%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM535+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 : 300s
% DateTime : Sat Jun 21 05:21:19 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM535+2 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:23:48 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(aElementOf0_type, type, (
% 0.20/0.39 aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.39 tff(sdtmndt0_type, type, (
% 0.20/0.39 sdtmndt0: ( $i * $i ) > $i)).
% 0.20/0.39 tff(xx_type, type, (
% 0.20/0.39 xx: $i)).
% 0.20/0.39 tff(xS_type, type, (
% 0.20/0.39 xS: $i)).
% 0.20/0.39 tff(tptp_fun_W0_4_type, type, (
% 0.20/0.39 tptp_fun_W0_4: $i)).
% 0.20/0.39 tff(aElement0_type, type, (
% 0.20/0.39 aElement0: $i > $o)).
% 0.20/0.39 tff(sdtpldt0_type, type, (
% 0.20/0.39 sdtpldt0: ( $i * $i ) > $i)).
% 0.20/0.39 tff(aSet0_type, type, (
% 0.20/0.39 aSet0: $i > $o)).
% 0.20/0.39 tff(aSubsetOf0_type, type, (
% 0.20/0.39 aSubsetOf0: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_W0_5_type, type, (
% 0.20/0.39 tptp_fun_W0_5: $i)).
% 0.20/0.39 tff(1,assumption,(~(aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))))), introduced(assumption)).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 ((aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx)))))) | ![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 ((~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))) | (~(((~aElement0(W0!5)) | (~aElementOf0(W0!5, xS)) | (W0!5 = xx)) <=> aElementOf0(W0!5, sdtmndt0(xS, xx))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (~(((~aElement0(W0!5)) | (~aElementOf0(W0!5, xS)) | (W0!5 = xx)) <=> aElementOf0(W0!5, sdtmndt0(xS, xx)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 ((aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx)))))) | (~aElementOf0(W0!5, xS))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (~aElementOf0(W0!5, xS)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (((~aElement0(W0!5)) | (~aElementOf0(W0!5, xS)) | (W0!5 = xx)) | aElementOf0(W0!5, xS)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 ((~aElement0(W0!5)) | (~aElementOf0(W0!5, xS)) | (W0!5 = xx)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ((((~aElement0(W0!5)) | (~aElementOf0(W0!5, xS)) | (W0!5 = xx)) <=> aElementOf0(W0!5, sdtmndt0(xS, xx))) | (~((~aElement0(W0!5)) | (~aElementOf0(W0!5, xS)) | (W0!5 = xx))) | (~aElementOf0(W0!5, sdtmndt0(xS, xx)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 ((((~aElement0(W0!5)) | (~aElementOf0(W0!5, xS)) | (W0!5 = xx)) <=> aElementOf0(W0!5, sdtmndt0(xS, xx))) | (~aElementOf0(W0!5, sdtmndt0(xS, xx)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (~aElementOf0(W0!5, sdtmndt0(xS, xx))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[11, 5])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 ((aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx)))))) | ![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[13, 1])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 ((~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~(((~aElement0(W0!5)) | (~((W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx))))) <=> aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (~(((~aElement0(W0!5)) | (~((W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx))))) <=> aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 ((aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx)))))) | aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[17, 1])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 ((((~aElement0(W0!5)) | (~((W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx))))) <=> aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aElement0(W0!5)) | (~((W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx)))))) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 ((((~aElement0(W0!5)) | (~((W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx))))) <=> aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aElement0(W0!5)) | (~((W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (~((~aElement0(W0!5)) | (~((W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[20, 16])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (((~aElement0(W0!5)) | (~((W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx))))) | ((W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ((W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ((~((W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx)))) | (W0!5 = xx) | aElementOf0(W0!5, sdtmndt0(xS, xx))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (W0!5 = xx),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[24, 23, 12])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (aElementOf0(W0!5, xS) <=> aElementOf0(xx, xS)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (aElementOf0(xx, xS) <=> aElementOf0(W0!5, xS)),
% 0.20/0.39 inference(symmetry,[status(thm)],[26])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (aElementOf0(xx, xS) <=> aElementOf0(xx, xS)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(29,axiom,(aElementOf0(xx, xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__617_02')).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (aElementOf0(xx, xS)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (aElementOf0(W0!5, xS)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[7, 31])).
% 0.20/0.39 tff(33,plain,(aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (((~(aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aElementOf0(W0!4, xS)) | aElementOf0(W0!4, sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx)))))))) <=> ((~(aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aElementOf0(W0!4, xS)) | aElementOf0(W0!4, sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (((~(aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aElementOf0(W0!4, xS)) | aElementOf0(W0!4, sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx)))))))) <=> ((~(aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aElementOf0(W0!4, xS)) | aElementOf0(W0!4, sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 ((((~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))) & (~((~aElementOf0(W0!4, xS)) | aElementOf0(W0!4, sdtpldt0(sdtmndt0(xS, xx), xx)))) & aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) & aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))) | ((~aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)) & aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) & aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))) & (~((~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS))))) <=> ((~(aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aElementOf0(W0!4, xS)) | aElementOf0(W0!4, sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS) | (~aSet0(sdtpldt0(sdtmndt0(xS, xx), xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) <=> aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))))) | (~aSet0(sdtmndt0(xS, xx))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xS)) | (W0 = xx)) <=> aElementOf0(W0, sdtmndt0(xS, xx))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ((((~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))) & (~((~aElementOf0(W0!4, xS)) | aElementOf0(W0!4, sdtpldt0(sdtmndt0(xS, xx), xx)))) & (aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx)))))) & (aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ((~aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)) & (aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx)))))) & (aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))) & (~((~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS))))) <=> (((~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))) & (~((~aElementOf0(W0!4, xS)) | aElementOf0(W0!4, sdtpldt0(sdtmndt0(xS, xx), xx)))) & aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) & aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))) | ((~aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)) & aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))) & aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))) & (~((~aElementOf0(W0!5, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0!5, xS)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))) & (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0, xS)))) <=> ((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))) & (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0, xS))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 ((~((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))) & (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0, xS))))) <=> (~((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))) & (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0, xS)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((~((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))) & (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0, xS))))) <=> (~((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))) & (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0, xS)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 ((~(((aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> ((aElement0(W0) & aElementOf0(W0, xS)) & (~(W0 = xx))))) => ((aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xS, xx)) | (W0 = xx))))) => (![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))))) & ((aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> ((aElement0(W0) & aElementOf0(W0, xS)) & (~(W0 = xx))))) => ((aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xS, xx)) | (W0 = xx))))) => (![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) => aElementOf0(W0, xS)) | aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)))))) <=> (~((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))) & (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0, xS)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(42,axiom,(~(((aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> ((aElement0(W0) & aElementOf0(W0, xS)) & (~(W0 = xx))))) => ((aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xS, xx)) | (W0 = xx))))) => (![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))))) & ((aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> ((aElement0(W0) & aElementOf0(W0, xS)) & (~(W0 = xx))))) => ((aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xS, xx)) | (W0 = xx))))) => (![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) => aElementOf0(W0, xS)) | aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (~((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))) & (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0, xS))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (~((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))) & (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0, xS))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (~((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))) & (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0, xS))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (~((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) | ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))) & (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx))) | aElementOf0(W0, xS))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[45, 39])).
% 0.20/0.42 unexpected number of arguments: (let ((a!1 (not (aSubsetOf0 xS (sdtpldt0 (sdtmndt0 xS xx) xx))))
% 0.20/0.42 (a!2 (forall ((W0 $i))
% 0.20/0.42 (or (not (aElementOf0 W0 xS))
% 0.20/0.42 (aElementOf0 W0 (sdtpldt0 (sdtmndt0 xS xx) xx)))))
% 0.20/0.42 (a!3 (or (not (aElementOf0 W0!4 xS))
% 0.20/0.42 (aElementOf0 W0!4 (sdtpldt0 (sdtmndt0 xS xx) xx))))
% 0.20/0.42 (a!4 (~ (aSet0 (sdtpldt0 (sdtmndt0 xS xx) xx))
% 0.20/0.42 (aSet0 (sdtpldt0 (sdtmndt0 xS xx) xx))))
% 0.20/0.42 (a!5 (proof-bind (lambda ((W0 $i))
% 0.20/0.42 (let ((a!1 (and (aElement0 W0)
% 0.20/0.42 (or (= W0 xx)
% 0.20/0.42 (aElementOf0 W0 (sdtmndt0 xS xx))))))
% 0.20/0.42 (let ((a!2 (= (aElementOf0 W0
% 0.20/0.42 (sdtpldt0 (sdtmndt0 xS xx)
% 0.20/0.42 xx))
% 0.20/0.42 a!1)))
% 0.20/0.42 (refl (~ a!2 a!2)))))))
% 0.20/0.42 (a!6 (forall ((W0 $i))
% 0.20/0.42 (let ((a!1 (and (aElement0 W0)
% 0.20/0.42 (or (= W0 xx) (aElementOf0 W0 (sdtmndt0 xS xx))))))
% 0.20/0.42 (= (aElementOf0 W0 (sdtpldt0 (sdtmndt0 xS xx) xx)) a!1))))
% 0.20/0.42 (a!9 (refl (~ (aSet0 (sdtmndt0 xS xx)) (aSet0 (sdtmndt0 xS xx)))))
% 0.20/0.42 (a!10 (proof-bind (lambda ((W0 $i))
% 0.20/0.42 (let ((a!1 (= (aElementOf0 W0 (sdtmndt0 xS xx))
% 0.20/0.42 (and (aElement0 W0)
% 0.20/0.42 (aElementOf0 W0 xS)
% 0.20/0.42 (not (= W0 xx))))))
% 0.20/0.42 (refl (~ a!1 a!1))))))
% 0.20/0.42 (a!11 (forall ((W0 $i))
% 0.20/0.42 (= (aElementOf0 W0 (sdtmndt0 xS xx))
% 0.20/0.42 (and (aElement0 W0) (aElementOf0 W0 xS) (not (= W0 xx))))))
% 0.20/0.42 (a!19 (not (aSubsetOf0 (sdtpldt0 (sdtmndt0 xS xx) xx) xS)))
% 0.20/0.42 (a!20 (forall ((W0 $i))
% 0.20/0.42 (let ((a!1 (not (aElementOf0 W0 (sdtpldt0 (sdtmndt0 xS xx) xx)))))
% 0.20/0.42 (or a!1 (aElementOf0 W0 xS)))))
% 0.20/0.42 (a!21 (not (aElementOf0 W0!5 (sdtpldt0 (sdtmndt0 xS xx) xx)))))
% 0.20/0.42 (let ((a!7 (and (aSet0 (sdtpldt0 (sdtmndt0 xS xx) xx)) a!6))
% 0.20/0.42 (a!12 (~ (and (aSet0 (sdtmndt0 xS xx)) a!11)
% 0.20/0.42 (and (aSet0 (sdtmndt0 xS xx)) a!11)))
% 0.20/0.42 (a!13 (not (and (aSet0 (sdtmndt0 xS xx)) a!11)))
% 0.20/0.42 (a!22 (~ (not a!20) (not (or a!21 (aElementOf0 W0!5 xS))))))
% 0.20/0.42 (let ((a!8 (nnf-neg (monotonicity (refl a!4)
% 0.20/0.42 (nnf-pos a!5 (~ a!6 a!6))
% 0.20/0.42 (~ a!7 a!7))
% 0.20/0.42 (~ (not (not a!7)) a!7)))
% 0.20/0.42 (a!14 (~ (not a!13) (and (aSet0 (sdtmndt0 xS xx)) a!11)))
% 0.20/0.42 (a!16 (or (aSubsetOf0 xS (sdtpldt0 (sdtmndt0 xS xx) xx))
% 0.20/0.42 a!2
% 0.20/0.42 (not a!7)
% 0.20/0.42 a!13))
% 0.20/0.42 (a!17 (and a!1 (not a!3) a!7 (and (aSet0 (sdtmndt0 xS xx)) a!11)))
% 0.20/0.42 (a!23 (or (aSubsetOf0 (sdtpldt0 (sdtmndt0 xS xx) xx) xS)
% 0.20/0.42 (not a!7)
% 0.20/0.42 a!13
% 0.20/0.42 a!20))
% 0.20/0.42 (a!24 (and a!19
% 0.20/0.42 a!7
% 0.20/0.42 (and (aSet0 (sdtmndt0 xS xx)) a!11)
% 0.20/0.42 (not (or a!21 (aElementOf0 W0!5 xS))))))
% 0.20/0.42 (let ((a!15 (nnf-neg (monotonicity a!9 (nnf-pos a!10 (~ a!11 a!11)) a!12) a!14)))
% 0.20/0.42 (let ((a!18 (nnf-neg (refl (~ a!1 a!1))
% 0.20/0.42 (sk (~ (not a!2) (not a!3)))
% 0.20/0.42 a!8
% 0.20/0.42 a!15
% 0.20/0.42 (~ (not a!16) a!17))))
% 0.20/0.42 (nnf-neg a!18
% 0.20/0.42 (nnf-neg (refl (~ a!19 a!19)) a!8 a!15 (sk a!22) (~ (not a!23) a!24))
% 0.20/0.42 (~ (not (and a!16 a!23)) (or a!17 a!24))))))))
% 0.20/0.42 Proof display could not be completed: unexpected number of arguments
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------