%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET588+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 : n019.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 05:42:27 EDT 2022 % Result : Theorem 0.18s 0.44s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET588+3 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n019.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 Jul 9 21:02:38 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.44 % SZS status Theorem % 0.18/0.44 (* PROOF-FOUND *) % 0.18/0.44 (* BEGIN-PROOF *) % 0.18/0.44 % SZS output start Proof % 0.18/0.44 1. (member T_0 (difference T_1 T_2)) (-. (member T_0 (difference T_1 T_2))) ### Axiom % 0.18/0.44 2. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom % 0.18/0.44 3. ((member T_0 T_1) /\ (-. (member T_0 T_2))) (-. (member T_0 T_1)) ### And 2 % 0.18/0.44 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 % 0.18/0.44 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 % 0.18/0.44 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 % 0.18/0.44 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 % 0.18/0.44 8. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom % 0.18/0.44 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 % 0.18/0.44 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 % 0.18/0.44 11. (member T_0 (difference T_1 T_2)) (-. (member T_0 (difference T_1 T_2))) ### Axiom % 0.18/0.44 12. (member T_0 T_2) (-. (member T_0 T_2)) ### Axiom % 0.18/0.44 13. ((member T_0 T_1) /\ (-. (member T_0 T_2))) (member T_0 T_2) ### And 12 % 0.18/0.44 14. ((member T_0 (difference T_1 T_2)) <=> ((member T_0 T_1) /\ (-. (member T_0 T_2)))) (member T_0 T_2) (member T_0 (difference T_1 T_2)) ### Equiv 11 13 % 0.18/0.44 15. (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_2) ### All 14 % 0.18/0.44 16. (All C, (All D, ((member D (difference T_1 C)) <=> ((member D T_1) /\ (-. (member D C)))))) (member T_0 T_2) (member T_0 (difference T_1 T_2)) ### All 15 % 0.18/0.44 17. (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_2) ### All 16 % 0.18/0.44 18. (-. (-. (member T_0 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))))))) ### NotNot 17 % 0.18/0.44 19. (-. ((member T_0 T_3) /\ (-. (member T_0 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 18 % 0.18/0.44 20. (-. (member T_0 (difference T_3 T_2))) (member T_0 (difference T_3 T_2)) ### Axiom % 0.18/0.44 21. ((member T_0 (difference T_3 T_2)) <=> ((member T_0 T_3) /\ (-. (member T_0 T_2)))) (-. (member T_0 (difference T_3 T_2))) (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)) ### Equiv 19 20 % 0.18/0.44 22. (All D, ((member D (difference T_3 T_2)) <=> ((member D T_3) /\ (-. (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_2))) ### All 21 % 0.18/0.44 23. (All C, (All D, ((member D (difference T_3 C)) <=> ((member D T_3) /\ (-. (member D C)))))) (-. (member T_0 (difference T_3 T_2))) (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 22 % 0.18/0.44 24. (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_2))) ### All 23 % 0.18/0.44 25. (-. ((member T_0 (difference T_1 T_2)) => (member T_0 (difference T_3 T_2)))) (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))))))) ### NotImply 24 % 0.18/0.44 26. (-. (All D, ((member D (difference T_1 T_2)) => (member D (difference T_3 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 25 % 0.18/0.44 27. (-. (subset (difference T_1 T_2) (difference T_3 T_2))) (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))))))) ### Definition-Pseudo(subset) 26 % 0.18/0.44 28. (subset T_1 T_3) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (-. (subset (difference T_1 T_2) (difference T_3 T_2))) ### Definition-Pseudo(subset) 27 % 0.18/0.44 29. (-. ((subset T_1 T_3) => (subset (difference T_1 T_2) (difference T_3 T_2)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotImply 28 % 0.18/0.44 30. (-. (All D, ((subset T_1 T_3) => (subset (difference T_1 D) (difference T_3 D))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotAllEx 29 % 0.18/0.44 31. (-. (All C, (All D, ((subset T_1 C) => (subset (difference T_1 D) (difference C D)))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotAllEx 30 % 0.18/0.44 32. (-. (All B, (All C, (All D, ((subset B C) => (subset (difference B D) (difference C D))))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotAllEx 31 % 0.18/0.44 % SZS output end Proof % 0.18/0.44 (* END-PROOF *) %------------------------------------------------------------------------------