%----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_130, type, disjointsetsI1: $o).
thf(func_def_131, type, binintersectRsub: $o).
thf(func_def_132, type, binintersectSubset4: $o).
thf(func_def_133, type, binintersectSubset1: $o).
thf(func_def_134, type, bs114d: $o).
thf(func_def_135, type, regular: ($i > $o)).
thf(func_def_136, type, setminus: ($i > $i > $i)).
thf(func_def_137, type, setminusI: $o).
thf(func_def_138, type, setminusEL: $o).
thf(func_def_139, type, setminusER: $o).
thf(func_def_140, type, setminusSubset2: $o).
thf(func_def_141, type, setminusERneg: $o).
thf(func_def_142, type, setminusELneg: $o).
thf(func_def_143, type, setminusILneg: $o).
thf(func_def_144, type, setminusIRneg: $o).
thf(func_def_145, type, setminusLsub: $o).
thf(func_def_146, type, setminusSubset1: $o).
thf(func_def_147, type, symdiff: ($i > $i > $i)).
thf(func_def_148, type, symdiffE: $o).
thf(func_def_149, type, symdiffI1: $o).
thf(func_def_150, type, symdiffI2: $o).
thf(func_def_151, type, symdiffIneg1: $o).
thf(func_def_152, type, symdiffIneg2: $o).
thf(func_def_153, type, iskpair: ($i > $o)).
thf(func_def_154, type, secondinupair: $o).
thf(func_def_155, type, setukpairIL: $o).
thf(func_def_156, type, setukpairIR: $o).
thf(func_def_157, type, kpairiskpair: $o).
thf(func_def_158, type, kpair: ($i > $i > $i)).
thf(func_def_159, type, kpairp: $o).
thf(func_def_160, type, cartprod: ($i > $i > $i)).
thf(func_def_161, type, singletonsubset: $o).
thf(func_def_162, type, singletoninpowerset: $o).
thf(func_def_163, type, singletoninpowunion: $o).
thf(func_def_164, type, upairset2E: $o).
thf(func_def_165, type, upairsubunion: $o).
thf(func_def_166, type, upairinpowunion: $o).
thf(func_def_167, type, ubforcartprodlem1: $o).
thf(func_def_168, type, ubforcartprodlem2: $o).
thf(func_def_169, type, ubforcartprodlem3: $o).
thf(func_def_170, type, cartprodpairin: $o).
thf(func_def_171, type, cartprodmempair1: $o).
thf(func_def_172, type, cartprodmempair: $o).
thf(func_def_173, type, setunionE2: $o).
thf(func_def_174, type, setunionsingleton1: $o).
thf(func_def_175, type, setunionsingleton2: $o).
thf(func_def_176, type, setunionsingleton: $o).
thf(func_def_177, type, singleton: ($i > $o)).
thf(func_def_178, type, singletonprop: $o).
thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)).
thf(func_def_180, type, ex1E1: $o).
thf(func_def_181, type, ex1I: $o).
thf(func_def_182, type, ex1I2: $o).
thf(func_def_183, type, singletonsuniq: $o).
thf(func_def_184, type, atmost1p: ($i > $o)).
thf(func_def_185, type, atleast2p: ($i > $o)).
thf(func_def_186, type, atmost2p: ($i > $o)).
thf(func_def_187, type, upairsetp: ($i > $o)).
thf(func_def_188, type, setukpairinjL1: $o).
thf(func_def_189, type, kfstsingleton: $o).
thf(func_def_190, type, theprop: $o).
thf(func_def_191, type, kfst: ($i > $i)).
thf(func_def_192, type, kfstpairEq: $o).
thf(func_def_193, type, cartprodfstin: $o).
thf(func_def_194, type, setukpairinjL2: $o).
thf(func_def_195, type, setukpairinjL: $o).
thf(func_def_196, type, setukpairinjR11: $o).
thf(func_def_197, type, setukpairinjR12: $o).
thf(func_def_198, type, setukpairinjR1: $o).
thf(func_def_199, type, upairequniteq: $o).
thf(func_def_200, type, setukpairinjR2: $o).
thf(func_def_201, type, setukpairinjR: $o).
thf(func_def_202, type, ksndsingleton: $o).
thf(func_def_203, type, ksnd: ($i > $i)).
thf(func_def_204, type, ksndpairEq: $o).
thf(func_def_205, type, kpairsurjEq: $o).
thf(func_def_206, type, cartprodsndin: $o).
thf(func_def_207, type, cartprodpairmemEL: $o).
thf(func_def_208, type, cartprodpairmemER: $o).
thf(func_def_209, type, cartprodmempaircEq: $o).
thf(func_def_210, type, cartprodfstpairEq: $o).
thf(func_def_211, type, cartprodsndpairEq: $o).
thf(func_def_212, type, cartprodpairsurjEq: $o).
thf(func_def_213, type, breln: ($i > $i > $i > $o)).
thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
thf(func_def_215, type, dpsetconstrI: $o).
thf(func_def_216, type, dpsetconstrSub: $o).
thf(func_def_217, type, setOfPairsIsBReln: $o).
thf(func_def_218, type, dpsetconstrERa: $o).
thf(func_def_219, type, dpsetconstrEL1: $o).
thf(func_def_220, type, dpsetconstrEL2: $o).
thf(func_def_221, type, dpsetconstrER: $o).
thf(func_def_222, type, func: ($i > $i > $i > $o)).
thf(func_def_223, type, funcSet: ($i > $i > $i)).
thf(func_def_224, type, funcImageSingleton: $o).
thf(func_def_225, type, apProp: $o).
thf(func_def_226, type, ap: ($i > $i > $i > $i > $i)).
thf(func_def_227, type, app: $o).
thf(func_def_228, type, infuncsetfunc: $o).
thf(func_def_229, type, ap2p: $o).
thf(func_def_230, type, funcinfuncset: $o).
thf(func_def_231, type, lamProp: $o).
thf(func_def_232, type, lam: ($i > $i > ($i > $i) > $i)).
thf(func_def_233, type, lamp: $o).
thf(func_def_234, type, lam2p: $o).
thf(func_def_235, type, brelnall1: $o).
thf(func_def_236, type, brelnall2: $o).
thf(func_def_237, type, ex1E2: $o).
thf(func_def_238, type, funcGraphProp1: $o).
thf(func_def_239, type, funcGraphProp3: $o).
thf(func_def_240, type, funcGraphProp2: $o).
thf(func_def_241, type, funcextLem: $o).
thf(func_def_242, type, funcGraphProp4: $o).
thf(func_def_243, type, subbreln: $o).
thf(func_def_244, type, eqbreln: $o).
thf(func_def_245, type, funcext: $o).
thf(func_def_248, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_249, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_250, type, vNOT: ($o > $o)).
thf(func_def_251, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_252, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_253, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_254, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_255, type, vAND: ($o > $o > $o)).
thf(func_def_256, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_257, type, vIMP: ($o > $o > $o)).
thf(func_def_258, type, sP0: ($i > $i > $o)).
thf(func_def_259, type, sP1: ($i > $o)).
thf(func_def_260, type, sP2: ($i > $i > $o)).
thf(func_def_261, type, sP3: ($i > $i > $o)).
thf(func_def_262, type, sP4: $o).
thf(func_def_263, type, sP5: $o).
thf(func_def_264, type, sP6: ($o > $i > $i > $i > $o)).
thf(func_def_265, type, sP7: $o).
thf(func_def_266, type, sP8: $o).
thf(func_def_267, type, sP9: ($i > $i > $i > $i > $o)).
thf(func_def_268, type, sP10: $o).
thf(func_def_276, type, sK18: ($i > $i)).
thf(func_def_279, type, sK21: ($i > $o)).
thf(func_def_280, type, sK22: ($i > $o)).
thf(func_def_281, type, sK23: (($i > $o) > ($i > $o) > $i)).
thf(func_def_282, type, sK24: (($i > $o) > ($i > $o) > $i)).
thf(func_def_284, type, sK26: ($i > $i > $o)).
thf(func_def_288, type, sK30: $o).
thf(func_def_289, type, sK31: ($i > $o)).
thf(func_def_292, type, sK34: ($i > ($i > $o) > $i)).
thf(func_def_307, type, sK49: $o).
thf(func_def_308, type, sK50: ($i > ($i > $o) > $i)).
thf(func_def_309, type, sK51: ($i > $o)).
thf(func_def_313, type, sK55: ($i > $o)).
thf(func_def_315, type, sK57: (($i > $o) > $i)).
thf(func_def_316, type, sK58: ($i > $o)).
thf(func_def_317, type, sK59: ($i > $i)).
thf(func_def_342, type, sK84: ($i > $o)).
thf(func_def_350, type, sK92: ($i > $o)).
thf(func_def_352, type, sK94: (($i > $o) > $i)).
thf(func_def_353, type, sK95: (($i > $o) > $i)).
thf(func_def_377, type, sK119: ($i > ($i > $o) > $i)).
thf(func_def_378, type, sK120: ($i > $o)).
thf(func_def_388, type, sK130: ($i > $i > $o)).
thf(func_def_400, type, sK142: ($i > $o)).
thf(func_def_418, type, sK160: ($i > $i > $i)).
thf(func_def_425, type, sK167: $o).
thf(func_def_431, type, sK173: ($i > $i > $i)).
thf(func_def_432, type, sK174: ($i > $i > $i)).
thf(func_def_433, type, sK175: ($i > $i > $i)).
thf(func_def_434, type, sK176: ($i > $i > $i)).
thf(func_def_435, type, sK177: ($i > $i > $i)).
thf(func_def_436, type, sK178: ($i > $i > $i > $i)).
thf(func_def_437, type, sK179: ($i > $i)).
thf(func_def_438, type, sK180: ($i > $i)).
thf(func_def_439, type, sK181: ($i > $i)).
thf(func_def_440, type, sK182: ($i > $i)).
thf(func_def_441, type, sK183: ($i > $i > $i > $i)).
thf(func_def_442, type, sK184: ($i > $i > $i > $i)).
thf(func_def_443, type, sK185: ($i > $i > $i)).
thf(func_def_444, type, sK186: ($i > $i > $i)).
thf(func_def_445, type, sK187: ($i > $i > $i)).
thf(func_def_447, type, sK189: ($i > $i)).
thf(func_def_448, type, sK190: ($i > $i)).
thf(func_def_449, type, sK191: ($i > $i)).
thf(func_def_450, type, sK192: ($i > $o)).
thf(func_def_451, type, sK193: ($i > $o)).
thf(func_def_452, type, sK194: (($i > $o) > ($i > $o) > $i)).
thf(func_def_453, type, sK195: (($i > $o) > ($i > $o) > $i)).
thf(func_def_461, type, sK203: ($i > $o)).
thf(func_def_463, type, sK205: ($i > $i > $o)).
thf(func_def_464, type, sK206: ($i > $i)).
thf(func_def_465, type, sK207: ($i > $i)).
thf(func_def_466, type, sK208: (($i > $i > $o) > $i > $i)).
thf(func_def_467, type, sK209: ($i > ($i > $i > $o) > $i > $i)).
thf(func_def_468, type, sK210: (($i > $i > $o) > $i > $i)).
thf(func_def_477, type, sK219: ($i > $i > $o)).
thf(func_def_486, type, sK228: ($i > $o)).
thf(func_def_488, type, sK230: (($i > $o) > $i > $i > $i > $i)).
thf(func_def_489, type, sK231: (($i > $o) > $i > $i > $i > $i)).
thf(func_def_490, type, sK232: $o).
thf(func_def_498, type, sK240: ($i > $i > $i > $i)).
thf(func_def_499, type, sK241: ($i > $i > $i > $i)).
thf(func_def_506, type, sK248: ($i > ($i > $o) > $i)).
thf(func_def_507, type, sK249: ($i > $o)).
thf(func_def_509, type, sK251: ($i > $o)).
thf(func_def_512, type, sK254: ($i > $o)).
thf(func_def_514, type, sK256: (($i > $o) > $i > $i)).
thf(func_def_525, type, sK267: ($i > $o)).
thf(func_def_528, type, sK270: ($i > ($i > $o) > $i)).
thf(func_def_529, type, sK271: ($i > ($i > $o) > $i)).
thf(func_def_530, type, sK272: ($i > $o)).
thf(func_def_536, type, sK278: $o).
thf(func_def_547, type, sK289: (($i > $o) > $i > $i)).
thf(func_def_549, type, sK291: ($i > $o)).
thf(func_def_560, type, sK302: ($i > $o)).
thf(func_def_561, type, sK303: ($i > $i)).
thf(func_def_564, type, sK306: ($i > $i > ($i > $i) > $i)).
thf(func_def_565, type, sK307: ($i > $i)).
thf(func_def_567, type, sK309: ($i > $i)).
thf(func_def_572, type, sK314: ($i > $o)).
thf(func_def_577, type, sK319: (($i > $o) > $i)).
thf(func_def_578, type, sK320: ($i > $o)).
thf(func_def_581, type, sK323: ($i > $i > $i)).
thf(func_def_584, type, sK326: ($i > $i > ($i > $o) > $i)).
thf(func_def_585, type, sK327: ($i > $o)).
thf(func_def_594, type, sK336: ($i > $i)).
thf(func_def_604, type, sK346: ($i > $o)).
thf(func_def_610, type, sK352: ($i > $i)).
thf(func_def_613, type, sK355: ($i > $i > $i)).
thf(func_def_619, type, sK361: ($i > $i > $i)).
thf(func_def_620, type, sK362: ($i > $o)).
thf(func_def_623, type, sK365: ($i > ($i > $o) > $i)).
thf(func_def_625, type, sK367: ($i > $i)).
thf(func_def_627, type, sK369: ($i > $i)).
thf(func_def_628, type, sK370: ($i > $o)).
thf(func_def_631, type, sK373: ($i > ($i > $o) > $i)).
thf(func_def_632, type, sK374: ($i > ($i > $o) > $i)).
thf(func_def_637, type, sK379: ($i > $o)).
thf(func_def_638, type, sK380: (($i > $o) > $i > $i)).
thf(func_def_642, type, sK384: ($i > $o)).
thf(func_def_648, type, sK390: ($i > $i > $i > $i > $i)).
thf(func_def_665, type, sK407: $o).
thf(func_def_669, type, sK411: ($i > $i > $o)).
thf(func_def_684, type, sK426: ($i > $o)).
thf(func_def_685, type, sK427: ($i > $o)).
thf(func_def_686, type, sK428: (($i > $o) > ($i > $o) > $i > $i > $i)).
thf(func_def_687, type, sK429: (($i > $o) > ($i > $o) > $i > $i > $i)).
thf(func_def_695, type, sK437: (($i > $o) > $i > $i)).
thf(func_def_697, type, sK439: ($i > $o)).
thf(func_def_728, type, sK470: ($i > $i > $o)).
thf(func_def_729, type, sK471: ($i > $o)).
thf(func_def_730, type, sK472: ($i > $i)).
thf(func_def_731, type, sK473: (($i > $o) > $i)).
thf(func_def_740, type, sK482: $o).
thf(func_def_744, type, sK486: ($i > $o)).
thf(func_def_749, type, sK491: ($i > $i > $o)).
thf(func_def_755, type, sK497: (($i > $i) > $i > $i > $i)).
thf(func_def_758, type, sK500: ($i > $i)).
thf(func_def_761, type, sK503: ($i > $i > $i)).
thf(func_def_776, type, sK518: ($i > $i > $i > $i > $i)).
thf(func_def_780, type, sK522: ($i > $o)).
thf(func_def_782, type, sK524: (($i > $o) > $i > $i > $i > $i)).
thf(func_def_783, type, sK525: (($i > $o) > $i > $i > $i > $i)).
thf(func_def_786, type, sK528: ($i > $i > $i)).
thf(func_def_787, type, sK529: ($i > $i > $i)).
thf(func_def_813, type, sK555: ($i > $o)).
thf(func_def_815, type, sK557: ($i > ($i > $i) > $i > $i)).
thf(func_def_817, type, sK559: ($i > $i)).
thf(func_def_824, type, sK566: ($i > $i > $i > $i > $i)).
thf(func_def_825, type, sK567: ($i > $i > $i > $i > $i)).
thf(func_def_826, type, sK568: ($i > $i > $i > $i > $i)).
thf(func_def_827, type, sK569: ($i > $i > $i > $i > $i)).
thf(func_def_834, type, sK576: ($i > $i > $o)).
thf(func_def_856, type, sK598: ($i > $i > $i)).
thf(func_def_865, type, sK607: ($i > $i > $i)).
thf(func_def_875, type, sK617: ($i > $o)).
thf(func_def_882, type, sK624: ($i > $i > $i > $i > $i)).
thf(func_def_883, type, sK625: ($i > $i > $i > $i > $i)).
thf(func_def_891, type, sK633: ($i > $i > $i)).
thf(func_def_892, type, sK634: ($o > $i > $i > $i)).
thf(func_def_895, type, sK637: $o).
thf(f197,axiom,(
  (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (func @ X0 @ X1 @ X2)) = infuncsetfunc)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc)).
thf(f214,axiom,(
  (funcext = ! [X1 : $i,X0 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((func @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => (((ap @ X0 @ X1 @ X2 @ X4)) = ((ap @ X0 @ X1 @ X3 @ X4)))) => (X2 = X3)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext)).
thf(f215,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 => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ (funcSet @ X0 @ X1)) => (! [X4 : $i] : ((in @ X4 @ X0) => (((ap @ X0 @ X1 @ X2 @ X4)) = ((ap @ X0 @ X1 @ X3 @ X4)))) => (X2 = X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2)).
thf(f216,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 => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ (funcSet @ X0 @ X1)) => (! [X4 : $i] : ((in @ X4 @ X0) => (((ap @ X0 @ X1 @ X2 @ X4)) = ((ap @ X0 @ X1 @ X3 @ X4)))) => (X2 = X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(negated_conjecture,[status(cth)],[f215])).
thf(f463,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 => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X1 @ X0)) => ! [X3 : $i] : ((in @ X3 @ (funcSet @ X1 @ X0)) => (! [X4 : $i] : ((in @ X4 @ X1) => (((ap @ X1 @ X0 @ X2 @ X4)) = ((ap @ X1 @ X0 @ X3 @ X4)))) => (X2 = X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(rectify,[],[f216])).
thf(f464,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) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X2 @ (funcSet @ X1 @ X0))) = $true) => ! [X3 : $i] : (($true = ((in @ X3 @ (funcSet @ X1 @ X0)))) => (! [X4 : $i] : ((((in @ X4 @ X1)) = $true) => (((ap @ X1 @ X0 @ X2 @ X4)) = ((ap @ X1 @ X0 @ X3 @ X4)))) => (X2 = X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(fool_elimination,[],[f463])).
thf(f475,plain,(
  (funcext = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X0 @ X2) => ! [X3 : $i] : ((func @ X1 @ X0 @ X3) => (! [X4 : $i] : ((in @ X4 @ X1) => (((ap @ X1 @ X0 @ X2 @ X4)) = ((ap @ X1 @ X0 @ X3 @ X4)))) => (X2 = X3)))))),
  inference(rectify,[],[f214])).
thf(f476,plain,(
  (funcext = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true = ((func @ X1 @ X0 @ X2))) => ! [X3 : $i] : ((((func @ X1 @ X0 @ X3)) = $true) => (! [X4 : $i] : ((((in @ X4 @ X1)) = $true) => (((ap @ X1 @ X0 @ X2 @ X4)) = ((ap @ X1 @ X0 @ X3 @ X4)))) => (X2 = X3))))),
  inference(fool_elimination,[],[f475])).
thf(f517,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X2 @ X0)) => (func @ X2 @ X0 @ X1)) = infuncsetfunc)),
  inference(rectify,[],[f197])).
thf(f518,plain,(
  (infuncsetfunc = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (funcSet @ X2 @ X0))) = $true) => ($true = ((func @ X2 @ X0 @ X1))))),
  inference(fool_elimination,[],[f517])).
thf(f686,plain,(
  (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X2 : $i,X1 : $i,X0 : $i] : (? [X3 : $i] : (((X2 != X3) & ! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | (((ap @ X1 @ X0 @ X2 @ X4)) = ((ap @ X1 @ X0 @ X3 @ X4))))) & ($true = ((in @ X3 @ (funcSet @ X1 @ X0))))) & (((in @ X2 @ (funcSet @ X1 @ X0))) = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $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,[],[f464])).
thf(f687,plain,(
  (kfstpairEq = $true) & (setadjoinSub = $true) & (notinemptyset = $true) & (funcGraphProp4 = $true) & (subsetTrans = $true) & (setextAx = $true) & (emptysetsubset = $true) & (setminusSubset1 = $true) & (lamProp = $true) & (descrp = $true) & (apProp = $true) & (binintersectI = $true) & (emptysetimpfalse = $true) & (upairsubunion = $true) & (upairinpowunion = $true) & (brelnall1 = $true) & (setadjoin__Cong = $true) & (powersetsubset = $true) & (binintersectLsub = $true) & (uniqinunit = $true) & (notequalI2 = $true) & (kpairp = $true) & (singletonsuniq = $true) & (setunionsingleton2 = $true) & (exuI2 = $true) & (cartprodsndin = $true) & (inPowerset = $true) & (emptyInPowerset = $true) & (upairset2E = $true) & (upairsetIL = $true) & (dpsetconstrSub = $true) & (binunionIL = $true) & (dsetconstrEL = $true) & (cartprodmempair = $true) & (ubforcartprodlem2 = $true) & (lamp = $true) & (symdiffI1 = $true) & (setminusELneg = $true) & (emptyset__Cong = $true) & (subsetI1 = $true) & (setOfPairsIsBReln = $true) & (upairsetE = $true) & (upairequniteq = $true) & (powersetI1 = $true) & (setunionAx = $true) & (upairsetIR = $true) & (cartprodmempair1 = $true) & (notequalI1 = $true) & (inCongP = $true) & (powerset__Cong = $true) & (ex1E1 = $true) & (descr__Cong = $true) & (binintersectSubset5 = $true) & (powersetI = $true) & (setminusI = $true) & (binunionE = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (binunionIR = $true) & (funcext = $true) & (exuI1 = $true) & (ex1I = $true) & (quantDeMorgan4 = $true) & (cartprodmempaircEq = $true) & (kpairiskpair = $true) & (lam2p = $true) & (cartprodpairmemEL = $true) & (subsetE2 = $true) & (dsetconstrI = $true) & (exuEu = $true) & (subbreln = $true) & (sepInPowerset = $true) & (exuE3u = $true) & (dpsetconstrER = $true) & (exuE2 = $true) & (setadjoinIR = $true) & (exu__Cong = $true) & (binunionRsub = $true) & (binintersectRsub = $true) & (dpsetconstrERa = $true) & (setukpairinjR12 = $true) & (setbeta = $true) & (setunionE2 = $true) & (setunionsingleton = $true) & (setextsub = $true) & (setukpairIL = $true) & (singletonsswitch = $true) & (dsetconstrER = $true) & (ksndpairEq = $true) & (setadjoinE = $true) & (setukpairinjL1 = $true) & (ex1I2 = $true) & (setunionsingleton1 = $true) & (in__Cong = $true) & (singletoninpowunion = $true) & (setminusIRneg = $true) & (funcImageSingleton = $true) & (powersetE = $true) & (omegaSAx = $true) & (notdallE = $true) & (quantDeMorgan3 = $true) & (ap2p = $true) & (secondinupair = $true) & (nonemptyImpWitness = $true) & (eqimpsubset2 = $true) & (wellorderingAx = $true) & (setadjoinSub2 = $true) & (funcGraphProp1 = $true) & (setukpairinjR1 = $true) & (kpairsurjEq = $true) & (setukpairinjR2 = $true) & (vacuousDall = $true) & (setunionI = $true) & (setukpairinjL = $true) & (emptysetAx = $true) & (cartprodfstin = $true) & (cartprodsndpairEq = $true) & (eqinunit = $true) & (symdiffIneg1 = $true) & (notinsingleton = $true) & (cartprodfstpairEq = $true) & (binunionLsub = $true) & (binunionEcases = $true) & (ubforcartprodlem1 = $true) & (exuE3e = $true) & (quantDeMorgan1 = $true) & (binintersectSubset2 = $true) & (emptyI = $true) & (infuncsetfunc = $true) & (singletonsubset = $true) & (ex1E2 = $true) & (emptyinPowerset = $true) & (exuE1 = $true) & (prop2set2propI = $true) & (ksndsingleton = $true) & (foundationAx = $true) & (exuI3 = $true) & (cartprodpairin = $true) & (omega0Ax = $true) & (binintersectSubset4 = $true) & (brelnall2 = $true) & (funcGraphProp3 = $true) & (dpsetconstrEL1 = $true) & (prop2setI = $true) & (dpsetconstrEL2 = $true) & (setadjoinAx = $true) & (setoftrueEq = $true) & (eqbreln = $true) & (setukpairinjL2 = $true) & (setadjoinIL = $true) & (noeltsimpempty = $true) & (funcextLem = $true) & (setminusERneg = $true) & (symdiffIneg2 = $true) & (setunion__Cong = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (funcSet @ X1 @ X0))) = $true) & ? [X3 : $i] : (! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | (((ap @ X1 @ X0 @ X2 @ X4)) = ((ap @ X1 @ X0 @ X3 @ X4)))) & (X2 != X3) & ($true = ((in @ X3 @ (funcSet @ X1 @ X0)))))) & (setadjoinOr = $true) & (subsetRefl = $true) & (dsetconstr__Cong = $true) & (setext = $true) & (setminusLsub = $true) & (setminusSubset2 = $true) & (notsubsetI = $true) & (funcGraphProp2 = $true) & (bs114d = $true) & (setukpairinjR = $true) & (setminusILneg = $true) & (powersetAx = $true) & (symdiffE = $true) & (emptyE1 = $true) & (upairset2IR = $true) & (singletoninpowerset = $true) & (subsetI2 = $true) & (ubforcartprodlem3 = $true) & (emptyinunitempty = $true) & (nonemptyE1 = $true) & (subPowSU = $true) & (binintersectSubset3 = $true) & (setminusEL = $true) & (subsetE = $true) & (binintersectEL = $true) & (nonemptyI1 = $true) & (setukpairinjR11 = $true) & (singletonprop = $true) & (setunionE = $true) & (binintersectSubset1 = $true) & (subset2powerset = $true) & (kfstsingleton = $true) & (disjointsetsI1 = $true) & (omega__Cong = $true) & (replAx = $true) & (cartprodpairmemER = $true) & (emptysetE = $true) & (app = $true) & (prop2setE = $true) & (nonemptyI = $true) & (theprop = $true) & (subsetemptysetimpeq = $true) & (symdiffI2 = $true) & (notdexE = $true) & (sepSubset = $true) & (powersetE1 = $true) & (funcinfuncset = $true) & (setminusER = $true) & (setukpairIR = $true) & (omegaIndAx = $true) & (eqimpsubset1 = $true) & (quantDeMorgan2 = $true) & (binintersectER = $true)),
  inference(flattening,[],[f686])).
thf(f761,plain,(
  ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ (funcSet @ X2 @ X0))) != $true) | ($true = ((func @ X2 @ X0 @ X1)))) <=> (infuncsetfunc = $true)),
  inference(ennf_transformation,[],[f518])).
thf(f795,plain,(
  (funcext = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (! [X3 : $i] : (((X2 = X3) | ? [X4 : $i] : ((((ap @ X1 @ X0 @ X2 @ X4)) != ((ap @ X1 @ X0 @ X3 @ X4))) & (((in @ X4 @ X1)) = $true))) | (((func @ X1 @ X0 @ X3)) != $true)) | ($true != ((func @ X1 @ X0 @ X2))))),
  inference(ennf_transformation,[],[f476])).
thf(f796,plain,(
  (funcext = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (! [X3 : $i] : ((X2 = X3) | ? [X4 : $i] : ((((ap @ X1 @ X0 @ X2 @ X4)) != ((ap @ X1 @ X0 @ X3 @ X4))) & (((in @ X4 @ X1)) = $true)) | (((func @ X1 @ X0 @ X3)) != $true)) | ($true != ((func @ X1 @ X0 @ X2))))),
  inference(flattening,[],[f795])).
thf(f1284,plain,(
  ((funcext = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (? [X3 : $i] : ((X2 != X3) & ! [X4 : $i] : ((((ap @ X1 @ X0 @ X2 @ X4)) = ((ap @ X1 @ X0 @ X3 @ X4))) | (((in @ X4 @ X1)) != $true)) & (((func @ X1 @ X0 @ X3)) = $true)) & ($true = ((func @ X1 @ X0 @ X2))))) & (! [X2 : $i,X1 : $i,X0 : $i] : (! [X3 : $i] : ((X2 = X3) | ? [X4 : $i] : ((((ap @ X1 @ X0 @ X2 @ X4)) != ((ap @ X1 @ X0 @ X3 @ X4))) & (((in @ X4 @ X1)) = $true)) | (((func @ X1 @ X0 @ X3)) != $true)) | ($true != ((func @ X1 @ X0 @ X2)))) | (funcext != $true))),
  inference(nnf_transformation,[],[f796])).
thf(f1285,plain,(
  ((funcext = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((X0 != X3) & ! [X4 : $i] : ((((ap @ X1 @ X2 @ X3 @ X4)) = ((ap @ X1 @ X2 @ X0 @ X4))) | (((in @ X4 @ X1)) != $true)) & (((func @ X1 @ X2 @ X3)) = $true)) & ($true = ((func @ X1 @ X2 @ X0))))) & (! [X5 : $i,X6 : $i,X7 : $i] : (! [X8 : $i] : ((X5 = X8) | ? [X9 : $i] : ((((ap @ X6 @ X7 @ X8 @ X9)) != ((ap @ X6 @ X7 @ X5 @ X9))) & (((in @ X9 @ X6)) = $true)) | (((func @ X6 @ X7 @ X8)) != $true)) | ($true != ((func @ X6 @ X7 @ X5)))) | (funcext != $true))),
  inference(rectify,[],[f1284])).
thf(f1286,plain,(
  ((funcext = $true) | (((sK389 != sK386) & ! [X4 : $i] : ((((ap @ sK387 @ sK388 @ sK389 @ X4)) = ((ap @ sK387 @ sK388 @ sK386 @ X4))) | (((in @ X4 @ sK387)) != $true)) & (((func @ sK387 @ sK388 @ sK389)) = $true)) & (((func @ sK387 @ sK388 @ sK386)) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i] : (! [X8 : $i] : ((X5 = X8) | ((((ap @ X6 @ X7 @ X8 @ (sK390 @ X8 @ X7 @ X6 @ X5))) != ((ap @ X6 @ X7 @ X5 @ (sK390 @ X8 @ X7 @ X6 @ X5)))) & (((in @ (sK390 @ X8 @ X7 @ X6 @ X5) @ X6)) = $true)) | (((func @ X6 @ X7 @ X8)) != $true)) | ($true != ((func @ X6 @ X7 @ X5)))) | (funcext != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK386,sK387,sK388,sK389,vAPP]),skolemize(X0,$thf(sK386)),skolemize(X1,$thf(sK387)),skolemize(X2,$thf(sK388)),skolemize(X3,$thf(sK389)),skolemize(X3,$thf(sK18 @ X2))],[f1285])).
thf(f1308,plain,(
  (! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ (funcSet @ X2 @ X0))) != $true) | ($true = ((func @ X2 @ X0 @ X1)))) | (infuncsetfunc != $true)) & ((infuncsetfunc = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ (funcSet @ X2 @ X0))) = $true) & ($true != ((func @ X2 @ X0 @ X1)))))),
  inference(nnf_transformation,[],[f761])).
thf(f1309,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (funcSet @ X2 @ X1))) != $true) | (((func @ X2 @ X1 @ X0)) = $true)) | (infuncsetfunc != $true)) & ((infuncsetfunc = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ (funcSet @ X5 @ X4))) = $true) & (((func @ X5 @ X4 @ X3)) != $true)))),
  inference(rectify,[],[f1308])).
thf(f1310,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (funcSet @ X2 @ X1))) != $true) | (((func @ X2 @ X1 @ X0)) = $true)) | (infuncsetfunc != $true)) & ((infuncsetfunc = $true) | ((((in @ sK408 @ (funcSet @ sK410 @ sK409))) = $true) & (((func @ sK410 @ sK409 @ sK408)) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK408,sK409,sK410]),skolemize(X3,$thf(sK408)),skolemize(X4,$thf(sK409)),skolemize(X5,$thf(sK410))],[f1309])).
thf(f1516,plain,(
  (kfstpairEq = $true) & (setadjoinSub = $true) & (notinemptyset = $true) & (funcGraphProp4 = $true) & (subsetTrans = $true) & (setextAx = $true) & (emptysetsubset = $true) & (setminusSubset1 = $true) & (lamProp = $true) & (descrp = $true) & (apProp = $true) & (binintersectI = $true) & (emptysetimpfalse = $true) & (upairsubunion = $true) & (upairinpowunion = $true) & (brelnall1 = $true) & (setadjoin__Cong = $true) & (powersetsubset = $true) & (binintersectLsub = $true) & (uniqinunit = $true) & (notequalI2 = $true) & (kpairp = $true) & (singletonsuniq = $true) & (setunionsingleton2 = $true) & (exuI2 = $true) & (cartprodsndin = $true) & (inPowerset = $true) & (emptyInPowerset = $true) & (upairset2E = $true) & (upairsetIL = $true) & (dpsetconstrSub = $true) & (binunionIL = $true) & (dsetconstrEL = $true) & (cartprodmempair = $true) & (ubforcartprodlem2 = $true) & (lamp = $true) & (symdiffI1 = $true) & (setminusELneg = $true) & (emptyset__Cong = $true) & (subsetI1 = $true) & (setOfPairsIsBReln = $true) & (upairsetE = $true) & (upairequniteq = $true) & (powersetI1 = $true) & (setunionAx = $true) & (upairsetIR = $true) & (cartprodmempair1 = $true) & (notequalI1 = $true) & (inCongP = $true) & (powerset__Cong = $true) & (ex1E1 = $true) & (descr__Cong = $true) & (binintersectSubset5 = $true) & (powersetI = $true) & (setminusI = $true) & (binunionE = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (binunionIR = $true) & (funcext = $true) & (exuI1 = $true) & (ex1I = $true) & (quantDeMorgan4 = $true) & (cartprodmempaircEq = $true) & (kpairiskpair = $true) & (lam2p = $true) & (cartprodpairmemEL = $true) & (subsetE2 = $true) & (dsetconstrI = $true) & (exuEu = $true) & (subbreln = $true) & (sepInPowerset = $true) & (exuE3u = $true) & (dpsetconstrER = $true) & (exuE2 = $true) & (setadjoinIR = $true) & (exu__Cong = $true) & (binunionRsub = $true) & (binintersectRsub = $true) & (dpsetconstrERa = $true) & (setukpairinjR12 = $true) & (setbeta = $true) & (setunionE2 = $true) & (setunionsingleton = $true) & (setextsub = $true) & (setukpairIL = $true) & (singletonsswitch = $true) & (dsetconstrER = $true) & (ksndpairEq = $true) & (setadjoinE = $true) & (setukpairinjL1 = $true) & (ex1I2 = $true) & (setunionsingleton1 = $true) & (in__Cong = $true) & (singletoninpowunion = $true) & (setminusIRneg = $true) & (funcImageSingleton = $true) & (powersetE = $true) & (omegaSAx = $true) & (notdallE = $true) & (quantDeMorgan3 = $true) & (ap2p = $true) & (secondinupair = $true) & (nonemptyImpWitness = $true) & (eqimpsubset2 = $true) & (wellorderingAx = $true) & (setadjoinSub2 = $true) & (funcGraphProp1 = $true) & (setukpairinjR1 = $true) & (kpairsurjEq = $true) & (setukpairinjR2 = $true) & (vacuousDall = $true) & (setunionI = $true) & (setukpairinjL = $true) & (emptysetAx = $true) & (cartprodfstin = $true) & (cartprodsndpairEq = $true) & (eqinunit = $true) & (symdiffIneg1 = $true) & (notinsingleton = $true) & (cartprodfstpairEq = $true) & (binunionLsub = $true) & (binunionEcases = $true) & (ubforcartprodlem1 = $true) & (exuE3e = $true) & (quantDeMorgan1 = $true) & (binintersectSubset2 = $true) & (emptyI = $true) & (infuncsetfunc = $true) & (singletonsubset = $true) & (ex1E2 = $true) & (emptyinPowerset = $true) & (exuE1 = $true) & (prop2set2propI = $true) & (ksndsingleton = $true) & (foundationAx = $true) & (exuI3 = $true) & (cartprodpairin = $true) & (omega0Ax = $true) & (binintersectSubset4 = $true) & (brelnall2 = $true) & (funcGraphProp3 = $true) & (dpsetconstrEL1 = $true) & (prop2setI = $true) & (dpsetconstrEL2 = $true) & (setadjoinAx = $true) & (setoftrueEq = $true) & (eqbreln = $true) & (setukpairinjL2 = $true) & (setadjoinIL = $true) & (noeltsimpempty = $true) & (funcextLem = $true) & (setminusERneg = $true) & (symdiffIneg2 = $true) & (setunion__Cong = $true) & ((((in @ sK603 @ (funcSet @ sK602 @ sK601))) = $true) & (! [X4 : $i] : (($true != ((in @ X4 @ sK602))) | (((ap @ sK602 @ sK601 @ sK603 @ X4)) = ((ap @ sK602 @ sK601 @ sK604 @ X4)))) & (sK604 != sK603) & (((in @ sK604 @ (funcSet @ sK602 @ sK601))) = $true))) & (setadjoinOr = $true) & (subsetRefl = $true) & (dsetconstr__Cong = $true) & (setext = $true) & (setminusLsub = $true) & (setminusSubset2 = $true) & (notsubsetI = $true) & (funcGraphProp2 = $true) & (bs114d = $true) & (setukpairinjR = $true) & (setminusILneg = $true) & (powersetAx = $true) & (symdiffE = $true) & (emptyE1 = $true) & (upairset2IR = $true) & (singletoninpowerset = $true) & (subsetI2 = $true) & (ubforcartprodlem3 = $true) & (emptyinunitempty = $true) & (nonemptyE1 = $true) & (subPowSU = $true) & (binintersectSubset3 = $true) & (setminusEL = $true) & (subsetE = $true) & (binintersectEL = $true) & (nonemptyI1 = $true) & (setukpairinjR11 = $true) & (singletonprop = $true) & (setunionE = $true) & (binintersectSubset1 = $true) & (subset2powerset = $true) & (kfstsingleton = $true) & (disjointsetsI1 = $true) & (omega__Cong = $true) & (replAx = $true) & (cartprodpairmemER = $true) & (emptysetE = $true) & (app = $true) & (prop2setE = $true) & (nonemptyI = $true) & (theprop = $true) & (subsetemptysetimpeq = $true) & (symdiffI2 = $true) & (notdexE = $true) & (sepSubset = $true) & (powersetE1 = $true) & (funcinfuncset = $true) & (setminusER = $true) & (setukpairIR = $true) & (omegaIndAx = $true) & (eqimpsubset1 = $true) & (quantDeMorgan2 = $true) & (binintersectER = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK601,sK602,sK603,sK604]),skolemize(X0,$thf(sK601)),skolemize(X1,$thf(sK602)),skolemize(X2,$thf(sK603)),skolemize(X3,$thf(sK604))],[f687])).
thf(f2058,plain,(
  ( ! [X8 : $i,X6 : $i,X7 : $i,X5 : $i] : ((((in @ (sK390 @ X8 @ X7 @ X6 @ X5) @ X6)) = $true) | (X5 = X8) | (((func @ X6 @ X7 @ X8)) != $true) | (funcext != $true) | ($true != ((func @ X6 @ X7 @ X5)))) )),
  inference(cnf_transformation,[],[f1286])).
thf(f2059,plain,(
  ( ! [X8 : $i,X6 : $i,X7 : $i,X5 : $i] : ((((ap @ X6 @ X7 @ X8 @ (sK390 @ X8 @ X7 @ X6 @ X5))) != ((ap @ X6 @ X7 @ X5 @ (sK390 @ X8 @ X7 @ X6 @ X5)))) | (X5 = X8) | ($true != ((func @ X6 @ X7 @ X5))) | (funcext != $true) | (((func @ X6 @ X7 @ X8)) != $true)) )),
  inference(cnf_transformation,[],[f1286])).
thf(f2092,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (funcSet @ X2 @ X1))) != $true) | (((func @ X2 @ X1 @ X0)) = $true) | (infuncsetfunc != $true)) )),
  inference(cnf_transformation,[],[f1310])).
thf(f2392,plain,(
  (((in @ sK604 @ (funcSet @ sK602 @ sK601))) = $true)),
  inference(cnf_transformation,[],[f1516])).
thf(f2393,plain,(
  (sK604 != sK603)),
  inference(cnf_transformation,[],[f1516])).
thf(f2394,plain,(
  ( ! [X4 : $i] : ((((ap @ sK602 @ sK601 @ sK603 @ X4)) = ((ap @ sK602 @ sK601 @ sK604 @ X4))) | ($true != ((in @ X4 @ sK602)))) )),
  inference(cnf_transformation,[],[f1516])).
thf(f2395,plain,(
  (((in @ sK603 @ (funcSet @ sK602 @ sK601))) = $true)),
  inference(cnf_transformation,[],[f1516])).
thf(f2422,plain,(
  (infuncsetfunc = $true)),
  inference(cnf_transformation,[],[f1516])).
thf(f2491,plain,(
  (funcext = $true)),
  inference(cnf_transformation,[],[f1516])).
thf(f2744,plain,(
  (((func @ sK602 @ sK601 @ sK604)) = $true) | ($true != $true) | (infuncsetfunc != $true)),
  inference(constrained_superposition,[],[f2092,f2392])).
thf(f2746,plain,(
  (((func @ sK602 @ sK601 @ sK604)) = $true) | (infuncsetfunc != $true)),
  inference(trivial_inequality_removal,[],[f2744])).
thf(f2748,plain,(
  (((func @ sK602 @ sK601 @ sK604)) = $true)),
  inference(forward_subsumption_resolution,[],[f2746,f2422])).
thf(f2750,plain,(
  (infuncsetfunc != $true) | ($true != $true) | (((func @ sK602 @ sK601 @ sK603)) = $true)),
  inference(constrained_superposition,[],[f2092,f2395])).
thf(f2753,plain,(
  (infuncsetfunc != $true) | (((func @ sK602 @ sK601 @ sK603)) = $true)),
  inference(trivial_inequality_removal,[],[f2750])).
thf(f2754,plain,(
  (((func @ sK602 @ sK601 @ sK603)) = $true)),
  inference(forward_subsumption_resolution,[],[f2753,f2422])).
thf(f2766,plain,(
  ( ! [X0 : $i] : ((((ap @ sK602 @ sK601 @ X0 @ (sK390 @ X0 @ sK601 @ sK602 @ sK603))) != ((ap @ sK602 @ sK601 @ sK604 @ (sK390 @ X0 @ sK601 @ sK602 @ sK603)))) | (((func @ sK602 @ sK601 @ sK603)) != $true) | (funcext != $true) | (((in @ (sK390 @ X0 @ sK601 @ sK602 @ sK603) @ sK602)) != $true) | (sK603 = X0) | ($true != ((func @ sK602 @ sK601 @ X0)))) )),
  inference(constrained_superposition,[],[f2059,f2394])).
thf(f2775,plain,(
  ( ! [X0 : $i] : ((funcext != $true) | (((ap @ sK602 @ sK601 @ X0 @ (sK390 @ X0 @ sK601 @ sK602 @ sK603))) != ((ap @ sK602 @ sK601 @ sK604 @ (sK390 @ X0 @ sK601 @ sK602 @ sK603)))) | ($true != ((func @ sK602 @ sK601 @ X0))) | (((func @ sK602 @ sK601 @ sK603)) != $true) | (sK603 = X0)) )),
  inference(forward_subsumption_resolution,[],[f2766,f2058])).
thf(f2787,plain,(
  ( ! [X0 : $i] : ((sK603 = X0) | (((func @ sK602 @ sK601 @ sK603)) != $true) | (((ap @ sK602 @ sK601 @ X0 @ (sK390 @ X0 @ sK601 @ sK602 @ sK603))) != ((ap @ sK602 @ sK601 @ sK604 @ (sK390 @ X0 @ sK601 @ sK602 @ sK603)))) | ($true != ((func @ sK602 @ sK601 @ X0)))) )),
  inference(forward_subsumption_resolution,[],[f2775,f2491])).
thf(f2809,plain,(
  ( ! [X0 : $i] : ((((ap @ sK602 @ sK601 @ X0 @ (sK390 @ X0 @ sK601 @ sK602 @ sK603))) != ((ap @ sK602 @ sK601 @ sK604 @ (sK390 @ X0 @ sK601 @ sK602 @ sK603)))) | ($true != ((func @ sK602 @ sK601 @ X0))) | (sK603 = X0)) )),
  inference(forward_subsumption_resolution,[],[f2787,f2754])).
thf(f3136,plain,(
  (((func @ sK602 @ sK601 @ sK604)) != $true) | (sK604 = sK603)),
  inference(equality_resolution,[],[f2809])).
thf(f3139,plain,(
  (sK604 = sK603)),
  inference(forward_subsumption_resolution,[],[f3136,f2748])).
thf(f3140,plain,(
  $false),
  inference(forward_subsumption_resolution,[],[f3139,f2393])).
% SZS output end Proof for theBenchmark