0.00/0.02	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.08/0.46	% Computer : n007.cluster.edu
0.08/0.46	% Model    : x86_64 x86_64
0.08/0.46	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.08/0.46	% Memory   : 8046.5625MB
0.08/0.46	% OS       : Linux 6.8.0-71-generic
0.08/0.46	% CPULimit : 1440
0.08/0.46	% WCLimit  : 180
0.08/0.46	% DateTime : Mon Jul 27 09:00:34 UTC 2026
0.08/0.47	% CPUTime  : 
0.08/0.47	Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.08/0.51	Running higher-order theorem proving
0.18/0.58	Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p
0.23/0.76	% Version: 3.5.1-ho
0.23/0.76	% Preprocessing class: HSLMSLSSLLLCHFA.
0.23/0.76	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
0.23/0.76	% Starting ehoh_best5 with 180s (1) cores
0.23/0.76	% Starting almost_fo_3_lam with 180s (1) cores
0.23/0.76	% Starting new_bool_5 with 180s (1) cores
0.23/0.76	% Starting pre_casc_3 with 180s (1) cores
0.23/0.76	% Starting ho_unfolding_8 with 180s (1) cores
0.23/0.76	% Starting new_ho_10_cnf2 with 180s (1) cores
0.23/0.76	% Starting new_bool_3 with 180s (1) cores
0.23/0.76	% Starting new_ho_5 with 180s (1) cores
0.23/0.76	% pre_casc_3 with pid 876104 completed with status 0
0.23/0.76	% Result found by pre_casc_3
0.23/0.76	% Preprocessing class: HSLMSLSSLLLCHFA.
0.23/0.76	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
0.23/0.76	% Starting ehoh_best5 with 180s (1) cores
0.23/0.76	% Starting almost_fo_3_lam with 180s (1) cores
0.23/0.76	% Starting new_bool_5 with 180s (1) cores
0.23/0.76	% Starting pre_casc_3 with 180s (1) cores
0.23/0.76	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
0.23/0.76	% SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
0.23/0.76	% Search class: HGHSM-FSLM32-MHFMMSBN
0.23/0.76	% Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
0.23/0.76	% Starting SubtermCWHack with 19s (1) cores
0.23/0.76	% SubtermCWHack with pid 876130 completed with status 0
0.23/0.76	% Result found by SubtermCWHack
0.23/0.76	% Preprocessing class: HSLMSLSSLLLCHFA.
0.23/0.76	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
0.23/0.76	% Starting ehoh_best5 with 180s (1) cores
0.23/0.76	% Starting almost_fo_3_lam with 180s (1) cores
0.23/0.76	% Starting new_bool_5 with 180s (1) cores
0.23/0.76	% Starting pre_casc_3 with 180s (1) cores
0.23/0.76	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
0.23/0.76	% SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
0.23/0.76	% Search class: HGHSM-FSLM32-MHFMMSBN
0.23/0.76	% Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
0.23/0.76	% Starting SubtermCWHack with 19s (1) cores
0.23/0.76	% Preprocessing time       : 0.006 s
0.23/0.76	
0.23/0.76	% Proof found!
0.23/0.76	% SZS status Theorem
0.23/0.76	% SZS output start CNFRefutation
0.23/0.76	thf(decl_23, type, in: $i > $i > $o).
0.23/0.76	thf(decl_24, type, exu: ($i > $o) > $o).
0.23/0.76	thf(decl_25, type, setextAx: $o).
0.23/0.76	thf(decl_26, type, emptyset: $i).
0.23/0.76	thf(decl_27, type, emptysetAx: $o).
0.23/0.76	thf(decl_28, type, setadjoin: $i > $i > $i).
0.23/0.76	thf(decl_29, type, setadjoinAx: $o).
0.23/0.76	thf(decl_30, type, powerset: $i > $i).
0.23/0.76	thf(decl_31, type, powersetAx: $o).
0.23/0.76	thf(decl_32, type, setunion: $i > $i).
0.23/0.76	thf(decl_33, type, setunionAx: $o).
0.23/0.76	thf(decl_34, type, omega: $i).
0.23/0.76	thf(decl_35, type, omega0Ax: $o).
0.23/0.76	thf(decl_36, type, omegaSAx: $o).
0.23/0.76	thf(decl_37, type, omegaIndAx: $o).
0.23/0.76	thf(decl_38, type, replAx: $o).
0.23/0.76	thf(decl_39, type, foundationAx: $o).
0.23/0.76	thf(decl_40, type, wellorderingAx: $o).
0.23/0.76	thf(decl_41, type, descr: ($i > $o) > $i).
0.23/0.76	thf(decl_42, type, descrp: $o).
0.23/0.76	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_44, type, dsetconstrI: $o).
0.23/0.76	thf(decl_45, type, dsetconstrEL: $o).
0.23/0.76	thf(decl_46, type, dsetconstrER: $o).
0.23/0.76	thf(decl_47, type, exuE1: $o).
0.23/0.76	thf(decl_48, type, prop2set: $o > $i).
0.23/0.76	thf(decl_49, type, prop2setE: $o).
0.23/0.76	thf(decl_50, type, emptysetE: $o).
0.23/0.76	thf(decl_51, type, emptysetimpfalse: $o).
0.23/0.76	thf(decl_52, type, notinemptyset: $o).
0.23/0.76	thf(decl_53, type, exuE3e: $o).
0.23/0.76	thf(decl_54, type, setext: $o).
0.23/0.76	thf(decl_55, type, emptyI: $o).
0.23/0.76	thf(decl_56, type, noeltsimpempty: $o).
0.23/0.76	thf(decl_57, type, setbeta: $o).
0.23/0.76	thf(decl_58, type, nonempty: $i > $o).
0.23/0.76	thf(decl_59, type, nonemptyE1: $o).
0.23/0.76	thf(decl_60, type, nonemptyI: $o).
0.23/0.76	thf(decl_61, type, nonemptyI1: $o).
0.23/0.76	thf(decl_62, type, setadjoinIL: $o).
0.23/0.76	thf(decl_63, type, emptyinunitempty: $o).
0.23/0.76	thf(decl_64, type, setadjoinIR: $o).
0.23/0.76	thf(decl_65, type, setadjoinE: $o).
0.23/0.76	thf(decl_66, type, setadjoinOr: $o).
0.23/0.76	thf(decl_67, type, setoftrueEq: $o).
0.23/0.76	thf(decl_68, type, powersetI: $o).
0.23/0.76	thf(decl_69, type, emptyinPowerset: $o).
0.23/0.76	thf(decl_70, type, emptyInPowerset: $o).
0.23/0.76	thf(decl_71, type, powersetE: $o).
0.23/0.76	thf(decl_72, type, setunionI: $o).
0.23/0.76	thf(decl_73, type, setunionE: $o).
0.23/0.76	thf(decl_74, type, subPowSU: $o).
0.23/0.76	thf(decl_75, type, exuE2: $o).
0.23/0.76	thf(decl_76, type, nonemptyImpWitness: $o).
0.23/0.76	thf(decl_77, type, uniqinunit: $o).
0.23/0.76	thf(decl_78, type, notinsingleton: $o).
0.23/0.76	thf(decl_79, type, eqinunit: $o).
0.23/0.76	thf(decl_80, type, singletonsswitch: $o).
0.23/0.76	thf(decl_81, type, upairsetE: $o).
0.23/0.76	thf(decl_82, type, upairsetIL: $o).
0.23/0.76	thf(decl_83, type, upairsetIR: $o).
0.23/0.76	thf(decl_84, type, emptyE1: $o).
0.23/0.76	thf(decl_85, type, vacuousDall: $o).
0.23/0.76	thf(decl_86, type, quantDeMorgan1: $o).
0.23/0.76	thf(decl_87, type, quantDeMorgan2: $o).
0.23/0.76	thf(decl_88, type, quantDeMorgan3: $o).
0.23/0.76	thf(decl_89, type, quantDeMorgan4: $o).
0.23/0.76	thf(decl_90, type, prop2setI: $o).
0.23/0.76	thf(decl_91, type, set2prop: $i > $o).
0.23/0.76	thf(decl_92, type, prop2set2propI: $o).
0.23/0.76	thf(decl_93, type, notdexE: $o).
0.23/0.76	thf(decl_94, type, notdallE: $o).
0.23/0.76	thf(decl_95, type, exuI1: $o).
0.23/0.76	thf(decl_96, type, exuI3: $o).
0.23/0.76	thf(decl_97, type, exuI2: $o).
0.23/0.76	thf(decl_98, type, inCongP: $o).
0.23/0.76	thf(decl_99, type, in__Cong: $o).
0.23/0.76	thf(decl_100, type, exuE3u: $o).
0.23/0.76	thf(decl_101, type, exu__Cong: $o).
0.23/0.76	thf(decl_102, type, emptyset__Cong: $o).
0.23/0.76	thf(decl_103, type, setadjoin__Cong: $o).
0.23/0.76	thf(decl_104, type, powerset__Cong: $o).
0.23/0.76	thf(decl_105, type, setunion__Cong: $o).
0.23/0.76	thf(decl_106, type, omega__Cong: $o).
0.23/0.76	thf(decl_107, type, exuEu: $o).
0.23/0.76	thf(decl_108, type, descr__Cong: $o).
0.23/0.76	thf(decl_109, type, dsetconstr__Cong: $o).
0.23/0.76	thf(decl_110, type, subset: $i > $i > $o).
0.23/0.76	thf(decl_113, type, subsetI1: $o).
0.23/0.76	thf(decl_114, type, eqimpsubset2: $o).
0.23/0.76	thf(decl_115, type, eqimpsubset1: $o).
0.23/0.76	thf(decl_116, type, subsetI2: $o).
0.23/0.76	thf(decl_117, type, emptysetsubset: $o).
0.23/0.76	thf(decl_118, type, subsetE: $o).
0.23/0.76	thf(decl_119, type, subsetE2: $o).
0.23/0.76	thf(decl_120, type, notsubsetI: $o).
0.23/0.76	thf(decl_121, type, notequalI1: $o).
0.23/0.76	thf(decl_122, type, notequalI2: $o).
0.23/0.76	thf(decl_123, type, subsetRefl: $o).
0.23/0.76	thf(decl_124, type, subsetTrans: $o).
0.23/0.76	thf(decl_125, type, setadjoinSub: $o).
0.23/0.76	thf(decl_126, type, setadjoinSub2: $o).
0.23/0.76	thf(decl_127, type, subset2powerset: $o).
0.23/0.76	thf(decl_128, type, setextsub: $o).
0.23/0.76	thf(decl_129, type, subsetemptysetimpeq: $o).
0.23/0.76	thf(decl_130, type, powersetI1: $o).
0.23/0.76	thf(decl_131, type, powersetE1: $o).
0.23/0.76	thf(decl_132, type, inPowerset: $o).
0.23/0.76	thf(decl_133, type, powersetsubset: $o).
0.23/0.76	thf(decl_134, type, sepInPowerset: $o).
0.23/0.76	thf(decl_135, type, sepSubset: $o).
0.23/0.76	thf(decl_136, type, binunion: $i > $i > $i).
0.23/0.76	thf(decl_137, type, binunionIL: $o).
0.23/0.76	thf(decl_138, type, upairset2IR: $o).
0.23/0.76	thf(decl_139, type, binunionIR: $o).
0.23/0.76	thf(decl_140, type, binunionEcases: $o).
0.23/0.76	thf(decl_141, type, binunionE: $o).
0.23/0.76	thf(decl_142, type, binunionLsub: $o).
0.23/0.76	thf(decl_143, type, binunionRsub: $o).
0.23/0.76	thf(decl_144, type, binintersect: $i > $i > $i).
0.23/0.76	thf(decl_145, type, binintersectI: $o).
0.23/0.76	thf(decl_146, type, binintersectSubset5: $o).
0.23/0.76	thf(decl_147, type, binintersectEL: $o).
0.23/0.76	thf(decl_148, type, binintersectLsub: $o).
0.23/0.76	thf(decl_149, type, binintersectSubset2: $o).
0.23/0.76	thf(decl_150, type, binintersectSubset3: $o).
0.23/0.76	thf(decl_151, type, binintersectER: $o).
0.23/0.76	thf(decl_152, type, disjointsetsI1: $o).
0.23/0.76	thf(decl_153, type, binintersectRsub: $o).
0.23/0.76	thf(decl_154, type, binintersectSubset4: $o).
0.23/0.76	thf(decl_155, type, binintersectSubset1: $o).
0.23/0.76	thf(decl_156, type, bs114d: $o).
0.23/0.76	thf(decl_158, type, setminus: $i > $i > $i).
0.23/0.76	thf(decl_159, type, setminusI: $o).
0.23/0.76	thf(decl_160, type, setminusEL: $o).
0.23/0.76	thf(decl_161, type, setminusER: $o).
0.23/0.76	thf(decl_162, type, setminusSubset2: $o).
0.23/0.76	thf(decl_163, type, setminusERneg: $o).
0.23/0.76	thf(decl_164, type, setminusELneg: $o).
0.23/0.76	thf(decl_165, type, setminusILneg: $o).
0.23/0.76	thf(decl_166, type, setminusIRneg: $o).
0.23/0.76	thf(decl_167, type, setminusLsub: $o).
0.23/0.76	thf(decl_168, type, setminusSubset1: $o).
0.23/0.76	thf(decl_169, type, symdiff: $i > $i > $i).
0.23/0.76	thf(decl_170, type, symdiffE: $o).
0.23/0.76	thf(decl_171, type, symdiffI1: $o).
0.23/0.76	thf(decl_172, type, symdiffI2: $o).
0.23/0.76	thf(decl_173, type, symdiffIneg1: $o).
0.23/0.76	thf(decl_174, type, symdiffIneg2: $o).
0.23/0.76	thf(decl_175, type, iskpair: $i > $o).
0.23/0.76	thf(decl_176, type, secondinupair: $o).
0.23/0.76	thf(decl_177, type, setukpairIL: $o).
0.23/0.76	thf(decl_178, type, setukpairIR: $o).
0.23/0.76	thf(decl_179, type, kpairiskpair: $o).
0.23/0.76	thf(decl_180, type, kpair: $i > $i > $i).
0.23/0.76	thf(decl_181, type, kpairp: $o).
0.23/0.76	thf(decl_182, type, cartprod: $i > $i > $i).
0.23/0.76	thf(decl_183, type, singletonsubset: $o).
0.23/0.76	thf(decl_184, type, singletoninpowerset: $o).
0.23/0.76	thf(decl_185, type, singletoninpowunion: $o).
0.23/0.76	thf(decl_186, type, upairset2E: $o).
0.23/0.76	thf(decl_187, type, upairsubunion: $o).
0.23/0.76	thf(decl_188, type, upairinpowunion: $o).
0.23/0.76	thf(decl_189, type, ubforcartprodlem1: $o).
0.23/0.76	thf(decl_190, type, ubforcartprodlem2: $o).
0.23/0.76	thf(decl_191, type, ubforcartprodlem3: $o).
0.23/0.76	thf(decl_192, type, cartprodpairin: $o).
0.23/0.76	thf(decl_193, type, cartprodmempair1: $o).
0.23/0.76	thf(decl_194, type, cartprodmempair: $o).
0.23/0.76	thf(decl_195, type, setunionE2: $o).
0.23/0.76	thf(decl_196, type, setunionsingleton1: $o).
0.23/0.76	thf(decl_197, type, setunionsingleton2: $o).
0.23/0.76	thf(decl_198, type, setunionsingleton: $o).
0.23/0.76	thf(decl_199, type, singleton: $i > $o).
0.23/0.76	thf(decl_200, type, singletonprop: $o).
0.23/0.76	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
0.23/0.76	thf(decl_202, type, ex1E1: $o).
0.23/0.76	thf(decl_203, type, ex1I: $o).
0.23/0.76	thf(decl_204, type, ex1I2: $o).
0.23/0.76	thf(decl_205, type, singletonsuniq: $o).
0.23/0.76	thf(decl_210, type, setukpairinjL1: $o).
0.23/0.76	thf(decl_211, type, kfstsingleton: $o).
0.23/0.76	thf(decl_212, type, theprop: $o).
0.23/0.76	thf(decl_213, type, kfst: $i > $i).
0.23/0.76	thf(decl_214, type, kfstpairEq: $o).
0.23/0.76	thf(decl_215, type, cartprodfstin: $o).
0.23/0.76	thf(decl_216, type, setukpairinjL2: $o).
0.23/0.76	thf(decl_217, type, setukpairinjL: $o).
0.23/0.76	thf(decl_218, type, setukpairinjR11: $o).
0.23/0.76	thf(decl_219, type, setukpairinjR12: $o).
0.23/0.76	thf(decl_220, type, setukpairinjR1: $o).
0.23/0.76	thf(decl_221, type, upairequniteq: $o).
0.23/0.76	thf(decl_222, type, setukpairinjR2: $o).
0.23/0.76	thf(decl_223, type, setukpairinjR: $o).
0.23/0.76	thf(decl_224, type, ksndsingleton: $o).
0.23/0.76	thf(decl_225, type, ksnd: $i > $i).
0.23/0.76	thf(decl_226, type, ksndpairEq: $o).
0.23/0.76	thf(decl_227, type, kpairsurjEq: $o).
0.23/0.76	thf(decl_228, type, cartprodsndin: $o).
0.23/0.76	thf(decl_229, type, cartprodpairmemEL: $o).
0.23/0.76	thf(decl_230, type, cartprodpairmemER: $o).
0.23/0.76	thf(decl_231, type, cartprodmempaircEq: $o).
0.23/0.76	thf(decl_232, type, cartprodfstpairEq: $o).
0.23/0.76	thf(decl_233, type, cartprodsndpairEq: $o).
0.23/0.76	thf(decl_234, type, cartprodpairsurjEq: $o).
0.23/0.76	thf(decl_235, type, breln: $i > $i > $i > $o).
0.23/0.76	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
0.23/0.76	thf(decl_237, type, dpsetconstrI: $o).
0.23/0.76	thf(decl_238, type, dpsetconstrSub: $o).
0.23/0.76	thf(decl_239, type, setOfPairsIsBReln: $o).
0.23/0.76	thf(decl_240, type, dpsetconstrERa: $o).
0.23/0.76	thf(decl_241, type, dpsetconstrEL1: $o).
0.23/0.76	thf(decl_242, type, dpsetconstrEL2: $o).
0.23/0.76	thf(decl_243, type, dpsetconstrER: $o).
0.23/0.76	thf(decl_244, type, func: $i > $i > $i > $o).
0.23/0.76	thf(decl_245, type, funcSet: $i > $i > $i).
0.23/0.76	thf(decl_246, type, funcImageSingleton: $o).
0.23/0.76	thf(decl_247, type, apProp: $o).
0.23/0.76	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
0.23/0.76	thf(decl_249, type, app: $o).
0.23/0.76	thf(decl_250, type, infuncsetfunc: $o).
0.23/0.76	thf(decl_251, type, ap2p: $o).
0.23/0.76	thf(decl_252, type, funcinfuncset: $o).
0.23/0.76	thf(decl_253, type, lamProp: $o).
0.23/0.76	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
0.23/0.76	thf(decl_255, type, lamp: $o).
0.23/0.76	thf(decl_256, type, lam2p: $o).
0.23/0.76	thf(decl_257, type, brelnall1: $o).
0.23/0.76	thf(decl_258, type, brelnall2: $o).
0.23/0.76	thf(decl_259, type, ex1E2: $o).
0.23/0.76	thf(decl_260, type, funcGraphProp1: $o).
0.23/0.76	thf(decl_261, type, funcGraphProp3: $o).
0.23/0.76	thf(decl_262, type, funcGraphProp2: $o).
0.23/0.76	thf(decl_263, type, funcextLem: $o).
0.23/0.76	thf(decl_264, type, funcGraphProp4: $o).
0.23/0.76	thf(decl_265, type, subbreln: $o).
0.23/0.76	thf(decl_266, type, eqbreln: $o).
0.23/0.76	thf(decl_267, type, funcext: $o).
0.23/0.76	thf(decl_268, type, funcext2: $o).
0.23/0.76	thf(decl_269, type, ap2apEq1: $o).
0.23/0.76	thf(decl_270, type, ap2apEq2: $o).
0.23/0.76	thf(decl_271, type, beta1: $o).
0.23/0.76	thf(decl_272, type, eta1: $o).
0.23/0.76	thf(decl_273, type, lam2lamEq: $o).
0.23/0.76	thf(decl_274, type, beta2: $o).
0.23/0.76	thf(decl_275, type, eta2: $o).
0.23/0.76	thf(decl_276, type, iffalseProp1: $o).
0.23/0.76	thf(decl_277, type, iffalseProp2: $o).
0.23/0.76	thf(decl_278, type, iftrueProp1: $o).
0.23/0.76	thf(decl_279, type, iftrueProp2: $o).
0.23/0.76	thf(decl_280, type, ifSingleton: $o).
0.23/0.76	thf(decl_281, type, if: $i > $o > $i > $i > $i).
0.23/0.76	thf(decl_282, type, ifp: $o).
0.23/0.76	thf(decl_283, type, theeq: $o).
0.23/0.76	thf(decl_284, type, iftrue: $o).
0.23/0.76	thf(decl_285, type, iffalse: $o).
0.23/0.76	thf(decl_286, type, iftrueorfalse: $o).
0.23/0.76	thf(decl_287, type, binintersectT_lem: $o).
0.23/0.76	thf(decl_288, type, binunionT_lem: $o).
0.23/0.76	thf(decl_289, type, powersetT_lem: $o).
0.23/0.76	thf(decl_290, type, setminusT_lem: $o).
0.23/0.76	thf(decl_291, type, complementT_lem: $o).
0.23/0.76	thf(decl_292, type, setextT: $o).
0.23/0.76	thf(decl_293, type, subsetTI: $o).
0.23/0.76	thf(decl_294, type, powersetTI1: $o).
0.23/0.76	thf(decl_295, type, powersetTE1: $o).
0.23/0.76	thf(decl_296, type, complementTI1: $o).
0.23/0.76	thf(decl_297, type, complementTE1: $o).
0.23/0.76	thf(decl_298, type, binintersectTELcontra: $o).
0.23/0.76	thf(decl_299, type, binintersectTERcontra: $o).
0.23/0.76	thf(decl_300, type, contrasubsetT: $o).
0.23/0.76	thf(decl_301, type, contrasubsetT1: $o).
0.23/0.76	thf(decl_302, type, contrasubsetT2: $o).
0.23/0.76	thf(decl_303, type, contrasubsetT3: $o).
0.23/0.76	thf(decl_304, type, doubleComplementI1: $o).
0.23/0.76	thf(decl_305, type, doubleComplementE1: $o).
0.23/0.76	thf(decl_306, type, doubleComplementSub1: $o).
0.23/0.76	thf(decl_307, type, doubleComplementSub2: $o).
0.23/0.76	thf(decl_308, type, doubleComplementEq: $o).
0.23/0.76	thf(decl_309, type, complementTnotintersectT: $o).
0.23/0.76	thf(decl_310, type, complementImpComplementIntersect: $o).
0.23/0.76	thf(decl_311, type, complementSubsetComplementIntersect: $o).
0.23/0.76	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
0.23/0.76	thf(decl_313, type, contraSubsetComplement: $o).
0.23/0.76	thf(decl_314, type, complementTcontraSubset: $o).
0.23/0.76	thf(decl_315, type, binunionTILcontra: $o).
0.23/0.76	thf(decl_316, type, binunionTIRcontra: $o).
0.23/0.76	thf(decl_317, type, inIntersectImpInUnion: $o).
0.23/0.76	thf(decl_318, type, inIntersectImpInUnion2: $o).
0.23/0.76	thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
0.23/0.76	thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
0.23/0.76	thf(decl_321, type, inComplementUnionImpNotIn1: $o).
0.23/0.76	thf(decl_322, type, inComplementUnionImpInComplement1: $o).
0.23/0.76	thf(decl_323, type, binunionTE: $o).
0.23/0.76	thf(decl_324, type, binunionTEcontra: $o).
0.23/0.76	thf(decl_325, type, demorgan2a1: $o).
0.23/0.76	thf(decl_326, type, complementUnionInPowersetComplement: $o).
0.23/0.76	thf(decl_327, type, demorgan2a2: $o).
0.23/0.76	thf(decl_328, type, demorgan1a: $o).
0.23/0.76	thf(decl_329, type, demorgan1b: $o).
0.23/0.76	thf(decl_330, type, demorgan1: $o).
0.23/0.76	thf(decl_331, type, demorgan2a: $o).
0.23/0.76	thf(decl_332, type, demorgan2b2: $o).
0.23/0.76	thf(decl_333, type, demorgan2b: $o).
0.23/0.76	thf(decl_334, type, demorgan2: $o).
0.23/0.76	thf(decl_335, type, woz13rule0: $o).
0.23/0.76	thf(decl_336, type, woz13rule1: $o).
0.23/0.76	thf(decl_337, type, woz13rule2: $o).
0.23/0.76	thf(decl_338, type, woz13rule3: $o).
0.23/0.76	thf(decl_339, type, woz13rule4: $o).
0.23/0.76	thf(decl_340, type, woz1_1: $o).
0.23/0.76	thf(decl_341, type, woz1_2: $o).
0.23/0.76	thf(decl_342, type, woz1_3: $o).
0.23/0.76	thf(decl_343, type, woz1_4: $o).
0.23/0.76	thf(decl_344, type, woz1_5: $o).
0.23/0.76	thf(decl_345, type, breln1: $i > $i > $o).
0.23/0.76	thf(decl_346, type, breln1all2: $o).
0.23/0.76	thf(decl_347, type, breln1Set: $i > $i).
0.23/0.76	thf(decl_348, type, breln1SetBreln1: $o).
0.23/0.76	thf(decl_354, type, reflwellordering: $i > $i > $o).
0.23/0.76	thf(decl_355, type, choice2fnsingleton: $o).
0.23/0.76	thf(decl_356, type, setOfPairsIsBReln1: $o).
0.23/0.76	thf(decl_357, type, breln1all1: $o).
0.23/0.76	thf(decl_358, type, subbreln1: $o).
0.23/0.76	thf(decl_359, type, eqbreln1: $o).
0.23/0.76	thf(decl_360, type, breln1invset: $i > $i > $i).
0.23/0.76	thf(decl_361, type, breln1invprop: $o).
0.23/0.76	thf(decl_362, type, breln1invI: $o).
0.23/0.76	thf(decl_363, type, breln1invE: $o).
0.23/0.76	thf(decl_364, type, breln1compset: $i > $i > $i > $i).
0.23/0.76	thf(decl_365, type, breln1compprop: $o).
0.23/0.76	thf(decl_366, type, breln1compI: $o).
0.23/0.76	thf(decl_367, type, breln1compE: $o).
0.23/0.76	thf(decl_368, type, breln1compEex: $o).
0.23/0.76	thf(decl_369, type, breln1unionprop: $o).
0.23/0.76	thf(decl_370, type, breln1unionIL: $o).
0.23/0.76	thf(decl_371, type, breln1unionIR: $o).
0.23/0.76	thf(decl_372, type, epred1_0: $o).
0.23/0.76	thf(decl_373, type, esk1_2: $i > $i > $i).
0.23/0.76	thf(decl_374, type, esk2_2: $i > $i > $i).
0.23/0.76	thf(decl_375, type, esk3_2: $i > $i > $i).
0.23/0.76	thf(decl_376, type, esk4_1: $i > $i).
0.23/0.76	thf(decl_377, type, esk5_2: ($i > $i > $o) > $i > $i).
0.23/0.76	thf(decl_378, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
0.23/0.76	thf(decl_379, type, esk7_2: ($i > $i > $o) > $i > $i).
0.23/0.76	thf(decl_380, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
0.23/0.76	thf(decl_381, type, esk9_1: $i > $i).
0.23/0.76	thf(decl_382, type, esk10_2: ($i > $o) > $i > $i).
0.23/0.76	thf(decl_383, type, esk11_2: ($i > $o) > $i > $i).
0.23/0.76	thf(decl_384, type, esk12_1: ($i > $o) > $i).
0.23/0.76	thf(decl_385, type, esk13_2: ($i > $o) > $i > $i).
0.23/0.76	thf(decl_386, type, esk14_1: ($i > $o) > $i).
0.23/0.76	thf(decl_387, type, esk15_2: $i > $i > $i).
0.23/0.76	thf(decl_388, type, esk16_2: $i > $i > $i).
0.23/0.76	thf(decl_389, type, esk17_1: $i > $i).
0.23/0.76	thf(decl_390, type, esk18_1: $i > $i).
0.23/0.76	thf(decl_391, type, esk19_1: $i > $i).
0.23/0.76	thf(decl_392, type, esk20_2: $i > $i > $i).
0.23/0.76	thf(decl_393, type, esk21_3: $i > $i > $o > $i).
0.23/0.76	thf(decl_394, type, esk22_2: ($i > $o) > $i > $i).
0.23/0.76	thf(decl_395, type, esk23_1: ($i > $o) > $i).
0.23/0.76	thf(decl_396, type, esk24_1: $i > $i).
0.23/0.76	thf(decl_397, type, esk25_2: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_398, type, esk26_2: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_399, type, esk27_2: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_400, type, esk28_2: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_401, type, esk29_2: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_402, type, esk30_2: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_403, type, esk31_2: ($i > $o) > $i > $i).
0.23/0.76	thf(decl_404, type, esk32_1: ($i > $o) > $i).
0.23/0.76	thf(decl_405, type, esk33_1: ($i > $o) > $i).
0.23/0.76	thf(decl_406, type, esk34_1: ($i > $o) > $i).
0.23/0.76	thf(decl_407, type, esk35_1: ($i > $o) > $i).
0.23/0.76	thf(decl_408, type, esk36_2: ($i > $o) > $i > $i).
0.23/0.76	thf(decl_409, type, esk37_1: ($i > $o) > $i).
0.23/0.76	thf(decl_410, type, esk38_2: ($i > $o) > $i > $i).
0.23/0.76	thf(decl_411, type, esk39_2: ($i > $o) > ($i > $o) > $i).
0.23/0.76	thf(decl_412, type, esk40_2: ($i > $o) > ($i > $o) > $i).
0.23/0.76	thf(decl_413, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
0.23/0.76	thf(decl_414, type, esk42_2: ($i > $o) > ($i > $o) > $i).
0.23/0.76	thf(decl_415, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
0.23/0.76	thf(decl_416, type, esk44_2: ($i > $o) > ($i > $o) > $i).
0.23/0.76	thf(decl_417, type, esk45_2: ($i > $o) > $i > $i).
0.23/0.76	thf(decl_418, type, esk46_2: ($i > $o) > ($i > $o) > $i).
0.23/0.76	thf(decl_419, type, esk47_2: ($i > $o) > ($i > $o) > $i).
0.23/0.76	thf(decl_420, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
0.23/0.76	thf(decl_421, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
0.23/0.76	thf(decl_422, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.23/0.76	thf(decl_423, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.23/0.76	thf(decl_424, type, esk52_2: $i > $i > $i).
0.23/0.76	thf(decl_425, type, esk53_2: $i > $i > $i).
0.23/0.76	thf(decl_426, type, esk54_2: $i > $i > $i).
0.23/0.76	thf(decl_427, type, esk55_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_428, type, esk56_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_429, type, esk57_2: $i > $i > $i).
0.23/0.76	thf(decl_430, type, esk58_2: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_431, type, esk59_2: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_432, type, esk60_2: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_433, type, esk61_3: $i > ($i > $o) > $i > $i).
0.23/0.76	thf(decl_434, type, esk62_2: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_435, type, esk63_2: $i > ($i > $o) > $i).
0.23/0.76	thf(decl_436, type, esk64_3: $i > $i > ($i > $i) > $i).
0.23/0.76	thf(decl_437, type, esk65_3: $i > $i > ($i > $i) > $i).
0.23/0.76	thf(decl_438, type, esk66_3: $i > $i > ($i > $i) > $i).
0.23/0.76	thf(decl_439, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
0.23/0.76	thf(decl_440, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
0.23/0.76	thf(decl_441, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
0.23/0.76	thf(decl_442, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
0.23/0.76	thf(decl_443, type, esk71_4: $i > $i > $i > $i > $i).
0.23/0.76	thf(decl_444, type, esk72_4: $i > $i > $i > $i > $i).
0.23/0.76	thf(decl_445, type, esk73_4: $i > $i > $i > $i > $i).
0.23/0.76	thf(decl_446, type, esk74_4: $i > $i > $i > $i > $i).
0.23/0.76	thf(decl_447, type, esk75_4: $i > $i > $i > $i > $i).
0.23/0.76	thf(decl_448, type, esk76_4: $i > $i > $i > $i > $i).
0.23/0.76	thf(decl_449, type, esk77_4: $i > $i > $i > $i > $i).
0.23/0.76	thf(decl_450, type, esk78_4: $i > $i > $i > $i > $i).
0.23/0.76	thf(decl_451, type, esk79_4: $i > $i > $i > $i > $i).
0.23/0.76	thf(decl_452, type, esk80_3: $i > $i > ($i > $i) > $i).
0.23/0.76	thf(decl_453, type, esk81_3: $i > $i > ($i > $i) > $i).
0.23/0.76	thf(decl_454, type, esk82_3: $i > $i > ($i > $i) > $i).
0.23/0.76	thf(decl_455, type, esk83_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_456, type, esk84_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_457, type, esk85_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_458, type, esk86_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_459, type, esk87_3: $i > $i > ($i > $o) > $i).
0.23/0.76	thf(decl_460, type, esk88_3: $i > $i > ($i > $o) > $i).
0.23/0.76	thf(decl_461, type, esk89_3: $i > $i > ($i > $i > $o) > $i).
0.23/0.76	thf(decl_462, type, esk90_3: $i > $i > ($i > $o) > $i).
0.23/0.76	thf(decl_463, type, esk91_3: $i > $i > ($i > $o) > $i).
0.23/0.76	thf(decl_464, type, esk92_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_465, type, esk93_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_466, type, esk94_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_467, type, esk95_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_468, type, esk96_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_469, type, esk97_3: $i > $i > $i > $i).
0.23/0.76	thf(decl_470, type, esk98_5: $i > $i > $i > $i > $i > $i).
0.23/0.76	thf(decl_471, type, esk99_6: $i > $i > $i > $i > $i > $o > $i).
0.23/0.76	thf(decl_472, type, esk100_0: $i).
0.23/0.76	thf(decl_473, type, esk101_0: $i).
0.23/0.76	thf(decl_474, type, esk102_0: $i).
0.23/0.76	thf(decl_475, type, esk103_0: $i).
0.23/0.76	thf(decl_476, type, esk104_0: $i).
0.23/0.76	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', descr__Cong)).
0.23/0.76	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', exu)).
0.23/0.76	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', exuI3)).
0.23/0.76	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', exuI1)).
0.23/0.76	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', nonempty)).
0.23/0.76	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', exuE2)).
0.23/0.76	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', nonemptyI)).
0.23/0.76	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', exuE3e)).
0.23/0.76	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', descrp)).
0.23/0.76	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', exuEu)).
0.23/0.76	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', exu__Cong)).
0.23/0.76	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', exuE3u)).
0.23/0.76	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', exuI2)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', exuE1)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', replAx)).
0.23/0.76	thf(breln1unionI, conjecture, ((setextAx)=>((emptysetAx)=>(((powersetAx)=>(((omega0Ax)=>((((replAx)=>(((((dsetconstrI)=>((((exuE1)=>((prop2setE)=>((((notinemptyset)=>((((emptyI)=>((noeltsimpempty)=>((setbeta)=>((((nonemptyI1)=>(((emptyinunitempty)=>(((((setoftrueEq)=>(((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((((((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>(((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>(((((((((notdallE)=>((((exuI2)=>(((in__Cong)=>((exuE3u)=>((exu__Cong)=>(((setadjoin__Cong)=>((powerset__Cong)=>(((omega__Cong)=>((exuEu)=>(((dsetconstr__Cong)=>((subsetI1)=>(((eqimpsubset1)=>(((emptysetsubset)=>(((((((subsetRefl)=>((subsetTrans)=>((((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>(((powersetE1)=>(((powersetsubset)=>((((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((((binintersectLsub)=>(((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((((binintersectSubset1)=>((bs114d)=>((setminusI)=>(((((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>((((symdiffI2)=>(((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>(((kpairiskpair)=>(((((singletoninpowunion)=>(((((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((cartprodpairin)=>((((((setunionsingleton2)=>(((singletonprop)=>((ex1E1)=>(((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>(((((((((upairequniteq)=>((setukpairinjR2)=>((((ksndpairEq)=>((kpairsurjEq)=>((((((cartprodfstpairEq)=>(((cartprodpairsurjEq)=>(((dpsetconstrSub)=>((setOfPairsIsBReln)=>(((((dpsetconstrER)=>((funcImageSingleton)=>((((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>(((((ex1E2)=>((funcGraphProp1)=>(((funcGraphProp2)=>((funcextLem)=>(((subbreln)=>(((funcext)=>(((ap2apEq1)=>((ap2apEq2)=>(((eta1)=>((((((iffalseProp2)=>(((iftrueProp2)=>((((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((((setminusT_lem)=>((complementT_lem)=>(((((((((((contrasubsetT1)=>(((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>(((doubleComplementSub2)=>((((complementImpComplementIntersect)=>((((contraSubsetComplement)=>((complementTcontraSubset)=>(((((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>(((demorgan2b2)=>(((demorgan2)=>((woz13rule0)=>(((woz13rule2)=>((woz13rule3)=>(((woz1_1)=>(((((((((((((((breln1invE)=>((breln1compprop)=>((breln1compI)=>(((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>((breln1unionIR)=>![X4:$i, X33:$i]:((![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))<=((in @ (kpair @ X2 @ X3) @ X35)|(in @ (kpair @ X2 @ X3) @ X33)))))))))<=(breln1 @ X4 @ X33)))))))<=(breln1compE)))))<=(breln1invI))<=(breln1invprop))<=(eqbreln1))<=(subbreln1))<=(breln1all1))<=(setOfPairsIsBReln1))<=(choice2fnsingleton))<=(breln1SetBreln1))<=(breln1all2))<=(woz1_5))<=(woz1_4))<=(woz1_3))<=(woz1_2)))<=(woz13rule4))))<=(woz13rule1))))<=(demorgan2b)))<=(demorgan2a))))))))))<=(inComplementUnionImpInComplement1))<=(inComplementUnionImpNotIn1)))))<=(inIntersectImpInUnion))<=(binunionTIRcontra))<=(binunionTILcontra))))<=(complementInPowersetComplementIntersect))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT))<=(doubleComplementEq)))<=(doubleComplementSub1)))))<=(contrasubsetT2)))<=(contrasubsetT))<=(binintersectTERcontra))<=(binintersectTELcontra))<=(complementTE1))<=(complementTI1))<=(powersetTE1))<=(powersetTI1))<=(subsetTI))<=(setextT))))<=(powersetT_lem))<=(binunionT_lem)))))))<=(ifp))<=(ifSingleton)))<=(iftrueProp1)))<=(iffalseProp1))<=(eta2))<=(beta2))<=(lam2lamEq)))<=(beta1))))<=(funcext2)))<=(eqbreln)))<=(funcGraphProp4))))<=(funcGraphProp3))))<=(brelnall2))<=(brelnall1))<=(lam2p)))))))<=(app))<=(apProp))))<=(dpsetconstrEL2))<=(dpsetconstrEL1))<=(dpsetconstrERa))))<=(dpsetconstrI)))<=(cartprodsndpairEq)))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin))))<=(ksndsingleton))<=(setukpairinjR))))<=(setukpairinjR1))<=(setukpairinjR12))<=(setukpairinjR11))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin))<=(kfstpairEq)))))))<=(ex1I))))<=(setunionsingleton)))<=(setunionsingleton1))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))))<=(ubforcartprodlem2)))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E)))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp)))<=(setukpairIR)))))<=(symdiffIneg1)))<=(symdiffI1))<=(symdiffE)))<=(setminusLsub))))<=(setminusELneg)))<=(setminusSubset2))<=(setminusER))<=(setminusEL)))))<=(binintersectSubset4))<=(binintersectRsub)))))<=(binintersectSubset2)))<=(binintersectEL))<=(binintersectSubset5))))))))))<=(sepSubset))<=(sepInPowerset)))<=(inPowerset)))<=(powersetI1)))))<=(setadjoinSub2))<=(setadjoinSub))))<=(notequalI2))<=(notequalI1))<=(notsubsetI))<=(subsetE2))<=(subsetE)))<=(subsetI2)))<=(eqimpsubset2))))<=(descr__Cong))))<=(setunion__Cong))))<=(emptyset__Cong)))))<=(inCongP)))<=(exuI3))<=(exuI1)))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))))))<=(upairsetE))))<=(notinsingleton)))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU))<=(setunionE)))<=(powersetE))))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR)))<=(setadjoinIL)))<=(nonemptyI))<=(nonemptyE1)))))<=(setext))<=(exuE3e)))<=(emptysetimpfalse))<=(emptysetE))))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx))<=(foundationAx)))<=(omegaIndAx))<=(omegaSAx)))<=(setunionAx)))<=(setadjoinAx)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1unionI)).
0.23/0.76	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', nonemptyImpWitness)).
0.23/0.76	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', singletonprop)).
0.23/0.76	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', nonemptyE1)).
0.23/0.76	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', dsetconstrER)).
0.23/0.76	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', dsetconstrEL)).
0.23/0.76	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', kfstsingleton)).
0.23/0.76	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ex1I2)).
0.23/0.76	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ex1E1)).
0.23/0.76	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', dpsetconstrER)).
0.23/0.76	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setOfPairsIsBReln)).
0.23/0.76	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', dpsetconstrSub)).
0.23/0.76	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', funcImageSingleton)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ex1E2)).
0.23/0.76	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', lamp)).
0.23/0.76	thf(lamProp, axiom, ((lamProp)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', lamProp)).
0.23/0.76	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', iffalseProp2)).
0.23/0.76	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', eta1)).
0.23/0.76	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', iftrueProp2)).
0.23/0.76	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', apProp)).
0.23/0.76	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', dpsetconstrI)).
0.23/0.76	thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((((X52 @ X2 @ X3))&(![X14:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ X3 @ X14) @ X33)))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', choice2fnsingleton)).
0.23/0.76	thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setOfPairsIsBReln1)).
0.23/0.76	thf(beta1, axiom, ((beta1)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', beta1)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', lam2lamEq)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', beta2)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', eta2)).
0.23/0.76	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', iffalseProp1)).
0.23/0.76	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', iftrueProp1)).
0.23/0.76	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ifSingleton)).
0.23/0.76	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', lam2p)).
0.23/0.76	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', dpsetconstrERa)).
0.23/0.76	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', dpsetconstrEL1)).
0.23/0.76	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', dpsetconstrEL2)).
0.23/0.76	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ksndsingleton)).
0.23/0.76	thf(ex1I, axiom, ((ex1I)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ex1I)).
0.23/0.76	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', sepInPowerset)).
0.23/0.76	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', sepSubset)).
0.23/0.76	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', dsetconstr__Cong)).
0.23/0.76	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', emptyE1)).
0.23/0.76	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setoftrueEq)).
0.23/0.76	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', nonemptyI1)).
0.23/0.76	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setbeta)).
0.23/0.76	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', dsetconstrI)).
0.23/0.76	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', notequalI1)).
0.23/0.76	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', notsubsetI)).
0.23/0.76	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subsetE2)).
0.23/0.76	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', symdiffI2)).
0.23/0.76	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subsetE)).
0.23/0.76	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setminusSubset1)).
0.23/0.76	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subsetI2)).
0.23/0.76	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setminusIRneg)).
0.23/0.76	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', eqimpsubset2)).
0.23/0.76	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setminusILneg)).
0.23/0.76	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setminusERneg)).
0.23/0.76	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setunion__Cong)).
0.23/0.76	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setminusI)).
0.23/0.76	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', emptyset__Cong)).
0.23/0.76	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', secondinupair)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', inCongP)).
0.23/0.76	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', notdexE)).
0.23/0.76	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', prop2set2propI)).
0.23/0.76	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', prop2setI)).
0.23/0.76	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', quantDeMorgan4)).
0.23/0.76	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', quantDeMorgan3)).
0.23/0.76	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', quantDeMorgan2)).
0.23/0.76	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', quantDeMorgan1)).
0.23/0.76	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', upairsetE)).
0.23/0.76	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', notinsingleton)).
0.23/0.76	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setunionsingleton2)).
0.23/0.76	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subPowSU)).
0.23/0.76	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', cartprodpairin)).
0.23/0.76	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setunionE)).
0.23/0.76	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ubforcartprodlem3)).
0.23/0.76	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', powersetE)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ubforcartprodlem1)).
0.23/0.76	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', powersetI)).
0.23/0.76	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', singletoninpowunion)).
0.23/0.76	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setadjoinOr)).
0.23/0.76	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', kpairiskpair)).
0.23/0.76	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setadjoinE)).
0.23/0.76	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setukpairIL)).
0.23/0.76	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setadjoinIR)).
0.23/0.76	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setadjoinIL)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setext)).
0.23/0.76	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', emptysetimpfalse)).
0.23/0.76	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', emptysetE)).
0.23/0.76	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', wellorderingAx)).
0.23/0.76	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', foundationAx)).
0.23/0.76	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', omegaIndAx)).
0.23/0.76	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', omegaSAx)).
0.23/0.76	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', upairequniteq)).
0.23/0.76	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setunionAx)).
0.23/0.76	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', theprop)).
0.23/0.76	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setadjoinAx)).
0.23/0.76	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setukpairinjL1)).
0.23/0.76	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', singletonsuniq)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setukpairinjR2)).
0.23/0.76	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', cartprodpairsurjEq)).
0.23/0.76	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', cartprodfstpairEq)).
0.23/0.76	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', kpairsurjEq)).
0.23/0.76	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ksndpairEq)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', funcGraphProp1)).
0.23/0.76	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', funcinfuncset)).
0.23/0.76	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ap2p)).
0.23/0.76	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', infuncsetfunc)).
0.23/0.76	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', funcGraphProp2)).
0.23/0.76	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ap2apEq2)).
0.23/0.76	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ap2apEq1)).
0.23/0.76	thf(funcext, axiom, ((funcext)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', funcext)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subbreln)).
0.23/0.76	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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', funcextLem)).
0.23/0.76	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', complementT_lem)).
0.23/0.76	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setminusT_lem)).
0.23/0.76	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectT_lem)).
0.23/0.76	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', iftrueorfalse)).
0.23/0.76	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', iffalse)).
0.23/0.76	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', iftrue)).
0.23/0.76	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', theeq)).
0.23/0.76	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', contrasubsetT1)).
0.23/0.76	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', funcGraphProp3)).
0.23/0.76	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', funcGraphProp4)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', eqbreln)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', cartprodpairmemER)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', cartprodmempaircEq)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', cartprodsndpairEq)).
0.23/0.76	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', complementTcontraSubset)).
0.23/0.76	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', contraSubsetComplement)).
0.23/0.76	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', complementImpComplementIntersect)).
0.23/0.76	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', doubleComplementSub2)).
0.23/0.76	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', doubleComplementE1)).
0.23/0.76	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', doubleComplementI1)).
0.23/0.76	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', contrasubsetT3)).
0.23/0.76	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', inIntersectImpInUnion2)).
0.23/0.76	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', demorgan2a2)).
0.23/0.76	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', complementUnionInPowersetComplement)).
0.23/0.76	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![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 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', demorgan2a1)).
0.23/0.76	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![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 @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binunionTEcontra)).
0.23/0.76	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binunionTE)).
0.23/0.76	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', intersectInPowersetIntersectUnions)).
0.23/0.76	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', inIntersectImpInIntersectUnions)).
0.23/0.76	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', demorgan1a)).
0.23/0.76	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', woz13rule3)).
0.23/0.76	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', woz13rule2)).
0.23/0.76	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', woz13rule0)).
0.23/0.76	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', demorgan2)).
0.23/0.76	thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', demorgan2b2)).
0.23/0.76	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', demorgan1)).
0.23/0.76	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', demorgan1b)).
0.23/0.76	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', woz1_1)).
0.23/0.76	thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1invE)).
0.23/0.76	thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1compprop)).
0.23/0.76	thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1compI)).
0.23/0.76	thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1compEex)).
0.23/0.76	thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1unionprop)).
0.23/0.76	thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1unionIL)).
0.23/0.76	thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1unionIR)).
0.23/0.76	thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1compE)).
0.23/0.76	thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1all1)).
0.23/0.76	thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subbreln1)).
0.23/0.76	thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', eqbreln1)).
0.23/0.76	thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1invprop)).
0.23/0.76	thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1invI)).
0.23/0.76	thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1SetBreln1)).
0.23/0.76	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', woz13rule1)).
0.23/0.76	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', woz13rule4)).
0.23/0.76	thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', woz1_2)).
0.23/0.76	thf(woz1_3, axiom, ((woz1_3)<=>![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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', woz1_3)).
0.23/0.76	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', woz1_4)).
0.23/0.76	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', woz1_5)).
0.23/0.76	thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', breln1all2)).
0.23/0.76	thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', demorgan2b)).
0.23/0.76	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', complementInPowersetComplementIntersect)).
0.23/0.76	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binunionTILcontra)).
0.23/0.76	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binunionTIRcontra)).
0.23/0.76	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', inIntersectImpInUnion)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', inComplementUnionImpNotIn1)).
0.23/0.76	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![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 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', inComplementUnionImpInComplement1)).
0.23/0.76	thf(demorgan2a, axiom, ((demorgan2a)<=>![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 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', demorgan2a)).
0.23/0.76	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', complementSubsetComplementIntersect)).
0.23/0.76	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectTELcontra)).
0.23/0.76	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectTERcontra)).
0.23/0.76	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', contrasubsetT)).
0.23/0.76	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', contrasubsetT2)).
0.23/0.76	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', doubleComplementSub1)).
0.23/0.76	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', doubleComplementEq)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', complementTnotintersectT)).
0.23/0.76	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', complementTE1)).
0.23/0.76	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binunionT_lem)).
0.23/0.76	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', powersetT_lem)).
0.23/0.76	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setextT)).
0.23/0.76	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subsetTI)).
0.23/0.76	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', powersetTI1)).
0.23/0.76	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', powersetTE1)).
0.23/0.76	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', complementTI1)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ifp)).
0.23/0.76	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', funcext2)).
0.23/0.76	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', app)).
0.23/0.76	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', brelnall1)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', brelnall2)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', cartprodpairmemEL)).
0.23/0.76	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setukpairinjL)).
0.23/0.76	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setukpairinjR11)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setukpairinjR12)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setukpairinjR1)).
0.23/0.76	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setukpairinjR)).
0.23/0.76	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', cartprodsndin)).
0.23/0.76	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setukpairinjL2)).
0.23/0.76	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', cartprodmempair)).
0.23/0.76	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setunionE2)).
0.23/0.76	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setunionsingleton1)).
0.23/0.76	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setunionsingleton)).
0.23/0.76	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', kfstpairEq)).
0.23/0.76	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', cartprodfstin)).
0.23/0.76	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', cartprodmempair1)).
0.23/0.76	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', kpairp)).
0.23/0.76	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', singletonsubset)).
0.23/0.76	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', singletoninpowerset)).
0.23/0.76	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', upairset2E)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', upairsubunion)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', upairinpowunion)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', ubforcartprodlem2)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setukpairIR)).
0.23/0.76	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setminusER)).
0.23/0.76	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setminusSubset2)).
0.23/0.76	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setminusELneg)).
0.23/0.76	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setminusLsub)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', symdiffE)).
0.23/0.76	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', symdiffI1)).
0.23/0.76	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', symdiffIneg1)).
0.23/0.76	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setminusEL)).
0.23/0.76	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectSubset5)).
0.23/0.76	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectEL)).
0.23/0.76	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectSubset2)).
0.23/0.76	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectRsub)).
0.23/0.76	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectSubset4)).
0.23/0.76	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', powersetI1)).
0.23/0.76	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setadjoinSub2)).
0.23/0.76	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setadjoinSub)).
0.23/0.76	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', notequalI2)).
0.23/0.76	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', inPowerset)).
0.23/0.76	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', symdiffIneg2)).
0.23/0.76	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', bs114d)).
0.23/0.76	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectSubset1)).
0.23/0.76	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', disjointsetsI1)).
0.23/0.76	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectER)).
0.23/0.76	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectSubset3)).
0.23/0.76	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectLsub)).
0.23/0.76	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binintersectI)).
0.23/0.76	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binunionRsub)).
0.23/0.76	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binunionLsub)).
0.23/0.76	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binunionE)).
0.23/0.76	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/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binunionEcases)).
0.23/0.76	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binunionIR)).
0.23/0.76	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', upairset2IR)).
0.23/0.76	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', binunionIL)).
0.23/0.76	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', powersetsubset)).
0.23/0.76	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', powersetE1)).
0.23/0.76	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subsetemptysetimpeq)).
0.23/0.76	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setextsub)).
0.23/0.76	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subset2powerset)).
0.23/0.76	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subsetTrans)).
0.23/0.76	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subsetRefl)).
0.23/0.76	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', emptysetsubset)).
0.23/0.76	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', eqimpsubset1)).
0.23/0.76	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', subsetI1)).
0.23/0.76	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', omega__Cong)).
0.23/0.76	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', powerset__Cong)).
0.23/0.76	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setadjoin__Cong)).
0.23/0.76	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', in__Cong)).
0.23/0.76	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', notdallE)).
0.23/0.76	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', vacuousDall)).
0.23/0.76	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', upairsetIR)).
0.23/0.76	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', upairsetIL)).
0.23/0.76	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', singletonsswitch)).
0.23/0.76	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', eqinunit)).
0.23/0.76	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', uniqinunit)).
0.23/0.76	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setunionI)).
0.23/0.76	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', emptyInPowerset)).
0.23/0.76	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', emptyinPowerset)).
0.23/0.76	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', emptyinunitempty)).
0.23/0.76	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', noeltsimpempty)).
0.23/0.76	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', emptyI)).
0.23/0.76	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', notinemptyset)).
0.23/0.76	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', prop2setE)).
0.23/0.76	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', omega0Ax)).
0.23/0.76	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', powersetAx)).
0.23/0.76	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', emptysetAx)).
0.23/0.76	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.67LLtnOeGY/E---3.1_876088.p', setextAx)).
0.23/0.76	thf(c_0_304, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
0.23/0.76	thf(c_0_305, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
0.23/0.76	thf(c_0_306, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
0.23/0.76	thf(c_0_307, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
0.23/0.76	thf(c_0_308, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
0.23/0.76	thf(c_0_309, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
0.23/0.76	thf(c_0_310, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
0.23/0.76	thf(c_0_311, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
0.23/0.76	thf(c_0_312, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
0.23/0.76	thf(c_0_313, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
0.23/0.76	thf(c_0_314, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
0.23/0.76	thf(c_0_315, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
0.23/0.76	thf(c_0_316, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
0.23/0.76	thf(c_0_317, 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])).
0.23/0.76	thf(c_0_318, 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])).
0.23/0.76	thf(c_0_319, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>(((powersetAx)=>(((omega0Ax)=>((((replAx)=>(((((dsetconstrI)=>((((exuE1)=>((prop2setE)=>((((notinemptyset)=>((((emptyI)=>((noeltsimpempty)=>((setbeta)=>((((nonemptyI1)=>(((emptyinunitempty)=>(((((setoftrueEq)=>(((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((((((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>(((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>(((((((((notdallE)=>((((exuI2)=>(((in__Cong)=>((exuE3u)=>((exu__Cong)=>(((setadjoin__Cong)=>((powerset__Cong)=>(((omega__Cong)=>((exuEu)=>(((dsetconstr__Cong)=>((subsetI1)=>(((eqimpsubset1)=>(((emptysetsubset)=>(((((((subsetRefl)=>((subsetTrans)=>((((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>(((powersetE1)=>(((powersetsubset)=>((((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((((binintersectLsub)=>(((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((((binintersectSubset1)=>((bs114d)=>((setminusI)=>(((((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>((((symdiffI2)=>(((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>(((kpairiskpair)=>(((((singletoninpowunion)=>(((((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((cartprodpairin)=>((((((setunionsingleton2)=>(((singletonprop)=>((ex1E1)=>(((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>(((((((((upairequniteq)=>((setukpairinjR2)=>((((ksndpairEq)=>((kpairsurjEq)=>((((((cartprodfstpairEq)=>(((cartprodpairsurjEq)=>(((dpsetconstrSub)=>((setOfPairsIsBReln)=>(((((dpsetconstrER)=>((funcImageSingleton)=>((((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>(((((ex1E2)=>((funcGraphProp1)=>(((funcGraphProp2)=>((funcextLem)=>(((subbreln)=>(((funcext)=>(((ap2apEq1)=>((ap2apEq2)=>(((eta1)=>((((((iffalseProp2)=>(((iftrueProp2)=>((((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((((setminusT_lem)=>((complementT_lem)=>(((((((((((contrasubsetT1)=>(((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>(((doubleComplementSub2)=>((((complementImpComplementIntersect)=>((((contraSubsetComplement)=>((complementTcontraSubset)=>(((((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>(((demorgan2b2)=>(((demorgan2)=>((woz13rule0)=>(((woz13rule2)=>((woz13rule3)=>(((woz1_1)=>(((((((((((((((breln1invE)=>((breln1compprop)=>((breln1compI)=>(((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>((breln1unionIR)=>![X4:$i, X33:$i]:((![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))<=((in @ (kpair @ X2 @ X3) @ X35)|(in @ (kpair @ X2 @ X3) @ X33)))))))))<=(breln1 @ X4 @ X33)))))))<=(breln1compE)))))<=(breln1invI))<=(breln1invprop))<=(eqbreln1))<=(subbreln1))<=(breln1all1))<=(setOfPairsIsBReln1))<=(choice2fnsingleton))<=(breln1SetBreln1))<=(breln1all2))<=(woz1_5))<=(woz1_4))<=(woz1_3))<=(woz1_2)))<=(woz13rule4))))<=(woz13rule1))))<=(demorgan2b)))<=(demorgan2a))))))))))<=(inComplementUnionImpInComplement1))<=(inComplementUnionImpNotIn1)))))<=(inIntersectImpInUnion))<=(binunionTIRcontra))<=(binunionTILcontra))))<=(complementInPowersetComplementIntersect))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT))<=(doubleComplementEq)))<=(doubleComplementSub1)))))<=(contrasubsetT2)))<=(contrasubsetT))<=(binintersectTERcontra))<=(binintersectTELcontra))<=(complementTE1))<=(complementTI1))<=(powersetTE1))<=(powersetTI1))<=(subsetTI))<=(setextT))))<=(powersetT_lem))<=(binunionT_lem)))))))<=(ifp))<=(ifSingleton)))<=(iftrueProp1)))<=(iffalseProp1))<=(eta2))<=(beta2))<=(lam2lamEq)))<=(beta1))))<=(funcext2)))<=(eqbreln)))<=(funcGraphProp4))))<=(funcGraphProp3))))<=(brelnall2))<=(brelnall1))<=(lam2p)))))))<=(app))<=(apProp))))<=(dpsetconstrEL2))<=(dpsetconstrEL1))<=(dpsetconstrERa))))<=(dpsetconstrI)))<=(cartprodsndpairEq)))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin))))<=(ksndsingleton))<=(setukpairinjR))))<=(setukpairinjR1))<=(setukpairinjR12))<=(setukpairinjR11))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin))<=(kfstpairEq)))))))<=(ex1I))))<=(setunionsingleton)))<=(setunionsingleton1))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))))<=(ubforcartprodlem2)))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E)))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp)))<=(setukpairIR)))))<=(symdiffIneg1)))<=(symdiffI1))<=(symdiffE)))<=(setminusLsub))))<=(setminusELneg)))<=(setminusSubset2))<=(setminusER))<=(setminusEL)))))<=(binintersectSubset4))<=(binintersectRsub)))))<=(binintersectSubset2)))<=(binintersectEL))<=(binintersectSubset5))))))))))<=(sepSubset))<=(sepInPowerset)))<=(inPowerset)))<=(powersetI1)))))<=(setadjoinSub2))<=(setadjoinSub))))<=(notequalI2))<=(notequalI1))<=(notsubsetI))<=(subsetE2))<=(subsetE)))<=(subsetI2)))<=(eqimpsubset2))))<=(descr__Cong))))<=(setunion__Cong))))<=(emptyset__Cong)))))<=(inCongP)))<=(exuI3))<=(exuI1)))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))))))<=(upairsetE))))<=(notinsingleton)))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU))<=(setunionE)))<=(powersetE))))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR)))<=(setadjoinIL)))<=(nonemptyI))<=(nonemptyE1)))))<=(setext))<=(exuE3e)))<=(emptysetimpfalse))<=(emptysetE))))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx))<=(foundationAx)))<=(omegaIndAx))<=(omegaSAx)))<=(setunionAx)))<=(setadjoinAx))))), inference(assume_negation,[status(cth)],[breln1unionI])).
0.23/0.76	thf(c_0_320, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1071:$i]:(((((X1 @ X1071)))&(![X1072:$i]:(((((X1 @ X1072)))=>(((X1071)=(X1072))))))))))=>((((?[X1073:$i]:(((((X17 @ X1073)))&(![X1074:$i]:(((((X17 @ X1074)))=>(((X1073)=(X1074))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_305])).
0.23/0.76	thf(c_0_321, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X1059:$i]:(((((X1 @ X1059)))&(![X1060:$i]:(((((X1 @ X1060)))=>(((X1059)=(X1060)))))))))))))))), inference(apply_def,[status(thm)],[c_0_306, c_0_305])).
0.23/0.76	thf(c_0_322, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X1057:$i]:(((((X1 @ X1057)))&(![X1058:$i]:(((((X1 @ X1058)))=>(((X1057)=(X1058)))))))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_305])).
0.23/0.76	thf(c_0_323, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_308])).
0.23/0.76	thf(c_0_324, plain, ((exuE2)=(![X1:$i > $o]:((((?[X1055:$i]:(((((X1 @ X1055)))&(![X1056:$i]:(((((X1 @ X1056)))=>(((X1055)=(X1056))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_309, c_0_305])).
0.23/0.76	thf(c_0_325, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
0.23/0.76	thf(c_0_326, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_310, c_0_308])).
0.23/0.76	thf(c_0_327, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_308])).
0.23/0.76	thf(c_0_328, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X1053:$i]:(((((X1 @ X1053)))&(![X1054:$i]:(((((X1 @ X1054)))=>(((X1053)=(X1054))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_311, c_0_305])).
0.23/0.76	thf(c_0_329, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
0.23/0.76	thf(c_0_330, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
0.23/0.76	thf(c_0_331, plain, ((descrp)=(![X1:$i > $o]:((((?[X1049:$i]:(((((X1 @ X1049)))&(![X1050:$i]:(((((X1 @ X1050)))=>(((X1049)=(X1050))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_312, c_0_305])).
0.23/0.76	thf(c_0_332, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
0.23/0.76	thf(c_0_333, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
0.23/0.76	thf(c_0_334, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
0.23/0.76	thf(c_0_335, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
0.23/0.76	thf(c_0_336, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
0.23/0.76	thf(c_0_337, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
0.23/0.76	thf(c_0_338, plain, ((funcImageSingleton)<=>![X4:$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])).
0.23/0.76	thf(c_0_339, 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])).
0.23/0.76	thf(c_0_340, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
0.23/0.76	thf(c_0_341, plain, ((lamProp)<=>![X4:$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])).
0.23/0.76	thf(c_0_342, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
0.23/0.76	thf(c_0_343, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
0.23/0.76	thf(c_0_344, plain, ((iftrueProp2)<=>![X4:$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])).
0.23/0.76	thf(c_0_345, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
0.23/0.76	thf(c_0_346, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
0.23/0.76	thf(c_0_347, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((((X52 @ X2 @ Z0))&(![X14:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ Z0 @ X14) @ X33)))))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])).
0.23/0.76	thf(c_0_348, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
0.23/0.76	thf(c_0_349, plain, ((beta1)<=>![X4:$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])).
0.23/0.76	thf(c_0_350, 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])).
0.23/0.76	thf(c_0_351, 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])).
0.23/0.76	thf(c_0_352, 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])).
0.23/0.76	thf(c_0_353, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
0.23/0.76	thf(c_0_354, plain, ((iftrueProp1)<=>![X4:$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])).
0.23/0.76	thf(c_0_355, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
0.23/0.76	thf(c_0_356, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
0.23/0.76	thf(c_0_357, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
0.23/0.76	thf(c_0_358, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
0.23/0.76	thf(c_0_359, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
0.23/0.76	thf(c_0_360, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
0.23/0.76	thf(c_0_361, plain, ((ex1I)<=>![X4:$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])).
0.23/0.76	thf(c_0_362, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
0.23/0.76	thf(c_0_363, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
0.23/0.76	thf(c_0_364, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
0.23/0.76	thf(c_0_365, plain, ((exuEu)=(![X1:$i > $o]:((((?[X1069:$i]:(((((X1 @ X1069)))&(![X1070:$i]:(((((X1 @ X1070)))=>(((X1069)=(X1070))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_313, c_0_305])).
0.23/0.76	thf(c_0_366, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1065:$i]:(((((X1 @ X1065)))&(![X1066:$i]:(((((X1 @ X1066)))=>(((X1065)=(X1066))))))))))<=>((?[X1067:$i]:(((((X17 @ X1067)))&(![X1068:$i]:(((((X17 @ X1068)))=>(((X1067)=(X1068)))))))))))))))), inference(apply_def,[status(thm)],[c_0_314, c_0_305])).
0.23/0.76	thf(c_0_367, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X1063:$i]:(((((X1 @ X1063)))&(![X1064:$i]:(((((X1 @ X1064)))=>(((X1063)=(X1064))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_315, c_0_305])).
0.23/0.76	thf(c_0_368, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X1061:$i]:(((((X1 @ X1061)))&(![X1062:$i]:(((((X1 @ X1062)))=>(((X1061)=(X1062)))))))))))))), inference(apply_def,[status(thm)],[c_0_316, c_0_305])).
0.23/0.76	thf(c_0_369, plain, ((emptyE1)<=>![X4:$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])).
0.23/0.76	thf(c_0_370, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
0.23/0.76	thf(c_0_371, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_308])).
0.23/0.76	thf(c_0_372, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
0.23/0.76	thf(c_0_373, plain, ((exuE1)=(![X1:$i > $o]:((((?[X1051:$i]:(((((X1 @ X1051)))&(![X1052:$i]:(((((X1 @ X1052)))=>(((X1051)=(X1052))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_317, c_0_305])).
0.23/0.76	thf(c_0_374, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
0.23/0.76	thf(c_0_375, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X1047:$i]:(((((X6 @ X2 @ X1047)))&(![X1048:$i]:(((((X6 @ X2 @ X1048)))=>(((X1047)=(X1048)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_318, c_0_305])).
0.23/0.76	thf(c_0_376, plain, ((epred1_0)<=>![X2058:$i]:(?[X2059:$i]:((((![X2060:$i]:(((in @ X2060 @ X2059)=>![X2061:$i]:(((in @ X2061 @ X2060)=>(in @ X2061 @ X2058)))))&![X2062:$i, X2063:$i]:((((in @ X2062 @ X2058)&(in @ X2063 @ X2058))=>(![X2064:$i]:(((in @ X2064 @ X2059)=>((in @ X2062 @ X2064)<=>(in @ X2063 @ X2064))))=>((X2062)=(X2063))))))&![X2065:$i, X2066:$i]:((((in @ X2065 @ X2059)&(in @ X2066 @ X2059))=>(![X2067:$i]:(((in @ X2067 @ X2065)=>(in @ X2067 @ X2066)))|![X2068:$i]:(((in @ X2068 @ X2066)=>(in @ X2068 @ X2065)))))))&![X2069:$i]:(((![X2070:$i]:(((in @ X2070 @ X2069)=>(in @ X2070 @ X2058)))&?[X2071:$i]:((in @ X2071 @ X2069)))=>?[X2072:$i, X2073:$i]:(((((in @ X2072 @ X2059)&(in @ X2073 @ X2069))&~(?[X2074:$i]:(((in @ X2074 @ X2072)&(in @ X2074 @ X2069)))))&![X2075:$i]:(((in @ X2075 @ X2059)=>(![X2076:$i]:(((in @ X2076 @ X2075)=>(in @ X2076 @ X2072)))|(in @ X2073 @ X2075)))))))))))), introduced(definition)).
0.23/0.76	thf(c_0_377, negated_conjecture, ~((![X1075:$i, X1076:$i]:((![X1077:$i]:(((in @ X1077 @ X1075)<=>(in @ X1077 @ X1076)))=>((X1075)=(X1076))))=>(![X1078:$i]:(~(in @ X1078 @ emptyset))=>(![X2088:$i, X2089:$i, X2090:$i]:(((in @ X2090 @ (setadjoin @ X2088 @ X2089))<=>(((X2090)=(X2088))|(in @ X2090 @ X2089))))=>(![X1079:$i, X1080:$i]:(((in @ X1080 @ (powerset @ X1079))<=>![X1081:$i]:(((in @ X1081 @ X1080)=>(in @ X1081 @ X1079)))))=>(![X2085:$i, X2086:$i]:(((in @ X2086 @ (setunion @ X2085))<=>?[X2087:$i]:(((in @ X2086 @ X2087)&(in @ X2087 @ X2085)))))=>((in @ emptyset @ omega)=>(![X2084:$i]:(((in @ X2084 @ omega)=>(in @ (setadjoin @ X2084 @ X2084) @ omega)))=>(![X2081:$i]:((((in @ emptyset @ X2081)&![X2082:$i]:((((in @ X2082 @ omega)&(in @ X2082 @ X2081))=>(in @ (setadjoin @ X2082 @ X2082) @ X2081))))=>![X2083:$i]:(((in @ X2083 @ omega)=>(in @ X2083 @ X2081)))))=>(![X1082:$i > $i > $o, X1083:$i]:((![X1084:$i]:(((in @ X1084 @ X1083)=>?[X1085:$i]:(((X1082 @ X1084 @ X1085)&![X1086:$i]:(((X1082 @ X1084 @ X1086)=>((X1085)=(X1086))))))))=>?[X1087:$i]:(![X1088:$i]:(((in @ X1088 @ X1087)<=>?[X1089:$i]:(((in @ X1089 @ X1083)&(X1082 @ X1089 @ X1088))))))))=>(![X2077:$i]:((?[X2078:$i]:((in @ X2078 @ X2077))=>?[X2079:$i]:(((in @ X2079 @ X2077)&~(?[X2080:$i]:(((in @ X2080 @ X2079)&(in @ X2080 @ X2077))))))))=>((epred1_0)=>(![X2055:$i > $o]:((?[X2056:$i]:(((X2055 @ X2056)&![X2057:$i]:(((X2055 @ X2057)=>((X2056)=(X2057))))))=>(X2055 @ (descr @ (^[Z0:$i]:(X2055 @ Z0))))))=>(![X1090:$i, X1091:$i > $o, X1092:$i]:(((in @ X1092 @ X1090)=>((X1091 @ X1092)=>(in @ X1092 @ (dsetconstr @ X1090 @ X1091)))))=>(![X2052:$i, X2053:$i > $o, X2054:$i]:(((in @ X2054 @ (dsetconstr @ X2052 @ X2053))=>(in @ X2054 @ X2052)))=>(![X2049:$i, X2050:$i > $o, X2051:$i]:(((in @ X2051 @ (dsetconstr @ X2049 @ X2050))=>(X2050 @ X2051)))=>(![X1093:$i > $o]:((?[X1094:$i]:(((X1093 @ X1094)&![X1095:$i]:(((X1093 @ X1095)=>((X1094)=(X1095))))))=>?[X1096:$i]:(((X1093 @ X1096)&![X1097:$i]:(((X1093 @ X1097)=>((X1096)=(X1097))))))))=>(![X1098:$o, X1099:$i]:(((in @ X1099 @ (prop2set @ ((X1098))))=>(X1098)))=>(![X2047:$i]:(((in @ X2047 @ emptyset)=>![X2048:$o]:((X2048))))=>(![X2046:$i]:(((in @ X2046 @ emptyset)=>~($true)))=>(![X1100:$i]:(~(in @ X1100 @ emptyset))=>(![X2042:$i > $o]:((?[X2043:$i]:(((X2042 @ X2043)&![X2044:$i]:(((X2042 @ X2044)=>((X2043)=(X2044))))))=>?[X2045:$i]:((X2042 @ X2045))))=>(![X2038:$i, X2039:$i]:((![X2040:$i]:(((in @ X2040 @ X2038)=>(in @ X2040 @ X2039)))=>(![X2041:$i]:(((in @ X2041 @ X2039)=>(in @ X2041 @ X2038)))=>((X2038)=(X2039)))))=>(![X1101:$i]:((![X1102:$i]:(~(in @ X1102 @ X1101))=>((X1101)=(emptyset))))=>(![X1103:$i]:((![X1104:$i]:(~(in @ X1104 @ X1103))=>((X1103)=(emptyset))))=>(![X1105:$i, X1106:$i > $o, X1107:$i]:(((in @ X1107 @ X1105)=>((in @ X1107 @ (dsetconstr @ X1105 @ X1106))<=>(X1106 @ X1107))))=>(![X2036:$i]:((((X2036)!=(emptyset))=>?[X2037:$i]:((in @ X2037 @ X2036))))=>(![X2033:$i, X2034:$i > $o, X2035:$i]:(((in @ X2035 @ X2033)=>((X2034 @ X2035)=>((dsetconstr @ X2033 @ X2034)!=(emptyset)))))=>(![X1108:$i]:((?[X1109:$i]:((in @ X1109 @ X1108))=>((X1108)!=(emptyset))))=>(![X2031:$i, X2032:$i]:((in @ X2031 @ (setadjoin @ X2031 @ X2032)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X2028:$i, X2029:$i, X2030:$i]:(((in @ X2030 @ X2029)=>(in @ X2030 @ (setadjoin @ X2028 @ X2029))))=>(![X2024:$i, X2025:$i, X2026:$i]:(((in @ X2026 @ (setadjoin @ X2024 @ X2025))=>![X2027:$o]:(((((X2026)=(X2024))=>(X2027))=>(((in @ X2026 @ X2025)=>(X2027))=>(X2027))))))=>(![X2021:$i, X2022:$i, X2023:$i]:(((in @ X2023 @ (setadjoin @ X2021 @ X2022))=>(((X2023)=(X2021))|(in @ X2023 @ X2022))))=>(![X1110:$i]:(((dsetconstr @ X1110 @ (^[Z0:$i]:($true)))=(X1110)))=>(![X2018:$i, X2019:$i]:((![X2020:$i]:(((in @ X2020 @ X2019)=>(in @ X2020 @ X2018)))=>(in @ X2019 @ (powerset @ X2018))))=>(![X1111:$i]:((in @ emptyset @ (powerset @ X1111)))=>(![X1112:$i]:((in @ emptyset @ (powerset @ X1112)))=>(![X2015:$i, X2016:$i, X2017:$i]:(((in @ X2016 @ (powerset @ X2015))=>((in @ X2017 @ X2016)=>(in @ X2017 @ X2015))))=>(![X1113:$i, X1114:$i, X1115:$i]:(((in @ X1114 @ X1115)=>((in @ X1115 @ X1113)=>(in @ X1114 @ (setunion @ X1113)))))=>(![X2011:$i, X2012:$i]:(((in @ X2012 @ (setunion @ X2011))=>![X2013:$o]:((![X2014:$i]:(((in @ X2012 @ X2014)=>((in @ X2014 @ X2011)=>(X2013))))=>(X2013)))))=>(![X2009:$i, X2010:$i]:(((in @ X2010 @ X2009)=>(in @ X2010 @ (powerset @ (setunion @ X2009)))))=>(![X2004:$i > $o]:((?[X2005:$i]:(((X2004 @ X2005)&![X2006:$i]:(((X2004 @ X2006)=>((X2005)=(X2006))))))=>?[X2007:$i]:(![X2008:$i]:(((X2004 @ X2008)<=>((X2008)=(X2007)))))))=>(![X2002:$i]:((((X2002)!=(emptyset))=>?[X2003:$i]:(((in @ X2003 @ X2002)&$true))))=>(![X1116:$i, X1117:$i]:(((in @ X1116 @ (setadjoin @ X1117 @ emptyset))=>((X1116)=(X1117))))=>(![X2000:$i, X2001:$i]:((((X2000)!=(X2001))=>~(in @ X2001 @ (setadjoin @ X2000 @ emptyset))))=>(![X1118:$i, X1119:$i]:((((X1118)=(X1119))=>(in @ X1118 @ (setadjoin @ X1119 @ emptyset))))=>(![X1120:$i, X1121:$i]:(((in @ X1120 @ (setadjoin @ X1121 @ emptyset))=>(in @ X1121 @ (setadjoin @ X1120 @ emptyset))))=>(![X1997:$i, X1998:$i, X1999:$i]:(((in @ X1999 @ (setadjoin @ X1997 @ (setadjoin @ X1998 @ emptyset)))=>(((X1999)=(X1997))|((X1999)=(X1998)))))=>(![X1122:$i, X1123:$i]:((in @ X1122 @ (setadjoin @ X1122 @ (setadjoin @ X1123 @ emptyset))))=>(![X1124:$i, X1125:$i]:((in @ X1125 @ (setadjoin @ X1124 @ (setadjoin @ X1125 @ emptyset))))=>(![X1126:$i, X1127:$i > $o]:((?[X1128:$i]:(((in @ X1128 @ X1126)&(X1127 @ X1128)))=>(((dsetconstr @ X1126 @ X1127)=(emptyset))=>~($true))))=>(![X1129:$i > $o, X1130:$i]:(((in @ X1130 @ emptyset)=>(X1129 @ X1130)))=>(![X1993:$i, X1994:$i > $o]:((~(![X1995:$i]:(((in @ X1995 @ X1993)=>(X1994 @ X1995))))=>?[X1996:$i]:(((in @ X1996 @ X1993)&~((X1994 @ X1996))))))=>(![X1989:$i, X1990:$i > $o]:((![X1991:$i]:(((in @ X1991 @ X1989)=>~((X1990 @ X1991))))=>~(?[X1992:$i]:(((in @ X1992 @ X1989)&(X1990 @ X1992))))))=>(![X1985:$i, X1986:$i > $o]:((~(?[X1987:$i]:(((in @ X1987 @ X1985)&(X1986 @ X1987))))=>![X1988:$i]:(((in @ X1988 @ X1985)=>~((X1986 @ X1988))))))=>(![X1981:$i, X1982:$i > $o]:((?[X1983:$i]:(((in @ X1983 @ X1981)&~((X1982 @ X1983))))=>~(![X1984:$i]:(((in @ X1984 @ X1981)=>(X1982 @ X1984))))))=>(![X1980:$o]:(((X1980)=>(in @ emptyset @ (prop2set @ ((X1980))))))=>(![X1979:$o]:(((X1979)=>(set2prop @ (prop2set @ ((X1979))))))=>(![X1975:$i, X1976:$i > $o]:((~(?[X1977:$i]:(((in @ X1977 @ X1975)&(X1976 @ X1977))))=>![X1978:$i]:(((in @ X1978 @ X1975)=>~((X1976 @ X1978))))))=>(![X1131:$i, X1132:$i > $o]:((~(![X1133:$i]:(((in @ X1133 @ X1131)=>(X1132 @ X1133))))=>?[X1134:$i]:(((in @ X1134 @ X1131)&~((X1132 @ X1134))))))=>(![X1970:$i > $o]:((?[X1971:$i]:(((X1970 @ X1971)&![X1972:$i]:(((X1970 @ X1972)=>((X1971)=(X1972))))))=>?[X1973:$i]:(((X1970 @ X1973)&![X1974:$i]:(((X1970 @ X1974)=>((X1973)=(X1974))))))))=>(![X1964:$i > $o]:((?[X1965:$i]:((X1964 @ X1965))=>(![X1966:$i, X1967:$i]:(((X1964 @ X1966)=>((X1964 @ X1967)=>((X1966)=(X1967)))))=>?[X1968:$i]:(((X1964 @ X1968)&![X1969:$i]:(((X1964 @ X1969)=>((X1968)=(X1969)))))))))=>(![X1135:$i > $o]:((?[X1136:$i]:(![X1137:$i]:(((X1135 @ X1137)<=>((X1137)=(X1136)))))=>?[X1138:$i]:(((X1135 @ X1138)&![X1139:$i]:(((X1135 @ X1139)=>((X1138)=(X1139))))))))=>(![X1960:$i, X1961:$i]:((((X1960)=(X1961))=>![X1962:$i, X1963:$i]:((((X1962)=(X1963))=>((in @ X1962 @ X1960)=>(in @ X1963 @ X1961))))))=>(![X1140:$i, X1141:$i]:((((X1140)=(X1141))=>![X1142:$i, X1143:$i]:((((X1142)=(X1143))=>((in @ X1142 @ X1140)<=>(in @ X1143 @ X1141))))))=>(![X1144:$i > $o]:((?[X1145:$i]:(((X1144 @ X1145)&![X1146:$i]:(((X1144 @ X1146)=>((X1145)=(X1146))))))=>![X1147:$i, X1148:$i]:(((X1144 @ X1147)=>((X1144 @ X1148)=>((X1147)=(X1148)))))))=>(![X1149:$i > $o, X1150:$i > $o]:((![X1151:$i, X1152:$i]:((((X1151)=(X1152))=>((X1149 @ X1151)<=>(X1150 @ X1152))))=>(?[X1153:$i]:(((X1149 @ X1153)&![X1154:$i]:(((X1149 @ X1154)=>((X1153)=(X1154))))))<=>?[X1155:$i]:(((X1150 @ X1155)&![X1156:$i]:(((X1150 @ X1156)=>((X1155)=(X1156)))))))))=>(((emptyset)=(emptyset))=>(![X1157:$i, X1158:$i]:((((X1157)=(X1158))=>![X1159:$i, X1160:$i]:((((X1159)=(X1160))=>((setadjoin @ X1157 @ X1159)=(setadjoin @ X1158 @ X1160))))))=>(![X1161:$i, X1162:$i]:((((X1161)=(X1162))=>((powerset @ X1161)=(powerset @ X1162))))=>(![X1958:$i, X1959:$i]:((((X1958)=(X1959))=>((setunion @ X1958)=(setunion @ X1959))))=>(((omega)=(omega))=>(![X1163:$i > $o]:((?[X1164:$i]:(((X1163 @ X1164)&![X1165:$i]:(((X1163 @ X1165)=>((X1164)=(X1165))))))=>![X1166:$i, X1167:$i]:(((X1163 @ X1166)=>((X1163 @ X1167)=>((X1166)=(X1167)))))))=>(![X1950:$i > $o, X1951:$i > $o]:((![X1952:$i, X1953:$i]:((((X1952)=(X1953))=>((X1950 @ X1952)<=>(X1951 @ X1953))))=>(?[X1954:$i]:(((X1950 @ X1954)&![X1955:$i]:(((X1950 @ X1955)=>((X1954)=(X1955))))))=>(?[X1956:$i]:(((X1951 @ X1956)&![X1957:$i]:(((X1951 @ X1957)=>((X1956)=(X1957))))))=>((descr @ X1950)=(descr @ X1951))))))=>(![X1168:$i, X1169:$i]:((((X1168)=(X1169))=>![X1170:$i > $o, X1171:$i > $o]:((![X1172:$i]:(((in @ X1172 @ X1168)=>![X1173:$i]:(((in @ X1173 @ X1169)=>(((X1172)=(X1173))=>((X1170 @ X1172)<=>(X1171 @ X1173)))))))=>((dsetconstr @ X1168 @ X1170)=(dsetconstr @ X1169 @ X1171))))))=>(![X1174:$i, X1175:$i]:((![X1176:$i]:(((in @ X1176 @ X1174)=>(in @ X1176 @ X1175)))=>(subset @ X1174 @ X1175)))=>(![X1948:$i, X1949:$i]:((((X1948)=(X1949))=>(subset @ X1949 @ X1948)))=>(![X1177:$i, X1178:$i]:((((X1177)=(X1178))=>(subset @ X1177 @ X1178)))=>(![X1945:$i, X1946:$i]:((![X1947:$i]:(((in @ X1947 @ X1945)=>(in @ X1947 @ X1946)))=>(subset @ X1945 @ X1946)))=>(![X1179:$i]:((subset @ emptyset @ X1179))=>(![X1942:$i, X1943:$i, X1944:$i]:(((subset @ X1942 @ X1943)=>((in @ X1944 @ X1942)=>(in @ X1944 @ X1943))))=>(![X1939:$i, X1940:$i, X1941:$i]:(((subset @ X1939 @ X1940)=>(~(in @ X1941 @ X1940)=>~(in @ X1941 @ X1939))))=>(![X1936:$i, X1937:$i, X1938:$i]:(((in @ X1938 @ X1936)=>(~(in @ X1938 @ X1937)=>~(subset @ X1936 @ X1937))))=>(![X1934:$i, X1935:$i]:((~(subset @ X1934 @ X1935)=>((X1934)!=(X1935))))=>(![X1931:$i, X1932:$i, X1933:$i]:(((in @ X1933 @ X1931)=>(~(in @ X1933 @ X1932)=>((X1931)!=(X1932)))))=>(![X1180:$i]:((subset @ X1180 @ X1180))=>(![X1181:$i, X1182:$i, X1183:$i]:(((subset @ X1181 @ X1182)=>((subset @ X1182 @ X1183)=>(subset @ X1181 @ X1183))))=>(![X1929:$i, X1930:$i]:((subset @ X1930 @ (setadjoin @ X1929 @ X1930)))=>(![X1926:$i, X1927:$i, X1928:$i]:(((subset @ X1926 @ X1928)=>(subset @ X1926 @ (setadjoin @ X1927 @ X1928))))=>(![X1184:$i, X1185:$i]:(((subset @ X1184 @ X1185)=>(in @ X1184 @ (powerset @ X1185))))=>(![X1186:$i, X1187:$i]:(((subset @ X1186 @ X1187)=>((subset @ X1187 @ X1186)=>((X1186)=(X1187)))))=>(![X1188:$i]:(((subset @ X1188 @ emptyset)=>((X1188)=(emptyset))))=>(![X1924:$i, X1925:$i]:(((subset @ X1925 @ X1924)=>(in @ X1925 @ (powerset @ X1924))))=>(![X1189:$i, X1190:$i]:(((in @ X1190 @ (powerset @ X1189))=>(subset @ X1190 @ X1189)))=>(![X1923:$i]:((in @ X1923 @ (powerset 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X1455)=>(X1457))=>(((in @ X1458 @ X1456)=>(X1457))=>(X1457))))))))))=>(![X1459:$i, X1460:$i]:(((in @ X1460 @ (powerset @ X1459))=>![X1461:$i]:(((in @ X1461 @ (powerset @ X1459))=>![X1462:$i]:(((in @ X1462 @ X1459)=>(~(in @ X1462 @ X1460)=>(~(in @ X1462 @ X1461)=>~(in @ X1462 @ (binunion @ X1460 @ X1461))))))))))=>(![X1463:$i, X1464:$i]:(((in @ X1464 @ (powerset @ X1463))=>![X1465:$i]:(((in @ X1465 @ (powerset @ X1463))=>![X1466:$i]:(((in @ X1466 @ X1463)=>((in @ X1466 @ (setminus @ X1463 @ (binunion @ X1464 @ X1465)))=>(in @ X1466 @ (setminus @ X1463 @ X1464)))))))))=>(![X1467:$i, X1468:$i]:(((in @ X1468 @ (powerset @ X1467))=>![X1469:$i]:(((in @ X1469 @ (powerset @ X1467))=>(in @ (setminus @ X1467 @ (binunion @ X1468 @ X1469)) @ (powerset @ (setminus @ X1467 @ X1468)))))))=>(![X1470:$i, X1471:$i]:(((in @ X1471 @ (powerset @ X1470))=>![X1472:$i]:(((in @ X1472 @ (powerset @ X1470))=>![X1473:$i]:(((in @ X1473 @ X1470)=>((in @ X1473 @ (setminus @ X1470 @ (binunion @ X1471 @ X1472)))=>(in @ X1473 @ (setminus @ X1470 @ X1472)))))))))=>(![X1474:$i, X1475:$i]:(((in @ X1475 @ (powerset @ X1474))=>![X1476:$i]:(((in @ X1476 @ (powerset @ X1474))=>![X1477:$i]:(((in @ X1477 @ X1474)=>((in @ X1477 @ (setminus @ X1474 @ (binintersect @ X1475 @ X1476)))=>(in @ X1477 @ (binunion @ (setminus @ X1474 @ X1475) @ (setminus @ X1474 @ X1476))))))))))=>(![X1478:$i, X1479:$i]:(((in @ X1479 @ (powerset @ X1478))=>![X1480:$i]:(((in @ X1480 @ (powerset @ X1478))=>![X1481:$i]:(((in @ X1481 @ X1478)=>((in @ X1481 @ (binunion @ (setminus @ X1478 @ X1479) @ (setminus @ X1478 @ X1480)))=>(in @ X1481 @ (setminus @ X1478 @ (binintersect @ X1479 @ X1480))))))))))=>(![X1482:$i, X1483:$i]:(((in @ X1483 @ (powerset @ X1482))=>![X1484:$i]:(((in @ X1484 @ (powerset @ X1482))=>((setminus @ X1482 @ (binintersect @ X1483 @ X1484))=(binunion @ (setminus @ X1482 @ X1483) @ (setminus @ X1482 @ X1484)))))))=>(![X1616:$i, X1617:$i]:(((in @ X1617 @ (powerset @ X1616))=>![X1618:$i]:(((in @ X1618 @ (powerset @ 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y_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_319, notequalI1]), notsubsetI]), subsetE2]), symdiffI2]), subsetE]), setminusSubset1]), subsetI2]), setminusIRneg]), eqimpsubset2]), setminusILneg]), c_0_320]), setminusERneg]), setunion__Cong]), setminusI]), emptyset__Cong]), secondinupair]), inCongP]), c_0_321]), c_0_322]), notdexE]), prop2set2propI]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), upairsetE]), notinsingleton]), c_0_323]), c_0_324]), setunionsingleton2]), subPowSU]), cartprodpairin]), setunionE]), ubforcartprodlem3]), powersetE]), ubforcartprodlem1]), powersetI]), singletoninpowunion]), setadjoinOr]), kpairiskpair]), setadjoinE]), setukpairIL]), setadjoinIR]), c_0_325]), setadjoinIL]), c_0_326]), c_0_327]), setext]), c_0_328]), emptysetimpfalse]), emptysetE]), c_0_329]), c_0_330]), c_0_331]), wellorderingAx]), foundationAx]), omegaIndAx]), omegaSAx]), upairequniteq]), setunionAx]), theprop]), setadjoinAx]), c_0_332]), setukpairinjL1]), singletonsuniq]), c_0_333]), c_0_334]), setukpairinjR2]), c_0_335]), c_0_336]), c_0_337]), cartprodpairsurjEq]), cartprodfstpairEq]), kpairsurjEq]), ksndpairEq]), c_0_338]), funcGraphProp1]), c_0_339]), c_0_340]), c_0_341]), funcinfuncset]), ap2p]), infuncsetfunc]), funcGraphProp2]), c_0_342]), c_0_343]), ap2apEq2]), ap2apEq1]), funcext]), subbreln]), funcextLem]), c_0_344]), complementT_lem]), setminusT_lem]), binintersectT_lem]), iftrueorfalse]), iffalse]), iftrue]), theeq]), contrasubsetT1]), funcGraphProp3]), funcGraphProp4]), eqbreln]), c_0_345]), cartprodpairmemER]), cartprodmempaircEq]), cartprodsndpairEq]), c_0_346]), complementTcontraSubset]), contraSubsetComplement]), complementImpComplementIntersect]), doubleComplementSub2]), doubleComplementE1]), doubleComplementI1]), contrasubsetT3]), inIntersectImpInUnion2]), demorgan2a2]), complementUnionInPowersetComplement]), demorgan2a1]), binunionTEcontra]), binunionTE]), intersectInPowersetIntersectUnions]), inIntersectImpInIntersectUnions]), demorgan1a]), woz13rule3]), woz13rule2]), woz13rule0]), demorgan2]), demorgan2b2]), demorgan1]), demorgan1b]), woz1_1]), breln1invE]), breln1compprop]), breln1compI]), breln1compEex]), breln1unionprop]), breln1unionIL]), breln1unionIR]), breln1compE]), c_0_347]), c_0_348]), breln1all1]), subbreln1]), eqbreln1]), breln1invprop]), breln1invI]), breln1SetBreln1]), woz13rule1]), woz13rule4]), woz1_2]), woz1_3]), woz1_4]), woz1_5]), breln1all2]), demorgan2b]), complementInPowersetComplementIntersect]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), demorgan2a]), complementSubsetComplementIntersect]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT2]), doubleComplementSub1]), doubleComplementEq]), complementTnotintersectT]), complementTE1]), binunionT_lem]), powersetT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), ifp]), c_0_349]), c_0_350]), c_0_351]), c_0_352]), c_0_353]), c_0_354]), c_0_355]), funcext2]), app]), c_0_356]), brelnall1]), brelnall2]), c_0_357]), c_0_358]), c_0_359]), cartprodpairmemEL]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), setukpairinjR]), c_0_360]), cartprodsndin]), setukpairinjL2]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton]), c_0_361]), kfstpairEq]), cartprodfstin]), cartprodmempair1]), kpairp]), singletonsubset]), singletoninpowerset]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem2]), setukpairIR]), setminusER]), setminusSubset2]), setminusELneg]), setminusLsub]), symdiffE]), symdiffI1]), symdiffIneg1]), setminusEL]), c_0_362]), c_0_363]), binintersectSubset5]), binintersectEL]), binintersectSubset2]), binintersectRsub]), binintersectSubset4]), powersetI1]), setadjoinSub2]), setadjoinSub]), notequalI2]), inPowerset]), symdiffIneg2]), bs114d]), binintersectSubset1]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectLsub]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), powersetsubset]), powersetE1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), subsetTrans]), subsetRefl]), emptysetsubset]), eqimpsubset1]), subsetI1]), c_0_364]), c_0_365]), omega__Cong]), powerset__Cong]), setadjoin__Cong]), c_0_366]), c_0_367]), in__Cong]), c_0_368]), notdallE]), vacuousDall]), c_0_369]), upairsetIR]), upairsetIL]), singletonsswitch]), eqinunit]), uniqinunit]), setunionI]), emptyInPowerset]), emptyinPowerset]), c_0_370]), emptyinunitempty]), c_0_371]), c_0_372]), noeltsimpempty]), emptyI]), notinemptyset]), prop2setE]), c_0_373]), c_0_374]), c_0_375]), omega0Ax]), powersetAx]), emptysetAx]), setextAx])])]), c_0_376])).
0.23/0.76	thf(c_0_378, negated_conjecture, ![X2091:$i, X2092:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2104:$i, X2105:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2113:$i, X2114:$i > $i > $o, X2115:$i, X2117:$i, X2120:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2127:$i, X2128:$i > $o, X2129:$i, X2131:$i, X2132:$i > $o, X2133:$i, X2134:$i, X2135:$i > $o, X2136:$i, X2137:$i, X2138:$i > $o, X2139:$i, X2140:$i > $o, X2141:$i, X2144:$i, X2145:$o, X2146:$i, X2147:$i, X2148:$o, X2149:$i, X2150:$i, X2151:$i > $o, X2152:$i, X2155:$i, X2156:$i, X2159:$i, X2161:$i, X2163:$i, X2164:$i > $o, X2165:$i, X2166:$i, X2168:$i, X2169:$i > $o, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$o, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$o, X2201:$i, X2202:$i, X2203:$i > $o, X2204:$i, X2207:$i, X2208:$i, X2209:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i > $o, X2228:$i, X2229:$i > $o, X2230:$i, X2231:$i, X2232:$i > $o, X2233:$i, X2235:$i, X2236:$i > $o, X2238:$i, X2239:$i, X2240:$i > $o, X2242:$i, X2243:$i, X2244:$i > $o, X2245:$i, X2247:$o, X2248:$o, X2249:$i, X2250:$i > $o, X2252:$i, X2253:$i, X2254:$i > $o, X2255:$i, X2257:$i > $o, X2258:$i, X2261:$i, X2262:$i > $o, X2263:$i, X2267:$i, X2268:$i > $o, X2269:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i > $o, X2282:$i, X2284:$i, X2285:$i, X2286:$i > $o, X2287:$i > $o, X2290:$i, X2293:$i, X2294:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i > $o, X2307:$i, X2309:$i, X2310:$i, X2311:$i > $o, X2312:$i > $o, X2315:$i, X2317:$i, X2319:$i, X2320:$i, X2321:$i > $o, X2322:$i > $o, X2325:$i, X2326:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i > $o, X2373:$i, X2374:$i > $o, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$o, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$o, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i > $o, X2529:$i, X2530:$i, X2531:$i > $o, X2533:$i, X2534:$i > $o, X2535:$i, X2537:$i, X2538:$i > $o, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i > $i > $o, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i > $i > $o, X2619:$i, X2620:$i, X2621:$i > $i > $o, X2622:$i, X2623:$i, X2624:$i > $i > $o, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i > $i > $o, X2630:$i, X2631:$i, X2632:$i, X2633:$i, X2634:$i > $i > $o, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i > $i > $o, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i, X2666:$i > $i, X2668:$i, X2669:$i, X2670:$i > $i, X2672:$i, X2673:$i, X2674:$i > $i, X2676:$i, X2677:$i, X2678:$i, X2679:$i > $o, X2682:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i > $o, X2689:$i, X2690:$i, X2691:$i > $o, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i > $i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i > $i, X2763:$i, X2764:$i, X2765:$i > $i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$o, X2773:$i, X2774:$i, X2775:$i, X2776:$o, X2777:$i, X2778:$i, X2779:$i, X2780:$o, X2781:$i, X2782:$i, X2783:$i, X2784:$o, X2785:$i, X2786:$i, X2787:$i, X2788:$o, X2789:$i, X2790:$i, X2791:$i, X2792:$o, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$o, X2799:$i, X2800:$i, X2801:$i, X2802:$o, X2803:$i, X2804:$i, X2805:$i, X2806:$o, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2827:$i, X2828:$i, X2829:$i, X2831:$i, X2832:$i, X2833:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2851:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2856:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i, X2871:$i, X2872:$i, X2873:$i, X2874:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$i, X2885:$i, X2886:$i, X2887:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2901:$i, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$o, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$i, X2951:$i, X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i, X2976:$i, X2977:$i, X2978:$i, X2979:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3002:$i, X3003:$i, X3004:$i, X3005:$i, X3006:$i, X3007:$i, X3008:$i, X3009:$i, X3010:$i, X3011:$i, X3012:$i, X3013:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i > $o, X3025:$i, X3026:$i, X3027:$i, X3028:$i, X3029:$i, X3030:$i > $i > $o, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i > $i > $o, X3037:$i, X3038:$i, X3039:$i > $o, X3042:$i, X3043:$i, 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X3049)))))&((((in @ (esk96_3 @ X3048 @ X3049 @ X3050) @ X3048)|((X3049)=(X3050))|(in @ (kpair @ (esk94_3 @ X3048 @ X3049 @ X3050) @ (esk95_3 @ X3048 @ X3049 @ X3050)) @ X3049)|~(breln1 @ X3048 @ X3050)|~(breln1 @ X3048 @ X3049))&(((in @ (esk97_3 @ X3048 @ X3049 @ X3050) @ X3048)|((X3049)=(X3050))|(in @ (kpair @ (esk94_3 @ X3048 @ X3049 @ X3050) @ (esk95_3 @ X3048 @ X3049 @ X3050)) @ X3049)|~(breln1 @ X3048 @ X3050)|~(breln1 @ X3048 @ X3049))&(((in @ (kpair @ (esk96_3 @ X3048 @ X3049 @ X3050) @ (esk97_3 @ X3048 @ X3049 @ X3050)) @ X3050)|((X3049)=(X3050))|(in @ (kpair @ (esk94_3 @ X3048 @ X3049 @ X3050) @ (esk95_3 @ X3048 @ X3049 @ X3050)) @ X3049)|~(breln1 @ X3048 @ X3050)|~(breln1 @ X3048 @ X3049))&(~(in @ (kpair @ (esk96_3 @ X3048 @ X3049 @ X3050) @ (esk97_3 @ X3048 @ X3049 @ X3050)) @ X3049)|((X3049)=(X3050))|(in @ (kpair @ (esk94_3 @ X3048 @ X3049 @ X3050) @ (esk95_3 @ X3048 @ X3049 @ X3050)) @ X3049)|~(breln1 @ X3048 @ X3050)|~(breln1 @ X3048 @ X3049)))))&(((in @ (esk96_3 @ X3048 @ X3049 @ X3050) @ X3048)|((X3049)=(X3050))|~(in @ (kpair @ (esk94_3 @ X3048 @ X3049 @ X3050) @ (esk95_3 @ X3048 @ X3049 @ X3050)) @ X3050)|~(breln1 @ X3048 @ X3050)|~(breln1 @ X3048 @ X3049))&(((in @ (esk97_3 @ X3048 @ X3049 @ X3050) @ X3048)|((X3049)=(X3050))|~(in @ (kpair @ (esk94_3 @ X3048 @ X3049 @ X3050) @ (esk95_3 @ X3048 @ X3049 @ X3050)) @ X3050)|~(breln1 @ X3048 @ X3050)|~(breln1 @ X3048 @ X3049))&(((in @ (kpair @ (esk96_3 @ X3048 @ X3049 @ X3050) @ (esk97_3 @ X3048 @ X3049 @ X3050)) @ X3050)|((X3049)=(X3050))|~(in @ (kpair @ (esk94_3 @ X3048 @ X3049 @ X3050) @ (esk95_3 @ X3048 @ X3049 @ X3050)) @ X3050)|~(breln1 @ X3048 @ X3050)|~(breln1 @ X3048 @ X3049))&(~(in @ (kpair @ (esk96_3 @ X3048 @ X3049 @ X3050) @ (esk97_3 @ X3048 @ X3049 @ X3050)) @ X3049)|((X3049)=(X3050))|~(in @ (kpair @ (esk94_3 @ X3048 @ X3049 @ X3050) @ (esk95_3 @ X3048 @ X3049 @ X3050)) @ X3050)|~(breln1 @ X3048 @ X3050)|~(breln1 @ X3048 @ X3049))))))))&((~(breln1 @ X3055 @ X3056)|(breln1 @ X3055 @ (breln1invset @ X3055 @ X3056)))&((~(breln1 @ X3057 @ X3058)|(~(in @ X3059 @ X3057)|(~(in @ X3060 @ X3057)|(~(in @ (kpair @ X3059 @ X3060) @ X3058)|(in @ (kpair @ X3060 @ X3059) @ (breln1invset @ X3057 @ X3058))))))&((~(breln1 @ X3061 @ X3062)|(~(in @ X3063 @ X3061)|(~(in @ X3064 @ X3061)|(~(in @ (kpair @ X3064 @ X3063) @ (breln1invset @ X3061 @ X3062))|(in @ (kpair @ X3063 @ X3064) @ X3062)))))&((~(breln1 @ X3065 @ X3066)|(~(breln1 @ X3065 @ X3067)|(breln1 @ X3065 @ (breln1compset @ X3065 @ X3066 @ X3067))))&((~(breln1 @ X3068 @ X3069)|(~(breln1 @ X3068 @ X3070)|(~(in @ X3071 @ X3068)|(~(in @ X3072 @ X3068)|(~(in @ X3073 @ X3068)|(~(in @ (kpair @ X3071 @ X3073) @ X3069)|(~(in @ (kpair @ X3073 @ X3072) @ X3070)|(in @ (kpair @ X3071 @ X3072) @ (breln1compset @ X3068 @ X3069 @ X3070)))))))))&(((((in @ (esk98_5 @ X3074 @ X3075 @ X3076 @ X3077 @ X3078) @ X3074)|~(in @ (kpair @ X3077 @ X3078) @ (breln1compset @ X3074 @ X3075 @ X3076))|~(in @ X3078 @ X3074)|~(in @ X3077 @ X3074)|~(breln1 @ X3074 @ X3076)|~(breln1 @ X3074 @ X3075))&((in @ (kpair @ X3077 @ (esk98_5 @ X3074 @ X3075 @ X3076 @ X3077 @ X3078)) @ X3075)|~(in @ (kpair @ X3077 @ X3078) @ (breln1compset @ X3074 @ X3075 @ X3076))|~(in @ X3078 @ X3074)|~(in @ X3077 @ X3074)|~(breln1 @ X3074 @ X3076)|~(breln1 @ X3074 @ X3075)))&((in @ (kpair @ (esk98_5 @ X3074 @ X3075 @ X3076 @ X3077 @ X3078) @ X3078) @ X3076)|~(in @ (kpair @ X3077 @ X3078) @ (breln1compset @ X3074 @ X3075 @ X3076))|~(in @ X3078 @ X3074)|~(in @ X3077 @ X3074)|~(breln1 @ X3074 @ X3076)|~(breln1 @ X3074 @ X3075)))&((((in @ (esk99_6 @ X3080 @ X3081 @ X3082 @ X3083 @ X3084 @ X3085) @ X3080)|(X3085)|~(in @ (kpair @ X3083 @ X3084) @ (breln1compset @ X3080 @ X3081 @ X3082))|~(in @ X3084 @ X3080)|~(in @ X3083 @ X3080)|~(breln1 @ X3080 @ X3082)|~(breln1 @ X3080 @ X3081))&(((in @ (kpair @ X3083 @ (esk99_6 @ X3080 @ X3081 @ X3082 @ X3083 @ X3084 @ X3085)) @ X3081)|(X3085)|~(in @ (kpair @ X3083 @ X3084) @ (breln1compset @ X3080 @ X3081 @ X3082))|~(in @ X3084 @ X3080)|~(in @ X3083 @ X3080)|~(breln1 @ X3080 @ X3082)|~(breln1 @ X3080 @ X3081))&(((in @ (kpair @ (esk99_6 @ X3080 @ X3081 @ X3082 @ X3083 @ X3084 @ X3085) @ X3084) @ X3082)|(X3085)|~(in @ (kpair @ X3083 @ X3084) @ (breln1compset @ X3080 @ X3081 @ X3082))|~(in @ X3084 @ X3080)|~(in @ X3083 @ X3080)|~(breln1 @ X3080 @ X3082)|~(breln1 @ X3080 @ X3081))&(~(X3085)|(X3085)|~(in @ (kpair @ X3083 @ X3084) @ (breln1compset @ X3080 @ X3081 @ X3082))|~(in @ X3084 @ X3080)|~(in @ X3083 @ X3080)|~(breln1 @ X3080 @ X3082)|~(breln1 @ X3080 @ X3081)))))&((~(breln1 @ X3087 @ X3088)|(~(breln1 @ X3087 @ X3089)|(breln1 @ X3087 @ (binunion @ X3088 @ X3089))))&((~(breln1 @ X3090 @ X3091)|(~(breln1 @ X3090 @ X3092)|(~(in @ X3093 @ X3090)|(~(in @ X3094 @ X3090)|(~(in @ (kpair @ X3093 @ X3094) @ X3091)|(in @ (kpair @ X3093 @ X3094) @ (binunion @ X3091 @ X3092)))))))&((~(breln1 @ X3095 @ X3096)|(~(breln1 @ X3095 @ X3097)|(~(in @ X3098 @ X3095)|(~(in @ X3099 @ X3095)|(~(in @ (kpair @ X3098 @ X3099) @ X3097)|(in @ (kpair @ X3098 @ X3099) @ (binunion @ X3096 @ X3097)))))))&((breln1 @ esk100_0 @ esk101_0)&((breln1 @ esk100_0 @ esk102_0)&((in @ esk103_0 @ esk100_0)&((in @ esk104_0 @ esk100_0)&(((in @ (kpair @ esk103_0 @ esk104_0) @ esk102_0)|(in @ (kpair @ esk103_0 @ esk104_0) @ esk101_0))&~(in @ (kpair @ esk103_0 @ esk104_0) @ (binunion @ esk101_0 @ esk102_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_377])])])])])])])).
0.23/0.76	thf(c_0_379, negated_conjecture, ~((in @ (kpair @ esk103_0 @ esk104_0) @ (binunion @ esk101_0 @ esk102_0))), inference(split_conjunct,[status(thm)],[c_0_378])).
0.23/0.76	thf(c_0_380, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_378])).
0.23/0.76	thf(c_0_381, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X4 @ X3))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_378])).
0.23/0.76	thf(c_0_382, negated_conjecture, ((in @ (kpair @ esk103_0 @ esk104_0) @ esk102_0)|(in @ (kpair @ esk103_0 @ esk104_0) @ esk101_0)), inference(split_conjunct,[status(thm)],[c_0_378])).
0.23/0.76	thf(c_0_383, negated_conjecture, ~((in @ (kpair @ esk103_0 @ esk104_0) @ esk101_0)), inference(spm,[status(thm)],[c_0_379, c_0_380])).
0.23/0.76	thf(c_0_384, negated_conjecture, ~((in @ (kpair @ esk103_0 @ esk104_0) @ esk102_0)), inference(spm,[status(thm)],[c_0_379, c_0_381])).
0.23/0.76	thf(c_0_385, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_382, c_0_383]), c_0_384]), ['proof']).
0.23/0.76	% SZS output end CNFRefutation
0.23/0.76	% Parsed axioms                        : 653
0.23/0.76	% Removed by relevancy pruning/SinE    : 349
0.23/0.76	% Initial clauses                      : 547
0.23/0.76	% Removed in clause preprocessing      : 38
0.23/0.76	% Initial clauses in saturation        : 509
0.23/0.76	% Processed clauses                    : 264
0.23/0.76	% ...of these trivial                  : 12
0.23/0.76	% ...subsumed                          : 67
0.23/0.76	% ...remaining for further processing  : 184
0.23/0.76	% Other redundant clauses eliminated   : 22
0.23/0.76	% Clauses deleted for lack of memory   : 0
0.23/0.76	% Backward-subsumed                    : 0
0.23/0.76	% Backward-rewritten                   : 2
0.23/0.76	% Generated clauses                    : 1012
0.23/0.76	% ...of the previous two non-redundant : 741
0.23/0.76	% ...aggressively subsumed             : 0
0.23/0.76	% Contextual simplify-reflections      : 0
0.23/0.76	% Paramodulations                      : 986
0.23/0.76	% Factorizations                       : 0
0.23/0.76	% NegExts                              : 0
0.23/0.76	% Equation resolutions                 : 25
0.23/0.76	% Disequality decompositions           : 0
0.23/0.76	% Total rewrite steps                  : 368
0.23/0.76	% ...of those cached                   : 305
0.23/0.76	% Propositional unsat checks           : 0
0.23/0.76	%    Propositional check models        : 0
0.23/0.76	%    Propositional check unsatisfiable : 0
0.23/0.76	%    Propositional clauses             : 0
0.23/0.76	%    Propositional clauses after purity: 0
0.23/0.76	%    Propositional unsat core size     : 0
0.23/0.76	%    Propositional preprocessing time  : 0.000
0.23/0.76	%    Propositional encoding time       : 0.000
0.23/0.76	%    Propositional solver time         : 0.000
0.23/0.76	%    Success case prop preproc time    : 0.000
0.23/0.76	%    Success case prop encoding time   : 0.000
0.23/0.76	%    Success case prop solver time     : 0.000
0.23/0.76	% Current number of processed clauses  : 172
0.23/0.76	%    Positive orientable unit clauses  : 74
0.23/0.76	%    Positive unorientable unit clauses: 0
0.23/0.76	%    Negative unit clauses             : 5
0.23/0.76	%    Non-unit-clauses                  : 93
0.23/0.76	% Current number of unprocessed clauses: 986
0.23/0.76	% ...number of literals in the above   : 2771
0.23/0.76	% Current number of archived formulas  : 0
0.23/0.76	% Current number of archived clauses   : 2
0.23/0.76	% Clause-clause subsumption calls (NU) : 1305
0.23/0.76	% Rec. Clause-clause subsumption calls : 1219
0.23/0.76	% Non-unit clause-clause subsumptions  : 53
0.23/0.76	% Unit Clause-clause subsumption calls : 110
0.23/0.76	% Rewrite failures with RHS unbound    : 0
0.23/0.76	% BW rewrite match attempts            : 12
0.23/0.76	% BW rewrite match successes           : 2
0.23/0.76	% Condensation attempts                : 0
0.23/0.76	% Condensation successes               : 0
0.23/0.76	% Termbank termtop insertions          : 95525
0.23/0.76	% Search garbage collected termcells   : 34042
0.23/0.76	
0.23/0.76	% -------------------------------------------------
0.23/0.76	% User time                : 0.122 s
0.23/0.76	% System time              : 0.015 s
0.23/0.76	% Total time               : 0.137 s
0.23/0.76	% Maximum resident set size: 12304 pages
0.23/0.76	
0.23/0.76	% -------------------------------------------------
0.23/0.76	% User time                : 0.140 s
0.23/0.76	% System time              : 0.023 s
0.23/0.76	% Total time               : 0.163 s
0.23/0.76	% Maximum resident set size: 5888 pages
0.23/0.76	% E exiting
0.23/0.77	EOF