TSTP Solution File: RNG106+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : RNG106+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 240.20s 240.36s
% Output : Proof 240.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : RNG106+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.15/0.35 % Computer : n027.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 11:59:31 EDT 2022
% 0.15/0.35 % CPUTime :
% 240.20/240.36 % SZS status Theorem
% 240.20/240.36 (* PROOF-FOUND *)
% 240.20/240.36 (* BEGIN-PROOF *)
% 240.20/240.36 % SZS output start Proof
% 240.20/240.36 1. (aElement0 (xc)) (-. (aElement0 (xc))) ### Axiom
% 240.20/240.36 2. ((slsdtgt0 (xc)) != (slsdtgt0 (xc))) ### Refl(=)
% 240.20/240.36 3. (-. (aSet0 (slsdtgt0 (xc)))) (aSet0 (slsdtgt0 (xc))) ### Axiom
% 240.20/240.36 4. ((aSet0 (slsdtgt0 (xc))) /\ (All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2)))))) (-. (aSet0 (slsdtgt0 (xc)))) ### And 3
% 240.20/240.36 5. (((slsdtgt0 (xc)) = (slsdtgt0 (xc))) <=> ((aSet0 (slsdtgt0 (xc))) /\ (All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2))))))) (-. (aSet0 (slsdtgt0 (xc)))) ### Equiv 2 4
% 240.20/240.36 6. (All W1, ((W1 = (slsdtgt0 (xc))) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2)))))))) (-. (aSet0 (slsdtgt0 (xc)))) ### All 5
% 240.20/240.36 7. ((aElement0 (xc)) => (All W1, ((W1 = (slsdtgt0 (xc))) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2))))))))) (-. (aSet0 (slsdtgt0 (xc)))) (aElement0 (xc)) ### Imply 1 6
% 240.20/240.36 8. (All W0, ((aElement0 W0) => (All W1, ((W1 = (slsdtgt0 W0)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 W0 W3) = W2)))))))))) (aElement0 (xc)) (-. (aSet0 (slsdtgt0 (xc)))) ### All 7
% 240.20/240.36 9. (aElementOf0 T_0 (slsdtgt0 (xc))) (-. (aElementOf0 T_0 (slsdtgt0 (xc)))) ### Axiom
% 240.20/240.36 10. (aElementOf0 T_1 (slsdtgt0 (xc))) (-. (aElementOf0 T_1 (slsdtgt0 (xc)))) ### Axiom
% 240.20/240.36 11. (aElement0 (sz00)) (-. (aElement0 (sz00))) ### Axiom
% 240.20/240.36 12. (-. (aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc)))) (aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc))) ### Axiom
% 240.20/240.36 13. ((aElement0 T_2) /\ (((sdtasdt0 (xc) T_2) = T_1) /\ (((sdtpldt0 T_0 T_1) = (sdtasdt0 (xc) (sdtpldt0 T_3 T_2))) /\ (((sdtasdt0 (sz00) T_0) = (sdtasdt0 (xc) (sdtasdt0 T_3 (sz00)))) /\ ((aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 (sz00) T_0) (slsdtgt0 (xc)))))))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc)))) ### ConjTree 12
% 240.20/240.36 14. (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = T_1) /\ (((sdtpldt0 T_0 T_1) = (sdtasdt0 (xc) (sdtpldt0 T_3 W4))) /\ (((sdtasdt0 (sz00) T_0) = (sdtasdt0 (xc) (sdtasdt0 T_3 (sz00)))) /\ ((aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 (sz00) T_0) (slsdtgt0 (xc))))))))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc)))) ### Exists 13
% 240.20/240.36 15. ((aElement0 T_3) /\ (((sdtasdt0 (xc) T_3) = T_0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = T_1) /\ (((sdtpldt0 T_0 T_1) = (sdtasdt0 (xc) (sdtpldt0 T_3 W4))) /\ (((sdtasdt0 (sz00) T_0) = (sdtasdt0 (xc) (sdtasdt0 T_3 (sz00)))) /\ ((aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 (sz00) T_0) (slsdtgt0 (xc))))))))))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc)))) ### ConjTree 14
% 240.20/240.36 16. (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = T_0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = T_1) /\ (((sdtpldt0 T_0 T_1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 (sz00) T_0) = (sdtasdt0 (xc) (sdtasdt0 W3 (sz00)))) /\ ((aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 (sz00) T_0) (slsdtgt0 (xc)))))))))))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc)))) ### Exists 15
% 240.20/240.36 17. (((aElementOf0 T_0 (slsdtgt0 (xc))) /\ ((aElementOf0 T_1 (slsdtgt0 (xc))) /\ (aElement0 (sz00)))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = T_0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = T_1) /\ (((sdtpldt0 T_0 T_1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 (sz00) T_0) = (sdtasdt0 (xc) (sdtasdt0 W3 (sz00)))) /\ ((aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 (sz00) T_0) (slsdtgt0 (xc))))))))))))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc)))) (aElement0 (sz00)) (aElementOf0 T_1 (slsdtgt0 (xc))) (aElementOf0 T_0 (slsdtgt0 (xc))) ### DisjTree 9 10 11 16
% 240.20/240.36 18. (All W2, (((aElementOf0 T_0 (slsdtgt0 (xc))) /\ ((aElementOf0 T_1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = T_0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = T_1) /\ (((sdtpldt0 T_0 T_1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 T_0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 T_0) (slsdtgt0 (xc)))))))))))))) (aElementOf0 T_0 (slsdtgt0 (xc))) (aElementOf0 T_1 (slsdtgt0 (xc))) (aElement0 (sz00)) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc)))) ### All 17
% 240.20/240.36 19. (All W1, (All W2, (((aElementOf0 T_0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = T_0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 T_0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 T_0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 T_0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 T_0) (slsdtgt0 (xc))))))))))))))) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc)))) (aElement0 (sz00)) (aElementOf0 T_1 (slsdtgt0 (xc))) (aElementOf0 T_0 (slsdtgt0 (xc))) ### All 18
% 240.20/240.36 20. (All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) (aElementOf0 T_0 (slsdtgt0 (xc))) (aElementOf0 T_1 (slsdtgt0 (xc))) (aElement0 (sz00)) (-. (aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc)))) ### All 19
% 240.20/240.36 21. (-. ((aElementOf0 T_1 (slsdtgt0 (xc))) => (aElementOf0 (sdtpldt0 T_0 T_1) (slsdtgt0 (xc))))) (aElement0 (sz00)) (aElementOf0 T_0 (slsdtgt0 (xc))) (All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) ### NotImply 20
% 240.20/240.36 22. (-. (All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) => (aElementOf0 (sdtpldt0 T_0 W2) (slsdtgt0 (xc)))))) (All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) (aElementOf0 T_0 (slsdtgt0 (xc))) (aElement0 (sz00)) ### NotAllEx 21
% 240.20/240.36 23. (aElementOf0 T_0 (slsdtgt0 (xc))) (-. (aElementOf0 T_0 (slsdtgt0 (xc)))) ### Axiom
% 240.20/240.36 24. (aElementOf0 T_0 (slsdtgt0 (xc))) (-. (aElementOf0 T_0 (slsdtgt0 (xc)))) ### Axiom
% 240.20/240.36 25. (aElement0 T_4) (-. (aElement0 T_4)) ### Axiom
% 240.20/240.36 26. (-. (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc)))) (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc))) ### Axiom
% 240.20/240.36 27. ((aElement0 T_5) /\ (((sdtasdt0 (xc) T_5) = T_0) /\ (((sdtpldt0 T_0 T_0) = (sdtasdt0 (xc) (sdtpldt0 T_6 T_5))) /\ (((sdtasdt0 T_4 T_0) = (sdtasdt0 (xc) (sdtasdt0 T_6 T_4))) /\ ((aElementOf0 (sdtpldt0 T_0 T_0) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc)))))))) (-. (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc)))) ### ConjTree 26
% 240.20/240.36 28. (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = T_0) /\ (((sdtpldt0 T_0 T_0) = (sdtasdt0 (xc) (sdtpldt0 T_6 W4))) /\ (((sdtasdt0 T_4 T_0) = (sdtasdt0 (xc) (sdtasdt0 T_6 T_4))) /\ ((aElementOf0 (sdtpldt0 T_0 T_0) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc))))))))) (-. (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc)))) ### Exists 27
% 240.20/240.36 29. ((aElement0 T_6) /\ (((sdtasdt0 (xc) T_6) = T_0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = T_0) /\ (((sdtpldt0 T_0 T_0) = (sdtasdt0 (xc) (sdtpldt0 T_6 W4))) /\ (((sdtasdt0 T_4 T_0) = (sdtasdt0 (xc) (sdtasdt0 T_6 T_4))) /\ ((aElementOf0 (sdtpldt0 T_0 T_0) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc))))))))))) (-. (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc)))) ### ConjTree 28
% 240.20/240.37 30. (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = T_0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = T_0) /\ (((sdtpldt0 T_0 T_0) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 T_4 T_0) = (sdtasdt0 (xc) (sdtasdt0 W3 T_4))) /\ ((aElementOf0 (sdtpldt0 T_0 T_0) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc)))))))))))) (-. (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc)))) ### Exists 29
% 240.20/240.37 31. (((aElementOf0 T_0 (slsdtgt0 (xc))) /\ ((aElementOf0 T_0 (slsdtgt0 (xc))) /\ (aElement0 T_4))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = T_0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = T_0) /\ (((sdtpldt0 T_0 T_0) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 T_4 T_0) = (sdtasdt0 (xc) (sdtasdt0 W3 T_4))) /\ ((aElementOf0 (sdtpldt0 T_0 T_0) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc))))))))))))) (-. (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc)))) (aElement0 T_4) (aElementOf0 T_0 (slsdtgt0 (xc))) ### DisjTree 23 24 25 30
% 240.20/240.37 32. (All W2, (((aElementOf0 T_0 (slsdtgt0 (xc))) /\ ((aElementOf0 T_0 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = T_0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = T_0) /\ (((sdtpldt0 T_0 T_0) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 T_0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 T_0 T_0) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 T_0) (slsdtgt0 (xc)))))))))))))) (aElementOf0 T_0 (slsdtgt0 (xc))) (aElement0 T_4) (-. (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc)))) ### All 31
% 240.20/240.37 33. (All W1, (All W2, (((aElementOf0 T_0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = T_0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 T_0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 T_0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 T_0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 T_0) (slsdtgt0 (xc))))))))))))))) (-. (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc)))) (aElement0 T_4) (aElementOf0 T_0 (slsdtgt0 (xc))) ### All 32
% 240.20/240.37 34. (All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) (aElementOf0 T_0 (slsdtgt0 (xc))) (aElement0 T_4) (-. (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc)))) ### All 33
% 240.20/240.37 35. (-. ((aElement0 T_4) => (aElementOf0 (sdtasdt0 T_4 T_0) (slsdtgt0 (xc))))) (aElementOf0 T_0 (slsdtgt0 (xc))) (All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) ### NotImply 34
% 240.20/240.37 36. (-. (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 T_0) (slsdtgt0 (xc)))))) (All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) (aElementOf0 T_0 (slsdtgt0 (xc))) ### NotAllEx 35
% 240.20/240.37 37. (-. ((All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) => (aElementOf0 (sdtpldt0 T_0 W2) (slsdtgt0 (xc))))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 T_0) (slsdtgt0 (xc))))))) (aElement0 (sz00)) (aElementOf0 T_0 (slsdtgt0 (xc))) (All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) ### NotAnd 22 36
% 240.20/240.37 38. (-. ((aElementOf0 T_0 (slsdtgt0 (xc))) => ((All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) => (aElementOf0 (sdtpldt0 T_0 W2) (slsdtgt0 (xc))))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 T_0) (slsdtgt0 (xc)))))))) (All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) (aElement0 (sz00)) ### NotImply 37
% 240.20/240.37 39. (-. (All W1, ((aElementOf0 W1 (slsdtgt0 (xc))) => ((All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) => (aElementOf0 (sdtpldt0 W1 W2) (slsdtgt0 (xc))))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (slsdtgt0 (xc))))))))) (aElement0 (sz00)) (All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) ### NotAllEx 38
% 240.20/240.37 40. (-. ((aSet0 (slsdtgt0 (xc))) /\ (All W1, ((aElementOf0 W1 (slsdtgt0 (xc))) => ((All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) => (aElementOf0 (sdtpldt0 W1 W2) (slsdtgt0 (xc))))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (slsdtgt0 (xc)))))))))) (All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) (aElement0 (sz00)) (aElement0 (xc)) (All W0, ((aElement0 W0) => (All W1, ((W1 = (slsdtgt0 W0)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 W0 W3) = W2)))))))))) ### NotAnd 8 39
% 240.20/240.37 41. (-. (aIdeal0 (slsdtgt0 (xc)))) (All W0, ((aElement0 W0) => (All W1, ((W1 = (slsdtgt0 W0)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 W0 W3) = W2)))))))))) (aElement0 (xc)) (aElement0 (sz00)) (All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) ### Definition-Pseudo(aIdeal0) 40
% 240.20/240.37 42. (-. ((All W0, (All W1, (All W2, (((aElementOf0 W0 (slsdtgt0 (xc))) /\ ((aElementOf0 W1 (slsdtgt0 (xc))) /\ (aElement0 W2))) => (Ex W3, ((aElement0 W3) /\ (((sdtasdt0 (xc) W3) = W0) /\ (Ex W4, ((aElement0 W4) /\ (((sdtasdt0 (xc) W4) = W1) /\ (((sdtpldt0 W0 W1) = (sdtasdt0 (xc) (sdtpldt0 W3 W4))) /\ (((sdtasdt0 W2 W0) = (sdtasdt0 (xc) (sdtasdt0 W3 W2))) /\ ((aElementOf0 (sdtpldt0 W0 W1) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 W2 W0) (slsdtgt0 (xc)))))))))))))))) => (aIdeal0 (slsdtgt0 (xc))))) (aElement0 (sz00)) (aElement0 (xc)) (All W0, ((aElement0 W0) => (All W1, ((W1 = (slsdtgt0 W0)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 W0 W3) = W2)))))))))) ### NotImply 41
% 240.20/240.37 % SZS output end Proof
% 240.20/240.37 (* END-PROOF *)
%------------------------------------------------------------------------------