TSTP Solution File: RNG105+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : RNG105+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 : n025.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 241.02s 241.24s
% Output : Proof 241.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : RNG105+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.11 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.11/0.31 % Computer : n025.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon May 30 15:14:42 EDT 2022
% 0.11/0.31 % CPUTime :
% 241.02/241.24 % SZS status Theorem
% 241.02/241.24 (* PROOF-FOUND *)
% 241.02/241.24 (* BEGIN-PROOF *)
% 241.02/241.24 % SZS output start Proof
% 241.02/241.24 1. (aElement0 (xc)) (-. (aElement0 (xc))) ### Axiom
% 241.02/241.24 2. ((slsdtgt0 (xc)) != (slsdtgt0 (xc))) ### Refl(=)
% 241.02/241.24 3. (aElement0 (xu)) (-. (aElement0 (xu))) ### Axiom
% 241.02/241.24 4. (aElement0 (xv)) (-. (aElement0 (xv))) ### Axiom
% 241.02/241.24 5. (-. (aElement0 (sdtpldt0 (xu) (xv)))) (aElement0 (sdtpldt0 (xu) (xv))) ### Axiom
% 241.02/241.24 6. (((aElement0 (xu)) /\ (aElement0 (xv))) => (aElement0 (sdtpldt0 (xu) (xv)))) (-. (aElement0 (sdtpldt0 (xu) (xv)))) (aElement0 (xv)) (aElement0 (xu)) ### DisjTree 3 4 5
% 241.02/241.24 7. (All W1, (((aElement0 (xu)) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 (xu) W1)))) (aElement0 (xu)) (aElement0 (xv)) (-. (aElement0 (sdtpldt0 (xu) (xv)))) ### All 6
% 241.02/241.24 8. (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) (-. (aElement0 (sdtpldt0 (xu) (xv)))) (aElement0 (xv)) (aElement0 (xu)) ### All 7
% 241.02/241.24 9. ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) ((sdtasdt0 (xc) (sdtpldt0 (xu) (xv))) != (sdtpldt0 (xx) (xy))) ### Sym(=)
% 241.02/241.24 10. (-. ((aElement0 (sdtpldt0 (xu) (xv))) /\ ((sdtasdt0 (xc) (sdtpldt0 (xu) (xv))) = (sdtpldt0 (xx) (xy))))) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (aElement0 (xu)) (aElement0 (xv)) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) ### NotAnd 8 9
% 241.02/241.24 11. (-. (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = (sdtpldt0 (xx) (xy)))))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) (aElement0 (xv)) (aElement0 (xu)) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) ### NotExists 10
% 241.02/241.24 12. (-. (aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc)))) (aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc))) ### Axiom
% 241.02/241.24 13. ((aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc))) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = (sdtpldt0 (xx) (xy)))))) (-. (aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc)))) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (aElement0 (xu)) (aElement0 (xv)) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) ### Equiv 11 12
% 241.02/241.24 14. (All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2))))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) (aElement0 (xv)) (aElement0 (xu)) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (-. (aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc)))) ### All 13
% 241.02/241.24 15. ((aSet0 (slsdtgt0 (xc))) /\ (All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2)))))) (-. (aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc)))) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (aElement0 (xu)) (aElement0 (xv)) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) ### And 14
% 241.02/241.24 16. (((slsdtgt0 (xc)) = (slsdtgt0 (xc))) <=> ((aSet0 (slsdtgt0 (xc))) /\ (All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2))))))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) (aElement0 (xv)) (aElement0 (xu)) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (-. (aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc)))) ### Equiv 2 15
% 241.02/241.24 17. (All W1, ((W1 = (slsdtgt0 (xc))) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2)))))))) (-. (aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc)))) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (aElement0 (xu)) (aElement0 (xv)) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) ### All 16
% 241.02/241.24 18. ((aElement0 (xc)) => (All W1, ((W1 = (slsdtgt0 (xc))) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2))))))))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) (aElement0 (xv)) (aElement0 (xu)) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (-. (aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc)))) (aElement0 (xc)) ### Imply 1 17
% 241.02/241.24 19. (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)) (-. (aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc)))) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (aElement0 (xu)) (aElement0 (xv)) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) ### All 18
% 241.02/241.24 20. (aElement0 (xc)) (-. (aElement0 (xc))) ### Axiom
% 241.02/241.24 21. ((slsdtgt0 (xc)) != (slsdtgt0 (xc))) ### Refl(=)
% 241.02/241.24 22. (aElement0 (xu)) (-. (aElement0 (xu))) ### Axiom
% 241.02/241.24 23. (aElement0 (xz)) (-. (aElement0 (xz))) ### Axiom
% 241.02/241.24 24. (-. (aElement0 (sdtasdt0 (xu) (xz)))) (aElement0 (sdtasdt0 (xu) (xz))) ### Axiom
% 241.02/241.24 25. (((aElement0 (xu)) /\ (aElement0 (xz))) => (aElement0 (sdtasdt0 (xu) (xz)))) (-. (aElement0 (sdtasdt0 (xu) (xz)))) (aElement0 (xz)) (aElement0 (xu)) ### DisjTree 22 23 24
% 241.02/241.24 26. (All W1, (((aElement0 (xu)) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 (xu) W1)))) (aElement0 (xu)) (aElement0 (xz)) (-. (aElement0 (sdtasdt0 (xu) (xz)))) ### All 25
% 241.02/241.24 27. (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) (-. (aElement0 (sdtasdt0 (xu) (xz)))) (aElement0 (xz)) (aElement0 (xu)) ### All 26
% 241.02/241.24 28. ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) ((sdtasdt0 (xc) (sdtasdt0 (xu) (xz))) != (sdtasdt0 (xz) (xx))) ### Sym(=)
% 241.02/241.24 29. (-. ((aElement0 (sdtasdt0 (xu) (xz))) /\ ((sdtasdt0 (xc) (sdtasdt0 (xu) (xz))) = (sdtasdt0 (xz) (xx))))) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (aElement0 (xu)) (aElement0 (xz)) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) ### NotAnd 27 28
% 241.02/241.24 30. (-. (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = (sdtasdt0 (xz) (xx)))))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) (aElement0 (xz)) (aElement0 (xu)) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) ### NotExists 29
% 241.02/241.24 31. (-. (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc)))) (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc))) ### Axiom
% 241.02/241.24 32. ((aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc))) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = (sdtasdt0 (xz) (xx)))))) (-. (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc)))) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (aElement0 (xu)) (aElement0 (xz)) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) ### Equiv 30 31
% 241.02/241.24 33. (All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2))))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) (aElement0 (xz)) (aElement0 (xu)) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (-. (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc)))) ### All 32
% 241.02/241.24 34. ((aSet0 (slsdtgt0 (xc))) /\ (All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2)))))) (-. (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc)))) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (aElement0 (xu)) (aElement0 (xz)) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) ### And 33
% 241.02/241.24 35. (((slsdtgt0 (xc)) = (slsdtgt0 (xc))) <=> ((aSet0 (slsdtgt0 (xc))) /\ (All W2, ((aElementOf0 W2 (slsdtgt0 (xc))) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2))))))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) (aElement0 (xz)) (aElement0 (xu)) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (-. (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc)))) ### Equiv 21 34
% 241.02/241.24 36. (All W1, ((W1 = (slsdtgt0 (xc))) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2)))))))) (-. (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc)))) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (aElement0 (xu)) (aElement0 (xz)) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) ### All 35
% 241.02/241.24 37. ((aElement0 (xc)) => (All W1, ((W1 = (slsdtgt0 (xc))) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) <=> (Ex W3, ((aElement0 W3) /\ ((sdtasdt0 (xc) W3) = W2))))))))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) (aElement0 (xz)) (aElement0 (xu)) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (-. (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc)))) (aElement0 (xc)) ### Imply 20 36
% 241.02/241.24 38. (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)) (-. (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc)))) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (aElement0 (xu)) (aElement0 (xz)) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) ### All 37
% 241.02/241.24 39. (-. ((aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc))))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) (aElement0 (xz)) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) (aElement0 (xv)) (aElement0 (xu)) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (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 19 38
% 241.02/241.24 40. ((aElementOf0 (xx) (slsdtgt0 (xc))) /\ ((aElementOf0 (xy) (slsdtgt0 (xc))) /\ (aElement0 (xz)))) (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)) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (aElement0 (xu)) (aElement0 (xv)) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) (-. ((aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc))))) ### ConjTree 39
% 241.02/241.24 41. ((aElement0 (xu)) /\ ((sdtasdt0 (xc) (xu)) = (xx))) (-. ((aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc))))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) (aElement0 (xv)) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (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)))))))))) ((aElementOf0 (xx) (slsdtgt0 (xc))) /\ ((aElementOf0 (xy) (slsdtgt0 (xc))) /\ (aElement0 (xz)))) ### And 40
% 241.02/241.24 42. ((aElement0 (xv)) /\ ((sdtasdt0 (xc) (xv)) = (xy))) ((aElementOf0 (xx) (slsdtgt0 (xc))) /\ ((aElementOf0 (xy) (slsdtgt0 (xc))) /\ (aElement0 (xz)))) (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)) ((sdtpldt0 (xx) (xy)) = (sdtasdt0 (xc) (sdtpldt0 (xu) (xv)))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtpldt0 W0 W1))))) ((sdtasdt0 (xz) (xx)) = (sdtasdt0 (xc) (sdtasdt0 (xu) (xz)))) (All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (aElement0 (sdtasdt0 W0 W1))))) (-. ((aElementOf0 (sdtpldt0 (xx) (xy)) (slsdtgt0 (xc))) /\ (aElementOf0 (sdtasdt0 (xz) (xx)) (slsdtgt0 (xc))))) ((aElement0 (xu)) /\ ((sdtasdt0 (xc) (xu)) = (xx))) ### And 41
% 241.02/241.24 % SZS output end Proof
% 241.02/241.24 (* END-PROOF *)
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