%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET628+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 : n010.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 05:42:57 EDT 2022 % Result : Theorem 0.21s 0.43s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0. % 0.10/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n010.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 : Mon Jul 11 02:20:00 EDT 2022 % 0.13/0.34 % CPUTime : % 0.21/0.43 % SZS status Theorem % 0.21/0.43 (* PROOF-FOUND *) % 0.21/0.43 (* BEGIN-PROOF *) % 0.21/0.43 % SZS output start Proof % 0.21/0.43 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 0.21/0.43 2. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 0.21/0.43 3. (-. ((member T_0 T_1) /\ (member T_0 T_1))) (member T_0 T_1) ### NotAnd 1 2 % 0.21/0.43 4. (-. (Ex D, ((member D T_1) /\ (member D T_1)))) (member T_0 T_1) ### NotExists 3 % 0.21/0.43 5. (member T_0 (empty_set)) (-. (member T_0 (empty_set))) ### Axiom % 0.21/0.43 6. (All B, (-. (member B (empty_set)))) (member T_0 (empty_set)) ### All 5 % 0.21/0.43 7. (-. ((member T_0 (empty_set)) <=> (member T_0 T_1))) (All B, (-. (member B (empty_set)))) (-. (Ex D, ((member D T_1) /\ (member D T_1)))) ### NotEquiv 4 6 % 0.21/0.43 8. (-. (All D, ((member D (empty_set)) <=> (member D T_1)))) (-. (Ex D, ((member D T_1) /\ (member D T_1)))) (All B, (-. (member B (empty_set)))) ### NotAllEx 7 % 0.21/0.43 9. (T_1 != (empty_set)) ((empty_set) = T_1) ### Sym(=) % 0.21/0.43 10. (((empty_set) = T_1) <=> (All D, ((member D (empty_set)) <=> (member D T_1)))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (-. (Ex D, ((member D T_1) /\ (member D T_1)))) ### Equiv 8 9 % 0.21/0.43 11. (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) (-. (Ex D, ((member D T_1) /\ (member D T_1)))) (All B, (-. (member B (empty_set)))) (T_1 != (empty_set)) ### All 10 % 0.21/0.43 12. (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (-. (Ex D, ((member D T_1) /\ (member D T_1)))) ### All 11 % 0.21/0.43 13. (not_equal T_1 (empty_set)) (-. (Ex D, ((member D T_1) /\ (member D T_1)))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### Definition-Pseudo(not_equal) 12 % 0.21/0.43 14. (-. (intersect T_1 T_1)) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (All B, (-. (member B (empty_set)))) (not_equal T_1 (empty_set)) ### Definition-Pseudo(intersect) 13 % 0.21/0.43 15. (T_1 = (empty_set)) (T_1 != (empty_set)) ### Axiom % 0.21/0.43 16. (member T_2 T_1) (-. (member T_2 T_1)) ### Axiom % 0.21/0.43 17. (-. (member T_2 (empty_set))) (member T_2 (empty_set)) ### Axiom % 0.21/0.43 18. ((member T_2 T_1) <=> (member T_2 (empty_set))) (-. (member T_2 (empty_set))) (member T_2 T_1) ### Equiv 16 17 % 0.21/0.43 19. (All D, ((member D T_1) <=> (member D (empty_set)))) (member T_2 T_1) (-. (member T_2 (empty_set))) ### All 18 % 0.21/0.43 20. (All B, (-. (member B (empty_set)))) (member T_2 T_1) (All D, ((member D T_1) <=> (member D (empty_set)))) ### All 19 % 0.21/0.43 21. ((T_1 = (empty_set)) <=> (All D, ((member D T_1) <=> (member D (empty_set))))) (member T_2 T_1) (All B, (-. (member B (empty_set)))) (T_1 = (empty_set)) ### Equiv 15 20 % 0.21/0.43 22. (All C, ((T_1 = C) <=> (All D, ((member D T_1) <=> (member D C))))) (T_1 = (empty_set)) (All B, (-. (member B (empty_set)))) (member T_2 T_1) ### All 21 % 0.21/0.43 23. (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (member T_2 T_1) (All B, (-. (member B (empty_set)))) (T_1 = (empty_set)) ### All 22 % 0.21/0.43 24. (-. (T_1 != (empty_set))) (All B, (-. (member B (empty_set)))) (member T_2 T_1) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### NotNot 23 % 0.21/0.43 25. (-. (not_equal T_1 (empty_set))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (member T_2 T_1) (All B, (-. (member B (empty_set)))) ### Definition-Pseudo(not_equal) 24 % 0.21/0.43 26. ((member T_2 T_1) /\ (member T_2 T_1)) (All B, (-. (member B (empty_set)))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (-. (not_equal T_1 (empty_set))) ### And 25 % 0.21/0.43 27. (Ex D, ((member D T_1) /\ (member D T_1))) (-. (not_equal T_1 (empty_set))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (All B, (-. (member B (empty_set)))) ### Exists 26 % 0.21/0.43 28. (intersect T_1 T_1) (All B, (-. (member B (empty_set)))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (-. (not_equal T_1 (empty_set))) ### Definition-Pseudo(intersect) 27 % 0.21/0.43 29. (-. ((intersect T_1 T_1) <=> (not_equal T_1 (empty_set)))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### NotEquiv 14 28 % 0.21/0.43 30. (-. (All B, ((intersect B B) <=> (not_equal B (empty_set))))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (All B, (-. (member B (empty_set)))) ### NotAllEx 29 % 0.21/0.43 % SZS output end Proof % 0.21/0.43 (* END-PROOF *) %------------------------------------------------------------------------------