%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET584+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n027.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 05:42:25 EDT 2022 % Result : Theorem 0.18s 0.52s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET584+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n027.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 Jul 10 03:13:47 EDT 2022 % 0.12/0.34 % CPUTime : % 0.18/0.52 % SZS status Theorem % 0.18/0.52 (* PROOF-FOUND *) % 0.18/0.52 (* BEGIN-PROOF *) % 0.18/0.52 % SZS output start Proof % 0.18/0.52 1. (T_0 != T_0) ### Refl(=) % 0.18/0.52 2. ((union T_1 T_2) = (union T_2 T_1)) ((union T_2 T_1) != (union T_1 T_2)) ### Sym(=) % 0.18/0.52 3. (-. (member T_0 (union T_1 T_2))) (member T_0 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) ### P-NotP 1 2 % 0.18/0.52 4. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom % 0.18/0.52 5. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom % 0.18/0.52 6. ((member T_0 T_1) \/ (member T_0 T_2)) (-. (member T_0 T_2)) (-. (member T_0 T_1)) ### Or 4 5 % 0.18/0.52 7. ((member T_0 (union T_1 T_2)) <=> ((member T_0 T_1) \/ (member T_0 T_2))) (-. (member T_0 T_1)) (-. (member T_0 T_2)) ((union T_1 T_2) = (union T_2 T_1)) (member T_0 (union T_2 T_1)) ### Equiv 3 6 % 0.18/0.52 8. (All D, ((member D (union T_1 T_2)) <=> ((member D T_1) \/ (member D T_2)))) (member T_0 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (-. (member T_0 T_2)) (-. (member T_0 T_1)) ### All 7 % 0.18/0.52 9. (All C, (All D, ((member D (union T_1 C)) <=> ((member D T_1) \/ (member D C))))) (-. (member T_0 T_1)) (-. (member T_0 T_2)) ((union T_1 T_2) = (union T_2 T_1)) (member T_0 (union T_2 T_1)) ### All 8 % 0.18/0.52 10. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom % 0.18/0.52 11. ((member T_0 T_2) => (member T_0 T_3)) (-. (member T_0 T_3)) (member T_0 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (-. (member T_0 T_1)) (All C, (All D, ((member D (union T_1 C)) <=> ((member D T_1) \/ (member D C))))) ### Imply 9 10 % 0.18/0.52 12. (All D, ((member D T_2) => (member D T_3))) (All C, (All D, ((member D (union T_1 C)) <=> ((member D T_1) \/ (member D C))))) (-. (member T_0 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (member T_0 (union T_2 T_1)) (-. (member T_0 T_3)) ### All 11 % 0.18/0.52 13. (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (-. (member T_0 T_3)) (member T_0 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (-. (member T_0 T_1)) (All D, ((member D T_2) => (member D T_3))) ### All 12 % 0.18/0.52 14. (-. ((member T_0 T_3) \/ (member T_0 T_1))) (All D, ((member D T_2) => (member D T_3))) ((union T_1 T_2) = (union T_2 T_1)) (member T_0 (union T_2 T_1)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotOr 13 % 0.18/0.52 15. (-. (member T_0 (union T_3 T_1))) (member T_0 (union T_3 T_1)) ### Axiom % 0.18/0.52 16. ((member T_0 (union T_3 T_1)) <=> ((member T_0 T_3) \/ (member T_0 T_1))) (-. (member T_0 (union T_3 T_1))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (member T_0 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) ### Equiv 14 15 % 0.18/0.52 17. (All D, ((member D (union T_3 T_1)) <=> ((member D T_3) \/ (member D T_1)))) (All D, ((member D T_2) => (member D T_3))) ((union T_1 T_2) = (union T_2 T_1)) (member T_0 (union T_2 T_1)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (-. (member T_0 (union T_3 T_1))) ### All 16 % 0.18/0.52 18. (All C, ((union T_1 C) = (union C T_1))) (-. (member T_0 (union T_3 T_1))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (member T_0 (union T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All D, ((member D (union T_3 T_1)) <=> ((member D T_3) \/ (member D T_1)))) ### All 17 % 0.18/0.52 19. (All C, (All D, ((member D (union T_3 C)) <=> ((member D T_3) \/ (member D C))))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (union T_2 T_1)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (-. (member T_0 (union T_3 T_1))) (All C, ((union T_1 C) = (union C T_1))) ### All 18 % 0.18/0.52 20. (All C, ((union T_1 C) = (union C T_1))) (-. (member T_0 (union T_3 T_1))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (member T_0 (union T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) ### All 19 % 0.18/0.52 21. (All B, (All C, ((union B C) = (union C B)))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (union T_2 T_1)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (-. (member T_0 (union T_3 T_1))) ### All 20 % 0.18/0.52 22. (-. ((member T_0 (union T_2 T_1)) => (member T_0 (union T_3 T_1)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, ((union B C) = (union C B)))) ### NotImply 21 % 0.18/0.52 23. (-. (All D, ((member D (union T_2 T_1)) => (member D (union T_3 T_1))))) (All B, (All C, ((union B C) = (union C B)))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAllEx 22 % 0.18/0.52 24. (-. (subset (union T_2 T_1) (union T_3 T_1))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, ((union B C) = (union C B)))) ### Definition-Pseudo(subset) 23 % 0.18/0.52 25. (subset T_2 T_3) (All B, (All C, ((union B C) = (union C B)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (-. (subset (union T_2 T_1) (union T_3 T_1))) ### Definition-Pseudo(subset) 24 % 0.18/0.52 26. (-. ((subset T_2 T_3) => (subset (union T_2 T_1) (union T_3 T_1)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, ((union B C) = (union C B)))) ### NotImply 25 % 0.18/0.52 27. (-. (All D, ((subset T_2 T_3) => (subset (union T_2 D) (union T_3 D))))) (All B, (All C, ((union B C) = (union C B)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAllEx 26 % 0.18/0.52 28. (-. (All C, (All D, ((subset T_2 C) => (subset (union T_2 D) (union C D)))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, ((union B C) = (union C B)))) ### NotAllEx 27 % 0.18/0.52 29. (-. (All B, (All C, (All D, ((subset B C) => (subset (union B D) (union C D))))))) (All B, (All C, ((union B C) = (union C B)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAllEx 28 % 0.18/0.52 % SZS output end Proof % 0.18/0.52 (* END-PROOF *) %------------------------------------------------------------------------------