TSTP Solution File: SEU032+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n026.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 : 600s
% DateTime : Tue Jul 19 14:48:02 EDT 2022
% Result : Theorem 39.48s 39.65s
% Output : Proof 39.48s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 19:22:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 39.48/39.65 % SZS status Theorem
% 39.48/39.65 (* PROOF-FOUND *)
% 39.48/39.65 (* BEGIN-PROOF *)
% 39.48/39.65 % SZS output start Proof
% 39.48/39.65 1. (relation T_0) (-. (relation T_0)) ### Axiom
% 39.48/39.65 2. (function T_0) (-. (function T_0)) ### Axiom
% 39.48/39.65 3. (one_to_one T_0) (-. (one_to_one T_0)) ### Axiom
% 39.48/39.65 4. (relation T_0) (-. (relation T_0)) ### Axiom
% 39.48/39.65 5. (function T_0) (-. (function T_0)) ### Axiom
% 39.48/39.65 6. (-. (relation (function_inverse T_0))) (relation (function_inverse T_0)) ### Axiom
% 39.48/39.65 7. ((relation (function_inverse T_0)) /\ (function (function_inverse T_0))) (-. (relation (function_inverse T_0))) ### And 6
% 39.48/39.65 8. (((relation T_0) /\ (function T_0)) => ((relation (function_inverse T_0)) /\ (function (function_inverse T_0)))) (-. (relation (function_inverse T_0))) (function T_0) (relation T_0) ### DisjTree 4 5 7
% 39.48/39.65 9. (All A, (((relation A) /\ (function A)) => ((relation (function_inverse A)) /\ (function (function_inverse A))))) (relation T_0) (function T_0) (-. (relation (function_inverse T_0))) ### All 8
% 39.48/39.65 10. (relation T_0) (-. (relation T_0)) ### Axiom
% 39.48/39.65 11. (function T_0) (-. (function T_0)) ### Axiom
% 39.48/39.65 12. (-. (function (function_inverse T_0))) (function (function_inverse T_0)) ### Axiom
% 39.48/39.65 13. ((relation (function_inverse T_0)) /\ (function (function_inverse T_0))) (-. (function (function_inverse T_0))) ### And 12
% 39.48/39.65 14. (((relation T_0) /\ (function T_0)) => ((relation (function_inverse T_0)) /\ (function (function_inverse T_0)))) (-. (function (function_inverse T_0))) (function T_0) (relation T_0) ### DisjTree 10 11 13
% 39.48/39.65 15. (All A, (((relation A) /\ (function A)) => ((relation (function_inverse A)) /\ (function (function_inverse A))))) (relation T_0) (function T_0) (-. (function (function_inverse T_0))) ### All 14
% 39.48/39.65 16. (relation T_0) (-. (relation T_0)) ### Axiom
% 39.48/39.65 17. (function T_0) (-. (function T_0)) ### Axiom
% 39.48/39.65 18. (relation T_0) (-. (relation T_0)) ### Axiom
% 39.48/39.65 19. (function T_0) (-. (function T_0)) ### Axiom
% 39.48/39.65 20. (one_to_one T_0) (-. (one_to_one T_0)) ### Axiom
% 39.48/39.65 21. (-. (one_to_one (function_inverse T_0))) (one_to_one (function_inverse T_0)) ### Axiom
% 39.48/39.65 22. (((relation T_0) /\ (function T_0)) => ((one_to_one T_0) => (one_to_one (function_inverse T_0)))) (-. (one_to_one (function_inverse T_0))) (one_to_one T_0) (function T_0) (relation T_0) ### DisjTree 18 19 20 21
% 39.48/39.65 23. (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (one_to_one (function_inverse A))))) (relation T_0) (function T_0) (one_to_one T_0) (-. (one_to_one (function_inverse T_0))) ### All 22
% 39.48/39.65 24. ((relation_dom T_0) = (relation_rng (function_inverse T_0))) ((relation_rng (function_inverse T_0)) != (relation_dom T_0)) ### Sym(=)
% 39.48/39.65 25. (relation T_0) (-. (relation T_0)) ### Axiom
% 39.48/39.65 26. (function T_0) (-. (function T_0)) ### Axiom
% 39.48/39.65 27. (one_to_one T_0) (-. (one_to_one T_0)) ### Axiom
% 39.48/39.65 28. ((relation_composition (function_inverse T_0) T_0) != (relation_composition (function_inverse T_0) T_0)) ### Refl(=)
% 39.48/39.65 29. ((relation_composition (function_inverse T_0) T_0) != (relation_composition (function_inverse T_0) T_0)) ### Refl(=)
% 39.48/39.65 30. ((relation_rng T_0) = (relation_dom (function_inverse T_0))) ((relation_rng T_0) != (relation_dom (function_inverse T_0))) ### Axiom
% 39.48/39.65 31. ((identity_relation (relation_rng T_0)) != (identity_relation (relation_dom (function_inverse T_0)))) ((relation_rng T_0) = (relation_dom (function_inverse T_0))) ### NotEqual 30
% 39.48/39.65 32. ((relation_composition (function_inverse T_0) T_0) != (identity_relation (relation_dom (function_inverse T_0)))) ((relation_composition (function_inverse T_0) T_0) = (identity_relation (relation_rng T_0))) ((relation_rng T_0) = (relation_dom (function_inverse T_0))) ### TransEq 28 29 31
% 39.48/39.65 33. (((relation_composition T_0 (function_inverse T_0)) = (identity_relation (relation_dom T_0))) /\ ((relation_composition (function_inverse T_0) T_0) = (identity_relation (relation_rng T_0)))) ((relation_rng T_0) = (relation_dom (function_inverse T_0))) ((relation_composition (function_inverse T_0) T_0) != (identity_relation (relation_dom (function_inverse T_0)))) ### And 32
% 39.48/39.65 34. (((relation T_0) /\ (function T_0)) => ((one_to_one T_0) => (((relation_composition T_0 (function_inverse T_0)) = (identity_relation (relation_dom T_0))) /\ ((relation_composition (function_inverse T_0) T_0) = (identity_relation (relation_rng T_0)))))) ((relation_composition (function_inverse T_0) T_0) != (identity_relation (relation_dom (function_inverse T_0)))) ((relation_rng T_0) = (relation_dom (function_inverse T_0))) (one_to_one T_0) (function T_0) (relation T_0) ### DisjTree 25 26 27 33
% 39.48/39.65 35. (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A))) /\ ((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))) (relation T_0) (function T_0) (one_to_one T_0) ((relation_rng T_0) = (relation_dom (function_inverse T_0))) ((relation_composition (function_inverse T_0) T_0) != (identity_relation (relation_dom (function_inverse T_0)))) ### All 34
% 39.48/39.65 36. ((function_inverse (function_inverse T_0)) != T_0) (T_0 = (function_inverse (function_inverse T_0))) ### Sym(=)
% 39.48/39.65 37. (((relation T_0) /\ (function T_0)) => (((one_to_one (function_inverse T_0)) /\ (((relation_rng (function_inverse T_0)) = (relation_dom T_0)) /\ ((relation_composition (function_inverse T_0) T_0) = (identity_relation (relation_dom (function_inverse T_0)))))) => (T_0 = (function_inverse (function_inverse T_0))))) ((function_inverse (function_inverse T_0)) != T_0) ((relation_rng T_0) = (relation_dom (function_inverse T_0))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A))) /\ ((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))) ((relation_dom T_0) = (relation_rng (function_inverse T_0))) (one_to_one T_0) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (one_to_one (function_inverse A))))) (function T_0) (relation T_0) ### DisjTree 16 17 23 24 35 36
% 39.48/39.65 38. (All B, (((relation B) /\ (function B)) => (((one_to_one (function_inverse T_0)) /\ (((relation_rng (function_inverse T_0)) = (relation_dom B)) /\ ((relation_composition (function_inverse T_0) B) = (identity_relation (relation_dom (function_inverse T_0)))))) => (B = (function_inverse (function_inverse T_0)))))) (relation T_0) (function T_0) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (one_to_one (function_inverse A))))) (one_to_one T_0) ((relation_dom T_0) = (relation_rng (function_inverse T_0))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A))) /\ ((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))) ((relation_rng T_0) = (relation_dom (function_inverse T_0))) ((function_inverse (function_inverse T_0)) != T_0) ### All 37
% 39.48/39.65 39. (((relation (function_inverse T_0)) /\ (function (function_inverse T_0))) => (All B, (((relation B) /\ (function B)) => (((one_to_one (function_inverse T_0)) /\ (((relation_rng (function_inverse T_0)) = (relation_dom B)) /\ ((relation_composition (function_inverse T_0) B) = (identity_relation (relation_dom (function_inverse T_0)))))) => (B = (function_inverse (function_inverse T_0))))))) ((function_inverse (function_inverse T_0)) != T_0) ((relation_rng T_0) = (relation_dom (function_inverse T_0))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A))) /\ ((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))) ((relation_dom T_0) = (relation_rng (function_inverse T_0))) (one_to_one T_0) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (one_to_one (function_inverse A))))) (function T_0) (relation T_0) (All A, (((relation A) /\ (function A)) => ((relation (function_inverse A)) /\ (function (function_inverse A))))) ### DisjTree 9 15 38
% 39.48/39.65 40. (All A, (((relation A) /\ (function A)) => (All B, (((relation B) /\ (function B)) => (((one_to_one A) /\ (((relation_rng A) = (relation_dom B)) /\ ((relation_composition A B) = (identity_relation (relation_dom A))))) => (B = (function_inverse A))))))) (All A, (((relation A) /\ (function A)) => ((relation (function_inverse A)) /\ (function (function_inverse A))))) (relation T_0) (function T_0) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (one_to_one (function_inverse A))))) (one_to_one T_0) ((relation_dom T_0) = (relation_rng (function_inverse T_0))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A))) /\ ((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))) ((relation_rng T_0) = (relation_dom (function_inverse T_0))) ((function_inverse (function_inverse T_0)) != T_0) ### All 39
% 39.48/39.66 41. (((relation_rng T_0) = (relation_dom (function_inverse T_0))) /\ ((relation_dom T_0) = (relation_rng (function_inverse T_0)))) ((function_inverse (function_inverse T_0)) != T_0) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A))) /\ ((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))) (one_to_one T_0) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (one_to_one (function_inverse A))))) (function T_0) (relation T_0) (All A, (((relation A) /\ (function A)) => ((relation (function_inverse A)) /\ (function (function_inverse A))))) (All A, (((relation A) /\ (function A)) => (All B, (((relation B) /\ (function B)) => (((one_to_one A) /\ (((relation_rng A) = (relation_dom B)) /\ ((relation_composition A B) = (identity_relation (relation_dom A))))) => (B = (function_inverse A))))))) ### And 40
% 39.48/39.66 42. (((relation T_0) /\ (function T_0)) => ((one_to_one T_0) => (((relation_rng T_0) = (relation_dom (function_inverse T_0))) /\ ((relation_dom T_0) = (relation_rng (function_inverse T_0)))))) (All A, (((relation A) /\ (function A)) => (All B, (((relation B) /\ (function B)) => (((one_to_one A) /\ (((relation_rng A) = (relation_dom B)) /\ ((relation_composition A B) = (identity_relation (relation_dom A))))) => (B = (function_inverse A))))))) (All A, (((relation A) /\ (function A)) => ((relation (function_inverse A)) /\ (function (function_inverse A))))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (one_to_one (function_inverse A))))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A))) /\ ((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))) ((function_inverse (function_inverse T_0)) != T_0) (one_to_one T_0) (function T_0) (relation T_0) ### DisjTree 1 2 3 41
% 39.48/39.66 43. (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_rng A) = (relation_dom (function_inverse A))) /\ ((relation_dom A) = (relation_rng (function_inverse A))))))) (relation T_0) (function T_0) (one_to_one T_0) ((function_inverse (function_inverse T_0)) != T_0) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A))) /\ ((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (one_to_one (function_inverse A))))) (All A, (((relation A) /\ (function A)) => ((relation (function_inverse A)) /\ (function (function_inverse A))))) (All A, (((relation A) /\ (function A)) => (All B, (((relation B) /\ (function B)) => (((one_to_one A) /\ (((relation_rng A) = (relation_dom B)) /\ ((relation_composition A B) = (identity_relation (relation_dom A))))) => (B = (function_inverse A))))))) ### All 42
% 39.48/39.66 44. (-. (((relation T_0) /\ (function T_0)) => ((one_to_one T_0) => ((function_inverse (function_inverse T_0)) = T_0)))) (All A, (((relation A) /\ (function A)) => (All B, (((relation B) /\ (function B)) => (((one_to_one A) /\ (((relation_rng A) = (relation_dom B)) /\ ((relation_composition A B) = (identity_relation (relation_dom A))))) => (B = (function_inverse A))))))) (All A, (((relation A) /\ (function A)) => ((relation (function_inverse A)) /\ (function (function_inverse A))))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (one_to_one (function_inverse A))))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A))) /\ ((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_rng A) = (relation_dom (function_inverse A))) /\ ((relation_dom A) = (relation_rng (function_inverse A))))))) ### ConjTree 43
% 39.48/39.66 45. (-. (All A, (((relation A) /\ (function A)) => ((one_to_one A) => ((function_inverse (function_inverse A)) = A))))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_rng A) = (relation_dom (function_inverse A))) /\ ((relation_dom A) = (relation_rng (function_inverse A))))))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A))) /\ ((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))) (All A, (((relation A) /\ (function A)) => ((one_to_one A) => (one_to_one (function_inverse A))))) (All A, (((relation A) /\ (function A)) => ((relation (function_inverse A)) /\ (function (function_inverse A))))) (All A, (((relation A) /\ (function A)) => (All B, (((relation B) /\ (function B)) => (((one_to_one A) /\ (((relation_rng A) = (relation_dom B)) /\ ((relation_composition A B) = (identity_relation (relation_dom A))))) => (B = (function_inverse A))))))) ### NotAllEx 44
% 39.48/39.66 % SZS output end Proof
% 39.48/39.66 (* END-PROOF *)
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