%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, in: ($i > $i > $o)).
thf(func_def_1, type, exu: (($i > $o) > $o)).
thf(func_def_3, type, setextAx: $o).
thf(func_def_5, type, emptysetAx: $o).
thf(func_def_6, type, setadjoin: ($i > $i > $i)).
thf(func_def_7, type, setadjoinAx: $o).
thf(func_def_8, type, powerset: ($i > $i)).
thf(func_def_9, type, powersetAx: $o).
thf(func_def_10, type, setunion: ($i > $i)).
thf(func_def_11, type, setunionAx: $o).
thf(func_def_13, type, omega0Ax: $o).
thf(func_def_14, type, omegaSAx: $o).
thf(func_def_15, type, omegaIndAx: $o).
thf(func_def_16, type, replAx: $o).
thf(func_def_17, type, foundationAx: $o).
thf(func_def_18, type, wellorderingAx: $o).
thf(func_def_19, type, descr: (($i > $o) > $i)).
thf(func_def_20, type, descrp: $o).
thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
thf(func_def_22, type, dsetconstrI: $o).
thf(func_def_23, type, dsetconstrEL: $o).
thf(func_def_24, type, dsetconstrER: $o).
thf(func_def_25, type, exuE1: $o).
thf(func_def_26, type, prop2set: ($o > $i)).
thf(func_def_27, type, prop2setE: $o).
thf(func_def_28, type, emptysetE: $o).
thf(func_def_29, type, emptysetimpfalse: $o).
thf(func_def_30, type, notinemptyset: $o).
thf(func_def_31, type, exuE3e: $o).
thf(func_def_32, type, setext: $o).
thf(func_def_33, type, emptyI: $o).
thf(func_def_34, type, noeltsimpempty: $o).
thf(func_def_35, type, setbeta: $o).
thf(func_def_36, type, nonempty: ($i > $o)).
thf(func_def_37, type, nonemptyE1: $o).
thf(func_def_38, type, nonemptyI: $o).
thf(func_def_39, type, nonemptyI1: $o).
thf(func_def_40, type, setadjoinIL: $o).
thf(func_def_41, type, emptyinunitempty: $o).
thf(func_def_42, type, setadjoinIR: $o).
thf(func_def_43, type, setadjoinE: $o).
thf(func_def_44, type, setadjoinOr: $o).
thf(func_def_45, type, setoftrueEq: $o).
thf(func_def_46, type, powersetI: $o).
thf(func_def_47, type, emptyinPowerset: $o).
thf(func_def_48, type, emptyInPowerset: $o).
thf(func_def_49, type, powersetE: $o).
thf(func_def_50, type, setunionI: $o).
thf(func_def_51, type, setunionE: $o).
thf(func_def_52, type, subPowSU: $o).
thf(func_def_53, type, exuE2: $o).
thf(func_def_54, type, nonemptyImpWitness: $o).
thf(func_def_55, type, uniqinunit: $o).
thf(func_def_56, type, notinsingleton: $o).
thf(func_def_57, type, eqinunit: $o).
thf(func_def_58, type, singletonsswitch: $o).
thf(func_def_59, type, upairsetE: $o).
thf(func_def_60, type, upairsetIL: $o).
thf(func_def_61, type, upairsetIR: $o).
thf(func_def_62, type, emptyE1: $o).
thf(func_def_63, type, vacuousDall: $o).
thf(func_def_64, type, quantDeMorgan1: $o).
thf(func_def_65, type, quantDeMorgan2: $o).
thf(func_def_66, type, quantDeMorgan3: $o).
thf(func_def_67, type, quantDeMorgan4: $o).
thf(func_def_68, type, prop2setI: $o).
thf(func_def_69, type, set2prop: ($i > $o)).
thf(func_def_70, type, prop2set2propI: $o).
thf(func_def_71, type, notdexE: $o).
thf(func_def_72, type, notdallE: $o).
thf(func_def_73, type, exuI1: $o).
thf(func_def_74, type, exuI3: $o).
thf(func_def_75, type, exuI2: $o).
thf(func_def_76, type, inCongP: $o).
thf(func_def_77, type, in__Cong: $o).
thf(func_def_78, type, exuE3u: $o).
thf(func_def_79, type, exu__Cong: $o).
thf(func_def_80, type, emptyset__Cong: $o).
thf(func_def_81, type, setadjoin__Cong: $o).
thf(func_def_82, type, powerset__Cong: $o).
thf(func_def_83, type, setunion__Cong: $o).
thf(func_def_84, type, omega__Cong: $o).
thf(func_def_85, type, exuEu: $o).
thf(func_def_86, type, descr__Cong: $o).
thf(func_def_87, type, dsetconstr__Cong: $o).
thf(func_def_88, type, subset: ($i > $i > $o)).
thf(func_def_89, type, disjoint: ($i > $i > $o)).
thf(func_def_90, type, setsmeet: ($i > $i > $o)).
thf(func_def_91, type, subsetI1: $o).
thf(func_def_92, type, eqimpsubset2: $o).
thf(func_def_93, type, eqimpsubset1: $o).
thf(func_def_94, type, subsetI2: $o).
thf(func_def_95, type, emptysetsubset: $o).
thf(func_def_96, type, subsetE: $o).
thf(func_def_97, type, subsetE2: $o).
thf(func_def_98, type, notsubsetI: $o).
thf(func_def_99, type, notequalI1: $o).
thf(func_def_100, type, notequalI2: $o).
thf(func_def_101, type, subsetRefl: $o).
thf(func_def_102, type, subsetTrans: $o).
thf(func_def_103, type, setadjoinSub: $o).
thf(func_def_104, type, setadjoinSub2: $o).
thf(func_def_105, type, subset2powerset: $o).
thf(func_def_106, type, setextsub: $o).
thf(func_def_107, type, subsetemptysetimpeq: $o).
thf(func_def_108, type, powersetI1: $o).
thf(func_def_111, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_112, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_113, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_114, type, vNOT: ($o > $o)).
thf(func_def_115, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_116, type, vAND: ($o > $o > $o)).
thf(func_def_117, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_118, type, vIMP: ($o > $o > $o)).
thf(func_def_119, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_120, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_121, type, sP0: ($i > $i > $o)).
thf(func_def_122, type, sP1: ($i > $o)).
thf(func_def_123, type, sP2: $o).
thf(func_def_126, type, sK5: ($i > $i)).
thf(func_def_129, type, sK8: ($i > ($i > $o) > $i)).
thf(func_def_130, type, sK9: ($i > $o)).
thf(func_def_133, type, sK12: ($i > $o)).
thf(func_def_137, type, sK16: ($i > $o)).
thf(func_def_139, type, sK18: $o).
thf(func_def_143, type, sK22: ($i > $i > $i)).
thf(func_def_144, type, sK23: ($i > ($i > $o) > $i)).
thf(func_def_145, type, sK24: ($i > $o)).
thf(func_def_153, type, sK32: ($i > ($i > $o) > $i)).
thf(func_def_154, type, sK33: ($i > $o)).
thf(func_def_157, type, sK36: $o).
thf(func_def_161, type, sK40: ($i > $i > $i)).
thf(func_def_167, type, sK46: ($i > $i > $o)).
thf(func_def_169, type, sK48: ($i > $i)).
thf(func_def_170, type, sK49: ($i > $i)).
thf(func_def_171, type, sK50: ($i > ($i > $i > $o) > $i)).
thf(func_def_172, type, sK51: ($i > ($i > $i > $o) > $i)).
thf(func_def_173, type, sK52: ($i > $i > ($i > $i > $o) > $i)).
thf(func_def_176, type, sK55: ($i > $o)).
thf(func_def_190, type, sK69: ($i > $i)).
thf(func_def_191, type, sK70: ($i > $o)).
thf(func_def_197, type, sK76: ($i > $i)).
thf(func_def_198, type, sK77: ($i > $i)).
thf(func_def_199, type, sK78: ($i > $i)).
thf(func_def_200, type, sK79: ($i > $i)).
thf(func_def_201, type, sK80: ($i > $i)).
thf(func_def_202, type, sK81: ($i > $i > $i > $i)).
thf(func_def_203, type, sK82: ($i > $i)).
thf(func_def_204, type, sK83: ($i > $i)).
thf(func_def_205, type, sK84: ($i > $i)).
thf(func_def_206, type, sK85: ($i > $i)).
thf(func_def_207, type, sK86: ($i > $i > $i)).
thf(func_def_208, type, sK87: ($i > $i > $i)).
thf(func_def_209, type, sK88: ($i > $i > $i > $i)).
thf(func_def_210, type, sK89: ($i > $i > $i > $i)).
thf(func_def_211, type, sK90: ($i > $i > $i > $i)).
thf(func_def_212, type, sK91: ($i > $i > $i)).
thf(func_def_213, type, sK92: ($i > $i > $i)).
thf(func_def_214, type, sK93: ($i > $i > $i)).
thf(func_def_215, type, sK94: ($i > $o)).
thf(func_def_217, type, sK96: ($i > ($i > $o) > $i)).
thf(func_def_221, type, sK100: ($i > $o)).
thf(func_def_222, type, sK101: ($i > $i)).
thf(func_def_223, type, sK102: (($i > $o) > $i)).
thf(func_def_224, type, sK103: ($o > $i > $i > $i)).
thf(func_def_227, type, sK106: $o).
thf(func_def_245, type, sK124: $o).
thf(func_def_246, type, sK125: ($i > $o)).
thf(func_def_254, type, sK133: ($i > $o)).
thf(func_def_257, type, sK136: ($i > $o)).
thf(func_def_267, type, sK146: ($i > $o)).
thf(func_def_272, type, sK151: ($i > $i)).
thf(func_def_274, type, sK153: (($i > $o) > ($i > $o) > $i > $i > $i)).
thf(func_def_275, type, sK154: (($i > $o) > ($i > $o) > $i > $i > $i)).
thf(func_def_278, type, sK157: ($i > $o)).
thf(func_def_279, type, sK158: ($i > $o)).
thf(func_def_283, type, sK162: ($i > $i > $i)).
thf(func_def_289, type, sK168: ($i > $o)).
thf(func_def_290, type, sK169: ($i > $o)).
thf(func_def_291, type, sK170: (($i > $o) > ($i > $o) > $i)).
thf(func_def_292, type, sK171: (($i > $o) > ($i > $o) > $i)).
thf(func_def_293, type, sK172: ($i > $o)).
thf(func_def_295, type, sK174: ($i > ($i > $o) > $i)).
thf(func_def_296, type, sK175: ($i > $o)).
thf(func_def_299, type, sK178: (($i > $o) > ($i > $o) > $i)).
thf(func_def_300, type, sK179: (($i > $o) > ($i > $o) > $i)).
thf(func_def_301, type, sK180: ($i > $o)).
thf(func_def_302, type, sK181: ($i > $o)).
thf(func_def_303, type, sK182: ($i > ($i > $o) > $i)).
thf(func_def_304, type, sK183: ($i > $o)).
thf(func_def_309, type, sK188: ($i > $i > $i)).
thf(func_def_314, type, sK193: ($i > $o)).
thf(func_def_316, type, sK195: (($i > $o) > $i > $i)).
thf(func_def_317, type, sK196: ($i > $o)).
thf(func_def_326, type, sK205: ($i > $i)).
thf(func_def_328, type, sK207: ($i > $i)).
thf(func_def_329, type, sK208: $o).
thf(func_def_340, type, sK219: ($i > $i)).
thf(func_def_341, type, sK220: ($i > $i > $i)).
thf(func_def_348, type, sK227: ($i > ($i > $o) > $i)).
thf(func_def_349, type, sK228: ($i > $o)).
thf(func_def_354, type, sK233: ($i > $i > $i)).
thf(func_def_355, type, sK234: ($i > $i > $i)).
thf(func_def_359, type, sK238: $o).
thf(func_def_360, type, sK239: ($i > $i > $i)).
thf(func_def_369, type, sK248: (($i > $o) > $i)).
thf(func_def_370, type, sK249: (($i > $o) > $i)).
thf(func_def_371, type, sK250: ($i > $o)).
thf(func_def_375, type, sK254: ($i > $o)).
thf(func_def_376, type, sK255: ($i > $i)).
thf(func_def_377, type, sK256: (($i > $o) > $i)).
thf(func_def_378, type, sK257: ($i > $o)).
thf(func_def_379, type, sK258: (($i > $o) > $i)).
thf(func_def_380, type, sK259: ($i > $i)).
thf(f40,axiom,(
  (powersetE = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE)).
thf(f78,axiom,(
  (subsetI1 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
thf(f96,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 => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1)).
thf(f97,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 => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(negated_conjecture,[status(cth)],[f96])).
thf(f106,plain,(
  (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((in @ X0 @ X2) => (in @ X0 @ X1))))),
  inference(rectify,[],[f40])).
thf(f107,plain,(
  ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => ((((in @ X0 @ X2)) = $true) => (((in @ X0 @ X1)) = $true))) <=> (powersetE = $true)),
  inference(fool_elimination,[],[f106])).
thf(f150,plain,(
  (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
  inference(rectify,[],[f78])).
thf(f151,plain,(
  (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true))),
  inference(fool_elimination,[],[f150])).
thf(f249,plain,(
  ~(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 => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(rectify,[],[f97])).
thf(f250,plain,(
  ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => (((subset @ X0 @ X1)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(fool_elimination,[],[f249])).
thf(f334,plain,(
  ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)) | (((subset @ X1 @ X0)) = $true)) <=> (subsetI1 = $true)),
  inference(ennf_transformation,[],[f151])).
thf(f358,plain,(
  ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) & (((subset @ X0 @ X1)) != $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
  inference(ennf_transformation,[],[f250])).
thf(f359,plain,(
  (setunionE = $true) & (subPowSU = $true) & (notequalI2 = $true) & (subset2powerset = $true) & (eqimpsubset2 = $true) & (vacuousDall = $true) & (nonemptyImpWitness = $true) & (setadjoinAx = $true) & (nonemptyI = $true) & (omegaSAx = $true) & (setext = $true) & (setunionAx = $true) & (subsetemptysetimpeq = $true) & (setoftrueEq = $true) & (exuEu = $true) & (dsetconstrI = $true) & (emptysetE = $true) & (singletonsswitch = $true) & (nonemptyI1 = $true) & (emptyinPowerset = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (noeltsimpempty = $true) & (quantDeMorgan3 = $true) & (setadjoinSub = $true) & (subsetI1 = $true) & (setadjoinIL = $true) & (notdexE = $true) & (emptysetsubset = $true) & (powersetI1 = $true) & (subsetTrans = $true) & (quantDeMorgan4 = $true) & (omega0Ax = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (replAx = $true) & (exuE1 = $true) & (dsetconstr__Cong = $true) & (nonemptyE1 = $true) & (exuI1 = $true) & (setadjoinOr = $true) & (subsetE = $true) & (emptyset__Cong = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) & (((subset @ X0 @ X1)) != $true)) & (setadjoin__Cong = $true) & (descr__Cong = $true) & (setextAx = $true) & (exuE3u = $true) & (upairsetIR = $true) & (powersetI = $true) & (eqinunit = $true) & (foundationAx = $true) & (upairsetIL = $true) & (notsubsetI = $true) & (notequalI1 = $true) & (upairsetE = $true) & (uniqinunit = $true) & (omegaIndAx = $true) & (emptyI = $true) & (powersetE = $true) & (powerset__Cong = $true) & (exuE2 = $true) & (setbeta = $true) & (in__Cong = $true) & (dsetconstrER = $true) & (notinsingleton = $true) & (notdallE = $true) & (dsetconstrEL = $true) & (subsetRefl = $true) & (setadjoinSub2 = $true) & (quantDeMorgan1 = $true) & (prop2setE = $true) & (notinemptyset = $true) & (powersetAx = $true) & (exuI2 = $true) & (subsetI2 = $true) & (wellorderingAx = $true) & (emptyInPowerset = $true) & (setunion__Cong = $true) & (emptyinunitempty = $true) & (exuI3 = $true) & (setextsub = $true) & (inCongP = $true) & (descrp = $true) & (setunionI = $true) & (exuE3e = $true) & (exu__Cong = $true) & (emptyE1 = $true) & (subsetE2 = $true) & (omega__Cong = $true) & (quantDeMorgan2 = $true) & (emptysetAx = $true) & (eqimpsubset1 = $true) & (emptysetimpfalse = $true)),
  inference(flattening,[],[f358])).
thf(f387,plain,(
  ! [X1 : $i,X2 : $i,X0 : $i] : (((((in @ X0 @ X1)) = $true) | (((in @ X0 @ X2)) != $true)) | (((in @ X2 @ (powerset @ X1))) != $true)) <=> (powersetE = $true)),
  inference(ennf_transformation,[],[f107])).
thf(f388,plain,(
  ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X1)) = $true) | (((in @ X0 @ X2)) != $true) | (((in @ X2 @ (powerset @ X1))) != $true)) <=> (powersetE = $true)),
  inference(flattening,[],[f387])).
thf(f546,plain,(
  (setunionE = $true) & (subPowSU = $true) & (notequalI2 = $true) & (subset2powerset = $true) & (eqimpsubset2 = $true) & (vacuousDall = $true) & (nonemptyImpWitness = $true) & (setadjoinAx = $true) & (nonemptyI = $true) & (omegaSAx = $true) & (setext = $true) & (setunionAx = $true) & (subsetemptysetimpeq = $true) & (setoftrueEq = $true) & (exuEu = $true) & (dsetconstrI = $true) & (emptysetE = $true) & (singletonsswitch = $true) & (nonemptyI1 = $true) & (emptyinPowerset = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (noeltsimpempty = $true) & (quantDeMorgan3 = $true) & (setadjoinSub = $true) & (subsetI1 = $true) & (setadjoinIL = $true) & (notdexE = $true) & (emptysetsubset = $true) & (powersetI1 = $true) & (subsetTrans = $true) & (quantDeMorgan4 = $true) & (omega0Ax = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (replAx = $true) & (exuE1 = $true) & (dsetconstr__Cong = $true) & (nonemptyE1 = $true) & (exuI1 = $true) & (setadjoinOr = $true) & (subsetE = $true) & (emptyset__Cong = $true) & (($true = ((in @ sK131 @ (powerset @ sK132)))) & ($true != ((subset @ sK131 @ sK132)))) & (setadjoin__Cong = $true) & (descr__Cong = $true) & (setextAx = $true) & (exuE3u = $true) & (upairsetIR = $true) & (powersetI = $true) & (eqinunit = $true) & (foundationAx = $true) & (upairsetIL = $true) & (notsubsetI = $true) & (notequalI1 = $true) & (upairsetE = $true) & (uniqinunit = $true) & (omegaIndAx = $true) & (emptyI = $true) & (powersetE = $true) & (powerset__Cong = $true) & (exuE2 = $true) & (setbeta = $true) & (in__Cong = $true) & (dsetconstrER = $true) & (notinsingleton = $true) & (notdallE = $true) & (dsetconstrEL = $true) & (subsetRefl = $true) & (setadjoinSub2 = $true) & (quantDeMorgan1 = $true) & (prop2setE = $true) & (notinemptyset = $true) & (powersetAx = $true) & (exuI2 = $true) & (subsetI2 = $true) & (wellorderingAx = $true) & (emptyInPowerset = $true) & (setunion__Cong = $true) & (emptyinunitempty = $true) & (exuI3 = $true) & (setextsub = $true) & (inCongP = $true) & (descrp = $true) & (setunionI = $true) & (exuE3e = $true) & (exu__Cong = $true) & (emptyE1 = $true) & (subsetE2 = $true) & (omega__Cong = $true) & (quantDeMorgan2 = $true) & (emptysetAx = $true) & (eqimpsubset1 = $true) & (emptysetimpfalse = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK131,sK132]),skolemize(X0,$thf(sK131)),skolemize(X1,$thf(sK132))],[f359])).
thf(f632,plain,(
  (! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X1)) = $true) | (((in @ X0 @ X2)) != $true) | (((in @ X2 @ (powerset @ X1))) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X1)) != $true) & (((in @ X0 @ X2)) = $true) & (((in @ X2 @ (powerset @ X1))) = $true)))),
  inference(nnf_transformation,[],[f388])).
thf(f633,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true) | (((in @ X0 @ (powerset @ X1))) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) != $true) & ($true = ((in @ X5 @ X3))) & ($true = ((in @ X3 @ (powerset @ X4))))))),
  inference(rectify,[],[f632])).
thf(f634,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true) | (((in @ X0 @ (powerset @ X1))) != $true)) | (powersetE != $true)) & ((powersetE = $true) | (($true != ((in @ sK217 @ sK216))) & ($true = ((in @ sK217 @ sK215))) & ($true = ((in @ sK215 @ (powerset @ sK216))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK215,sK216,sK217]),skolemize(X3,$thf(sK215)),skolemize(X4,sK216),skolemize(X5,sK217)],[f633])).
thf(f638,plain,(
  (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)) | (((subset @ X1 @ X0)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) & (((subset @ X1 @ X0)) != $true)))),
  inference(nnf_transformation,[],[f334])).
thf(f639,plain,(
  (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (($true != ((in @ X5 @ X3))) | (((in @ X5 @ X4)) = $true)) & (((subset @ X3 @ X4)) != $true)))),
  inference(rectify,[],[f638])).
thf(f640,plain,(
  (! [X0 : $i,X1 : $i] : ((($true = ((in @ (sK220 @ X1 @ X0) @ X0))) & ($true != ((in @ (sK220 @ X1 @ X0) @ X1)))) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | (! [X5 : $i] : (($true != ((in @ X5 @ sK221))) | ($true = ((in @ X5 @ sK222)))) & (((subset @ sK221 @ sK222)) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK221,sK222]),skolemize(X1,$thf(sK5 @ X0)),skolemize(X3,$thf(sK221)),skolemize(X4,$thf(sK222))],[f639])).
thf(f934,plain,(
  (powersetE = $true)),
  inference(cnf_transformation,[],[f546])).
thf(f950,plain,(
  ($true != ((subset @ sK131 @ sK132)))),
  inference(cnf_transformation,[],[f546])).
thf(f951,plain,(
  ($true = ((in @ sK131 @ (powerset @ sK132))))),
  inference(cnf_transformation,[],[f546])).
thf(f969,plain,(
  (subsetI1 = $true)),
  inference(cnf_transformation,[],[f546])).
thf(f1109,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X0 @ (powerset @ X1))) != $true) | (((in @ X2 @ X0)) != $true) | (powersetE != $true)) )),
  inference(cnf_transformation,[],[f634])).
thf(f1115,plain,(
  ( ! [X0 : $i,X1 : $i] : ((subsetI1 != $true) | (((subset @ X0 @ X1)) = $true) | ($true != ((in @ (sK220 @ X1 @ X0) @ X1)))) )),
  inference(cnf_transformation,[],[f640])).
thf(f1116,plain,(
  ( ! [X0 : $i,X1 : $i] : ((subsetI1 != $true) | (((subset @ X0 @ X1)) = $true) | ($true = ((in @ (sK220 @ X1 @ X0) @ X0)))) )),
  inference(cnf_transformation,[],[f640])).
thf(f1420,definition,(
  spl261_24 <=> (subsetI1 = $true)),
  introduced(definition,[new_symbols(definition,[spl261_24])],[avatar_definition])).
thf(f1424,definition,(
  spl261_25 <=> ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ($true = ((in @ (sK220 @ X1 @ X0) @ X0))))),
  introduced(definition,[new_symbols(definition,[spl261_25])],[avatar_definition])).
thf(f1425,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK220 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true)) ) | ~spl261_25),
  inference(avatar_component_clause,[],[f1424])).
thf(f1426,plain,(
  ~spl261_24 | spl261_25),
  inference(avatar_split_clause,[],[f1116,f1424,f1420])).
thf(f1871,definition,(
  spl261_126 <=> (powersetE = $true)),
  introduced(definition,[new_symbols(definition,[spl261_126])],[avatar_definition])).
thf(f1914,plain,(
  spl261_126),
  inference(avatar_split_clause,[],[f934,f1871])).
thf(f2011,plain,(
  spl261_24),
  inference(avatar_split_clause,[],[f969,f1420])).
thf(f2194,definition,(
  spl261_198 <=> ($true = ((subset @ sK131 @ sK132)))),
  introduced(definition,[new_symbols(definition,[spl261_198])],[avatar_definition])).
thf(f2196,plain,(
  ($true != ((subset @ sK131 @ sK132))) | spl261_198),
  inference(avatar_component_clause,[],[f2194])).
thf(f2197,plain,(
  ~spl261_198),
  inference(avatar_split_clause,[],[f950,f2194])).
thf(f2289,definition,(
  spl261_219 <=> ! [X4 : $i,X5 : $i,X7 : $i] : (($true != ((in @ X5 @ (powerset @ X4)))) | ($true = ((in @ X7 @ X4))) | ($true != ((in @ X7 @ X5))))),
  introduced(definition,[new_symbols(definition,[spl261_219])],[avatar_definition])).
thf(f2290,plain,(
  ( ! [X7 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ (powerset @ X4)))) | ($true = ((in @ X7 @ X4))) | ($true != ((in @ X7 @ X5)))) ) | ~spl261_219),
  inference(avatar_component_clause,[],[f2289])).
thf(f2398,plain,(
  spl261_219 | ~spl261_126),
  inference(avatar_split_clause,[],[f1109,f1871,f2289])).
thf(f3185,definition,(
  spl261_405 <=> ($true = ((in @ sK131 @ (powerset @ sK132))))),
  introduced(definition,[new_symbols(definition,[spl261_405])],[avatar_definition])).
thf(f3187,plain,(
  ($true = ((in @ sK131 @ (powerset @ sK132)))) | ~spl261_405),
  inference(avatar_component_clause,[],[f3185])).
thf(f3188,plain,(
  spl261_405),
  inference(avatar_split_clause,[],[f951,f3185])).
thf(f3371,definition,(
  spl261_444 <=> ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ($true != ((in @ (sK220 @ X1 @ X0) @ X1))))),
  introduced(definition,[new_symbols(definition,[spl261_444])],[avatar_definition])).
thf(f3372,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK220 @ X1 @ X0) @ X1))) | (((subset @ X0 @ X1)) = $true)) ) | ~spl261_444),
  inference(avatar_component_clause,[],[f3371])).
thf(f3373,plain,(
  ~spl261_24 | spl261_444),
  inference(avatar_split_clause,[],[f1115,f3371,f1420])).
thf(f3890,plain,(
  ( ! [X0 : $i] : (($true != ((in @ X0 @ sK131))) | ($true != $true) | (((in @ X0 @ sK132)) = $true)) ) | (~spl261_219 | ~spl261_405)),
  inference(superposition,[],[f2290,f3187])).
thf(f3904,plain,(
  ( ! [X0 : $i] : ((((in @ X0 @ sK132)) = $true) | ($true != ((in @ X0 @ sK131)))) ) | (~spl261_219 | ~spl261_405)),
  inference(trivial_inequality_removal,[],[f3890])).
thf(f3922,plain,(
  ( ! [X0 : $i] : (($true != $true) | (((subset @ X0 @ sK132)) = $true) | ($true != ((in @ (sK220 @ sK132 @ X0) @ sK131)))) ) | (~spl261_219 | ~spl261_405 | ~spl261_444)),
  inference(superposition,[],[f3372,f3904])).
thf(f3931,plain,(
  ( ! [X0 : $i] : (($true != ((in @ (sK220 @ sK132 @ X0) @ sK131))) | (((subset @ X0 @ sK132)) = $true)) ) | (~spl261_219 | ~spl261_405 | ~spl261_444)),
  inference(trivial_inequality_removal,[],[f3922])).
thf(f4172,plain,(
  ($true = ((subset @ sK131 @ sK132))) | ($true = ((subset @ sK131 @ sK132))) | ($true != $true) | (~spl261_25 | ~spl261_219 | ~spl261_405 | ~spl261_444)),
  inference(superposition,[],[f3931,f1425])).
thf(f4175,plain,(
  ($true != $true) | ($true = ((subset @ sK131 @ sK132))) | (~spl261_25 | ~spl261_219 | ~spl261_405 | ~spl261_444)),
  inference(duplicate_literal_removal,[],[f4172])).
thf(f4176,plain,(
  ($true = ((subset @ sK131 @ sK132))) | (~spl261_25 | ~spl261_219 | ~spl261_405 | ~spl261_444)),
  inference(trivial_inequality_removal,[],[f4175])).
thf(f4177,plain,(
  $false | (~spl261_25 | spl261_198 | ~spl261_219 | ~spl261_405 | ~spl261_444)),
  inference(forward_subsumption_resolution,[],[f4176,f2196])).
thf(f4178,plain,(
  ~spl261_25 | spl261_198 | ~spl261_219 | ~spl261_405 | ~spl261_444),
  inference(avatar_contradiction_clause,[],[f4177])).
cnf(s18, plain, ~spl261_24 | spl261_25, inference(sat_conversion,[],[f1426])).
cnf(s94, plain, spl261_126, inference(sat_conversion,[],[f1914])).
cnf(s113, plain, spl261_24, inference(sat_conversion,[],[f2011])).
cnf(s152, plain, ~spl261_198, inference(sat_conversion,[],[f2197])).
cnf(s196, plain, ~spl261_126 | spl261_219, inference(sat_conversion,[],[f2398])).
cnf(s398, plain, spl261_405, inference(sat_conversion,[],[f3188])).
cnf(s449, plain, ~spl261_24 | spl261_444, inference(sat_conversion,[],[f3373])).
cnf(s490, plain, ~spl261_25 | spl261_198 | ~spl261_219 | ~spl261_405 | ~spl261_444, inference(sat_conversion,[],[f4178])).
cnf(s563, plain, spl261_444, inference(rat,[],[s449,s113])).
cnf(s567, plain, spl261_219, inference(rat,[],[s196,s94])).
cnf(s568, plain, ~spl261_25, inference(rat,[],[s490,s563,s398,s152,s567])).
cnf(s606, plain, $false, inference(rat,[],[s18,s568,s113])).
thf(f4179,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s606])).
% SZS output end Proof for theBenchmark