%----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, subsetTI: $o). thf(func_def_272, type, powersetTI1: $o). thf(func_def_273, type, powersetTE1: $o). thf(func_def_274, type, complementTI1: $o). thf(func_def_275, type, complementTE1: $o). thf(func_def_276, type, binintersectTELcontra: $o). thf(func_def_277, type, binintersectTERcontra: $o). thf(func_def_278, type, contrasubsetT: $o). thf(func_def_279, type, contrasubsetT1: $o). thf(func_def_280, type, contrasubsetT2: $o). thf(func_def_281, type, contrasubsetT3: $o). thf(func_def_282, type, doubleComplementI1: $o). thf(func_def_283, type, doubleComplementE1: $o). thf(func_def_284, type, doubleComplementSub1: $o). thf(func_def_285, type, doubleComplementSub2: $o). thf(func_def_286, type, doubleComplementEq: $o). thf(func_def_287, type, complementTnotintersectT: $o). thf(func_def_288, type, complementImpComplementIntersect: $o). thf(func_def_289, type, complementSubsetComplementIntersect: $o). thf(func_def_290, type, complementInPowersetComplementIntersect: $o). thf(func_def_291, type, contraSubsetComplement: $o). thf(func_def_292, type, complementTcontraSubset: $o). thf(func_def_293, type, binunionTILcontra: $o). thf(func_def_294, type, binunionTIRcontra: $o). thf(func_def_295, type, inIntersectImpInUnion: $o). thf(func_def_296, type, inIntersectImpInUnion2: $o). thf(func_def_297, type, inIntersectImpInIntersectUnions: $o). thf(func_def_298, type, intersectInPowersetIntersectUnions: $o). thf(func_def_299, type, inComplementUnionImpNotIn1: $o). thf(func_def_300, type, inComplementUnionImpInComplement1: $o). thf(func_def_301, type, binunionTE: $o). thf(func_def_302, type, binunionTEcontra: $o). thf(func_def_303, type, demorgan2a1: $o). thf(func_def_304, type, complementUnionInPowersetComplement: $o). thf(func_def_305, type, demorgan2a2: $o). thf(func_def_306, type, demorgan1a: $o). thf(func_def_307, type, demorgan1b: $o). thf(func_def_308, type, demorgan1: $o). thf(func_def_309, type, demorgan2a: $o). thf(func_def_310, type, demorgan2b2: $o). thf(func_def_311, type, demorgan2b: $o). thf(func_def_312, type, demorgan2: $o). thf(func_def_313, type, woz13rule0: $o). thf(func_def_314, type, woz13rule1: $o). thf(func_def_315, type, woz13rule2: $o). thf(func_def_316, type, woz13rule3: $o). thf(func_def_317, type, woz13rule4: $o). thf(func_def_318, type, woz1_1: $o). thf(func_def_319, type, woz1_2: $o). thf(func_def_320, type, woz1_3: $o). thf(func_def_321, type, woz1_4: $o). thf(func_def_322, type, woz1_5: $o). thf(func_def_323, type, breln1: ($i > $i > $o)). thf(func_def_324, type, breln1all2: $o). thf(func_def_325, type, breln1Set: ($i > $i)). thf(func_def_326, type, breln1SetBreln1: $o). thf(func_def_327, type, transitive: ($i > $i > $o)). thf(func_def_328, type, antisymmetric: ($i > $i > $o)). thf(func_def_329, type, reflexive: ($i > $i > $o)). thf(func_def_330, type, refltransitive: ($i > $i > $o)). thf(func_def_331, type, refllinearorder: ($i > $i > $o)). thf(func_def_332, type, reflwellordering: ($i > $i > $o)). thf(func_def_333, type, choice2fnsingleton: $o). thf(func_def_334, type, setOfPairsIsBReln1: $o). thf(func_def_335, type, breln1all1: $o). thf(func_def_336, type, subbreln1: $o). thf(func_def_337, type, eqbreln1: $o). thf(func_def_338, type, breln1invset: ($i > $i > $i)). thf(func_def_339, type, breln1invprop: $o). thf(func_def_340, type, breln1invI: $o). thf(func_def_341, type, breln1invE: $o). thf(func_def_342, type, breln1compset: ($i > $i > $i > $i)). thf(func_def_343, type, breln1compprop: $o). thf(func_def_344, type, breln1compI: $o). thf(func_def_345, type, breln1compE: $o). thf(func_def_346, type, breln1compEex: $o). thf(func_def_347, type, breln1unionprop: $o). thf(func_def_348, type, breln1unionIL: $o). thf(func_def_349, type, breln1unionIR: $o). thf(func_def_350, type, breln1unionI: $o). thf(func_def_351, type, breln1unionE: $o). thf(func_def_352, type, breln1unionEcases: $o). thf(func_def_353, type, breln1unionCommutes: $o). thf(func_def_354, type, woz2Ex: $o). thf(func_def_355, type, woz2W: $o). thf(func_def_356, type, woz2A: $o). thf(func_def_357, type, woz2B: $o). thf(func_def_358, type, image1Ex: $o). thf(func_def_359, type, image1Ex1: $o). thf(func_def_360, type, image1: ($i > ($i > $i) > $i)). thf(func_def_361, type, image1Equiv: $o). thf(func_def_362, type, image1E: $o). thf(func_def_363, type, image1I: $o). thf(func_def_364, type, injective: ($i > $i > $i > $o)). thf(func_def_365, type, injFuncSet: ($i > $i > $i)). thf(func_def_366, type, injFuncInInjFuncSet: $o). thf(func_def_367, type, injFuncSetFuncIn: $o). thf(func_def_368, type, injFuncSetFuncInj: $o). thf(func_def_369, type, surjective: ($i > $i > $i > $o)). thf(func_def_370, type, surjFuncSet: ($i > $i > $i)). thf(func_def_371, type, surjFuncSetFuncIn: $o). thf(func_def_372, type, surjFuncSetFuncSurj: $o). thf(func_def_373, type, leftInvIsSurj: $o). thf(func_def_374, type, surjCantorThm: $o). thf(func_def_375, type, foundation2: $o). thf(func_def_376, type, notinself: $o). thf(func_def_377, type, notinself2: $o). thf(func_def_378, type, omegaS: ($i > $i)). thf(func_def_379, type, omegaSp: $o). thf(func_def_380, type, omegaSclos: $o). thf(func_def_381, type, peano0notS: $o). thf(func_def_382, type, peano3: ($i > $i > $i > $o)). thf(func_def_383, type, peano4: ($i > $i > $i > $o)). thf(func_def_384, type, peano5: ($i > $i > $i > $o)). thf(func_def_385, type, peanoSinj: $o). thf(func_def_386, type, peano: ($i > $i > $i > $o)). thf(func_def_387, type, transitiveset: ($i > $o)). thf(func_def_388, type, transitivesetOp1: $o). thf(func_def_389, type, binintTransitive: $o). thf(func_def_390, type, transitivesetOp2: $o). thf(func_def_391, type, setunionTransitive: $o). thf(func_def_392, type, stricttotalorderedByIn: ($i > $o)). thf(func_def_393, type, wellorderedByIn: ($i > $o)). thf(func_def_394, type, ordinal: ($i > $o)). thf(func_def_395, type, limitOrdinal: ($i > $o)). thf(func_def_396, type, ordinalMinLem1: $o). thf(func_def_397, type, ordinalTransSet: $o). thf(func_def_398, type, ordinalTransSet1: $o). thf(func_def_401, type, db0: !>[X0: $tType]:(X0)). thf(func_def_402, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). thf(func_def_403, type, db1: !>[X0: $tType]:(X0)). thf(func_def_404, type, vAND: ($o > $o > $o)). thf(func_def_405, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). thf(func_def_406, type, vIMP: ($o > $o > $o)). thf(func_def_407, type, db2: !>[X0: $tType]:(X0)). thf(func_def_408, type, db3: !>[X0: $tType]:(X0)). thf(func_def_409, type, vOR: ($o > $o > $o)). thf(func_def_410, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). thf(func_def_411, type, vNOT: ($o > $o)). thf(func_def_412, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))). thf(func_def_413, type, vIFF: ($o > $o > $o)). thf(func_def_414, type, sP0: ($i > $i > $o)). thf(func_def_415, type, sP1: ($i > $o)). thf(func_def_418, type, sK4: ($i > $i > $o)). thf(func_def_427, type, sK13: ($i > $o)). thf(func_def_436, type, sK22: ($i > $o)). thf(func_def_438, type, sK24: (($i > $o) > $i > $i)). thf(func_def_439, type, sK25: (($i > $o) > $i > $i > $i)). thf(func_def_440, type, sK26: (($i > $o) > $i > $i > $i)). thf(func_def_443, type, sK29: ($i > $o)). thf(func_def_451, type, sK37: $o). thf(func_def_453, type, sK39: ($i > $i > $i > $i > $i > $i)). thf(func_def_468, type, sK54: ($i > $i)). thf(func_def_486, type, sK72: ($i > $i)). thf(func_def_489, type, sK75: ($i > ($i > $i) > $i > $i)). thf(func_def_498, type, sK84: ($o > $i > $i > $i > $i > $i > $i)). thf(func_def_504, type, sK90: $o). thf(func_def_508, type, sK94: ($i > $i)). thf(func_def_512, type, sK98: ($i > $i > ($i > $i) > $i)). thf(func_def_520, type, sK106: $o). thf(func_def_522, type, sK108: ($i > $i)). thf(func_def_526, type, sK112: $o). thf(func_def_533, type, sK119: (($i > $o) > $i > $i)). thf(func_def_535, type, sK121: ($i > $o)). thf(func_def_538, type, sK124: ($i > $i > $i > $i > $i)). thf(func_def_539, type, sK125: ($i > $i > $i > $i > $i)). thf(func_def_571, type, sK157: ($i > $i > ($i > $o) > $i)). thf(func_def_572, type, sK158: ($i > $o)). thf(func_def_582, type, sK168: ($i > ($i > $o) > $i)). thf(func_def_583, type, sK169: ($i > $o)). thf(func_def_588, type, sK174: ($i > $i)). thf(func_def_589, type, sK175: (($i > $i) > $i > $i > $i)). thf(func_def_590, type, sK176: ($i > $i)). thf(func_def_593, type, sK179: ($i > $i)). thf(func_def_596, type, sK182: ($i > ($i > $i) > $i > $i)). thf(func_def_605, type, sK191: ($i > $o)). thf(func_def_628, type, sK214: ($i > $o)). thf(func_def_633, type, sK219: $o). thf(func_def_639, type, sK225: ($i > $i > $i)). thf(func_def_640, type, sK226: ($i > $i > $i)). thf(func_def_657, type, sK243: ($i > $i)). thf(func_def_659, type, sK245: ($i > ($i > $i) > $i > $i)). thf(func_def_682, type, sK268: ($i > $i > $i > $i)). thf(func_def_683, type, sK269: $o). thf(func_def_696, type, sK282: ($i > $i > $o)). thf(func_def_698, type, sK284: (($i > $i) > $i > $i > $i)). thf(func_def_699, type, sK285: ($i > ($i > $i) > $i > $i > $i)). thf(func_def_702, type, sK288: ($i > $i)). thf(func_def_707, type, sK293: ($i > $o)). thf(func_def_708, type, sK294: ($i > $o)). thf(func_def_709, type, sK295: (($i > $o) > ($i > $o) > $i)). thf(func_def_710, type, sK296: (($i > $o) > ($i > $o) > $i)). thf(func_def_711, type, sK297: ($i > $o)). thf(func_def_713, type, sK299: ($i > ($i > $o) > $i)). thf(func_def_714, type, sK300: ($i > $o)). thf(func_def_717, type, sK303: ($i > ($i > $o) > $i)). thf(func_def_718, type, sK304: ($i > $o)). thf(func_def_728, type, sK314: ($i > $i > $o)). thf(func_def_736, type, sK322: ($i > $i > $i > $i > $i)). thf(func_def_749, type, sK335: ($i > $i > $i > $i)). thf(func_def_768, type, sK354: ($i > $i > $o)). thf(func_def_773, type, sK359: ($i > $o)). thf(func_def_779, type, sK365: ($i > $i > $i > $i)). thf(func_def_780, type, sK366: ($i > $i > $i > $i)). thf(func_def_781, type, sK367: ($i > $i > $i > $i)). thf(func_def_782, type, sK368: ($i > $i > $i > $i)). thf(func_def_789, type, sK375: ($i > $i > $i > $i)). thf(func_def_790, type, sK376: ($i > $i > $i > $i)). thf(func_def_794, type, sK380: ($i > $o)). thf(func_def_796, type, sK382: ($i > $i > $o)). thf(func_def_799, type, sK385: ($i > $i > $i)). thf(func_def_803, type, sK389: ($i > $i > $i > $i)). thf(func_def_804, type, sK390: ($i > $i > $i > $i)). thf(func_def_818, type, sK404: $o). thf(func_def_821, type, sK407: (($i > $o) > $i > $i)). thf(func_def_823, type, sK409: ($i > $o)). thf(func_def_840, type, sK426: ($i > $i > $i > $i > $i)). thf(func_def_841, type, sK427: ($i > $i > $i > $i > $i)). thf(func_def_842, type, sK428: ($i > $i > $i > $i > $i)). thf(func_def_843, type, sK429: ($i > $i > $i > $i > $i)). thf(func_def_868, type, sK454: ($i > $o)). thf(func_def_870, type, sK456: (($i > $o) > $i > $i)). thf(func_def_871, type, sK457: (($i > $o) > $i > $i)). thf(func_def_875, type, sK461: ($i > $o)). thf(func_def_883, type, sK469: ($i > $i)). thf(func_def_885, type, sK471: ($i > ($i > $i) > $i > $i)). thf(func_def_896, type, sK482: ($i > $i > ($i > $i) > $i)). thf(func_def_897, type, sK483: ($i > $i)). thf(func_def_916, type, sK502: ($i > ($i > $o) > $i)). thf(func_def_917, type, sK503: ($i > $o)). thf(func_def_926, type, sK512: ($i > ($i > $o) > $i)). thf(func_def_927, type, sK513: ($i > $o)). thf(func_def_937, type, sK523: ($i > $i)). thf(func_def_940, type, sK526: $o). thf(func_def_953, type, sK539: ($i > $i > $i)). thf(func_def_965, type, sK551: ($i > $i > $i)). thf(func_def_976, type, sK562: ($i > $i > $o)). thf(func_def_980, type, sK566: ($i > $o)). thf(func_def_990, type, sK576: (($i > $i > $o) > $i > $i)). thf(func_def_991, type, sK577: ($i > ($i > $i > $o) > $i > $i)). thf(func_def_992, type, sK578: (($i > $i > $o) > $i > $i)). thf(func_def_994, type, sK580: ($i > $i > $o)). thf(func_def_995, type, sK581: ($i > $i)). thf(func_def_996, type, sK582: ($i > $i)). thf(func_def_1001, type, sK587: $o). thf(func_def_1015, type, sK601: (($i > $o) > $i > $i > $i)). thf(func_def_1016, type, sK602: (($i > $o) > $i > $i > $i)). thf(func_def_1019, type, sK605: ($i > $o)). thf(func_def_1025, type, sK611: $o). thf(func_def_1031, type, sK617: ($i > $o)). thf(func_def_1033, type, sK619: ($i > ($i > $o) > $i)). thf(func_def_1034, type, sK620: ($i > $i)). thf(func_def_1036, type, sK622: (($i > $o) > $i > $i > $i > $i)). thf(func_def_1037, type, sK623: (($i > $o) > $i > $i > $i > $i)). thf(func_def_1041, type, sK627: ($i > $o)). thf(func_def_1051, type, sK637: $o). thf(func_def_1057, type, sK643: $o). thf(func_def_1063, type, sK649: ($i > $i > $o)). thf(func_def_1072, type, sK658: ($i > $i > $i)). thf(func_def_1073, type, sK659: ($i > ($i > $i) > $i > $i)). thf(func_def_1075, type, sK661: ($i > $i)). thf(func_def_1083, type, sK669: ($i > $o)). thf(func_def_1084, type, sK670: ($i > $o)). thf(func_def_1085, type, sK671: (($i > $o) > ($i > $o) > $i)). thf(func_def_1086, type, sK672: (($i > $o) > ($i > $o) > $i)). thf(func_def_1094, type, sK680: ($i > $i)). thf(func_def_1097, type, sK683: ($i > $o)). thf(func_def_1106, type, sK692: $o). thf(func_def_1116, type, sK702: ($i > $i > $i)). thf(func_def_1119, type, sK705: ($i > $o)). thf(func_def_1120, type, sK706: ($i > $i)). thf(func_def_1121, type, sK707: (($i > $o) > $i)). thf(func_def_1149, type, sK735: ($i > $o)). thf(func_def_1158, type, sK744: ($i > $o)). thf(func_def_1160, type, sK746: (($i > $o) > $i)). thf(func_def_1161, type, sK747: (($i > $o) > $i)). thf(func_def_1172, type, sK758: ($i > $o)). thf(func_def_1173, type, sK759: ($i > $i)). thf(func_def_1174, type, sK760: (($i > $o) > $i)). thf(func_def_1182, type, sK768: ($i > $o)). thf(func_def_1185, type, sK771: ($i > $i)). thf(func_def_1188, type, sK774: ($i > $i)). thf(func_def_1192, type, sK778: $o). thf(func_def_1202, type, sK788: ($i > $i)). thf(func_def_1205, type, sK791: ($i > $i)). thf(func_def_1206, type, sK792: ($i > $i)). thf(func_def_1207, type, sK793: ($i > $i)). thf(func_def_1208, type, sK794: ($i > $i)). thf(func_def_1209, type, sK795: ($i > $i > $i)). thf(func_def_1210, type, sK796: ($i > $i > $i > $i)). thf(func_def_1211, type, sK797: ($i > $i > $i > $i)). thf(func_def_1212, type, sK798: ($i > $i > $i > $i)). thf(func_def_1213, type, sK799: ($i > $i > $i)). thf(func_def_1214, type, sK800: ($i > $i > $i)). thf(func_def_1215, type, sK801: ($i > $i > $i)). thf(func_def_1216, type, sK802: ($i > $i > $i)). thf(func_def_1217, type, sK803: ($i > $i)). thf(func_def_1218, type, sK804: ($i > $i > $i > $i)). thf(func_def_1220, type, sK806: ($i > $i)). thf(func_def_1221, type, sK807: ($i > $i)). thf(func_def_1222, type, sK808: ($i > $i)). thf(func_def_1223, type, sK809: ($i > $i)). thf(func_def_1230, type, sK816: ($i > $i > ($i > $i > $o) > $i)). thf(func_def_1231, type, sK817: ($i > $i > $o)). thf(func_def_1236, type, sK822: ($i > $i)). thf(func_def_1237, type, sK823: ($o > $i > $i > $i)). thf(func_def_1240, type, sK826: $o). thf(func_def_1242, type, sK828: ($i > $i)). thf(func_def_1246, type, sK832: ($i > $i > $i)). thf(func_def_1260, type, sK846: ($i > $o)). thf(func_def_1309, type, sK895: ($i > $i > $o)). thf(func_def_1324, type, sK910: ($i > $o)). thf(func_def_1325, type, sK911: ($i > $o)). thf(func_def_1326, type, sK912: (($i > $o) > ($i > $o) > $i > $i > $i)). thf(func_def_1327, type, sK913: (($i > $o) > ($i > $o) > $i > $i > $i)). thf(func_def_1337, type, sK923: $o). thf(func_def_1342, type, sK928: ($i > $i > $i > $i > $i)). thf(func_def_1356, type, sK942: ($i > $o)). thf(func_def_1360, type, sK946: $o). thf(func_def_1364, type, sK950: $o). thf(func_def_1373, type, sK959: (($i > $i) > $i > $i)). thf(func_def_1374, type, sK960: ($i > ($i > $i) > $i > $i)). thf(func_def_1376, type, sK962: ($i > $i)). thf(func_def_1377, type, sK963: ($i > $i)). thf(func_def_1378, type, sK964: ($i > $i)). thf(func_def_1385, type, sK971: ($i > $i)). thf(func_def_1409, type, sK995: ($i > $i > $i > $i > $i)). thf(func_def_1415, type, sK1001: (($i > $o) > $i)). thf(func_def_1416, type, sK1002: ($i > $o)). thf(func_def_1425, type, sK1011: ($i > $o)). thf(func_def_1427, type, sK1013: (($i > $o) > $i > $i > $i > $i)). thf(func_def_1428, type, sK1014: (($i > $o) > $i > $i > $i > $i)). thf(func_def_1433, type, sK1019: (($i > $o) > $i > $i)). thf(func_def_1434, type, sK1020: (($i > $o) > $i > $i)). thf(func_def_1436, type, sK1022: ($i > $o)). thf(func_def_1446, type, sK1032: $o). thf(func_def_1457, type, sK1043: ($i > $i > $i > $i)). thf(func_def_1458, type, sK1044: ($i > $i > $i > $i)). thf(func_def_1470, type, sK1056: $o). thf(func_def_1480, type, sK1066: ($i > $i > $i)). thf(func_def_1485, type, sK1071: ($i > $i > $i)). thf(f79,axiom,( (! [X1 : $i,X0 : $i] : ((X0 = X1) => (subset @ X1 @ X0)) = eqimpsubset2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2)). thf(f112,axiom,( (binintersectSubset2 = ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (((binintersect @ X0 @ X1)) = X0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2)). thf(f335,axiom,( (setunionTransitive = ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionTransitive)). thf(f339,axiom,( (! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((ordinal @ X1) => (transitiveset @ (binintersect @ X0 @ X1)))) = ordinalMinLem1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalMinLem1)). thf(f342,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 => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => (transitivesetOp2 => (setunionTransitive => (ordinalMinLem1 => (ordinalTransSet => (ordinalTransSet1 => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (ordinal @ X1)) => (transitiveset @ (setunion @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionOrdinalLem1)). thf(f343,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 => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => (transitivesetOp2 => (setunionTransitive => (ordinalMinLem1 => (ordinalTransSet => (ordinalTransSet1 => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (ordinal @ X1)) => (transitiveset @ (setunion @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(negated_conjecture,[status(cth)],[f342])). thf(f393,plain,( (binintersectSubset2 = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (((binintersect @ X1 @ X0)) = X1)))), inference(rectify,[],[f112])). thf(f394,plain,( (binintersectSubset2 = $true) <=> ! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) => (((binintersect @ X1 @ X0)) = X1))), inference(fool_elimination,[],[f393])). thf(f621,plain,( (! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((ordinal @ X1) => (transitiveset @ (binintersect @ X0 @ X1)))) = ordinalMinLem1)), inference(rectify,[],[f339])). thf(f622,plain,( ! [X0 : $i] : ((((ordinal @ X0)) = $true) => ! [X1 : $i] : ((((ordinal @ X1)) = $true) => (((transitiveset @ (binintersect @ X0 @ X1))) = $true))) <=> (ordinalMinLem1 = $true)), inference(fool_elimination,[],[f621])). thf(f722,plain,( (! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X0 @ X1)) = eqimpsubset2)), inference(rectify,[],[f79])). thf(f723,plain,( ! [X0 : $i,X1 : $i] : ((X0 = X1) => (((subset @ X0 @ X1)) = $true)) <=> (eqimpsubset2 = $true)), inference(fool_elimination,[],[f722])). thf(f886,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 => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => (transitivesetOp2 => (setunionTransitive => (ordinalMinLem1 => (ordinalTransSet => (ordinalTransSet1 => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (ordinal @ X1)) => (transitiveset @ (setunion @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(rectify,[],[f343])). thf(f887,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) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ((woz13rule4 = $true) => ((woz1_1 = $true) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ((breln1invE = $true) => ((breln1compprop = $true) => ((breln1compI = $true) => ((breln1compE = $true) => ((breln1compEex = $true) => ((breln1unionprop = $true) => ((breln1unionIL = $true) => ((breln1unionIR = $true) => ((breln1unionI = $true) => ((breln1unionE = $true) => ((breln1unionEcases = $true) => ((breln1unionCommutes = $true) => ((woz2Ex = $true) => ((woz2W = $true) => ((woz2A = $true) => ((woz2B = $true) => ((image1Ex = $true) => ((image1Ex1 = $true) => ((image1Equiv = $true) => ((image1E = $true) => ((image1I = $true) => ((injFuncInInjFuncSet = $true) => ((injFuncSetFuncIn = $true) => ((injFuncSetFuncInj = $true) => ((surjFuncSetFuncIn = $true) => ((surjFuncSetFuncSurj = $true) => ((leftInvIsSurj = $true) => ((surjCantorThm = $true) => ((foundation2 = $true) => ((notinself = $true) => ((notinself2 = $true) => ((omegaSp = $true) => ((omegaSclos = $true) => ((peano0notS = $true) => ((peanoSinj = $true) => ((transitivesetOp1 = $true) => ((binintTransitive = $true) => ((transitivesetOp2 = $true) => ((setunionTransitive = $true) => ((ordinalMinLem1 = $true) => ((ordinalTransSet = $true) => ((ordinalTransSet1 = $true) => ! [X0 : $i] : (! [X1 : $i] : ((((in @ X1 @ X0)) = $true) => (((ordinal @ X1)) = $true)) => (((transitiveset @ (setunion @ X0))) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(fool_elimination,[],[f886])). thf(f973,plain,( (setunionTransitive = ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X0))))), inference(rectify,[],[f335])). thf(f974,plain,( (setunionTransitive = $true) <=> ! [X0 : $i] : (! [X1 : $i] : ((((in @ X1 @ X0)) = $true) => (((transitiveset @ X1)) = $true)) => (((transitiveset @ (setunion @ X0))) = $true))), inference(fool_elimination,[],[f973])). thf(f1094,plain,( (eqimpsubset2 = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 != X1) | (((subset @ X0 @ X1)) = $true))), inference(ennf_transformation,[],[f723])). thf(f1269,plain,( ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i] : (! [X1 : $i] : ((((ordinal @ X1)) = $true) | (((in @ X1 @ X0)) != $true)) & (((transitiveset @ (setunion @ X0))) != $true)) & (ordinalTransSet1 = $true)) & (ordinalTransSet = $true)) & (ordinalMinLem1 = $true)) & (setunionTransitive = $true)) & (transitivesetOp2 = $true)) & (binintTransitive = $true)) & (transitivesetOp1 = $true)) & (peanoSinj = $true)) & (peano0notS = $true)) & (omegaSclos = $true)) & (omegaSp = $true)) & (notinself2 = $true)) & (notinself = $true)) & (foundation2 = $true)) & (surjCantorThm = $true)) & (leftInvIsSurj = $true)) & (surjFuncSetFuncSurj = $true)) & (surjFuncSetFuncIn = $true)) & (injFuncSetFuncInj = $true)) & (injFuncSetFuncIn = $true)) & (injFuncInInjFuncSet = $true)) & (image1I = $true)) & (image1E = $true)) & (image1Equiv = $true)) & (image1Ex1 = $true)) & (image1Ex = $true)) & (woz2B = $true)) & (woz2A = $true)) & (woz2W = $true)) & (woz2Ex = $true)) & (breln1unionCommutes = $true)) & (breln1unionEcases = $true)) & (breln1unionE = $true)) & (breln1unionI = $true)) & (breln1unionIR = $true)) & (breln1unionIL = $true)) & (breln1unionprop = $true)) & (breln1compEex = $true)) & (breln1compE = $true)) & (breln1compI = $true)) & (breln1compprop = $true)) & (breln1invE = $true)) & (breln1invI = $true)) & (breln1invprop = $true)) & (eqbreln1 = $true)) & (subbreln1 = $true)) & (breln1all1 = $true)) & (setOfPairsIsBReln1 = $true)) & (choice2fnsingleton = $true)) & (breln1SetBreln1 = $true)) & (breln1all2 = $true)) & (woz1_5 = $true)) & (woz1_4 = $true)) & (woz1_3 = $true)) & (woz1_2 = $true)) & (woz1_1 = $true)) & (woz13rule4 = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $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,[],[f887])). thf(f1270,plain,( (quantDeMorgan1 = $true) & (breln1unionCommutes = $true) & (ex1E1 = $true) & (emptyinunitempty = $true) & (funcext = $true) & (demorgan2b2 = $true) & (funcextLem = $true) & (image1Ex = $true) & (descrp = $true) & (binunionIR = $true) & (complementTE1 = $true) & (inPowerset = $true) & (woz2A = $true) & (upairequniteq = $true) & (complementUnionInPowersetComplement = $true) & (brelnall2 = $true) & (ordinalMinLem1 = $true) & (inIntersectImpInIntersectUnions = $true) & (exuI1 = $true) & (setadjoin__Cong = $true) & (subsetE = $true) & (powerset__Cong = $true) & (doubleComplementE1 = $true) & (setminusSubset2 = $true) & (upairset2IR = $true) & (setadjoinSub = $true) & (ifSingleton = $true) & (breln1unionEcases = $true) & (breln1invI = $true) & (dsetconstrER = $true) & (setbeta = $true) & (nonemptyImpWitness = $true) & (symdiffI2 = $true) & (setminusER = $true) & (ifp = $true) & (emptysetE = $true) & (notinemptyset = $true) & (omega__Cong = $true) & (notsubsetI = $true) & (cartprodsndin = $true) & (dpsetconstrER = $true) & (kpairiskpair = $true) & (complementTI1 = $true) & (image1E = $true) & (binunionIL = $true) & (setoftrueEq = $true) & (binintersectSubset4 = $true) & (subsetemptysetimpeq = $true) & (binunionTEcontra = $true) & (binintersectLsub = $true) & (contrasubsetT1 = $true) & (setminusERneg = $true) & (breln1SetBreln1 = $true) & (powersetE1 = $true) & (upairsubunion = $true) & (transitivesetOp1 = $true) & (iffalseProp2 = $true) & (contrasubsetT2 = $true) & (setunionsingleton1 = $true) & (dsetconstr__Cong = $true) & (demorgan2a = $true) & (surjFuncSetFuncIn = $true) & (omegaSp = $true) & (notinself2 = $true) & (woz1_4 = $true) & (setOfPairsIsBReln1 = $true) & (nonemptyE1 = $true) & (iftrueProp2 = $true) & (singletonsubset = $true) & (complementTnotintersectT = $true) & (woz13rule1 = $true) & (binintersectTERcontra = $true) & (doubleComplementSub1 = $true) & (emptyInPowerset = $true) & (peano0notS = $true) & (binunionTIRcontra = $true) & (demorgan1b = $true) & (subsetRefl = $true) & (binunionTILcontra = $true) & (replAx = $true) & (complementImpComplementIntersect = $true) & (dsetconstrI = $true) & (funcGraphProp3 = $true) & (image1Ex1 = $true) & (cartprodpairmemER = $true) & (eqbreln1 = $true) & (disjointsetsI1 = $true) & (injFuncSetFuncIn = $true) & (dpsetconstrEL2 = $true) & (inCongP = $true) & (cartprodmempair = $true) & (complementSubsetComplementIntersect = $true) & (setunionE = $true) & (brelnall1 = $true) & (singletoninpowunion = $true) & (iftrueProp1 = $true) & (singletonprop = $true) & (setukpairIL = $true) & (doubleComplementI1 = $true) & (bs114d = $true) & (notdexE = $true) & (breln1compEex = $true) & (funcinfuncset = $true) & (woz1_1 = $true) & (powersetE = $true) & (setukpairinjL = $true) & (omegaIndAx = $true) & (omega0Ax = $true) & (woz2Ex = $true) & (notinsingleton = $true) & (subbreln1 = $true) & (surjFuncSetFuncSurj = $true) & (breln1all1 = $true) & (ubforcartprodlem1 = $true) & (upairsetIL = $true) & (uniqinunit = $true) & (ex1I2 = $true) & (binunionLsub = $true) & (singletonsswitch = $true) & (contraSubsetComplement = $true) & (contrasubsetT = $true) & (singletoninpowerset = $true) & (binunionE = $true) & (cartprodfstpairEq = $true) & (cartprodsndpairEq = $true) & (quantDeMorgan2 = $true) & (theprop = $true) & (quantDeMorgan4 = $true) & (breln1compE = $true) & (contrasubsetT3 = $true) & (inIntersectImpInUnion2 = $true) & (in__Cong = $true) & (setminusILneg = $true) & (cartprodmempair1 = $true) & (setminusI = $true) & (notinself = $true) & (singletonsuniq = $true) & (binintersectSubset5 = $true) & (ksndsingleton = $true) & (notequalI1 = $true) & (setadjoinAx = $true) & (setminusT_lem = $true) & (binintersectRsub = $true) & (dpsetconstrI = $true) & (ksndpairEq = $true) & (binunionEcases = $true) & (apProp = $true) & (powersetT_lem = $true) & (dsetconstrEL = $true) & (prop2setE = $true) & (upairsetE = $true) & (sepSubset = $true) & (kpairsurjEq = $true) & (breln1unionE = $true) & (powersetsubset = $true) & (nonemptyI = $true) & (binintersectSubset1 = $true) & (ubforcartprodlem3 = $true) & (kfstpairEq = $true) & (subPowSU = $true) & (emptyI = $true) & (dpsetconstrEL1 = $true) & (upairset2E = $true) & (binintersectSubset3 = $true) & (image1I = $true) & (powersetTI1 = $true) & (prop2setI = $true) & (iffalseProp1 = $true) & (upairinpowunion = $true) & (theeq = $true) & (injFuncSetFuncInj = $true) & (emptysetAx = $true) & (breln1invE = $true) & (beta2 = $true) & (infuncsetfunc = $true) & (dpsetconstrERa = $true) & (setunionI = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (setunionsingleton = $true) & (subset2powerset = $true) & (sepInPowerset = $true) & (binintTransitive = $true) & (subsetTI = $true) & (descr__Cong = $true) & (peanoSinj = $true) & (demorgan2a1 = $true) & (eqimpsubset2 = $true) & (setadjoinIR = $true) & (subsetI1 = $true) & (nonemptyI1 = $true) & (woz13rule4 = $true) & (setunion__Cong = $true) & (complementTcontraSubset = $true) & (symdiffE = $true) & (demorgan1 = $true) & ? [X0 : $i] : (! [X1 : $i] : ((((ordinal @ X1)) = $true) | (((in @ X1 @ X0)) != $true)) & (((transitiveset @ (setunion @ X0))) != $true)) & (binintersectTELcontra = $true) & (setukpairinjR11 = $true) & (lam2lamEq = $true) & (transitivesetOp2 = $true) & (image1Equiv = $true) & (omegaSclos = $true) & (binunionTE = $true) & (upairsetIR = $true) & (breln1unionI = $true) & (setext = $true) & (dpsetconstrSub = $true) & (noeltsimpempty = $true) & (ex1I = $true) & (lam2p = $true) & (setminusSubset1 = $true) & (eqimpsubset1 = $true) & (breln1unionprop = $true) & (eqbreln = $true) & (breln1invprop = $true) & (woz13rule0 = $true) & (cartprodpairin = $true) & (choice2fnsingleton = $true) & (prop2set2propI = $true) & (setadjoinE = $true) & (exuE1 = $true) & (powersetI = $true) & (eta1 = $true) & (exuE3e = $true) & (iftrueorfalse = $true) & (setukpairinjR2 = $true) & (cartprodmempaircEq = $true) & (exu__Cong = $true) & (ex1E2 = $true) & (symdiffI1 = $true) & (ap2apEq2 = $true) & (setunionAx = $true) & (setadjoinSub2 = $true) & (woz13rule2 = $true) & (breln1all2 = $true) & (woz1_5 = $true) & (setukpairinjL1 = $true) & (setukpairinjL2 = $true) & (binunionRsub = $true) & (inComplementUnionImpInComplement1 = $true) & (setunionE2 = $true) & (exuEu = $true) & (binintersectER = $true) & (vacuousDall = $true) & (setextAx = $true) & (setukpairinjR = $true) & (breln1unionIR = $true) & (setminusELneg = $true) & (binintersectEL = $true) & (binintersectI = $true) & (surjCantorThm = $true) & (wellorderingAx = $true) & (complementT_lem = $true) & (cartprodpairmemEL = $true) & (funcGraphProp2 = $true) & (notdallE = $true) & (kpairp = $true) & (setextT = $true) & (setunionsingleton2 = $true) & (demorgan1a = $true) & (lamProp = $true) & (foundationAx = $true) & (app = $true) & (omegaSAx = $true) & (iffalse = $true) & (demorgan2 = $true) & (eqinunit = $true) & (injFuncInInjFuncSet = $true) & (setunionTransitive = $true) & (setminusLsub = $true) & (subsetE2 = $true) & (notequalI2 = $true) & (ap2apEq1 = $true) & (woz1_3 = $true) & (doubleComplementSub2 = $true) & (breln1compprop = $true) & (setukpairinjR1 = $true) & (eta2 = $true) & (subbreln = $true) & (inComplementUnionImpNotIn1 = $true) & (woz13rule3 = $true) & (emptyinPowerset = $true) & (binintersectT_lem = $true) & (exuI2 = $true) & (ordinalTransSet1 = $true) & (woz2W = $true) & (setextsub = $true) & (complementInPowersetComplementIntersect = $true) & (setadjoinIL = $true) & (binintersectSubset2 = $true) & (lamp = $true) & (setukpairinjR12 = $true) & (setukpairIR = $true) & (binunionT_lem = $true) & (ordinalTransSet = $true) & (secondinupair = $true) & (setminusEL = $true) & (funcGraphProp4 = $true) & (doubleComplementEq = $true) & (breln1unionIL = $true) & (foundation2 = $true) & (woz1_2 = $true) & (setOfPairsIsBReln = $true) & (setadjoinOr = $true) & (cartprodfstin = $true) & (inIntersectImpInUnion = $true) & (kfstsingleton = $true) & (funcext2 = $true) & (powersetI1 = $true) & (funcImageSingleton = $true) & (subsetI2 = $true) & (cartprodpairsurjEq = $true) & (exuI3 = $true) & (demorgan2b = $true) & (emptysetimpfalse = $true) & (emptysetsubset = $true) & (intersectInPowersetIntersectUnions = $true) & (emptyset__Cong = $true) & (funcGraphProp1 = $true) & (ap2p = $true) & (ubforcartprodlem2 = $true) & (subsetTrans = $true) & (demorgan2a2 = $true) & (emptyE1 = $true) & (iftrue = $true) & (exuE3u = $true) & (exuE2 = $true) & (setminusIRneg = $true) & (woz2B = $true) & (beta1 = $true) & (leftInvIsSurj = $true) & (breln1compI = $true) & (quantDeMorgan3 = $true) & (powersetTE1 = $true) & (powersetAx = $true)), inference(flattening,[],[f1269])). thf(f1361,plain,( (setunionTransitive = $true) <=> ! [X0 : $i] : (? [X1 : $i] : ((((transitiveset @ X1)) != $true) & (((in @ X1 @ X0)) = $true)) | (((transitiveset @ (setunion @ X0))) = $true))), inference(ennf_transformation,[],[f974])). thf(f1387,plain,( ! [X0 : $i] : ((((ordinal @ X0)) != $true) | ! [X1 : $i] : ((((transitiveset @ (binintersect @ X0 @ X1))) = $true) | (((ordinal @ X1)) != $true))) <=> (ordinalMinLem1 = $true)), inference(ennf_transformation,[],[f622])). thf(f1396,plain,( (binintersectSubset2 = $true) <=> ! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) | (((binintersect @ X1 @ X0)) = X1))), inference(ennf_transformation,[],[f394])). thf(f1584,plain,( ((setunionTransitive = $true) | ? [X0 : $i] : (! [X1 : $i] : ((((transitiveset @ X1)) = $true) | (((in @ X1 @ X0)) != $true)) & (((transitiveset @ (setunion @ X0))) != $true))) & (! [X0 : $i] : (? [X1 : $i] : ((((transitiveset @ X1)) != $true) & (((in @ X1 @ X0)) = $true)) | (((transitiveset @ (setunion @ X0))) = $true)) | (setunionTransitive != $true))), inference(nnf_transformation,[],[f1361])). thf(f1585,plain,( ((setunionTransitive = $true) | ? [X0 : $i] : (! [X1 : $i] : ((((transitiveset @ X1)) = $true) | (((in @ X1 @ X0)) != $true)) & (((transitiveset @ (setunion @ X0))) != $true))) & (! [X2 : $i] : (? [X3 : $i] : (($true != ((transitiveset @ X3))) & (((in @ X3 @ X2)) = $true)) | (((transitiveset @ (setunion @ X2))) = $true)) | (setunionTransitive != $true))), inference(rectify,[],[f1584])). thf(f1586,plain,( ((setunionTransitive = $true) | (! [X1 : $i] : ((((transitiveset @ X1)) = $true) | ($true != ((in @ X1 @ sK107)))) & ($true != ((transitiveset @ (setunion @ sK107)))))) & (! [X2 : $i] : ((($true != ((transitiveset @ (sK108 @ X2)))) & ($true = ((in @ (sK108 @ X2) @ X2)))) | (((transitiveset @ (setunion @ X2))) = $true)) | (setunionTransitive != $true))), inference(skolemize,[status(esa),new_symbols(skolem,[sK107,vAPP]),skolemize(X0,$thf(sK107)),skolemize(X6,$thf(sK24 @ X5 @ X4))],[f1585])). thf(f1599,plain,( ((binintersectSubset2 = $true) | ? [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) & (((binintersect @ X1 @ X0)) != X1))) & (! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) | (((binintersect @ X1 @ X0)) = X1)) | (binintersectSubset2 != $true))), inference(nnf_transformation,[],[f1396])). thf(f1600,plain,( ((binintersectSubset2 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) & (((binintersect @ X0 @ X1)) != X0))) & (! [X2 : $i,X3 : $i] : ((((subset @ X2 @ X3)) != $true) | (((binintersect @ X2 @ X3)) = X2)) | (binintersectSubset2 != $true))), inference(rectify,[],[f1599])). thf(f1601,plain,( ((binintersectSubset2 = $true) | (($true = ((subset @ sK122 @ sK123))) & (((binintersect @ sK122 @ sK123)) != sK122))) & (! [X2 : $i,X3 : $i] : ((((subset @ X2 @ X3)) != $true) | (((binintersect @ X2 @ X3)) = X2)) | (binintersectSubset2 != $true))), inference(skolemize,[status(esa),new_symbols(skolem,[sK122,sK123]),skolemize(X0,$thf(sK122)),skolemize(X1,$thf(sK123))],[f1600])). thf(f1867,plain,( (! [X0 : $i] : ((((ordinal @ X0)) != $true) | ! [X1 : $i] : ((((transitiveset @ (binintersect @ X0 @ X1))) = $true) | (((ordinal @ X1)) != $true))) | (ordinalMinLem1 != $true)) & ((ordinalMinLem1 = $true) | ? [X0 : $i] : ((((ordinal @ X0)) = $true) & ? [X1 : $i] : ((((transitiveset @ (binintersect @ X0 @ X1))) != $true) & (((ordinal @ X1)) = $true))))), inference(nnf_transformation,[],[f1387])). thf(f1868,plain,( (! [X0 : $i] : ((((ordinal @ X0)) != $true) | ! [X1 : $i] : ((((transitiveset @ (binintersect @ X0 @ X1))) = $true) | (((ordinal @ X1)) != $true))) | (ordinalMinLem1 != $true)) & ((ordinalMinLem1 = $true) | ? [X2 : $i] : (($true = ((ordinal @ X2))) & ? [X3 : $i] : (($true != ((transitiveset @ (binintersect @ X2 @ X3)))) & ($true = ((ordinal @ X3))))))), inference(rectify,[],[f1867])). thf(f1869,plain,( (! [X0 : $i] : ((((ordinal @ X0)) != $true) | ! [X1 : $i] : ((((transitiveset @ (binintersect @ X0 @ X1))) = $true) | (((ordinal @ X1)) != $true))) | (ordinalMinLem1 != $true)) & ((ordinalMinLem1 = $true) | (($true = ((ordinal @ sK424))) & (($true != ((transitiveset @ (binintersect @ sK424 @ sK425)))) & ($true = ((ordinal @ sK425))))))), inference(skolemize,[status(esa),new_symbols(skolem,[sK424,sK425]),skolemize(X2,$thf(sK424)),skolemize(X3,$thf(sK425))],[f1868])). thf(f2020,plain,( (quantDeMorgan1 = $true) & (breln1unionCommutes = $true) & (ex1E1 = $true) & (emptyinunitempty = $true) & (funcext = $true) & (demorgan2b2 = $true) & (funcextLem = $true) & (image1Ex = $true) & (descrp = $true) & (binunionIR = $true) & (complementTE1 = $true) & (inPowerset = $true) & (woz2A = $true) & (upairequniteq = $true) & (complementUnionInPowersetComplement = $true) & (brelnall2 = $true) & (ordinalMinLem1 = $true) & (inIntersectImpInIntersectUnions = $true) & (exuI1 = $true) & (setadjoin__Cong = $true) & (subsetE = $true) & (powerset__Cong = $true) & (doubleComplementE1 = $true) & (setminusSubset2 = $true) & (upairset2IR = $true) & (setadjoinSub = $true) & (ifSingleton = $true) & (breln1unionEcases = $true) & (breln1invI = $true) & (dsetconstrER = $true) & (setbeta = $true) & (nonemptyImpWitness = $true) & (symdiffI2 = $true) & (setminusER = $true) & (ifp = $true) & (emptysetE = $true) & (notinemptyset = $true) & (omega__Cong = $true) & (notsubsetI = $true) & (cartprodsndin = $true) & (dpsetconstrER = $true) & (kpairiskpair = $true) & (complementTI1 = $true) & (image1E = $true) & (binunionIL = $true) & (setoftrueEq = $true) & (binintersectSubset4 = $true) & (subsetemptysetimpeq = $true) & (binunionTEcontra = $true) & (binintersectLsub = $true) & (contrasubsetT1 = $true) & (setminusERneg = $true) & (breln1SetBreln1 = $true) & (powersetE1 = $true) & (upairsubunion = $true) & (transitivesetOp1 = $true) & (iffalseProp2 = $true) & (contrasubsetT2 = $true) & (setunionsingleton1 = $true) & (dsetconstr__Cong = $true) & (demorgan2a = $true) & (surjFuncSetFuncIn = $true) & (omegaSp = $true) & (notinself2 = $true) & (woz1_4 = $true) & (setOfPairsIsBReln1 = $true) & (nonemptyE1 = $true) & (iftrueProp2 = $true) & (singletonsubset = $true) & (complementTnotintersectT = $true) & (woz13rule1 = $true) & (binintersectTERcontra = $true) & (doubleComplementSub1 = $true) & (emptyInPowerset = $true) & (peano0notS = $true) & (binunionTIRcontra = $true) & (demorgan1b = $true) & (subsetRefl = $true) & (binunionTILcontra = $true) & (replAx = $true) & (complementImpComplementIntersect = $true) & (dsetconstrI = $true) & (funcGraphProp3 = $true) & (image1Ex1 = $true) & (cartprodpairmemER = $true) & (eqbreln1 = $true) & (disjointsetsI1 = $true) & (injFuncSetFuncIn = $true) & (dpsetconstrEL2 = $true) & (inCongP = $true) & (cartprodmempair = $true) & (complementSubsetComplementIntersect = $true) & (setunionE = $true) & (brelnall1 = $true) & (singletoninpowunion = $true) & (iftrueProp1 = $true) & (singletonprop = $true) & (setukpairIL = $true) & (doubleComplementI1 = $true) & (bs114d = $true) & (notdexE = $true) & (breln1compEex = $true) & (funcinfuncset = $true) & (woz1_1 = $true) & (powersetE = $true) & (setukpairinjL = $true) & (omegaIndAx = $true) & (omega0Ax = $true) & (woz2Ex = $true) & (notinsingleton = $true) & (subbreln1 = $true) & (surjFuncSetFuncSurj = $true) & (breln1all1 = $true) & (ubforcartprodlem1 = $true) & (upairsetIL = $true) & (uniqinunit = $true) & (ex1I2 = $true) & (binunionLsub = $true) & (singletonsswitch = $true) & (contraSubsetComplement = $true) & (contrasubsetT = $true) & (singletoninpowerset = $true) & (binunionE = $true) & (cartprodfstpairEq = $true) & (cartprodsndpairEq = $true) & (quantDeMorgan2 = $true) & (theprop = $true) & (quantDeMorgan4 = $true) & (breln1compE = $true) & (contrasubsetT3 = $true) & (inIntersectImpInUnion2 = $true) & (in__Cong = $true) & (setminusILneg = $true) & (cartprodmempair1 = $true) & (setminusI = $true) & (notinself = $true) & (singletonsuniq = $true) & (binintersectSubset5 = $true) & (ksndsingleton = $true) & (notequalI1 = $true) & (setadjoinAx = $true) & (setminusT_lem = $true) & (binintersectRsub = $true) & (dpsetconstrI = $true) & (ksndpairEq = $true) & (binunionEcases = $true) & (apProp = $true) & (powersetT_lem = $true) & (dsetconstrEL = $true) & (prop2setE = $true) & (upairsetE = $true) & (sepSubset = $true) & (kpairsurjEq = $true) & (breln1unionE = $true) & (powersetsubset = $true) & (nonemptyI = $true) & (binintersectSubset1 = $true) & (ubforcartprodlem3 = $true) & (kfstpairEq = $true) & (subPowSU = $true) & (emptyI = $true) & (dpsetconstrEL1 = $true) & (upairset2E = $true) & (binintersectSubset3 = $true) & (image1I = $true) & (powersetTI1 = $true) & (prop2setI = $true) & (iffalseProp1 = $true) & (upairinpowunion = $true) & (theeq = $true) & (injFuncSetFuncInj = $true) & (emptysetAx = $true) & (breln1invE = $true) & (beta2 = $true) & (infuncsetfunc = $true) & (dpsetconstrERa = $true) & (setunionI = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (setunionsingleton = $true) & (subset2powerset = $true) & (sepInPowerset = $true) & (binintTransitive = $true) & (subsetTI = $true) & (descr__Cong = $true) & (peanoSinj = $true) & (demorgan2a1 = $true) & (eqimpsubset2 = $true) & (setadjoinIR = $true) & (subsetI1 = $true) & (nonemptyI1 = $true) & (woz13rule4 = $true) & (setunion__Cong = $true) & (complementTcontraSubset = $true) & (symdiffE = $true) & (demorgan1 = $true) & (! [X1 : $i] : ((((ordinal @ X1)) = $true) | ($true != ((in @ X1 @ sK590)))) & (((transitiveset @ (setunion @ sK590))) != $true)) & (binintersectTELcontra = $true) & (setukpairinjR11 = $true) & (lam2lamEq = $true) & (transitivesetOp2 = $true) & (image1Equiv = $true) & (omegaSclos = $true) & (binunionTE = $true) & (upairsetIR = $true) & (breln1unionI = $true) & (setext = $true) & (dpsetconstrSub = $true) & (noeltsimpempty = $true) & (ex1I = $true) & (lam2p = $true) & (setminusSubset1 = $true) & (eqimpsubset1 = $true) & (breln1unionprop = $true) & (eqbreln = $true) & (breln1invprop = $true) & (woz13rule0 = $true) & (cartprodpairin = $true) & (choice2fnsingleton = $true) & (prop2set2propI = $true) & (setadjoinE = $true) & (exuE1 = $true) & (powersetI = $true) & (eta1 = $true) & (exuE3e = $true) & (iftrueorfalse = $true) & (setukpairinjR2 = $true) & (cartprodmempaircEq = $true) & (exu__Cong = $true) & (ex1E2 = $true) & (symdiffI1 = $true) & (ap2apEq2 = $true) & (setunionAx = $true) & (setadjoinSub2 = $true) & (woz13rule2 = $true) & (breln1all2 = $true) & (woz1_5 = $true) & (setukpairinjL1 = $true) & (setukpairinjL2 = $true) & (binunionRsub = $true) & (inComplementUnionImpInComplement1 = $true) & (setunionE2 = $true) & (exuEu = $true) & (binintersectER = $true) & (vacuousDall = $true) & (setextAx = $true) & (setukpairinjR = $true) & (breln1unionIR = $true) & (setminusELneg = $true) & (binintersectEL = $true) & (binintersectI = $true) & (surjCantorThm = $true) & (wellorderingAx = $true) & (complementT_lem = $true) & (cartprodpairmemEL = $true) & (funcGraphProp2 = $true) & (notdallE = $true) & (kpairp = $true) & (setextT = $true) & (setunionsingleton2 = $true) & (demorgan1a = $true) & (lamProp = $true) & (foundationAx = $true) & (app = $true) & (omegaSAx = $true) & (iffalse = $true) & (demorgan2 = $true) & (eqinunit = $true) & (injFuncInInjFuncSet = $true) & (setunionTransitive = $true) & (setminusLsub = $true) & (subsetE2 = $true) & (notequalI2 = $true) & (ap2apEq1 = $true) & (woz1_3 = $true) & (doubleComplementSub2 = $true) & (breln1compprop = $true) & (setukpairinjR1 = $true) & (eta2 = $true) & (subbreln = $true) & (inComplementUnionImpNotIn1 = $true) & (woz13rule3 = $true) & (emptyinPowerset = $true) & (binintersectT_lem = $true) & (exuI2 = $true) & (ordinalTransSet1 = $true) & (woz2W = $true) & (setextsub = $true) & (complementInPowersetComplementIntersect = $true) & (setadjoinIL = $true) & (binintersectSubset2 = $true) & (lamp = $true) & (setukpairinjR12 = $true) & (setukpairIR = $true) & (binunionT_lem = $true) & (ordinalTransSet = $true) & (secondinupair = $true) & (setminusEL = $true) & (funcGraphProp4 = $true) & (doubleComplementEq = $true) & (breln1unionIL = $true) & (foundation2 = $true) & (woz1_2 = $true) & (setOfPairsIsBReln = $true) & (setadjoinOr = $true) & (cartprodfstin = $true) & (inIntersectImpInUnion = $true) & (kfstsingleton = $true) & (funcext2 = $true) & (powersetI1 = $true) & (funcImageSingleton = $true) & (subsetI2 = $true) & (cartprodpairsurjEq = $true) & (exuI3 = $true) & (demorgan2b = $true) & (emptysetimpfalse = $true) & (emptysetsubset = $true) & (intersectInPowersetIntersectUnions = $true) & (emptyset__Cong = $true) & (funcGraphProp1 = $true) & (ap2p = $true) & (ubforcartprodlem2 = $true) & (subsetTrans = $true) & (demorgan2a2 = $true) & (emptyE1 = $true) & (iftrue = $true) & (exuE3u = $true) & (exuE2 = $true) & (setminusIRneg = $true) & (woz2B = $true) & (beta1 = $true) & (leftInvIsSurj = $true) & (breln1compI = $true) & (quantDeMorgan3 = $true) & (powersetTE1 = $true) & (powersetAx = $true)), inference(skolemize,[status(esa),new_symbols(skolem,[sK590]),skolemize(X0,$thf(sK590))],[f1270])). thf(f2279,plain,( ((eqimpsubset2 = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & (((subset @ X0 @ X1)) != $true))) & (! [X0 : $i,X1 : $i] : ((X0 != X1) | (((subset @ X0 @ X1)) = $true)) | (eqimpsubset2 != $true))), inference(nnf_transformation,[],[f1094])). thf(f2280,plain,( ((eqimpsubset2 = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & (((subset @ X0 @ X1)) != $true))) & (! [X2 : $i,X3 : $i] : ((X2 != X3) | (((subset @ X2 @ X3)) = $true)) | (eqimpsubset2 != $true))), inference(rectify,[],[f2279])). thf(f2281,plain,( ((eqimpsubset2 = $true) | ((sK864 = sK863) & ($true != ((subset @ sK863 @ sK864))))) & (! [X2 : $i,X3 : $i] : ((X2 != X3) | (((subset @ X2 @ X3)) = $true)) | (eqimpsubset2 != $true))), inference(skolemize,[status(esa),new_symbols(skolem,[sK863,sK864]),skolemize(X0,$thf(sK863)),skolemize(X1,$thf(sK864))],[f2280])). thf(f2633,plain,( ( ! [X2 : $i] : (($true = ((in @ (sK108 @ X2) @ X2))) | (setunionTransitive != $true) | (((transitiveset @ (setunion @ X2))) = $true)) )), inference(cnf_transformation,[],[f1586])). thf(f2634,plain,( ( ! [X2 : $i] : ((((transitiveset @ (setunion @ X2))) = $true) | ($true != ((transitiveset @ (sK108 @ X2)))) | (setunionTransitive != $true)) )), inference(cnf_transformation,[],[f1586])). thf(f2654,plain,( ( ! [X2 : $i,X3 : $i] : ((((binintersect @ X2 @ X3)) = X2) | (((subset @ X2 @ X3)) != $true) | (binintersectSubset2 != $true)) )), inference(cnf_transformation,[],[f1601])). thf(f3063,plain,( ( ! [X0 : $i,X1 : $i] : ((((ordinal @ X0)) != $true) | (ordinalMinLem1 != $true) | (((ordinal @ X1)) != $true) | (((transitiveset @ (binintersect @ X0 @ X1))) = $true)) )), inference(cnf_transformation,[],[f1869])). thf(f3331,plain,( (binintersectSubset2 = $true)), inference(cnf_transformation,[],[f2020])). thf(f3352,plain,( (setunionTransitive = $true)), inference(cnf_transformation,[],[f2020])). thf(f3425,plain,( (((transitiveset @ (setunion @ sK590))) != $true)), inference(cnf_transformation,[],[f2020])). thf(f3426,plain,( ( ! [X1 : $i] : (($true != ((in @ X1 @ sK590))) | (((ordinal @ X1)) = $true)) )), inference(cnf_transformation,[],[f2020])). thf(f3435,plain,( (eqimpsubset2 = $true)), inference(cnf_transformation,[],[f2020])). thf(f3606,plain,( (ordinalMinLem1 = $true)), inference(cnf_transformation,[],[f2020])). thf(f4028,plain,( ( ! [X2 : $i,X3 : $i] : ((X2 != X3) | (((subset @ X2 @ X3)) = $true) | (eqimpsubset2 != $true)) )), inference(cnf_transformation,[],[f2281])). thf(f4396,plain,( ( ! [X3 : $i] : (($true = ((subset @ X3 @ X3))) | (eqimpsubset2 != $true)) )), inference(equality_resolution,[],[f4028])). thf(f5391,definition,( spl1095_192 <=> (setunionTransitive = $true)), introduced(definition,[new_symbols(definition,[spl1095_192])],[avatar_definition])). thf(f5395,definition,( spl1095_193 <=> ! [X2 : $i] : ((((transitiveset @ (setunion @ X2))) = $true) | ($true != ((transitiveset @ (sK108 @ X2)))))), introduced(definition,[new_symbols(definition,[spl1095_193])],[avatar_definition])). thf(f5396,plain,( ( ! [X2 : $i] : (($true != ((transitiveset @ (sK108 @ X2)))) | (((transitiveset @ (setunion @ X2))) = $true)) ) | ~spl1095_193), inference(avatar_component_clause,[],[f5395])). thf(f5397,plain,( ~spl1095_192 | spl1095_193), inference(avatar_split_clause,[],[f2634,f5395,f5391])). thf(f6732,definition,( spl1095_489 <=> (binintersectSubset2 = $true)), introduced(definition,[new_symbols(definition,[spl1095_489])],[avatar_definition])). thf(f6736,definition,( spl1095_490 <=> ! [X2 : $i,X3 : $i] : ((((binintersect @ X2 @ X3)) = X2) | (((subset @ X2 @ X3)) != $true))), introduced(definition,[new_symbols(definition,[spl1095_490])],[avatar_definition])). thf(f6737,plain,( ( ! [X2 : $i,X3 : $i] : ((((subset @ X2 @ X3)) != $true) | (((binintersect @ X2 @ X3)) = X2)) ) | ~spl1095_490), inference(avatar_component_clause,[],[f6736])). thf(f6738,plain,( ~spl1095_489 | spl1095_490), inference(avatar_split_clause,[],[f2654,f6736,f6732])). thf(f6831,definition,( spl1095_512 <=> (eqimpsubset2 = $true)), introduced(definition,[new_symbols(definition,[spl1095_512])],[avatar_definition])). thf(f7937,definition,( spl1095_748 <=> (ordinalMinLem1 = $true)), introduced(definition,[new_symbols(definition,[spl1095_748])],[avatar_definition])). thf(f7941,definition,( spl1095_749 <=> ! [X0 : $i,X1 : $i] : ((((ordinal @ X0)) != $true) | (((transitiveset @ (binintersect @ X0 @ X1))) = $true) | (((ordinal @ X1)) != $true))), introduced(definition,[new_symbols(definition,[spl1095_749])],[avatar_definition])). thf(f7942,plain,( ( ! [X0 : $i,X1 : $i] : ((((ordinal @ X1)) != $true) | (((transitiveset @ (binintersect @ X0 @ X1))) = $true) | (((ordinal @ X0)) != $true)) ) | ~spl1095_749), inference(avatar_component_clause,[],[f7941])). thf(f7943,plain,( ~spl1095_748 | spl1095_749), inference(avatar_split_clause,[],[f3063,f7941,f7937])). thf(f8411,definition,( spl1095_848 <=> (((transitiveset @ (setunion @ sK590))) = $true)), introduced(definition,[new_symbols(definition,[spl1095_848])],[avatar_definition])). thf(f8413,plain,( (((transitiveset @ (setunion @ sK590))) != $true) | spl1095_848), inference(avatar_component_clause,[],[f8411])). thf(f8414,plain,( ~spl1095_848), inference(avatar_split_clause,[],[f3425,f8411])). thf(f9104,plain,( spl1095_748), inference(avatar_split_clause,[],[f3606,f7937])). thf(f10065,definition,( spl1095_1191 <=> ! [X3 : $i] : ($true = ((subset @ X3 @ X3)))), introduced(definition,[new_symbols(definition,[spl1095_1191])],[avatar_definition])). thf(f10066,plain,( ( ! [X3 : $i] : (($true = ((subset @ X3 @ X3)))) ) | ~spl1095_1191), inference(avatar_component_clause,[],[f10065])). thf(f10627,plain,( spl1095_192), inference(avatar_split_clause,[],[f3352,f5391])). thf(f11764,definition,( spl1095_1538 <=> ! [X2 : $i] : (($true = ((in @ (sK108 @ X2) @ X2))) | (((transitiveset @ (setunion @ X2))) = $true))), introduced(definition,[new_symbols(definition,[spl1095_1538])],[avatar_definition])). thf(f11765,plain,( ( ! [X2 : $i] : (($true = ((in @ (sK108 @ X2) @ X2))) | (((transitiveset @ (setunion @ X2))) = $true)) ) | ~spl1095_1538), inference(avatar_component_clause,[],[f11764])). thf(f11766,plain,( spl1095_1538 | ~spl1095_192), inference(avatar_split_clause,[],[f2633,f5391,f11764])). thf(f12391,plain,( spl1095_489), inference(avatar_split_clause,[],[f3331,f6732])). thf(f12660,plain,( spl1095_512), inference(avatar_split_clause,[],[f3435,f6831])). thf(f12729,plain,( spl1095_1191 | ~spl1095_512), inference(avatar_split_clause,[],[f4396,f6831,f10065])). thf(f13373,plain,( ( ! [X0 : $i] : ((((binintersect @ X0 @ X0)) = X0) | ($true != $true)) ) | (~spl1095_490 | ~spl1095_1191)), inference(superposition,[],[f6737,f10066])). thf(f13381,plain,( ( ! [X0 : $i] : ((((binintersect @ X0 @ X0)) = X0)) ) | (~spl1095_490 | ~spl1095_1191)), inference(trivial_inequality_removal,[],[f13373])). thf(f13479,plain,( ($true = ((ordinal @ (sK108 @ sK590)))) | ($true != $true) | (((transitiveset @ (setunion @ sK590))) = $true) | ~spl1095_1538), inference(superposition,[],[f3426,f11765])). thf(f13487,plain,( (((transitiveset @ (setunion @ sK590))) = $true) | ($true = ((ordinal @ (sK108 @ sK590)))) | ~spl1095_1538), inference(trivial_inequality_removal,[],[f13479])). thf(f13500,plain,( ($true = ((ordinal @ (sK108 @ sK590)))) | (spl1095_848 | ~spl1095_1538)), inference(forward_subsumption_resolution,[],[f13487,f8413])). thf(f13509,definition,( spl1095_1786 <=> ($true = ((ordinal @ (sK108 @ sK590))))), introduced(definition,[new_symbols(definition,[spl1095_1786])],[avatar_definition])). thf(f13511,plain,( ($true = ((ordinal @ (sK108 @ sK590)))) | ~spl1095_1786), inference(avatar_component_clause,[],[f13509])). thf(f13512,plain,( spl1095_1786 | spl1095_848 | ~spl1095_1538), inference(avatar_split_clause,[],[f13500,f11764,f8411,f13509])). thf(f13752,plain,( ( ! [X0 : $i] : (($true != $true) | ($true = ((transitiveset @ (binintersect @ X0 @ (sK108 @ sK590))))) | (((ordinal @ X0)) != $true)) ) | (~spl1095_749 | ~spl1095_1786)), inference(superposition,[],[f7942,f13511])). thf(f13753,plain,( ( ! [X0 : $i] : ((((ordinal @ X0)) != $true) | ($true = ((transitiveset @ (binintersect @ X0 @ (sK108 @ sK590)))))) ) | (~spl1095_749 | ~spl1095_1786)), inference(trivial_inequality_removal,[],[f13752])). thf(f14782,plain,( ($true != $true) | ($true = ((transitiveset @ (binintersect @ (sK108 @ sK590) @ (sK108 @ sK590))))) | (~spl1095_749 | ~spl1095_1786)), inference(superposition,[],[f13753,f13511])). thf(f14784,plain,( ($true = ((transitiveset @ (binintersect @ (sK108 @ sK590) @ (sK108 @ sK590))))) | (~spl1095_749 | ~spl1095_1786)), inference(trivial_inequality_removal,[],[f14782])). thf(f14792,definition,( spl1095_1810 <=> ($true = ((transitiveset @ (binintersect @ (sK108 @ sK590) @ (sK108 @ sK590)))))), introduced(definition,[new_symbols(definition,[spl1095_1810])],[avatar_definition])). thf(f14794,plain,( ($true = ((transitiveset @ (binintersect @ (sK108 @ sK590) @ (sK108 @ sK590))))) | ~spl1095_1810), inference(avatar_component_clause,[],[f14792])). thf(f14795,plain,( spl1095_1810 | ~spl1095_749 | ~spl1095_1786), inference(avatar_split_clause,[],[f14784,f13509,f7941,f14792])). thf(f21985,plain,( ($true = ((transitiveset @ (sK108 @ sK590)))) | (~spl1095_490 | ~spl1095_1191 | ~spl1095_1810)), inference(superposition,[],[f14794,f13381])). thf(f22140,definition,( spl1095_2058 <=> ($true = ((transitiveset @ (sK108 @ sK590))))), introduced(definition,[new_symbols(definition,[spl1095_2058])],[avatar_definition])). thf(f22142,plain,( ($true = ((transitiveset @ (sK108 @ sK590)))) | ~spl1095_2058), inference(avatar_component_clause,[],[f22140])). thf(f22143,plain,( spl1095_2058 | ~spl1095_490 | ~spl1095_1191 | ~spl1095_1810), inference(avatar_split_clause,[],[f21985,f14792,f10065,f6736,f22140])). thf(f24690,plain,( ($true != $true) | (((transitiveset @ (setunion @ sK590))) = $true) | (~spl1095_193 | ~spl1095_2058)), inference(superposition,[],[f5396,f22142])). thf(f24698,plain,( (((transitiveset @ (setunion @ sK590))) = $true) | (~spl1095_193 | ~spl1095_2058)), inference(trivial_inequality_removal,[],[f24690])). thf(f24704,plain,( $false | (~spl1095_193 | spl1095_848 | ~spl1095_2058)), inference(forward_subsumption_resolution,[],[f24698,f8413])). thf(f24705,plain,( ~spl1095_193 | spl1095_848 | ~spl1095_2058), inference(avatar_contradiction_clause,[],[f24704])). cnf(s110, plain, ~spl1095_192 | spl1095_193, inference(sat_conversion,[],[f5397])). cnf(s330, plain, ~spl1095_489 | spl1095_490, inference(sat_conversion,[],[f6738])). cnf(s563, plain, ~spl1095_748 | spl1095_749, inference(sat_conversion,[],[f7943])). cnf(s669, plain, ~spl1095_848, inference(sat_conversion,[],[f8414])). cnf(s831, plain, spl1095_748, inference(sat_conversion,[],[f9104])). cnf(s1209, plain, spl1095_192, inference(sat_conversion,[],[f10627])). cnf(s1502, plain, ~spl1095_192 | spl1095_1538, inference(sat_conversion,[],[f11766])). cnf(s1673, plain, spl1095_489, inference(sat_conversion,[],[f12391])). cnf(s1739, plain, spl1095_512, inference(sat_conversion,[],[f12660])). cnf(s1759, plain, ~spl1095_512 | spl1095_1191, inference(sat_conversion,[],[f12729])). cnf(s1826, plain, spl1095_848 | ~spl1095_1538 | spl1095_1786, inference(sat_conversion,[],[f13512])). cnf(s1852, plain, ~spl1095_749 | ~spl1095_1786 | spl1095_1810, inference(sat_conversion,[],[f14795])). cnf(s2195, plain, ~spl1095_490 | ~spl1095_1191 | ~spl1095_1810 | spl1095_2058, inference(sat_conversion,[],[f22143])). cnf(s2671, plain, ~spl1095_193 | spl1095_848 | ~spl1095_2058, inference(sat_conversion,[],[f24705])). cnf(s2677, plain, spl1095_1191, inference(rat,[],[s1759,s1739])). cnf(s2741, plain, spl1095_1538, inference(rat,[],[s1502,s1209])). cnf(s2873, plain, spl1095_1786, inference(rat,[],[s1826,s2741,s669])). cnf(s2917, plain, spl1095_749, inference(rat,[],[s563,s831])). cnf(s2919, plain, spl1095_1810, inference(rat,[],[s1852,s2873,s2917])). cnf(s3023, plain, spl1095_490, inference(rat,[],[s330,s1673])). cnf(s3026, plain, spl1095_2058, inference(rat,[],[s2195,s2919,s2677,s3023])). cnf(s3029, plain, ~spl1095_193, inference(rat,[],[s2671,s669,s3026])). cnf(s3143, plain, $false, inference(rat,[],[s110,s3029,s1209])). thf(f24711,plain,( $false), inference(avatar_sat_refutation,[],[s3143])). % SZS output end Proof for theBenchmark