%------------------------------------------------------------------------------ % 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 *) %------------------------------------------------------------------------------