%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET632+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 : n004.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 05:42:59 EDT 2022 % Result : Theorem 0.58s 0.75s % Output : Proof 0.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET632+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.34 % Computer : n004.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jul 10 13:12:22 EDT 2022 % 0.12/0.34 % CPUTime : % 0.58/0.75 % SZS status Theorem % 0.58/0.75 (* PROOF-FOUND *) % 0.58/0.75 (* BEGIN-PROOF *) % 0.58/0.75 % SZS output start Proof % 0.58/0.75 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 0.58/0.75 2. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 0.58/0.75 3. (member T_0 T_2) (-. (member T_0 T_2)) ### Axiom % 0.58/0.75 4. (member T_0 T_3) (-. (member T_0 T_3)) ### Axiom % 0.58/0.75 5. (-. ((member T_0 T_2) /\ (member T_0 T_3))) (member T_0 T_3) (member T_0 T_2) ### NotAnd 3 4 % 0.58/0.75 6. (-. (Ex D, ((member D T_2) /\ (member D T_3)))) (member T_0 T_2) (member T_0 T_3) ### NotExists 5 % 0.58/0.75 7. ((member T_0 T_1) => (member T_0 T_3)) (member T_0 T_2) (-. (Ex D, ((member D T_2) /\ (member D T_3)))) (member T_0 T_1) ### Imply 2 6 % 0.58/0.75 8. (All D, ((member D T_1) => (member D T_3))) (member T_0 T_1) (-. (Ex D, ((member D T_2) /\ (member D T_3)))) (member T_0 T_2) ### All 7 % 0.58/0.75 9. ((member T_0 T_1) => (member T_0 T_2)) (-. (Ex D, ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (member T_0 T_1) ### Imply 1 8 % 0.58/0.75 10. (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_3))) (-. (Ex D, ((member D T_2) /\ (member D T_3)))) ### All 9 % 0.58/0.75 11. (-. ((member T_0 T_1) => (member T_0 (empty_set)))) (-. (Ex D, ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D T_1) => (member D T_2))) ### NotImply 10 % 0.58/0.75 12. (-. (All D, ((member D T_1) => (member D (empty_set))))) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D T_1) => (member D T_3))) (-. (Ex D, ((member D T_2) /\ (member D T_3)))) ### NotAllEx 11 % 0.58/0.75 13. (-. (subset T_1 (empty_set))) (-. (Ex D, ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D T_1) => (member D T_2))) ### Definition-Pseudo(subset) 12 % 0.58/0.75 14. (member T_4 (empty_set)) (-. (member T_4 (empty_set))) ### Axiom % 0.58/0.75 15. (All B, (-. (member B (empty_set)))) (member T_4 (empty_set)) ### All 14 % 0.58/0.75 16. (-. ((member T_4 (empty_set)) => (member T_4 T_1))) (All B, (-. (member B (empty_set)))) ### NotImply 15 % 0.58/0.75 17. (-. (All D, ((member D (empty_set)) => (member D T_1)))) (All B, (-. (member B (empty_set)))) ### NotAllEx 16 % 0.58/0.75 18. (-. (subset (empty_set) T_1)) (All B, (-. (member B (empty_set)))) ### Definition-Pseudo(subset) 17 % 0.58/0.75 19. (-. ((subset T_1 (empty_set)) /\ (subset (empty_set) T_1))) (All B, (-. (member B (empty_set)))) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D T_1) => (member D T_3))) (-. (Ex D, ((member D T_2) /\ (member D T_3)))) ### NotAnd 13 18 % 0.58/0.75 20. (T_1 != (empty_set)) (T_1 = (empty_set)) ### Axiom % 0.58/0.75 21. ((T_1 = (empty_set)) <=> ((subset T_1 (empty_set)) /\ (subset (empty_set) T_1))) (T_1 != (empty_set)) (-. (Ex D, ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D T_1) => (member D T_2))) (All B, (-. (member B (empty_set)))) ### Equiv 19 20 % 0.58/0.75 22. (All C, ((T_1 = C) <=> ((subset T_1 C) /\ (subset C T_1)))) (All B, (-. (member B (empty_set)))) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D T_1) => (member D T_3))) (-. (Ex D, ((member D T_2) /\ (member D T_3)))) (T_1 != (empty_set)) ### All 21 % 0.58/0.75 23. (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (T_1 != (empty_set)) (-. (Ex D, ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D T_1) => (member D T_2))) (All B, (-. (member B (empty_set)))) ### All 22 % 0.58/0.75 24. (-. (intersect T_2 T_3)) (All B, (-. (member B (empty_set)))) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D T_1) => (member D T_3))) (T_1 != (empty_set)) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) ### Definition-Pseudo(intersect) 23 % 0.58/0.75 25. (disjoint T_2 T_3) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (T_1 != (empty_set)) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D T_1) => (member D T_2))) (All B, (-. (member B (empty_set)))) ### Definition-Pseudo(disjoint) 24 % 0.58/0.75 26. (subset T_1 T_3) (All B, (-. (member B (empty_set)))) (All D, ((member D T_1) => (member D T_2))) (T_1 != (empty_set)) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (disjoint T_2 T_3) ### Definition-Pseudo(subset) 25 % 0.58/0.75 27. (subset T_1 T_2) (disjoint T_2 T_3) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (subset T_1 T_3) ### Definition-Pseudo(subset) 26 % 0.58/0.75 28. (-. (((subset T_1 T_2) /\ ((subset T_1 T_3) /\ (disjoint T_2 T_3))) => (T_1 = (empty_set)))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) ### ConjTree 27 % 0.58/0.75 29. (-. (All D, (((subset T_1 T_2) /\ ((subset T_1 D) /\ (disjoint T_2 D))) => (T_1 = (empty_set))))) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (All B, (-. (member B (empty_set)))) ### NotAllEx 28 % 0.58/0.75 30. (-. (All C, (All D, (((subset T_1 C) /\ ((subset T_1 D) /\ (disjoint C D))) => (T_1 = (empty_set)))))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) ### NotAllEx 29 % 0.58/0.75 31. (-. (All B, (All C, (All D, (((subset B C) /\ ((subset B D) /\ (disjoint C D))) => (B = (empty_set))))))) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (All B, (-. (member B (empty_set)))) ### NotAllEx 30 % 0.58/0.75 % SZS output end Proof % 0.58/0.75 (* END-PROOF *) %------------------------------------------------------------------------------