%----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_246, type, funcext2: $o).
thf(func_def_247, type, ap2apEq1: $o).
thf(func_def_248, type, ap2apEq2: $o).
thf(func_def_249, type, beta1: $o).
thf(func_def_250, type, eta1: $o).
thf(func_def_251, type, lam2lamEq: $o).
thf(func_def_252, type, beta2: $o).
thf(func_def_253, type, eta2: $o).
thf(func_def_254, type, iffalseProp1: $o).
thf(func_def_255, type, iffalseProp2: $o).
thf(func_def_256, type, iftrueProp1: $o).
thf(func_def_257, type, iftrueProp2: $o).
thf(func_def_258, type, ifSingleton: $o).
thf(func_def_259, type, if: ($i > $o > $i > $i > $i)).
thf(func_def_260, type, ifp: $o).
thf(func_def_261, type, theeq: $o).
thf(func_def_262, type, iftrue: $o).
thf(func_def_263, type, iffalse: $o).
thf(func_def_264, type, iftrueorfalse: $o).
thf(func_def_265, type, binintersectT_lem: $o).
thf(func_def_266, type, binunionT_lem: $o).
thf(func_def_267, type, powersetT_lem: $o).
thf(func_def_268, type, setminusT_lem: $o).
thf(func_def_269, type, complementT_lem: $o).
thf(func_def_270, type, setextT: $o).
thf(func_def_271, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_272, type, vAND: ($o > $o > $o)).
thf(func_def_273, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_274, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_275, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_276, type, vIMP: ($o > $o > $o)).
thf(func_def_277, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_278, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_279, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_282, type, vOR: ($o > $o > $o)).
thf(func_def_283, type, vNOT: ($o > $o)).
thf(func_def_284, type, sP0: ($i > $i > $o)).
thf(func_def_285, type, sP1: ($i > $o)).
thf(func_def_286, type, sP2: $o).
thf(func_def_287, type, sP3: $o).
thf(func_def_291, type, sK7: ($i > $i > $i > $i > $i)).
thf(func_def_292, type, sK8: ($i > $i > $i > $i > $i)).
thf(func_def_304, type, sK20: ($i > $i > ($i > $i) > $i)).
thf(func_def_305, type, sK21: ($i > $i)).
thf(func_def_308, type, sK24: ($i > $o)).
thf(func_def_311, type, sK27: $o).
thf(func_def_314, type, sK30: ($i > ($i > $o) > $i)).
thf(func_def_315, type, sK31: ($i > $o)).
thf(func_def_330, type, sK46: ($i > $o)).
thf(func_def_357, type, sK73: ($i > ($i > $o) > $i)).
thf(func_def_358, type, sK74: ($i > $o)).
thf(func_def_363, type, sK79: $o).
thf(func_def_370, type, sK86: $o).
thf(func_def_381, type, sK97: ($i > $i > $i)).
thf(func_def_386, type, sK102: (($i > $o) > $i > $i)).
thf(func_def_388, type, sK104: ($i > $o)).
thf(func_def_395, type, sK111: ($i > $i)).
thf(func_def_411, type, sK127: ($i > $o)).
thf(func_def_427, type, sK143: ($i > $o)).
thf(func_def_436, type, sK152: (($i > $o) > $i > $i > $i > $i)).
thf(func_def_437, type, sK153: (($i > $o) > $i > $i > $i > $i)).
thf(func_def_441, type, sK157: ($i > $o)).
thf(func_def_443, type, sK159: ($i > $i > $i > $i > $i)).
thf(func_def_448, type, sK164: ($i > $i)).
thf(func_def_453, type, sK169: ($i > $i)).
thf(func_def_455, type, sK171: ($i > $i)).
thf(func_def_456, type, sK172: ($i > ($i > $i) > $i > $i)).
thf(func_def_458, type, sK174: ($i > $i)).
thf(func_def_460, type, sK176: (($i > $o) > $i)).
thf(func_def_461, type, sK177: ($i > $o)).
thf(func_def_462, type, sK178: ($i > $i)).
thf(func_def_466, type, sK182: (($i > $i) > $i > $i > $i)).
thf(func_def_469, type, sK185: ($i > $i)).
thf(func_def_470, type, sK186: ($i > $i > $i)).
thf(func_def_479, type, sK195: ($i > $o)).
thf(func_def_483, type, sK199: ($i > $i > $o)).
thf(func_def_488, type, sK204: ($i > $o)).
thf(func_def_491, type, sK207: ($i > $i)).
thf(func_def_496, type, sK212: ($i > $i > $o)).
thf(func_def_511, type, sK227: $o).
thf(func_def_521, type, sK237: ($i > $o)).
thf(func_def_523, type, sK239: (($i > $o) > $i > $i)).
thf(func_def_535, type, sK251: ($i > $i > $i)).
thf(func_def_539, type, sK255: ($i > $i)).
thf(func_def_540, type, sK256: ($i > $i)).
thf(func_def_541, type, sK257: ($i > $i)).
thf(func_def_542, type, sK258: ($i > $i)).
thf(func_def_543, type, sK259: ($i > $i)).
thf(func_def_544, type, sK260: ($i > $i > $i > $i)).
thf(func_def_545, type, sK261: ($i > $i)).
thf(func_def_546, type, sK262: ($i > $i)).
thf(func_def_547, type, sK263: ($i > $i)).
thf(func_def_548, type, sK264: ($i > $i)).
thf(func_def_549, type, sK265: ($i > $i > $i)).
thf(func_def_550, type, sK266: ($i > $i > $i > $i)).
thf(func_def_551, type, sK267: ($i > $i > $i > $i)).
thf(func_def_552, type, sK268: ($i > $i > $i > $i)).
thf(func_def_553, type, sK269: ($i > $i > $i)).
thf(func_def_554, type, sK270: ($i > $i > $i)).
thf(func_def_555, type, sK271: ($i > $i > $i)).
thf(func_def_556, type, sK272: ($i > $i > $i)).
thf(func_def_565, type, sK281: $o).
thf(func_def_566, type, sK282: ($i > $i > $i)).
thf(func_def_569, type, sK285: ($i > $o)).
thf(func_def_577, type, sK293: ($i > $i > $o)).
thf(func_def_582, type, sK298: (($i > $o) > ($i > $o) > $i)).
thf(func_def_583, type, sK299: (($i > $o) > ($i > $o) > $i)).
thf(func_def_584, type, sK300: ($i > $o)).
thf(func_def_585, type, sK301: ($i > $o)).
thf(func_def_596, type, sK312: ($i > $i > $i)).
thf(func_def_598, type, sK314: ($i > $o)).
thf(func_def_600, type, sK316: (($i > $o) > $i > $i)).
thf(func_def_601, type, sK317: (($i > $o) > $i > $i)).
thf(func_def_604, type, sK320: $o).
thf(func_def_618, type, sK334: $o).
thf(func_def_631, type, sK347: ($i > $o)).
thf(func_def_632, type, sK348: (($i > $o) > $i > $i)).
thf(func_def_649, type, sK365: (($i > $o) > $i)).
thf(func_def_650, type, sK366: (($i > $o) > $i)).
thf(func_def_651, type, sK367: ($i > $o)).
thf(func_def_661, type, sK377: ($i > $o)).
thf(func_def_666, type, sK382: $o).
thf(func_def_670, type, sK386: ($i > $i > $o)).
thf(func_def_672, type, sK388: ($i > $i > $i)).
thf(func_def_677, type, sK393: $o).
thf(func_def_678, type, sK394: ($o > $i > $i > $i)).
thf(func_def_681, type, sK397: $o).
thf(func_def_688, type, sK404: (($i > $o) > ($i > $o) > $i > $i > $i)).
thf(func_def_689, type, sK405: (($i > $o) > ($i > $o) > $i > $i > $i)).
thf(func_def_692, type, sK408: ($i > $o)).
thf(func_def_693, type, sK409: ($i > $o)).
thf(func_def_697, type, sK413: ($i > $i > $i > $i)).
thf(func_def_698, type, sK414: ($i > $i > $i > $i)).
thf(func_def_712, type, sK428: ($i > $i > $i > $i > $i)).
thf(func_def_719, type, sK435: ($i > $i > $i)).
thf(func_def_726, type, sK442: $o).
thf(func_def_733, type, sK449: ($i > $i > $i > $i)).
thf(func_def_734, type, sK450: ($i > $i > $i > $i)).
thf(func_def_738, type, sK454: ($i > $i > $o)).
thf(func_def_748, type, sK464: $o).
thf(func_def_751, type, sK467: $o).
thf(func_def_753, type, sK469: ($i > $i > $i)).
thf(func_def_757, type, sK473: ($i > $o)).
thf(func_def_764, type, sK480: ($i > $o)).
thf(func_def_766, type, sK482: (($i > $o) > $i > $i > $i > $i)).
thf(func_def_767, type, sK483: (($i > $o) > $i > $i > $i > $i)).
thf(func_def_787, type, sK503: ($i > $o)).
thf(func_def_793, type, sK509: ($i > ($i > $o) > $i > $i)).
thf(func_def_795, type, sK511: ($i > $o)).
thf(func_def_797, type, sK513: ($i > ($i > $o) > $i)).
thf(func_def_798, type, sK514: ($i > $o)).
thf(func_def_807, type, sK523: (($i > $i) > $i > $i > $i)).
thf(func_def_810, type, sK526: ($i > $i)).
thf(func_def_812, type, sK528: ($i > $o)).
thf(func_def_816, type, sK532: ($i > $i > $o)).
thf(func_def_821, type, sK537: ($i > ($i > $o) > $i)).
thf(func_def_822, type, sK538: ($i > $o)).
thf(func_def_842, type, sK558: $o).
thf(func_def_844, type, sK560: ($i > $o)).
thf(func_def_856, type, sK572: ($i > $i > $o)).
thf(func_def_863, type, sK579: ($i > $i)).
thf(func_def_865, type, sK581: ($i > ($i > $i) > $i > $i)).
thf(func_def_875, type, sK591: (($i > $o) > $i)).
thf(func_def_876, type, sK592: ($i > $o)).
thf(func_def_877, type, sK593: ($i > $i)).
thf(func_def_884, type, sK600: ($i > $i > $i > $i > $i)).
thf(func_def_888, type, sK604: $o).
thf(func_def_894, type, sK610: ($i > $i > $i > $i > $i)).
thf(func_def_895, type, sK611: ($i > $i > $i > $i > $i)).
thf(func_def_896, type, sK612: ($i > $i > $i > $i > $i)).
thf(func_def_897, type, sK613: ($i > $i > $i > $i > $i)).
thf(func_def_900, type, sK616: ($i > $i)).
thf(func_def_903, type, sK619: ($i > ($i > $i) > $i > $i)).
thf(func_def_909, type, sK625: (($i > $o) > $i)).
thf(func_def_910, type, sK626: ($i > $o)).
thf(func_def_929, type, sK645: ($i > $o)).
thf(func_def_934, type, sK650: ($i > $o)).
thf(func_def_937, type, sK653: ($i > ($i > $o) > $i)).
thf(func_def_938, type, sK654: ($i > ($i > $o) > $i)).
thf(func_def_939, type, sK655: ($i > ($i > $o) > $i)).
thf(func_def_940, type, sK656: ($i > $o)).
thf(func_def_945, type, sK661: (($i > $i > $o) > $i > $i)).
thf(func_def_946, type, sK662: (($i > $i > $o) > $i > $i)).
thf(func_def_947, type, sK663: ($i > ($i > $i > $o) > $i > $i)).
thf(func_def_949, type, sK665: ($i > $i > $o)).
thf(func_def_950, type, sK666: ($i > $i)).
thf(func_def_951, type, sK667: ($i > $i)).
thf(func_def_956, type, sK672: ($i > $i)).
thf(func_def_964, type, sK680: (($i > $o) > ($i > $o) > $i)).
thf(func_def_965, type, sK681: (($i > $o) > ($i > $o) > $i)).
thf(func_def_966, type, sK682: ($i > $o)).
thf(func_def_967, type, sK683: ($i > $o)).
thf(func_def_972, type, sK688: $o).
thf(func_def_978, type, sK694: ($i > $i)).
thf(func_def_997, type, sK713: $o).
thf(func_def_1001, type, sK717: ($i > ($i > $o) > $i)).
thf(func_def_1002, type, sK718: ($i > $o)).
thf(func_def_1006, type, sK722: ($i > $i > $i)).
thf(func_def_1007, type, sK723: ($i > $i > $i)).
thf(f81,axiom,(
  (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
thf(f83,axiom,(
  (! [X0 : $i,X2 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
thf(f86,axiom,(
  (! [X0 : $i,X1 : $i] : (~(subset @ X0 @ X1) => (X0 != X1)) = notequalI1)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1)).
thf(f89,axiom,(
  (! [X2 : $i,X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X2) => (subset @ X0 @ X2))) = subsetTrans)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans)).
thf(f96,axiom,(
  (powersetE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1)).
thf(f237,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 => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (subset @ X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI)).
thf(f238,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 => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (subset @ X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(negated_conjecture,[status(cth)],[f237])).
thf(f306,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ X2))) = subsetE)),
  inference(rectify,[],[f83])).
thf(f307,plain,(
  (subsetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((subset @ X0 @ X2)) = $true) => ((((in @ X1 @ X0)) = $true) => (((in @ X1 @ X2)) = $true)))),
  inference(fool_elimination,[],[f306])).
thf(f435,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 => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (subset @ X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(rectify,[],[f238])).
thf(f436,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) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ((((in @ X3 @ X1)) = $true) => (((in @ X3 @ X2)) = $true))) => (((subset @ X1 @ X2)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
  inference(fool_elimination,[],[f435])).
thf(f520,plain,(
  (powersetE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))),
  inference(rectify,[],[f96])).
thf(f521,plain,(
  ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => (((subset @ X1 @ X0)) = $true)) <=> (powersetE1 = $true)),
  inference(fool_elimination,[],[f520])).
thf(f546,plain,(
  (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI2)),
  inference(rectify,[],[f81])).
thf(f547,plain,(
  (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true))),
  inference(fool_elimination,[],[f546])).
thf(f560,plain,(
  (! [X0 : $i,X1 : $i] : (~(subset @ X0 @ X1) => (X0 != X1)) = notequalI1)),
  inference(rectify,[],[f86])).
thf(f561,plain,(
  ! [X0 : $i,X1 : $i] : (~ (((subset @ X0 @ X1)) = $true) => (X0 != X1)) <=> (notequalI1 = $true)),
  inference(fool_elimination,[],[f560])).
thf(f672,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X1) => ((subset @ X1 @ X0) => (subset @ X2 @ X0))) = subsetTrans)),
  inference(rectify,[],[f89])).
thf(f673,plain,(
  ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X2 @ X1)) = $true) => ((((subset @ X1 @ X0)) = $true) => (((subset @ X2 @ X0)) = $true))) <=> (subsetTrans = $true)),
  inference(fool_elimination,[],[f672])).
thf(f729,plain,(
  ! [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) != $true) => (X0 != X1)) <=> (notequalI1 = $true)),
  inference(flattening,[],[f561])).
thf(f745,plain,(
  ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true)) <=> (subsetI2 = $true)),
  inference(ennf_transformation,[],[f547])).
thf(f845,plain,(
  (subsetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((((in @ X1 @ X2)) = $true) | (((in @ X1 @ X0)) != $true)) | (((subset @ X0 @ X2)) != $true))),
  inference(ennf_transformation,[],[f307])).
thf(f846,plain,(
  (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X1 @ X2)) = $true) | (((subset @ X0 @ X2)) != $true))),
  inference(flattening,[],[f845])).
thf(f856,plain,(
  (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((((subset @ X1 @ X2)) != $true) & ! [X3 : $i] : (((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X1)) != $true)) | (((in @ X3 @ X0)) != $true))) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $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,[],[f436])).
thf(f857,plain,(
  (prop2setI = $true) & (powersetT_lem = $true) & (binintersectI = $true) & (brelnall2 = $true) & (notdallE = $true) & (funcGraphProp4 = $true) & (powersetAx = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((in @ X3 @ X2)) = $true) | (((in @ X3 @ X0)) != $true)) & (((subset @ X1 @ X2)) != $true) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (upairinpowunion = $true) & (ex1E1 = $true) & (ex1I2 = $true) & (binintersectSubset2 = $true) & (binintersectER = $true) & (binintersectSubset5 = $true) & (uniqinunit = $true) & (iftrue = $true) & (app = $true) & (upairsetIR = $true) & (binintersectSubset3 = $true) & (iffalse = $true) & (subsetTrans = $true) & (subset2powerset = $true) & (upairset2E = $true) & (sepSubset = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (eqinunit = $true) & (symdiffI1 = $true) & (binintersectRsub = $true) & (setbeta = $true) & (ubforcartprodlem3 = $true) & (subsetemptysetimpeq = $true) & (cartprodsndin = $true) & (quantDeMorgan4 = $true) & (lamProp = $true) & (powersetE = $true) & (upairset2IR = $true) & (iffalseProp2 = $true) & (eta2 = $true) & (quantDeMorgan1 = $true) & (upairequniteq = $true) & (brelnall1 = $true) & (cartprodfstin = $true) & (exuEu = $true) & (setukpairinjR1 = $true) & (emptyE1 = $true) & (descrp = $true) & (exuE1 = $true) & (singletoninpowerset = $true) & (dsetconstrER = $true) & (upairsetE = $true) & (setoftrueEq = $true) & (emptyinunitempty = $true) & (inPowerset = $true) & (funcImageSingleton = $true) & (cartprodsndpairEq = $true) & (notinsingleton = $true) & (nonemptyI = $true) & (setminusEL = $true) & (singletoninpowunion = $true) & (dsetconstrI = $true) & (setminusERneg = $true) & (dpsetconstrERa = $true) & (subsetI1 = $true) & (setextT = $true) & (dsetconstr__Cong = $true) & (powerset__Cong = $true) & (omega__Cong = $true) & (binintersectT_lem = $true) & (eqimpsubset2 = $true) & (lamp = $true) & (cartprodpairsurjEq = $true) & (subsetI2 = $true) & (setukpairinjL2 = $true) & (sepInPowerset = $true) & (emptyinPowerset = $true) & (singletonsswitch = $true) & (setminusT_lem = $true) & (omegaSAx = $true) & (in__Cong = $true) & (emptysetimpfalse = $true) & (binintersectSubset4 = $true) & (setadjoinAx = $true) & (subsetRefl = $true) & (setadjoin__Cong = $true) & (binunionEcases = $true) & (setminusIRneg = $true) & (binunionE = $true) & (exuI3 = $true) & (notinemptyset = $true) & (notequalI1 = $true) & (eqbreln = $true) & (setunionsingleton = $true) & (setukpairinjL1 = $true) & (cartprodmempair1 = $true) & (emptysetE = $true) & (iffalseProp1 = $true) & (setunionsingleton2 = $true) & (iftrueProp1 = $true) & (setadjoinE = $true) & (cartprodpairmemEL = $true) & (setminusLsub = $true) & (emptyInPowerset = $true) & (setadjoinSub2 = $true) & (binunionT_lem = $true) & (funcext = $true) & (binunionIL = $true) & (setminusSubset2 = $true) & (binunionLsub = $true) & (dpsetconstrEL1 = $true) & (exuE2 = $true) & (subsetE = $true) & (powersetsubset = $true) & (dpsetconstrEL2 = $true) & (descr__Cong = $true) & (ap2apEq2 = $true) & (setukpairinjL = $true) & (setukpairIL = $true) & (dpsetconstrSub = $true) & (prop2setE = $true) & (lam2p = $true) & (exu__Cong = $true) & (cartprodpairmemER = $true) & (setukpairinjR = $true) & (setadjoinOr = $true) & (ifSingleton = $true) & (setminusSubset1 = $true) & (setukpairinjR12 = $true) & (powersetE1 = $true) & (singletonsubset = $true) & (disjointsetsI1 = $true) & (binintersectEL = $true) & (cartprodfstpairEq = $true) & (notequalI2 = $true) & (kpairiskpair = $true) & (bs114d = $true) & (ubforcartprodlem2 = $true) & (quantDeMorgan3 = $true) & (inCongP = $true) & (setukpairIR = $true) & (subsetE2 = $true) & (foundationAx = $true) & (noeltsimpempty = $true) & (symdiffE = $true) & (ap2apEq1 = $true) & (singletonprop = $true) & (ifp = $true) & (cartprodmempair = $true) & (setadjoinSub = $true) & (binunionIR = $true) & (notdexE = $true) & (setminusILneg = $true) & (setukpairinjR11 = $true) & (ksndpairEq = $true) & (setunionAx = $true) & (setunionE = $true) & (iftrueorfalse = $true) & (ksndsingleton = $true) & (funcGraphProp3 = $true) & (nonemptyImpWitness = $true) & (symdiffIneg1 = $true) & (setminusELneg = $true) & (setunionI = $true) & (setunionsingleton1 = $true) & (nonemptyI1 = $true) & (exuI1 = $true) & (nonemptyE1 = $true) & (funcextLem = $true) & (emptyset__Cong = $true) & (beta1 = $true) & (theprop = $true) & (funcGraphProp2 = $true) & (emptysetsubset = $true) & (setminusER = $true) & (setminusI = $true) & (powersetI1 = $true) & (cartprodmempaircEq = $true) & (kpairsurjEq = $true) & (exuI2 = $true) & (setextsub = $true) & (secondinupair = $true) & (quantDeMorgan2 = $true) & (ubforcartprodlem1 = $true) & (cartprodpairin = $true) & (omegaIndAx = $true) & (eqimpsubset1 = $true) & (emptysetAx = $true) & (iftrueProp2 = $true) & (replAx = $true) & (kpairp = $true) & (setunion__Cong = $true) & (funcinfuncset = $true) & (setOfPairsIsBReln = $true) & (subbreln = $true) & (exuE3u = $true) & (dpsetconstrER = $true) & (binunionRsub = $true) & (prop2set2propI = $true) & (setunionE2 = $true) & (lam2lamEq = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (setextAx = $true) & (dsetconstrEL = $true) & (notsubsetI = $true) & (setukpairinjR2 = $true) & (symdiffI2 = $true) & (ap2p = $true) & (upairsubunion = $true) & (complementT_lem = $true) & (kfstsingleton = $true) & (vacuousDall = $true) & (setext = $true) & (dpsetconstrI = $true) & (omega0Ax = $true) & (theeq = $true) & (powersetI = $true) & (emptyI = $true) & (infuncsetfunc = $true) & (ex1I = $true) & (wellorderingAx = $true) & (apProp = $true) & (subPowSU = $true) & (singletonsuniq = $true) & (binintersectLsub = $true) & (beta2 = $true) & (eta1 = $true) & (funcext2 = $true) & (kfstpairEq = $true) & (binintersectSubset1 = $true) & (symdiffIneg2 = $true) & (upairsetIL = $true) & (setadjoinIL = $true)),
  inference(flattening,[],[f856])).
thf(f908,plain,(
  (powersetE1 = $true) <=> ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | (((subset @ X1 @ X0)) = $true))),
  inference(ennf_transformation,[],[f521])).
thf(f921,plain,(
  ! [X0 : $i,X1 : $i] : ((X0 != X1) | (((subset @ X0 @ X1)) = $true)) <=> (notequalI1 = $true)),
  inference(ennf_transformation,[],[f729])).
thf(f963,plain,(
  ! [X2 : $i,X0 : $i,X1 : $i] : (((((subset @ X2 @ X0)) = $true) | (((subset @ X1 @ X0)) != $true)) | (((subset @ X2 @ X1)) != $true)) <=> (subsetTrans = $true)),
  inference(ennf_transformation,[],[f673])).
thf(f964,plain,(
  ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X2 @ X1)) != $true) | (((subset @ X2 @ X0)) = $true) | (((subset @ X1 @ X0)) != $true)) <=> (subsetTrans = $true)),
  inference(flattening,[],[f963])).
thf(f1062,plain,(
  (! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X2 @ X1)) != $true) | (((subset @ X2 @ X0)) = $true) | (((subset @ X1 @ X0)) != $true)) | (subsetTrans != $true)) & ((subsetTrans = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X2 @ X1)) = $true) & (((subset @ X2 @ X0)) != $true) & (((subset @ X1 @ X0)) = $true)))),
  inference(nnf_transformation,[],[f964])).
thf(f1063,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X0 @ X2)) != $true) | (((subset @ X0 @ X1)) = $true) | (((subset @ X2 @ X1)) != $true)) | (subsetTrans != $true)) & ((subsetTrans = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = ((subset @ X3 @ X5))) & ($true != ((subset @ X3 @ X4))) & ($true = ((subset @ X5 @ X4)))))),
  inference(rectify,[],[f1062])).
thf(f1064,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X0 @ X2)) != $true) | (((subset @ X0 @ X1)) = $true) | (((subset @ X2 @ X1)) != $true)) | (subsetTrans != $true)) & ((subsetTrans = $true) | ((((subset @ sK67 @ sK69)) = $true) & ($true != ((subset @ sK67 @ sK68))) & (((subset @ sK69 @ sK68)) = $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK67,sK68,sK69]),skolemize(X3,$thf(sK67)),skolemize(X4,$thf(sK68)),skolemize(X5,$thf(sK69))],[f1063])).
thf(f1080,plain,(
  ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) & (((in @ X1 @ X2)) != $true) & (((subset @ X0 @ X2)) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X1 @ X2)) = $true) | (((subset @ X0 @ X2)) != $true)) | (subsetE != $true))),
  inference(nnf_transformation,[],[f846])).
thf(f1081,plain,(
  ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) & (((in @ X1 @ X2)) != $true) & (((subset @ X0 @ X2)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X3))) | (((in @ X4 @ X5)) = $true) | ($true != ((subset @ X3 @ X5)))) | (subsetE != $true))),
  inference(rectify,[],[f1080])).
thf(f1082,plain,(
  ((subsetE = $true) | (($true = ((in @ sK89 @ sK88))) & (((in @ sK89 @ sK90)) != $true) & ($true = ((subset @ sK88 @ sK90))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X3))) | (((in @ X4 @ X5)) = $true) | ($true != ((subset @ X3 @ X5)))) | (subsetE != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK88,sK89,sK90]),skolemize(X0,$thf(sK88)),skolemize(X1,$thf(sK89)),skolemize(X2,$thf(sK90))],[f1081])).
thf(f1240,plain,(
  (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) & (((subset @ X1 @ X0)) != $true)))),
  inference(nnf_transformation,[],[f745])).
thf(f1241,plain,(
  (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (($true = ((in @ X5 @ X3))) | (((in @ X5 @ X4)) != $true)) & (((subset @ X4 @ X3)) != $true)))),
  inference(rectify,[],[f1240])).
thf(f1242,plain,(
  (! [X0 : $i,X1 : $i] : ((($true != ((in @ (sK251 @ X1 @ X0) @ X0))) & (((in @ (sK251 @ X1 @ X0) @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | (! [X5 : $i] : ((((in @ X5 @ sK252)) = $true) | ($true != ((in @ X5 @ sK253)))) & ($true != ((subset @ sK253 @ sK252)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK252,sK253]),skolemize(X5,$thf(sK8 @ X3 @ X2 @ X1 @ X0)),skolemize(X3,$thf(sK252)),skolemize(X4,$thf(sK253))],[f1241])).
thf(f1256,plain,(
  ((powersetE1 = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) & (((subset @ X1 @ X0)) != $true))) & (! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | (((subset @ X1 @ X0)) = $true)) | (powersetE1 != $true))),
  inference(nnf_transformation,[],[f908])).
thf(f1257,plain,(
  ((powersetE1 = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) & (((subset @ X1 @ X0)) != $true))) & (! [X2 : $i,X3 : $i] : (($true != ((in @ X3 @ (powerset @ X2)))) | (((subset @ X3 @ X2)) = $true)) | (powersetE1 != $true))),
  inference(rectify,[],[f1256])).
thf(f1258,plain,(
  ((powersetE1 = $true) | (($true = ((in @ sK277 @ (powerset @ sK276)))) & (((subset @ sK277 @ sK276)) != $true))) & (! [X2 : $i,X3 : $i] : (($true != ((in @ X3 @ (powerset @ X2)))) | (((subset @ X3 @ X2)) = $true)) | (powersetE1 != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK276,sK277]),skolemize(X0,$thf(sK276)),skolemize(X1,$thf(sK277))],[f1257])).
thf(f1334,plain,(
  (prop2setI = $true) & (powersetT_lem = $true) & (binintersectI = $true) & (brelnall2 = $true) & (notdallE = $true) & (funcGraphProp4 = $true) & (powersetAx = $true) & ((! [X3 : $i] : ((((in @ X3 @ sK359)) != $true) | ($true = ((in @ X3 @ sK360))) | (((in @ X3 @ sK358)) != $true)) & ($true != ((subset @ sK359 @ sK360))) & ($true = ((in @ sK360 @ (powerset @ sK358))))) & (((in @ sK359 @ (powerset @ sK358))) = $true)) & (upairinpowunion = $true) & (ex1E1 = $true) & (ex1I2 = $true) & (binintersectSubset2 = $true) & (binintersectER = $true) & (binintersectSubset5 = $true) & (uniqinunit = $true) & (iftrue = $true) & (app = $true) & (upairsetIR = $true) & (binintersectSubset3 = $true) & (iffalse = $true) & (subsetTrans = $true) & (subset2powerset = $true) & (upairset2E = $true) & (sepSubset = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (eqinunit = $true) & (symdiffI1 = $true) & (binintersectRsub = $true) & (setbeta = $true) & (ubforcartprodlem3 = $true) & (subsetemptysetimpeq = $true) & (cartprodsndin = $true) & (quantDeMorgan4 = $true) & (lamProp = $true) & (powersetE = $true) & (upairset2IR = $true) & (iffalseProp2 = $true) & (eta2 = $true) & (quantDeMorgan1 = $true) & (upairequniteq = $true) & (brelnall1 = $true) & (cartprodfstin = $true) & (exuEu = $true) & (setukpairinjR1 = $true) & (emptyE1 = $true) & (descrp = $true) & (exuE1 = $true) & (singletoninpowerset = $true) & (dsetconstrER = $true) & (upairsetE = $true) & (setoftrueEq = $true) & (emptyinunitempty = $true) & (inPowerset = $true) & (funcImageSingleton = $true) & (cartprodsndpairEq = $true) & (notinsingleton = $true) & (nonemptyI = $true) & (setminusEL = $true) & (singletoninpowunion = $true) & (dsetconstrI = $true) & (setminusERneg = $true) & (dpsetconstrERa = $true) & (subsetI1 = $true) & (setextT = $true) & (dsetconstr__Cong = $true) & (powerset__Cong = $true) & (omega__Cong = $true) & (binintersectT_lem = $true) & (eqimpsubset2 = $true) & (lamp = $true) & (cartprodpairsurjEq = $true) & (subsetI2 = $true) & (setukpairinjL2 = $true) & (sepInPowerset = $true) & (emptyinPowerset = $true) & (singletonsswitch = $true) & (setminusT_lem = $true) & (omegaSAx = $true) & (in__Cong = $true) & (emptysetimpfalse = $true) & (binintersectSubset4 = $true) & (setadjoinAx = $true) & (subsetRefl = $true) & (setadjoin__Cong = $true) & (binunionEcases = $true) & (setminusIRneg = $true) & (binunionE = $true) & (exuI3 = $true) & (notinemptyset = $true) & (notequalI1 = $true) & (eqbreln = $true) & (setunionsingleton = $true) & (setukpairinjL1 = $true) & (cartprodmempair1 = $true) & (emptysetE = $true) & (iffalseProp1 = $true) & (setunionsingleton2 = $true) & (iftrueProp1 = $true) & (setadjoinE = $true) & (cartprodpairmemEL = $true) & (setminusLsub = $true) & (emptyInPowerset = $true) & (setadjoinSub2 = $true) & (binunionT_lem = $true) & (funcext = $true) & (binunionIL = $true) & (setminusSubset2 = $true) & (binunionLsub = $true) & (dpsetconstrEL1 = $true) & (exuE2 = $true) & (subsetE = $true) & (powersetsubset = $true) & (dpsetconstrEL2 = $true) & (descr__Cong = $true) & (ap2apEq2 = $true) & (setukpairinjL = $true) & (setukpairIL = $true) & (dpsetconstrSub = $true) & (prop2setE = $true) & (lam2p = $true) & (exu__Cong = $true) & (cartprodpairmemER = $true) & (setukpairinjR = $true) & (setadjoinOr = $true) & (ifSingleton = $true) & (setminusSubset1 = $true) & (setukpairinjR12 = $true) & (powersetE1 = $true) & (singletonsubset = $true) & (disjointsetsI1 = $true) & (binintersectEL = $true) & (cartprodfstpairEq = $true) & (notequalI2 = $true) & (kpairiskpair = $true) & (bs114d = $true) & (ubforcartprodlem2 = $true) & (quantDeMorgan3 = $true) & (inCongP = $true) & (setukpairIR = $true) & (subsetE2 = $true) & (foundationAx = $true) & (noeltsimpempty = $true) & (symdiffE = $true) & (ap2apEq1 = $true) & (singletonprop = $true) & (ifp = $true) & (cartprodmempair = $true) & (setadjoinSub = $true) & (binunionIR = $true) & (notdexE = $true) & (setminusILneg = $true) & (setukpairinjR11 = $true) & (ksndpairEq = $true) & (setunionAx = $true) & (setunionE = $true) & (iftrueorfalse = $true) & (ksndsingleton = $true) & (funcGraphProp3 = $true) & (nonemptyImpWitness = $true) & (symdiffIneg1 = $true) & (setminusELneg = $true) & (setunionI = $true) & (setunionsingleton1 = $true) & (nonemptyI1 = $true) & (exuI1 = $true) & (nonemptyE1 = $true) & (funcextLem = $true) & (emptyset__Cong = $true) & (beta1 = $true) & (theprop = $true) & (funcGraphProp2 = $true) & (emptysetsubset = $true) & (setminusER = $true) & (setminusI = $true) & (powersetI1 = $true) & (cartprodmempaircEq = $true) & (kpairsurjEq = $true) & (exuI2 = $true) & (setextsub = $true) & (secondinupair = $true) & (quantDeMorgan2 = $true) & (ubforcartprodlem1 = $true) & (cartprodpairin = $true) & (omegaIndAx = $true) & (eqimpsubset1 = $true) & (emptysetAx = $true) & (iftrueProp2 = $true) & (replAx = $true) & (kpairp = $true) & (setunion__Cong = $true) & (funcinfuncset = $true) & (setOfPairsIsBReln = $true) & (subbreln = $true) & (exuE3u = $true) & (dpsetconstrER = $true) & (binunionRsub = $true) & (prop2set2propI = $true) & (setunionE2 = $true) & (lam2lamEq = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (setextAx = $true) & (dsetconstrEL = $true) & (notsubsetI = $true) & (setukpairinjR2 = $true) & (symdiffI2 = $true) & (ap2p = $true) & (upairsubunion = $true) & (complementT_lem = $true) & (kfstsingleton = $true) & (vacuousDall = $true) & (setext = $true) & (dpsetconstrI = $true) & (omega0Ax = $true) & (theeq = $true) & (powersetI = $true) & (emptyI = $true) & (infuncsetfunc = $true) & (ex1I = $true) & (wellorderingAx = $true) & (apProp = $true) & (subPowSU = $true) & (singletonsuniq = $true) & (binintersectLsub = $true) & (beta2 = $true) & (eta1 = $true) & (funcext2 = $true) & (kfstpairEq = $true) & (binintersectSubset1 = $true) & (symdiffIneg2 = $true) & (upairsetIL = $true) & (setadjoinIL = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK358,sK359,sK360]),skolemize(X0,$thf(sK358)),skolemize(X1,$thf(sK359)),skolemize(X2,$thf(sK360))],[f857])).
thf(f1649,plain,(
  (! [X0 : $i,X1 : $i] : ((X0 != X1) | (((subset @ X0 @ X1)) = $true)) | (notequalI1 != $true)) & ((notequalI1 = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & (((subset @ X0 @ X1)) != $true)))),
  inference(nnf_transformation,[],[f921])).
thf(f1650,plain,(
  (! [X0 : $i,X1 : $i] : ((X0 != X1) | (((subset @ X0 @ X1)) = $true)) | (notequalI1 != $true)) & ((notequalI1 = $true) | ? [X2 : $i,X3 : $i] : ((X2 = X3) & (((subset @ X2 @ X3)) != $true)))),
  inference(rectify,[],[f1649])).
thf(f1651,plain,(
  (! [X0 : $i,X1 : $i] : ((X0 != X1) | (((subset @ X0 @ X1)) = $true)) | (notequalI1 != $true)) & ((notequalI1 = $true) | ((sK678 = sK679) & ($true != ((subset @ sK678 @ sK679)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK678,sK679]),skolemize(X2,$thf(sK678)),skolemize(X3,$thf($thf(sK679)))],[f1650])).
thf(f1776,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X2)) != $true) | (((subset @ X2 @ X1)) != $true) | (subsetTrans != $true) | (((subset @ X0 @ X1)) = $true)) )),
  inference(cnf_transformation,[],[f1064])).
thf(f1798,plain,(
  ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X5)) = $true) | (subsetE != $true) | ($true != ((in @ X4 @ X3))) | ($true != ((subset @ X3 @ X5)))) )),
  inference(cnf_transformation,[],[f1082])).
thf(f1997,plain,(
  ( ! [X0 : $i,X1 : $i] : ((subsetI2 != $true) | (((in @ (sK251 @ X1 @ X0) @ X1)) = $true) | (((subset @ X1 @ X0)) = $true)) )),
  inference(cnf_transformation,[],[f1242])).
thf(f1998,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | (subsetI2 != $true) | ($true != ((in @ (sK251 @ X1 @ X0) @ X0)))) )),
  inference(cnf_transformation,[],[f1242])).
thf(f2046,plain,(
  ( ! [X2 : $i,X3 : $i] : ((((subset @ X3 @ X2)) = $true) | ($true != ((in @ X3 @ (powerset @ X2)))) | (powersetE1 != $true)) )),
  inference(cnf_transformation,[],[f1258])).
thf(f2263,plain,(
  (powersetE1 = $true)),
  inference(cnf_transformation,[],[f1334])).
thf(f2280,plain,(
  (subsetE = $true)),
  inference(cnf_transformation,[],[f1334])).
thf(f2301,plain,(
  (notequalI1 = $true)),
  inference(cnf_transformation,[],[f1334])).
thf(f2319,plain,(
  (subsetI2 = $true)),
  inference(cnf_transformation,[],[f1334])).
thf(f2371,plain,(
  (subsetTrans = $true)),
  inference(cnf_transformation,[],[f1334])).
thf(f2384,plain,(
  (((in @ sK359 @ (powerset @ sK358))) = $true)),
  inference(cnf_transformation,[],[f1334])).
thf(f2386,plain,(
  ($true != ((subset @ sK359 @ sK360)))),
  inference(cnf_transformation,[],[f1334])).
thf(f2387,plain,(
  ( ! [X3 : $i] : (($true = ((in @ X3 @ sK360))) | (((in @ X3 @ sK359)) != $true) | (((in @ X3 @ sK358)) != $true)) )),
  inference(cnf_transformation,[],[f1334])).
thf(f2829,plain,(
  ( ! [X0 : $i,X1 : $i] : ((X0 != X1) | (((subset @ X0 @ X1)) = $true) | (notequalI1 != $true)) )),
  inference(cnf_transformation,[],[f1651])).
thf(f2928,plain,(
  ( ! [X1 : $i] : (($true = ((subset @ X1 @ X1))) | (notequalI1 != $true)) )),
  inference(equality_resolution,[],[f2829])).
thf(f3164,definition,(
  spl724_12 <=> ! [X3 : $i] : ($true = ((subset @ X3 @ X3)))),
  introduced(definition,[new_symbols(definition,[spl724_12])],[avatar_definition])).
thf(f3165,plain,(
  ( ! [X3 : $i] : (($true = ((subset @ X3 @ X3)))) ) | ~spl724_12),
  inference(avatar_component_clause,[],[f3164])).
thf(f3372,definition,(
  spl724_59 <=> (notequalI1 = $true)),
  introduced(definition,[new_symbols(definition,[spl724_59])],[avatar_definition])).
thf(f3398,definition,(
  spl724_65 <=> (powersetE1 = $true)),
  introduced(definition,[new_symbols(definition,[spl724_65])],[avatar_definition])).
thf(f3401,plain,(
  spl724_65),
  inference(avatar_split_clause,[],[f2263,f3398])).
thf(f3673,definition,(
  spl724_127 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X1 @ X2)) = $true) | (((subset @ X0 @ X2)) != $true))),
  introduced(definition,[new_symbols(definition,[spl724_127])],[avatar_definition])).
thf(f3674,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X2)) = $true) | (((subset @ X0 @ X2)) != $true) | (((in @ X1 @ X0)) != $true)) ) | ~spl724_127),
  inference(avatar_component_clause,[],[f3673])).
thf(f3865,definition,(
  spl724_170 <=> (subsetE = $true)),
  introduced(definition,[new_symbols(definition,[spl724_170])],[avatar_definition])).
thf(f4111,definition,(
  spl724_224 <=> (((in @ sK359 @ (powerset @ sK358))) = $true)),
  introduced(definition,[new_symbols(definition,[spl724_224])],[avatar_definition])).
thf(f4113,plain,(
  (((in @ sK359 @ (powerset @ sK358))) = $true) | ~spl724_224),
  inference(avatar_component_clause,[],[f4111])).
thf(f4114,plain,(
  spl724_224),
  inference(avatar_split_clause,[],[f2384,f4111])).
thf(f4320,definition,(
  spl724_270 <=> (subsetI2 = $true)),
  introduced(definition,[new_symbols(definition,[spl724_270])],[avatar_definition])).
thf(f4324,definition,(
  spl724_271 <=> ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | ($true != ((in @ (sK251 @ X1 @ X0) @ X0))))),
  introduced(definition,[new_symbols(definition,[spl724_271])],[avatar_definition])).
thf(f4325,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK251 @ X1 @ X0) @ X0))) | (((subset @ X1 @ X0)) = $true)) ) | ~spl724_271),
  inference(avatar_component_clause,[],[f4324])).
thf(f4326,plain,(
  ~spl724_270 | spl724_271),
  inference(avatar_split_clause,[],[f1998,f4324,f4320])).
thf(f4864,definition,(
  spl724_389 <=> ($true = ((subset @ sK359 @ sK360)))),
  introduced(definition,[new_symbols(definition,[spl724_389])],[avatar_definition])).
thf(f4866,plain,(
  ($true != ((subset @ sK359 @ sK360))) | spl724_389),
  inference(avatar_component_clause,[],[f4864])).
thf(f4867,plain,(
  ~spl724_389),
  inference(avatar_split_clause,[],[f2386,f4864])).
thf(f4979,definition,(
  spl724_413 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X2)) != $true) | (((subset @ X0 @ X1)) = $true) | (((subset @ X2 @ X1)) != $true))),
  introduced(definition,[new_symbols(definition,[spl724_413])],[avatar_definition])).
thf(f4980,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (((subset @ X0 @ X2)) != $true) | (((subset @ X2 @ X1)) != $true)) ) | ~spl724_413),
  inference(avatar_component_clause,[],[f4979])).
thf(f4982,definition,(
  spl724_414 <=> (subsetTrans = $true)),
  introduced(definition,[new_symbols(definition,[spl724_414])],[avatar_definition])).
thf(f4985,plain,(
  spl724_413 | ~spl724_414),
  inference(avatar_split_clause,[],[f1776,f4982,f4979])).
thf(f5371,plain,(
  spl724_270),
  inference(avatar_split_clause,[],[f2319,f4320])).
thf(f6100,plain,(
  spl724_414),
  inference(avatar_split_clause,[],[f2371,f4982])).
thf(f6564,plain,(
  spl724_59),
  inference(avatar_split_clause,[],[f2301,f3372])).
thf(f7331,definition,(
  spl724_907 <=> ! [X2 : $i,X3 : $i] : ((((subset @ X3 @ X2)) = $true) | ($true != ((in @ X3 @ (powerset @ X2)))))),
  introduced(definition,[new_symbols(definition,[spl724_907])],[avatar_definition])).
thf(f7332,plain,(
  ( ! [X2 : $i,X3 : $i] : (($true != ((in @ X3 @ (powerset @ X2)))) | (((subset @ X3 @ X2)) = $true)) ) | ~spl724_907),
  inference(avatar_component_clause,[],[f7331])).
thf(f7333,plain,(
  spl724_907 | ~spl724_65),
  inference(avatar_split_clause,[],[f2046,f3398,f7331])).
thf(f7389,plain,(
  ~spl724_59 | spl724_12),
  inference(avatar_split_clause,[],[f2928,f3164,f3372])).
thf(f7539,plain,(
  spl724_127 | ~spl724_170),
  inference(avatar_split_clause,[],[f1798,f3865,f3673])).
thf(f7839,definition,(
  spl724_1012 <=> ! [X0 : $i,X1 : $i] : ((((in @ (sK251 @ X1 @ X0) @ X1)) = $true) | (((subset @ X1 @ X0)) = $true))),
  introduced(definition,[new_symbols(definition,[spl724_1012])],[avatar_definition])).
thf(f7840,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK251 @ X1 @ X0) @ X1)) = $true) | (((subset @ X1 @ X0)) = $true)) ) | ~spl724_1012),
  inference(avatar_component_clause,[],[f7839])).
thf(f7841,plain,(
  spl724_1012 | ~spl724_270),
  inference(avatar_split_clause,[],[f1997,f4320,f7839])).
thf(f8096,plain,(
  spl724_170),
  inference(avatar_split_clause,[],[f2280,f3865])).
thf(f9089,plain,(
  ($true != $true) | ($true = ((subset @ sK359 @ sK358))) | (~spl724_224 | ~spl724_907)),
  inference(superposition,[],[f7332,f4113])).
thf(f9108,plain,(
  ($true = ((subset @ sK359 @ sK358))) | (~spl724_224 | ~spl724_907)),
  inference(trivial_inequality_removal,[],[f9089])).
thf(f9115,definition,(
  spl724_1164 <=> ($true = ((subset @ sK359 @ sK358)))),
  introduced(definition,[new_symbols(definition,[spl724_1164])],[avatar_definition])).
thf(f9117,plain,(
  ($true = ((subset @ sK359 @ sK358))) | ~spl724_1164),
  inference(avatar_component_clause,[],[f9115])).
thf(f9118,plain,(
  spl724_1164 | ~spl724_224 | ~spl724_907),
  inference(avatar_split_clause,[],[f9108,f7331,f4111,f9115])).
thf(f9221,plain,(
  ( ! [X0 : $i] : ((((in @ (sK251 @ X0 @ sK360) @ sK358)) != $true) | ($true = ((subset @ X0 @ sK360))) | ($true != $true) | (((in @ (sK251 @ X0 @ sK360) @ sK359)) != $true)) ) | ~spl724_271),
  inference(superposition,[],[f4325,f2387])).
thf(f9225,plain,(
  ( ! [X0 : $i] : ((((in @ (sK251 @ X0 @ sK360) @ sK359)) != $true) | (((in @ (sK251 @ X0 @ sK360) @ sK358)) != $true) | ($true = ((subset @ X0 @ sK360)))) ) | ~spl724_271),
  inference(trivial_inequality_removal,[],[f9221])).
thf(f9509,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK251 @ X0 @ sK360) @ sK358)) != $true) | ($true != $true) | ($true = ((subset @ X0 @ sK360))) | ($true != ((subset @ X1 @ sK359))) | (((in @ (sK251 @ X0 @ sK360) @ X1)) != $true)) ) | (~spl724_127 | ~spl724_271)),
  inference(superposition,[],[f9225,f3674])).
thf(f9533,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK251 @ X0 @ sK360) @ sK358)) != $true) | ($true != ((subset @ X1 @ sK359))) | (((in @ (sK251 @ X0 @ sK360) @ X1)) != $true) | ($true = ((subset @ X0 @ sK360)))) ) | (~spl724_127 | ~spl724_271)),
  inference(trivial_inequality_removal,[],[f9509])).
thf(f9548,plain,(
  ( ! [X0 : $i] : (($true != ((subset @ X0 @ sK360))) | ($true != $true) | ($true != ((subset @ sK359 @ X0)))) ) | (spl724_389 | ~spl724_413)),
  inference(superposition,[],[f4866,f4980])).
thf(f9551,plain,(
  ( ! [X0 : $i] : (($true != ((subset @ sK359 @ X0))) | ($true != ((subset @ X0 @ sK360)))) ) | (spl724_389 | ~spl724_413)),
  inference(trivial_inequality_removal,[],[f9548])).
thf(f9553,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK251 @ X0 @ sK360) @ X2)) != $true) | (((in @ (sK251 @ X0 @ sK360) @ X1)) != $true) | ($true = ((subset @ X0 @ sK360))) | ($true != ((subset @ X1 @ sK359))) | ($true != $true) | (((subset @ X2 @ sK358)) != $true)) ) | (~spl724_127 | ~spl724_271)),
  inference(superposition,[],[f9533,f3674])).
thf(f9556,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK251 @ X0 @ sK360) @ X2)) != $true) | ($true != ((subset @ X1 @ sK359))) | (((subset @ X2 @ sK358)) != $true) | ($true = ((subset @ X0 @ sK360))) | (((in @ (sK251 @ X0 @ sK360) @ X1)) != $true)) ) | (~spl724_127 | ~spl724_271)),
  inference(trivial_inequality_removal,[],[f9553])).
thf(f9682,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((subset @ X0 @ sK358))) | ($true = ((subset @ X0 @ sK360))) | ($true != ((subset @ X1 @ sK359))) | ($true = ((subset @ X0 @ sK360))) | (((in @ (sK251 @ X0 @ sK360) @ X1)) != $true) | ($true != $true)) ) | (~spl724_127 | ~spl724_271 | ~spl724_1012)),
  inference(superposition,[],[f9556,f7840])).
thf(f9709,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((subset @ X0 @ sK358))) | ($true != ((subset @ X1 @ sK359))) | ($true != $true) | (((in @ (sK251 @ X0 @ sK360) @ X1)) != $true) | ($true = ((subset @ X0 @ sK360)))) ) | (~spl724_127 | ~spl724_271 | ~spl724_1012)),
  inference(duplicate_literal_removal,[],[f9682])).
thf(f9710,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK251 @ X0 @ sK360) @ X1)) != $true) | ($true != ((subset @ X0 @ sK358))) | ($true = ((subset @ X0 @ sK360))) | ($true != ((subset @ X1 @ sK359)))) ) | (~spl724_127 | ~spl724_271 | ~spl724_1012)),
  inference(trivial_inequality_removal,[],[f9709])).
thf(f9729,plain,(
  ( ! [X0 : $i] : (($true = ((subset @ X0 @ sK360))) | ($true != $true) | (((subset @ X0 @ sK359)) != $true) | ($true != ((subset @ X0 @ sK358))) | ($true = ((subset @ X0 @ sK360)))) ) | (~spl724_127 | ~spl724_271 | ~spl724_1012)),
  inference(superposition,[],[f9710,f7840])).
thf(f9746,plain,(
  ( ! [X0 : $i] : (($true != $true) | ($true = ((subset @ X0 @ sK360))) | ($true != ((subset @ X0 @ sK358))) | (((subset @ X0 @ sK359)) != $true)) ) | (~spl724_127 | ~spl724_271 | ~spl724_1012)),
  inference(duplicate_literal_removal,[],[f9729])).
thf(f9747,plain,(
  ( ! [X0 : $i] : (($true = ((subset @ X0 @ sK360))) | (((subset @ X0 @ sK359)) != $true) | ($true != ((subset @ X0 @ sK358)))) ) | (~spl724_127 | ~spl724_271 | ~spl724_1012)),
  inference(trivial_inequality_removal,[],[f9746])).
thf(f9764,plain,(
  ($true != ((subset @ sK360 @ sK360))) | ($true != $true) | ($true != ((subset @ sK359 @ sK359))) | ($true != ((subset @ sK359 @ sK358))) | (~spl724_127 | ~spl724_271 | spl724_389 | ~spl724_413 | ~spl724_1012)),
  inference(superposition,[],[f9551,f9747])).
thf(f9765,plain,(
  ($true != ((subset @ sK359 @ sK358))) | ($true != ((subset @ sK359 @ sK359))) | ($true != ((subset @ sK360 @ sK360))) | (~spl724_127 | ~spl724_271 | spl724_389 | ~spl724_413 | ~spl724_1012)),
  inference(trivial_inequality_removal,[],[f9764])).
thf(f9768,plain,(
  ($true != ((subset @ sK359 @ sK359))) | ($true != ((subset @ sK360 @ sK360))) | (~spl724_127 | ~spl724_271 | spl724_389 | ~spl724_413 | ~spl724_1012 | ~spl724_1164)),
  inference(forward_subsumption_resolution,[],[f9765,f9117])).
thf(f9770,plain,(
  ($true != ((subset @ sK359 @ sK359))) | (~spl724_12 | ~spl724_127 | ~spl724_271 | spl724_389 | ~spl724_413 | ~spl724_1012 | ~spl724_1164)),
  inference(forward_subsumption_resolution,[],[f9768,f3165])).
thf(f9773,plain,(
  $false | (~spl724_12 | ~spl724_127 | ~spl724_271 | spl724_389 | ~spl724_413 | ~spl724_1012 | ~spl724_1164)),
  inference(forward_subsumption_resolution,[],[f9770,f3165])).
thf(f9774,plain,(
  ~spl724_12 | ~spl724_127 | ~spl724_271 | spl724_389 | ~spl724_413 | ~spl724_1012 | ~spl724_1164),
  inference(avatar_contradiction_clause,[],[f9773])).
cnf(s39, plain, spl724_65, inference(sat_conversion,[],[f3401])).
cnf(s145, plain, spl724_224, inference(sat_conversion,[],[f4114])).
cnf(s182, plain, ~spl724_270 | spl724_271, inference(sat_conversion,[],[f4326])).
cnf(s284, plain, ~spl724_389, inference(sat_conversion,[],[f4867])).
cnf(s309, plain, spl724_413 | ~spl724_414, inference(sat_conversion,[],[f4985])).
cnf(s398, plain, spl724_270, inference(sat_conversion,[],[f5371])).
cnf(s563, plain, spl724_414, inference(sat_conversion,[],[f6100])).
cnf(s677, plain, spl724_59, inference(sat_conversion,[],[f6564])).
cnf(s868, plain, ~spl724_65 | spl724_907, inference(sat_conversion,[],[f7333])).
cnf(s886, plain, spl724_12 | ~spl724_59, inference(sat_conversion,[],[f7389])).
cnf(s921, plain, spl724_127 | ~spl724_170, inference(sat_conversion,[],[f7539])).
cnf(s996, plain, ~spl724_270 | spl724_1012, inference(sat_conversion,[],[f7841])).
cnf(s1068, plain, spl724_170, inference(sat_conversion,[],[f8096])).
cnf(s1190, plain, ~spl724_224 | ~spl724_907 | spl724_1164, inference(sat_conversion,[],[f9118])).
cnf(s1215, plain, ~spl724_12 | ~spl724_127 | ~spl724_271 | spl724_389 | ~spl724_413 | ~spl724_1012 | ~spl724_1164, inference(sat_conversion,[],[f9774])).
cnf(s1229, plain, spl724_127, inference(rat,[],[s921,s1068])).
cnf(s1272, plain, spl724_12, inference(rat,[],[s886,s677])).
cnf(s1353, plain, spl724_1012, inference(rat,[],[s996,s398])).
cnf(s1387, plain, spl724_413, inference(rat,[],[s309,s563])).
cnf(s1435, plain, spl724_271, inference(rat,[],[s182,s398])).
cnf(s1437, plain, ~spl724_1164, inference(rat,[],[s1215,s284,s1353,s1387,s1272,s1229,s1435])).
cnf(s1455, plain, ~spl724_907, inference(rat,[],[s1190,s1437,s145])).
cnf(s1458, plain, ~spl724_65, inference(rat,[],[s868,s1455])).
cnf(s1505, plain, $false, inference(rat,[],[s39,s1458])).
thf(f9775,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s1505])).
% SZS output end Proof for theBenchmark