%----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_109, type, powersetE1: $o).
thf(func_def_110, type, inPowerset: $o).
thf(func_def_111, type, powersetsubset: $o).
thf(func_def_112, type, sepInPowerset: $o).
thf(func_def_113, type, sepSubset: $o).
thf(func_def_114, type, binunion: ($i > $i > $i)).
thf(func_def_115, type, binunionIL: $o).
thf(func_def_116, type, upairset2IR: $o).
thf(func_def_117, type, binunionIR: $o).
thf(func_def_118, type, binunionEcases: $o).
thf(func_def_119, type, binunionE: $o).
thf(func_def_120, type, binunionLsub: $o).
thf(func_def_121, type, binunionRsub: $o).
thf(func_def_122, type, binintersect: ($i > $i > $i)).
thf(func_def_123, type, binintersectI: $o).
thf(func_def_124, type, binintersectSubset5: $o).
thf(func_def_125, type, binintersectEL: $o).
thf(func_def_126, type, binintersectLsub: $o).
thf(func_def_127, type, binintersectSubset2: $o).
thf(func_def_128, type, binintersectSubset3: $o).
thf(func_def_129, type, binintersectER: $o).
thf(func_def_132, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_133, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_134, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_135, type, vNOT: ($o > $o)).
thf(func_def_136, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_137, type, vAND: ($o > $o > $o)).
thf(func_def_138, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_139, type, vIMP: ($o > $o > $o)).
thf(func_def_140, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_141, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_142, type, sP0: ($i > $i > $o)).
thf(func_def_143, type, sP1: ($i > $o)).
thf(func_def_144, type, sP2: $o).
thf(func_def_159, type, sK17: ($i > $o)).
thf(func_def_160, type, sK18: ($i > $i)).
thf(func_def_161, type, sK19: (($i > $o) > $i)).
thf(func_def_170, type, sK28: ($i > $i > $i)).
thf(func_def_178, type, sK36: ($i > $i > $i)).
thf(func_def_184, type, sK42: ($i > $i)).
thf(func_def_187, type, sK45: ($i > $i)).
thf(func_def_193, type, sK51: ($i > $i > $i)).
thf(func_def_197, type, sK55: ($i > $i)).
thf(func_def_200, type, sK58: $o).
thf(func_def_204, type, sK62: ($i > $o)).
thf(func_def_207, type, sK65: ($i > ($i > $o) > $i)).
thf(func_def_210, type, sK68: ($o > $i > $i > $i)).
thf(func_def_213, type, sK71: $o).
thf(func_def_217, type, sK75: ($i > $o)).
thf(func_def_220, type, sK78: ($i > $o)).
thf(func_def_221, type, sK79: (($i > $o) > $i)).
thf(func_def_225, type, sK83: ($i > $o)).
thf(func_def_228, type, sK86: ($i > $o)).
thf(func_def_231, type, sK89: (($i > $o) > $i)).
thf(func_def_232, type, sK90: (($i > $o) > $i)).
thf(func_def_233, type, sK91: ($i > $o)).
thf(func_def_237, type, sK95: ($i > $o)).
thf(func_def_240, type, sK98: ($i > ($i > $o) > $i)).
thf(func_def_247, type, sK105: $o).
thf(func_def_250, type, sK108: ($i > $o)).
thf(func_def_253, type, sK111: (($i > $o) > $i > $i)).
thf(func_def_255, type, sK113: ($i > $o)).
thf(func_def_257, type, sK115: ($i > $o)).
thf(func_def_263, type, sK121: ($i > $o)).
thf(func_def_266, type, sK124: ($i > $o)).
thf(func_def_268, type, sK126: ($i > ($i > $o) > $i)).
thf(func_def_271, type, sK129: ($i > $i > $i)).
thf(func_def_272, type, sK130: ($i > $i > $i)).
thf(func_def_275, type, sK133: ($i > $i > $i)).
thf(func_def_278, type, sK136: ($i > $i > $i)).
thf(func_def_285, type, sK143: $o).
thf(func_def_295, type, sK153: (($i > $o) > ($i > $o) > $i > $i > $i)).
thf(func_def_296, type, sK154: (($i > $o) > ($i > $o) > $i > $i > $i)).
thf(func_def_299, type, sK157: ($i > $o)).
thf(func_def_300, type, sK158: ($i > $o)).
thf(func_def_305, type, sK163: (($i > $o) > $i)).
thf(func_def_306, type, sK164: ($i > $o)).
thf(func_def_307, type, sK165: ($i > $i)).
thf(func_def_309, type, sK167: ($i > $i)).
thf(func_def_310, type, sK168: (($i > $o) > ($i > $o) > $i)).
thf(func_def_311, type, sK169: (($i > $o) > ($i > $o) > $i)).
thf(func_def_312, type, sK170: ($i > $o)).
thf(func_def_313, type, sK171: ($i > $o)).
thf(func_def_316, type, sK174: ($i > ($i > $o) > $i)).
thf(func_def_317, type, sK175: ($i > $o)).
thf(func_def_326, type, sK184: $o).
thf(func_def_327, type, sK185: ($i > ($i > $o) > $i)).
thf(func_def_328, type, sK186: ($i > $o)).
thf(func_def_333, type, sK191: ($i > $o)).
thf(func_def_340, type, sK198: ($i > $o)).
thf(func_def_342, type, sK200: $o).
thf(func_def_351, type, sK209: ($i > $i)).
thf(func_def_352, type, sK210: ($i > $i)).
thf(func_def_353, type, sK211: ($i > $i)).
thf(func_def_354, type, sK212: ($i > $i)).
thf(func_def_355, type, sK213: ($i > $i)).
thf(func_def_356, type, sK214: ($i > $i > $i > $i)).
thf(func_def_357, type, sK215: ($i > $i)).
thf(func_def_358, type, sK216: ($i > $i)).
thf(func_def_359, type, sK217: ($i > $i)).
thf(func_def_360, type, sK218: ($i > $i)).
thf(func_def_361, type, sK219: ($i > $i > $i)).
thf(func_def_362, type, sK220: ($i > $i > $i)).
thf(func_def_363, type, sK221: ($i > $i > $i > $i)).
thf(func_def_364, type, sK222: ($i > $i > $i > $i)).
thf(func_def_365, type, sK223: ($i > $i > $i > $i)).
thf(func_def_366, type, sK224: ($i > $i > $i)).
thf(func_def_367, type, sK225: ($i > $i > $i)).
thf(func_def_368, type, sK226: ($i > $i > $i)).
thf(func_def_371, type, sK229: ($i > $o)).
thf(func_def_372, type, sK230: ($i > $o)).
thf(func_def_373, type, sK231: (($i > $o) > ($i > $o) > $i)).
thf(func_def_374, type, sK232: (($i > $o) > ($i > $o) > $i)).
thf(func_def_376, type, sK234: ($i > $o)).
thf(func_def_379, type, sK237: ($i > $i)).
thf(func_def_380, type, sK238: $o).
thf(func_def_387, type, sK245: ($i > $o)).
thf(func_def_396, type, sK254: ($i > $i)).
thf(func_def_398, type, sK256: ($i > $o)).
thf(func_def_399, type, sK257: ($i > ($i > $o) > $i)).
thf(func_def_400, type, sK258: ($i > $o)).
thf(func_def_409, type, sK267: ($i > $i)).
thf(func_def_422, type, sK280: ($i > $o)).
thf(func_def_423, type, sK281: ($i > ($i > $i > $o) > $i)).
thf(func_def_424, type, sK282: ($i > $i > ($i > $i > $o) > $i)).
thf(func_def_425, type, sK283: ($i > ($i > $i > $o) > $i)).
thf(func_def_426, type, sK284: ($i > $i > $o)).
thf(func_def_428, type, sK286: ($i > $i)).
thf(func_def_429, type, sK287: ($i > $i)).
thf(func_def_430, type, sK288: ($i > $i > $i)).
thf(func_def_446, type, sK304: ($i > $o)).
thf(func_def_448, type, sK306: (($i > $o) > $i > $i)).
thf(f25,axiom,(
  (noeltsimpempty = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty)).
thf(f111,axiom,(
  (binintersectLsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub)).
thf(f112,axiom,(
  (! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (((binintersect @ X0 @ X1)) = X0)) = binintersectSubset2)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2)).
thf(f114,axiom,(
  (binintersectER = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER)).
thf(f115,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 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => ! [X1 : $i,X0 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (((binintersect @ X0 @ X1)) = emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1)).
thf(f116,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 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => ! [X1 : $i,X0 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (((binintersect @ X0 @ X1)) = emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(negated_conjecture,[status(cth)],[f115])).
thf(f122,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 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => ! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (emptyset = ((binintersect @ X1 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(rectify,[],[f116])).
thf(f123,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) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) = $true)) => (emptyset = ((binintersect @ X1 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(fool_elimination,[],[f122])).
thf(f140,plain,(
  (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X1 @ X2)) => (in @ X0 @ X2)))),
  inference(rectify,[],[f114])).
thf(f141,plain,(
  (binintersectER = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X0 @ (binintersect @ X1 @ X2))) = $true) => ($true = ((in @ X0 @ X2))))),
  inference(fool_elimination,[],[f140])).
thf(f152,plain,(
  (binintersectLsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0))),
  inference(rectify,[],[f111])).
thf(f153,plain,(
  ! [X1 : $i,X0 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X0)) = $true) <=> (binintersectLsub = $true)),
  inference(fool_elimination,[],[f152])).
thf(f291,plain,(
  (noeltsimpempty = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
  inference(rectify,[],[f25])).
thf(f292,plain,(
  (noeltsimpempty = $true) <=> ! [X0 : $i] : (! [X1 : $i] : ~ (((in @ X1 @ X0)) = $true) => (emptyset = X0))),
  inference(fool_elimination,[],[f291])).
thf(f299,plain,(
  (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (((binintersect @ X1 @ X0)) = X1)) = binintersectSubset2)),
  inference(rectify,[],[f112])).
thf(f300,plain,(
  (binintersectSubset2 = $true) <=> ! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) => (((binintersect @ X1 @ X0)) = X1))),
  inference(fool_elimination,[],[f299])).
thf(f359,plain,(
  (noeltsimpempty = $true) <=> ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) => (emptyset = X0))),
  inference(flattening,[],[f292])).
thf(f411,plain,(
  (binintersectER = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ (binintersect @ X1 @ X2))) != $true) | ($true = ((in @ X0 @ X2))))),
  inference(ennf_transformation,[],[f141])).
thf(f416,plain,(
  (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((emptyset != ((binintersect @ X1 @ X0))) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) != $true))) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $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,[],[f123])).
thf(f417,plain,(
  (binintersectI = $true) & (binintersectLsub = $true) & (nonemptyI1 = $true) & (inCongP = $true) & (exu__Cong = $true) & (setunion__Cong = $true) & (exuE3e = $true) & (upairsetE = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (emptyE1 = $true) & (omegaSAx = $true) & (powersetE = $true) & (subsetE = $true) & (nonemptyI = $true) & (setoftrueEq = $true) & (powersetAx = $true) & (notdexE = $true) & (dsetconstrER = $true) & (eqimpsubset1 = $true) & (nonemptyE1 = $true) & (vacuousDall = $true) & (omega__Cong = $true) & (setadjoinSub2 = $true) & (binunionLsub = $true) & (notdallE = $true) & (subsetE2 = $true) & (prop2setI = $true) & (exuE2 = $true) & (quantDeMorgan3 = $true) & (emptysetsubset = $true) & (exuEu = $true) & (powersetsubset = $true) & (quantDeMorgan4 = $true) & (setbeta = $true) & (binunionE = $true) & (sepSubset = $true) & (notsubsetI = $true) & (binunionRsub = $true) & (notinemptyset = $true) & ? [X0 : $i,X1 : $i] : ((emptyset != ((binintersect @ X1 @ X0))) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) != $true))) & (binunionIL = $true) & (subsetI1 = $true) & (prop2setE = $true) & (singletonsswitch = $true) & (in__Cong = $true) & (setadjoinIR = $true) & (setadjoin__Cong = $true) & (binunionIR = $true) & (exuI3 = $true) & (emptysetAx = $true) & (emptyInPowerset = $true) & (setunionI = $true) & (exuI1 = $true) & (binunionEcases = $true) & (notinsingleton = $true) & (emptyinPowerset = $true) & (descrp = $true) & (subset2powerset = $true) & (emptysetE = $true) & (nonemptyImpWitness = $true) & (binintersectER = $true) & (eqimpsubset2 = $true) & (omega0Ax = $true) & (quantDeMorgan2 = $true) & (prop2set2propI = $true) & (setunionE = $true) & (subPowSU = $true) & (notequalI2 = $true) & (powersetI = $true) & (omegaIndAx = $true) & (replAx = $true) & (upairsetIL = $true) & (setext = $true) & (binintersectSubset5 = $true) & (exuE3u = $true) & (uniqinunit = $true) & (emptyI = $true) & (quantDeMorgan1 = $true) & (upairsetIR = $true) & (binintersectSubset2 = $true) & (powerset__Cong = $true) & (setadjoinE = $true) & (emptysetimpfalse = $true) & (subsetTrans = $true) & (emptyset__Cong = $true) & (binintersectEL = $true) & (subsetRefl = $true) & (foundationAx = $true) & (upairset2IR = $true) & (powersetI1 = $true) & (emptyinunitempty = $true) & (dsetconstr__Cong = $true) & (setadjoinIL = $true) & (setextAx = $true) & (noeltsimpempty = $true) & (exuI2 = $true) & (inPowerset = $true) & (notequalI1 = $true) & (setadjoinAx = $true) & (setadjoinOr = $true) & (powersetE1 = $true) & (subsetI2 = $true) & (binintersectSubset3 = $true) & (setadjoinSub = $true) & (exuE1 = $true) & (wellorderingAx = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (setunionAx = $true) & (sepInPowerset = $true) & (descr__Cong = $true) & (eqinunit = $true)),
  inference(flattening,[],[f416])).
thf(f421,plain,(
  (binintersectSubset2 = $true) <=> ! [X1 : $i,X0 : $i] : ((((binintersect @ X1 @ X0)) = X1) | (((subset @ X1 @ X0)) != $true))),
  inference(ennf_transformation,[],[f300])).
thf(f441,plain,(
  ! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (emptyset = X0)) <=> (noeltsimpempty = $true)),
  inference(ennf_transformation,[],[f359])).
thf(f493,plain,(
  (binintersectI = $true) & (binintersectLsub = $true) & (nonemptyI1 = $true) & (inCongP = $true) & (exu__Cong = $true) & (setunion__Cong = $true) & (exuE3e = $true) & (upairsetE = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (emptyE1 = $true) & (omegaSAx = $true) & (powersetE = $true) & (subsetE = $true) & (nonemptyI = $true) & (setoftrueEq = $true) & (powersetAx = $true) & (notdexE = $true) & (dsetconstrER = $true) & (eqimpsubset1 = $true) & (nonemptyE1 = $true) & (vacuousDall = $true) & (omega__Cong = $true) & (setadjoinSub2 = $true) & (binunionLsub = $true) & (notdallE = $true) & (subsetE2 = $true) & (prop2setI = $true) & (exuE2 = $true) & (quantDeMorgan3 = $true) & (emptysetsubset = $true) & (exuEu = $true) & (powersetsubset = $true) & (quantDeMorgan4 = $true) & (setbeta = $true) & (binunionE = $true) & (sepSubset = $true) & (notsubsetI = $true) & (binunionRsub = $true) & (notinemptyset = $true) & ((emptyset != ((binintersect @ sK9 @ sK8))) & ! [X2 : $i] : (($true != ((in @ X2 @ sK9))) | ($true != ((in @ X2 @ sK8))))) & (binunionIL = $true) & (subsetI1 = $true) & (prop2setE = $true) & (singletonsswitch = $true) & (in__Cong = $true) & (setadjoinIR = $true) & (setadjoin__Cong = $true) & (binunionIR = $true) & (exuI3 = $true) & (emptysetAx = $true) & (emptyInPowerset = $true) & (setunionI = $true) & (exuI1 = $true) & (binunionEcases = $true) & (notinsingleton = $true) & (emptyinPowerset = $true) & (descrp = $true) & (subset2powerset = $true) & (emptysetE = $true) & (nonemptyImpWitness = $true) & (binintersectER = $true) & (eqimpsubset2 = $true) & (omega0Ax = $true) & (quantDeMorgan2 = $true) & (prop2set2propI = $true) & (setunionE = $true) & (subPowSU = $true) & (notequalI2 = $true) & (powersetI = $true) & (omegaIndAx = $true) & (replAx = $true) & (upairsetIL = $true) & (setext = $true) & (binintersectSubset5 = $true) & (exuE3u = $true) & (uniqinunit = $true) & (emptyI = $true) & (quantDeMorgan1 = $true) & (upairsetIR = $true) & (binintersectSubset2 = $true) & (powerset__Cong = $true) & (setadjoinE = $true) & (emptysetimpfalse = $true) & (subsetTrans = $true) & (emptyset__Cong = $true) & (binintersectEL = $true) & (subsetRefl = $true) & (foundationAx = $true) & (upairset2IR = $true) & (powersetI1 = $true) & (emptyinunitempty = $true) & (dsetconstr__Cong = $true) & (setadjoinIL = $true) & (setextAx = $true) & (noeltsimpempty = $true) & (exuI2 = $true) & (inPowerset = $true) & (notequalI1 = $true) & (setadjoinAx = $true) & (setadjoinOr = $true) & (powersetE1 = $true) & (subsetI2 = $true) & (binintersectSubset3 = $true) & (setadjoinSub = $true) & (exuE1 = $true) & (wellorderingAx = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (setunionAx = $true) & (sepInPowerset = $true) & (descr__Cong = $true) & (eqinunit = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,$thf(sK8)),skolemize(X1,$thf(sK9))],[f417])).
thf(f521,plain,(
  ((binintersectSubset2 = $true) | ? [X1 : $i,X0 : $i] : ((((binintersect @ X1 @ X0)) != X1) & (((subset @ X1 @ X0)) = $true))) & (! [X1 : $i,X0 : $i] : ((((binintersect @ X1 @ X0)) = X1) | (((subset @ X1 @ X0)) != $true)) | (binintersectSubset2 != $true))),
  inference(nnf_transformation,[],[f421])).
thf(f522,plain,(
  ((binintersectSubset2 = $true) | ? [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) != X0) & (((subset @ X0 @ X1)) = $true))) & (! [X2 : $i,X3 : $i] : ((((binintersect @ X2 @ X3)) = X2) | ($true != ((subset @ X2 @ X3)))) | (binintersectSubset2 != $true))),
  inference(rectify,[],[f521])).
thf(f523,plain,(
  ((binintersectSubset2 = $true) | ((((binintersect @ sK32 @ sK33)) != sK32) & ($true = ((subset @ sK32 @ sK33))))) & (! [X2 : $i,X3 : $i] : ((((binintersect @ X2 @ X3)) = X2) | ($true != ((subset @ X2 @ X3)))) | (binintersectSubset2 != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK32,sK33]),skolemize(X0,$thf(sK32)),skolemize(X1,$thf(sK33))],[f522])).
thf(f530,plain,(
  (! [X1 : $i,X0 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X0)) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ? [X1 : $i,X0 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X0)) != $true))),
  inference(nnf_transformation,[],[f153])).
thf(f531,plain,(
  (! [X0 : $i,X1 : $i] : ($true = ((subset @ (binintersect @ X1 @ X0) @ X1))) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ? [X2 : $i,X3 : $i] : (((subset @ (binintersect @ X3 @ X2) @ X3)) != $true))),
  inference(rectify,[],[f530])).
thf(f532,plain,(
  (! [X0 : $i,X1 : $i] : ($true = ((subset @ (binintersect @ X1 @ X0) @ X1))) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | (((subset @ (binintersect @ sK41 @ sK40) @ sK41)) != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41]),skolemize(X2,$thf(sK40)),skolemize(X3,sK41)],[f531])).
thf(f536,plain,(
  ((binintersectER = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ (binintersect @ X1 @ X2))) = $true) & ($true != ((in @ X0 @ X2))))) & (! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ (binintersect @ X1 @ X2))) != $true) | ($true = ((in @ X0 @ X2)))) | (binintersectER != $true))),
  inference(nnf_transformation,[],[f411])).
thf(f537,plain,(
  ((binintersectER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (binintersect @ X0 @ X1))) = $true) & (((in @ X2 @ X1)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ (binintersect @ X3 @ X4))) != $true) | (((in @ X5 @ X4)) = $true)) | (binintersectER != $true))),
  inference(rectify,[],[f536])).
thf(f538,plain,(
  ((binintersectER = $true) | ((((in @ sK48 @ (binintersect @ sK46 @ sK47))) = $true) & (((in @ sK48 @ sK47)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ (binintersect @ X3 @ X4))) != $true) | (((in @ X5 @ X4)) = $true)) | (binintersectER != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK46,sK47,sK48]),skolemize(X0,$thf(sK46)),skolemize(X1,sK47),skolemize(X2,sK48)],[f537])).
thf(f548,plain,(
  (! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (emptyset = X0)) | (noeltsimpempty != $true)) & ((noeltsimpempty = $true) | ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) & (emptyset != X0)))),
  inference(nnf_transformation,[],[f441])).
thf(f549,plain,(
  (! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (emptyset = X0)) | (noeltsimpempty != $true)) & ((noeltsimpempty = $true) | ? [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X2)) != $true) & (emptyset != X2)))),
  inference(rectify,[],[f548])).
thf(f550,plain,(
  (! [X0 : $i] : (($true = ((in @ (sK55 @ X0) @ X0))) | (emptyset = X0)) | (noeltsimpempty != $true)) & ((noeltsimpempty = $true) | (! [X3 : $i] : ($true != ((in @ X3 @ sK56))) & (emptyset != sK56)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK56]),skolemize(X4,$thf(sK19 @ X3)),skolemize(X2,$thf(sK56))],[f549])).
thf(f845,plain,(
  (noeltsimpempty = $true)),
  inference(cnf_transformation,[],[f493])).
thf(f860,plain,(
  (binintersectSubset2 = $true)),
  inference(cnf_transformation,[],[f493])).
thf(f879,plain,(
  (binintersectER = $true)),
  inference(cnf_transformation,[],[f493])).
thf(f900,plain,(
  ( ! [X2 : $i] : (($true != ((in @ X2 @ sK9))) | ($true != ((in @ X2 @ sK8)))) )),
  inference(cnf_transformation,[],[f493])).
thf(f901,plain,(
  (emptyset != ((binintersect @ sK9 @ sK8)))),
  inference(cnf_transformation,[],[f493])).
thf(f940,plain,(
  (binintersectLsub = $true)),
  inference(cnf_transformation,[],[f493])).
thf(f973,plain,(
  ( ! [X2 : $i,X3 : $i] : (($true != ((subset @ X2 @ X3))) | (binintersectSubset2 != $true) | (((binintersect @ X2 @ X3)) = X2)) )),
  inference(cnf_transformation,[],[f523])).
thf(f985,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ (binintersect @ X1 @ X0) @ X1))) | (binintersectLsub != $true)) )),
  inference(cnf_transformation,[],[f532])).
thf(f991,plain,(
  ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ (binintersect @ X3 @ X4))) != $true) | (binintersectER != $true) | (((in @ X5 @ X4)) = $true)) )),
  inference(cnf_transformation,[],[f538])).
thf(f1005,plain,(
  ( ! [X0 : $i] : (($true = ((in @ (sK55 @ X0) @ X0))) | (noeltsimpempty != $true) | (emptyset = X0)) )),
  inference(cnf_transformation,[],[f550])).
thf(f1754,definition,(
  spl307_54 <=> (binintersectLsub = $true)),
  introduced(definition,[new_symbols(definition,[spl307_54])],[avatar_definition])).
thf(f1758,definition,(
  spl307_55 <=> ! [X0 : $i,X1 : $i] : ($true = ((subset @ (binintersect @ X1 @ X0) @ X1)))),
  introduced(definition,[new_symbols(definition,[spl307_55])],[avatar_definition])).
thf(f1759,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ (binintersect @ X1 @ X0) @ X1)))) ) | ~spl307_55),
  inference(avatar_component_clause,[],[f1758])).
thf(f1760,plain,(
  ~spl307_54 | spl307_55),
  inference(avatar_split_clause,[],[f985,f1758,f1754])).
thf(f1776,definition,(
  spl307_59 <=> (binintersectSubset2 = $true)),
  introduced(definition,[new_symbols(definition,[spl307_59])],[avatar_definition])).
thf(f2093,plain,(
  spl307_59),
  inference(avatar_split_clause,[],[f860,f1776])).
thf(f2152,definition,(
  spl307_143 <=> ! [X0 : $i] : (($true = ((in @ (sK55 @ X0) @ X0))) | (emptyset = X0))),
  introduced(definition,[new_symbols(definition,[spl307_143])],[avatar_definition])).
thf(f2153,plain,(
  ( ! [X0 : $i] : (($true = ((in @ (sK55 @ X0) @ X0))) | (emptyset = X0)) ) | ~spl307_143),
  inference(avatar_component_clause,[],[f2152])).
thf(f2155,definition,(
  spl307_144 <=> (noeltsimpempty = $true)),
  introduced(definition,[new_symbols(definition,[spl307_144])],[avatar_definition])).
thf(f2158,plain,(
  spl307_143 | ~spl307_144),
  inference(avatar_split_clause,[],[f1005,f2155,f2152])).
thf(f2465,definition,(
  spl307_211 <=> (binintersectER = $true)),
  introduced(definition,[new_symbols(definition,[spl307_211])],[avatar_definition])).
thf(f2565,plain,(
  spl307_144),
  inference(avatar_split_clause,[],[f845,f2155])).
thf(f2913,plain,(
  spl307_54),
  inference(avatar_split_clause,[],[f940,f1754])).
thf(f2973,definition,(
  spl307_321 <=> ! [X2 : $i,X3 : $i] : (($true != ((subset @ X2 @ X3))) | (((binintersect @ X2 @ X3)) = X2))),
  introduced(definition,[new_symbols(definition,[spl307_321])],[avatar_definition])).
thf(f2974,plain,(
  ( ! [X2 : $i,X3 : $i] : ((((binintersect @ X2 @ X3)) = X2) | ($true != ((subset @ X2 @ X3)))) ) | ~spl307_321),
  inference(avatar_component_clause,[],[f2973])).
thf(f2975,plain,(
  ~spl307_59 | spl307_321),
  inference(avatar_split_clause,[],[f973,f2973,f1776])).
thf(f3012,definition,(
  spl307_329 <=> ! [X4 : $i,X5 : $i,X3 : $i] : ((((in @ X5 @ (binintersect @ X3 @ X4))) != $true) | (((in @ X5 @ X4)) = $true))),
  introduced(definition,[new_symbols(definition,[spl307_329])],[avatar_definition])).
thf(f3013,plain,(
  ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ (binintersect @ X3 @ X4))) != $true) | (((in @ X5 @ X4)) = $true)) ) | ~spl307_329),
  inference(avatar_component_clause,[],[f3012])).
thf(f3014,plain,(
  ~spl307_211 | spl307_329),
  inference(avatar_split_clause,[],[f991,f3012,f2465])).
thf(f3494,plain,(
  spl307_211),
  inference(avatar_split_clause,[],[f879,f2465])).
thf(f3841,definition,(
  spl307_500 <=> (emptyset = ((binintersect @ sK9 @ sK8)))),
  introduced(definition,[new_symbols(definition,[spl307_500])],[avatar_definition])).
thf(f3843,plain,(
  (emptyset != ((binintersect @ sK9 @ sK8))) | spl307_500),
  inference(avatar_component_clause,[],[f3841])).
thf(f3844,plain,(
  ~spl307_500),
  inference(avatar_split_clause,[],[f901,f3841])).
thf(f4348,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK55 @ (binintersect @ X0 @ X1)) @ X1))) | ($true != $true) | (emptyset = ((binintersect @ X0 @ X1)))) ) | (~spl307_143 | ~spl307_329)),
  inference(superposition,[],[f3013,f2153])).
thf(f4356,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK55 @ (binintersect @ X0 @ X1)) @ X1))) | (emptyset = ((binintersect @ X0 @ X1)))) ) | (~spl307_143 | ~spl307_329)),
  inference(trivial_inequality_removal,[],[f4348])).
thf(f6733,plain,(
  ( ! [X0 : $i] : ((((in @ (sK55 @ (binintersect @ X0 @ sK9)) @ sK8)) != $true) | ($true != $true) | (emptyset = ((binintersect @ X0 @ sK9)))) ) | (~spl307_143 | ~spl307_329)),
  inference(superposition,[],[f900,f4356])).
thf(f6747,plain,(
  ( ! [X0 : $i] : ((((in @ (sK55 @ (binintersect @ X0 @ sK9)) @ sK8)) != $true) | (emptyset = ((binintersect @ X0 @ sK9)))) ) | (~spl307_143 | ~spl307_329)),
  inference(trivial_inequality_removal,[],[f6733])).
thf(f6807,plain,(
  ( ! [X0 : $i] : (($true != ((in @ (sK55 @ X0) @ sK8))) | (emptyset = X0) | ($true != ((subset @ X0 @ sK9)))) ) | (~spl307_143 | ~spl307_321 | ~spl307_329)),
  inference(superposition,[],[f6747,f2974])).
thf(f6844,plain,(
  ( ! [X0 : $i] : ((emptyset = ((binintersect @ X0 @ sK8))) | (emptyset = ((binintersect @ X0 @ sK8))) | ($true != ((subset @ (binintersect @ X0 @ sK8) @ sK9))) | ($true != $true)) ) | (~spl307_143 | ~spl307_321 | ~spl307_329)),
  inference(superposition,[],[f6807,f4356])).
thf(f6846,plain,(
  ( ! [X0 : $i] : (($true != ((subset @ (binintersect @ X0 @ sK8) @ sK9))) | ($true != $true) | (emptyset = ((binintersect @ X0 @ sK8)))) ) | (~spl307_143 | ~spl307_321 | ~spl307_329)),
  inference(duplicate_literal_removal,[],[f6844])).
thf(f6847,plain,(
  ( ! [X0 : $i] : (($true != ((subset @ (binintersect @ X0 @ sK8) @ sK9))) | (emptyset = ((binintersect @ X0 @ sK8)))) ) | (~spl307_143 | ~spl307_321 | ~spl307_329)),
  inference(trivial_inequality_removal,[],[f6846])).
thf(f8387,plain,(
  (emptyset = ((binintersect @ sK9 @ sK8))) | ($true != $true) | (~spl307_55 | ~spl307_143 | ~spl307_321 | ~spl307_329)),
  inference(superposition,[],[f6847,f1759])).
thf(f8394,plain,(
  (emptyset = ((binintersect @ sK9 @ sK8))) | (~spl307_55 | ~spl307_143 | ~spl307_321 | ~spl307_329)),
  inference(trivial_inequality_removal,[],[f8387])).
thf(f8395,plain,(
  $false | (~spl307_55 | ~spl307_143 | ~spl307_321 | ~spl307_329 | spl307_500)),
  inference(forward_subsumption_resolution,[],[f8394,f3843])).
thf(f8396,plain,(
  ~spl307_55 | ~spl307_143 | ~spl307_321 | ~spl307_329 | spl307_500),
  inference(avatar_contradiction_clause,[],[f8395])).
cnf(s28, plain, ~spl307_54 | spl307_55, inference(sat_conversion,[],[f1760])).
cnf(s82, plain, spl307_59, inference(sat_conversion,[],[f2093])).
cnf(s91, plain, spl307_143 | ~spl307_144, inference(sat_conversion,[],[f2158])).
cnf(s170, plain, spl307_144, inference(sat_conversion,[],[f2565])).
cnf(s247, plain, spl307_54, inference(sat_conversion,[],[f2913])).
cnf(s262, plain, ~spl307_59 | spl307_321, inference(sat_conversion,[],[f2975])).
cnf(s270, plain, ~spl307_211 | spl307_329, inference(sat_conversion,[],[f3014])).
cnf(s404, plain, spl307_211, inference(sat_conversion,[],[f3494])).
cnf(s493, plain, ~spl307_500, inference(sat_conversion,[],[f3844])).
cnf(s692, plain, ~spl307_55 | ~spl307_143 | ~spl307_321 | ~spl307_329 | spl307_500, inference(sat_conversion,[],[f8396])).
cnf(s732, plain, spl307_329, inference(rat,[],[s270,s404])).
cnf(s820, plain, spl307_143, inference(rat,[],[s91,s170])).
cnf(s827, plain, spl307_321, inference(rat,[],[s262,s82])).
cnf(s828, plain, ~spl307_55, inference(rat,[],[s692,s493,s732,s820,s827])).
cnf(s852, plain, $false, inference(rat,[],[s28,s828,s247])).
thf(f8397,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s852])).
% SZS output end Proof for theBenchmark