0.00/0.04	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.07	% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.16/0.47	% Computer : n021.cluster.edu
0.16/0.47	% Model    : x86_64 x86_64
0.16/0.47	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.16/0.47	% Memory   : 8046.5625MB
0.16/0.47	% OS       : Linux 6.8.0-71-generic
0.16/0.48	% CPULimit : 1440
0.16/0.48	% WCLimit  : 180
0.16/0.48	% DateTime : Mon Jul 27 09:10:11 UTC 2026
0.16/0.48	% CPUTime  : 
0.16/0.48	Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.22/0.55	Running higher-order theorem proving
0.26/0.61	Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p
0.33/0.88	% Version: 3.5.1-ho
0.33/0.88	% Preprocessing class: HSLMSLSSLLLCHFA.
0.33/0.88	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
0.33/0.88	% Starting ehoh_best5 with 180s (1) cores
0.33/0.88	% Starting almost_fo_3_lam with 180s (1) cores
0.33/0.88	% Starting new_bool_5 with 180s (1) cores
0.33/0.88	% Starting pre_casc_3 with 180s (1) cores
0.33/0.88	% Starting ho_unfolding_8 with 180s (1) cores
0.33/0.88	% Starting new_ho_10_cnf2 with 180s (1) cores
0.33/0.88	% Starting new_bool_3 with 180s (1) cores
0.33/0.88	% Starting new_ho_5 with 180s (1) cores
0.33/0.88	% ehoh_best5 with pid 608128 completed with status 0
0.33/0.88	% Result found by ehoh_best5
0.33/0.88	% Preprocessing class: HSLMSLSSLLLCHFA.
0.33/0.88	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
0.33/0.88	% Starting ehoh_best5 with 180s (1) cores
0.33/0.88	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
0.33/0.88	% No SInE strategy applied
0.33/0.88	% Search class: HGHSM-FSLM32-MHFMMSBN
0.33/0.88	% Scheduled 11 strats onto 1 cores with 180 seconds (180 total)
0.33/0.88	% Starting SubtermCWHack with 17s (1) cores
0.33/0.88	% SubtermCWHack with pid 608136 completed with status 0
0.33/0.88	% Result found by SubtermCWHack
0.33/0.88	% Preprocessing class: HSLMSLSSLLLCHFA.
0.33/0.88	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
0.33/0.88	% Starting ehoh_best5 with 180s (1) cores
0.33/0.88	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
0.33/0.88	% No SInE strategy applied
0.33/0.88	% Search class: HGHSM-FSLM32-MHFMMSBN
0.33/0.88	% Scheduled 11 strats onto 1 cores with 180 seconds (180 total)
0.33/0.88	% Starting SubtermCWHack with 17s (1) cores
0.33/0.88	% Preprocessing time       : 0.007 s
0.33/0.88	
0.33/0.88	% Proof found!
0.33/0.88	% SZS status Theorem
0.33/0.88	% SZS output start CNFRefutation
0.33/0.88	thf(decl_23, type, in: $i > $i > $o).
0.33/0.88	thf(decl_24, type, exu: ($i > $o) > $o).
0.33/0.88	thf(decl_25, type, setextAx: $o).
0.33/0.88	thf(decl_26, type, emptyset: $i).
0.33/0.88	thf(decl_27, type, emptysetAx: $o).
0.33/0.88	thf(decl_28, type, setadjoin: $i > $i > $i).
0.33/0.88	thf(decl_29, type, setadjoinAx: $o).
0.33/0.88	thf(decl_30, type, powerset: $i > $i).
0.33/0.88	thf(decl_31, type, powersetAx: $o).
0.33/0.88	thf(decl_32, type, setunion: $i > $i).
0.33/0.88	thf(decl_33, type, setunionAx: $o).
0.33/0.88	thf(decl_34, type, omega: $i).
0.33/0.88	thf(decl_35, type, omega0Ax: $o).
0.33/0.88	thf(decl_36, type, omegaSAx: $o).
0.33/0.88	thf(decl_37, type, omegaIndAx: $o).
0.33/0.88	thf(decl_38, type, replAx: $o).
0.33/0.88	thf(decl_39, type, foundationAx: $o).
0.33/0.88	thf(decl_40, type, wellorderingAx: $o).
0.33/0.88	thf(decl_41, type, descr: ($i > $o) > $i).
0.33/0.88	thf(decl_42, type, descrp: $o).
0.33/0.88	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
0.33/0.88	thf(decl_44, type, dsetconstrI: $o).
0.33/0.88	thf(decl_45, type, dsetconstrEL: $o).
0.33/0.88	thf(decl_46, type, dsetconstrER: $o).
0.33/0.88	thf(decl_47, type, exuE1: $o).
0.33/0.88	thf(decl_48, type, prop2set: $o > $i).
0.33/0.88	thf(decl_49, type, prop2setE: $o).
0.33/0.88	thf(decl_50, type, emptysetE: $o).
0.33/0.88	thf(decl_51, type, emptysetimpfalse: $o).
0.33/0.88	thf(decl_52, type, notinemptyset: $o).
0.33/0.88	thf(decl_53, type, exuE3e: $o).
0.33/0.88	thf(decl_54, type, setext: $o).
0.33/0.88	thf(decl_55, type, emptyI: $o).
0.33/0.88	thf(decl_56, type, noeltsimpempty: $o).
0.33/0.88	thf(decl_57, type, setbeta: $o).
0.33/0.88	thf(decl_58, type, nonempty: $i > $o).
0.33/0.88	thf(decl_59, type, nonemptyE1: $o).
0.33/0.88	thf(decl_60, type, nonemptyI: $o).
0.33/0.88	thf(decl_61, type, nonemptyI1: $o).
0.33/0.88	thf(decl_62, type, setadjoinIL: $o).
0.33/0.88	thf(decl_63, type, emptyinunitempty: $o).
0.33/0.88	thf(decl_64, type, setadjoinIR: $o).
0.33/0.88	thf(decl_65, type, setadjoinE: $o).
0.33/0.88	thf(decl_66, type, setadjoinOr: $o).
0.33/0.88	thf(decl_67, type, setoftrueEq: $o).
0.33/0.88	thf(decl_68, type, powersetI: $o).
0.33/0.88	thf(decl_69, type, emptyinPowerset: $o).
0.33/0.88	thf(decl_70, type, emptyInPowerset: $o).
0.33/0.88	thf(decl_71, type, powersetE: $o).
0.33/0.88	thf(decl_72, type, setunionI: $o).
0.33/0.88	thf(decl_73, type, setunionE: $o).
0.33/0.88	thf(decl_74, type, subPowSU: $o).
0.33/0.88	thf(decl_75, type, exuE2: $o).
0.33/0.88	thf(decl_76, type, nonemptyImpWitness: $o).
0.33/0.88	thf(decl_77, type, uniqinunit: $o).
0.33/0.88	thf(decl_78, type, notinsingleton: $o).
0.33/0.88	thf(decl_79, type, eqinunit: $o).
0.33/0.88	thf(decl_80, type, singletonsswitch: $o).
0.33/0.88	thf(decl_81, type, upairsetE: $o).
0.33/0.88	thf(decl_82, type, upairsetIL: $o).
0.33/0.88	thf(decl_83, type, upairsetIR: $o).
0.33/0.88	thf(decl_84, type, emptyE1: $o).
0.33/0.88	thf(decl_85, type, vacuousDall: $o).
0.33/0.88	thf(decl_86, type, quantDeMorgan1: $o).
0.33/0.88	thf(decl_87, type, quantDeMorgan2: $o).
0.33/0.88	thf(decl_88, type, quantDeMorgan3: $o).
0.33/0.88	thf(decl_89, type, quantDeMorgan4: $o).
0.33/0.88	thf(decl_90, type, prop2setI: $o).
0.33/0.88	thf(decl_91, type, set2prop: $i > $o).
0.33/0.88	thf(decl_92, type, prop2set2propI: $o).
0.33/0.88	thf(decl_93, type, notdexE: $o).
0.33/0.88	thf(decl_94, type, notdallE: $o).
0.33/0.88	thf(decl_95, type, exuI1: $o).
0.33/0.88	thf(decl_96, type, exuI3: $o).
0.33/0.88	thf(decl_97, type, exuI2: $o).
0.33/0.88	thf(decl_98, type, inCongP: $o).
0.33/0.88	thf(decl_99, type, in__Cong: $o).
0.33/0.88	thf(decl_100, type, exuE3u: $o).
0.33/0.88	thf(decl_101, type, exu__Cong: $o).
0.33/0.88	thf(decl_102, type, emptyset__Cong: $o).
0.33/0.88	thf(decl_103, type, setadjoin__Cong: $o).
0.33/0.88	thf(decl_104, type, powerset__Cong: $o).
0.33/0.88	thf(decl_105, type, setunion__Cong: $o).
0.33/0.88	thf(decl_106, type, omega__Cong: $o).
0.33/0.88	thf(decl_107, type, exuEu: $o).
0.33/0.88	thf(decl_108, type, descr__Cong: $o).
0.33/0.88	thf(decl_109, type, dsetconstr__Cong: $o).
0.33/0.88	thf(decl_110, type, subset: $i > $i > $o).
0.33/0.88	thf(decl_113, type, subsetI1: $o).
0.33/0.88	thf(decl_114, type, eqimpsubset2: $o).
0.33/0.88	thf(decl_115, type, eqimpsubset1: $o).
0.33/0.88	thf(decl_116, type, subsetI2: $o).
0.33/0.88	thf(decl_117, type, emptysetsubset: $o).
0.33/0.88	thf(decl_118, type, subsetE: $o).
0.33/0.88	thf(decl_119, type, subsetE2: $o).
0.33/0.88	thf(decl_120, type, notsubsetI: $o).
0.33/0.88	thf(decl_121, type, notequalI1: $o).
0.33/0.88	thf(decl_122, type, notequalI2: $o).
0.33/0.88	thf(decl_123, type, subsetRefl: $o).
0.33/0.88	thf(decl_124, type, subsetTrans: $o).
0.33/0.88	thf(decl_125, type, setadjoinSub: $o).
0.33/0.88	thf(decl_126, type, setadjoinSub2: $o).
0.33/0.88	thf(decl_127, type, subset2powerset: $o).
0.33/0.88	thf(decl_128, type, setextsub: $o).
0.33/0.88	thf(decl_129, type, subsetemptysetimpeq: $o).
0.33/0.88	thf(decl_130, type, powersetI1: $o).
0.33/0.88	thf(decl_131, type, powersetE1: $o).
0.33/0.88	thf(decl_132, type, inPowerset: $o).
0.33/0.88	thf(decl_133, type, powersetsubset: $o).
0.33/0.88	thf(decl_134, type, sepInPowerset: $o).
0.33/0.88	thf(decl_135, type, sepSubset: $o).
0.33/0.88	thf(decl_136, type, binunion: $i > $i > $i).
0.33/0.88	thf(decl_137, type, binunionIL: $o).
0.33/0.88	thf(decl_138, type, upairset2IR: $o).
0.33/0.88	thf(decl_139, type, binunionIR: $o).
0.33/0.88	thf(decl_140, type, binunionEcases: $o).
0.33/0.88	thf(decl_141, type, binunionE: $o).
0.33/0.88	thf(decl_142, type, binunionLsub: $o).
0.33/0.88	thf(decl_143, type, binunionRsub: $o).
0.33/0.88	thf(decl_144, type, binintersect: $i > $i > $i).
0.33/0.88	thf(decl_145, type, binintersectI: $o).
0.33/0.88	thf(decl_146, type, binintersectSubset5: $o).
0.33/0.88	thf(decl_147, type, binintersectEL: $o).
0.33/0.88	thf(decl_148, type, binintersectLsub: $o).
0.33/0.88	thf(decl_149, type, binintersectSubset2: $o).
0.33/0.88	thf(decl_150, type, binintersectSubset3: $o).
0.33/0.88	thf(decl_151, type, binintersectER: $o).
0.33/0.88	thf(decl_152, type, disjointsetsI1: $o).
0.33/0.88	thf(decl_153, type, binintersectRsub: $o).
0.33/0.88	thf(decl_154, type, binintersectSubset4: $o).
0.33/0.88	thf(decl_155, type, binintersectSubset1: $o).
0.33/0.88	thf(decl_156, type, bs114d: $o).
0.33/0.88	thf(decl_158, type, setminus: $i > $i > $i).
0.33/0.88	thf(decl_159, type, setminusI: $o).
0.33/0.88	thf(decl_160, type, setminusEL: $o).
0.33/0.88	thf(decl_161, type, setminusER: $o).
0.33/0.88	thf(decl_162, type, setminusSubset2: $o).
0.33/0.88	thf(decl_163, type, setminusERneg: $o).
0.33/0.88	thf(decl_164, type, setminusELneg: $o).
0.33/0.88	thf(decl_165, type, setminusILneg: $o).
0.33/0.88	thf(decl_166, type, setminusIRneg: $o).
0.33/0.88	thf(decl_167, type, setminusLsub: $o).
0.33/0.88	thf(decl_168, type, setminusSubset1: $o).
0.33/0.88	thf(decl_169, type, symdiff: $i > $i > $i).
0.33/0.88	thf(decl_170, type, symdiffE: $o).
0.33/0.88	thf(decl_171, type, symdiffI1: $o).
0.33/0.88	thf(decl_172, type, symdiffI2: $o).
0.33/0.88	thf(decl_173, type, symdiffIneg1: $o).
0.33/0.88	thf(decl_174, type, symdiffIneg2: $o).
0.33/0.88	thf(decl_175, type, iskpair: $i > $o).
0.33/0.88	thf(decl_176, type, secondinupair: $o).
0.33/0.88	thf(decl_177, type, setukpairIL: $o).
0.33/0.88	thf(decl_178, type, setukpairIR: $o).
0.33/0.88	thf(decl_179, type, kpairiskpair: $o).
0.33/0.88	thf(decl_180, type, kpair: $i > $i > $i).
0.33/0.88	thf(decl_181, type, kpairp: $o).
0.33/0.88	thf(decl_182, type, cartprod: $i > $i > $i).
0.33/0.88	thf(decl_183, type, singletonsubset: $o).
0.33/0.88	thf(decl_184, type, singletoninpowerset: $o).
0.33/0.88	thf(decl_185, type, singletoninpowunion: $o).
0.33/0.88	thf(decl_186, type, upairset2E: $o).
0.33/0.88	thf(decl_187, type, upairsubunion: $o).
0.33/0.88	thf(decl_188, type, upairinpowunion: $o).
0.33/0.88	thf(decl_189, type, ubforcartprodlem1: $o).
0.33/0.88	thf(decl_190, type, ubforcartprodlem2: $o).
0.33/0.88	thf(decl_191, type, ubforcartprodlem3: $o).
0.33/0.88	thf(decl_192, type, cartprodpairin: $o).
0.33/0.88	thf(decl_193, type, cartprodmempair1: $o).
0.33/0.88	thf(decl_194, type, cartprodmempair: $o).
0.33/0.88	thf(decl_195, type, setunionE2: $o).
0.33/0.88	thf(decl_196, type, setunionsingleton1: $o).
0.33/0.88	thf(decl_197, type, setunionsingleton2: $o).
0.33/0.88	thf(decl_198, type, setunionsingleton: $o).
0.33/0.89	thf(decl_199, type, singleton: $i > $o).
0.33/0.89	thf(decl_200, type, singletonprop: $o).
0.33/0.89	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
0.33/0.89	thf(decl_202, type, ex1E1: $o).
0.33/0.89	thf(decl_203, type, ex1I: $o).
0.33/0.89	thf(decl_204, type, ex1I2: $o).
0.33/0.89	thf(decl_205, type, singletonsuniq: $o).
0.33/0.89	thf(decl_210, type, setukpairinjL1: $o).
0.33/0.89	thf(decl_211, type, kfstsingleton: $o).
0.33/0.89	thf(decl_212, type, theprop: $o).
0.33/0.89	thf(decl_213, type, kfst: $i > $i).
0.33/0.89	thf(decl_214, type, kfstpairEq: $o).
0.33/0.89	thf(decl_215, type, cartprodfstin: $o).
0.33/0.89	thf(decl_216, type, setukpairinjL2: $o).
0.33/0.89	thf(decl_217, type, setukpairinjL: $o).
0.33/0.89	thf(decl_218, type, setukpairinjR11: $o).
0.33/0.89	thf(decl_219, type, setukpairinjR12: $o).
0.33/0.89	thf(decl_220, type, setukpairinjR1: $o).
0.33/0.89	thf(decl_221, type, upairequniteq: $o).
0.33/0.89	thf(decl_222, type, setukpairinjR2: $o).
0.33/0.89	thf(decl_223, type, setukpairinjR: $o).
0.33/0.89	thf(decl_224, type, ksndsingleton: $o).
0.33/0.89	thf(decl_225, type, ksnd: $i > $i).
0.33/0.89	thf(decl_226, type, ksndpairEq: $o).
0.33/0.89	thf(decl_227, type, kpairsurjEq: $o).
0.33/0.89	thf(decl_228, type, cartprodsndin: $o).
0.33/0.89	thf(decl_229, type, cartprodpairmemEL: $o).
0.33/0.89	thf(decl_230, type, cartprodpairmemER: $o).
0.33/0.89	thf(decl_231, type, cartprodmempaircEq: $o).
0.33/0.89	thf(decl_232, type, cartprodfstpairEq: $o).
0.33/0.89	thf(decl_233, type, cartprodsndpairEq: $o).
0.33/0.89	thf(decl_234, type, cartprodpairsurjEq: $o).
0.33/0.89	thf(decl_235, type, breln: $i > $i > $i > $o).
0.33/0.89	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
0.33/0.89	thf(decl_237, type, dpsetconstrI: $o).
0.33/0.89	thf(decl_238, type, dpsetconstrSub: $o).
0.33/0.89	thf(decl_239, type, setOfPairsIsBReln: $o).
0.33/0.89	thf(decl_240, type, dpsetconstrERa: $o).
0.33/0.89	thf(decl_241, type, dpsetconstrEL1: $o).
0.33/0.89	thf(decl_242, type, dpsetconstrEL2: $o).
0.33/0.89	thf(decl_243, type, dpsetconstrER: $o).
0.33/0.89	thf(decl_244, type, func: $i > $i > $i > $o).
0.33/0.89	thf(decl_245, type, funcSet: $i > $i > $i).
0.33/0.89	thf(decl_246, type, funcImageSingleton: $o).
0.33/0.89	thf(decl_247, type, apProp: $o).
0.33/0.89	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
0.33/0.89	thf(decl_249, type, app: $o).
0.33/0.89	thf(decl_250, type, infuncsetfunc: $o).
0.33/0.89	thf(decl_251, type, ap2p: $o).
0.33/0.89	thf(decl_252, type, funcinfuncset: $o).
0.33/0.89	thf(decl_253, type, lamProp: $o).
0.33/0.89	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
0.33/0.89	thf(decl_255, type, lamp: $o).
0.33/0.89	thf(decl_256, type, lam2p: $o).
0.33/0.89	thf(decl_257, type, brelnall1: $o).
0.33/0.89	thf(decl_258, type, brelnall2: $o).
0.33/0.89	thf(decl_259, type, ex1E2: $o).
0.33/0.89	thf(decl_260, type, funcGraphProp1: $o).
0.33/0.89	thf(decl_261, type, funcGraphProp3: $o).
0.33/0.89	thf(decl_262, type, funcGraphProp2: $o).
0.33/0.89	thf(decl_263, type, funcextLem: $o).
0.33/0.89	thf(decl_264, type, funcGraphProp4: $o).
0.33/0.89	thf(decl_265, type, subbreln: $o).
0.33/0.89	thf(decl_266, type, eqbreln: $o).
0.33/0.89	thf(decl_267, type, funcext: $o).
0.33/0.89	thf(decl_268, type, funcext2: $o).
0.33/0.89	thf(decl_269, type, ap2apEq1: $o).
0.33/0.89	thf(decl_270, type, ap2apEq2: $o).
0.33/0.89	thf(decl_271, type, beta1: $o).
0.33/0.89	thf(decl_272, type, eta1: $o).
0.33/0.89	thf(decl_273, type, lam2lamEq: $o).
0.33/0.89	thf(decl_274, type, beta2: $o).
0.33/0.89	thf(decl_275, type, eta2: $o).
0.33/0.89	thf(decl_276, type, iffalseProp1: $o).
0.33/0.89	thf(decl_277, type, iffalseProp2: $o).
0.33/0.89	thf(decl_278, type, iftrueProp1: $o).
0.33/0.89	thf(decl_279, type, iftrueProp2: $o).
0.33/0.89	thf(decl_280, type, ifSingleton: $o).
0.33/0.89	thf(decl_281, type, if: $i > $o > $i > $i > $i).
0.33/0.89	thf(decl_282, type, ifp: $o).
0.33/0.89	thf(decl_283, type, theeq: $o).
0.33/0.89	thf(decl_284, type, iftrue: $o).
0.33/0.89	thf(decl_285, type, iffalse: $o).
0.33/0.89	thf(decl_286, type, iftrueorfalse: $o).
0.33/0.89	thf(decl_287, type, binintersectT_lem: $o).
0.33/0.89	thf(decl_288, type, binunionT_lem: $o).
0.33/0.89	thf(decl_289, type, powersetT_lem: $o).
0.33/0.89	thf(decl_290, type, setminusT_lem: $o).
0.33/0.89	thf(decl_291, type, complementT_lem: $o).
0.33/0.89	thf(decl_292, type, setextT: $o).
0.33/0.89	thf(decl_293, type, subsetTI: $o).
0.33/0.89	thf(decl_294, type, powersetTI1: $o).
0.33/0.89	thf(decl_295, type, powersetTE1: $o).
0.33/0.89	thf(decl_296, type, complementTI1: $o).
0.33/0.89	thf(decl_297, type, complementTE1: $o).
0.33/0.89	thf(decl_298, type, binintersectTELcontra: $o).
0.33/0.89	thf(decl_299, type, binintersectTERcontra: $o).
0.33/0.89	thf(decl_300, type, contrasubsetT: $o).
0.33/0.89	thf(decl_301, type, contrasubsetT1: $o).
0.33/0.89	thf(decl_302, type, contrasubsetT2: $o).
0.33/0.89	thf(decl_303, type, contrasubsetT3: $o).
0.33/0.89	thf(decl_304, type, doubleComplementI1: $o).
0.33/0.89	thf(decl_305, type, doubleComplementE1: $o).
0.33/0.89	thf(decl_306, type, doubleComplementSub1: $o).
0.33/0.89	thf(decl_307, type, doubleComplementSub2: $o).
0.33/0.89	thf(decl_308, type, doubleComplementEq: $o).
0.33/0.89	thf(decl_309, type, complementTnotintersectT: $o).
0.33/0.89	thf(decl_310, type, complementImpComplementIntersect: $o).
0.33/0.89	thf(decl_311, type, complementSubsetComplementIntersect: $o).
0.33/0.89	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
0.33/0.89	thf(decl_313, type, contraSubsetComplement: $o).
0.33/0.89	thf(decl_314, type, complementTcontraSubset: $o).
0.33/0.89	thf(decl_315, type, binunionTILcontra: $o).
0.33/0.89	thf(decl_316, type, binunionTIRcontra: $o).
0.33/0.89	thf(decl_317, type, inIntersectImpInUnion: $o).
0.33/0.89	thf(decl_318, type, inIntersectImpInUnion2: $o).
0.33/0.89	thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
0.33/0.89	thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
0.33/0.89	thf(decl_321, type, inComplementUnionImpNotIn1: $o).
0.33/0.89	thf(decl_322, type, epred1_0: $o).
0.33/0.89	thf(decl_323, type, esk1_2: $i > $i > $i).
0.33/0.89	thf(decl_324, type, esk2_2: $i > $i > $i).
0.33/0.89	thf(decl_325, type, esk3_2: $i > $i > $i).
0.33/0.89	thf(decl_326, type, esk4_1: $i > $i).
0.33/0.89	thf(decl_327, type, esk5_2: ($i > $i > $o) > $i > $i).
0.33/0.89	thf(decl_328, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
0.33/0.89	thf(decl_329, type, esk7_2: ($i > $i > $o) > $i > $i).
0.33/0.89	thf(decl_330, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
0.33/0.89	thf(decl_331, type, esk9_1: $i > $i).
0.33/0.89	thf(decl_332, type, esk10_2: ($i > $o) > $i > $i).
0.33/0.89	thf(decl_333, type, esk11_2: ($i > $o) > $i > $i).
0.33/0.89	thf(decl_334, type, esk12_1: ($i > $o) > $i).
0.33/0.89	thf(decl_335, type, esk13_2: ($i > $o) > $i > $i).
0.33/0.89	thf(decl_336, type, esk14_1: ($i > $o) > $i).
0.33/0.89	thf(decl_337, type, esk15_2: $i > $i > $i).
0.33/0.89	thf(decl_338, type, esk16_2: $i > $i > $i).
0.33/0.89	thf(decl_339, type, esk17_1: $i > $i).
0.33/0.89	thf(decl_340, type, esk18_1: $i > $i).
0.33/0.89	thf(decl_341, type, esk19_1: $i > $i).
0.33/0.89	thf(decl_342, type, esk20_2: $i > $i > $i).
0.33/0.89	thf(decl_343, type, esk21_3: $i > $i > $o > $i).
0.33/0.89	thf(decl_344, type, esk22_2: ($i > $o) > $i > $i).
0.33/0.89	thf(decl_345, type, esk23_1: ($i > $o) > $i).
0.33/0.89	thf(decl_346, type, esk24_1: $i > $i).
0.33/0.89	thf(decl_347, type, esk25_2: $i > ($i > $o) > $i).
0.33/0.89	thf(decl_348, type, esk26_2: $i > ($i > $o) > $i).
0.33/0.89	thf(decl_349, type, esk27_2: $i > ($i > $o) > $i).
0.33/0.89	thf(decl_350, type, esk28_2: $i > ($i > $o) > $i).
0.33/0.89	thf(decl_351, type, esk29_2: $i > ($i > $o) > $i).
0.33/0.89	thf(decl_352, type, esk30_2: $i > ($i > $o) > $i).
0.33/0.89	thf(decl_353, type, esk31_2: ($i > $o) > $i > $i).
0.33/0.89	thf(decl_354, type, esk32_1: ($i > $o) > $i).
0.33/0.89	thf(decl_355, type, esk33_1: ($i > $o) > $i).
0.33/0.89	thf(decl_356, type, esk34_1: ($i > $o) > $i).
0.33/0.89	thf(decl_357, type, esk35_1: ($i > $o) > $i).
0.33/0.89	thf(decl_358, type, esk36_2: ($i > $o) > $i > $i).
0.33/0.89	thf(decl_359, type, esk37_1: ($i > $o) > $i).
0.33/0.89	thf(decl_360, type, esk38_2: ($i > $o) > $i > $i).
0.33/0.89	thf(decl_361, type, esk39_2: ($i > $o) > ($i > $o) > $i).
0.33/0.89	thf(decl_362, type, esk40_2: ($i > $o) > ($i > $o) > $i).
0.33/0.89	thf(decl_363, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
0.33/0.89	thf(decl_364, type, esk42_2: ($i > $o) > ($i > $o) > $i).
0.33/0.89	thf(decl_365, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
0.33/0.89	thf(decl_366, type, esk44_2: ($i > $o) > ($i > $o) > $i).
0.33/0.89	thf(decl_367, type, esk45_2: ($i > $o) > $i > $i).
0.33/0.89	thf(decl_368, type, esk46_2: ($i > $o) > ($i > $o) > $i).
0.33/0.89	thf(decl_369, type, esk47_2: ($i > $o) > ($i > $o) > $i).
0.33/0.89	thf(decl_370, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
0.33/0.89	thf(decl_371, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
0.33/0.89	thf(decl_372, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.33/0.89	thf(decl_373, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.33/0.89	thf(decl_374, type, esk52_2: $i > $i > $i).
0.33/0.89	thf(decl_375, type, esk53_2: $i > $i > $i).
0.33/0.89	thf(decl_376, type, esk54_2: $i > $i > $i).
0.33/0.89	thf(decl_377, type, esk55_3: $i > $i > $i > $i).
0.33/0.89	thf(decl_378, type, esk56_3: $i > $i > $i > $i).
0.33/0.89	thf(decl_379, type, esk57_2: $i > $i > $i).
0.33/0.89	thf(decl_380, type, esk58_2: $i > ($i > $o) > $i).
0.33/0.89	thf(decl_381, type, esk59_2: $i > ($i > $o) > $i).
0.33/0.89	thf(decl_382, type, esk60_2: $i > ($i > $o) > $i).
0.33/0.89	thf(decl_383, type, esk61_3: $i > ($i > $o) > $i > $i).
0.33/0.89	thf(decl_384, type, esk62_2: $i > ($i > $o) > $i).
0.33/0.89	thf(decl_385, type, esk63_2: $i > ($i > $o) > $i).
0.33/0.89	thf(decl_386, type, esk64_3: $i > $i > ($i > $i) > $i).
0.33/0.89	thf(decl_387, type, esk65_3: $i > $i > ($i > $i) > $i).
0.33/0.89	thf(decl_388, type, esk66_3: $i > $i > ($i > $i) > $i).
0.33/0.89	thf(decl_389, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
0.33/0.89	thf(decl_390, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
0.33/0.89	thf(decl_391, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
0.33/0.89	thf(decl_392, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
0.33/0.89	thf(decl_393, type, esk71_4: $i > $i > $i > $i > $i).
0.33/0.89	thf(decl_394, type, esk72_4: $i > $i > $i > $i > $i).
0.33/0.89	thf(decl_395, type, esk73_4: $i > $i > $i > $i > $i).
0.33/0.89	thf(decl_396, type, esk74_4: $i > $i > $i > $i > $i).
0.33/0.89	thf(decl_397, type, esk75_4: $i > $i > $i > $i > $i).
0.33/0.89	thf(decl_398, type, esk76_4: $i > $i > $i > $i > $i).
0.33/0.89	thf(decl_399, type, esk77_4: $i > $i > $i > $i > $i).
0.33/0.89	thf(decl_400, type, esk78_4: $i > $i > $i > $i > $i).
0.33/0.89	thf(decl_401, type, esk79_4: $i > $i > $i > $i > $i).
0.33/0.89	thf(decl_402, type, esk80_3: $i > $i > ($i > $i) > $i).
0.33/0.89	thf(decl_403, type, esk81_3: $i > $i > ($i > $i) > $i).
0.33/0.89	thf(decl_404, type, esk82_3: $i > $i > ($i > $i) > $i).
0.33/0.89	thf(decl_405, type, esk83_3: $i > $i > $i > $i).
0.33/0.89	thf(decl_406, type, esk84_3: $i > $i > $i > $i).
0.33/0.89	thf(decl_407, type, esk85_3: $i > $i > $i > $i).
0.33/0.89	thf(decl_408, type, esk86_3: $i > $i > $i > $i).
0.33/0.89	thf(decl_409, type, esk87_0: $i).
0.33/0.89	thf(decl_410, type, esk88_0: $i).
0.33/0.89	thf(decl_411, type, esk89_0: $i).
0.33/0.89	thf(decl_412, type, esk90_0: $i).
0.33/0.89	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', replAx)).
0.33/0.89	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', exu)).
0.33/0.89	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', descrp)).
0.33/0.89	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', exuE1)).
0.33/0.89	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', exuE3e)).
0.33/0.89	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', nonempty)).
0.33/0.89	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', nonemptyI)).
0.33/0.89	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', exuE2)).
0.33/0.89	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', exuI1)).
0.33/0.89	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', exuI3)).
0.33/0.89	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', exuI2)).
0.33/0.89	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', exuE3u)).
0.33/0.89	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', exu__Cong)).
0.33/0.89	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', exuEu)).
0.33/0.89	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', descr__Cong)).
0.33/0.89	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ex1E1)).
0.33/0.89	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ex1)).
0.33/0.89	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ex1I)).
0.33/0.89	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ex1I2)).
0.33/0.89	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setOfPairsIsBReln)).
0.33/0.89	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', breln)).
0.33/0.89	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ex1E2)).
0.33/0.89	thf(inComplementUnionImpInComplement1, conjecture, ((setextAx)=>((((powersetAx)=>((((((((wellorderingAx)=>((descrp)=>(((((((emptysetE)=>(((notinemptyset)=>((exuE3e)=>((setext)=>((((setbeta)=>(((nonemptyI)=>((nonemptyI1)=>((((setadjoinIR)=>((setadjoinE)=>(((setoftrueEq)=>(((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>(((setunionE)=>((subPowSU)=>(((((((singletonsswitch)=>((((upairsetIR)=>((((quantDeMorgan1)=>((quantDeMorgan2)=>(((quantDeMorgan4)=>(((prop2set2propI)=>((((exuI1)=>((exuI3)=>((((in__Cong)=>((exuE3u)=>((exu__Cong)=>(((setadjoin__Cong)=>((powerset__Cong)=>(((omega__Cong)=>(((((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>(((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>(((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>(((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>(((binunionEcases)=>(((((((binintersectEL)=>((binintersectLsub)=>(((((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((((setminusER)=>((setminusSubset2)=>((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>((symdiffE)=>(((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>(((((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>(((cartprodmempair1)=>((((setunionsingleton1)=>((setunionsingleton2)=>(((singletonprop)=>(((ex1I)=>((ex1I2)=>((singletonsuniq)=>(((((kfstpairEq)=>(((((setukpairinjR11)=>(((setukpairinjR1)=>(((((((((cartprodpairmemEL)=>(((((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((((dpsetconstrERa)=>((((dpsetconstrER)=>((((app)=>((infuncsetfunc)=>((ap2p)=>(((lamProp)=>((((brelnall1)=>(((ex1E2)=>(((funcGraphProp3)=>((funcGraphProp2)=>(((((eqbreln)=>((((((((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>(((iftrueProp1)=>((iftrueProp2)=>(((ifp)=>((theeq)=>(((iffalse)=>((iftrueorfalse)=>((((powersetT_lem)=>(((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>(((complementTI1)=>((complementTE1)=>((((contrasubsetT)=>((contrasubsetT1)=>(((((doubleComplementE1)=>((doubleComplementSub1)=>((((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>(((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((((inIntersectImpInUnion2)=>(((intersectInPowersetIntersectUnions)=>(![X4:$i, X21:$i]:((![X48:$i]:((![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))<=(in @ X48 @ (powerset @ X4))))<=(in @ X21 @ (powerset @ X4))))<=(inComplementUnionImpNotIn1)))<=(inIntersectImpInIntersectUnions)))<=(inIntersectImpInUnion))<=(binunionTIRcontra)))))<=(complementInPowersetComplementIntersect)))))<=(doubleComplementEq))<=(doubleComplementSub2))))<=(doubleComplementI1))<=(contrasubsetT3))<=(contrasubsetT2))))<=(binintersectTERcontra))<=(binintersectTELcontra))))<=(powersetTE1))))))<=(setminusT_lem)))<=(binunionT_lem))<=(binintersectT_lem))))<=(iftrue))))<=(ifSingleton))))<=(iffalseProp2))))))<=(eta1))<=(beta1))<=(ap2apEq2))<=(ap2apEq1))<=(funcext2))<=(funcext)))<=(subbreln))<=(funcGraphProp4))<=(funcextLem))))<=(funcGraphProp1)))<=(brelnall2)))<=(lam2p))<=(lamp)))<=(funcinfuncset)))))<=(apProp))<=(funcImageSingleton)))<=(dpsetconstrEL2))<=(dpsetconstrEL1)))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER)))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12)))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1)))))<=(ex1E1)))<=(setunionsingleton))))<=(setunionE2))<=(cartprodmempair)))<=(cartprodpairin)))))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E)))))<=(kpairp))<=(kpairiskpair)))))<=(symdiffIneg2))))<=(symdiffI1))))<=(setminusLsub))))<=(setminusELneg)))))<=(setminusEL))<=(setminusI)))))))<=(binintersectER))<=(binintersectSubset3))<=(binintersectSubset2))))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))<=(binunionLsub))<=(binunionE)))<=(binunionIR)))))))<=(inPowerset))))))<=(subset2powerset)))))))))<=(subsetE2))))))))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong))))<=(emptyset__Cong)))))<=(inCongP))<=(exuI2))))<=(notdallE))<=(notdexE)))<=(prop2setI)))<=(quantDeMorgan3))))<=(vacuousDall))<=(emptyE1)))<=(upairsetIL))<=(upairsetE)))<=(eqinunit))<=(notinsingleton))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))))<=(setunionI)))))<=(powersetI)))<=(setadjoinOr))))<=(emptyinunitempty))<=(setadjoinIL))))<=(nonemptyE1)))<=(noeltsimpempty))<=(emptyI)))))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI))))<=(foundationAx))<=(replAx))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))<=(setunionAx)))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', inComplementUnionImpInComplement1)).
0.33/0.89	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', dsetconstrI)).
0.33/0.89	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', dsetconstrEL)).
0.33/0.89	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', dsetconstrER)).
0.33/0.89	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setbeta)).
0.33/0.89	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', nonemptyE1)).
0.33/0.89	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', nonemptyI1)).
0.33/0.89	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setoftrueEq)).
0.33/0.89	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', nonemptyImpWitness)).
0.33/0.89	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', emptyE1)).
0.33/0.89	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', dsetconstr__Cong)).
0.33/0.89	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', sepInPowerset)).
0.33/0.89	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', sepSubset)).
0.33/0.89	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', singletonprop)).
0.33/0.89	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', kfstsingleton)).
0.33/0.89	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ksndsingleton)).
0.33/0.89	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', dpsetconstrI)).
0.33/0.89	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', dpsetconstrSub)).
0.33/0.89	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', dpsetconstrERa)).
0.33/0.89	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', dpsetconstrEL1)).
0.33/0.89	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', dpsetconstrEL2)).
0.33/0.89	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', dpsetconstrER)).
0.33/0.89	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', funcImageSingleton)).
0.33/0.89	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', apProp)).
0.33/0.89	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', lamProp)).
0.33/0.89	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', lamp)).
0.33/0.89	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', lam2p)).
0.33/0.89	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', brelnall1)).
0.33/0.89	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', brelnall2)).
0.33/0.89	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', subbreln)).
0.33/0.89	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', eqbreln)).
0.33/0.89	thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', beta1)).
0.33/0.89	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', eta1)).
0.33/0.89	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', lam2lamEq)).
0.33/0.89	thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', beta2)).
0.33/0.89	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', eta2)).
0.33/0.89	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', iffalseProp1)).
0.33/0.89	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', iffalseProp2)).
0.33/0.89	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', iftrueProp1)).
0.33/0.89	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', iftrueProp2)).
0.33/0.89	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ifSingleton)).
0.33/0.89	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setextAx)).
0.33/0.89	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', emptysetAx)).
0.33/0.89	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setadjoinAx)).
0.33/0.89	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', powersetAx)).
0.33/0.89	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setunionAx)).
0.33/0.89	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', omega0Ax)).
0.33/0.89	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', omegaSAx)).
0.33/0.89	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', omegaIndAx)).
0.33/0.89	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', foundationAx)).
0.33/0.89	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', wellorderingAx)).
0.33/0.89	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', prop2setE)).
0.33/0.89	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', emptysetE)).
0.33/0.89	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', emptysetimpfalse)).
0.33/0.89	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', notinemptyset)).
0.33/0.89	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setext)).
0.33/0.89	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', emptyI)).
0.33/0.89	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', noeltsimpempty)).
0.33/0.89	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setadjoinIL)).
0.33/0.89	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', emptyinunitempty)).
0.33/0.89	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setadjoinIR)).
0.33/0.89	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setadjoinE)).
0.33/0.89	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setadjoinOr)).
0.33/0.89	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', powersetI)).
0.33/0.89	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', emptyinPowerset)).
0.33/0.89	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', emptyInPowerset)).
0.33/0.89	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', powersetE)).
0.33/0.89	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setunionI)).
0.33/0.89	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setunionE)).
0.33/0.89	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', subPowSU)).
0.33/0.89	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', uniqinunit)).
0.33/0.89	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', notinsingleton)).
0.33/0.89	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', eqinunit)).
0.33/0.89	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', singletonsswitch)).
0.33/0.89	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', upairsetE)).
0.33/0.89	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', upairsetIL)).
0.33/0.89	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', upairsetIR)).
0.33/0.89	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', vacuousDall)).
0.33/0.89	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', quantDeMorgan1)).
0.33/0.89	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', quantDeMorgan2)).
0.33/0.89	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', quantDeMorgan3)).
0.33/0.89	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', quantDeMorgan4)).
0.33/0.89	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', prop2setI)).
0.33/0.89	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', prop2set2propI)).
0.33/0.89	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', notdexE)).
0.33/0.89	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', notdallE)).
0.33/0.89	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', inCongP)).
0.33/0.89	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', in__Cong)).
0.33/0.89	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', emptyset__Cong)).
0.33/0.89	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setadjoin__Cong)).
0.33/0.89	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', powerset__Cong)).
0.33/0.89	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setunion__Cong)).
0.33/0.89	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', omega__Cong)).
0.33/0.89	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', subsetI1)).
0.33/0.89	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', eqimpsubset2)).
0.33/0.89	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', eqimpsubset1)).
0.33/0.89	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', subsetI2)).
0.33/0.89	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', emptysetsubset)).
0.33/0.89	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', subsetE)).
0.33/0.89	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', subsetE2)).
0.33/0.89	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', notsubsetI)).
0.33/0.89	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', notequalI1)).
0.33/0.89	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', notequalI2)).
0.33/0.89	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', subsetRefl)).
0.33/0.89	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', subsetTrans)).
0.33/0.89	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setadjoinSub)).
0.33/0.89	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setadjoinSub2)).
0.33/0.89	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', subset2powerset)).
0.33/0.89	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setextsub)).
0.33/0.89	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', subsetemptysetimpeq)).
0.33/0.89	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', powersetI1)).
0.33/0.89	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', powersetE1)).
0.33/0.89	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', inPowerset)).
0.33/0.89	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', powersetsubset)).
0.33/0.89	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binunionIL)).
0.33/0.89	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', upairset2IR)).
0.33/0.89	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binunionIR)).
0.33/0.89	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binunionEcases)).
0.33/0.89	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binunionE)).
0.33/0.89	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binunionLsub)).
0.33/0.89	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binunionRsub)).
0.33/0.89	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectI)).
0.33/0.89	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectSubset5)).
0.33/0.89	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectEL)).
0.33/0.89	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectLsub)).
0.33/0.89	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectSubset2)).
0.33/0.89	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectSubset3)).
0.33/0.89	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectER)).
0.33/0.89	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', disjointsetsI1)).
0.33/0.89	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectRsub)).
0.33/0.89	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectSubset4)).
0.33/0.89	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectSubset1)).
0.33/0.89	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', bs114d)).
0.33/0.89	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setminusI)).
0.33/0.89	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setminusEL)).
0.33/0.89	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setminusER)).
0.33/0.89	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setminusSubset2)).
0.33/0.89	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setminusERneg)).
0.33/0.89	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setminusELneg)).
0.33/0.89	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setminusILneg)).
0.33/0.89	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setminusIRneg)).
0.33/0.89	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setminusLsub)).
0.33/0.89	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setminusSubset1)).
0.33/0.89	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', symdiffE)).
0.33/0.89	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', symdiffI1)).
0.33/0.89	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', symdiffI2)).
0.33/0.89	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', symdiffIneg1)).
0.33/0.89	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', symdiffIneg2)).
0.33/0.89	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', secondinupair)).
0.33/0.89	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setukpairIL)).
0.33/0.89	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setukpairIR)).
0.33/0.89	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', kpairiskpair)).
0.33/0.89	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', kpairp)).
0.33/0.89	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', singletonsubset)).
0.33/0.89	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', singletoninpowerset)).
0.33/0.89	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', singletoninpowunion)).
0.33/0.89	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', upairset2E)).
0.33/0.89	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', upairsubunion)).
0.33/0.89	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', upairinpowunion)).
0.33/0.89	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ubforcartprodlem1)).
0.33/0.89	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ubforcartprodlem2)).
0.33/0.89	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ubforcartprodlem3)).
0.33/0.89	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', cartprodpairin)).
0.33/0.89	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', cartprodmempair1)).
0.33/0.89	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', cartprodmempair)).
0.33/0.89	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setunionE2)).
0.33/0.89	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setunionsingleton1)).
0.33/0.89	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setunionsingleton2)).
0.33/0.89	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setunionsingleton)).
0.33/0.89	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', singletonsuniq)).
0.33/0.89	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setukpairinjL1)).
0.33/0.89	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', theprop)).
0.33/0.89	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', kfstpairEq)).
0.33/0.89	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', cartprodfstin)).
0.33/0.89	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setukpairinjL2)).
0.33/0.89	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setukpairinjL)).
0.33/0.89	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setukpairinjR11)).
0.33/0.89	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setukpairinjR12)).
0.33/0.89	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setukpairinjR1)).
0.33/0.89	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', upairequniteq)).
0.33/0.89	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setukpairinjR2)).
0.33/0.89	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setukpairinjR)).
0.33/0.89	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ksndpairEq)).
0.33/0.89	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', kpairsurjEq)).
0.33/0.89	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', cartprodsndin)).
0.33/0.89	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', cartprodpairmemEL)).
0.33/0.89	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', cartprodpairmemER)).
0.33/0.89	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', cartprodmempaircEq)).
0.33/0.89	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', cartprodfstpairEq)).
0.33/0.89	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', cartprodsndpairEq)).
0.33/0.89	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', cartprodpairsurjEq)).
0.33/0.89	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', app)).
0.33/0.89	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', infuncsetfunc)).
0.33/0.89	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ap2p)).
0.33/0.89	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', funcinfuncset)).
0.33/0.89	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', funcGraphProp1)).
0.33/0.89	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', funcGraphProp3)).
0.33/0.89	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', funcGraphProp2)).
0.33/0.89	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', funcextLem)).
0.33/0.89	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', funcGraphProp4)).
0.33/0.89	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', funcext)).
0.33/0.89	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', funcext2)).
0.33/0.89	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ap2apEq1)).
0.33/0.89	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ap2apEq2)).
0.33/0.89	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', ifp)).
0.33/0.89	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', theeq)).
0.33/0.89	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', iftrue)).
0.33/0.89	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', iffalse)).
0.33/0.89	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', iftrueorfalse)).
0.33/0.89	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectT_lem)).
0.33/0.89	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binunionT_lem)).
0.33/0.89	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', powersetT_lem)).
0.33/0.89	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setminusT_lem)).
0.33/0.89	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', complementT_lem)).
0.33/0.89	thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', setextT)).
0.33/0.89	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', subsetTI)).
0.33/0.89	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', powersetTI1)).
0.33/0.89	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', powersetTE1)).
0.33/0.89	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', complementTI1)).
0.33/0.89	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', complementTE1)).
0.33/0.89	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectTELcontra)).
0.33/0.89	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binintersectTERcontra)).
0.33/0.89	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', contrasubsetT)).
0.33/0.89	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', contrasubsetT1)).
0.33/0.89	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', contrasubsetT2)).
0.33/0.89	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', contrasubsetT3)).
0.33/0.89	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', doubleComplementI1)).
0.33/0.89	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', doubleComplementE1)).
0.33/0.89	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', doubleComplementSub1)).
0.33/0.89	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', doubleComplementSub2)).
0.33/0.89	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', doubleComplementEq)).
0.33/0.89	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', complementTnotintersectT)).
0.33/0.89	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', complementImpComplementIntersect)).
0.33/0.89	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', complementSubsetComplementIntersect)).
0.33/0.89	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', complementInPowersetComplementIntersect)).
0.33/0.89	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', contraSubsetComplement)).
0.33/0.89	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', complementTcontraSubset)).
0.33/0.89	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binunionTILcontra)).
0.33/0.89	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', binunionTIRcontra)).
0.33/0.89	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', inIntersectImpInUnion)).
0.33/0.89	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', inIntersectImpInUnion2)).
0.33/0.89	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', inIntersectImpInIntersectUnions)).
0.33/0.89	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', intersectInPowersetIntersectUnions)).
0.33/0.89	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dO3GsNCwhM/E---3.1_608115.p', inComplementUnionImpNotIn1)).
0.33/0.89	thf(c_0_266, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
0.33/0.89	thf(c_0_267, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
0.33/0.89	thf(c_0_268, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
0.33/0.89	thf(c_0_269, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
0.33/0.89	thf(c_0_270, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
0.33/0.89	thf(c_0_271, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
0.33/0.89	thf(c_0_272, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
0.33/0.89	thf(c_0_273, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
0.33/0.89	thf(c_0_274, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
0.33/0.89	thf(c_0_275, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
0.33/0.89	thf(c_0_276, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
0.33/0.89	thf(c_0_277, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
0.33/0.89	thf(c_0_278, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
0.33/0.89	thf(c_0_279, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
0.33/0.89	thf(c_0_280, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
0.33/0.89	thf(c_0_281, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
0.33/0.89	thf(c_0_282, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
0.33/0.89	thf(c_0_283, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
0.33/0.89	thf(c_0_284, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
0.33/0.89	thf(c_0_285, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
0.33/0.89	thf(c_0_286, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
0.33/0.89	thf(c_0_287, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
0.33/0.89	thf(c_0_288, negated_conjecture, ~(((setextAx)=>((((powersetAx)=>((((((((wellorderingAx)=>((descrp)=>(((((((emptysetE)=>(((notinemptyset)=>((exuE3e)=>((setext)=>((((setbeta)=>(((nonemptyI)=>((nonemptyI1)=>((((setadjoinIR)=>((setadjoinE)=>(((setoftrueEq)=>(((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>(((setunionE)=>((subPowSU)=>(((((((singletonsswitch)=>((((upairsetIR)=>((((quantDeMorgan1)=>((quantDeMorgan2)=>(((quantDeMorgan4)=>(((prop2set2propI)=>((((exuI1)=>((exuI3)=>((((in__Cong)=>((exuE3u)=>((exu__Cong)=>(((setadjoin__Cong)=>((powerset__Cong)=>(((omega__Cong)=>(((((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>(((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>(((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>(((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>(((binunionEcases)=>(((((((binintersectEL)=>((binintersectLsub)=>(((((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((((setminusER)=>((setminusSubset2)=>((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>((symdiffE)=>(((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>(((((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>(((cartprodmempair1)=>((((setunionsingleton1)=>((setunionsingleton2)=>(((singletonprop)=>(((ex1I)=>((ex1I2)=>((singletonsuniq)=>(((((kfstpairEq)=>(((((setukpairinjR11)=>(((setukpairinjR1)=>(((((((((cartprodpairmemEL)=>(((((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((((dpsetconstrERa)=>((((dpsetconstrER)=>((((app)=>((infuncsetfunc)=>((ap2p)=>(((lamProp)=>((((brelnall1)=>(((ex1E2)=>(((funcGraphProp3)=>((funcGraphProp2)=>(((((eqbreln)=>((((((((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>(((iftrueProp1)=>((iftrueProp2)=>(((ifp)=>((theeq)=>(((iffalse)=>((iftrueorfalse)=>((((powersetT_lem)=>(((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>(((complementTI1)=>((complementTE1)=>((((contrasubsetT)=>((contrasubsetT1)=>(((((doubleComplementE1)=>((doubleComplementSub1)=>((((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>(((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((((inIntersectImpInUnion2)=>(((intersectInPowersetIntersectUnions)=>(![X4:$i, X21:$i]:((![X48:$i]:((![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))<=(in @ X48 @ (powerset @ X4))))<=(in @ X21 @ (powerset @ X4))))<=(inComplementUnionImpNotIn1)))<=(inIntersectImpInIntersectUnions)))<=(inIntersectImpInUnion))<=(binunionTIRcontra)))))<=(complementInPowersetComplementIntersect)))))<=(doubleComplementEq))<=(doubleComplementSub2))))<=(doubleComplementI1))<=(contrasubsetT3))<=(contrasubsetT2))))<=(binintersectTERcontra))<=(binintersectTELcontra))))<=(powersetTE1))))))<=(setminusT_lem)))<=(binunionT_lem))<=(binintersectT_lem))))<=(iftrue))))<=(ifSingleton))))<=(iffalseProp2))))))<=(eta1))<=(beta1))<=(ap2apEq2))<=(ap2apEq1))<=(funcext2))<=(funcext)))<=(subbreln))<=(funcGraphProp4))<=(funcextLem))))<=(funcGraphProp1)))<=(brelnall2)))<=(lam2p))<=(lamp)))<=(funcinfuncset)))))<=(apProp))<=(funcImageSingleton)))<=(dpsetconstrEL2))<=(dpsetconstrEL1)))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER)))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12)))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1)))))<=(ex1E1)))<=(setunionsingleton))))<=(setunionE2))<=(cartprodmempair)))<=(cartprodpairin)))))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E)))))<=(kpairp))<=(kpairiskpair)))))<=(symdiffIneg2))))<=(symdiffI1))))<=(setminusLsub))))<=(setminusELneg)))))<=(setminusEL))<=(setminusI)))))))<=(binintersectER))<=(binintersectSubset3))<=(binintersectSubset2))))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))<=(binunionLsub))<=(binunionE)))<=(binunionIR)))))))<=(inPowerset))))))<=(subset2powerset)))))))))<=(subsetE2))))))))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong))))<=(emptyset__Cong)))))<=(inCongP))<=(exuI2))))<=(notdallE))<=(notdexE)))<=(prop2setI)))<=(quantDeMorgan3))))<=(vacuousDall))<=(emptyE1)))<=(upairsetIL))<=(upairsetE)))<=(eqinunit))<=(notinsingleton))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))))<=(setunionI)))))<=(powersetI)))<=(setadjoinOr))))<=(emptyinunitempty))<=(setadjoinIL))))<=(nonemptyE1)))<=(noeltsimpempty))<=(emptyI)))))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI))))<=(foundationAx))<=(replAx))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))<=(setunionAx)))<=(setadjoinAx))<=(emptysetAx)))), inference(assume_negation,[status(cth)],[inComplementUnionImpInComplement1])).
0.33/0.89	thf(c_0_289, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X872:$i]:(((((X6 @ X2 @ X872)))&(![X873:$i]:(((((X6 @ X2 @ X873)))=>(((X872)=(X873)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_266, c_0_267])).
0.33/0.89	thf(c_0_290, plain, ((descrp)=(![X1:$i > $o]:((((?[X874:$i]:(((((X1 @ X874)))&(![X875:$i]:(((((X1 @ X875)))=>(((X874)=(X875))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_268, c_0_267])).
0.33/0.89	thf(c_0_291, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
0.33/0.89	thf(c_0_292, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
0.33/0.89	thf(c_0_293, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
0.33/0.89	thf(c_0_294, plain, ((exuE1)=(![X1:$i > $o]:((((?[X876:$i]:(((((X1 @ X876)))&(![X877:$i]:(((((X1 @ X877)))=>(((X876)=(X877))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_269, c_0_267])).
0.33/0.89	thf(c_0_295, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X878:$i]:(((((X1 @ X878)))&(![X879:$i]:(((((X1 @ X879)))=>(((X878)=(X879))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_270, c_0_267])).
0.33/0.89	thf(c_0_296, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
0.33/0.89	thf(c_0_297, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_271])).
0.33/0.89	thf(c_0_298, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_272, c_0_271])).
0.33/0.89	thf(c_0_299, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_271])).
0.33/0.89	thf(c_0_300, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
0.33/0.89	thf(c_0_301, plain, ((exuE2)=(![X1:$i > $o]:((((?[X880:$i]:(((((X1 @ X880)))&(![X881:$i]:(((((X1 @ X881)))=>(((X880)=(X881))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_273, c_0_267])).
0.33/0.89	thf(c_0_302, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_271])).
0.33/0.89	thf(c_0_303, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
0.33/0.89	thf(c_0_304, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X882:$i]:(((((X1 @ X882)))&(![X883:$i]:(((((X1 @ X883)))=>(((X882)=(X883)))))))))))))), inference(apply_def,[status(thm)],[c_0_274, c_0_267])).
0.33/0.89	thf(c_0_305, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X884:$i]:(((((X1 @ X884)))&(![X885:$i]:(((((X1 @ X885)))=>(((X884)=(X885)))))))))))))))), inference(apply_def,[status(thm)],[c_0_275, c_0_267])).
0.33/0.89	thf(c_0_306, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X886:$i]:(((((X1 @ X886)))&(![X887:$i]:(((((X1 @ X887)))=>(((X886)=(X887)))))))))))))), inference(apply_def,[status(thm)],[c_0_276, c_0_267])).
0.33/0.89	thf(c_0_307, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X888:$i]:(((((X1 @ X888)))&(![X889:$i]:(((((X1 @ X889)))=>(((X888)=(X889))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_277, c_0_267])).
0.33/0.89	thf(c_0_308, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X890:$i]:(((((X1 @ X890)))&(![X891:$i]:(((((X1 @ X891)))=>(((X890)=(X891))))))))))<=>((?[X892:$i]:(((((X17 @ X892)))&(![X893:$i]:(((((X17 @ X893)))=>(((X892)=(X893)))))))))))))))), inference(apply_def,[status(thm)],[c_0_278, c_0_267])).
0.33/0.89	thf(c_0_309, plain, ((exuEu)=(![X1:$i > $o]:((((?[X894:$i]:(((((X1 @ X894)))&(![X895:$i]:(((((X1 @ X895)))=>(((X894)=(X895))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_279, c_0_267])).
0.33/0.89	thf(c_0_310, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X896:$i]:(((((X1 @ X896)))&(![X897:$i]:(((((X1 @ X897)))=>(((X896)=(X897))))))))))=>((((?[X898:$i]:(((((X17 @ X898)))&(![X899:$i]:(((((X17 @ X899)))=>(((X898)=(X899))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_280, c_0_267])).
0.33/0.89	thf(c_0_311, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
0.33/0.89	thf(c_0_312, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
0.33/0.89	thf(c_0_313, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
0.33/0.89	thf(c_0_314, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
0.33/0.89	thf(c_0_315, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_281, c_0_282])).
0.33/0.89	thf(c_0_316, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))))), inference(apply_def,[status(thm)],[c_0_283, c_0_282])).
0.33/0.89	thf(c_0_317, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))))=>(((?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2)))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_284, c_0_282])).
0.33/0.89	thf(c_0_318, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
0.33/0.89	thf(c_0_319, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
0.33/0.89	thf(c_0_320, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
0.33/0.89	thf(c_0_321, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
0.33/0.89	thf(c_0_322, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_285, c_0_286])).
0.33/0.89	thf(c_0_323, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
0.33/0.89	thf(c_0_324, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
0.33/0.89	thf(c_0_325, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
0.33/0.89	thf(c_0_326, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
0.33/0.89	thf(c_0_327, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
0.33/0.89	thf(c_0_328, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
0.33/0.89	thf(c_0_329, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
0.33/0.89	thf(c_0_330, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
0.33/0.89	thf(c_0_331, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
0.33/0.89	thf(c_0_332, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_286])).
0.33/0.89	thf(c_0_333, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_286])).
0.33/0.89	thf(c_0_334, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_287, c_0_282])).
0.33/0.89	thf(c_0_335, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_286])).
0.33/0.89	thf(c_0_336, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_286])).
0.33/0.89	thf(c_0_337, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
0.33/0.89	thf(c_0_338, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
0.33/0.89	thf(c_0_339, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
0.33/0.89	thf(c_0_340, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
0.33/0.89	thf(c_0_341, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
0.33/0.89	thf(c_0_342, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
0.33/0.89	thf(c_0_343, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
0.33/0.89	thf(c_0_344, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
0.33/0.89	thf(c_0_345, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
0.33/0.89	thf(c_0_346, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
0.33/0.89	thf(c_0_347, plain, ((epred1_0)<=>![X906:$i]:(?[X907:$i]:((((![X908:$i]:(((in @ X908 @ X907)=>![X909:$i]:(((in @ X909 @ X908)=>(in @ X909 @ X906)))))&![X910:$i, X911:$i]:((((in @ X910 @ X906)&(in @ X911 @ X906))=>(![X912:$i]:(((in @ X912 @ X907)=>((in @ X910 @ X912)<=>(in @ X911 @ X912))))=>((X910)=(X911))))))&![X913:$i, X914:$i]:((((in @ X913 @ X907)&(in @ X914 @ X907))=>(![X915:$i]:(((in @ X915 @ X913)=>(in @ X915 @ X914)))|![X916:$i]:(((in @ X916 @ X914)=>(in @ X916 @ X913)))))))&![X917:$i]:(((![X918:$i]:(((in @ X918 @ X917)=>(in @ X918 @ X906)))&?[X919:$i]:((in @ X919 @ X917)))=>?[X920:$i, X921:$i]:(((((in @ X920 @ X907)&(in @ X921 @ X917))&~(?[X922:$i]:(((in @ X922 @ X920)&(in @ X922 @ X917)))))&![X923:$i]:(((in @ X923 @ X907)=>(![X924:$i]:(((in @ X924 @ X923)=>(in @ X924 @ X920)))|(in @ X921 @ X923)))))))))))), introduced(definition)).
0.33/0.89	thf(c_0_348, negated_conjecture, ~((![X900:$i, X901:$i]:((![X902:$i]:(((in @ X902 @ X900)<=>(in @ X902 @ X901)))=>((X900)=(X901))))=>(![X1745:$i]:(~(in @ X1745 @ emptyset))=>(![X1742:$i, X1743:$i, X1744:$i]:(((in @ X1744 @ (setadjoin @ X1742 @ X1743))<=>(((X1744)=(X1742))|(in @ X1744 @ X1743))))=>(![X903:$i, X904:$i]:(((in @ X904 @ (powerset @ X903))<=>![X905:$i]:(((in @ X905 @ X904)=>(in @ X905 @ X903)))))=>(![X1739:$i, X1740:$i]:(((in @ X1740 @ (setunion @ X1739))<=>?[X1741:$i]:(((in @ X1740 @ X1741)&(in @ X1741 @ X1739)))))=>((in @ emptyset @ omega)=>(![X1738:$i]:(((in @ X1738 @ omega)=>(in @ (setadjoin @ X1738 @ X1738) @ omega)))=>(![X1735:$i]:((((in @ emptyset @ X1735)&![X1736:$i]:((((in @ X1736 @ omega)&(in @ X1736 @ X1735))=>(in @ (setadjoin @ X1736 @ X1736) @ X1735))))=>![X1737:$i]:(((in @ X1737 @ omega)=>(in @ X1737 @ X1735)))))=>(![X1727:$i > $i > $o, X1728:$i]:((![X1729:$i]:(((in @ X1729 @ X1728)=>?[X1730:$i]:(((X1727 @ X1729 @ X1730)&![X1731:$i]:(((X1727 @ X1729 @ X1731)=>((X1730)=(X1731))))))))=>?[X1732:$i]:(![X1733:$i]:(((in @ X1733 @ X1732)<=>?[X1734:$i]:(((in @ X1734 @ X1728)&(X1727 @ X1734 @ X1733))))))))=>(![X1723:$i]:((?[X1724:$i]:((in @ X1724 @ X1723))=>?[X1725:$i]:(((in @ X1725 @ X1723)&~(?[X1726:$i]:(((in @ X1726 @ X1725)&(in @ X1726 @ X1723))))))))=>((epred1_0)=>(![X925:$i > $o]:((?[X926:$i]:(((X925 @ X926)&![X927:$i]:(((X925 @ X927)=>((X926)=(X927))))))=>(X925 @ (descr @ (^[Z0:$i]:(X925 @ Z0))))))=>(![X1720:$i, X1721:$i > $o, X1722:$i]:(((in @ X1722 @ X1720)=>((X1721 @ X1722)=>(in @ X1722 @ (dsetconstr @ X1720 @ X1721)))))=>(![X1717:$i, X1718:$i > $o, X1719:$i]:(((in @ X1719 @ (dsetconstr @ X1717 @ X1718))=>(in @ X1719 @ X1717)))=>(![X1714:$i, X1715:$i > $o, X1716:$i]:(((in @ X1716 @ (dsetconstr @ X1714 @ X1715))=>(X1715 @ X1716)))=>(![X1709:$i > $o]:((?[X1710:$i]:(((X1709 @ X1710)&![X1711:$i]:(((X1709 @ X1711)=>((X1710)=(X1711))))))=>?[X1712:$i]:(((X1709 @ X1712)&![X1713:$i]:(((X1709 @ X1713)=>((X1712)=(X1713))))))))=>(![X1707:$o, X1708:$i]:(((in @ X1708 @ (prop2set @ ((X1707))))=>(X1707)))=>(![X928:$i]:(((in @ X928 @ emptyset)=>![X929:$o]:((X929))))=>(![X1706:$i]:(((in @ X1706 @ emptyset)=>~($true)))=>(![X930:$i]:(~(in @ X930 @ emptyset))=>(![X931:$i > $o]:((?[X932:$i]:(((X931 @ X932)&![X933:$i]:(((X931 @ X933)=>((X932)=(X933))))))=>?[X934:$i]:((X931 @ X934))))=>(![X935:$i, X936:$i]:((![X937:$i]:(((in @ X937 @ X935)=>(in @ X937 @ X936)))=>(![X938:$i]:(((in @ X938 @ X936)=>(in @ X938 @ X935)))=>((X935)=(X936)))))=>(![X1704:$i]:((![X1705:$i]:(~(in @ X1705 @ X1704))=>((X1704)=(emptyset))))=>(![X1702:$i]:((![X1703:$i]:(~(in @ X1703 @ X1702))=>((X1702)=(emptyset))))=>(![X939:$i, X940:$i > $o, X941:$i]:(((in @ X941 @ X939)=>((in @ X941 @ (dsetconstr @ X939 @ X940))<=>(X940 @ X941))))=>(![X1700:$i]:((((X1700)!=(emptyset))=>?[X1701:$i]:((in @ X1701 @ X1700))))=>(![X942:$i, X943:$i > $o, X944:$i]:(((in @ X944 @ X942)=>((X943 @ X944)=>((dsetconstr @ X942 @ X943)!=(emptyset)))))=>(![X945:$i]:((?[X946:$i]:((in @ X946 @ X945))=>((X945)!=(emptyset))))=>(![X1698:$i, X1699:$i]:((in @ X1698 @ (setadjoin @ X1698 @ X1699)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X947:$i, X948:$i, X949:$i]:(((in @ X949 @ X948)=>(in @ X949 @ (setadjoin @ X947 @ X948))))=>(![X950:$i, X951:$i, X952:$i]:(((in @ X952 @ (setadjoin @ X950 @ X951))=>![X953:$o]:(((((X952)=(X950))=>(X953))=>(((in @ X952 @ X951)=>(X953))=>(X953))))))=>(![X1695:$i, X1696:$i, X1697:$i]:(((in @ X1697 @ (setadjoin @ X1695 @ X1696))=>(((X1697)=(X1695))|(in @ X1697 @ X1696))))=>(![X954:$i]:(((dsetconstr @ X954 @ (^[Z0:$i]:($true)))=(X954)))=>(![X1692:$i, X1693:$i]:((![X1694:$i]:(((in @ X1694 @ X1693)=>(in @ X1694 @ X1692)))=>(in @ X1693 @ (powerset @ X1692))))=>(![X955:$i]:((in @ emptyset @ (powerset @ X955)))=>(![X956:$i]:((in @ emptyset @ (powerset @ X956)))=>(![X957:$i, X958:$i, X959:$i]:(((in @ X958 @ (powerset @ X957))=>((in @ X959 @ X958)=>(in @ X959 @ X957))))=>(![X1689:$i, X1690:$i, X1691:$i]:(((in @ X1690 @ X1691)=>((in @ X1691 @ X1689)=>(in @ X1690 @ (setunion @ X1689)))))=>(![X960:$i, X961:$i]:(((in @ X961 @ (setunion @ X960))=>![X962:$o]:((![X963:$i]:(((in @ X961 @ X963)=>((in @ X963 @ X960)=>(X962))))=>(X962)))))=>(![X964:$i, X965:$i]:(((in @ X965 @ X964)=>(in @ X965 @ (powerset @ (setunion @ X964)))))=>(![X1684:$i > $o]:((?[X1685:$i]:(((X1684 @ X1685)&![X1686:$i]:(((X1684 @ X1686)=>((X1685)=(X1686))))))=>?[X1687:$i]:(![X1688:$i]:(((X1684 @ X1688)<=>((X1688)=(X1687)))))))=>(![X1682:$i]:((((X1682)!=(emptyset))=>?[X1683:$i]:(((in @ X1683 @ X1682)&$true))))=>(![X1680:$i, X1681:$i]:(((in @ X1680 @ (setadjoin @ X1681 @ emptyset))=>((X1680)=(X1681))))=>(![X1678:$i, X1679:$i]:((((X1678)!=(X1679))=>~(in @ X1679 @ (setadjoin @ X1678 @ emptyset))))=>(![X1676:$i, X1677:$i]:((((X1676)=(X1677))=>(in @ X1676 @ (setadjoin @ X1677 @ emptyset))))=>(![X966:$i, X967:$i]:(((in @ X966 @ (setadjoin @ X967 @ emptyset))=>(in @ X967 @ (setadjoin @ X966 @ emptyset))))=>(![X1673:$i, X1674:$i, X1675:$i]:(((in @ X1675 @ (setadjoin @ X1673 @ (setadjoin @ X1674 @ emptyset)))=>(((X1675)=(X1673))|((X1675)=(X1674)))))=>(![X1671:$i, X1672:$i]:((in @ X1671 @ (setadjoin @ X1671 @ (setadjoin @ X1672 @ emptyset))))=>(![X968:$i, X969:$i]:((in @ X969 @ (setadjoin @ X968 @ (setadjoin @ X969 @ emptyset))))=>(![X1668:$i, X1669:$i > $o]:((?[X1670:$i]:(((in @ X1670 @ X1668)&(X1669 @ X1670)))=>(((dsetconstr @ X1668 @ X1669)=(emptyset))=>~($true))))=>(![X1666:$i > $o, X1667:$i]:(((in @ X1667 @ emptyset)=>(X1666 @ X1667)))=>(![X970:$i, X971:$i > $o]:((~(![X972:$i]:(((in @ X972 @ X970)=>(X971 @ X972))))=>?[X973:$i]:(((in @ X973 @ X970)&~((X971 @ X973))))))=>(![X974:$i, X975:$i > $o]:((![X976:$i]:(((in @ X976 @ X974)=>~((X975 @ X976))))=>~(?[X977:$i]:(((in @ X977 @ X974)&(X975 @ X977))))))=>(![X1662:$i, X1663:$i > $o]:((~(?[X1664:$i]:(((in @ X1664 @ X1662)&(X1663 @ X1664))))=>![X1665:$i]:(((in @ X1665 @ X1662)=>~((X1663 @ X1665))))))=>(![X978:$i, X979:$i > $o]:((?[X980:$i]:(((in @ X980 @ X978)&~((X979 @ X980))))=>~(![X981:$i]:(((in @ X981 @ X978)=>(X979 @ X981))))))=>(![X1661:$o]:(((X1661)=>(in @ emptyset @ (prop2set @ ((X1661))))))=>(![X982:$o]:(((X982)=>(set2prop @ (prop2set @ ((X982))))))=>(![X1657:$i, X1658:$i > $o]:((~(?[X1659:$i]:(((in @ X1659 @ X1657)&(X1658 @ X1659))))=>![X1660:$i]:(((in @ X1660 @ X1657)=>~((X1658 @ X1660))))))=>(![X1653:$i, X1654:$i > $o]:((~(![X1655:$i]:(((in @ X1655 @ X1653)=>(X1654 @ X1655))))=>?[X1656:$i]:(((in @ X1656 @ X1653)&~((X1654 @ X1656))))))=>(![X983:$i > $o]:((?[X984:$i]:(((X983 @ X984)&![X985:$i]:(((X983 @ X985)=>((X984)=(X985))))))=>?[X986:$i]:(((X983 @ X986)&![X987:$i]:(((X983 @ X987)=>((X986)=(X987))))))))=>(![X988:$i > $o]:((?[X989:$i]:((X988 @ X989))=>(![X990:$i, X991:$i]:(((X988 @ X990)=>((X988 @ X991)=>((X990)=(X991)))))=>?[X992:$i]:(((X988 @ X992)&![X993:$i]:(((X988 @ X993)=>((X992)=(X993)))))))))=>(![X1648:$i > $o]:((?[X1649:$i]:(![X1650:$i]:(((X1648 @ X1650)<=>((X1650)=(X1649)))))=>?[X1651:$i]:(((X1648 @ X1651)&![X1652:$i]:(((X1648 @ X1652)=>((X1651)=(X1652))))))))=>(![X1644:$i, X1645:$i]:((((X1644)=(X1645))=>![X1646:$i, X1647:$i]:((((X1646)=(X1647))=>((in @ X1646 @ X1644)=>(in @ X1647 @ X1645))))))=>(![X994:$i, X995:$i]:((((X994)=(X995))=>![X996:$i, X997:$i]:((((X996)=(X997))=>((in @ X996 @ X994)<=>(in @ X997 @ X995))))))=>(![X998:$i > $o]:((?[X999:$i]:(((X998 @ X999)&![X1000:$i]:(((X998 @ X1000)=>((X999)=(X1000))))))=>![X1001:$i, X1002:$i]:(((X998 @ X1001)=>((X998 @ X1002)=>((X1001)=(X1002)))))))=>(![X1003:$i > $o, X1004:$i > $o]:((![X1005:$i, X1006:$i]:((((X1005)=(X1006))=>((X1003 @ X1005)<=>(X1004 @ X1006))))=>(?[X1007:$i]:(((X1003 @ X1007)&![X1008:$i]:(((X1003 @ X1008)=>((X1007)=(X1008))))))<=>?[X1009:$i]:(((X1004 @ X1009)&![X1010:$i]:(((X1004 @ X1010)=>((X1009)=(X1010)))))))))=>(((emptyset)=(emptyset))=>(![X1011:$i, X1012:$i]:((((X1011)=(X1012))=>![X1013:$i, X1014:$i]:((((X1013)=(X1014))=>((setadjoin @ X1011 @ X1013)=(setadjoin @ X1012 @ X1014))))))=>(![X1015:$i, X1016:$i]:((((X1015)=(X1016))=>((powerset @ X1015)=(powerset @ X1016))))=>(![X1642:$i, X1643:$i]:((((X1642)=(X1643))=>((setunion @ X1642)=(setunion @ X1643))))=>(((omega)=(omega))=>(![X1637:$i > $o]:((?[X1638:$i]:(((X1637 @ X1638)&![X1639:$i]:(((X1637 @ X1639)=>((X1638)=(X1639))))))=>![X1640:$i, X1641:$i]:(((X1637 @ X1640)=>((X1637 @ X1641)=>((X1640)=(X1641)))))))=>(![X1629:$i > $o, X1630:$i > $o]:((![X1631:$i, X1632:$i]:((((X1631)=(X1632))=>((X1629 @ X1631)<=>(X1630 @ X1632))))=>(?[X1633:$i]:(((X1629 @ X1633)&![X1634:$i]:(((X1629 @ X1634)=>((X1633)=(X1634))))))=>(?[X1635:$i]:(((X1630 @ X1635)&![X1636:$i]:(((X1630 @ X1636)=>((X1635)=(X1636))))))=>((descr @ X1629)=(descr @ X1630))))))=>(![X1623:$i, X1624:$i]:((((X1623)=(X1624))=>![X1625:$i > $o, X1626:$i > $o]:((![X1627:$i]:(((in @ X1627 @ X1623)=>![X1628:$i]:(((in @ X1628 @ X1624)=>(((X1627)=(X1628))=>((X1625 @ X1627)<=>(X1626 @ X1628)))))))=>((dsetconstr @ X1623 @ X1625)=(dsetconstr @ X1624 @ X1626))))))=>(![X1017:$i, X1018:$i]:((![X1019:$i]:(((in @ X1019 @ X1017)=>(in @ X1019 @ X1018)))=>(subset @ X1017 @ X1018)))=>(![X1020:$i, X1021:$i]:((((X1020)=(X1021))=>(subset @ X1021 @ X1020)))=>(![X1022:$i, X1023:$i]:((((X1022)=(X1023))=>(subset @ X1022 @ X1023)))=>(![X1024:$i, X1025:$i]:((![X1026:$i]:(((in @ X1026 @ X1024)=>(in @ X1026 @ X1025)))=>(subset @ X1024 @ X1025)))=>(![X1027:$i]:((subset @ emptyset @ X1027))=>(![X1028:$i, X1029:$i, X1030:$i]:(((subset @ X1028 @ X1029)=>((in @ X1030 @ X1028)=>(in @ X1030 @ X1029))))=>(![X1620:$i, X1621:$i, X1622:$i]:(((subset @ X1620 @ X1621)=>(~(in @ X1622 @ X1621)=>~(in @ X1622 @ X1620))))=>(![X1031:$i, X1032:$i, X1033:$i]:(((in @ X1033 @ X1031)=>(~(in @ X1033 @ X1032)=>~(subset @ X1031 @ X1032))))=>(![X1034:$i, X1035:$i]:((~(subset @ X1034 @ X1035)=>((X1034)!=(X1035))))=>(![X1036:$i, X1037:$i, X1038:$i]:(((in @ X1038 @ X1036)=>(~(in @ X1038 @ X1037)=>((X1036)!=(X1037)))))=>(![X1039:$i]:((subset @ X1039 @ X1039))=>(![X1040:$i, X1041:$i, X1042:$i]:(((subset @ X1040 @ X1041)=>((subset @ X1041 @ X1042)=>(subset @ X1040 @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_288, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_289]), foundationAx]), wellorderingAx]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_295]), setext]), emptyI]), noeltsimpempty]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_300]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_301]), c_0_302]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_303]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_304]), c_0_305]), c_0_306]), inCongP]), in__Cong]), c_0_307]), c_0_308]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_309]), c_0_310]), c_0_311]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_312]), c_0_313]), 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]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), singletonsuniq]), setukpairinjL1]), c_0_318]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_319]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), c_0_324]), c_0_325]), c_0_326]), c_0_327]), c_0_328]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_329]), c_0_330]), c_0_331]), c_0_332]), c_0_333]), c_0_334]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_335]), c_0_336]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_337]), c_0_338]), c_0_339]), c_0_340]), c_0_341]), c_0_342]), c_0_343]), c_0_344]), c_0_345]), c_0_346]), 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])])]), c_0_347])).
0.33/0.89	thf(c_0_349, negated_conjecture, ![X1746:$i, X1747:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1759:$i, X1760:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1768:$i, X1769:$i > $i > $o, X1770:$i, X1772:$i, X1775:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1782:$i, X1783:$i > $o, X1784:$i, X1786:$i, X1787:$i > $o, X1788:$i, X1789:$i, X1790:$i > $o, X1791:$i, X1792:$i, X1793:$i > $o, X1794:$i, X1795:$i > $o, X1796:$i, X1799:$i, X1800:$o, X1801:$i, X1802:$i, X1803:$o, X1804:$i, X1805:$i, X1806:$i > $o, X1807:$i, X1810:$i, X1811:$i, X1814:$i, X1816:$i, X1818:$i, X1819:$i > $o, X1820:$i, X1821:$i, X1823:$i, X1824:$i > $o, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$o, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$o, X1856:$i, X1857:$i, X1858:$i > $o, X1859:$i, X1862:$i, X1863:$i, X1864:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i > $o, X1883:$i, X1884:$i > $o, X1885:$i, X1886:$i, X1887:$i > $o, X1888:$i, X1890:$i, X1891:$i > $o, X1893:$i, X1894:$i, X1895:$i > $o, X1897:$i, X1898:$i, X1899:$i > $o, X1900:$i, X1902:$o, X1903:$o, X1904:$i, X1905:$i > $o, X1907:$i, X1908:$i, X1909:$i > $o, X1910:$i, X1912:$i > $o, X1913:$i, X1916:$i, X1917:$i > $o, X1918:$i, X1922:$i, X1923:$i > $o, X1924:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i > $o, X1937:$i, X1939:$i, X1940:$i, X1941:$i > $o, X1942:$i > $o, X1945:$i, X1948:$i, X1949:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i > $o, X1962:$i, X1964:$i, X1965:$i, X1966:$i > $o, X1967:$i > $o, X1970:$i, X1972:$i, X1974:$i, X1975:$i, X1976:$i > $o, X1977:$i > $o, X1980:$i, X1981:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i > $o, X2028:$i, X2029:$i > $o, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$o, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$o, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i > 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X2383 @ (cartprod @ X2380 @ X2381))|~(subset @ X2382 @ (cartprod @ X2380 @ X2381)))&(((in @ (kpair @ (esk76_4 @ X2380 @ X2381 @ X2382 @ X2383) @ (esk77_4 @ X2380 @ X2381 @ X2382 @ X2383)) @ X2383)|((X2382)=(X2383))|(in @ (kpair @ (esk74_4 @ X2380 @ X2381 @ X2382 @ X2383) @ (esk75_4 @ X2380 @ X2381 @ X2382 @ X2383)) @ X2382)|~(subset @ X2383 @ (cartprod @ X2380 @ X2381))|~(subset @ X2382 @ (cartprod @ X2380 @ X2381)))&(~(in @ (kpair @ (esk76_4 @ X2380 @ X2381 @ X2382 @ X2383) @ (esk77_4 @ X2380 @ X2381 @ X2382 @ X2383)) @ X2382)|((X2382)=(X2383))|(in @ (kpair @ (esk74_4 @ X2380 @ X2381 @ X2382 @ X2383) @ (esk75_4 @ X2380 @ X2381 @ X2382 @ X2383)) @ X2382)|~(subset @ X2383 @ (cartprod @ X2380 @ X2381))|~(subset @ X2382 @ (cartprod @ X2380 @ X2381))))))&(((in @ (esk76_4 @ X2380 @ X2381 @ X2382 @ X2383) @ X2380)|((X2382)=(X2383))|~(in @ (kpair @ (esk74_4 @ X2380 @ X2381 @ X2382 @ X2383) @ (esk75_4 @ X2380 @ X2381 @ X2382 @ X2383)) @ X2383)|~(subset @ X2383 @ (cartprod @ X2380 @ X2381))|~(subset @ X2382 @ (cartprod @ X2380 @ X2381)))&(((in @ (esk77_4 @ X2380 @ X2381 @ X2382 @ X2383) @ X2381)|((X2382)=(X2383))|~(in @ (kpair @ (esk74_4 @ X2380 @ X2381 @ X2382 @ X2383) @ (esk75_4 @ X2380 @ X2381 @ X2382 @ X2383)) @ X2383)|~(subset @ X2383 @ (cartprod @ X2380 @ X2381))|~(subset @ X2382 @ (cartprod @ X2380 @ X2381)))&(((in @ (kpair @ (esk76_4 @ X2380 @ X2381 @ X2382 @ X2383) @ (esk77_4 @ X2380 @ X2381 @ X2382 @ X2383)) @ X2383)|((X2382)=(X2383))|~(in @ (kpair @ (esk74_4 @ X2380 @ X2381 @ X2382 @ X2383) @ (esk75_4 @ X2380 @ X2381 @ X2382 @ X2383)) @ X2383)|~(subset @ X2383 @ (cartprod @ X2380 @ X2381))|~(subset @ X2382 @ (cartprod @ X2380 @ X2381)))&(~(in @ (kpair @ (esk76_4 @ X2380 @ X2381 @ X2382 @ X2383) @ (esk77_4 @ X2380 @ X2381 @ X2382 @ X2383)) @ X2382)|((X2382)=(X2383))|~(in @ (kpair @ (esk74_4 @ X2380 @ X2381 @ X2382 @ X2383) @ (esk75_4 @ X2380 @ X2381 @ X2382 @ X2383)) @ X2383)|~(subset @ X2383 @ (cartprod @ X2380 @ X2381))|~(subset @ X2382 @ (cartprod @ X2380 @ X2381)))))))))&((((in @ (esk78_4 @ X2388 @ X2389 @ X2390 @ X2391) @ X2388)|((X2390)=(X2391))|~(func @ X2388 @ X2389 @ X2391)|~(func @ X2388 @ X2389 @ X2390))&(((ap @ X2388 @ X2389 @ X2390 @ (esk78_4 @ X2388 @ X2389 @ X2390 @ X2391))!=(ap @ X2388 @ X2389 @ X2391 @ (esk78_4 @ X2388 @ X2389 @ X2390 @ X2391)))|((X2390)=(X2391))|~(func @ X2388 @ X2389 @ X2391)|~(func @ X2388 @ X2389 @ X2390)))&((((in @ (esk79_4 @ X2393 @ X2394 @ X2395 @ X2396) @ X2393)|((X2395)=(X2396))|~(in @ X2396 @ (funcSet @ X2393 @ X2394))|~(in @ X2395 @ (funcSet @ X2393 @ X2394)))&(((ap @ X2393 @ X2394 @ X2395 @ (esk79_4 @ X2393 @ X2394 @ X2395 @ X2396))!=(ap @ X2393 @ X2394 @ X2396 @ (esk79_4 @ X2393 @ X2394 @ X2395 @ X2396)))|((X2395)=(X2396))|~(in @ X2396 @ (funcSet @ X2393 @ X2394))|~(in @ X2395 @ (funcSet @ X2393 @ X2394))))&((~(in @ X2400 @ (funcSet @ X2398 @ X2399))|(~(in @ X2401 @ X2398)|((ap @ X2398 @ X2399 @ X2400 @ X2401)=(ap @ X2398 @ X2399 @ X2400 @ X2401))))&((~(func @ X2402 @ X2403 @ X2404)|(~(in @ X2405 @ X2402)|((ap @ X2402 @ X2403 @ X2404 @ X2405)=(ap @ X2402 @ X2403 @ X2404 @ X2405))))&((((in @ (esk80_3 @ X2406 @ X2407 @ X2408) @ X2406)|(~(in @ X2410 @ X2406)|((ap @ X2406 @ X2407 @ (lam @ X2406 @ X2407 @ X2408) @ X2410)=(X2408 @ X2410))))&(~(in @ (X2408 @ (esk80_3 @ X2406 @ X2407 @ X2408)) @ X2407)|(~(in @ X2410 @ X2406)|((ap @ X2406 @ X2407 @ (lam @ X2406 @ X2407 @ X2408) @ X2410)=(X2408 @ X2410)))))&((~(func @ X2411 @ X2412 @ X2413)|((lam @ X2411 @ X2412 @ (ap @ X2411 @ X2412 @ X2413))=(X2413)))&((((in @ (esk81_3 @ X2414 @ X2415 @ X2416) @ X2414)|((lam @ X2414 @ X2415 @ X2416)=(lam @ X2414 @ X2415 @ X2416)))&(~(in @ (X2416 @ (esk81_3 @ X2414 @ X2415 @ X2416)) @ X2415)|((lam @ X2414 @ X2415 @ X2416)=(lam @ X2414 @ X2415 @ X2416))))&((((in @ (esk82_3 @ X2418 @ X2419 @ X2420) @ X2418)|(~(in @ X2422 @ X2418)|((ap @ X2418 @ X2419 @ (lam @ X2418 @ X2419 @ X2420) @ X2422)=(X2420 @ X2422))))&(~(in @ (X2420 @ (esk82_3 @ X2418 @ X2419 @ X2420)) @ X2419)|(~(in @ X2422 @ X2418)|((ap @ X2418 @ X2419 @ (lam @ X2418 @ X2419 @ X2420) @ X2422)=(X2420 @ X2422)))))&((~(in @ X2425 @ (funcSet @ X2423 @ X2424))|((lam @ X2423 @ X2424 @ (ap @ X2423 @ X2424 @ X2425))=(X2425)))&((~(in @ X2428 @ X2426)|(~(in @ X2429 @ X2426)|((X2427)|(in @ X2429 @ (dsetconstr @ X2426 @ (^[Z0:$i]:((((((X2427))&(((Z0)=(X2428)))))|(((~((X2427)))&(((Z0)=(X2429)))))))))))))&((~(in @ X2432 @ X2430)|(~(in @ X2433 @ X2430)|((X2431)|((dsetconstr @ X2430 @ (^[Z0:$i]:((((((X2431))&(((Z0)=(X2432)))))|(((~((X2431)))&(((Z0)=(X2433)))))))))=(setadjoin @ X2433 @ emptyset)))))&((~(in @ X2436 @ X2434)|(~(in @ X2437 @ X2434)|(~(X2435)|(in @ X2436 @ (dsetconstr @ X2434 @ (^[Z0:$i]:((((((X2435))&(((Z0)=(X2436)))))|(((~((X2435)))&(((Z0)=(X2437)))))))))))))&((~(in @ X2440 @ X2438)|(~(in @ X2441 @ X2438)|(~(X2439)|((dsetconstr @ X2438 @ (^[Z0:$i]:((((((X2439))&(((Z0)=(X2440)))))|(((~((X2439)))&(((Z0)=(X2441)))))))))=(setadjoin @ X2440 @ emptyset)))))&((~(in @ X2444 @ X2442)|(~(in @ X2445 @ X2442)|(singleton @ (dsetconstr @ X2442 @ (^[Z0:$i]:((((((X2443))&(((Z0)=(X2444)))))|(((~((X2443)))&(((Z0)=(X2445))))))))))))&((~(in @ X2448 @ X2446)|(~(in @ X2449 @ X2446)|(in @ (if @ X2446 @ ((X2447)) @ X2448 @ X2449) @ X2446)))&((~(singleton @ X2450)|(~(in @ X2451 @ X2450)|((setunion @ X2450)=(X2451))))&((~(in @ X2454 @ X2452)|(~(in @ X2455 @ X2452)|(~(X2453)|((if @ X2452 @ ((X2453)) @ X2454 @ X2455)=(X2454)))))&((~(in @ X2458 @ X2456)|(~(in @ X2459 @ X2456)|((X2457)|((if @ X2456 @ ((X2457)) @ X2458 @ X2459)=(X2459)))))&((~(in @ X2462 @ X2460)|(~(in @ X2463 @ X2460)|(in @ (if @ X2460 @ ((X2461)) @ X2462 @ X2463) @ (setadjoin @ X2462 @ (setadjoin @ X2463 @ emptyset)))))&((~(in @ X2465 @ (powerset @ X2464))|(~(in @ X2466 @ (powerset @ X2464))|(in @ (binintersect @ X2465 @ X2466) @ (powerset @ X2464))))&((~(in @ X2468 @ (powerset @ X2467))|(~(in @ X2469 @ (powerset @ X2467))|(in @ (binunion @ X2468 @ X2469) @ (powerset @ X2467))))&((~(in @ X2471 @ (powerset @ X2470))|(in @ (powerset @ X2471) @ (powerset @ (powerset @ X2470))))&((~(in @ X2473 @ (powerset @ X2472))|(~(in @ X2474 @ (powerset @ X2472))|(in @ (setminus @ X2473 @ X2474) @ (powerset @ X2472))))&((~(in @ X2476 @ (powerset @ X2475))|(in @ (setminus @ X2475 @ X2476) @ (powerset @ X2475)))&(((((in @ (esk84_3 @ X2477 @ X2478 @ X2479) @ X2477)|((X2478)=(X2479))|(in @ (esk83_3 @ X2477 @ X2478 @ X2479) @ X2477)|~(in @ X2479 @ (powerset @ X2477))|~(in @ X2478 @ (powerset @ X2477)))&(((in @ (esk84_3 @ X2477 @ X2478 @ X2479) @ X2479)|((X2478)=(X2479))|(in @ (esk83_3 @ X2477 @ X2478 @ X2479) @ X2477)|~(in @ X2479 @ (powerset @ X2477))|~(in @ X2478 @ (powerset @ X2477)))&(~(in @ (esk84_3 @ X2477 @ X2478 @ X2479) @ X2478)|((X2478)=(X2479))|(in @ (esk83_3 @ X2477 @ X2478 @ X2479) @ X2477)|~(in @ X2479 @ (powerset @ X2477))|~(in @ X2478 @ (powerset @ X2477)))))&((((in @ (esk84_3 @ X2477 @ X2478 @ X2479) @ X2477)|((X2478)=(X2479))|(in @ (esk83_3 @ X2477 @ X2478 @ X2479) @ X2478)|~(in @ X2479 @ (powerset @ X2477))|~(in @ X2478 @ (powerset @ X2477)))&(((in @ (esk84_3 @ X2477 @ X2478 @ X2479) @ X2479)|((X2478)=(X2479))|(in @ (esk83_3 @ X2477 @ X2478 @ X2479) @ X2478)|~(in @ X2479 @ (powerset @ X2477))|~(in @ X2478 @ (powerset @ X2477)))&(~(in @ (esk84_3 @ X2477 @ X2478 @ X2479) @ X2478)|((X2478)=(X2479))|(in @ (esk83_3 @ X2477 @ X2478 @ X2479) @ X2478)|~(in @ X2479 @ (powerset @ X2477))|~(in @ X2478 @ (powerset @ X2477)))))&(((in @ (esk84_3 @ X2477 @ X2478 @ X2479) @ X2477)|((X2478)=(X2479))|~(in @ (esk83_3 @ X2477 @ X2478 @ X2479) @ X2479)|~(in @ X2479 @ (powerset @ X2477))|~(in @ X2478 @ (powerset @ X2477)))&(((in @ (esk84_3 @ X2477 @ X2478 @ X2479) @ X2479)|((X2478)=(X2479))|~(in @ (esk83_3 @ X2477 @ X2478 @ X2479) @ X2479)|~(in @ X2479 @ (powerset @ X2477))|~(in @ X2478 @ (powerset @ X2477)))&(~(in @ (esk84_3 @ X2477 @ X2478 @ X2479) @ X2478)|((X2478)=(X2479))|~(in @ (esk83_3 @ X2477 @ X2478 @ X2479) @ X2479)|~(in @ X2479 @ (powerset @ X2477))|~(in @ X2478 @ (powerset @ X2477)))))))&((((in @ (esk85_3 @ X2482 @ X2483 @ X2484) @ X2482)|(subset @ X2483 @ X2484)|~(in @ X2484 @ (powerset @ X2482))|~(in @ X2483 @ (powerset @ X2482)))&(((in @ (esk85_3 @ X2482 @ X2483 @ X2484) @ X2483)|(subset @ X2483 @ X2484)|~(in @ X2484 @ (powerset @ X2482))|~(in @ X2483 @ (powerset @ X2482)))&(~(in @ (esk85_3 @ X2482 @ X2483 @ X2484) @ X2484)|(subset @ X2483 @ X2484)|~(in @ X2484 @ (powerset @ X2482))|~(in @ X2483 @ (powerset @ X2482)))))&((((in @ (esk86_3 @ X2486 @ X2487 @ X2488) @ X2486)|(in @ X2487 @ (powerset @ X2488))|~(in @ X2488 @ (powerset @ X2486))|~(in @ X2487 @ (powerset @ X2486)))&(((in @ (esk86_3 @ X2486 @ X2487 @ X2488) @ X2487)|(in @ X2487 @ (powerset @ X2488))|~(in @ X2488 @ (powerset @ X2486))|~(in @ X2487 @ (powerset @ X2486)))&(~(in @ (esk86_3 @ X2486 @ X2487 @ X2488) @ X2488)|(in @ X2487 @ (powerset @ X2488))|~(in @ X2488 @ (powerset @ X2486))|~(in @ X2487 @ (powerset @ X2486)))))&((~(in @ X2491 @ (powerset @ X2490))|(~(in @ X2492 @ (powerset @ X2490))|(~(in @ X2493 @ X2490)|(~(in @ X2491 @ (powerset @ X2492))|(~(in @ X2493 @ X2491)|(in @ X2493 @ X2492))))))&((~(in @ X2495 @ (powerset @ X2494))|(~(in @ X2496 @ X2494)|(~(in @ X2496 @ X2495)|~(in @ X2496 @ (setminus @ X2494 @ X2495)))))&((~(in @ X2498 @ (powerset @ X2497))|(~(in @ X2499 @ X2497)|((in @ X2499 @ (setminus @ X2497 @ X2498))|(in @ X2499 @ X2498))))&((~(in @ X2501 @ (powerset @ X2500))|(~(in @ X2502 @ (powerset @ X2500))|(~(in @ X2503 @ X2500)|((in @ X2503 @ X2501)|~(in @ X2503 @ (binintersect @ X2501 @ X2502))))))&((~(in @ X2505 @ (powerset @ X2504))|(~(in @ X2506 @ (powerset @ X2504))|(~(in @ X2507 @ X2504)|((in @ X2507 @ X2506)|~(in @ X2507 @ (binintersect @ X2505 @ X2506))))))&((~(in @ X2509 @ (powerset @ X2508))|(~(in @ X2510 @ (powerset @ X2508))|(~(in @ X2511 @ X2508)|(~(subset @ X2509 @ (setminus @ X2508 @ X2510))|(~(in @ X2511 @ X2510)|~(in @ X2511 @ X2509))))))&((~(in @ X2513 @ (powerset @ X2512))|(~(in @ X2514 @ (powerset @ X2512))|(~(in @ X2515 @ X2512)|(~(subset @ X2513 @ X2514)|((in @ X2515 @ X2514)|~(in @ X2515 @ X2513))))))&((~(in @ X2517 @ (powerset @ X2516))|(~(in @ X2518 @ (powerset @ X2516))|(~(subset @ X2517 @ X2518)|(subset @ (setminus @ X2516 @ X2518) @ (setminus @ X2516 @ X2517)))))&((~(in @ X2520 @ (powerset @ X2519))|(~(in @ X2521 @ (powerset @ X2519))|(~(subset @ (setminus @ X2519 @ X2521) @ (setminus @ X2519 @ X2520))|(subset @ X2520 @ X2521))))&((~(in @ X2523 @ (powerset @ X2522))|(~(in @ X2524 @ X2522)|(~(in @ X2524 @ X2523)|(in @ X2524 @ (setminus @ X2522 @ (setminus @ X2522 @ X2523))))))&((~(in @ X2526 @ (powerset @ X2525))|(~(in @ X2527 @ X2525)|(~(in @ X2527 @ (setminus @ X2525 @ (setminus @ X2525 @ X2526)))|(in @ X2527 @ X2526))))&((~(in @ X2529 @ (powerset @ X2528))|(subset @ X2529 @ (setminus @ X2528 @ (setminus @ X2528 @ X2529))))&((~(in @ X2531 @ (powerset @ X2530))|(subset @ (setminus @ X2530 @ (setminus @ X2530 @ X2531)) @ X2531))&((~(in @ X2533 @ (powerset @ X2532))|((X2533)=(setminus @ X2532 @ (setminus @ X2532 @ X2533))))&((~(in @ X2535 @ (powerset @ X2534))|(~(in @ X2536 @ (powerset @ X2534))|(~(in @ X2537 @ X2534)|(~(in @ X2537 @ (setminus @ X2534 @ X2535))|~(in @ X2537 @ (binintersect @ X2535 @ X2536))))))&((~(in @ X2539 @ (powerset @ X2538))|(~(in @ X2540 @ (powerset @ X2538))|(~(in @ X2541 @ X2538)|(~(in @ X2541 @ (setminus @ X2538 @ X2539))|(in @ X2541 @ (setminus @ X2538 @ (binintersect @ X2539 @ X2540)))))))&((~(in @ X2543 @ (powerset @ X2542))|(~(in @ X2544 @ (powerset @ X2542))|(subset @ (setminus @ X2542 @ X2543) @ (setminus @ X2542 @ (binintersect @ X2543 @ X2544)))))&((~(in @ X2546 @ (powerset @ X2545))|(~(in @ X2547 @ (powerset @ X2545))|(in @ (setminus @ X2545 @ X2546) @ (powerset @ (setminus @ X2545 @ (binintersect @ X2546 @ X2547))))))&((~(in @ X2549 @ (powerset @ X2548))|(~(in @ X2550 @ (powerset @ X2548))|(~(subset @ X2549 @ (setminus @ X2548 @ X2550))|(~(in @ X2551 @ X2548)|(~(in @ X2551 @ X2550)|(in @ X2551 @ (setminus @ X2548 @ X2549)))))))&((~(in @ X2553 @ (powerset @ X2552))|(~(in @ X2554 @ (powerset @ X2552))|(~(subset @ X2553 @ (setminus @ X2552 @ X2554))|(subset @ X2554 @ (setminus @ X2552 @ X2553)))))&((~(in @ X2556 @ (powerset @ X2555))|(~(in @ X2557 @ (powerset @ X2555))|(~(in @ X2558 @ X2555)|((in @ X2558 @ (binunion @ X2556 @ X2557))|~(in @ X2558 @ X2556)))))&((~(in @ X2560 @ (powerset @ X2559))|(~(in @ X2561 @ (powerset @ X2559))|(~(in @ X2562 @ X2559)|((in @ X2562 @ (binunion @ X2560 @ X2561))|~(in @ X2562 @ X2561)))))&((~(in @ X2564 @ (powerset @ X2563))|(~(in @ X2565 @ (powerset @ X2563))|(~(in @ X2566 @ (powerset @ X2563))|(~(in @ X2567 @ X2563)|(~(in @ X2567 @ (binintersect @ X2564 @ X2565))|(in @ X2567 @ (binunion @ X2564 @ X2566)))))))&((~(in @ X2569 @ (powerset @ X2568))|(~(in @ X2570 @ (powerset @ X2568))|(~(in @ X2571 @ (powerset @ X2568))|(~(in @ X2572 @ X2568)|(~(in @ X2572 @ (binintersect @ X2569 @ X2570))|(in @ X2572 @ (binunion @ X2570 @ X2571)))))))&((~(in @ X2574 @ (powerset @ X2573))|(~(in @ X2575 @ (powerset @ X2573))|(~(in @ X2576 @ (powerset @ X2573))|(~(in @ X2577 @ X2573)|(~(in @ X2577 @ (binintersect @ X2574 @ X2575))|(in @ X2577 @ (binintersect @ (binunion @ X2574 @ X2576) @ (binunion @ X2575 @ X2576))))))))&((~(in @ X2579 @ (powerset @ X2578))|(~(in @ X2580 @ (powerset @ X2578))|(~(in @ X2581 @ (powerset @ X2578))|(in @ (binintersect @ X2579 @ X2580) @ (powerset @ (binintersect @ (binunion @ X2579 @ X2581) @ (binunion @ X2580 @ X2581)))))))&((~(in @ X2583 @ (powerset @ X2582))|(~(in @ X2584 @ (powerset @ X2582))|(~(in @ X2585 @ X2582)|(~(in @ X2585 @ (setminus @ X2582 @ (binunion @ X2583 @ X2584)))|~(in @ X2585 @ X2583)))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((in @ esk90_0 @ esk87_0)&((in @ esk90_0 @ (setminus @ esk87_0 @ (binunion @ esk88_0 @ esk89_0)))&~(in @ esk90_0 @ (setminus @ esk87_0 @ esk88_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_348])])])])])])])).
0.33/0.89	thf(c_0_350, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_349])).
0.33/0.89	thf(c_0_351, negated_conjecture, (in @ esk90_0 @ (setminus @ esk87_0 @ (binunion @ esk88_0 @ esk89_0))), inference(split_conjunct,[status(thm)],[c_0_349])).
0.33/0.89	thf(c_0_352, negated_conjecture, ~((in @ esk90_0 @ (binunion @ esk88_0 @ esk89_0))), inference(spm,[status(thm)],[c_0_350, c_0_351])).
0.33/0.89	thf(c_0_353, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_349])).
0.33/0.89	thf(c_0_354, negated_conjecture, ~((in @ esk90_0 @ (setminus @ esk87_0 @ esk88_0))), inference(split_conjunct,[status(thm)],[c_0_349])).
0.33/0.89	thf(c_0_355, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_349])).
0.33/0.89	thf(c_0_356, negated_conjecture, (in @ esk90_0 @ esk87_0), inference(split_conjunct,[status(thm)],[c_0_349])).
0.33/0.89	thf(c_0_357, negated_conjecture, ~((in @ esk90_0 @ esk88_0)), inference(spm,[status(thm)],[c_0_352, c_0_353])).
0.33/0.89	thf(c_0_358, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_354, c_0_355]), c_0_356])]), c_0_357]), ['proof']).
0.33/0.89	% SZS output end CNFRefutation
0.33/0.89	% Parsed axioms                        : 565
0.33/0.89	% Removed by relevancy pruning/SinE    : 0
0.33/0.89	% Initial clauses                      : 767
0.33/0.89	% Removed in clause preprocessing      : 333
0.33/0.89	% Initial clauses in saturation        : 434
0.33/0.89	% Processed clauses                    : 627
0.33/0.89	% ...of these trivial                  : 17
0.33/0.89	% ...subsumed                          : 238
0.33/0.89	% ...remaining for further processing  : 372
0.33/0.89	% Other redundant clauses eliminated   : 30
0.33/0.89	% Clauses deleted for lack of memory   : 0
0.33/0.89	% Backward-subsumed                    : 2
0.33/0.89	% Backward-rewritten                   : 8
0.33/0.89	% Generated clauses                    : 4172
0.33/0.89	% ...of the previous two non-redundant : 3129
0.33/0.89	% ...aggressively subsumed             : 0
0.33/0.89	% Contextual simplify-reflections      : 0
0.33/0.89	% Paramodulations                      : 4138
0.33/0.89	% Factorizations                       : 0
0.33/0.89	% NegExts                              : 0
0.33/0.89	% Equation resolutions                 : 33
0.33/0.89	% Disequality decompositions           : 0
0.33/0.89	% Total rewrite steps                  : 1383
0.33/0.89	% ...of those cached                   : 1246
0.33/0.89	% Propositional unsat checks           : 0
0.33/0.89	%    Propositional check models        : 0
0.33/0.89	%    Propositional check unsatisfiable : 0
0.33/0.89	%    Propositional clauses             : 0
0.33/0.89	%    Propositional clauses after purity: 0
0.33/0.89	%    Propositional unsat core size     : 0
0.33/0.89	%    Propositional preprocessing time  : 0.000
0.33/0.89	%    Propositional encoding time       : 0.000
0.33/0.89	%    Propositional solver time         : 0.000
0.33/0.89	%    Success case prop preproc time    : 0.000
0.33/0.89	%    Success case prop encoding time   : 0.000
0.33/0.89	%    Success case prop solver time     : 0.000
0.33/0.89	% Current number of processed clauses  : 351
0.33/0.89	%    Positive orientable unit clauses  : 140
0.33/0.89	%    Positive unorientable unit clauses: 0
0.33/0.89	%    Negative unit clauses             : 14
0.33/0.89	%    Non-unit-clauses                  : 197
0.33/0.89	% Current number of unprocessed clauses: 2915
0.33/0.89	% ...number of literals in the above   : 7644
0.33/0.89	% Current number of archived formulas  : 0
0.33/0.89	% Current number of archived clauses   : 10
0.33/0.89	% Clause-clause subsumption calls (NU) : 3457
0.33/0.89	% Rec. Clause-clause subsumption calls : 2986
0.33/0.89	% Non-unit clause-clause subsumptions  : 170
0.33/0.89	% Unit Clause-clause subsumption calls : 309
0.33/0.89	% Rewrite failures with RHS unbound    : 0
0.33/0.89	% BW rewrite match attempts            : 69
0.33/0.89	% BW rewrite match successes           : 5
0.33/0.89	% Condensation attempts                : 0
0.33/0.89	% Condensation successes               : 0
0.33/0.89	% Termbank termtop insertions          : 118286
0.33/0.89	% Search garbage collected termcells   : 27765
0.33/0.89	
0.33/0.89	% -------------------------------------------------
0.33/0.89	% User time                : 0.191 s
0.33/0.89	% System time              : 0.023 s
0.33/0.89	% Total time               : 0.214 s
0.33/0.89	% Maximum resident set size: 10404 pages
0.33/0.89	
0.33/0.89	% -------------------------------------------------
0.33/0.89	% User time                : 0.216 s
0.33/0.89	% System time              : 0.033 s
0.33/0.89	% Total time               : 0.249 s
0.33/0.89	% Maximum resident set size: 5632 pages
0.33/0.89	% E exiting
0.22/0.90	EOF