TSTP Solution File: BOO074-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO074-1 : 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 : n007.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 : Wed Aug 30 18:11:37 EDT 2023
% Result : Unsatisfiable 0.21s 0.50s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO074-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 08:20:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.50 Command-line arguments: --no-flatten-goal
% 0.21/0.50
% 0.21/0.50 % SZS status Unsatisfiable
% 0.21/0.50
% 0.21/0.53 % SZS output start Proof
% 0.21/0.53 Axiom 1 (dn1): inverse(add(inverse(add(inverse(add(X, Y)), Z)), inverse(add(X, inverse(add(inverse(Z), inverse(add(Z, W)))))))) = Z.
% 0.21/0.53
% 0.21/0.53 Lemma 2: inverse(add(inverse(X), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y)))))))) = X.
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(add(inverse(X), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y))))))))
% 0.21/0.53 = { by axiom 1 (dn1) R->L }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X)), Z)), X)), inverse(add(inverse(inverse(X)), inverse(add(inverse(X), inverse(add(X, W)))))))), inverse(X))), inverse(add(inverse(add(inverse(add(inverse(inverse(X)), Z)), X)), inverse(add(inverse(inverse(X)), inverse(add(inverse(X), inverse(add(X, V)))))))))), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y))))))))
% 0.21/0.53 = { by axiom 1 (dn1) }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X)), Z)), X)), inverse(add(inverse(inverse(X)), inverse(add(inverse(X), inverse(add(X, W)))))))), inverse(X))), X)), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y))))))))
% 0.21/0.53 = { by axiom 1 (dn1) }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(X, inverse(X))), X)), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y))))))))
% 0.21/0.53 = { by axiom 1 (dn1) }
% 0.21/0.53 X
% 0.21/0.53
% 0.21/0.53 Lemma 3: inverse(add(inverse(add(inverse(add(X, Y)), Z)), inverse(add(X, Z)))) = Z.
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(add(inverse(add(inverse(add(X, Y)), Z)), inverse(add(X, Z))))
% 0.21/0.53 = { by lemma 2 R->L }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(X, Y)), Z)), inverse(add(X, inverse(add(inverse(Z), inverse(add(Z, inverse(add(inverse(Z), inverse(add(Z, W))))))))))))
% 0.21/0.53 = { by axiom 1 (dn1) }
% 0.21/0.53 Z
% 0.21/0.53
% 0.21/0.53 Lemma 4: inverse(add(inverse(add(X, Y)), inverse(add(inverse(X), Y)))) = Y.
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(add(inverse(add(X, Y)), inverse(add(inverse(X), Y))))
% 0.21/0.53 = { by lemma 2 R->L }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(inverse(X), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Z)))))))), Y)), inverse(add(inverse(X), Y))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 Y
% 0.21/0.53
% 0.21/0.53 Lemma 5: inverse(add(X, inverse(add(Y, inverse(add(inverse(Y), X)))))) = inverse(add(inverse(Y), X)).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(add(X, inverse(add(Y, inverse(add(inverse(Y), X))))))
% 0.21/0.53 = { by lemma 4 R->L }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(Y, X)), inverse(add(inverse(Y), X)))), inverse(add(Y, inverse(add(inverse(Y), X))))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 inverse(add(inverse(Y), X))
% 0.21/0.53
% 0.21/0.53 Lemma 6: inverse(add(inverse(X), inverse(X))) = X.
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(add(inverse(X), inverse(X)))
% 0.21/0.53 = { by lemma 5 R->L }
% 0.21/0.53 inverse(add(inverse(X), inverse(add(X, inverse(add(inverse(X), inverse(X)))))))
% 0.21/0.53 = { by lemma 5 R->L }
% 0.21/0.53 inverse(add(inverse(X), inverse(add(X, inverse(add(inverse(X), inverse(add(X, inverse(add(inverse(X), inverse(X)))))))))))
% 0.21/0.53 = { by lemma 2 }
% 0.21/0.53 X
% 0.21/0.53
% 0.21/0.53 Lemma 7: inverse(add(inverse(X), inverse(add(X, X)))) = X.
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(add(inverse(X), inverse(add(X, X))))
% 0.21/0.53 = { by lemma 2 R->L }
% 0.21/0.53 inverse(add(inverse(X), inverse(add(X, inverse(add(inverse(X), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y))))))))))))
% 0.21/0.53 = { by lemma 2 }
% 0.21/0.53 X
% 0.21/0.53
% 0.21/0.53 Lemma 8: inverse(add(inverse(add(X, X)), inverse(add(X, X)))) = X.
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(add(inverse(add(X, X)), inverse(add(X, X))))
% 0.21/0.53 = { by lemma 4 R->L }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(X, inverse(add(X, X)))), inverse(add(inverse(X), inverse(add(X, X)))))), inverse(add(X, X))))
% 0.21/0.53 = { by lemma 7 }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(X, inverse(add(X, X)))), X)), inverse(add(X, X))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 X
% 0.21/0.53
% 0.21/0.53 Lemma 9: add(X, X) = X.
% 0.21/0.53 Proof:
% 0.21/0.53 add(X, X)
% 0.21/0.53 = { by lemma 6 R->L }
% 0.21/0.53 inverse(add(inverse(add(X, X)), inverse(add(X, X))))
% 0.21/0.53 = { by lemma 8 }
% 0.21/0.53 X
% 0.21/0.53
% 0.21/0.53 Lemma 10: inverse(add(X, inverse(add(inverse(add(Y, Z)), inverse(add(Y, X)))))) = inverse(add(Y, X)).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(add(X, inverse(add(inverse(add(Y, Z)), inverse(add(Y, X))))))
% 0.21/0.53 = { by lemma 3 R->L }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(inverse(add(Y, Z)), X)), inverse(add(Y, X)))), inverse(add(inverse(add(Y, Z)), inverse(add(Y, X))))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 inverse(add(Y, X))
% 0.21/0.53
% 0.21/0.53 Lemma 11: inverse(inverse(X)) = X.
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(inverse(X))
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 inverse(inverse(add(X, X)))
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 inverse(add(inverse(add(X, X)), inverse(add(X, X))))
% 0.21/0.53 = { by lemma 8 }
% 0.21/0.53 X
% 0.21/0.53
% 0.21/0.53 Lemma 12: add(inverse(add(X, Y)), inverse(add(inverse(X), Y))) = inverse(Y).
% 0.21/0.53 Proof:
% 0.21/0.53 add(inverse(add(X, Y)), inverse(add(inverse(X), Y)))
% 0.21/0.53 = { by lemma 6 R->L }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(X, Y)), inverse(add(inverse(X), Y)))), inverse(add(inverse(add(X, Y)), inverse(add(inverse(X), Y))))))
% 0.21/0.53 = { by lemma 4 }
% 0.21/0.53 inverse(add(Y, inverse(add(inverse(add(X, Y)), inverse(add(inverse(X), Y))))))
% 0.21/0.53 = { by lemma 4 }
% 0.21/0.53 inverse(add(Y, Y))
% 0.21/0.53 = { by lemma 9 }
% 0.21/0.53 inverse(Y)
% 0.21/0.53
% 0.21/0.53 Lemma 13: add(inverse(add(inverse(X), Y)), inverse(add(X, Y))) = inverse(Y).
% 0.21/0.53 Proof:
% 0.21/0.53 add(inverse(add(inverse(X), Y)), inverse(add(X, Y)))
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 add(inverse(add(add(inverse(X), inverse(X)), Y)), inverse(add(X, Y)))
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 add(inverse(add(add(inverse(X), inverse(add(X, X))), Y)), inverse(add(X, Y)))
% 0.21/0.53 = { by lemma 7 R->L }
% 0.21/0.53 add(inverse(add(add(inverse(X), inverse(add(X, X))), Y)), inverse(add(inverse(add(inverse(X), inverse(add(X, X)))), Y)))
% 0.21/0.53 = { by lemma 12 }
% 0.21/0.53 inverse(Y)
% 0.21/0.53
% 0.21/0.53 Lemma 14: inverse(add(X, add(Y, X))) = inverse(add(Y, X)).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(add(X, add(Y, X)))
% 0.21/0.53 = { by lemma 3 R->L }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(inverse(add(Y, X)), X)), inverse(add(Y, X)))), add(Y, X)))
% 0.21/0.53 = { by lemma 6 R->L }
% 0.21/0.53 inverse(add(inverse(add(inverse(add(inverse(add(Y, X)), X)), inverse(add(Y, X)))), inverse(add(inverse(add(Y, X)), inverse(add(Y, X))))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 inverse(add(Y, X))
% 0.21/0.53
% 0.21/0.53 Lemma 15: inverse(add(X, inverse(add(Y, inverse(X))))) = inverse(X).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(add(X, inverse(add(Y, inverse(X)))))
% 0.21/0.53 = { by lemma 11 R->L }
% 0.21/0.53 inverse(add(inverse(inverse(X)), inverse(add(Y, inverse(X)))))
% 0.21/0.54 = { by lemma 13 R->L }
% 0.21/0.54 inverse(add(inverse(add(inverse(add(inverse(Y), X)), inverse(add(Y, X)))), inverse(add(Y, inverse(X)))))
% 0.21/0.54 = { by lemma 6 R->L }
% 0.21/0.54 inverse(add(inverse(inverse(add(inverse(add(inverse(add(inverse(Y), X)), inverse(add(Y, X)))), inverse(add(inverse(add(inverse(Y), X)), inverse(add(Y, X))))))), inverse(add(Y, inverse(X)))))
% 0.21/0.54 = { by lemma 14 R->L }
% 0.21/0.54 inverse(add(inverse(inverse(add(inverse(add(inverse(add(inverse(Y), X)), inverse(add(Y, X)))), inverse(add(inverse(add(Y, X)), add(inverse(add(inverse(Y), X)), inverse(add(Y, X)))))))), inverse(add(Y, inverse(X)))))
% 0.21/0.54 = { by lemma 9 R->L }
% 0.21/0.54 inverse(add(inverse(inverse(add(inverse(add(inverse(add(inverse(Y), X)), inverse(add(Y, X)))), inverse(add(add(inverse(add(Y, X)), add(inverse(add(inverse(Y), X)), inverse(add(Y, X)))), add(inverse(add(Y, X)), add(inverse(add(inverse(Y), X)), inverse(add(Y, X))))))))), inverse(add(Y, inverse(X)))))
% 0.21/0.54 = { by lemma 14 R->L }
% 0.21/0.54 inverse(add(inverse(inverse(add(inverse(add(inverse(add(Y, X)), add(inverse(add(inverse(Y), X)), inverse(add(Y, X))))), inverse(add(add(inverse(add(Y, X)), add(inverse(add(inverse(Y), X)), inverse(add(Y, X)))), add(inverse(add(Y, X)), add(inverse(add(inverse(Y), X)), inverse(add(Y, X))))))))), inverse(add(Y, inverse(X)))))
% 0.21/0.54 = { by lemma 7 }
% 0.21/0.54 inverse(add(inverse(add(inverse(add(Y, X)), add(inverse(add(inverse(Y), X)), inverse(add(Y, X))))), inverse(add(Y, inverse(X)))))
% 0.21/0.54 = { by lemma 13 }
% 0.21/0.54 inverse(add(inverse(add(inverse(add(Y, X)), inverse(X))), inverse(add(Y, inverse(X)))))
% 0.21/0.54 = { by lemma 3 }
% 0.21/0.54 inverse(X)
% 0.21/0.54
% 0.21/0.54 Lemma 16: add(Y, X) = add(X, Y).
% 0.21/0.54 Proof:
% 0.21/0.54 add(Y, X)
% 0.21/0.54 = { by lemma 2 R->L }
% 0.21/0.54 add(Y, inverse(add(inverse(X), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y)))))))))
% 0.21/0.54 = { by lemma 6 R->L }
% 0.21/0.54 add(Y, inverse(add(inverse(X), inverse(inverse(add(inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y)))))), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y))))))))))))
% 0.21/0.54 = { by lemma 10 R->L }
% 0.21/0.54 add(Y, inverse(add(inverse(X), inverse(inverse(add(inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y)))))), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(add(X, Y)), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y))))))))))))))))
% 0.21/0.54 = { by lemma 9 R->L }
% 0.21/0.54 add(Y, inverse(add(inverse(X), inverse(inverse(add(inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y)))))), inverse(add(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(add(X, Y)), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y))))))))), add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(add(X, Y)), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y)))))))))))))))))
% 0.21/0.54 = { by lemma 10 R->L }
% 0.21/0.54 add(Y, inverse(add(inverse(X), inverse(inverse(add(inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(add(X, Y)), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y)))))))))), inverse(add(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(add(X, Y)), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y))))))))), add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(add(X, Y)), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y)))))))))))))))))
% 0.21/0.54 = { by lemma 7 }
% 0.21/0.54 add(Y, inverse(add(inverse(X), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(add(X, Y)), inverse(add(X, inverse(add(inverse(X), inverse(add(X, Y)))))))))))))
% 0.21/0.54 = { by lemma 5 }
% 0.21/0.54 add(Y, inverse(add(inverse(X), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(X), inverse(add(X, Y)))))))))
% 0.21/0.54 = { by lemma 9 }
% 0.21/0.54 add(Y, inverse(add(inverse(X), inverse(inverse(add(inverse(X), inverse(add(X, Y))))))))
% 0.21/0.54 = { by lemma 11 }
% 0.21/0.54 add(Y, inverse(add(inverse(X), add(inverse(X), inverse(add(X, Y))))))
% 0.21/0.54 = { by lemma 6 R->L }
% 0.21/0.54 add(Y, inverse(inverse(add(inverse(add(inverse(X), add(inverse(X), inverse(add(X, Y))))), inverse(add(inverse(X), add(inverse(X), inverse(add(X, Y)))))))))
% 0.21/0.54 = { by lemma 10 R->L }
% 0.21/0.54 add(Y, inverse(inverse(add(inverse(add(inverse(X), add(inverse(X), inverse(add(X, Y))))), inverse(add(add(inverse(X), inverse(add(X, Y))), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(X), add(inverse(X), inverse(add(X, Y)))))))))))))
% 0.21/0.54 = { by lemma 5 }
% 0.21/0.54 add(Y, inverse(inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(X), add(inverse(X), inverse(add(X, Y)))))))))
% 0.21/0.54 = { by lemma 9 R->L }
% 0.21/0.54 add(Y, inverse(inverse(add(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(X), inverse(add(X, Y))))), inverse(add(inverse(X), add(inverse(X), inverse(add(X, Y)))))))))
% 0.21/0.54 = { by lemma 9 R->L }
% 0.21/0.54 add(Y, inverse(inverse(add(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))), inverse(add(inverse(X), add(inverse(X), inverse(add(X, Y)))))))))
% 0.21/0.54 = { by lemma 7 R->L }
% 0.21/0.54 add(Y, inverse(inverse(add(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))), inverse(add(inverse(X), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))))))))))
% 0.21/0.54 = { by lemma 7 R->L }
% 0.21/0.54 add(Y, inverse(inverse(inverse(add(inverse(add(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))), inverse(add(inverse(X), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y))))))))))), inverse(add(add(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))), inverse(add(inverse(X), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))))))), add(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))), inverse(add(inverse(X), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))))))))))))))
% 0.21/0.54 = { by lemma 15 }
% 0.21/0.54 add(Y, inverse(inverse(inverse(add(inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y))))))), inverse(add(add(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))), inverse(add(inverse(X), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))))))), add(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))), inverse(add(inverse(X), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))))))))))))))
% 0.21/0.54 = { by lemma 9 }
% 0.21/0.54 add(Y, inverse(inverse(inverse(add(inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y))))))), inverse(add(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))), inverse(add(inverse(X), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y))))))))))))))))
% 0.21/0.54 = { by lemma 15 }
% 0.21/0.54 add(Y, inverse(inverse(inverse(add(inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y))))))), inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y))))))))))))
% 0.21/0.54 = { by lemma 6 }
% 0.21/0.54 add(Y, inverse(inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(add(inverse(X), inverse(add(X, Y))), add(inverse(X), inverse(add(X, Y)))))))))
% 0.21/0.54 = { by lemma 9 }
% 0.21/0.54 add(Y, inverse(inverse(add(inverse(add(inverse(X), inverse(add(X, Y)))), inverse(add(inverse(X), inverse(add(X, Y))))))))
% 0.21/0.54 = { by lemma 9 }
% 0.21/0.54 add(Y, inverse(inverse(inverse(add(inverse(X), inverse(add(X, Y)))))))
% 0.21/0.54 = { by lemma 11 }
% 0.21/0.54 add(Y, inverse(add(inverse(X), inverse(add(X, Y)))))
% 0.21/0.54 = { by lemma 9 R->L }
% 0.21/0.54 add(Y, inverse(add(add(inverse(X), inverse(X)), inverse(add(X, Y)))))
% 0.21/0.54 = { by lemma 9 R->L }
% 0.21/0.54 add(Y, inverse(add(add(inverse(X), inverse(add(X, X))), inverse(add(X, Y)))))
% 0.21/0.54 = { by lemma 7 R->L }
% 0.21/0.54 add(Y, inverse(add(add(inverse(X), inverse(add(X, X))), inverse(add(inverse(add(inverse(X), inverse(add(X, X)))), Y)))))
% 0.21/0.54 = { by lemma 6 R->L }
% 0.21/0.54 inverse(add(inverse(add(Y, inverse(add(add(inverse(X), inverse(add(X, X))), inverse(add(inverse(add(inverse(X), inverse(add(X, X)))), Y)))))), inverse(add(Y, inverse(add(add(inverse(X), inverse(add(X, X))), inverse(add(inverse(add(inverse(X), inverse(add(X, X)))), Y))))))))
% 0.21/0.54 = { by lemma 5 }
% 0.21/0.54 inverse(add(inverse(add(inverse(add(inverse(X), inverse(add(X, X)))), Y)), inverse(add(Y, inverse(add(add(inverse(X), inverse(add(X, X))), inverse(add(inverse(add(inverse(X), inverse(add(X, X)))), Y))))))))
% 0.21/0.54 = { by lemma 5 }
% 0.21/0.54 inverse(add(inverse(add(inverse(add(inverse(X), inverse(add(X, X)))), Y)), inverse(add(inverse(add(inverse(X), inverse(add(X, X)))), Y))))
% 0.21/0.54 = { by lemma 6 }
% 0.21/0.54 add(inverse(add(inverse(X), inverse(add(X, X)))), Y)
% 0.21/0.54 = { by lemma 7 }
% 0.21/0.54 add(X, Y)
% 0.21/0.54
% 0.21/0.54 Goal 1 (huntinton_3): add(inverse(add(inverse(a), b)), inverse(add(inverse(a), inverse(b)))) = a.
% 0.21/0.54 Proof:
% 0.21/0.54 add(inverse(add(inverse(a), b)), inverse(add(inverse(a), inverse(b))))
% 0.21/0.54 = { by lemma 16 R->L }
% 0.21/0.54 add(inverse(add(b, inverse(a))), inverse(add(inverse(a), inverse(b))))
% 0.21/0.54 = { by lemma 16 R->L }
% 0.21/0.54 add(inverse(add(b, inverse(a))), inverse(add(inverse(b), inverse(a))))
% 0.21/0.55 = { by lemma 12 }
% 0.21/0.55 inverse(inverse(a))
% 0.21/0.55 = { by lemma 11 }
% 0.21/0.55 a
% 0.21/0.55 % SZS output end Proof
% 0.21/0.55
% 0.21/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------