%------------------------------------------------------------------------------ % 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 : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----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 *) %------------------------------------------------------------------------------