%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SEU044+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 14:48:05 EDT 2022 % Result : Theorem 3.63s 3.79s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU044+1 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n011.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 20:26:38 EDT 2022 % 0.13/0.34 % CPUTime : % 3.63/3.79 % SZS status Theorem % 3.63/3.79 (* PROOF-FOUND *) % 3.63/3.79 (* BEGIN-PROOF *) % 3.63/3.79 % SZS output start Proof % 3.63/3.79 1. (relation T_0) (-. (relation T_0)) ### Axiom % 3.63/3.79 2. (-. (relation (relation_rng_restriction T_1 T_0))) (relation (relation_rng_restriction T_1 T_0)) ### Axiom % 3.63/3.79 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 % 3.63/3.79 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 % 3.63/3.79 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 % 3.63/3.79 6. (relation T_0) (-. (relation T_0)) ### Axiom % 3.63/3.79 7. (function T_0) (-. (function T_0)) ### Axiom % 3.63/3.79 8. (-. (function (relation_rng_restriction T_1 T_0))) (function (relation_rng_restriction T_1 T_0)) ### Axiom % 3.63/3.79 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 % 3.63/3.79 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 % 3.63/3.79 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 % 3.63/3.79 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 % 3.63/3.79 13. (relation T_0) (-. (relation T_0)) ### Axiom % 3.63/3.79 14. (function T_0) (-. (function T_0)) ### Axiom % 3.63/3.79 15. ((relation_rng_restriction T_1 T_0) != (relation_rng_restriction T_1 T_0)) ### Refl(=) % 3.63/3.79 16. (-. ((in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in T_2 (relation_dom T_0)) /\ (in (apply T_0 T_2) T_1)))) ((in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in T_2 (relation_dom T_0)) /\ (in (apply T_0 T_2) T_1))) ### Axiom % 3.63/3.79 17. (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)))) (-. ((in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in T_2 (relation_dom T_0)) /\ (in (apply T_0 T_2) T_1)))) ### All 16 % 3.63/3.79 18. ((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))) <=> ((in T_2 (relation_dom T_0)) /\ (in (apply T_0 T_2) T_1)))) ### And 17 % 3.63/3.79 19. (((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))) <=> ((in T_2 (relation_dom T_0)) /\ (in (apply T_0 T_2) T_1)))) ### Equiv 15 18 % 3.63/3.79 20. (((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))))))) (-. ((in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in T_2 (relation_dom T_0)) /\ (in (apply T_0 T_2) T_1)))) (function T_0) (relation T_0) ### DisjTree 13 14 19 % 3.63/3.79 21. (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))) <=> ((in T_2 (relation_dom T_0)) /\ (in (apply T_0 T_2) T_1)))) ### All 20 % 3.63/3.79 22. (((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))))))))) (-. ((in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in T_2 (relation_dom T_0)) /\ (in (apply T_0 T_2) T_1)))) (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 21 % 3.63/3.79 23. (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))) <=> ((in T_2 (relation_dom T_0)) /\ (in (apply T_0 T_2) T_1)))) ### All 22 % 3.63/3.79 24. (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))))))))))) (-. ((in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in T_2 (relation_dom T_0)) /\ (in (apply T_0 T_2) T_1)))) (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 23 % 3.63/3.79 25. (-. (((relation T_0) /\ (function T_0)) => ((in T_2 (relation_dom (relation_rng_restriction T_1 T_0))) <=> ((in T_2 (relation_dom T_0)) /\ (in (apply T_0 T_2) T_1))))) (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 24 % 3.63/3.79 26. (-. (All C, (((relation C) /\ (function C)) => ((in T_2 (relation_dom (relation_rng_restriction T_1 C))) <=> ((in T_2 (relation_dom C)) /\ (in (apply C T_2) T_1)))))) (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 25 % 3.63/3.80 27. (-. (All B, (All C, (((relation C) /\ (function C)) => ((in B (relation_dom (relation_rng_restriction T_1 C))) <=> ((in B (relation_dom C)) /\ (in (apply C B) T_1))))))) (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 26 % 3.63/3.80 28. (-. (All A, (All B, (All C, (((relation C) /\ (function C)) => ((in B (relation_dom (relation_rng_restriction A C))) <=> ((in B (relation_dom C)) /\ (in (apply C B) A)))))))) (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 % 3.63/3.80 % SZS output end Proof % 3.63/3.80 (* END-PROOF *) %------------------------------------------------------------------------------