TSTP Solution File: RNG109+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : RNG109+1 : 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 : n027.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 20:42:00 EDT 2022
% Result : Theorem 10.07s 10.25s
% Output : Proof 10.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG109+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 10:09:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 10.07/10.25 % SZS status Theorem
% 10.07/10.25 (* PROOF-FOUND *)
% 10.07/10.25 (* BEGIN-PROOF *)
% 10.07/10.25 % SZS output start Proof
% 10.07/10.25 1. (aElement0 (xa)) (-. (aElement0 (xa))) ### Axiom
% 10.07/10.25 2. (aElement0 (xa)) (-. (aElement0 (xa))) ### Axiom
% 10.07/10.25 3. (-. (aSet0 (slsdtgt0 (xa)))) (aSet0 (slsdtgt0 (xa))) ### Axiom
% 10.07/10.25 4. ((aSet0 (slsdtgt0 (xa))) /\ (All W1, ((aElementOf0 W1 (slsdtgt0 (xa))) => ((All W2, ((aElementOf0 W2 (slsdtgt0 (xa))) => (aElementOf0 (sdtpldt0 W1 W2) (slsdtgt0 (xa))))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (slsdtgt0 (xa))))))))) (-. (aSet0 (slsdtgt0 (xa)))) ### And 3
% 10.07/10.25 5. (aIdeal0 (slsdtgt0 (xa))) (-. (aSet0 (slsdtgt0 (xa)))) ### Definition-Pseudo(aIdeal0) 4
% 10.07/10.25 6. ((aElement0 (xa)) => (aIdeal0 (slsdtgt0 (xa)))) (-. (aSet0 (slsdtgt0 (xa)))) (aElement0 (xa)) ### Imply 2 5
% 10.07/10.25 7. (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (aElement0 (xa)) (-. (aSet0 (slsdtgt0 (xa)))) ### All 6
% 10.07/10.25 8. (aElement0 (xb)) (-. (aElement0 (xb))) ### Axiom
% 10.07/10.25 9. (-. (aSet0 (slsdtgt0 (xb)))) (aSet0 (slsdtgt0 (xb))) ### Axiom
% 10.07/10.25 10. ((aSet0 (slsdtgt0 (xb))) /\ (All W1, ((aElementOf0 W1 (slsdtgt0 (xb))) => ((All W2, ((aElementOf0 W2 (slsdtgt0 (xb))) => (aElementOf0 (sdtpldt0 W1 W2) (slsdtgt0 (xb))))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (slsdtgt0 (xb))))))))) (-. (aSet0 (slsdtgt0 (xb)))) ### And 9
% 10.07/10.25 11. (aIdeal0 (slsdtgt0 (xb))) (-. (aSet0 (slsdtgt0 (xb)))) ### Definition-Pseudo(aIdeal0) 10
% 10.07/10.25 12. ((aElement0 (xb)) => (aIdeal0 (slsdtgt0 (xb)))) (-. (aSet0 (slsdtgt0 (xb)))) (aElement0 (xb)) ### Imply 8 11
% 10.07/10.25 13. (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (aElement0 (xb)) (-. (aSet0 (slsdtgt0 (xb)))) ### All 12
% 10.07/10.25 14. ((sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))) != (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) ### Refl(=)
% 10.07/10.25 15. (aElementOf0 (xa) (slsdtgt0 (xa))) (-. (aElementOf0 (xa) (slsdtgt0 (xa)))) ### Axiom
% 10.07/10.25 16. (aElementOf0 (sz00) (slsdtgt0 (xb))) (-. (aElementOf0 (sz00) (slsdtgt0 (xb)))) ### Axiom
% 10.07/10.25 17. ((sdtpldt0 (xa) (sz00)) != (sdtpldt0 (xa) (sz00))) ### Refl(=)
% 10.07/10.25 18. (-. ((aElementOf0 (xa) (slsdtgt0 (xa))) /\ ((aElementOf0 (sz00) (slsdtgt0 (xb))) /\ ((sdtpldt0 (xa) (sz00)) = (sdtpldt0 (xa) (sz00)))))) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElementOf0 (xa) (slsdtgt0 (xa))) ### DisjTree 15 16 17
% 10.07/10.25 19. (-. (Ex W5, ((aElementOf0 (xa) (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 (xa) W5) = (sdtpldt0 (xa) (sz00))))))) (aElementOf0 (xa) (slsdtgt0 (xa))) (aElementOf0 (sz00) (slsdtgt0 (xb))) ### NotExists 18
% 10.07/10.25 20. (-. (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = (sdtpldt0 (xa) (sz00)))))))) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElementOf0 (xa) (slsdtgt0 (xa))) ### NotExists 19
% 10.07/10.25 21. (aElementOf0 (sdtpldt0 (xa) (sz00)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) (-. (aElementOf0 (sdtpldt0 (xa) (sz00)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))))) ### Axiom
% 10.07/10.25 22. ((sz00) != (sdtpldt0 (xa) (sz00))) ((sdtpldt0 (xa) (sz00)) = (sz00)) ### Sym(=)
% 10.07/10.25 23. (-. ((sdtpldt0 (xa) (sz00)) != (sz00))) ((sz00) != (sdtpldt0 (xa) (sz00))) ### NotNot 22
% 10.07/10.25 24. (-. ((aElementOf0 (sdtpldt0 (xa) (sz00)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ ((sdtpldt0 (xa) (sz00)) != (sz00)))) ((sz00) != (sdtpldt0 (xa) (sz00))) (aElementOf0 (sdtpldt0 (xa) (sz00)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) ### NotAnd 21 23
% 10.07/10.25 25. (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (sdtpldt0 (xa) (sz00)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) ((sz00) != (sdtpldt0 (xa) (sz00))) ### NotExists 24
% 10.07/10.25 26. ((aElementOf0 (sdtpldt0 (xa) (sz00)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = (sdtpldt0 (xa) (sz00)))))))) ((sz00) != (sdtpldt0 (xa) (sz00))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (xa) (slsdtgt0 (xa))) (aElementOf0 (sz00) (slsdtgt0 (xb))) ### Equiv 20 25
% 10.07/10.25 27. (All W3, ((aElementOf0 W3 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))))) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElementOf0 (xa) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((sz00) != (sdtpldt0 (xa) (sz00))) ### All 26
% 10.07/10.25 28. ((xa) != (xa)) ### NotEqual
% 10.07/10.25 29. ((xa) != (sz00)) ((sdtpldt0 (xa) (sz00)) = (xa)) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (xa) (slsdtgt0 (xa))) (aElementOf0 (sz00) (slsdtgt0 (xb))) (All W3, ((aElementOf0 W3 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))))) ### TransEq-sym 27 28 28
% 10.07/10.25 30. ((aSet0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (All W3, ((aElementOf0 W3 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3)))))))) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElementOf0 (xa) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((sdtpldt0 (xa) (sz00)) = (xa)) ((xa) != (sz00)) ### And 29
% 10.07/10.25 31. (((sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))) = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> ((aSet0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (All W3, ((aElementOf0 W3 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))))))) ((xa) != (sz00)) ((sdtpldt0 (xa) (sz00)) = (xa)) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (xa) (slsdtgt0 (xa))) (aElementOf0 (sz00) (slsdtgt0 (xb))) ### Equiv 14 30
% 10.07/10.25 32. (All W2, ((W2 = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3)))))))))) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElementOf0 (xa) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((sdtpldt0 (xa) (sz00)) = (xa)) ((xa) != (sz00)) ### All 31
% 10.07/10.25 33. (((aSet0 (slsdtgt0 (xa))) /\ (aSet0 (slsdtgt0 (xb)))) => (All W2, ((W2 = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))))))))) ((xa) != (sz00)) ((sdtpldt0 (xa) (sz00)) = (xa)) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (xa) (slsdtgt0 (xa))) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElement0 (xb)) (aElement0 (xa)) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) ### DisjTree 7 13 32
% 10.07/10.25 34. (All W1, (((aSet0 (slsdtgt0 (xa))) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 (slsdtgt0 (xa)) W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3)))))))))))) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (aElement0 (xa)) (aElement0 (xb)) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElementOf0 (xa) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((sdtpldt0 (xa) (sz00)) = (xa)) ((xa) != (sz00)) ### All 33
% 10.07/10.25 35. (All W0, (All W1, (((aSet0 W0) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 W0 W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 W0) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3))))))))))))) ((xa) != (sz00)) ((sdtpldt0 (xa) (sz00)) = (xa)) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (xa) (slsdtgt0 (xa))) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElement0 (xb)) (aElement0 (xa)) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) ### All 34
% 10.07/10.25 36. (((sdtpldt0 (xa) (sz00)) = (xa)) /\ ((xa) = (sdtpldt0 (sz00) (xa)))) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (aElement0 (xa)) (aElement0 (xb)) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElementOf0 (xa) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((xa) != (sz00)) (All W0, (All W1, (((aSet0 W0) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 W0 W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 W0) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3))))))))))))) ### And 35
% 10.07/10.25 37. ((aElement0 (xa)) => (((sdtpldt0 (xa) (sz00)) = (xa)) /\ ((xa) = (sdtpldt0 (sz00) (xa))))) (All W0, (All W1, (((aSet0 W0) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 W0 W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 W0) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3))))))))))))) ((xa) != (sz00)) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (xa) (slsdtgt0 (xa))) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElement0 (xb)) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (aElement0 (xa)) ### Imply 1 36
% 10.07/10.25 38. (All W0, ((aElement0 W0) => (((sdtpldt0 W0 (sz00)) = W0) /\ (W0 = (sdtpldt0 (sz00) W0))))) (aElement0 (xa)) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (aElement0 (xb)) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElementOf0 (xa) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((xa) != (sz00)) (All W0, (All W1, (((aSet0 W0) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 W0 W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 W0) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3))))))))))))) ### All 37
% 10.07/10.25 39. (aElement0 (xb)) (-. (aElement0 (xb))) ### Axiom
% 10.07/10.25 40. ((sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))) != (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) ### Refl(=)
% 10.07/10.25 41. ((xb) != (xb)) ### NotEqual
% 10.07/10.25 42. (aElementOf0 (sz00) (slsdtgt0 (xa))) (-. (aElementOf0 (sz00) (slsdtgt0 (xa)))) ### Axiom
% 10.07/10.25 43. (aElementOf0 (xb) (slsdtgt0 (xb))) (-. (aElementOf0 (xb) (slsdtgt0 (xb)))) ### Axiom
% 10.07/10.25 44. ((sdtpldt0 (sz00) (xb)) != (sdtpldt0 (sz00) (xb))) ### Refl(=)
% 10.07/10.25 45. (-. ((aElementOf0 (sz00) (slsdtgt0 (xa))) /\ ((aElementOf0 (xb) (slsdtgt0 (xb))) /\ ((sdtpldt0 (sz00) (xb)) = (sdtpldt0 (sz00) (xb)))))) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElementOf0 (sz00) (slsdtgt0 (xa))) ### DisjTree 42 43 44
% 10.07/10.25 46. (-. (Ex W5, ((aElementOf0 (sz00) (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 (sz00) W5) = (sdtpldt0 (sz00) (xb))))))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (aElementOf0 (xb) (slsdtgt0 (xb))) ### NotExists 45
% 10.07/10.25 47. (-. (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = (sdtpldt0 (sz00) (xb)))))))) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElementOf0 (sz00) (slsdtgt0 (xa))) ### NotExists 46
% 10.07/10.25 48. (aElementOf0 (sdtpldt0 (sz00) (xb)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) (-. (aElementOf0 (sdtpldt0 (sz00) (xb)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))))) ### Axiom
% 10.07/10.25 49. ((sdtpldt0 (sz00) (xb)) != (sz00)) ((sdtpldt0 (sz00) (xb)) = (sz00)) ### Axiom
% 10.07/10.25 50. (-. ((sdtpldt0 (sz00) (xb)) != (sz00))) ((sdtpldt0 (sz00) (xb)) != (sz00)) ### NotNot 49
% 10.07/10.25 51. (-. ((aElementOf0 (sdtpldt0 (sz00) (xb)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ ((sdtpldt0 (sz00) (xb)) != (sz00)))) ((sdtpldt0 (sz00) (xb)) != (sz00)) (aElementOf0 (sdtpldt0 (sz00) (xb)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) ### NotAnd 48 50
% 10.07/10.25 52. (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (sdtpldt0 (sz00) (xb)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) ((sdtpldt0 (sz00) (xb)) != (sz00)) ### NotExists 51
% 10.07/10.25 53. ((aElementOf0 (sdtpldt0 (sz00) (xb)) (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = (sdtpldt0 (sz00) (xb)))))))) ((sdtpldt0 (sz00) (xb)) != (sz00)) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (aElementOf0 (xb) (slsdtgt0 (xb))) ### Equiv 47 52
% 10.07/10.25 54. (All W3, ((aElementOf0 W3 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))))) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((sdtpldt0 (sz00) (xb)) != (sz00)) ### All 53
% 10.07/10.25 55. ((xb) != (sz00)) ((xb) = (sdtpldt0 (sz00) (xb))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (aElementOf0 (xb) (slsdtgt0 (xb))) (All W3, ((aElementOf0 W3 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))))) ### TransEq 41 41 54
% 10.07/10.25 56. ((aSet0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (All W3, ((aElementOf0 W3 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3)))))))) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((xb) = (sdtpldt0 (sz00) (xb))) ((xb) != (sz00)) ### And 55
% 10.07/10.25 57. (((sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))) = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> ((aSet0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (All W3, ((aElementOf0 W3 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))))))) ((xb) != (sz00)) ((xb) = (sdtpldt0 (sz00) (xb))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (aElementOf0 (xb) (slsdtgt0 (xb))) ### Equiv 40 56
% 10.07/10.25 58. (All W2, ((W2 = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3)))))))))) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((xb) = (sdtpldt0 (sz00) (xb))) ((xb) != (sz00)) ### All 57
% 10.07/10.25 59. (((aSet0 (slsdtgt0 (xa))) /\ (aSet0 (slsdtgt0 (xb)))) => (All W2, ((W2 = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))))))))) ((xb) != (sz00)) ((xb) = (sdtpldt0 (sz00) (xb))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElement0 (xb)) (aElement0 (xa)) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) ### DisjTree 7 13 58
% 10.07/10.25 60. (All W1, (((aSet0 (slsdtgt0 (xa))) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 (slsdtgt0 (xa)) W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3)))))))))))) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (aElement0 (xa)) (aElement0 (xb)) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((xb) = (sdtpldt0 (sz00) (xb))) ((xb) != (sz00)) ### All 59
% 10.07/10.25 61. (((sdtpldt0 (xb) (sz00)) = (xb)) /\ ((xb) = (sdtpldt0 (sz00) (xb)))) ((xb) != (sz00)) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElement0 (xb)) (aElement0 (xa)) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (All W1, (((aSet0 (slsdtgt0 (xa))) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 (slsdtgt0 (xa)) W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3)))))))))))) ### And 60
% 10.07/10.25 62. ((aElement0 (xb)) => (((sdtpldt0 (xb) (sz00)) = (xb)) /\ ((xb) = (sdtpldt0 (sz00) (xb))))) (All W1, (((aSet0 (slsdtgt0 (xa))) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 (slsdtgt0 (xa)) W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3)))))))))))) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (aElement0 (xa)) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((xb) != (sz00)) (aElement0 (xb)) ### Imply 39 61
% 10.07/10.25 63. (All W0, ((aElement0 W0) => (((sdtpldt0 W0 (sz00)) = W0) /\ (W0 = (sdtpldt0 (sz00) W0))))) (aElement0 (xb)) ((xb) != (sz00)) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElement0 (xa)) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (All W1, (((aSet0 (slsdtgt0 (xa))) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 (slsdtgt0 (xa)) W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3)))))))))))) ### All 62
% 10.07/10.25 64. (All W0, (All W1, (((aSet0 W0) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 W0 W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 W0) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3))))))))))))) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (aElement0 (xa)) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) ((xb) != (sz00)) (aElement0 (xb)) (All W0, ((aElement0 W0) => (((sdtpldt0 W0 (sz00)) = W0) /\ (W0 = (sdtpldt0 (sz00) W0))))) ### All 63
% 10.07/10.25 65. (((xa) != (sz00)) \/ ((xb) != (sz00))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (aElementOf0 (xb) (slsdtgt0 (xb))) (All W0, (All W1, (((aSet0 W0) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 W0 W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 W0) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3))))))))))))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (aElementOf0 (xa) (slsdtgt0 (xa))) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElement0 (xb)) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (aElement0 (xa)) (All W0, ((aElement0 W0) => (((sdtpldt0 W0 (sz00)) = W0) /\ (W0 = (sdtpldt0 (sz00) W0))))) ### Or 38 64
% 10.07/10.25 66. ((aElement0 (xa)) /\ (aElement0 (xb))) (All W0, ((aElement0 W0) => (((sdtpldt0 W0 (sz00)) = W0) /\ (W0 = (sdtpldt0 (sz00) W0))))) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (aElementOf0 (sz00) (slsdtgt0 (xb))) (aElementOf0 (xa) (slsdtgt0 (xa))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (All W0, (All W1, (((aSet0 W0) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 W0 W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 W0) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3))))))))))))) (aElementOf0 (xb) (slsdtgt0 (xb))) (aElementOf0 (sz00) (slsdtgt0 (xa))) (((xa) != (sz00)) \/ ((xb) != (sz00))) ### And 65
% 10.07/10.25 67. ((aElementOf0 (sz00) (slsdtgt0 (xa))) /\ ((aElementOf0 (xa) (slsdtgt0 (xa))) /\ ((aElementOf0 (sz00) (slsdtgt0 (xb))) /\ (aElementOf0 (xb) (slsdtgt0 (xb)))))) (((xa) != (sz00)) \/ ((xb) != (sz00))) (All W0, (All W1, (((aSet0 W0) /\ (aSet0 W1)) => (All W2, ((W2 = (sdtpldt1 W0 W1)) <=> ((aSet0 W2) /\ (All W3, ((aElementOf0 W3 W2) <=> (Ex W4, (Ex W5, ((aElementOf0 W4 W0) /\ ((aElementOf0 W5 W1) /\ ((sdtpldt0 W4 W5) = W3))))))))))))) (-. (Ex W0, ((aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))) /\ (W0 != (sz00))))) (All W0, ((aElement0 W0) => (aIdeal0 (slsdtgt0 W0)))) (All W0, ((aElement0 W0) => (((sdtpldt0 W0 (sz00)) = W0) /\ (W0 = (sdtpldt0 (sz00) W0))))) ((aElement0 (xa)) /\ (aElement0 (xb))) ### ConjTree 66
% 10.07/10.25 % SZS output end Proof
% 10.07/10.25 (* END-PROOF *)
%------------------------------------------------------------------------------