%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET201+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 : n013.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 05:40:20 EDT 2022 % Result : Theorem 1.46s 1.67s % Output : Proof 1.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SET201+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.11 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.11/0.32 % Computer : n013.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Sat Jul 9 18:38:59 EDT 2022 % 0.11/0.32 % CPUTime : % 1.46/1.67 % SZS status Theorem % 1.46/1.67 (* PROOF-FOUND *) % 1.46/1.67 (* BEGIN-PROOF *) % 1.46/1.67 % SZS output start Proof % 1.46/1.67 1. (T_0 != T_0) ### Refl(=) % 1.46/1.67 2. ((intersection T_1 T_2) = (intersection T_2 T_1)) ((intersection T_2 T_1) != (intersection T_1 T_2)) ### Sym(=) % 1.46/1.67 3. (-. (member T_0 (intersection T_1 T_2))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) ### P-NotP 1 2 % 1.46/1.67 4. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom % 1.46/1.67 5. ((member T_0 T_1) /\ (member T_0 T_2)) (-. (member T_0 T_2)) ### And 4 % 1.46/1.67 6. ((member T_0 (intersection T_1 T_2)) <=> ((member T_0 T_1) /\ (member T_0 T_2))) (-. (member T_0 T_2)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) ### Equiv 3 5 % 1.46/1.67 7. (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 T_2)) ### All 6 % 1.46/1.67 8. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom % 1.46/1.67 9. ((member T_0 T_2) => (member T_0 T_3)) (-. (member T_0 T_3)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) ### Imply 7 8 % 1.46/1.67 10. (All D, ((member D T_2) => (member D T_3))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 T_3)) ### All 9 % 1.46/1.67 11. (All C, ((intersection T_1 C) = (intersection C T_1))) (-. (member T_0 T_3)) (member T_0 (intersection T_2 T_1)) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (All D, ((member D T_2) => (member D T_3))) ### All 10 % 1.46/1.67 12. (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 T_3)) (All C, ((intersection T_1 C) = (intersection C T_1))) ### All 11 % 1.46/1.67 13. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All C, ((intersection T_1 C) = (intersection C T_1))) (-. (member T_0 T_3)) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) ### All 12 % 1.46/1.67 14. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom % 1.46/1.67 15. ((member T_0 T_1) /\ (member T_0 T_2)) (-. (member T_0 T_1)) ### And 14 % 1.46/1.67 16. ((member T_0 (intersection T_1 T_2)) <=> ((member T_0 T_1) /\ (member T_0 T_2))) (-. (member T_0 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) ### Equiv 3 15 % 1.46/1.67 17. (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 T_1)) ### All 16 % 1.46/1.67 18. (-. (member T_0 T_4)) (member T_0 T_4) ### Axiom % 1.46/1.67 19. ((member T_0 T_1) => (member T_0 T_4)) (-. (member T_0 T_4)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) ### Imply 17 18 % 1.46/1.67 20. (All D, ((member D T_1) => (member D T_4))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 T_4)) ### All 19 % 1.46/1.67 21. (All C, ((intersection T_1 C) = (intersection C T_1))) (-. (member T_0 T_4)) (member T_0 (intersection T_2 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_4))) ### All 20 % 1.46/1.67 22. (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (All D, ((member D T_1) => (member D T_4))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 T_4)) (All C, ((intersection T_1 C) = (intersection C T_1))) ### All 21 % 1.46/1.67 23. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All C, ((intersection T_1 C) = (intersection C T_1))) (-. (member T_0 T_4)) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_1) => (member D T_4))) ### All 22 % 1.46/1.67 24. (-. ((member T_0 T_3) /\ (member T_0 T_4))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (All C, ((intersection T_1 C) = (intersection C T_1))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### NotAnd 13 23 % 1.46/1.67 25. (-. (member T_0 (intersection T_3 T_4))) (member T_0 (intersection T_3 T_4)) ### Axiom % 1.46/1.67 26. ((member T_0 (intersection T_3 T_4)) <=> ((member T_0 T_3) /\ (member T_0 T_4))) (-. (member T_0 (intersection T_3 T_4))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All C, ((intersection T_1 C) = (intersection C T_1))) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) ### Equiv 24 25 % 1.46/1.67 27. (All D, ((member D (intersection T_3 T_4)) <=> ((member D T_3) /\ (member D T_4)))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (All C, ((intersection T_1 C) = (intersection C T_1))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (intersection T_3 T_4))) ### All 26 % 1.46/1.67 28. (All C, (All D, ((member D (intersection T_3 C)) <=> ((member D T_3) /\ (member D C))))) (-. (member T_0 (intersection T_3 T_4))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All C, ((intersection T_1 C) = (intersection C T_1))) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) ### All 27 % 1.46/1.67 29. (All B, (All C, ((intersection B C) = (intersection C B)))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (intersection T_3 T_4))) (All C, (All D, ((member D (intersection T_3 C)) <=> ((member D T_3) /\ (member D C))))) ### All 28 % 1.46/1.67 30. (-. (member T_0 (intersection T_3 T_4))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### All 29 % 1.46/1.67 31. (-. ((member T_0 (intersection T_2 T_1)) => (member T_0 (intersection T_3 T_4)))) (All B, (All C, ((intersection B C) = (intersection C B)))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### NotImply 30 % 1.46/1.67 32. (-. (All D, ((member D (intersection T_2 T_1)) => (member D (intersection T_3 T_4))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### NotAllEx 31 % 1.46/1.67 33. (-. (subset (intersection T_2 T_1) (intersection T_3 T_4))) (All B, (All C, ((intersection B C) = (intersection C B)))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### Definition-Pseudo(subset) 32 % 1.46/1.67 34. (subset T_1 T_4) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, ((intersection B C) = (intersection C B)))) (-. (subset (intersection T_2 T_1) (intersection T_3 T_4))) ### Definition-Pseudo(subset) 33 % 1.46/1.67 35. (subset T_2 T_3) (-. (subset (intersection T_2 T_1) (intersection T_3 T_4))) (All B, (All C, ((intersection B C) = (intersection C B)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (subset T_1 T_4) ### Definition-Pseudo(subset) 34 % 1.46/1.67 36. (-. (((subset T_2 T_3) /\ (subset T_1 T_4)) => (subset (intersection T_2 T_1) (intersection T_3 T_4)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### ConjTree 35 % 1.46/1.67 37. (-. (All E, (((subset T_2 T_3) /\ (subset T_1 E)) => (subset (intersection T_2 T_1) (intersection T_3 E))))) (All B, (All C, ((intersection B C) = (intersection C B)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### NotAllEx 36 % 1.46/1.67 38. (-. (All D, (All E, (((subset T_2 T_3) /\ (subset D E)) => (subset (intersection T_2 D) (intersection T_3 E)))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### NotAllEx 37 % 1.46/1.67 39. (-. (All C, (All D, (All E, (((subset T_2 C) /\ (subset D E)) => (subset (intersection T_2 D) (intersection C E))))))) (All B, (All C, ((intersection B C) = (intersection C B)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### NotAllEx 38 % 1.46/1.67 40. (-. (All B, (All C, (All D, (All E, (((subset B C) /\ (subset D E)) => (subset (intersection B D) (intersection C E)))))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### NotAllEx 39 % 1.46/1.67 % SZS output end Proof % 1.46/1.67 (* END-PROOF *) %------------------------------------------------------------------------------