 0.21/0.59 = { by lemma 10 }
% 0.21/0.59 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Y))), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 0.21/0.59 = { by lemma 5 R->L }
% 0.21/0.59 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), Y))), inverse(multiply(U, multiply(inverse(U), U)))))
% 0.21/0.59 = { by lemma 4 }
% 0.21/0.59 Y
% 0.21/0.59
% 0.21/0.59 Lemma 12: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.21/0.59 Proof:
% 0.21/0.59 inverse(multiply(inverse(X), X))
% 0.21/0.59 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.59 multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(X), X)))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.59 = { by lemma 10 }
% 0.21/0.59 multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.59 = { by lemma 11 }
% 0.21/0.59 multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.59 = { by lemma 11 }
% 0.21/0.59 multiply(inverse(Y), Y)
% 0.21/0.59
% 0.21/0.59 Lemma 13: multiply(multiply(inverse(X), X), multiply(inverse(Y), Z)) = multiply(inverse(multiply(W, Y)), multiply(W, Z)).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(multiply(inverse(X), X), multiply(inverse(Y), Z))
% 0.21/0.59 = { by lemma 12 R->L }
% 0.21/0.59 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 0.21/0.59 = { by lemma 7 }
% 0.21/0.59 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.21/0.59
% 0.21/0.59 Lemma 14: multiply(multiply(inverse(X), X), Y) = Y.
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(multiply(inverse(X), X), Y)
% 0.21/0.59 = { by lemma 12 R->L }
% 0.21/0.59 multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), Y)
% 0.21/0.59 = { by lemma 12 }
% 0.21/0.59 multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), Y)
% 0.21/0.59 = { by lemma 11 R->L }
% 0.21/0.59 multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), Y)), multiply(inverse(U), U))))), multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), Y)), multiply(inverse(U), U)))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.59 = { by lemma 11 }
% 0.21/0.59 multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), Y)), multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), Y)), multiply(inverse(U), U)))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.59 = { by lemma 12 }
% 0.21/0.59 multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), Y)), multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), Y)), multiply(inverse(U), U)))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 0.21/0.59 = { by axiom 1 (single_axiom) }
% 0.21/0.59 multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), Y)), multiply(inverse(U), U))))
% 0.21/0.59 = { by lemma 12 R->L }
% 0.21/0.59 multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), Y)), inverse(multiply(inverse(multiply(T, multiply(inverse(Z), Z))), multiply(T, multiply(inverse(Z), Z)))))))
% 0.21/0.59 = { by lemma 13 R->L }
% 0.21/0.59 multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Z), Z))), Y)), inverse(multiply(multiply(inverse(Z), Z), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))
% 0.21/0.59 = { by axiom 1 (single_axiom) }
% 0.21/0.59 Y
% 0.21/0.59
% 0.21/0.59 Lemma 15: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(inverse(Y), Z).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.21/0.59 = { by lemma 7 R->L }
% 0.21/0.59 multiply(inverse(multiply(multiply(inverse(W), W), Y)), multiply(multiply(inverse(W), W), Z))
% 0.21/0.59 = { by lemma 14 }
% 0.21/0.59 multiply(inverse(Y), multiply(multiply(inverse(W), W), Z))
% 0.21/0.59 = { by lemma 14 }
% 0.21/0.59 multiply(inverse(Y), Z)
% 0.21/0.59
% 0.21/0.59 Lemma 16: multiply(X, multiply(inverse(multiply(inverse(Y), X)), Z)) = multiply(Y, Z).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(X, multiply(inverse(multiply(inverse(Y), X)), Z))
% 0.21/0.59 = { by lemma 15 R->L }
% 0.21/0.59 multiply(X, multiply(inverse(multiply(inverse(multiply(W, Y)), multiply(W, X))), Z))
% 0.21/0.59 = { by lemma 9 R->L }
% 0.21/0.59 multiply(Y, multiply(inverse(multiply(inverse(multiply(V, Y)), multiply(V, Y))), Z))
% 0.21/0.59 = { by lemma 15 }
% 0.21/0.59 multiply(Y, multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.21/0.59 = { by lemma 12 }
% 0.21/0.59 multiply(Y, multiply(multiply(inverse(U), U), Z))
% 0.21/0.59 = { by lemma 14 }
% 0.21/0.59 multiply(Y, Z)
% 0.21/0.59
% 0.21/0.59 Lemma 17: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(X, multiply(inverse(X), Y))
% 0.21/0.59 = { by lemma 16 R->L }
% 0.21/0.59 multiply(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(W, multiply(inverse(V), V)))), multiply(inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(W, multiply(inverse(V), V)))))), multiply(inverse(X), Y)))
% 0.21/0.59 = { by lemma 15 }
% 0.21/0.59 multiply(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(W, multiply(inverse(V), V)))), multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(W, multiply(inverse(V), V))))), Y))
% 0.21/0.59 = { by lemma 11 }
% 0.21/0.59 multiply(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(W, multiply(inverse(V), V)))), multiply(W, Y))
% 0.21/0.59 = { by lemma 12 }
% 0.21/0.59 multiply(multiply(multiply(inverse(U), U), inverse(multiply(W, multiply(inverse(V), V)))), multiply(W, Y))
% 0.21/0.59 = { by lemma 14 }
% 0.21/0.59 multiply(inverse(multiply(W, multiply(inverse(V), V))), multiply(W, Y))
% 0.21/0.59 = { by lemma 15 }
% 0.21/0.59 multiply(inverse(multiply(inverse(V), V)), Y)
% 0.21/0.59 = { by lemma 12 }
% 0.21/0.59 multiply(multiply(inverse(T), T), Y)
% 0.21/0.59 = { by lemma 14 }
% 0.21/0.59 Y
% 0.21/0.59
% 0.21/0.59 Lemma 18: multiply(X, multiply(inverse(Y), Y)) = X.
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(X, multiply(inverse(Y), Y))
% 0.21/0.59 = { by lemma 10 }
% 0.21/0.59 multiply(X, multiply(inverse(multiply(inverse(Z), X)), multiply(inverse(Z), X)))
% 0.21/0.59 = { by lemma 16 }
% 0.21/0.59 multiply(Z, multiply(inverse(Z), X))
% 0.21/0.59 = { by lemma 17 }
% 0.21/0.59 X
% 0.21/0.59
% 0.21/0.59 Lemma 19: inverse(inverse(X)) = X.
% 0.21/0.59 Proof:
% 0.21/0.59 inverse(inverse(X))
% 0.21/0.59 = { by lemma 17 R->L }
% 0.21/0.59 inverse(inverse(multiply(X, multiply(inverse(X), X))))
% 0.21/0.59 = { by lemma 18 R->L }
% 0.21/0.59 multiply(inverse(inverse(multiply(X, multiply(inverse(X), X)))), multiply(inverse(multiply(Y, X)), multiply(Y, X)))
% 0.21/0.59 = { by lemma 15 R->L }
% 0.21/0.59 multiply(inverse(multiply(inverse(Z), inverse(multiply(X, multiply(inverse(X), X))))), multiply(inverse(Z), multiply(inverse(multiply(Y, X)), multiply(Y, X))))
% 0.21/0.59 = { by lemma 3 R->L }
% 0.21/0.59 multiply(inverse(multiply(inverse(Z), inverse(multiply(X, multiply(inverse(X), X))))), multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(multiply(inverse(Z), inverse(multiply(X, multiply(inverse(X), X)))))))), multiply(inverse(multiply(Y, X)), multiply(Y, X))))
% 0.21/0.59 = { by lemma 15 }
% 0.21/0.59 multiply(inverse(multiply(inverse(Z), inverse(multiply(X, multiply(inverse(X), X))))), multiply(inverse(multiply(Y, inverse(multiply(inverse(Z), inverse(multiply(X, multiply(inverse(X), X))))))), multiply(Y, X)))
% 0.21/0.59 = { by lemma 15 }
% 0.21/0.59 multiply(inverse(multiply(inverse(Z), inverse(multiply(X, multiply(inverse(X), X))))), multiply(inverse(inverse(multiply(inverse(Z), inverse(multiply(X, multiply(inverse(X), X)))))), X))
% 0.21/0.59 = { by lemma 17 }
% 0.21/0.59 X
% 0.21/0.59
% 0.21/0.59 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(multiply(a3, b3), c3)
% 0.21/0.59 = { by lemma 19 R->L }
% 0.21/0.59 multiply(inverse(inverse(multiply(a3, b3))), c3)
% 0.21/0.59 = { by lemma 15 R->L }
% 0.21/0.59 multiply(inverse(multiply(b3, inverse(multiply(a3, b3)))), multiply(b3, c3))
% 0.21/0.59 = { by lemma 11 R->L }
% 0.21/0.59 multiply(inverse(multiply(b3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(a3, multiply(inverse(Y), Y))))), b3)))), multiply(b3, c3))
% 0.21/0.59 = { by lemma 15 R->L }
% 0.21/0.59 multiply(inverse(multiply(b3, inverse(multiply(inverse(multiply(inverse(b3), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(a3, multiply(inverse(Y), Y)))))), multiply(inverse(b3), b3))))), multiply(b3, c3))
% 0.21/0.59 = { by lemma 12 R->L }
% 0.21/0.59 multiply(inverse(multiply(b3, inverse(multiply(inverse(multiply(inverse(b3), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(a3, multiply(inverse(Y), Y)))))), inverse(multiply(inverse(Z), Z)))))), multiply(b3, c3))
% 0.21/0.59 = { by lemma 15 R->L }
% 0.21/0.59 multiply(inverse(multiply(b3, inverse(multiply(inverse(multiply(inverse(b3), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(a3, multiply(inverse(Y), Y)))))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))))), multiply(b3, c3))
% 0.21/0.59 = { by lemma 15 R->L }
% 0.21/0.59 multiply(inverse(multiply(b3, inverse(multiply(inverse(multiply(inverse(b3), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(a3, multiply(inverse(Y), Y)))))), inverse(multiply(inverse(multiply(W, multiply(inverse(Z), Z))), multiply(W, multiply(inverse(Z), Z)))))))), multiply(b3, c3))
% 0.21/0.59 = { by lemma 13 R->L }
% 0.21/0.59 multiply(inverse(multiply(b3, inverse(multiply(inverse(multiply(inverse(b3), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(a3, multiply(inverse(Y), Y)))))), inverse(multiply(multiply(inverse(Z), Z), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))), multiply(b3, c3))
% 0.21/0.59 = { by lemma 18 R->L }
% 0.21/0.59 multiply(inverse(multiply(b3, inverse(multiply(inverse(multiply(inverse(multiply(b3, multiply(inverse(Z), Z))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(a3, multiply(inverse(Y), Y)))))), inverse(multiply(multiply(inverse(Z), Z), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))), multiply(b3, c3))
% 0.21/0.59 = { by axiom 1 (single_axiom) }
% 0.21/0.59 multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(a3, multiply(inverse(Y), Y))))), multiply(b3, c3))
% 0.21/0.59 = { by lemma 12 }
% 0.21/0.60 multiply(inverse(multiply(multiply(inverse(V), V), inverse(multiply(a3, multiply(inverse(Y), Y))))), multiply(b3, c3))
% 0.21/0.60 = { by lemma 14 }
% 0.21/0.60 multiply(inverse(inverse(multiply(a3, multiply(inverse(Y), Y)))), multiply(b3, c3))
% 0.21/0.60 = { by lemma 18 }
% 0.21/0.60 multiply(inverse(inverse(a3)), multiply(b3, c3))
% 0.21/0.60 = { by lemma 19 }
% 0.21/0.60 multiply(a3, multiply(b3, c3))
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60
% 0.21/0.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------