%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET626+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 : n019.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 05:42:55 EDT 2022 % Result : Theorem 24.91s 25.09s % Output : Proof 24.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET626+3 : TPTP v8.1.0. Released v2.2.0. % 0.04/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n019.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 08:54:38 EDT 2022 % 0.13/0.34 % CPUTime : % 24.91/25.09 % SZS status Theorem % 24.91/25.09 (* PROOF-FOUND *) % 24.91/25.09 (* BEGIN-PROOF *) % 24.91/25.09 % SZS output start Proof % 24.91/25.09 1. (T_0 != T_0) ### Refl(=) % 24.91/25.09 2. ((intersection T_1 T_2) = (intersection T_2 T_1)) ((intersection T_2 T_1) != (intersection T_1 T_2)) ### Sym(=) % 24.91/25.09 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 % 24.91/25.09 4. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom % 24.91/25.09 5. ((member T_0 T_1) /\ (member T_0 T_2)) (-. (member T_0 T_2)) ### And 4 % 24.91/25.09 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 % 24.91/25.09 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 % 24.91/25.09 8. (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (-. (member T_0 T_2)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) ### All 7 % 24.91/25.09 9. (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)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 T_2)) ### All 8 % 24.91/25.09 10. (member T_0 T_3) (-. (member T_0 T_3)) ### Axiom % 24.91/25.09 11. (-. ((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 B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### NotAnd 9 10 % 24.91/25.09 12. (member T_0 T_3) (-. (member T_0 T_3)) ### Axiom % 24.91/25.09 13. (member T_0 T_2) (-. (member T_0 T_2)) ### Axiom % 24.91/25.09 14. (-. ((member T_0 T_3) /\ (member T_0 T_2))) (member T_0 T_2) (member T_0 T_3) ### NotAnd 12 13 % 24.91/25.09 15. (-. (Ex D, ((member D T_3) /\ (member D T_2)))) (member T_0 T_3) (member T_0 T_2) ### NotExists 14 % 24.91/25.09 16. ((member T_0 T_2) /\ (member T_0 T_3)) (member T_0 T_3) (-. (Ex D, ((member D T_3) /\ (member D T_2)))) ### And 15 % 24.91/25.09 17. ((member T_0 (intersection T_2 T_3)) <=> ((member T_0 T_2) /\ (member T_0 T_3))) (-. (Ex D, ((member D T_3) /\ (member D T_2)))) (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)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_3) ### Equiv 11 16 % 24.91/25.09 18. (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D 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 B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (Ex D, ((member D T_3) /\ (member D T_2)))) ### All 17 % 24.91/25.09 19. (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) (-. (Ex D, ((member D T_3) /\ (member D T_2)))) (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)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_3) ### All 18 % 24.91/25.09 20. (All C, ((intersection T_1 C) = (intersection C T_1))) (member T_0 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)))))) (-. (Ex D, ((member D T_3) /\ (member D T_2)))) (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) ### All 19 % 24.91/25.09 21. (All B, (All C, ((intersection B C) = (intersection C B)))) (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) (-. (Ex D, ((member D T_3) /\ (member D T_2)))) (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)) (member T_0 T_3) ### All 20 % 24.91/25.09 22. (member T_0 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)))))) (-. (Ex D, ((member D T_3) /\ (member D T_2)))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### All 21 % 24.91/25.09 23. (-. (intersect T_3 T_2)) (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)))))) (member T_0 (intersection T_2 T_1)) (member T_0 T_3) ### Definition-Pseudo(intersect) 22 % 24.91/25.09 24. ((member T_0 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)))))) (All B, (All C, ((intersection B C) = (intersection C B)))) (-. (intersect T_3 T_2)) ### And 23 % 24.91/25.09 25. (Ex D, ((member D T_3) /\ (member D (intersection T_2 T_1)))) (-. (intersect T_3 T_2)) (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)))))) ### Exists 24 % 24.91/25.09 26. (intersect T_3 (intersection T_2 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)))) (-. (intersect T_3 T_2)) ### Definition-Pseudo(intersect) 25 % 24.91/25.09 27. (-. ((intersect T_3 (intersection T_2 T_1)) => (intersect T_3 T_2))) (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)))))) ### NotImply 26 % 24.91/25.09 28. (-. (All D, ((intersect T_3 (intersection T_2 D)) => (intersect T_3 T_2)))) (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 27 % 24.91/25.09 29. (-. (All C, (All D, ((intersect T_3 (intersection C D)) => (intersect T_3 C))))) (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 28 % 24.91/25.09 30. (-. (All B, (All C, (All D, ((intersect B (intersection C D)) => (intersect B C)))))) (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 29 % 24.91/25.09 % SZS output end Proof % 24.91/25.09 (* END-PROOF *) %------------------------------------------------------------------------------