%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET639+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 05:43:04 EDT 2022 % Result : Theorem 35.14s 35.38s % Output : Proof 35.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0. % 0.10/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n004.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 21:02:52 EDT 2022 % 0.12/0.33 % CPUTime : % 35.14/35.38 % SZS status Theorem % 35.14/35.38 (* PROOF-FOUND *) % 35.14/35.38 (* BEGIN-PROOF *) % 35.14/35.38 % SZS output start Proof % 35.14/35.38 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 35.14/35.38 2. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 35.14/35.38 3. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom % 35.14/35.38 4. ((member T_0 T_1) => (member T_0 T_2)) (-. (member T_0 T_2)) (member T_0 T_1) ### Imply 2 3 % 35.14/35.38 5. (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (-. (member T_0 T_2)) ### All 4 % 35.14/35.38 6. (-. ((member T_0 T_1) /\ (member T_0 T_2))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ### NotAnd 1 5 % 35.14/35.38 7. (T_0 != T_0) ### Refl(=) % 35.14/35.38 8. ((intersection T_1 T_2) = (intersection T_2 T_1)) ((intersection T_1 T_2) != (intersection T_2 T_1)) ### Axiom % 35.14/35.38 9. (-. (member T_0 (intersection T_2 T_1))) (member T_0 (intersection T_1 T_2)) ((intersection T_1 T_2) = (intersection T_2 T_1)) ### P-NotP 7 8 % 35.14/35.38 10. ((member T_0 (intersection T_1 T_2)) <=> ((member T_0 T_1) /\ (member T_0 T_2))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 (intersection T_2 T_1))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) ### Equiv 6 9 % 35.14/35.38 11. (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (-. (member T_0 (intersection T_2 T_1))) ((intersection T_1 T_2) = (intersection T_2 T_1)) ### All 10 % 35.14/35.38 12. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 35.14/35.38 13. (-. ((member T_0 (intersection T_2 T_1)) /\ (member T_0 T_1))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) ### NotAnd 11 12 % 35.14/35.38 14. (T_0 != T_0) ### Refl(=) % 35.14/35.38 15. ((intersection T_2 T_1) = (empty_set)) ((intersection T_2 T_1) != (empty_set)) ### Axiom % 35.14/35.38 16. (T_1 != T_1) ### Refl(=) % 35.14/35.38 17. ((intersection (intersection T_2 T_1) T_1) != (intersection (empty_set) T_1)) ((intersection T_2 T_1) = (empty_set)) ### NotEqual 15 16 % 35.14/35.38 18. (-. (member T_0 (intersection (empty_set) T_1))) (member T_0 (intersection (intersection T_2 T_1) T_1)) ((intersection T_2 T_1) = (empty_set)) ### P-NotP 14 17 % 35.14/35.38 19. ((member T_0 (intersection (intersection T_2 T_1) T_1)) <=> ((member T_0 (intersection T_2 T_1)) /\ (member T_0 T_1))) ((intersection T_2 T_1) = (empty_set)) (-. (member T_0 (intersection (empty_set) T_1))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ((intersection T_1 T_2) = (intersection T_2 T_1)) ### Equiv 13 18 % 35.14/35.38 20. (All D, ((member D (intersection (intersection T_2 T_1) T_1)) <=> ((member D (intersection T_2 T_1)) /\ (member D T_1)))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (-. (member T_0 (intersection (empty_set) T_1))) ((intersection T_2 T_1) = (empty_set)) ### All 19 % 35.14/35.38 21. (All C, (All D, ((member D (intersection (intersection T_2 T_1) C)) <=> ((member D (intersection T_2 T_1)) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (-. (member T_0 (intersection (empty_set) T_1))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ((intersection T_1 T_2) = (intersection T_2 T_1)) ### All 20 % 35.14/35.38 22. (-. (member T_0 (empty_set))) (member T_0 (empty_set)) ### Axiom % 35.14/35.38 23. ((member T_0 (empty_set)) /\ (member T_0 T_1)) (-. (member T_0 (empty_set))) ### And 22 % 35.14/35.38 24. ((member T_0 (intersection (empty_set) T_1)) <=> ((member T_0 (empty_set)) /\ (member T_0 T_1))) (-. (member T_0 (empty_set))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) ((intersection T_2 T_1) = (empty_set)) (All C, (All D, ((member D (intersection (intersection T_2 T_1) C)) <=> ((member D (intersection T_2 T_1)) /\ (member D C))))) ### Equiv 21 23 % 35.14/35.38 25. (All D, ((member D (intersection (empty_set) T_1)) <=> ((member D (empty_set)) /\ (member D T_1)))) (All C, (All D, ((member D (intersection (intersection T_2 T_1) C)) <=> ((member D (intersection T_2 T_1)) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 (empty_set))) ### All 24 % 35.14/35.38 26. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (empty_set))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D (intersection (empty_set) T_1)) <=> ((member D (empty_set)) /\ (member D T_1)))) ### All 25 % 35.14/35.38 27. (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 (empty_set))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 26 % 35.14/35.38 28. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (empty_set))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) ((intersection T_2 T_1) = (empty_set)) ### All 27 % 35.14/35.38 29. (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 (empty_set))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 28 % 35.14/35.38 30. (member T_0 (empty_set)) (-. (member T_0 (empty_set))) ### Axiom % 35.14/35.38 31. (All B, (-. (member B (empty_set)))) (member T_0 (empty_set)) ### All 30 % 35.14/35.38 32. (-. ((member T_0 (empty_set)) <=> (member T_0 T_1))) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (All D, ((member D T_1) => (member D T_2))) ((intersection T_2 T_1) = (empty_set)) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ### NotEquiv 29 31 % 35.14/35.38 33. (-. (All D, ((member D (empty_set)) <=> (member D T_1)))) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D T_1) => (member D T_2))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) ### NotAllEx 32 % 35.14/35.38 34. (T_1 != (empty_set)) ((empty_set) = T_1) ### Sym(=) % 35.14/35.38 35. (((empty_set) = T_1) <=> (All D, ((member D (empty_set)) <=> (member D T_1)))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (All D, ((member D T_1) => (member D T_2))) ((intersection T_2 T_1) = (empty_set)) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ### Equiv 33 34 % 35.14/35.38 36. (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D T_1) => (member D T_2))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (T_1 != (empty_set)) ### All 35 % 35.21/35.40 37. (All C, ((intersection T_1 C) = (intersection C T_1))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_1) => (member D T_2))) ((intersection T_2 T_1) = (empty_set)) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) ### All 36 % 35.21/35.40 38. (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D T_1) => (member D T_2))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (T_1 != (empty_set)) (All C, ((intersection T_1 C) = (intersection C T_1))) ### All 37 % 35.21/35.40 39. (All B, (All C, ((intersection B C) = (intersection C B)))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_1) => (member D T_2))) ((intersection T_2 T_1) = (empty_set)) (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) ### All 38 % 35.21/35.40 40. (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D T_1) => (member D T_2))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (T_1 != (empty_set)) (All B, (All C, ((intersection B C) = (intersection C B)))) ### All 39 % 35.21/35.40 41. (subset T_1 T_2) (All B, (All C, ((intersection B C) = (intersection C B)))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ((intersection T_2 T_1) = (empty_set)) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### Definition-Pseudo(subset) 40 % 35.21/35.40 42. (-. (((subset T_1 T_2) /\ ((intersection T_2 T_1) = (empty_set))) => (T_1 = (empty_set)))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### ConjTree 41 % 35.21/35.40 43. (-. (All C, (((subset T_1 C) /\ ((intersection C T_1) = (empty_set))) => (T_1 = (empty_set))))) (All B, (All C, ((intersection B C) = (intersection C B)))) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### NotAllEx 42 % 35.21/35.40 44. (-. (All B, (All C, (((subset B C) /\ ((intersection C B) = (empty_set))) => (B = (empty_set)))))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### NotAllEx 43 % 35.21/35.40 % SZS output end Proof % 35.21/35.40 (* END-PROOF *) %------------------------------------------------------------------------------