%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET586+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 05:42:26 EDT 2022 % Result : Theorem 0.63s 0.85s % Output : Proof 0.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0. % 0.11/0.12 % 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 : Mon Jul 11 07:20:52 EDT 2022 % 0.12/0.33 % CPUTime : % 0.63/0.85 % SZS status Theorem % 0.63/0.85 (* PROOF-FOUND *) % 0.63/0.85 (* BEGIN-PROOF *) % 0.63/0.85 % SZS output start Proof % 0.63/0.85 1. (T_0 != T_0) ### Refl(=) % 0.63/0.85 2. ((intersection T_1 T_2) = (intersection T_2 T_1)) ((intersection T_2 T_1) != (intersection T_1 T_2)) ### Sym(=) % 0.63/0.85 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 % 0.63/0.85 4. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom % 0.63/0.85 5. ((member T_0 T_1) /\ (member T_0 T_2)) (-. (member T_0 T_2)) ### And 4 % 0.63/0.85 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 % 0.63/0.85 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 % 0.63/0.85 8. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom % 0.63/0.85 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 % 0.63/0.85 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 % 0.63/0.85 11. (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (-. (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 T_2) => (member D T_3))) ### All 10 % 0.63/0.85 12. (member T_0 (intersection T_2 T_1)) (-. (member T_0 (intersection T_2 T_1))) ### Axiom % 0.63/0.85 13. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom % 0.63/0.85 14. ((member T_0 T_2) /\ (member T_0 T_1)) (-. (member T_0 T_1)) ### And 13 % 0.63/0.85 15. ((member T_0 (intersection T_2 T_1)) <=> ((member T_0 T_2) /\ (member T_0 T_1))) (-. (member T_0 T_1)) (member T_0 (intersection T_2 T_1)) ### Equiv 12 14 % 0.63/0.85 16. (All D, ((member D (intersection T_2 T_1)) <=> ((member D T_2) /\ (member D T_1)))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 T_1)) ### All 15 % 0.63/0.85 17. (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) (-. (member T_0 T_1)) (member T_0 (intersection T_2 T_1)) ### All 16 % 0.63/0.85 18. (-. ((member T_0 T_3) /\ (member T_0 T_1))) (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ### NotAnd 11 17 % 0.63/0.85 19. (-. (member T_0 (intersection T_3 T_1))) (member T_0 (intersection T_3 T_1)) ### Axiom % 0.63/0.85 20. ((member T_0 (intersection T_3 T_1)) <=> ((member T_0 T_3) /\ (member T_0 T_1))) (-. (member T_0 (intersection T_3 T_1))) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) ### Equiv 18 19 % 0.63/0.85 21. (All D, ((member D (intersection T_3 T_1)) <=> ((member D T_3) /\ (member D T_1)))) (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (-. (member T_0 (intersection T_3 T_1))) ### All 20 % 0.63/0.85 22. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (intersection T_3 T_1))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) (All D, ((member D (intersection T_3 T_1)) <=> ((member D T_3) /\ (member D T_1)))) ### All 21 % 0.63/0.85 23. (All D, ((member D (intersection T_3 T_1)) <=> ((member D T_3) /\ (member D T_1)))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 (intersection T_3 T_1))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 22 % 0.63/0.85 24. (All C, (All D, ((member D (intersection T_3 C)) <=> ((member D T_3) /\ (member D C))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (intersection T_3 T_1))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) ### All 23 % 0.63/0.85 25. (All C, ((intersection T_1 C) = (intersection C T_1))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 (intersection T_3 T_1))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All C, (All D, ((member D (intersection T_3 C)) <=> ((member D T_3) /\ (member D C))))) ### All 24 % 0.63/0.85 26. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (intersection T_3 T_1))) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All C, ((intersection T_1 C) = (intersection C T_1))) ### All 25 % 0.63/0.85 27. (All B, (All C, ((intersection B C) = (intersection C B)))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 (intersection T_3 T_1))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 26 % 0.63/0.85 28. (-. ((member T_0 (intersection T_2 T_1)) => (member T_0 (intersection T_3 T_1)))) (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)))) ### NotImply 27 % 0.63/0.85 29. (-. (All D, ((member D (intersection T_2 T_1)) => (member D (intersection T_3 T_1))))) (All B, (All C, ((intersection B C) = (intersection C B)))) (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)))))) ### NotAllEx 28 % 0.63/0.85 30. (-. (subset (intersection T_2 T_1) (intersection T_3 T_1))) (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)))) ### Definition-Pseudo(subset) 29 % 0.63/0.85 31. (subset T_2 T_3) (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 (intersection T_2 T_1) (intersection T_3 T_1))) ### Definition-Pseudo(subset) 30 % 0.63/0.85 32. (-. ((subset T_2 T_3) => (subset (intersection T_2 T_1) (intersection T_3 T_1)))) (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)))) ### NotImply 31 % 0.63/0.85 33. (-. (All D, ((subset T_2 T_3) => (subset (intersection T_2 D) (intersection T_3 D))))) (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 32 % 0.63/0.85 34. (-. (All C, (All D, ((subset T_2 C) => (subset (intersection T_2 D) (intersection C D)))))) (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 33 % 0.63/0.85 35. (-. (All B, (All C, (All D, ((subset B C) => (subset (intersection B D) (intersection C D))))))) (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 34 % 0.63/0.86 % SZS output end Proof % 0.63/0.86 (* END-PROOF *) %------------------------------------------------------------------------------