%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET589+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 : n014.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 05:42:28 EDT 2022 % Result : Theorem 3.24s 3.40s % Output : Proof 3.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET589+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.33 % Computer : n014.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sun Jul 10 12:53:05 EDT 2022 % 0.13/0.33 % CPUTime : % 3.24/3.40 % SZS status Theorem % 3.24/3.40 (* PROOF-FOUND *) % 3.24/3.40 (* BEGIN-PROOF *) % 3.24/3.40 % SZS output start Proof % 3.24/3.40 1. (member T_0 (difference T_1 T_2)) (-. (member T_0 (difference T_1 T_2))) ### Axiom % 3.24/3.40 2. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom % 3.24/3.40 3. ((member T_0 T_1) /\ (-. (member T_0 T_2))) (-. (member T_0 T_1)) ### And 2 % 3.24/3.40 4. ((member T_0 (difference T_1 T_2)) <=> ((member T_0 T_1) /\ (-. (member T_0 T_2)))) (-. (member T_0 T_1)) (member T_0 (difference T_1 T_2)) ### Equiv 1 3 % 3.24/3.40 5. (All D, ((member D (difference T_1 T_2)) <=> ((member D T_1) /\ (-. (member D T_2))))) (member T_0 (difference T_1 T_2)) (-. (member T_0 T_1)) ### All 4 % 3.24/3.40 6. (All C, (All D, ((member D (difference T_1 C)) <=> ((member D T_1) /\ (-. (member D C)))))) (-. (member T_0 T_1)) (member T_0 (difference T_1 T_2)) ### All 5 % 3.24/3.40 7. (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_0 (difference T_1 T_2)) (-. (member T_0 T_1)) ### All 6 % 3.24/3.40 8. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom % 3.24/3.40 9. ((member T_0 T_1) => (member T_0 T_3)) (-. (member T_0 T_3)) (member T_0 (difference T_1 T_2)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### Imply 7 8 % 3.24/3.40 10. (All D, ((member D T_1) => (member D T_3))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_0 (difference T_1 T_2)) (-. (member T_0 T_3)) ### All 9 % 3.24/3.40 11. (All D, ((member D T_4) => (member D T_2))) (-. (All D, ((member D T_4) => (member D T_2)))) ### Axiom % 3.24/3.40 12. (-. (subset T_4 T_2)) (All D, ((member D T_4) => (member D T_2))) ### Definition-Pseudo(subset) 11 % 3.24/3.40 13. (member T_0 (difference T_1 T_2)) (-. (member T_0 (difference T_1 T_2))) ### Axiom % 3.24/3.40 14. (-. (member T_0 (difference T_1 T_4))) (member T_0 (difference T_1 T_4)) ### Axiom % 3.24/3.40 15. ((member T_0 (difference T_1 T_2)) => (member T_0 (difference T_1 T_4))) (-. (member T_0 (difference T_1 T_4))) (member T_0 (difference T_1 T_2)) ### Imply 13 14 % 3.24/3.40 16. (All D, ((member D (difference T_1 T_2)) => (member D (difference T_1 T_4)))) (member T_0 (difference T_1 T_2)) (-. (member T_0 (difference T_1 T_4))) ### All 15 % 3.24/3.40 17. (subset (difference T_1 T_2) (difference T_1 T_4)) (-. (member T_0 (difference T_1 T_4))) (member T_0 (difference T_1 T_2)) ### Definition-Pseudo(subset) 16 % 3.24/3.40 18. ((subset T_4 T_2) => (subset (difference T_1 T_2) (difference T_1 T_4))) (member T_0 (difference T_1 T_2)) (-. (member T_0 (difference T_1 T_4))) (All D, ((member D T_4) => (member D T_2))) ### Imply 12 17 % 3.24/3.40 19. (All D, ((subset T_4 T_2) => (subset (difference D T_2) (difference D T_4)))) (All D, ((member D T_4) => (member D T_2))) (-. (member T_0 (difference T_1 T_4))) (member T_0 (difference T_1 T_2)) ### All 18 % 3.24/3.40 20. (member T_0 T_4) (-. (member T_0 T_4)) ### Axiom % 3.24/3.40 21. ((member T_0 T_1) /\ (-. (member T_0 T_4))) (member T_0 T_4) ### And 20 % 3.24/3.40 22. ((member T_0 (difference T_1 T_4)) <=> ((member T_0 T_1) /\ (-. (member T_0 T_4)))) (member T_0 T_4) (member T_0 (difference T_1 T_2)) (All D, ((member D T_4) => (member D T_2))) (All D, ((subset T_4 T_2) => (subset (difference D T_2) (difference D T_4)))) ### Equiv 19 21 % 3.24/3.40 23. (All D, ((member D (difference T_1 T_4)) <=> ((member D T_1) /\ (-. (member D T_4))))) (All D, ((subset T_4 T_2) => (subset (difference D T_2) (difference D T_4)))) (All D, ((member D T_4) => (member D T_2))) (member T_0 (difference T_1 T_2)) (member T_0 T_4) ### All 22 % 3.24/3.40 24. (All C, (All D, ((member D (difference T_1 C)) <=> ((member D T_1) /\ (-. (member D C)))))) (member T_0 T_4) (member T_0 (difference T_1 T_2)) (All D, ((member D T_4) => (member D T_2))) (All D, ((subset T_4 T_2) => (subset (difference D T_2) (difference D T_4)))) ### All 23 % 3.24/3.40 25. (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((subset T_4 T_2) => (subset (difference D T_2) (difference D T_4)))) (All D, ((member D T_4) => (member D T_2))) (member T_0 (difference T_1 T_2)) (member T_0 T_4) ### All 24 % 3.24/3.40 26. (-. (-. (member T_0 T_4))) (member T_0 (difference T_1 T_2)) (All D, ((member D T_4) => (member D T_2))) (All D, ((subset T_4 T_2) => (subset (difference D T_2) (difference D T_4)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotNot 25 % 3.24/3.40 27. (-. ((member T_0 T_3) /\ (-. (member T_0 T_4)))) (All D, ((subset T_4 T_2) => (subset (difference D T_2) (difference D T_4)))) (All D, ((member D T_4) => (member D T_2))) (member T_0 (difference T_1 T_2)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D T_3))) ### NotAnd 10 26 % 3.24/3.40 28. (-. (member T_0 (difference T_3 T_4))) (member T_0 (difference T_3 T_4)) ### Axiom % 3.24/3.40 29. ((member T_0 (difference T_3 T_4)) <=> ((member T_0 T_3) /\ (-. (member T_0 T_4)))) (-. (member T_0 (difference T_3 T_4))) (All D, ((member D T_1) => (member D T_3))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_0 (difference T_1 T_2)) (All D, ((member D T_4) => (member D T_2))) (All D, ((subset T_4 T_2) => (subset (difference D T_2) (difference D T_4)))) ### Equiv 27 28 % 3.24/3.40 30. (All D, ((member D (difference T_3 T_4)) <=> ((member D T_3) /\ (-. (member D T_4))))) (All D, ((subset T_4 T_2) => (subset (difference D T_2) (difference D T_4)))) (All D, ((member D T_4) => (member D T_2))) (member T_0 (difference T_1 T_2)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D T_3))) (-. (member T_0 (difference T_3 T_4))) ### All 29 % 3.24/3.40 31. (All C, (All D, ((member D (difference T_3 C)) <=> ((member D T_3) /\ (-. (member D C)))))) (-. (member T_0 (difference T_3 T_4))) (All D, ((member D T_1) => (member D T_3))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_0 (difference T_1 T_2)) (All D, ((member D T_4) => (member D T_2))) (All D, ((subset T_4 T_2) => (subset (difference D T_2) (difference D T_4)))) ### All 30 % 3.24/3.40 32. (All C, (All D, ((subset T_4 C) => (subset (difference D C) (difference D T_4))))) (All D, ((member D T_4) => (member D T_2))) (member T_0 (difference T_1 T_2)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D T_3))) (-. (member T_0 (difference T_3 T_4))) (All C, (All D, ((member D (difference T_3 C)) <=> ((member D T_3) /\ (-. (member D C)))))) ### All 31 % 3.24/3.40 33. (-. (member T_0 (difference T_3 T_4))) (All D, ((member D T_1) => (member D T_3))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_0 (difference T_1 T_2)) (All D, ((member D T_4) => (member D T_2))) (All C, (All D, ((subset T_4 C) => (subset (difference D C) (difference D T_4))))) ### All 32 % 3.24/3.40 34. (All B, (All C, (All D, ((subset B C) => (subset (difference D C) (difference D B)))))) (All D, ((member D T_4) => (member D T_2))) (member T_0 (difference T_1 T_2)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D T_3))) (-. (member T_0 (difference T_3 T_4))) ### All 33 % 3.24/3.40 35. (-. ((member T_0 (difference T_1 T_2)) => (member T_0 (difference T_3 T_4)))) (All D, ((member D T_1) => (member D T_3))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_4) => (member D T_2))) (All B, (All C, (All D, ((subset B C) => (subset (difference D C) (difference D B)))))) ### NotImply 34 % 3.24/3.40 36. (-. (All D, ((member D (difference T_1 T_2)) => (member D (difference T_3 T_4))))) (All B, (All C, (All D, ((subset B C) => (subset (difference D C) (difference D B)))))) (All D, ((member D T_4) => (member D T_2))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D T_3))) ### NotAllEx 35 % 3.24/3.40 37. (-. (subset (difference T_1 T_2) (difference T_3 T_4))) (All D, ((member D T_1) => (member D T_3))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_4) => (member D T_2))) (All B, (All C, (All D, ((subset B C) => (subset (difference D C) (difference D B)))))) ### Definition-Pseudo(subset) 36 % 3.24/3.41 38. (subset T_4 T_2) (All B, (All C, (All D, ((subset B C) => (subset (difference D C) (difference D B)))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D T_3))) (-. (subset (difference T_1 T_2) (difference T_3 T_4))) ### Definition-Pseudo(subset) 37 % 3.24/3.41 39. (subset T_1 T_3) (-. (subset (difference T_1 T_2) (difference T_3 T_4))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All B, (All C, (All D, ((subset B C) => (subset (difference D C) (difference D B)))))) (subset T_4 T_2) ### Definition-Pseudo(subset) 38 % 3.24/3.41 40. (-. (((subset T_1 T_3) /\ (subset T_4 T_2)) => (subset (difference T_1 T_2) (difference T_3 T_4)))) (All B, (All C, (All D, ((subset B C) => (subset (difference D C) (difference D B)))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### ConjTree 39 % 3.24/3.41 41. (-. (All E, (((subset T_1 T_3) /\ (subset T_4 E)) => (subset (difference T_1 E) (difference T_3 T_4))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All B, (All C, (All D, ((subset B C) => (subset (difference D C) (difference D B)))))) ### NotAllEx 40 % 3.24/3.41 42. (-. (All D, (All E, (((subset T_1 T_3) /\ (subset D E)) => (subset (difference T_1 E) (difference T_3 D)))))) (All B, (All C, (All D, ((subset B C) => (subset (difference D C) (difference D B)))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotAllEx 41 % 3.24/3.41 43. (-. (All C, (All D, (All E, (((subset T_1 C) /\ (subset D E)) => (subset (difference T_1 E) (difference C D))))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All B, (All C, (All D, ((subset B C) => (subset (difference D C) (difference D B)))))) ### NotAllEx 42 % 3.24/3.41 44. (-. (All B, (All C, (All D, (All E, (((subset B C) /\ (subset D E)) => (subset (difference B E) (difference C D)))))))) (All B, (All C, (All D, ((subset B C) => (subset (difference D C) (difference D B)))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotAllEx 43 % 3.24/3.41 % SZS output end Proof % 3.24/3.41 (* END-PROOF *) %------------------------------------------------------------------------------