%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SEU045+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 : n011.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 14:48:06 EDT 2022 % Result : Theorem 5.84s 6.01s % Output : Proof 5.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU045+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 : n011.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 : Sun Jun 19 20:30:54 EDT 2022 % 0.12/0.33 % CPUTime : % 5.84/6.01 % SZS status Theorem % 5.84/6.01 (* PROOF-FOUND *) % 5.84/6.01 (* BEGIN-PROOF *) % 5.84/6.01 % SZS output start Proof % 5.84/6.01 1. (relation T_0) (-. (relation T_0)) ### Axiom % 5.84/6.01 2. (-. (relation (relation_rng_restriction T_1 T_0))) (relation (relation_rng_restriction T_1 T_0)) ### Axiom % 5.84/6.01 3. ((relation T_0) => (relation (relation_rng_restriction T_1 T_0))) (-. (relation (relation_rng_restriction T_1 T_0))) (relation T_0) ### Imply 1 2 % 5.84/6.01 4. (All B, ((relation B) => (relation (relation_rng_restriction T_1 B)))) (relation T_0) (-. (relation (relation_rng_restriction T_1 T_0))) ### All 3 % 5.84/6.01 5. (All A, (All B, ((relation B) => (relation (relation_rng_restriction A B))))) (-. (relation (relation_rng_restriction T_1 T_0))) (relation T_0) ### All 4 % 5.84/6.01 6. (relation T_0) (-. (relation T_0)) ### Axiom % 5.84/6.01 7. (function T_0) (-. (function T_0)) ### Axiom % 5.84/6.01 8. (-. (function (relation_rng_restriction T_1 T_0))) (function (relation_rng_restriction T_1 T_0)) ### Axiom % 5.84/6.01 9. ((relation (relation_rng_restriction T_1 T_0)) /\ (function (relation_rng_restriction T_1 T_0))) (-. (function (relation_rng_restriction T_1 T_0))) ### And 8 % 5.84/6.01 10. (((relation T_0) /\ (function T_0)) => ((relation (relation_rng_restriction T_1 T_0)) /\ (function (relation_rng_restriction T_1 T_0)))) (-. (function (relation_rng_restriction T_1 T_0))) (function T_0) (relation T_0) ### DisjTree 6 7 9 % 5.84/6.01 11. (All B, (((relation B) /\ (function B)) => ((relation (relation_rng_restriction T_1 B)) /\ (function (relation_rng_restriction T_1 B))))) (relation T_0) (function T_0) (-. (function (relation_rng_restriction T_1 T_0))) ### All 10 % 5.84/6.01 12. (All A, (All B, (((relation B) /\ (function B)) => ((relation (relation_rng_restriction A B)) /\ (function (relation_rng_restriction A B)))))) (-. (function (relation_rng_restriction T_1 T_0))) (function T_0) (relation T_0) ### All 11 % 5.84/6.01 13. (relation T_0) (-. (relation T_0)) ### Axiom % 5.84/6.01 14. (function T_0) (-. (function T_0)) ### Axiom % 5.84/6.01 15. ((relation_rng_restriction T_1 T_0) != (relation_rng_restriction T_1 T_0)) ### Refl(=) % 5.84/6.01 16. (in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) (-. (in T_2 (relation_dom (relation_rng_restriction T_1 T_0)))) ### Axiom % 5.84/6.01 17. ((apply (relation_rng_restriction T_1 T_0) T_2) != (apply T_0 T_2)) ((apply (relation_rng_restriction T_1 T_0) T_2) = (apply T_0 T_2)) ### Axiom % 5.84/6.01 18. ((in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) => ((apply (relation_rng_restriction T_1 T_0) T_2) = (apply T_0 T_2))) ((apply (relation_rng_restriction T_1 T_0) T_2) != (apply T_0 T_2)) (in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) ### Imply 16 17 % 5.84/6.01 19. (All D, ((in D (relation_dom (relation_rng_restriction T_1 T_0))) => ((apply (relation_rng_restriction T_1 T_0) D) = (apply T_0 D)))) (in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) ((apply (relation_rng_restriction T_1 T_0) T_2) != (apply T_0 T_2)) ### All 18 % 5.84/6.01 20. ((All D, ((in D (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in D (relation_dom T_0)) /\ (in (apply T_0 D) T_1)))) /\ (All D, ((in D (relation_dom (relation_rng_restriction T_1 T_0))) => ((apply (relation_rng_restriction T_1 T_0) D) = (apply T_0 D))))) ((apply (relation_rng_restriction T_1 T_0) T_2) != (apply T_0 T_2)) (in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) ### And 19 % 5.84/6.01 21. (((relation_rng_restriction T_1 T_0) = (relation_rng_restriction T_1 T_0)) <=> ((All D, ((in D (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in D (relation_dom T_0)) /\ (in (apply T_0 D) T_1)))) /\ (All D, ((in D (relation_dom (relation_rng_restriction T_1 T_0))) => ((apply (relation_rng_restriction T_1 T_0) D) = (apply T_0 D)))))) (in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) ((apply (relation_rng_restriction T_1 T_0) T_2) != (apply T_0 T_2)) ### Equiv 15 20 % 5.84/6.01 22. (((relation T_0) /\ (function T_0)) => (((relation_rng_restriction T_1 T_0) = (relation_rng_restriction T_1 T_0)) <=> ((All D, ((in D (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in D (relation_dom T_0)) /\ (in (apply T_0 D) T_1)))) /\ (All D, ((in D (relation_dom (relation_rng_restriction T_1 T_0))) => ((apply (relation_rng_restriction T_1 T_0) D) = (apply T_0 D))))))) ((apply (relation_rng_restriction T_1 T_0) T_2) != (apply T_0 T_2)) (in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) (function T_0) (relation T_0) ### DisjTree 13 14 21 % 5.84/6.01 23. (All C, (((relation C) /\ (function C)) => (((relation_rng_restriction T_1 T_0) = (relation_rng_restriction T_1 C)) <=> ((All D, ((in D (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in D (relation_dom C)) /\ (in (apply C D) T_1)))) /\ (All D, ((in D (relation_dom (relation_rng_restriction T_1 T_0))) => ((apply (relation_rng_restriction T_1 T_0) D) = (apply C D)))))))) (relation T_0) (function T_0) (in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) ((apply (relation_rng_restriction T_1 T_0) T_2) != (apply T_0 T_2)) ### All 22 % 5.84/6.01 24. (((relation (relation_rng_restriction T_1 T_0)) /\ (function (relation_rng_restriction T_1 T_0))) => (All C, (((relation C) /\ (function C)) => (((relation_rng_restriction T_1 T_0) = (relation_rng_restriction T_1 C)) <=> ((All D, ((in D (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in D (relation_dom C)) /\ (in (apply C D) T_1)))) /\ (All D, ((in D (relation_dom (relation_rng_restriction T_1 T_0))) => ((apply (relation_rng_restriction T_1 T_0) D) = (apply C D))))))))) ((apply (relation_rng_restriction T_1 T_0) T_2) != (apply T_0 T_2)) (in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) (function T_0) (All A, (All B, (((relation B) /\ (function B)) => ((relation (relation_rng_restriction A B)) /\ (function (relation_rng_restriction A B)))))) (relation T_0) (All A, (All B, ((relation B) => (relation (relation_rng_restriction A B))))) ### DisjTree 5 12 23 % 5.84/6.01 25. (All B, (((relation B) /\ (function B)) => (All C, (((relation C) /\ (function C)) => ((B = (relation_rng_restriction T_1 C)) <=> ((All D, ((in D (relation_dom B)) <=> ((in D (relation_dom C)) /\ (in (apply C D) T_1)))) /\ (All D, ((in D (relation_dom B)) => ((apply B D) = (apply C D)))))))))) (All A, (All B, ((relation B) => (relation (relation_rng_restriction A B))))) (relation T_0) (All A, (All B, (((relation B) /\ (function B)) => ((relation (relation_rng_restriction A B)) /\ (function (relation_rng_restriction A B)))))) (function T_0) (in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) ((apply (relation_rng_restriction T_1 T_0) T_2) != (apply T_0 T_2)) ### All 24 % 5.84/6.01 26. (All A, (All B, (((relation B) /\ (function B)) => (All C, (((relation C) /\ (function C)) => ((B = (relation_rng_restriction A C)) <=> ((All D, ((in D (relation_dom B)) <=> ((in D (relation_dom C)) /\ (in (apply C D) A)))) /\ (All D, ((in D (relation_dom B)) => ((apply B D) = (apply C D))))))))))) ((apply (relation_rng_restriction T_1 T_0) T_2) != (apply T_0 T_2)) (in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) (function T_0) (All A, (All B, (((relation B) /\ (function B)) => ((relation (relation_rng_restriction A B)) /\ (function (relation_rng_restriction A B)))))) (relation T_0) (All A, (All B, ((relation B) => (relation (relation_rng_restriction A B))))) ### All 25 % 5.84/6.01 27. (-. (((relation T_0) /\ (function T_0)) => ((in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) => ((apply (relation_rng_restriction T_1 T_0) T_2) = (apply T_0 T_2))))) (All A, (All B, ((relation B) => (relation (relation_rng_restriction A B))))) (All A, (All B, (((relation B) /\ (function B)) => ((relation (relation_rng_restriction A B)) /\ (function (relation_rng_restriction A B)))))) (All A, (All B, (((relation B) /\ (function B)) => (All C, (((relation C) /\ (function C)) => ((B = (relation_rng_restriction A C)) <=> ((All D, ((in D (relation_dom B)) <=> ((in D (relation_dom C)) /\ (in (apply C D) A)))) /\ (All D, ((in D (relation_dom B)) => ((apply B D) = (apply C D))))))))))) ### ConjTree 26 % 5.84/6.01 28. (-. (All C, (((relation C) /\ (function C)) => ((in T_2 (relation_dom (relation_rng_restriction T_1 C))) => ((apply (relation_rng_restriction T_1 C) T_2) = (apply C T_2)))))) (All A, (All B, (((relation B) /\ (function B)) => (All C, (((relation C) /\ (function C)) => ((B = (relation_rng_restriction A C)) <=> ((All D, ((in D (relation_dom B)) <=> ((in D (relation_dom C)) /\ (in (apply C D) A)))) /\ (All D, ((in D (relation_dom B)) => ((apply B D) = (apply C D))))))))))) (All A, (All B, (((relation B) /\ (function B)) => ((relation (relation_rng_restriction A B)) /\ (function (relation_rng_restriction A B)))))) (All A, (All B, ((relation B) => (relation (relation_rng_restriction A B))))) ### NotAllEx 27 % 5.84/6.02 29. (-. (All B, (All C, (((relation C) /\ (function C)) => ((in B (relation_dom (relation_rng_restriction T_1 C))) => ((apply (relation_rng_restriction T_1 C) B) = (apply C B))))))) (All A, (All B, ((relation B) => (relation (relation_rng_restriction A B))))) (All A, (All B, (((relation B) /\ (function B)) => ((relation (relation_rng_restriction A B)) /\ (function (relation_rng_restriction A B)))))) (All A, (All B, (((relation B) /\ (function B)) => (All C, (((relation C) /\ (function C)) => ((B = (relation_rng_restriction A C)) <=> ((All D, ((in D (relation_dom B)) <=> ((in D (relation_dom C)) /\ (in (apply C D) A)))) /\ (All D, ((in D (relation_dom B)) => ((apply B D) = (apply C D))))))))))) ### NotAllEx 28 % 5.84/6.02 30. (-. (All A, (All B, (All C, (((relation C) /\ (function C)) => ((in B (relation_dom (relation_rng_restriction A C))) => ((apply (relation_rng_restriction A C) B) = (apply C B)))))))) (All A, (All B, (((relation B) /\ (function B)) => (All C, (((relation C) /\ (function C)) => ((B = (relation_rng_restriction A C)) <=> ((All D, ((in D (relation_dom B)) <=> ((in D (relation_dom C)) /\ (in (apply C D) A)))) /\ (All D, ((in D (relation_dom B)) => ((apply B D) = (apply C D))))))))))) (All A, (All B, (((relation B) /\ (function B)) => ((relation (relation_rng_restriction A B)) /\ (function (relation_rng_restriction A B)))))) (All A, (All B, ((relation B) => (relation (relation_rng_restriction A B))))) ### NotAllEx 29 % 5.84/6.02 % SZS output end Proof % 5.84/6.02 (* END-PROOF *) %------------------------------------------------------------------------------