TSTP Solution File: RNG093+2 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% 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 *)
%------------------------------------------------------------------------------