%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : RNG093+2 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n018.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 : Mon Jul 18 20:41:58 EDT 2022 % Result : Theorem 0.22s 0.50s % Output : Proof 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : RNG093+2 : TPTP v8.1.0. Released v4.0.0. % 0.08/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.15/0.35 % Computer : n018.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 600 % 0.15/0.35 % DateTime : Mon May 30 04:41:26 EDT 2022 % 0.15/0.35 % CPUTime : % 0.22/0.50 % SZS status Theorem % 0.22/0.50 (* PROOF-FOUND *) % 0.22/0.50 (* BEGIN-PROOF *) % 0.22/0.50 % SZS output start Proof % 0.22/0.50 1. (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ)))) ### Axiom % 0.22/0.50 2. (-. (aElementOf0 T_0 (xI))) (aElementOf0 T_0 (xI)) ### Axiom % 0.22/0.50 3. ((aElementOf0 T_0 (xI)) /\ (aElementOf0 T_0 (xJ))) (-. (aElementOf0 T_0 (xI))) ### And 2 % 0.22/0.50 4. ((aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 T_0 (xI)) /\ (aElementOf0 T_0 (xJ)))) (-. (aElementOf0 T_0 (xI))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) ### Equiv 1 3 % 0.22/0.50 5. (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 T_0 (xI))) ### All 4 % 0.22/0.50 6. (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ)))) ### Axiom % 0.22/0.50 7. (-. (aElementOf0 T_1 (xI))) (aElementOf0 T_1 (xI)) ### Axiom % 0.22/0.50 8. ((aElementOf0 T_1 (xI)) /\ (aElementOf0 T_1 (xJ))) (-. (aElementOf0 T_1 (xI))) ### And 7 % 0.22/0.50 9. ((aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 T_1 (xI)) /\ (aElementOf0 T_1 (xJ)))) (-. (aElementOf0 T_1 (xI))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) ### Equiv 6 8 % 0.22/0.50 10. (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 T_1 (xI))) ### All 9 % 0.22/0.50 11. (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xI))) (aElementOf0 (sdtpldt0 T_0 T_1) (xI)) ### Axiom % 0.22/0.50 12. ((aElementOf0 T_1 (xI)) => (aElementOf0 (sdtpldt0 T_0 T_1) (xI))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xI))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) ### Imply 10 11 % 0.22/0.50 13. (All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 T_0 W1) (xI)))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xI))) ### All 12 % 0.22/0.50 14. ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 T_0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (xI))))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xI))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) ### And 13 % 0.22/0.50 15. ((aElementOf0 T_0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 T_0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (xI)))))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xI))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) ### Imply 5 14 % 0.22/0.50 16. (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xI))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) ### All 15 % 0.22/0.50 17. (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ)))) ### Axiom % 0.22/0.50 18. (-. (aElementOf0 T_0 (xJ))) (aElementOf0 T_0 (xJ)) ### Axiom % 0.22/0.50 19. ((aElementOf0 T_0 (xI)) /\ (aElementOf0 T_0 (xJ))) (-. (aElementOf0 T_0 (xJ))) ### And 18 % 0.22/0.50 20. ((aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 T_0 (xI)) /\ (aElementOf0 T_0 (xJ)))) (-. (aElementOf0 T_0 (xJ))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) ### Equiv 17 19 % 0.22/0.50 21. (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 T_0 (xJ))) ### All 20 % 0.22/0.50 22. (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ)))) ### Axiom % 0.22/0.50 23. (-. (aElementOf0 T_1 (xJ))) (aElementOf0 T_1 (xJ)) ### Axiom % 0.22/0.50 24. ((aElementOf0 T_1 (xI)) /\ (aElementOf0 T_1 (xJ))) (-. (aElementOf0 T_1 (xJ))) ### And 23 % 0.22/0.50 25. ((aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 T_1 (xI)) /\ (aElementOf0 T_1 (xJ)))) (-. (aElementOf0 T_1 (xJ))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) ### Equiv 22 24 % 0.22/0.50 26. (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 T_1 (xJ))) ### All 25 % 0.22/0.50 27. (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xJ))) (aElementOf0 (sdtpldt0 T_0 T_1) (xJ)) ### Axiom % 0.22/0.50 28. ((aElementOf0 T_1 (xJ)) => (aElementOf0 (sdtpldt0 T_0 T_1) (xJ))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xJ))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) ### Imply 26 27 % 0.22/0.50 29. (All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 T_0 W1) (xJ)))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xJ))) ### All 28 % 0.22/0.50 30. ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 T_0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (xJ))))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xJ))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) ### And 29 % 0.22/0.50 31. ((aElementOf0 T_0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 T_0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (xJ)))))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xJ))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) ### Imply 21 30 % 0.22/0.50 32. (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (xJ))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) ### All 31 % 0.22/0.50 33. (-. ((aElementOf0 (sdtpldt0 T_0 T_1) (xI)) /\ (aElementOf0 (sdtpldt0 T_0 T_1) (xJ)))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) ### NotAnd 16 32 % 0.22/0.50 34. (-. (aElementOf0 (sdtpldt0 T_0 T_1) (sdtasasdt0 (xI) (xJ)))) (aElementOf0 (sdtpldt0 T_0 T_1) (sdtasasdt0 (xI) (xJ))) ### Axiom % 0.22/0.50 35. ((aElementOf0 (sdtpldt0 T_0 T_1) (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 (sdtpldt0 T_0 T_1) (xI)) /\ (aElementOf0 (sdtpldt0 T_0 T_1) (xJ)))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (sdtasasdt0 (xI) (xJ)))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) ### Equiv 33 34 % 0.22/0.50 36. (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (sdtasasdt0 (xI) (xJ)))) ### All 35 % 0.22/0.50 37. (-. ((aElementOf0 T_1 (sdtasasdt0 (xI) (xJ))) => (aElementOf0 (sdtpldt0 T_0 T_1) (sdtasasdt0 (xI) (xJ))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) ### NotImply 36 % 0.22/0.50 38. (-. (All W1, ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ))) => (aElementOf0 (sdtpldt0 T_0 W1) (sdtasasdt0 (xI) (xJ)))))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) ### NotAllEx 37 % 0.22/0.50 39. (aElement0 T_2) (-. (aElement0 T_2)) ### Axiom % 0.22/0.50 40. (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xI))) (aElementOf0 (sdtasdt0 T_2 T_0) (xI)) ### Axiom % 0.22/0.50 41. ((aElement0 T_2) => (aElementOf0 (sdtasdt0 T_2 T_0) (xI))) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xI))) (aElement0 T_2) ### Imply 39 40 % 0.22/0.50 42. (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (xI)))) (aElement0 T_2) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xI))) ### All 41 % 0.22/0.50 43. ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 T_0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (xI))))) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xI))) (aElement0 T_2) ### And 42 % 0.22/0.50 44. ((aElementOf0 T_0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 T_0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (xI)))))) (aElement0 T_2) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xI))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) ### Imply 5 43 % 0.22/0.50 45. (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xI))) (aElement0 T_2) ### All 44 % 0.22/0.50 46. (aElement0 T_2) (-. (aElement0 T_2)) ### Axiom % 0.22/0.50 47. (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xJ))) (aElementOf0 (sdtasdt0 T_2 T_0) (xJ)) ### Axiom % 0.22/0.50 48. ((aElement0 T_2) => (aElementOf0 (sdtasdt0 T_2 T_0) (xJ))) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xJ))) (aElement0 T_2) ### Imply 46 47 % 0.22/0.50 49. (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (xJ)))) (aElement0 T_2) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xJ))) ### All 48 % 0.22/0.50 50. ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 T_0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (xJ))))) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xJ))) (aElement0 T_2) ### And 49 % 0.22/0.50 51. ((aElementOf0 T_0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 T_0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (xJ)))))) (aElement0 T_2) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xJ))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) ### Imply 21 50 % 0.22/0.50 52. (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (xJ))) (aElement0 T_2) ### All 51 % 0.22/0.50 53. (-. ((aElementOf0 (sdtasdt0 T_2 T_0) (xI)) /\ (aElementOf0 (sdtasdt0 T_2 T_0) (xJ)))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (aElement0 T_2) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) ### NotAnd 45 52 % 0.22/0.50 54. (-. (aElementOf0 (sdtasdt0 T_2 T_0) (sdtasasdt0 (xI) (xJ)))) (aElementOf0 (sdtasdt0 T_2 T_0) (sdtasasdt0 (xI) (xJ))) ### Axiom % 0.22/0.50 55. ((aElementOf0 (sdtasdt0 T_2 T_0) (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 (sdtasdt0 T_2 T_0) (xI)) /\ (aElementOf0 (sdtasdt0 T_2 T_0) (xJ)))) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (sdtasasdt0 (xI) (xJ)))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (aElement0 T_2) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) ### Equiv 53 54 % 0.22/0.50 56. (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (aElement0 T_2) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (-. (aElementOf0 (sdtasdt0 T_2 T_0) (sdtasasdt0 (xI) (xJ)))) ### All 55 % 0.22/0.50 57. (-. ((aElement0 T_2) => (aElementOf0 (sdtasdt0 T_2 T_0) (sdtasasdt0 (xI) (xJ))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) ### NotImply 56 % 0.22/0.50 58. (-. (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (sdtasasdt0 (xI) (xJ)))))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) ### NotAllEx 57 % 0.22/0.50 59. (-. ((All W1, ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ))) => (aElementOf0 (sdtpldt0 T_0 W1) (sdtasasdt0 (xI) (xJ))))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (sdtasasdt0 (xI) (xJ))))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) ### NotAnd 38 58 % 0.22/0.50 60. (-. ((aElementOf0 T_0 (sdtasasdt0 (xI) (xJ))) => ((All W1, ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ))) => (aElementOf0 (sdtpldt0 T_0 W1) (sdtasasdt0 (xI) (xJ))))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 T_0) (sdtasasdt0 (xI) (xJ)))))))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) ### NotImply 59 % 0.22/0.50 61. (-. (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) => ((All W1, ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ))) => (aElementOf0 (sdtpldt0 W0 W1) (sdtasasdt0 (xI) (xJ))))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (sdtasasdt0 (xI) (xJ))))))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ))))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) ### NotAllEx 60 % 0.22/0.50 62. (-. (((aSet0 (sdtasasdt0 (xI) (xJ))) /\ (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ)))))) => ((All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) => ((All W1, ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ))) => (aElementOf0 (sdtpldt0 W0 W1) (sdtasasdt0 (xI) (xJ))))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (sdtasasdt0 (xI) (xJ)))))))) \/ (aIdeal0 (sdtasasdt0 (xI) (xJ)))))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) ### ConjTree 61 % 0.22/0.50 63. ((aSet0 (xI)) /\ ((All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) /\ ((aIdeal0 (xI)) /\ ((aSet0 (xJ)) /\ ((All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) /\ (aIdeal0 (xJ))))))) (-. (((aSet0 (sdtasasdt0 (xI) (xJ))) /\ (All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) <=> ((aElementOf0 W0 (xI)) /\ (aElementOf0 W0 (xJ)))))) => ((All W0, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ))) => ((All W1, ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ))) => (aElementOf0 (sdtpldt0 W0 W1) (sdtasasdt0 (xI) (xJ))))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (sdtasasdt0 (xI) (xJ)))))))) \/ (aIdeal0 (sdtasasdt0 (xI) (xJ)))))) ### ConjTree 62 % 0.22/0.50 % SZS output end Proof % 0.22/0.50 (* END-PROOF *) %------------------------------------------------------------------------------