TSTP Solution File: SEU522^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU522^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 : Tue Jul 19 13:52:46 EDT 2022
% Result : Theorem 47.72s 47.93s
% Output : Proof 47.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU522^1 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n023.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 : Sat Jun 18 19:26:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 47.72/47.93 % SZS status Theorem
% 47.72/47.93 % Mode: mode371
% 47.72/47.93 % Inferences: 4133
% 47.72/47.93 % SZS output start Proof
% 47.72/47.93 thf(def_exu,definition,(exu = (^[X1:$i>$o]:(~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3)))))))))))).
% 47.72/47.93 thf(def_setextAx,definition,(setextAx = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))))).
% 47.72/47.93 thf(def_emptysetAx,definition,(emptysetAx = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 47.72/47.93 thf(def_setadjoinAx,definition,(setadjoinAx = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))))).
% 47.72/47.93 thf(def_powersetAx,definition,(powersetAx = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))))).
% 47.72/47.93 thf(def_setunionAx,definition,(setunionAx = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))))).
% 47.72/47.93 thf(def_omega0Ax,definition,(omega0Ax = ((in @ emptyset) @ omega))).
% 47.72/47.93 thf(def_omegaSAx,definition,(omegaSAx = (![X1:$i]:(((in @ X1) @ omega) => ((in @ ((setadjoin @ X1) @ X1)) @ omega))))).
% 47.72/47.93 thf(def_omegaIndAx,definition,(omegaIndAx = (![X1:$i]:((~((((in @ emptyset) @ X1) => (~((![X2:$i]:((~((((in @ X2) @ omega) => (~(((in @ X2) @ X1)))))) => ((in @ ((setadjoin @ X2) @ X2)) @ X1)))))))) => (![X2:$i]:(((in @ X2) @ omega) => ((in @ X2) @ X1))))))).
% 47.72/47.93 thf(def_replAx,definition,(replAx = (![X1:$i>$i>$o]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => (exu @ (X1 @ X3)))) => (~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X1 @ X5) @ X4))))))))))))))))))).
% 47.72/47.93 thf(def_foundationAx,definition,(foundationAx = (![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))))).
% 47.72/47.93 thf(def_wellorderingAx,definition,(wellorderingAx = (![X1:$i]:(~((![X2:$i]:((~(((~(((![X3:$i]:(((in @ X3) @ X2) => (![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X1) => (~(((in @ X4) @ X1)))))) => ((![X5:$i]:(((in @ X5) @ X2) => (((in @ X3) @ X5) = ((in @ X4) @ X5)))) => (X3 = X4)))))))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X2) => (~(((in @ X4) @ X2)))))) => ((~((![X5:$i]:(((in @ X5) @ X3) => ((in @ X5) @ X4))))) => (![X5:$i]:(((in @ X5) @ X4) => ((in @ X5) @ X3)))))))))))) => (~((![X3:$i]:((~(((![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))) => (![X4:$i]:(~(((in @ X4) @ X3))))))) => (~((![X4:$i]:(![X5:$i]:((~(((~((((in @ X4) @ X2) => (~(((in @ X5) @ X3)))))) => (~((![X6:$i]:(((in @ X6) @ X4) => (~(((in @ X6) @ X3)))))))))) => (~((![X6:$i]:(((in @ X6) @ X2) => ((~((![X7:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))))).
% 47.72/47.93 thf(def_descrp,definition,(descrp = (![X1:$i>$o]:((exu @ X1) => (X1 @ (descr @ X1)))))).
% 47.72/47.93 thf(def_dsetconstrI,definition,(dsetconstrI = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))))).
% 47.72/47.93 thf(def_dsetconstrEL,definition,(dsetconstrEL = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))))).
% 47.72/47.93 thf(def_dsetconstrER,definition,(dsetconstrER = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => (X2 @ X3))))))).
% 47.72/47.93 thf(def_exuE1,definition,(exuE1 = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))))).
% 47.72/47.93 thf(def_prop2set,definition,(prop2set = (^[X1:$o]:((dsetconstr @ (powerset @ emptyset)) @ (^[X2:$i]:X1))))).
% 47.72/47.93 thf(def_prop2setE,definition,(prop2setE = (![X1:$o]:(![X2:$i]:(((in @ X2) @ (prop2set @ X1)) => X1))))).
% 47.72/47.93 thf(def_emptysetE,definition,(emptysetE = (![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))))).
% 47.72/47.93 thf(def_emptysetimpfalse,definition,(emptysetimpfalse = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 47.72/47.93 thf(def_notinemptyset,definition,(notinemptyset = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 47.72/47.93 thf(def_exuE3e,definition,(exuE3e = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:(~((X1 @ X2)))))))))).
% 47.72/47.93 thf(def_setext,definition,(setext = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))))).
% 47.72/47.93 thf(def_emptyI,definition,(emptyI = (![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))))).
% 47.72/47.93 thf(def_noeltsimpempty,definition,(noeltsimpempty = (![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))))).
% 47.72/47.93 thf(def_setbeta,definition,(setbeta = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((dsetconstr @ X1) @ X2)) = (X2 @ X3)))))))).
% 47.72/47.93 thf(def_nonempty,definition,(nonempty = (^[X1:$i]:(~((X1 = emptyset)))))).
% 47.72/47.93 thf(def_nonemptyE1,definition,(nonemptyE1 = (![X1:$i]:((nonempty @ X1) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))))).
% 47.72/47.93 thf(def_nonemptyI,definition,(nonemptyI = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (nonempty @ ((dsetconstr @ X1) @ X2))))))))).
% 47.72/47.93 thf(def_nonemptyI1,definition,(nonemptyI1 = (![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (nonempty @ X1))))).
% 47.72/47.93 thf(def_setadjoinIL,definition,(setadjoinIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))))).
% 47.72/47.93 thf(def_emptyinunitempty,definition,(emptyinunitempty = ((in @ emptyset) @ ((setadjoin @ emptyset) @ emptyset)))).
% 47.72/47.93 thf(def_setadjoinIR,definition,(setadjoinIR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))))).
% 47.72/47.93 thf(def_setadjoinE,definition,(setadjoinE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))))).
% 47.72/47.93 thf(def_setadjoinOr,definition,(setadjoinOr = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => ((~((X3 = X1))) => ((in @ X3) @ X2)))))))).
% 47.72/47.93 thf(def_setoftrueEq,definition,(setoftrueEq = (![X1:$i]:(((dsetconstr @ X1) @ (^[X2:$i]:(~($false)))) = X1)))).
% 47.72/47.93 thf(def_powersetI,definition,(powersetI = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => ((in @ X2) @ (powerset @ X1))))))).
% 47.72/47.93 thf(def_emptyinPowerset,definition,(emptyinPowerset = (![X1:$i]:((in @ emptyset) @ (powerset @ X1))))).
% 47.72/47.93 thf(def_emptyInPowerset,definition,(emptyInPowerset = (![X1:$i]:((in @ emptyset) @ (powerset @ X1))))).
% 47.72/47.93 thf(def_powersetE,definition,(powersetE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ (powerset @ X1)) => (((in @ X3) @ X2) => ((in @ X3) @ X1)))))))).
% 47.72/47.93 thf(setunionI,conjecture,(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1)))))))))))))))))))))))))))))))))))))))))))))).
% 47.72/47.93 thf(h0,negated_conjecture,(~((setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))))))))))))))))))))))))))))))))))))))))))),inference(assume_negation,[status(cth)],[setunionI])).
% 47.72/47.93 thf(ax305, axiom, (p1|~(p44)), file('<stdin>', ax305)).
% 47.72/47.93 thf(ax348, axiom, ~(p1), file('<stdin>', ax348)).
% 47.72/47.93 thf(ax303, axiom, (p44|~(p46)), file('<stdin>', ax303)).
% 47.72/47.93 thf(ax301, axiom, (p46|~(p48)), file('<stdin>', ax301)).
% 47.72/47.93 thf(ax299, axiom, (p48|~(p50)), file('<stdin>', ax299)).
% 47.72/47.93 thf(ax297, axiom, (p50|~(p52)), file('<stdin>', ax297)).
% 47.72/47.93 thf(ax295, axiom, (p52|~(p54)), file('<stdin>', ax295)).
% 47.72/47.93 thf(ax293, axiom, (p54|~(p56)), file('<stdin>', ax293)).
% 47.72/47.93 thf(ax291, axiom, (p56|~(p58)), file('<stdin>', ax291)).
% 47.72/47.93 thf(ax289, axiom, (p58|~(p60)), file('<stdin>', ax289)).
% 47.72/47.93 thf(ax287, axiom, (p60|~(p62)), file('<stdin>', ax287)).
% 47.72/47.93 thf(ax285, axiom, (p62|~(p64)), file('<stdin>', ax285)).
% 47.72/47.93 thf(ax283, axiom, (p64|~(p66)), file('<stdin>', ax283)).
% 47.72/47.93 thf(ax281, axiom, (p66|~(p68)), file('<stdin>', ax281)).
% 47.72/47.93 thf(ax279, axiom, (p68|~(p70)), file('<stdin>', ax279)).
% 47.72/47.93 thf(ax277, axiom, (p70|~(p72)), file('<stdin>', ax277)).
% 47.72/47.93 thf(ax275, axiom, (p72|~(p74)), file('<stdin>', ax275)).
% 47.72/47.93 thf(ax273, axiom, (p74|~(p76)), file('<stdin>', ax273)).
% 47.72/47.93 thf(ax271, axiom, (p76|~(p78)), file('<stdin>', ax271)).
% 47.72/47.93 thf(ax269, axiom, (p78|~(p80)), file('<stdin>', ax269)).
% 47.72/47.93 thf(ax267, axiom, (p80|~(p82)), file('<stdin>', ax267)).
% 47.72/47.93 thf(ax265, axiom, (p82|~(p84)), file('<stdin>', ax265)).
% 47.72/47.93 thf(ax263, axiom, (p84|~(p86)), file('<stdin>', ax263)).
% 47.72/47.93 thf(ax261, axiom, (p86|~(p88)), file('<stdin>', ax261)).
% 47.72/47.93 thf(ax259, axiom, (p88|~(p90)), file('<stdin>', ax259)).
% 47.72/47.93 thf(ax257, axiom, (p90|~(p92)), file('<stdin>', ax257)).
% 47.72/47.93 thf(ax255, axiom, (p92|~(p94)), file('<stdin>', ax255)).
% 47.72/47.93 thf(ax253, axiom, (p94|~(p96)), file('<stdin>', ax253)).
% 47.72/47.93 thf(ax251, axiom, (p96|~(p98)), file('<stdin>', ax251)).
% 47.72/47.93 thf(ax249, axiom, (p98|~(p100)), file('<stdin>', ax249)).
% 47.72/47.93 thf(ax247, axiom, (p100|~(p102)), file('<stdin>', ax247)).
% 47.72/47.93 thf(ax245, axiom, (p102|~(p104)), file('<stdin>', ax245)).
% 47.72/47.93 thf(ax243, axiom, (p104|~(p106)), file('<stdin>', ax243)).
% 47.72/47.93 thf(ax241, axiom, (p106|~(p108)), file('<stdin>', ax241)).
% 47.72/47.93 thf(ax239, axiom, (p108|~(p110)), file('<stdin>', ax239)).
% 47.72/47.93 thf(ax237, axiom, (p110|~(p112)), file('<stdin>', ax237)).
% 47.72/47.93 thf(ax235, axiom, (p112|~(p114)), file('<stdin>', ax235)).
% 47.72/47.93 thf(ax233, axiom, (p114|~(p116)), file('<stdin>', ax233)).
% 47.72/47.93 thf(nax1, axiom, (p1<=(fsetextAx=>(femptysetAx=>(fsetadjoinAx=>(fpowersetAx=>(fsetunionAx=>(fomega0Ax=>(fomegaSAx=>(fomegaIndAx=>(freplAx=>(ffoundationAx=>(fwellorderingAx=>(fdescrp=>(fdsetconstrI=>(fdsetconstrEL=>(fdsetconstrER=>(fexuE1=>(fprop2setE=>(femptysetE=>(femptysetimpfalse=>(fnotinemptyset=>(fexuE3e=>(fsetext=>(femptyI=>(fnoeltsimpempty=>(fsetbeta=>(fnonemptyE1=>(fnonemptyI=>(fnonemptyI1=>(fsetadjoinIL=>(femptyinunitempty=>(fsetadjoinIR=>(fsetadjoinE=>(fsetadjoinOr=>(fsetoftrueEq=>(fpowersetI=>(femptyinPowerset=>(femptyInPowerset=>(fpowersetE=>![X1:$i, X2:$i, X3:$i]:(fin @ X2 @ X3=>(fin @ X3 @ X1=>fin @ X2 @ (fsetunion @ X1)))))))))))))))))))))))))))))))))))))))))), file('<stdin>', nax1)).
% 47.72/47.93 thf(ax231, axiom, (p116|~(p118)), file('<stdin>', ax231)).
% 47.72/47.93 thf(ax230, axiom, (p118|~(p119)), file('<stdin>', ax230)).
% 47.72/47.93 thf(ax46, axiom, (~(p7)|~(p51)|p292), file('<stdin>', ax46)).
% 47.72/47.93 thf(nax51, axiom, (p51<=fsetunionAx), file('<stdin>', nax51)).
% 47.72/47.93 thf(ax23, axiom, (~(p299)|p320), file('<stdin>', ax23)).
% 47.72/47.93 thf(ax229, axiom, (p119|~(p120)), file('<stdin>', ax229)).
% 47.72/47.93 thf(ax342, axiom, p7, file('<stdin>', ax342)).
% 47.72/47.93 thf(ax22, axiom, (~(p320)|p319), file('<stdin>', ax22)).
% 47.72/47.93 thf(ax45, axiom, p299, file('<stdin>', ax45)).
% 47.72/47.93 thf(ax228, axiom, (p120|~(p121)), file('<stdin>', ax228)).
% 47.72/47.93 thf(ax38, axiom, (~(p292)|p300), file('<stdin>', ax38)).
% 47.72/47.93 thf(ax21, axiom, (~(p319)|p125|p318), file('<stdin>', ax21)).
% 47.72/47.93 thf(ax226, axiom, (p121|~(p123)), file('<stdin>', ax226)).
% 47.72/47.93 thf(ax224, axiom, (p123|~(p125)), file('<stdin>', ax224)).
% 47.72/47.93 thf(ax18, axiom, (~(p300)|p316), file('<stdin>', ax18)).
% 47.72/47.93 thf(ax19, axiom, (~(p317)|~(p316)|p315), file('<stdin>', ax19)).
% 47.72/47.93 thf(ax20, axiom, (~(p318)|p317), file('<stdin>', ax20)).
% 47.72/47.93 thf(pax315, axiom, (p315=>![X1:$i]:(fin @ f__1 @ X1=>~(fin @ X1 @ f__0))), file('<stdin>', pax315)).
% 47.72/47.93 thf(nax120, axiom, (p120<=![X1:$i]:(fin @ f__1 @ X1=>(fin @ X1 @ f__0=>fin @ f__1 @ (fsetunion @ f__0)))), file('<stdin>', nax120)).
% 47.72/47.93 thf(c_0_58, plain, (p1|~p44), inference(fof_simplification,[status(thm)],[ax305])).
% 47.72/47.93 thf(c_0_59, plain, ~p1, inference(fof_simplification,[status(thm)],[ax348])).
% 47.72/47.93 thf(c_0_60, plain, (p44|~p46), inference(fof_simplification,[status(thm)],[ax303])).
% 47.72/47.93 thf(c_0_61, plain, (p1|~p44), inference(split_conjunct,[status(thm)],[c_0_58])).
% 47.72/47.93 thf(c_0_62, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_59])).
% 47.72/47.93 thf(c_0_63, plain, (p46|~p48), inference(fof_simplification,[status(thm)],[ax301])).
% 47.72/47.93 thf(c_0_64, plain, (p44|~p46), inference(split_conjunct,[status(thm)],[c_0_60])).
% 47.72/47.93 thf(c_0_65, plain, ~p44, inference(sr,[status(thm)],[c_0_61, c_0_62])).
% 47.72/47.93 thf(c_0_66, plain, (p48|~p50), inference(fof_simplification,[status(thm)],[ax299])).
% 47.72/47.93 thf(c_0_67, plain, (p46|~p48), inference(split_conjunct,[status(thm)],[c_0_63])).
% 47.72/47.93 thf(c_0_68, plain, ~p46, inference(sr,[status(thm)],[c_0_64, c_0_65])).
% 47.72/47.93 thf(c_0_69, plain, (p50|~p52), inference(fof_simplification,[status(thm)],[ax297])).
% 47.72/47.93 thf(c_0_70, plain, (p48|~p50), inference(split_conjunct,[status(thm)],[c_0_66])).
% 47.72/47.93 thf(c_0_71, plain, ~p48, inference(sr,[status(thm)],[c_0_67, c_0_68])).
% 47.72/47.93 thf(c_0_72, plain, (p52|~p54), inference(fof_simplification,[status(thm)],[ax295])).
% 47.72/47.93 thf(c_0_73, plain, (p50|~p52), inference(split_conjunct,[status(thm)],[c_0_69])).
% 47.72/47.93 thf(c_0_74, plain, ~p50, inference(sr,[status(thm)],[c_0_70, c_0_71])).
% 47.72/47.93 thf(c_0_75, plain, (p54|~p56), inference(fof_simplification,[status(thm)],[ax293])).
% 47.72/47.93 thf(c_0_76, plain, (p52|~p54), inference(split_conjunct,[status(thm)],[c_0_72])).
% 47.72/47.93 thf(c_0_77, plain, ~p52, inference(sr,[status(thm)],[c_0_73, c_0_74])).
% 47.72/47.93 thf(c_0_78, plain, (p56|~p58), inference(fof_simplification,[status(thm)],[ax291])).
% 47.72/47.93 thf(c_0_79, plain, (p54|~p56), inference(split_conjunct,[status(thm)],[c_0_75])).
% 47.72/47.93 thf(c_0_80, plain, ~p54, inference(sr,[status(thm)],[c_0_76, c_0_77])).
% 47.72/47.93 thf(c_0_81, plain, (p58|~p60), inference(fof_simplification,[status(thm)],[ax289])).
% 47.72/47.93 thf(c_0_82, plain, (p56|~p58), inference(split_conjunct,[status(thm)],[c_0_78])).
% 47.72/47.93 thf(c_0_83, plain, ~p56, inference(sr,[status(thm)],[c_0_79, c_0_80])).
% 47.72/47.93 thf(c_0_84, plain, (p60|~p62), inference(fof_simplification,[status(thm)],[ax287])).
% 47.72/47.93 thf(c_0_85, plain, (p58|~p60), inference(split_conjunct,[status(thm)],[c_0_81])).
% 47.72/47.93 thf(c_0_86, plain, ~p58, inference(sr,[status(thm)],[c_0_82, c_0_83])).
% 47.72/47.93 thf(c_0_87, plain, (p62|~p64), inference(fof_simplification,[status(thm)],[ax285])).
% 47.72/47.93 thf(c_0_88, plain, (p60|~p62), inference(split_conjunct,[status(thm)],[c_0_84])).
% 47.72/47.93 thf(c_0_89, plain, ~p60, inference(sr,[status(thm)],[c_0_85, c_0_86])).
% 47.72/47.93 thf(c_0_90, plain, (p64|~p66), inference(fof_simplification,[status(thm)],[ax283])).
% 47.72/47.93 thf(c_0_91, plain, (p62|~p64), inference(split_conjunct,[status(thm)],[c_0_87])).
% 47.72/47.93 thf(c_0_92, plain, ~p62, inference(sr,[status(thm)],[c_0_88, c_0_89])).
% 47.72/47.93 thf(c_0_93, plain, (p66|~p68), inference(fof_simplification,[status(thm)],[ax281])).
% 47.72/47.93 thf(c_0_94, plain, (p64|~p66), inference(split_conjunct,[status(thm)],[c_0_90])).
% 47.72/47.93 thf(c_0_95, plain, ~p64, inference(sr,[status(thm)],[c_0_91, c_0_92])).
% 47.72/47.93 thf(c_0_96, plain, (p68|~p70), inference(fof_simplification,[status(thm)],[ax279])).
% 47.72/47.93 thf(c_0_97, plain, (p66|~p68), inference(split_conjunct,[status(thm)],[c_0_93])).
% 47.72/47.93 thf(c_0_98, plain, ~p66, inference(sr,[status(thm)],[c_0_94, c_0_95])).
% 47.72/47.93 thf(c_0_99, plain, (p70|~p72), inference(fof_simplification,[status(thm)],[ax277])).
% 47.72/47.93 thf(c_0_100, plain, (p68|~p70), inference(split_conjunct,[status(thm)],[c_0_96])).
% 47.72/47.93 thf(c_0_101, plain, ~p68, inference(sr,[status(thm)],[c_0_97, c_0_98])).
% 47.72/47.93 thf(c_0_102, plain, (p72|~p74), inference(fof_simplification,[status(thm)],[ax275])).
% 47.72/47.93 thf(c_0_103, plain, (p70|~p72), inference(split_conjunct,[status(thm)],[c_0_99])).
% 47.72/47.93 thf(c_0_104, plain, ~p70, inference(sr,[status(thm)],[c_0_100, c_0_101])).
% 47.72/47.93 thf(c_0_105, plain, (p74|~p76), inference(fof_simplification,[status(thm)],[ax273])).
% 47.72/47.93 thf(c_0_106, plain, (p72|~p74), inference(split_conjunct,[status(thm)],[c_0_102])).
% 47.72/47.93 thf(c_0_107, plain, ~p72, inference(sr,[status(thm)],[c_0_103, c_0_104])).
% 47.72/47.93 thf(c_0_108, plain, (p76|~p78), inference(fof_simplification,[status(thm)],[ax271])).
% 47.72/47.93 thf(c_0_109, plain, (p74|~p76), inference(split_conjunct,[status(thm)],[c_0_105])).
% 47.72/47.93 thf(c_0_110, plain, ~p74, inference(sr,[status(thm)],[c_0_106, c_0_107])).
% 47.72/47.93 thf(c_0_111, plain, (p78|~p80), inference(fof_simplification,[status(thm)],[ax269])).
% 47.72/47.93 thf(c_0_112, plain, (p76|~p78), inference(split_conjunct,[status(thm)],[c_0_108])).
% 47.72/47.93 thf(c_0_113, plain, ~p76, inference(sr,[status(thm)],[c_0_109, c_0_110])).
% 47.72/47.93 thf(c_0_114, plain, (p80|~p82), inference(fof_simplification,[status(thm)],[ax267])).
% 47.72/47.93 thf(c_0_115, plain, (p78|~p80), inference(split_conjunct,[status(thm)],[c_0_111])).
% 47.72/47.93 thf(c_0_116, plain, ~p78, inference(sr,[status(thm)],[c_0_112, c_0_113])).
% 47.72/47.93 thf(c_0_117, plain, (p82|~p84), inference(fof_simplification,[status(thm)],[ax265])).
% 47.72/47.93 thf(c_0_118, plain, (p80|~p82), inference(split_conjunct,[status(thm)],[c_0_114])).
% 47.72/47.93 thf(c_0_119, plain, ~p80, inference(sr,[status(thm)],[c_0_115, c_0_116])).
% 47.72/47.93 thf(c_0_120, plain, (p84|~p86), inference(fof_simplification,[status(thm)],[ax263])).
% 47.72/47.93 thf(c_0_121, plain, (p82|~p84), inference(split_conjunct,[status(thm)],[c_0_117])).
% 47.72/47.93 thf(c_0_122, plain, ~p82, inference(sr,[status(thm)],[c_0_118, c_0_119])).
% 47.72/47.93 thf(c_0_123, plain, (p86|~p88), inference(fof_simplification,[status(thm)],[ax261])).
% 47.72/47.93 thf(c_0_124, plain, (p84|~p86), inference(split_conjunct,[status(thm)],[c_0_120])).
% 47.72/47.93 thf(c_0_125, plain, ~p84, inference(sr,[status(thm)],[c_0_121, c_0_122])).
% 47.72/47.93 thf(c_0_126, plain, (p88|~p90), inference(fof_simplification,[status(thm)],[ax259])).
% 47.72/47.93 thf(c_0_127, plain, (p86|~p88), inference(split_conjunct,[status(thm)],[c_0_123])).
% 47.72/47.93 thf(c_0_128, plain, ~p86, inference(sr,[status(thm)],[c_0_124, c_0_125])).
% 47.72/47.93 thf(c_0_129, plain, (p90|~p92), inference(fof_simplification,[status(thm)],[ax257])).
% 47.72/47.93 thf(c_0_130, plain, (p88|~p90), inference(split_conjunct,[status(thm)],[c_0_126])).
% 47.72/47.93 thf(c_0_131, plain, ~p88, inference(sr,[status(thm)],[c_0_127, c_0_128])).
% 47.72/47.93 thf(c_0_132, plain, (p92|~p94), inference(fof_simplification,[status(thm)],[ax255])).
% 47.72/47.93 thf(c_0_133, plain, (p90|~p92), inference(split_conjunct,[status(thm)],[c_0_129])).
% 47.72/47.93 thf(c_0_134, plain, ~p90, inference(sr,[status(thm)],[c_0_130, c_0_131])).
% 47.72/47.93 thf(c_0_135, plain, (p94|~p96), inference(fof_simplification,[status(thm)],[ax253])).
% 47.72/47.93 thf(c_0_136, plain, (p92|~p94), inference(split_conjunct,[status(thm)],[c_0_132])).
% 47.72/47.93 thf(c_0_137, plain, ~p92, inference(sr,[status(thm)],[c_0_133, c_0_134])).
% 47.72/47.93 thf(c_0_138, plain, (p96|~p98), inference(fof_simplification,[status(thm)],[ax251])).
% 47.72/47.93 thf(c_0_139, plain, (p94|~p96), inference(split_conjunct,[status(thm)],[c_0_135])).
% 47.72/47.93 thf(c_0_140, plain, ~p94, inference(sr,[status(thm)],[c_0_136, c_0_137])).
% 47.72/47.93 thf(c_0_141, plain, (p98|~p100), inference(fof_simplification,[status(thm)],[ax249])).
% 47.72/47.93 thf(c_0_142, plain, (p96|~p98), inference(split_conjunct,[status(thm)],[c_0_138])).
% 47.72/47.93 thf(c_0_143, plain, ~p96, inference(sr,[status(thm)],[c_0_139, c_0_140])).
% 47.72/47.93 thf(c_0_144, plain, (p100|~p102), inference(fof_simplification,[status(thm)],[ax247])).
% 47.72/47.93 thf(c_0_145, plain, (p98|~p100), inference(split_conjunct,[status(thm)],[c_0_141])).
% 47.72/47.93 thf(c_0_146, plain, ~p98, inference(sr,[status(thm)],[c_0_142, c_0_143])).
% 47.72/47.93 thf(c_0_147, plain, (p102|~p104), inference(fof_simplification,[status(thm)],[ax245])).
% 47.72/47.93 thf(c_0_148, plain, (p100|~p102), inference(split_conjunct,[status(thm)],[c_0_144])).
% 47.72/47.93 thf(c_0_149, plain, ~p100, inference(sr,[status(thm)],[c_0_145, c_0_146])).
% 47.72/47.93 thf(c_0_150, plain, (p104|~p106), inference(fof_simplification,[status(thm)],[ax243])).
% 47.72/47.93 thf(c_0_151, plain, (p102|~p104), inference(split_conjunct,[status(thm)],[c_0_147])).
% 47.72/47.93 thf(c_0_152, plain, ~p102, inference(sr,[status(thm)],[c_0_148, c_0_149])).
% 47.72/47.93 thf(c_0_153, plain, (p106|~p108), inference(fof_simplification,[status(thm)],[ax241])).
% 47.72/47.93 thf(c_0_154, plain, (p104|~p106), inference(split_conjunct,[status(thm)],[c_0_150])).
% 47.72/47.93 thf(c_0_155, plain, ~p104, inference(sr,[status(thm)],[c_0_151, c_0_152])).
% 47.72/47.93 thf(c_0_156, plain, (p108|~p110), inference(fof_simplification,[status(thm)],[ax239])).
% 47.72/47.93 thf(c_0_157, plain, (p106|~p108), inference(split_conjunct,[status(thm)],[c_0_153])).
% 47.72/47.93 thf(c_0_158, plain, ~p106, inference(sr,[status(thm)],[c_0_154, c_0_155])).
% 47.72/47.93 thf(c_0_159, plain, (p110|~p112), inference(fof_simplification,[status(thm)],[ax237])).
% 47.72/47.93 thf(c_0_160, plain, (p108|~p110), inference(split_conjunct,[status(thm)],[c_0_156])).
% 47.72/47.93 thf(c_0_161, plain, ~p108, inference(sr,[status(thm)],[c_0_157, c_0_158])).
% 47.72/47.93 thf(c_0_162, plain, (p112|~p114), inference(fof_simplification,[status(thm)],[ax235])).
% 47.72/47.93 thf(c_0_163, plain, (p110|~p112), inference(split_conjunct,[status(thm)],[c_0_159])).
% 47.72/47.93 thf(c_0_164, plain, ~p110, inference(sr,[status(thm)],[c_0_160, c_0_161])).
% 47.72/47.93 thf(c_0_165, plain, (epred1_0<=>(fprop2setE=>(femptysetE=>(femptysetimpfalse=>(fnotinemptyset=>(fexuE3e=>(fsetext=>(femptyI=>(fnoeltsimpempty=>(fsetbeta=>(fnonemptyE1=>(fnonemptyI=>(fnonemptyI1=>(fsetadjoinIL=>(femptyinunitempty=>(fsetadjoinIR=>(fsetadjoinE=>(fsetadjoinOr=>(fsetoftrueEq=>(fpowersetI=>(femptyinPowerset=>(femptyInPowerset=>(fpowersetE=>![X1:$i, X2:$i, X3:$i]:(fin @ X2 @ X3=>(fin @ X3 @ X1=>fin @ X2 @ (fsetunion @ X1)))))))))))))))))))))))))), introduced(definition)).
% 47.72/47.93 thf(c_0_166, plain, (p114|~p116), inference(fof_simplification,[status(thm)],[ax233])).
% 47.72/47.93 thf(c_0_167, plain, (p112|~p114), inference(split_conjunct,[status(thm)],[c_0_162])).
% 47.72/47.93 thf(c_0_168, plain, ~p112, inference(sr,[status(thm)],[c_0_163, c_0_164])).
% 47.72/47.93 thf(c_0_169, axiom, (p1<=(fsetextAx=>(femptysetAx=>(fsetadjoinAx=>(fpowersetAx=>(fsetunionAx=>(fomega0Ax=>(fomegaSAx=>(fomegaIndAx=>(freplAx=>(ffoundationAx=>(fwellorderingAx=>(fdescrp=>(fdsetconstrI=>(fdsetconstrEL=>(fdsetconstrER=>(fexuE1=>epred1_0))))))))))))))))), inference(apply_def,[status(thm)],[nax1, c_0_165])).
% 47.72/47.93 thf(c_0_170, plain, (p116|~p118), inference(fof_simplification,[status(thm)],[ax231])).
% 47.72/47.93 thf(c_0_171, plain, (p114|~p116), inference(split_conjunct,[status(thm)],[c_0_166])).
% 47.72/47.93 thf(c_0_172, plain, ~p114, inference(sr,[status(thm)],[c_0_167, c_0_168])).
% 47.72/47.93 thf(c_0_173, plain, ((fsetextAx|p1)&((femptysetAx|p1)&((fsetadjoinAx|p1)&((fpowersetAx|p1)&((fsetunionAx|p1)&((fomega0Ax|p1)&((fomegaSAx|p1)&((fomegaIndAx|p1)&((freplAx|p1)&((ffoundationAx|p1)&((fwellorderingAx|p1)&((fdescrp|p1)&((fdsetconstrI|p1)&((fdsetconstrEL|p1)&((fdsetconstrER|p1)&((fexuE1|p1)&(~epred1_0|p1))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_169])])])).
% 47.72/47.93 thf(c_0_174, plain, (p118|~p119), inference(fof_simplification,[status(thm)],[ax230])).
% 47.72/47.93 thf(c_0_175, plain, (p116|~p118), inference(split_conjunct,[status(thm)],[c_0_170])).
% 47.72/47.93 thf(c_0_176, plain, ~p116, inference(sr,[status(thm)],[c_0_171, c_0_172])).
% 47.72/47.93 thf(c_0_177, plain, (~p7|~p51|p292), inference(fof_simplification,[status(thm)],[ax46])).
% 47.72/47.93 thf(c_0_178, plain, (~fsetunionAx|p51), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax51])])).
% 47.72/47.93 thf(c_0_179, plain, (fsetunionAx|p1), inference(split_conjunct,[status(thm)],[c_0_173])).
% 47.72/47.93 thf(c_0_180, plain, (~p299|p320), inference(fof_simplification,[status(thm)],[ax23])).
% 47.72/47.93 thf(c_0_181, plain, (p119|~p120), inference(fof_simplification,[status(thm)],[ax229])).
% 47.72/47.93 thf(c_0_182, plain, (p118|~p119), inference(split_conjunct,[status(thm)],[c_0_174])).
% 47.72/47.93 thf(c_0_183, plain, ~p118, inference(sr,[status(thm)],[c_0_175, c_0_176])).
% 47.72/47.93 thf(c_0_184, plain, (p292|~p7|~p51), inference(split_conjunct,[status(thm)],[c_0_177])).
% 47.72/47.93 thf(c_0_185, plain, p7, inference(split_conjunct,[status(thm)],[ax342])).
% 47.72/47.93 thf(c_0_186, plain, (p51|~fsetunionAx), inference(split_conjunct,[status(thm)],[c_0_178])).
% 47.72/47.93 thf(c_0_187, plain, fsetunionAx, inference(sr,[status(thm)],[c_0_179, c_0_62])).
% 47.72/47.93 thf(c_0_188, plain, (~p320|p319), inference(fof_simplification,[status(thm)],[ax22])).
% 47.72/47.93 thf(c_0_189, plain, (p320|~p299), inference(split_conjunct,[status(thm)],[c_0_180])).
% 47.72/47.93 thf(c_0_190, plain, p299, inference(split_conjunct,[status(thm)],[ax45])).
% 47.72/47.93 thf(c_0_191, plain, (p120|~p121), inference(fof_simplification,[status(thm)],[ax228])).
% 47.72/47.93 thf(c_0_192, plain, (p119|~p120), inference(split_conjunct,[status(thm)],[c_0_181])).
% 47.72/47.93 thf(c_0_193, plain, ~p119, inference(sr,[status(thm)],[c_0_182, c_0_183])).
% 47.72/47.93 thf(c_0_194, plain, (~p292|p300), inference(fof_simplification,[status(thm)],[ax38])).
% 47.72/47.93 thf(c_0_195, plain, (p292|~p51), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_184, c_0_185])])).
% 47.72/47.93 thf(c_0_196, plain, p51, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_186, c_0_187])])).
% 47.72/47.93 thf(c_0_197, plain, (~p319|p125|p318), inference(fof_simplification,[status(thm)],[ax21])).
% 47.72/47.93 thf(c_0_198, plain, (p319|~p320), inference(split_conjunct,[status(thm)],[c_0_188])).
% 47.72/47.93 thf(c_0_199, plain, p320, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_189, c_0_190])])).
% 47.72/47.93 thf(c_0_200, plain, (p121|~p123), inference(fof_simplification,[status(thm)],[ax226])).
% 47.72/47.93 thf(c_0_201, plain, (p123|~p125), inference(fof_simplification,[status(thm)],[ax224])).
% 47.72/47.93 thf(c_0_202, plain, (p120|~p121), inference(split_conjunct,[status(thm)],[c_0_191])).
% 47.72/47.93 thf(c_0_203, plain, ~p120, inference(sr,[status(thm)],[c_0_192, c_0_193])).
% 47.72/47.93 thf(c_0_204, plain, (~p300|p316), inference(fof_simplification,[status(thm)],[ax18])).
% 47.72/47.93 thf(c_0_205, plain, (p300|~p292), inference(split_conjunct,[status(thm)],[c_0_194])).
% 47.72/47.93 thf(c_0_206, plain, p292, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_195, c_0_196])])).
% 47.72/47.93 thf(c_0_207, plain, (p125|p318|~p319), inference(split_conjunct,[status(thm)],[c_0_197])).
% 47.72/47.93 thf(c_0_208, plain, p319, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_198, c_0_199])])).
% 47.72/47.93 thf(c_0_209, plain, (p121|~p123), inference(split_conjunct,[status(thm)],[c_0_200])).
% 47.72/47.93 thf(c_0_210, plain, (p123|~p125), inference(split_conjunct,[status(thm)],[c_0_201])).
% 47.72/47.93 thf(c_0_211, plain, ~p121, inference(sr,[status(thm)],[c_0_202, c_0_203])).
% 47.72/47.93 thf(c_0_212, plain, (~p317|~p316|p315), inference(fof_simplification,[status(thm)],[ax19])).
% 47.72/47.93 thf(c_0_213, plain, (p316|~p300), inference(split_conjunct,[status(thm)],[c_0_204])).
% 47.72/47.93 thf(c_0_214, plain, p300, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_205, c_0_206])])).
% 47.72/47.93 thf(c_0_215, plain, (~p318|p317), inference(fof_simplification,[status(thm)],[ax20])).
% 47.72/47.93 thf(c_0_216, plain, (p318|p125), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_207, c_0_208])])).
% 47.72/47.93 thf(c_0_217, plain, ~p125, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_209, c_0_210]), c_0_211])).
% 47.72/47.93 thf(c_0_218, plain, (p315|~p317|~p316), inference(split_conjunct,[status(thm)],[c_0_212])).
% 47.72/47.93 thf(c_0_219, plain, p316, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_213, c_0_214])])).
% 47.72/47.93 thf(c_0_220, plain, (p317|~p318), inference(split_conjunct,[status(thm)],[c_0_215])).
% 47.72/47.93 thf(c_0_221, plain, p318, inference(sr,[status(thm)],[c_0_216, c_0_217])).
% 47.72/47.93 thf(c_0_222, plain, ![X12:$i]:(~p315|(~fin @ f__1 @ X12|~fin @ X12 @ f__0)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax315])])])])).
% 47.72/47.93 thf(c_0_223, plain, (p315|~p317), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_218, c_0_219])])).
% 47.72/47.93 thf(c_0_224, plain, p317, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_220, c_0_221])])).
% 47.72/47.93 thf(c_0_225, plain, ((fin @ f__1 @ esk14_0|p120)&((fin @ esk14_0 @ f__0|p120)&(~fin @ f__1 @ (fsetunion @ f__0)|p120))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax120])])])])])).
% 47.72/47.93 thf(c_0_226, plain, ![X1:$i]:(~p315|~fin @ f__1 @ X1|~fin @ X1 @ f__0), inference(split_conjunct,[status(thm)],[c_0_222])).
% 47.72/47.93 thf(c_0_227, plain, p315, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_223, c_0_224])])).
% 47.72/47.93 thf(c_0_228, plain, (fin @ esk14_0 @ f__0|p120), inference(split_conjunct,[status(thm)],[c_0_225])).
% 47.72/47.93 thf(c_0_229, plain, (fin @ f__1 @ esk14_0|p120), inference(split_conjunct,[status(thm)],[c_0_225])).
% 47.72/47.93 thf(c_0_230, plain, ![X1:$i]:(~fin @ X1 @ f__0|~fin @ f__1 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_226, c_0_227])])).
% 47.72/47.93 thf(c_0_231, plain, fin @ esk14_0 @ f__0, inference(sr,[status(thm)],[c_0_228, c_0_203])).
% 47.72/47.93 thf(c_0_232, plain, fin @ f__1 @ esk14_0, inference(sr,[status(thm)],[c_0_229, c_0_203])).
% 47.72/47.93 thf(c_0_233, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230, c_0_231]), c_0_232])]), ['proof']).
% 47.72/47.93 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 47.72/47.93 thf(0,theorem,(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))))))))))))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 47.72/47.93 % SZS output end Proof
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