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
0.09/0.35	% Computer : n029.cluster.edu
0.09/0.35	% Model    : x86_64 x86_64
0.09/0.35	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.35	% Memory   : 8046.5625MB
0.09/0.35	% OS       : Linux 6.8.0-71-generic
0.09/0.35	% CPULimit : 1440
0.09/0.35	% WCLimit  : 180
0.09/0.35	% DateTime : Mon Jul 27 12:00:31 UTC 2026
0.09/0.35	% CPUTime  : 
0.09/0.35	Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.13/0.39	Running higher-order theorem proving
0.20/0.47	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.qLAuhH5oxD/E---3.1_2798186.p
2.09/0.82	% Version: 3.5.1-ho
2.09/0.82	% Preprocessing class: HSLMSLSSLLLCHFA.
2.09/0.82	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.09/0.82	% Starting ehoh_best5 with 180s (1) cores
2.09/0.82	% Starting almost_fo_3_lam with 180s (1) cores
2.09/0.82	% Starting new_bool_5 with 180s (1) cores
2.09/0.82	% Starting pre_casc_3 with 180s (1) cores
2.09/0.82	% Starting ho_unfolding_8 with 180s (1) cores
2.09/0.82	% Starting new_ho_10_cnf2 with 180s (1) cores
2.09/0.82	% Starting new_bool_3 with 180s (1) cores
2.09/0.82	% Starting new_ho_5 with 180s (1) cores
2.09/0.82	% new_ho_5 with pid 2798206 completed with status 0
2.09/0.82	% Result found by new_ho_5
2.09/0.82	% Preprocessing class: HSLMSLSSLLLCHFA.
2.09/0.82	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.09/0.82	% Starting ehoh_best5 with 180s (1) cores
2.09/0.82	% Starting almost_fo_3_lam with 180s (1) cores
2.09/0.82	% Starting new_bool_5 with 180s (1) cores
2.09/0.82	% Starting pre_casc_3 with 180s (1) cores
2.09/0.82	% Starting ho_unfolding_8 with 180s (1) cores
2.09/0.82	% Starting new_ho_10_cnf2 with 180s (1) cores
2.09/0.82	% Starting new_bool_3 with 180s (1) cores
2.09/0.82	% Starting new_ho_5 with 180s (1) cores
2.09/0.82	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
2.09/0.82	% SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
2.09/0.82	% Search class: HGHSM-FSLM32-MHFMMSBN
2.09/0.82	% Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
2.09/0.82	% Starting SubtermCWHack with 19s (1) cores
2.09/0.82	% SubtermCWHack with pid 2798207 completed with status 0
2.09/0.82	% Result found by SubtermCWHack
2.09/0.82	% Preprocessing class: HSLMSLSSLLLCHFA.
2.09/0.82	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.09/0.82	% Starting ehoh_best5 with 180s (1) cores
2.09/0.82	% Starting almost_fo_3_lam with 180s (1) cores
2.09/0.82	% Starting new_bool_5 with 180s (1) cores
2.09/0.82	% Starting pre_casc_3 with 180s (1) cores
2.09/0.82	% Starting ho_unfolding_8 with 180s (1) cores
2.09/0.82	% Starting new_ho_10_cnf2 with 180s (1) cores
2.09/0.82	% Starting new_bool_3 with 180s (1) cores
2.09/0.82	% Starting new_ho_5 with 180s (1) cores
2.09/0.82	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
2.09/0.82	% SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
2.09/0.82	% Search class: HGHSM-FSLM32-MHFMMSBN
2.09/0.82	% Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
2.09/0.82	% Starting SubtermCWHack with 19s (1) cores
2.09/0.82	% Preprocessing time       : 0.006 s
2.09/0.82	
2.09/0.82	% Proof found!
2.09/0.82	% SZS status Theorem
2.09/0.82	% SZS output start CNFRefutation
2.09/0.82	thf(decl_23, type, in: $i > $i > $o).
2.09/0.82	thf(decl_24, type, exu: ($i > $o) > $o).
2.09/0.82	thf(decl_25, type, setextAx: $o).
2.09/0.82	thf(decl_26, type, emptyset: $i).
2.09/0.82	thf(decl_27, type, emptysetAx: $o).
2.09/0.82	thf(decl_28, type, setadjoin: $i > $i > $i).
2.09/0.82	thf(decl_29, type, setadjoinAx: $o).
2.09/0.82	thf(decl_30, type, powerset: $i > $i).
2.09/0.82	thf(decl_31, type, powersetAx: $o).
2.09/0.82	thf(decl_32, type, setunion: $i > $i).
2.09/0.82	thf(decl_33, type, setunionAx: $o).
2.09/0.82	thf(decl_34, type, omega: $i).
2.09/0.82	thf(decl_35, type, omega0Ax: $o).
2.09/0.82	thf(decl_36, type, omegaSAx: $o).
2.09/0.82	thf(decl_37, type, omegaIndAx: $o).
2.09/0.82	thf(decl_38, type, replAx: $o).
2.09/0.82	thf(decl_39, type, foundationAx: $o).
2.09/0.82	thf(decl_40, type, wellorderingAx: $o).
2.09/0.82	thf(decl_41, type, descr: ($i > $o) > $i).
2.09/0.82	thf(decl_42, type, descrp: $o).
2.09/0.82	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
2.09/0.82	thf(decl_44, type, dsetconstrI: $o).
2.09/0.82	thf(decl_45, type, dsetconstrEL: $o).
2.09/0.82	thf(decl_46, type, dsetconstrER: $o).
2.09/0.82	thf(decl_47, type, exuE1: $o).
2.09/0.82	thf(decl_48, type, prop2set: $o > $i).
2.09/0.82	thf(decl_49, type, prop2setE: $o).
2.09/0.82	thf(decl_50, type, emptysetE: $o).
2.09/0.82	thf(decl_51, type, emptysetimpfalse: $o).
2.09/0.82	thf(decl_52, type, notinemptyset: $o).
2.09/0.82	thf(decl_53, type, exuE3e: $o).
2.09/0.82	thf(decl_54, type, setext: $o).
2.09/0.82	thf(decl_55, type, emptyI: $o).
2.09/0.82	thf(decl_56, type, noeltsimpempty: $o).
2.09/0.82	thf(decl_57, type, setbeta: $o).
2.09/0.82	thf(decl_58, type, nonempty: $i > $o).
2.09/0.82	thf(decl_59, type, nonemptyE1: $o).
2.09/0.82	thf(decl_60, type, nonemptyI: $o).
2.09/0.82	thf(decl_61, type, nonemptyI1: $o).
2.09/0.82	thf(decl_62, type, setadjoinIL: $o).
2.09/0.82	thf(decl_63, type, emptyinunitempty: $o).
2.09/0.82	thf(decl_64, type, setadjoinIR: $o).
2.09/0.82	thf(decl_65, type, setadjoinE: $o).
2.09/0.82	thf(decl_66, type, setadjoinOr: $o).
2.09/0.82	thf(decl_67, type, setoftrueEq: $o).
2.09/0.82	thf(decl_68, type, powersetI: $o).
2.09/0.82	thf(decl_69, type, emptyinPowerset: $o).
2.09/0.82	thf(decl_70, type, emptyInPowerset: $o).
2.09/0.82	thf(decl_71, type, powersetE: $o).
2.09/0.82	thf(decl_72, type, setunionI: $o).
2.09/0.82	thf(decl_73, type, setunionE: $o).
2.09/0.82	thf(decl_74, type, subPowSU: $o).
2.09/0.82	thf(decl_75, type, exuE2: $o).
2.09/0.82	thf(decl_76, type, nonemptyImpWitness: $o).
2.09/0.82	thf(decl_77, type, uniqinunit: $o).
2.09/0.82	thf(decl_78, type, notinsingleton: $o).
2.09/0.82	thf(decl_79, type, eqinunit: $o).
2.09/0.82	thf(decl_80, type, singletonsswitch: $o).
2.09/0.82	thf(decl_81, type, upairsetE: $o).
2.09/0.82	thf(decl_82, type, upairsetIL: $o).
2.09/0.82	thf(decl_83, type, upairsetIR: $o).
2.09/0.82	thf(decl_84, type, emptyE1: $o).
2.09/0.82	thf(decl_85, type, vacuousDall: $o).
2.09/0.82	thf(decl_86, type, quantDeMorgan1: $o).
2.09/0.82	thf(decl_87, type, quantDeMorgan2: $o).
2.09/0.82	thf(decl_88, type, quantDeMorgan3: $o).
2.09/0.82	thf(decl_89, type, quantDeMorgan4: $o).
2.09/0.82	thf(decl_90, type, prop2setI: $o).
2.09/0.82	thf(decl_91, type, set2prop: $i > $o).
2.09/0.82	thf(decl_92, type, prop2set2propI: $o).
2.09/0.82	thf(decl_93, type, notdexE: $o).
2.09/0.82	thf(decl_94, type, notdallE: $o).
2.09/0.82	thf(decl_95, type, exuI1: $o).
2.09/0.82	thf(decl_96, type, exuI3: $o).
2.09/0.82	thf(decl_97, type, exuI2: $o).
2.09/0.82	thf(decl_98, type, inCongP: $o).
2.09/0.82	thf(decl_99, type, in__Cong: $o).
2.09/0.82	thf(decl_100, type, exuE3u: $o).
2.09/0.82	thf(decl_101, type, exu__Cong: $o).
2.09/0.82	thf(decl_102, type, emptyset__Cong: $o).
2.09/0.82	thf(decl_103, type, setadjoin__Cong: $o).
2.09/0.82	thf(decl_104, type, powerset__Cong: $o).
2.09/0.82	thf(decl_105, type, setunion__Cong: $o).
2.09/0.82	thf(decl_106, type, omega__Cong: $o).
2.09/0.82	thf(decl_107, type, exuEu: $o).
2.09/0.82	thf(decl_108, type, descr__Cong: $o).
2.09/0.82	thf(decl_109, type, dsetconstr__Cong: $o).
2.09/0.82	thf(decl_110, type, subset: $i > $i > $o).
2.09/0.82	thf(decl_113, type, subsetI1: $o).
2.09/0.82	thf(decl_114, type, eqimpsubset2: $o).
2.09/0.82	thf(decl_115, type, eqimpsubset1: $o).
2.09/0.82	thf(decl_116, type, subsetI2: $o).
2.09/0.82	thf(decl_117, type, emptysetsubset: $o).
2.09/0.82	thf(decl_118, type, subsetE: $o).
2.09/0.82	thf(decl_119, type, subsetE2: $o).
2.09/0.82	thf(decl_120, type, notsubsetI: $o).
2.09/0.82	thf(decl_121, type, notequalI1: $o).
2.09/0.82	thf(decl_122, type, notequalI2: $o).
2.09/0.82	thf(decl_123, type, subsetRefl: $o).
2.09/0.82	thf(decl_124, type, subsetTrans: $o).
2.09/0.82	thf(decl_125, type, setadjoinSub: $o).
2.09/0.82	thf(decl_126, type, setadjoinSub2: $o).
2.09/0.82	thf(decl_127, type, subset2powerset: $o).
2.09/0.82	thf(decl_128, type, setextsub: $o).
2.09/0.82	thf(decl_129, type, subsetemptysetimpeq: $o).
2.09/0.82	thf(decl_130, type, powersetI1: $o).
2.09/0.82	thf(decl_131, type, powersetE1: $o).
2.09/0.82	thf(decl_132, type, inPowerset: $o).
2.09/0.82	thf(decl_133, type, powersetsubset: $o).
2.09/0.82	thf(decl_134, type, sepInPowerset: $o).
2.09/0.82	thf(decl_135, type, sepSubset: $o).
2.09/0.82	thf(decl_136, type, binunion: $i > $i > $i).
2.09/0.82	thf(decl_137, type, binunionIL: $o).
2.09/0.82	thf(decl_138, type, upairset2IR: $o).
2.09/0.82	thf(decl_139, type, binunionIR: $o).
2.09/0.82	thf(decl_140, type, binunionEcases: $o).
2.09/0.82	thf(decl_141, type, binunionE: $o).
2.09/0.82	thf(decl_142, type, binunionLsub: $o).
2.09/0.82	thf(decl_143, type, binunionRsub: $o).
2.09/0.82	thf(decl_144, type, binintersect: $i > $i > $i).
2.09/0.82	thf(decl_145, type, binintersectI: $o).
2.09/0.82	thf(decl_146, type, binintersectSubset5: $o).
2.09/0.82	thf(decl_147, type, binintersectEL: $o).
2.09/0.82	thf(decl_148, type, binintersectLsub: $o).
2.09/0.82	thf(decl_149, type, binintersectSubset2: $o).
2.09/0.82	thf(decl_150, type, binintersectSubset3: $o).
2.09/0.82	thf(decl_151, type, binintersectER: $o).
2.09/0.82	thf(decl_152, type, disjointsetsI1: $o).
2.09/0.82	thf(decl_153, type, binintersectRsub: $o).
2.09/0.82	thf(decl_154, type, binintersectSubset4: $o).
2.09/0.82	thf(decl_155, type, binintersectSubset1: $o).
2.09/0.82	thf(decl_156, type, bs114d: $o).
2.09/0.82	thf(decl_158, type, setminus: $i > $i > $i).
2.09/0.82	thf(decl_159, type, setminusI: $o).
2.09/0.82	thf(decl_160, type, setminusEL: $o).
2.09/0.82	thf(decl_161, type, setminusER: $o).
2.09/0.82	thf(decl_162, type, setminusSubset2: $o).
2.09/0.82	thf(decl_163, type, setminusERneg: $o).
2.09/0.82	thf(decl_164, type, setminusELneg: $o).
2.09/0.82	thf(decl_165, type, setminusILneg: $o).
2.09/0.82	thf(decl_166, type, setminusIRneg: $o).
2.09/0.82	thf(decl_167, type, setminusLsub: $o).
2.09/0.82	thf(decl_168, type, setminusSubset1: $o).
2.09/0.82	thf(decl_169, type, symdiff: $i > $i > $i).
2.09/0.82	thf(decl_170, type, symdiffE: $o).
2.09/0.82	thf(decl_171, type, symdiffI1: $o).
2.09/0.82	thf(decl_172, type, symdiffI2: $o).
2.09/0.82	thf(decl_173, type, symdiffIneg1: $o).
2.09/0.82	thf(decl_174, type, symdiffIneg2: $o).
2.09/0.82	thf(decl_175, type, iskpair: $i > $o).
2.09/0.82	thf(decl_176, type, secondinupair: $o).
2.09/0.82	thf(decl_177, type, setukpairIL: $o).
2.09/0.82	thf(decl_178, type, setukpairIR: $o).
2.09/0.82	thf(decl_179, type, kpairiskpair: $o).
2.09/0.82	thf(decl_180, type, kpair: $i > $i > $i).
2.09/0.82	thf(decl_181, type, kpairp: $o).
2.09/0.82	thf(decl_182, type, cartprod: $i > $i > $i).
2.09/0.82	thf(decl_183, type, singletonsubset: $o).
2.09/0.82	thf(decl_184, type, singletoninpowerset: $o).
2.09/0.82	thf(decl_185, type, singletoninpowunion: $o).
2.09/0.82	thf(decl_186, type, upairset2E: $o).
2.09/0.82	thf(decl_187, type, upairsubunion: $o).
2.09/0.82	thf(decl_188, type, upairinpowunion: $o).
2.09/0.82	thf(decl_189, type, ubforcartprodlem1: $o).
2.09/0.82	thf(decl_190, type, ubforcartprodlem2: $o).
2.09/0.82	thf(decl_191, type, ubforcartprodlem3: $o).
2.09/0.82	thf(decl_192, type, cartprodpairin: $o).
2.09/0.82	thf(decl_193, type, cartprodmempair1: $o).
2.09/0.82	thf(decl_194, type, cartprodmempair: $o).
2.09/0.82	thf(decl_195, type, setunionE2: $o).
2.09/0.82	thf(decl_196, type, setunionsingleton1: $o).
2.09/0.82	thf(decl_197, type, setunionsingleton2: $o).
2.09/0.82	thf(decl_198, type, setunionsingleton: $o).
2.09/0.82	thf(decl_199, type, singleton: $i > $o).
2.09/0.82	thf(decl_200, type, singletonprop: $o).
2.09/0.82	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
2.09/0.82	thf(decl_202, type, ex1E1: $o).
2.09/0.82	thf(decl_203, type, ex1I: $o).
2.09/0.82	thf(decl_204, type, ex1I2: $o).
2.09/0.82	thf(decl_205, type, singletonsuniq: $o).
2.09/0.82	thf(decl_210, type, setukpairinjL1: $o).
2.09/0.82	thf(decl_211, type, kfstsingleton: $o).
2.09/0.82	thf(decl_212, type, theprop: $o).
2.09/0.82	thf(decl_213, type, kfst: $i > $i).
2.09/0.82	thf(decl_214, type, kfstpairEq: $o).
2.09/0.82	thf(decl_215, type, cartprodfstin: $o).
2.09/0.82	thf(decl_216, type, setukpairinjL2: $o).
2.09/0.82	thf(decl_217, type, setukpairinjL: $o).
2.09/0.82	thf(decl_218, type, setukpairinjR11: $o).
2.09/0.82	thf(decl_219, type, setukpairinjR12: $o).
2.09/0.82	thf(decl_220, type, setukpairinjR1: $o).
2.09/0.82	thf(decl_221, type, upairequniteq: $o).
2.09/0.82	thf(decl_222, type, setukpairinjR2: $o).
2.09/0.82	thf(decl_223, type, setukpairinjR: $o).
2.09/0.82	thf(decl_224, type, ksndsingleton: $o).
2.09/0.82	thf(decl_225, type, ksnd: $i > $i).
2.09/0.82	thf(decl_226, type, ksndpairEq: $o).
2.09/0.82	thf(decl_227, type, kpairsurjEq: $o).
2.09/0.82	thf(decl_228, type, cartprodsndin: $o).
2.09/0.82	thf(decl_229, type, cartprodpairmemEL: $o).
2.09/0.82	thf(decl_230, type, cartprodpairmemER: $o).
2.09/0.82	thf(decl_231, type, cartprodmempaircEq: $o).
2.09/0.82	thf(decl_232, type, cartprodfstpairEq: $o).
2.09/0.82	thf(decl_233, type, cartprodsndpairEq: $o).
2.09/0.82	thf(decl_234, type, cartprodpairsurjEq: $o).
2.09/0.82	thf(decl_235, type, breln: $i > $i > $i > $o).
2.09/0.82	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
2.09/0.82	thf(decl_237, type, dpsetconstrI: $o).
2.09/0.82	thf(decl_238, type, dpsetconstrSub: $o).
2.09/0.82	thf(decl_239, type, setOfPairsIsBReln: $o).
2.09/0.82	thf(decl_240, type, dpsetconstrERa: $o).
2.09/0.82	thf(decl_241, type, dpsetconstrEL1: $o).
2.09/0.82	thf(decl_242, type, dpsetconstrEL2: $o).
2.09/0.82	thf(decl_243, type, dpsetconstrER: $o).
2.09/0.82	thf(decl_244, type, func: $i > $i > $i > $o).
2.09/0.82	thf(decl_245, type, funcSet: $i > $i > $i).
2.09/0.82	thf(decl_246, type, funcImageSingleton: $o).
2.09/0.82	thf(decl_247, type, apProp: $o).
2.09/0.82	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
2.09/0.82	thf(decl_249, type, app: $o).
2.09/0.82	thf(decl_250, type, infuncsetfunc: $o).
2.09/0.82	thf(decl_251, type, ap2p: $o).
2.09/0.82	thf(decl_252, type, funcinfuncset: $o).
2.09/0.82	thf(decl_253, type, lamProp: $o).
2.09/0.82	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
2.09/0.82	thf(decl_255, type, lamp: $o).
2.09/0.82	thf(decl_256, type, lam2p: $o).
2.09/0.82	thf(decl_257, type, brelnall1: $o).
2.09/0.82	thf(decl_258, type, brelnall2: $o).
2.09/0.82	thf(decl_259, type, ex1E2: $o).
2.09/0.82	thf(decl_260, type, funcGraphProp1: $o).
2.09/0.82	thf(decl_261, type, funcGraphProp3: $o).
2.09/0.82	thf(decl_262, type, funcGraphProp2: $o).
2.09/0.82	thf(decl_263, type, funcextLem: $o).
2.09/0.82	thf(decl_264, type, funcGraphProp4: $o).
2.09/0.82	thf(decl_265, type, subbreln: $o).
2.09/0.82	thf(decl_266, type, eqbreln: $o).
2.09/0.82	thf(decl_267, type, funcext: $o).
2.09/0.82	thf(decl_268, type, funcext2: $o).
2.09/0.82	thf(decl_269, type, ap2apEq1: $o).
2.09/0.82	thf(decl_270, type, ap2apEq2: $o).
2.09/0.82	thf(decl_271, type, beta1: $o).
2.09/0.82	thf(decl_272, type, eta1: $o).
2.09/0.82	thf(decl_273, type, lam2lamEq: $o).
2.09/0.82	thf(decl_274, type, beta2: $o).
2.09/0.82	thf(decl_275, type, eta2: $o).
2.09/0.82	thf(decl_276, type, iffalseProp1: $o).
2.09/0.82	thf(decl_277, type, iffalseProp2: $o).
2.09/0.82	thf(decl_278, type, iftrueProp1: $o).
2.09/0.82	thf(decl_279, type, iftrueProp2: $o).
2.09/0.82	thf(decl_280, type, ifSingleton: $o).
2.09/0.82	thf(decl_281, type, if: $i > $o > $i > $i > $i).
2.09/0.82	thf(decl_282, type, ifp: $o).
2.09/0.82	thf(decl_283, type, theeq: $o).
2.09/0.82	thf(decl_284, type, iftrue: $o).
2.09/0.82	thf(decl_285, type, iffalse: $o).
2.09/0.82	thf(decl_286, type, iftrueorfalse: $o).
2.09/0.82	thf(decl_287, type, binintersectT_lem: $o).
2.09/0.82	thf(decl_288, type, binunionT_lem: $o).
2.09/0.82	thf(decl_289, type, powersetT_lem: $o).
2.09/0.82	thf(decl_290, type, setminusT_lem: $o).
2.09/0.82	thf(decl_291, type, complementT_lem: $o).
2.09/0.82	thf(decl_292, type, setextT: $o).
2.09/0.82	thf(decl_293, type, subsetTI: $o).
2.09/0.82	thf(decl_294, type, powersetTI1: $o).
2.09/0.82	thf(decl_295, type, powersetTE1: $o).
2.09/0.82	thf(decl_296, type, complementTI1: $o).
2.09/0.82	thf(decl_297, type, complementTE1: $o).
2.09/0.82	thf(decl_298, type, binintersectTELcontra: $o).
2.09/0.82	thf(decl_299, type, binintersectTERcontra: $o).
2.09/0.82	thf(decl_300, type, contrasubsetT: $o).
2.09/0.82	thf(decl_301, type, contrasubsetT1: $o).
2.09/0.82	thf(decl_302, type, contrasubsetT2: $o).
2.09/0.82	thf(decl_303, type, contrasubsetT3: $o).
2.09/0.82	thf(decl_304, type, doubleComplementI1: $o).
2.09/0.82	thf(decl_305, type, doubleComplementE1: $o).
2.09/0.82	thf(decl_306, type, doubleComplementSub1: $o).
2.09/0.82	thf(decl_307, type, doubleComplementSub2: $o).
2.09/0.82	thf(decl_308, type, doubleComplementEq: $o).
2.09/0.82	thf(decl_309, type, complementTnotintersectT: $o).
2.09/0.82	thf(decl_310, type, complementImpComplementIntersect: $o).
2.09/0.82	thf(decl_311, type, complementSubsetComplementIntersect: $o).
2.09/0.82	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
2.09/0.82	thf(decl_313, type, contraSubsetComplement: $o).
2.09/0.82	thf(decl_314, type, complementTcontraSubset: $o).
2.09/0.82	thf(decl_315, type, binunionTILcontra: $o).
2.09/0.82	thf(decl_316, type, binunionTIRcontra: $o).
2.09/0.82	thf(decl_317, type, inIntersectImpInUnion: $o).
2.09/0.82	thf(decl_318, type, inIntersectImpInUnion2: $o).
2.09/0.82	thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
2.09/0.82	thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
2.09/0.82	thf(decl_321, type, inComplementUnionImpNotIn1: $o).
2.09/0.82	thf(decl_322, type, inComplementUnionImpInComplement1: $o).
2.09/0.82	thf(decl_323, type, binunionTE: $o).
2.09/0.82	thf(decl_324, type, binunionTEcontra: $o).
2.09/0.82	thf(decl_325, type, demorgan2a1: $o).
2.09/0.82	thf(decl_326, type, complementUnionInPowersetComplement: $o).
2.09/0.82	thf(decl_327, type, demorgan2a2: $o).
2.09/0.82	thf(decl_328, type, demorgan1a: $o).
2.09/0.82	thf(decl_329, type, demorgan1b: $o).
2.09/0.82	thf(decl_330, type, demorgan1: $o).
2.09/0.82	thf(decl_331, type, demorgan2a: $o).
2.09/0.82	thf(decl_332, type, demorgan2b2: $o).
2.09/0.82	thf(decl_333, type, demorgan2b: $o).
2.09/0.82	thf(decl_334, type, demorgan2: $o).
2.09/0.82	thf(decl_335, type, woz13rule0: $o).
2.09/0.82	thf(decl_336, type, woz13rule1: $o).
2.09/0.82	thf(decl_337, type, woz13rule2: $o).
2.09/0.82	thf(decl_338, type, woz13rule3: $o).
2.09/0.82	thf(decl_339, type, woz13rule4: $o).
2.09/0.82	thf(decl_340, type, woz1_1: $o).
2.09/0.82	thf(decl_341, type, woz1_2: $o).
2.09/0.82	thf(decl_342, type, woz1_3: $o).
2.09/0.82	thf(decl_343, type, woz1_4: $o).
2.09/0.82	thf(decl_344, type, woz1_5: $o).
2.09/0.82	thf(decl_345, type, breln1: $i > $i > $o).
2.09/0.82	thf(decl_346, type, breln1all2: $o).
2.09/0.82	thf(decl_347, type, breln1Set: $i > $i).
2.09/0.82	thf(decl_348, type, breln1SetBreln1: $o).
2.09/0.82	thf(decl_354, type, reflwellordering: $i > $i > $o).
2.09/0.82	thf(decl_355, type, choice2fnsingleton: $o).
2.09/0.82	thf(decl_356, type, setOfPairsIsBReln1: $o).
2.09/0.82	thf(decl_357, type, breln1all1: $o).
2.09/0.82	thf(decl_358, type, subbreln1: $o).
2.09/0.82	thf(decl_359, type, eqbreln1: $o).
2.09/0.82	thf(decl_360, type, breln1invset: $i > $i > $i).
2.09/0.82	thf(decl_361, type, breln1invprop: $o).
2.09/0.82	thf(decl_362, type, breln1invI: $o).
2.09/0.82	thf(decl_363, type, breln1invE: $o).
2.09/0.82	thf(decl_364, type, breln1compset: $i > $i > $i > $i).
2.09/0.82	thf(decl_365, type, breln1compprop: $o).
2.09/0.82	thf(decl_366, type, breln1compI: $o).
2.09/0.82	thf(decl_367, type, breln1compE: $o).
2.09/0.82	thf(decl_368, type, breln1compEex: $o).
2.09/0.82	thf(decl_369, type, breln1unionprop: $o).
2.09/0.82	thf(decl_370, type, breln1unionIL: $o).
2.09/0.82	thf(decl_371, type, breln1unionIR: $o).
2.09/0.82	thf(decl_372, type, breln1unionI: $o).
2.09/0.82	thf(decl_373, type, breln1unionE: $o).
2.09/0.82	thf(decl_374, type, breln1unionEcases: $o).
2.09/0.82	thf(decl_375, type, breln1unionCommutes: $o).
2.09/0.82	thf(decl_376, type, woz2Ex: $o).
2.09/0.82	thf(decl_377, type, woz2W: $o).
2.09/0.82	thf(decl_378, type, woz2A: $o).
2.09/0.82	thf(decl_379, type, woz2B: $o).
2.09/0.82	thf(decl_380, type, image1Ex: $o).
2.09/0.82	thf(decl_381, type, image1Ex1: $o).
2.09/0.82	thf(decl_382, type, image1: $i > ($i > $i) > $i).
2.09/0.82	thf(decl_383, type, image1Equiv: $o).
2.09/0.82	thf(decl_384, type, image1E: $o).
2.09/0.82	thf(decl_385, type, image1I: $o).
2.09/0.82	thf(decl_386, type, injective: $i > $i > $i > $o).
2.09/0.82	thf(decl_387, type, injFuncSet: $i > $i > $i).
2.09/0.82	thf(decl_388, type, injFuncInInjFuncSet: $o).
2.09/0.82	thf(decl_389, type, injFuncSetFuncIn: $o).
2.09/0.82	thf(decl_390, type, injFuncSetFuncInj: $o).
2.09/0.82	thf(decl_391, type, surjective: $i > $i > $i > $o).
2.09/0.82	thf(decl_392, type, surjFuncSet: $i > $i > $i).
2.09/0.82	thf(decl_393, type, surjFuncSetFuncIn: $o).
2.09/0.82	thf(decl_394, type, surjFuncSetFuncSurj: $o).
2.09/0.82	thf(decl_395, type, leftInvIsSurj: $o).
2.09/0.82	thf(decl_396, type, surjCantorThm: $o).
2.09/0.82	thf(decl_397, type, foundation2: $o).
2.09/0.82	thf(decl_398, type, notinself: $o).
2.09/0.82	thf(decl_399, type, notinself2: $o).
2.09/0.82	thf(decl_400, type, omegaS: $i > $i).
2.09/0.82	thf(decl_401, type, omegaSp: $o).
2.09/0.82	thf(decl_402, type, omegaSclos: $o).
2.09/0.82	thf(decl_403, type, peano0notS: $o).
2.09/0.82	thf(decl_407, type, peanoSinj: $o).
2.09/0.82	thf(decl_409, type, transitiveset: $i > $o).
2.09/0.82	thf(decl_410, type, transitivesetOp1: $o).
2.09/0.82	thf(decl_411, type, epred1_0: $o).
2.09/0.82	thf(decl_412, type, esk1_2: $i > $i > $i).
2.09/0.82	thf(decl_413, type, esk2_2: $i > $i > $i).
2.09/0.82	thf(decl_414, type, esk3_2: $i > $i > $i).
2.09/0.82	thf(decl_415, type, esk4_1: $i > $i).
2.09/0.82	thf(decl_416, type, esk5_2: ($i > $i > $o) > $i > $i).
2.09/0.82	thf(decl_417, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
2.09/0.82	thf(decl_418, type, esk7_2: ($i > $i > $o) > $i > $i).
2.09/0.82	thf(decl_419, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
2.09/0.82	thf(decl_420, type, esk9_1: $i > $i).
2.09/0.82	thf(decl_421, type, esk10_2: ($i > $o) > $i > $i).
2.09/0.82	thf(decl_422, type, esk11_2: ($i > $o) > $i > $i).
2.09/0.82	thf(decl_423, type, esk12_1: ($i > $o) > $i).
2.09/0.82	thf(decl_424, type, esk13_2: ($i > $o) > $i > $i).
2.09/0.82	thf(decl_425, type, esk14_1: ($i > $o) > $i).
2.09/0.82	thf(decl_426, type, esk15_2: $i > $i > $i).
2.09/0.82	thf(decl_427, type, esk16_2: $i > $i > $i).
2.09/0.82	thf(decl_428, type, esk17_1: $i > $i).
2.09/0.82	thf(decl_429, type, esk18_1: $i > $i).
2.09/0.82	thf(decl_430, type, esk19_1: $i > $i).
2.09/0.82	thf(decl_431, type, esk20_2: $i > $i > $i).
2.09/0.82	thf(decl_432, type, esk21_3: $i > $i > $o > $i).
2.09/0.82	thf(decl_433, type, esk22_2: ($i > $o) > $i > $i).
2.09/0.82	thf(decl_434, type, esk23_1: ($i > $o) > $i).
2.09/0.82	thf(decl_435, type, esk24_1: $i > $i).
2.09/0.82	thf(decl_436, type, esk25_2: $i > ($i > $o) > $i).
2.09/0.82	thf(decl_437, type, esk26_2: $i > ($i > $o) > $i).
2.09/0.82	thf(decl_438, type, esk27_2: $i > ($i > $o) > $i).
2.09/0.82	thf(decl_439, type, esk28_2: $i > ($i > $o) > $i).
2.09/0.82	thf(decl_440, type, esk29_2: $i > ($i > $o) > $i).
2.09/0.82	thf(decl_441, type, esk30_2: $i > ($i > $o) > $i).
2.09/0.82	thf(decl_442, type, esk31_2: ($i > $o) > $i > $i).
2.09/0.82	thf(decl_443, type, esk32_1: ($i > $o) > $i).
2.09/0.82	thf(decl_444, type, esk33_1: ($i > $o) > $i).
2.09/0.82	thf(decl_445, type, esk34_1: ($i > $o) > $i).
2.09/0.82	thf(decl_446, type, esk35_1: ($i > $o) > $i).
2.09/0.82	thf(decl_447, type, esk36_2: ($i > $o) > $i > $i).
2.09/0.82	thf(decl_448, type, esk37_1: ($i > $o) > $i).
2.09/0.82	thf(decl_449, type, esk38_2: ($i > $o) > $i > $i).
2.09/0.82	thf(decl_450, type, esk39_2: ($i > $o) > ($i > $o) > $i).
2.09/0.82	thf(decl_451, type, esk40_2: ($i > $o) > ($i > $o) > $i).
2.09/0.82	thf(decl_452, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
2.09/0.82	thf(decl_453, type, esk42_2: ($i > $o) > ($i > $o) > $i).
2.09/0.82	thf(decl_454, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
2.09/0.82	thf(decl_455, type, esk44_2: ($i > $o) > ($i > $o) > $i).
2.09/0.82	thf(decl_456, type, esk45_2: ($i > $o) > $i > $i).
2.09/0.82	thf(decl_457, type, esk46_2: ($i > $o) > ($i > $o) > $i).
2.09/0.82	thf(decl_458, type, esk47_2: ($i > $o) > ($i > $o) > $i).
2.09/0.82	thf(decl_459, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
2.09/0.83	thf(decl_460, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
2.09/0.83	thf(decl_461, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.09/0.83	thf(decl_462, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.09/0.83	thf(decl_463, type, esk52_2: $i > $i > $i).
2.09/0.83	thf(decl_464, type, esk53_2: $i > $i > $i).
2.09/0.83	thf(decl_465, type, esk54_2: $i > $i > $i).
2.09/0.83	thf(decl_466, type, esk55_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_467, type, esk56_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_468, type, esk57_2: $i > $i > $i).
2.09/0.83	thf(decl_469, type, esk58_2: $i > ($i > $o) > $i).
2.09/0.83	thf(decl_470, type, esk59_2: $i > ($i > $o) > $i).
2.09/0.83	thf(decl_471, type, esk60_2: $i > ($i > $o) > $i).
2.09/0.83	thf(decl_472, type, esk61_3: $i > ($i > $o) > $i > $i).
2.09/0.83	thf(decl_473, type, esk62_2: $i > ($i > $o) > $i).
2.09/0.83	thf(decl_474, type, esk63_2: $i > ($i > $o) > $i).
2.09/0.83	thf(decl_475, type, esk64_3: $i > $i > ($i > $i) > $i).
2.09/0.83	thf(decl_476, type, esk65_3: $i > $i > ($i > $i) > $i).
2.09/0.83	thf(decl_477, type, esk66_3: $i > $i > ($i > $i) > $i).
2.09/0.83	thf(decl_478, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
2.09/0.83	thf(decl_479, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
2.09/0.83	thf(decl_480, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
2.09/0.83	thf(decl_481, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
2.09/0.83	thf(decl_482, type, esk71_4: $i > $i > $i > $i > $i).
2.09/0.83	thf(decl_483, type, esk72_4: $i > $i > $i > $i > $i).
2.09/0.83	thf(decl_484, type, esk73_4: $i > $i > $i > $i > $i).
2.09/0.83	thf(decl_485, type, esk74_4: $i > $i > $i > $i > $i).
2.09/0.83	thf(decl_486, type, esk75_4: $i > $i > $i > $i > $i).
2.09/0.83	thf(decl_487, type, esk76_4: $i > $i > $i > $i > $i).
2.09/0.83	thf(decl_488, type, esk77_4: $i > $i > $i > $i > $i).
2.09/0.83	thf(decl_489, type, esk78_4: $i > $i > $i > $i > $i).
2.09/0.83	thf(decl_490, type, esk79_4: $i > $i > $i > $i > $i).
2.09/0.83	thf(decl_491, type, esk80_3: $i > $i > ($i > $i) > $i).
2.09/0.83	thf(decl_492, type, esk81_3: $i > $i > ($i > $i) > $i).
2.09/0.83	thf(decl_493, type, esk82_3: $i > $i > ($i > $i) > $i).
2.09/0.83	thf(decl_494, type, esk83_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_495, type, esk84_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_496, type, esk85_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_497, type, esk86_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_498, type, esk87_3: $i > $i > ($i > $o) > $i).
2.09/0.83	thf(decl_499, type, esk88_3: $i > $i > ($i > $o) > $i).
2.09/0.83	thf(decl_500, type, esk89_3: $i > $i > ($i > $i > $o) > $i).
2.09/0.83	thf(decl_501, type, esk90_3: $i > $i > ($i > $o) > $i).
2.09/0.83	thf(decl_502, type, esk91_3: $i > $i > ($i > $o) > $i).
2.09/0.83	thf(decl_503, type, esk92_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_504, type, esk93_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_505, type, esk94_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_506, type, esk95_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_507, type, esk96_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_508, type, esk97_3: $i > $i > $i > $i).
2.09/0.83	thf(decl_509, type, esk98_5: $i > $i > $i > $i > $i > $i).
2.09/0.83	thf(decl_510, type, esk99_6: $i > $i > $i > $i > $i > $o > $i).
2.09/0.83	thf(decl_511, type, esk100_2: $i > ($i > $i) > $i).
2.09/0.83	thf(decl_512, type, esk101_3: $i > ($i > $i) > $i > $i).
2.09/0.83	thf(decl_513, type, esk102_2: $i > ($i > $i) > $i).
2.09/0.83	thf(decl_514, type, esk103_3: $i > ($i > $i) > $i > $i).
2.09/0.83	thf(decl_515, type, esk104_3: $i > ($i > $i) > $i > $i).
2.09/0.83	thf(decl_516, type, esk105_3: $i > ($i > $i) > $i > $i).
2.09/0.83	thf(decl_517, type, esk106_3: $i > ($i > $i) > $i > $i).
2.09/0.83	thf(decl_518, type, esk107_3: $i > ($i > $i) > $i > $i).
2.09/0.83	thf(decl_519, type, esk108_3: $i > $i > ($i > $i) > $i).
2.09/0.83	thf(decl_520, type, esk109_4: $i > $i > ($i > $i) > $i > $i).
2.09/0.83	thf(decl_521, type, esk110_1: $i > $i).
2.09/0.83	thf(decl_522, type, esk111_1: $i > $i).
2.09/0.83	thf(decl_523, type, esk112_0: $i).
2.09/0.83	thf(decl_524, type, esk113_0: $i).
2.09/0.83	thf(decl_525, type, esk114_0: $i).
2.09/0.83	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', exu__Cong)).
2.09/0.83	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', exu)).
2.09/0.83	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', exuE3u)).
2.09/0.83	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', exuI3)).
2.09/0.83	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', exuI1)).
2.09/0.83	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', nonempty)).
2.09/0.83	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', exuE1)).
2.09/0.83	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', descrp)).
2.09/0.83	thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', image1Ex1)).
2.09/0.83	thf(transitiveset, axiom, ((transitiveset)=(^[X4:$i]:(![X21:$i]:((((in @ X21 @ X4))=>((subset @ X21 @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', transitiveset)).
2.09/0.83	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', descr__Cong)).
2.09/0.83	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', exuEu)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', exuI2)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', exuE2)).
2.09/0.83	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', nonemptyI)).
2.09/0.83	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', exuE3e)).
2.09/0.83	thf(replAx, axiom, ((replAx)<=>![X6:$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.qLAuhH5oxD/E---3.1_2798186.p', replAx)).
2.09/0.83	thf(binintTransitive, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((((omegaSAx)=>(((replAx)=>(((((((dsetconstrER)=>(((((((exuE3e)=>((setext)=>(((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>(((setadjoinIL)=>(((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>(((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((((subPowSU)=>((exuE2)=>(((uniqinunit)=>((notinsingleton)=>(((singletonsswitch)=>((upairsetE)=>(((upairsetIR)=>((((quantDeMorgan1)=>(((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>((((((exuI2)=>((inCongP)=>((((((setadjoin__Cong)=>(((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((((subset2powerset)=>((((powersetI1)=>((((((sepSubset)=>((((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>(((((binintersectSubset2)=>((((disjointsetsI1)=>(((((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((((setminusSubset1)=>((symdiffE)=>(((((symdiffIneg2)=>(((setukpairIL)=>((((((singletoninpowerset)=>(((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>(((setunionsingleton)=>(((ex1E1)=>((((singletonsuniq)=>((((theprop)=>((((setukpairinjL2)=>((setukpairinjL)=>(((setukpairinjR12)=>((setukpairinjR1)=>(((setukpairinjR2)=>(((((((cartprodpairmemEL)=>(((((cartprodsndpairEq)=>(((((((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>(((ap2p)=>(((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>(((ex1E2)=>((((funcGraphProp2)=>(((funcGraphProp4)=>((((funcext)=>((funcext2)=>((ap2apEq1)=>(((beta1)=>((eta1)=>(((beta2)=>((((iffalseProp2)=>(((((((iftrue)=>(((iftrueorfalse)=>(((binunionT_lem)=>(((((setextT)=>((((powersetTE1)=>((complementTI1)=>((((((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>(((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>(((complementImpComplementIntersect)=>((((((binunionTILcontra)=>((((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>(((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((((((demorgan1a)=>(((demorgan1)=>(((((demorgan2)=>((woz13rule0)=>((((((((woz1_3)=>(((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>(((setOfPairsIsBReln1)=>(((subbreln1)=>((((((breln1compprop)=>(((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((((((breln1unionEcases)=>((((woz2W)=>(((woz2B)=>(((image1Ex1)=>((((image1I)=>(((injFuncSetFuncIn)=>(((((leftInvIsSurj)=>(((foundation2)=>(((((((peanoSinj)=>(![X21:$i]:((![X48:$i]:(((transitiveset @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))<=(transitiveset @ X21)))<=(transitivesetOp1)))<=(peano0notS))<=(omegaSclos))<=(omegaSp))<=(notinself2))<=(notinself)))<=(surjCantorThm)))<=(surjFuncSetFuncSurj))<=(surjFuncSetFuncIn))<=(injFuncSetFuncInj)))<=(injFuncInInjFuncSet)))<=(image1E))<=(image1Equiv)))<=(image1Ex)))<=(woz2A)))<=(woz2Ex))<=(breln1unionCommutes)))<=(breln1unionE))<=(breln1unionI))<=(breln1unionIR))<=(breln1unionIL)))))<=(breln1compI)))<=(breln1invE))<=(breln1invI))<=(breln1invprop))<=(eqbreln1)))<=(breln1all1)))<=(choice2fnsingleton)))))<=(woz1_4)))<=(woz1_2))<=(woz1_1))<=(woz13rule4))<=(woz13rule3))<=(woz13rule2))<=(woz13rule1))))<=(demorgan2b))<=(demorgan2b2))<=(demorgan2a)))<=(demorgan1b)))<=(demorgan2a2))<=(complementUnionInPowersetComplement))<=(demorgan2a1))<=(binunionTEcontra)))))<=(intersectInPowersetIntersectUnions))))<=(inIntersectImpInUnion))<=(binunionTIRcontra)))<=(complementTcontraSubset))<=(contraSubsetComplement))<=(complementInPowersetComplementIntersect))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT)))))<=(doubleComplementE1))))))<=(contrasubsetT))<=(binintersectTERcontra))<=(binintersectTELcontra))<=(complementTE1))))<=(powersetTI1))<=(subsetTI)))<=(complementT_lem))<=(setminusT_lem))<=(powersetT_lem)))<=(binintersectT_lem)))<=(iffalse)))<=(theeq))<=(ifp))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1)))<=(iffalseProp1))<=(eta2)))<=(lam2lamEq))))<=(ap2apEq2)))))<=(eqbreln))<=(subbreln)))<=(funcextLem)))<=(funcGraphProp3))<=(funcGraphProp1)))<=(brelnall2))))))<=(funcinfuncset)))<=(infuncsetfunc))))))))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER)))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR)))<=(upairequniteq))))<=(setukpairinjR11))))<=(cartprodfstin))<=(kfstpairEq)))<=(kfstsingleton))<=(setukpairinjL1)))<=(ex1I2))<=(ex1I)))<=(singletonprop)))<=(setunionsingleton2))))))<=(cartprodpairin))<=(ubforcartprodlem3)))))))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR)))<=(secondinupair)))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1))))<=(setminusLsub))<=(setminusIRneg))))))))))<=(binintersectSubset1))<=(binintersectSubset4))<=(binintersectRsub)))<=(binintersectER))<=(binintersectSubset3)))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))))))))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset))<=(powersetsubset))<=(inPowerset))<=(powersetE1)))<=(subsetemptysetimpeq))<=(setextsub)))<=(setadjoinSub2))<=(setadjoinSub)))))<=(notequalI1))<=(notsubsetI))))))<=(eqimpsubset1))<=(eqimpsubset2))))))))<=(powerset__Cong)))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))<=(in__Cong))))<=(exuI3))<=(exuI1))<=(notdallE))<=(notdexE))))<=(quantDeMorgan4)))<=(quantDeMorgan2)))<=(vacuousDall))<=(emptyE1)))<=(upairsetIL))))<=(eqinunit))))<=(nonemptyImpWitness))))<=(setunionE))<=(setunionI))))))<=(setoftrueEq)))))<=(emptyinunitempty)))<=(nonemptyI1))))))<=(emptyI))))<=(notinemptyset))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE))<=(exuE1)))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))<=(wellorderingAx))<=(foundationAx)))<=(omegaIndAx)))<=(omega0Ax))<=(setunionAx)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintTransitive)).
2.09/0.83	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', sepInPowerset)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', emptyE1)).
2.09/0.83	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', nonemptyImpWitness)).
2.09/0.83	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setoftrueEq)).
2.09/0.83	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', nonemptyI1)).
2.09/0.83	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', dsetconstrEL)).
2.09/0.83	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', dsetconstrI)).
2.09/0.83	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', ex1E1)).
2.09/0.83	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', eta1)).
2.09/0.83	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', dpsetconstrEL1)).
2.09/0.83	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', dpsetconstrEL2)).
2.09/0.83	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', lamp)).
2.09/0.83	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', lamProp)).
2.09/0.83	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', apProp)).
2.09/0.83	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', funcImageSingleton)).
2.09/0.83	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:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', dpsetconstrER)).
2.09/0.83	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', lam2p)).
2.09/0.83	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', ex1E2)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', beta1)).
2.09/0.83	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', iffalseProp2)).
2.09/0.83	thf(beta2, axiom, ((beta2)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', beta2)).
2.09/0.83	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:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ X3 @ X14) @ X33)))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', choice2fnsingleton)).
2.09/0.83	thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setOfPairsIsBReln1)).
2.09/0.83	thf(foundation2, axiom, ((foundation2)<=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', foundation2)).
2.09/0.83	thf(image1I, axiom, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X61 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', image1I)).
2.09/0.83	thf(transitivesetOp1, axiom, ((transitivesetOp1)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', transitivesetOp1)).
2.09/0.83	thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', image1Equiv)).
2.09/0.83	thf(image1E, axiom, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', image1E)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', lam2lamEq)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', eta2)).
2.09/0.83	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', iffalseProp1)).
2.09/0.83	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', iftrueProp1)).
2.09/0.83	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', iftrueProp2)).
2.09/0.83	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', ifSingleton)).
2.09/0.83	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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', dpsetconstrERa)).
2.09/0.83	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', dpsetconstrI)).
2.09/0.83	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', dpsetconstrSub)).
2.09/0.83	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setOfPairsIsBReln)).
2.09/0.83	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', ksndsingleton)).
2.09/0.83	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', singletonprop)).
2.09/0.83	thf(ex1I, axiom, ((ex1I)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', ex1I)).
2.09/0.83	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', ex1I2)).
2.09/0.83	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', kfstsingleton)).
2.09/0.83	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', sepSubset)).
2.09/0.83	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', dsetconstr__Cong)).
2.09/0.83	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', nonemptyE1)).
2.09/0.83	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setbeta)).
2.09/0.83	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', dsetconstrER)).
2.09/0.83	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintersectSubset4)).
2.09/0.83	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintersectRsub)).
2.09/0.83	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintersectER)).
2.09/0.83	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintersectSubset3)).
2.09/0.83	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintersectLsub)).
2.09/0.83	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintersectEL)).
2.09/0.83	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintersectSubset5)).
2.09/0.83	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', upairset2IR)).
2.09/0.83	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binunionIL)).
2.09/0.83	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', symdiffE)).
2.09/0.83	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setminusSubset1)).
2.09/0.83	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', powersetsubset)).
2.09/0.83	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setminusILneg)).
2.09/0.83	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', inPowerset)).
2.09/0.83	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setminusELneg)).
2.09/0.83	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', powersetE1)).
2.09/0.83	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setminusERneg)).
2.09/0.83	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', subsetemptysetimpeq)).
2.09/0.83	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setminusEL)).
2.09/0.83	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setextsub)).
2.09/0.83	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setminusSubset2)).
2.09/0.83	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setadjoinSub2)).
2.09/0.83	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setminusER)).
2.09/0.83	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setadjoinSub)).
2.09/0.83	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', symdiffIneg2)).
2.09/0.83	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', notequalI1)).
2.09/0.83	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', notsubsetI)).
2.09/0.83	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', eqimpsubset1)).
2.09/0.83	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', eqimpsubset2)).
2.09/0.83	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', powerset__Cong)).
2.09/0.83	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', emptyset__Cong)).
2.09/0.83	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', in__Cong)).
2.09/0.83	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', notdallE)).
2.09/0.83	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', notdexE)).
2.09/0.83	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', ubforcartprodlem2)).
2.09/0.83	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', quantDeMorgan4)).
2.09/0.83	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', ubforcartprodlem1)).
2.09/0.83	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', quantDeMorgan2)).
2.09/0.83	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', upairinpowunion)).
2.09/0.83	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', vacuousDall)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', upairsubunion)).
2.09/0.83	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', upairset2E)).
2.09/0.83	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', upairsetIL)).
2.09/0.83	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', singletoninpowerset)).
2.09/0.83	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', eqinunit)).
2.09/0.83	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setukpairIL)).
2.09/0.83	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', cartprodmempair1)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', setunionE)).
2.09/0.83	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setunionI)).
2.09/0.83	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', emptyinunitempty)).
2.09/0.83	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', emptyI)).
2.09/0.83	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', notinemptyset)).
2.09/0.83	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', emptysetimpfalse)).
2.09/0.83	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', emptysetE)).
2.09/0.83	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', prop2setE)).
2.09/0.83	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', theprop)).
2.09/0.83	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', wellorderingAx)).
2.09/0.83	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', singletonsuniq)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', foundationAx)).
2.09/0.83	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', omegaIndAx)).
2.09/0.83	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setunionsingleton)).
2.09/0.83	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', omega0Ax)).
2.09/0.83	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setunionsingleton1)).
2.09/0.83	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setunionAx)).
2.09/0.83	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setunionE2)).
2.09/0.83	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', cartprodmempair)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', setukpairinjL2)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', powersetTE1)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', cartprodsndpairEq)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', cartprodpairmemEL)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', setukpairinjR2)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', setukpairinjR1)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', setukpairinjR12)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', setukpairinjL)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', ap2p)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', app)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', ap2apEq1)).
2.09/0.83	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', funcext2)).
2.09/0.83	thf(funcext, axiom, ((funcext)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', funcext)).
2.09/0.83	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', funcGraphProp4)).
2.09/0.83	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', funcGraphProp2)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', brelnall1)).
2.09/0.83	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setextT)).
2.09/0.83	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', binunionT_lem)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', iftrueorfalse)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', iftrue)).
2.09/0.83	thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1unionE)).
2.09/0.83	thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1invprop)).
2.09/0.83	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', woz13rule4)).
2.09/0.83	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz1_1)).
2.09/0.83	thf(woz1_2, axiom, ((woz1_2)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', woz1_2)).
2.09/0.83	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz1_4)).
2.09/0.83	thf(breln1all1, axiom, ((breln1all1)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', breln1all1)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', doubleComplementSub2)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', doubleComplementSub1)).
2.09/0.83	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', doubleComplementI1)).
2.09/0.83	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', contrasubsetT3)).
2.09/0.83	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', contrasubsetT2)).
2.09/0.83	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', contrasubsetT1)).
2.09/0.83	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', complementTI1)).
2.09/0.83	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', doubleComplementEq)).
2.09/0.83	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binunionTE)).
2.09/0.83	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', inComplementUnionImpInComplement1)).
2.09/0.83	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', inComplementUnionImpNotIn1)).
2.09/0.83	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', inIntersectImpInIntersectUnions)).
2.09/0.83	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', inIntersectImpInUnion2)).
2.09/0.83	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binunionTILcontra)).
2.09/0.83	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', complementImpComplementIntersect)).
2.09/0.83	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', demorgan1a)).
2.09/0.83	thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1SetBreln1)).
2.09/0.83	thf(breln1all2, axiom, ((breln1all2)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', breln1all2)).
2.09/0.83	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz1_5)).
2.09/0.83	thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz1_3)).
2.09/0.83	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz13rule0)).
2.09/0.83	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', demorgan2)).
2.09/0.83	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', demorgan1)).
2.09/0.83	thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz2W)).
2.09/0.83	thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1unionEcases)).
2.09/0.83	thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1unionprop)).
2.09/0.83	thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', breln1compEex)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', breln1compE)).
2.09/0.83	thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1compprop)).
2.09/0.83	thf(subbreln1, axiom, ((subbreln1)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', subbreln1)).
2.09/0.83	thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz2B)).
2.09/0.83	thf(peanoSinj, axiom, ((peanoSinj)<=>![X2:$i]:(((in @ X2 @ omega)=>![X3:$i]:(((in @ X3 @ omega)=>(((omegaS @ X2)=(omegaS @ X3))=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', peanoSinj)).
2.09/0.83	thf(leftInvIsSurj, axiom, ((leftInvIsSurj)<=>![X4:$i, X5:$i, X62:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X62 @ X2) @ X5)))=>![X34:$i]:(((in @ X34 @ (funcSet @ X5 @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X5 @ X4 @ X34 @ (X62 @ X2))=(X2))))=>(surjective @ X5 @ X4 @ X34))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', leftInvIsSurj)).
2.09/0.83	thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', injFuncSetFuncIn)).
2.09/0.83	thf(surjFuncSetFuncSurj, axiom, ((surjFuncSetFuncSurj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X2 @ X3))=>(surjective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', surjFuncSetFuncSurj)).
2.09/0.83	thf(surjCantorThm, axiom, ((surjCantorThm)<=>![X4:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ (powerset @ X4)))=>~((surjective @ X4 @ (powerset @ X4) @ X29))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', surjCantorThm)).
2.09/0.83	thf(notinself, axiom, ((notinself)<=>![X4:$i]:(~((in @ X4 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', notinself)).
2.09/0.83	thf(notinself2, axiom, ((notinself2)<=>![X4:$i, X5:$i]:(((in @ X4 @ X5)=>~((in @ X5 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', notinself2)).
2.09/0.83	thf(omegaSp, axiom, ((omegaSp)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (omegaS @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', omegaSp)).
2.09/0.83	thf(omegaSclos, axiom, ((omegaSclos)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', omegaSclos)).
2.09/0.83	thf(peano0notS, axiom, ((peano0notS)<=>![X2:$i]:(((in @ X2 @ omega)=>((omegaS @ X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', peano0notS)).
2.09/0.83	thf(surjFuncSetFuncIn, axiom, ((surjFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', surjFuncSetFuncIn)).
2.09/0.83	thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz2Ex)).
2.09/0.83	thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz2A)).
2.09/0.83	thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', image1Ex)).
2.09/0.83	thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', injFuncInInjFuncSet)).
2.09/0.83	thf(injFuncSetFuncInj, axiom, ((injFuncSetFuncInj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', injFuncSetFuncInj)).
2.09/0.83	thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1unionCommutes)).
2.09/0.83	thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1invI)).
2.09/0.83	thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1invE)).
2.09/0.83	thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1compI)).
2.09/0.83	thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', breln1unionIL)).
2.09/0.83	thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1unionIR)).
2.09/0.83	thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$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))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', breln1unionI)).
2.09/0.83	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:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', eqbreln1)).
2.09/0.83	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz13rule3)).
2.09/0.83	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', demorgan2a2)).
2.09/0.83	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', demorgan1b)).
2.09/0.83	thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', demorgan2a)).
2.09/0.83	thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', demorgan2b2)).
2.09/0.83	thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', demorgan2b)).
2.09/0.83	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz13rule1)).
2.09/0.83	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', woz13rule2)).
2.09/0.83	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', complementUnionInPowersetComplement)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', contraSubsetComplement)).
2.09/0.83	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', complementTcontraSubset)).
2.09/0.83	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binunionTIRcontra)).
2.09/0.83	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', inIntersectImpInUnion)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', intersectInPowersetIntersectUnions)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', binunionTEcontra)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', demorgan2a1)).
2.09/0.83	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', complementInPowersetComplementIntersect)).
2.09/0.83	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', complementTE1)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', binintersectTELcontra)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', binintersectTERcontra)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', contrasubsetT)).
2.09/0.83	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', doubleComplementE1)).
2.09/0.83	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', complementTnotintersectT)).
2.09/0.83	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', complementSubsetComplementIntersect)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', powersetTI1)).
2.09/0.83	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', theeq)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', iffalse)).
2.09/0.83	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintersectT_lem)).
2.09/0.83	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', powersetT_lem)).
2.09/0.83	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.qLAuhH5oxD/E---3.1_2798186.p', setminusT_lem)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', complementT_lem)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', subsetTI)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', ifp)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', ap2apEq2)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', eqbreln)).
2.09/0.83	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', infuncsetfunc)).
2.09/0.83	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', funcinfuncset)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', brelnall2)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', funcGraphProp1)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', funcGraphProp3)).
2.09/0.83	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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', funcextLem)).
2.09/0.83	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', subbreln)).
2.09/0.83	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', cartprodpairmemER)).
2.09/0.83	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', cartprodmempaircEq)).
2.09/0.83	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', cartprodfstpairEq)).
2.09/0.83	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', cartprodpairsurjEq)).
2.09/0.83	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', cartprodsndin)).
2.09/0.83	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', cartprodfstin)).
2.09/0.83	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setukpairinjR11)).
2.09/0.83	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', upairequniteq)).
2.09/0.83	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setukpairinjR)).
2.09/0.83	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', ksndpairEq)).
2.09/0.83	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', kpairsurjEq)).
2.09/0.83	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', kfstpairEq)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', cartprodpairin)).
2.09/0.83	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setunionsingleton2)).
2.09/0.83	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.qLAuhH5oxD/E---3.1_2798186.p', setukpairinjL1)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', ubforcartprodlem3)).
2.09/0.83	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', symdiffIneg1)).
2.09/0.83	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', secondinupair)).
2.09/0.83	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setukpairIR)).
2.09/0.83	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', kpairiskpair)).
2.09/0.83	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', kpairp)).
2.09/0.83	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', singletonsubset)).
2.09/0.83	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', singletoninpowunion)).
2.09/0.83	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', symdiffI2)).
2.09/0.83	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', symdiffI1)).
2.09/0.83	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setminusLsub)).
2.09/0.83	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setminusIRneg)).
2.09/0.83	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintersectSubset1)).
2.09/0.83	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setminusI)).
2.09/0.83	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', bs114d)).
2.09/0.83	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', disjointsetsI1)).
2.09/0.83	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintersectSubset2)).
2.09/0.83	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binintersectI)).
2.09/0.83	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binunionRsub)).
2.09/0.83	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binunionLsub)).
2.09/0.83	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binunionE)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', binunionEcases)).
2.09/0.83	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', binunionIR)).
2.09/0.83	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', powersetI1)).
2.09/0.83	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', subset2powerset)).
2.09/0.83	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', subsetTrans)).
2.09/0.83	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', subsetRefl)).
2.09/0.83	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', notequalI2)).
2.09/0.83	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', subsetE2)).
2.09/0.83	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', subsetE)).
2.09/0.83	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', emptysetsubset)).
2.09/0.83	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', subsetI2)).
2.09/0.83	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', subsetI1)).
2.09/0.83	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', omega__Cong)).
2.09/0.83	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setunion__Cong)).
2.09/0.83	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setadjoin__Cong)).
2.09/0.83	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', inCongP)).
2.09/0.83	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', prop2set2propI)).
2.09/0.83	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', prop2setI)).
2.09/0.83	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', quantDeMorgan3)).
2.09/0.83	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', quantDeMorgan1)).
2.09/0.83	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', upairsetIR)).
2.09/0.83	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', upairsetE)).
2.09/0.83	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', singletonsswitch)).
2.09/0.83	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', notinsingleton)).
2.09/0.83	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', uniqinunit)).
2.09/0.83	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', subPowSU)).
2.09/0.83	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', powersetE)).
2.09/0.83	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', emptyInPowerset)).
2.09/0.83	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', emptyinPowerset)).
2.09/0.83	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', powersetI)).
2.09/0.83	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setadjoinOr)).
2.09/0.83	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setadjoinE)).
2.09/0.83	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setadjoinIR)).
2.09/0.83	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setadjoinIL)).
2.09/0.83	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', noeltsimpempty)).
2.09/0.83	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.qLAuhH5oxD/E---3.1_2798186.p', setext)).
2.09/0.83	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', omegaSAx)).
2.09/0.83	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', powersetAx)).
2.09/0.83	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setadjoinAx)).
2.09/0.83	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', emptysetAx)).
2.09/0.83	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.qLAuhH5oxD/E---3.1_2798186.p', setextAx)).
2.09/0.83	thf(c_0_333, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
2.09/0.83	thf(c_0_334, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
2.09/0.83	thf(c_0_335, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
2.09/0.83	thf(c_0_336, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
2.09/0.83	thf(c_0_337, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
2.09/0.83	thf(c_0_338, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
2.09/0.83	thf(c_0_339, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
2.09/0.83	thf(c_0_340, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
2.09/0.83	thf(c_0_341, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0:$i]:(![X2:$i]:((((in @ X2 @ Z0))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])).
2.09/0.83	thf(c_0_342, plain, ((transitiveset)=(^[Z0:$i]:(![X21:$i]:((((in @ X21 @ Z0))=>((subset @ X21 @ Z0))))))), inference(fof_simplification,[status(thm)],[transitiveset])).
2.09/0.83	thf(c_0_343, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
2.09/0.83	thf(c_0_344, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
2.09/0.83	thf(c_0_345, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
2.09/0.83	thf(c_0_346, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
2.09/0.83	thf(c_0_347, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
2.09/0.83	thf(c_0_348, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
2.09/0.83	thf(c_0_349, plain, ((replAx)<=>![X6:$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])).
2.09/0.83	thf(c_0_350, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((((omegaSAx)=>(((replAx)=>(((((((dsetconstrER)=>(((((((exuE3e)=>((setext)=>(((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>(((setadjoinIL)=>(((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>(((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((((subPowSU)=>((exuE2)=>(((uniqinunit)=>((notinsingleton)=>(((singletonsswitch)=>((upairsetE)=>(((upairsetIR)=>((((quantDeMorgan1)=>(((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>((((((exuI2)=>((inCongP)=>((((((setadjoin__Cong)=>(((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((((subset2powerset)=>((((powersetI1)=>((((((sepSubset)=>((((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>(((((binintersectSubset2)=>((((disjointsetsI1)=>(((((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((((setminusSubset1)=>((symdiffE)=>(((((symdiffIneg2)=>(((setukpairIL)=>((((((singletoninpowerset)=>(((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>(((setunionsingleton)=>(((ex1E1)=>((((singletonsuniq)=>((((theprop)=>((((setukpairinjL2)=>((setukpairinjL)=>(((setukpairinjR12)=>((setukpairinjR1)=>(((setukpairinjR2)=>(((((((cartprodpairmemEL)=>(((((cartprodsndpairEq)=>(((((((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>(((ap2p)=>(((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>(((ex1E2)=>((((funcGraphProp2)=>(((funcGraphProp4)=>((((funcext)=>((funcext2)=>((ap2apEq1)=>(((beta1)=>((eta1)=>(((beta2)=>((((iffalseProp2)=>(((((((iftrue)=>(((iftrueorfalse)=>(((binunionT_lem)=>(((((setextT)=>((((powersetTE1)=>((complementTI1)=>((((((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>(((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>(((complementImpComplementIntersect)=>((((((binunionTILcontra)=>((((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>(((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((((((demorgan1a)=>(((demorgan1)=>(((((demorgan2)=>((woz13rule0)=>((((((((woz1_3)=>(((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>(((setOfPairsIsBReln1)=>(((subbreln1)=>((((((breln1compprop)=>(((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((((((breln1unionEcases)=>((((woz2W)=>(((woz2B)=>(((image1Ex1)=>((((image1I)=>(((injFuncSetFuncIn)=>(((((leftInvIsSurj)=>(((foundation2)=>(((((((peanoSinj)=>(![X21:$i]:((![X48:$i]:(((transitiveset @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))<=(transitiveset @ X21)))<=(transitivesetOp1)))<=(peano0notS))<=(omegaSclos))<=(omegaSp))<=(notinself2))<=(notinself)))<=(surjCantorThm)))<=(surjFuncSetFuncSurj))<=(surjFuncSetFuncIn))<=(injFuncSetFuncInj)))<=(injFuncInInjFuncSet)))<=(image1E))<=(image1Equiv)))<=(image1Ex)))<=(woz2A)))<=(woz2Ex))<=(breln1unionCommutes)))<=(breln1unionE))<=(breln1unionI))<=(breln1unionIR))<=(breln1unionIL)))))<=(breln1compI)))<=(breln1invE))<=(breln1invI))<=(breln1invprop))<=(eqbreln1)))<=(breln1all1)))<=(choice2fnsingleton)))))<=(woz1_4)))<=(woz1_2))<=(woz1_1))<=(woz13rule4))<=(woz13rule3))<=(woz13rule2))<=(woz13rule1))))<=(demorgan2b))<=(demorgan2b2))<=(demorgan2a)))<=(demorgan1b)))<=(demorgan2a2))<=(complementUnionInPowersetComplement))<=(demorgan2a1))<=(binunionTEcontra)))))<=(intersectInPowersetIntersectUnions))))<=(inIntersectImpInUnion))<=(binunionTIRcontra)))<=(complementTcontraSubset))<=(contraSubsetComplement))<=(complementInPowersetComplementIntersect))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT)))))<=(doubleComplementE1))))))<=(contrasubsetT))<=(binintersectTERcontra))<=(binintersectTELcontra))<=(complementTE1))))<=(powersetTI1))<=(subsetTI)))<=(complementT_lem))<=(setminusT_lem))<=(powersetT_lem)))<=(binintersectT_lem)))<=(iffalse)))<=(theeq))<=(ifp))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1)))<=(iffalseProp1))<=(eta2)))<=(lam2lamEq))))<=(ap2apEq2)))))<=(eqbreln))<=(subbreln)))<=(funcextLem)))<=(funcGraphProp3))<=(funcGraphProp1)))<=(brelnall2))))))<=(funcinfuncset)))<=(infuncsetfunc))))))))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER)))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR)))<=(upairequniteq))))<=(setukpairinjR11))))<=(cartprodfstin))<=(kfstpairEq)))<=(kfstsingleton))<=(setukpairinjL1)))<=(ex1I2))<=(ex1I)))<=(singletonprop)))<=(setunionsingleton2))))))<=(cartprodpairin))<=(ubforcartprodlem3)))))))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR)))<=(secondinupair)))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1))))<=(setminusLsub))<=(setminusIRneg))))))))))<=(binintersectSubset1))<=(binintersectSubset4))<=(binintersectRsub)))<=(binintersectER))<=(binintersectSubset3)))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))))))))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset))<=(powersetsubset))<=(inPowerset))<=(powersetE1)))<=(subsetemptysetimpeq))<=(setextsub)))<=(setadjoinSub2))<=(setadjoinSub)))))<=(notequalI1))<=(notsubsetI))))))<=(eqimpsubset1))<=(eqimpsubset2))))))))<=(powerset__Cong)))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))<=(in__Cong))))<=(exuI3))<=(exuI1))<=(notdallE))<=(notdexE))))<=(quantDeMorgan4)))<=(quantDeMorgan2)))<=(vacuousDall))<=(emptyE1)))<=(upairsetIL))))<=(eqinunit))))<=(nonemptyImpWitness))))<=(setunionE))<=(setunionI))))))<=(setoftrueEq)))))<=(emptyinunitempty)))<=(nonemptyI1))))))<=(emptyI))))<=(notinemptyset))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE))<=(exuE1)))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))<=(wellorderingAx))<=(foundationAx)))<=(omegaIndAx)))<=(omega0Ax))<=(setunionAx))))))), inference(assume_negation,[status(cth)],[binintTransitive])).
2.09/0.83	thf(c_0_351, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
2.09/0.83	thf(c_0_352, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1156:$i]:(((((X1 @ X1156)))&(![X1157:$i]:(((((X1 @ X1157)))=>(((X1156)=(X1157))))))))))<=>((?[X1158:$i]:(((((X17 @ X1158)))&(![X1159:$i]:(((((X17 @ X1159)))=>(((X1158)=(X1159)))))))))))))))), inference(apply_def,[status(thm)],[c_0_333, c_0_334])).
2.09/0.83	thf(c_0_353, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X1154:$i]:(((((X1 @ X1154)))&(![X1155:$i]:(((((X1 @ X1155)))=>(((X1154)=(X1155))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_335, c_0_334])).
2.09/0.83	thf(c_0_354, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X1150:$i]:(((((X1 @ X1150)))&(![X1151:$i]:(((((X1 @ X1151)))=>(((X1150)=(X1151)))))))))))))))), inference(apply_def,[status(thm)],[c_0_336, c_0_334])).
2.09/0.83	thf(c_0_355, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X1148:$i]:(((((X1 @ X1148)))&(![X1149:$i]:(((((X1 @ X1149)))=>(((X1148)=(X1149)))))))))))))), inference(apply_def,[status(thm)],[c_0_337, c_0_334])).
2.09/0.83	thf(c_0_356, plain, ((emptyE1)<=>![X4:$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])).
2.09/0.83	thf(c_0_357, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_338])).
2.09/0.83	thf(c_0_358, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
2.09/0.83	thf(c_0_359, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_338])).
2.09/0.83	thf(c_0_360, plain, ((exuE1)=(![X1:$i > $o]:((((?[X1142:$i]:(((((X1 @ X1142)))&(![X1143:$i]:(((((X1 @ X1143)))=>(((X1142)=(X1143))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_339, c_0_334])).
2.09/0.83	thf(c_0_361, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
2.09/0.83	thf(c_0_362, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
2.09/0.83	thf(c_0_363, plain, ((descrp)=(![X1:$i > $o]:((((?[X1140:$i]:(((((X1 @ X1140)))&(![X1141:$i]:(((((X1 @ X1141)))=>(((X1140)=(X1141))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_340, c_0_334])).
2.09/0.83	thf(c_0_364, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
2.09/0.83	thf(c_0_365, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
2.09/0.83	thf(c_0_366, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
2.09/0.83	thf(c_0_367, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
2.09/0.83	thf(c_0_368, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
2.09/0.83	thf(c_0_369, plain, ((lamProp)<=>![X4:$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])).
2.09/0.83	thf(c_0_370, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
2.09/0.83	thf(c_0_371, plain, ((funcImageSingleton)<=>![X4:$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])).
2.09/0.83	thf(c_0_372, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
2.09/0.83	thf(c_0_373, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
2.09/0.83	thf(c_0_374, plain, ((ex1E2)<=>![X4:$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])).
2.09/0.83	thf(c_0_375, 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])).
2.09/0.83	thf(c_0_376, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
2.09/0.83	thf(c_0_377, plain, ((beta2)<=>![X4:$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])).
2.09/0.83	thf(c_0_378, 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:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ Z0 @ X14) @ X33)))))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])).
2.09/0.83	thf(c_0_379, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
2.09/0.83	thf(c_0_380, axiom, ((foundation2)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X21:$i]:((((in @ X21 @ X4))&(((binintersect @ X21 @ X4)=(emptyset)))))))))), inference(apply_def,[status(thm)],[foundation2, c_0_338])).
2.09/0.83	thf(c_0_381, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])).
2.09/0.83	thf(c_0_382, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1166:$i]:((((![X2:$i]:((((in @ X2 @ X1166))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))&(![X1167:$i]:((((![X2:$i]:((((in @ X2 @ X1167))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))=>(((X1166)=(X1167)))))))))))), inference(apply_def,[status(thm)],[c_0_341, c_0_334])).
2.09/0.83	thf(c_0_383, axiom, ((transitivesetOp1)=(![X21:$i]:((((![X1168:$i]:((((in @ X1168 @ X21))=>((subset @ X1168 @ X21))))))=>(![X4:$i]:((((in @ X4 @ X21))=>((subset @ X4 @ X21))))))))), inference(apply_def,[status(thm)],[transitivesetOp1, c_0_342])).
2.09/0.83	thf(c_0_384, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])).
2.09/0.83	thf(c_0_385, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])).
2.09/0.83	thf(c_0_386, 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])).
2.09/0.83	thf(c_0_387, 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])).
2.09/0.83	thf(c_0_388, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
2.09/0.83	thf(c_0_389, plain, ((iftrueProp1)<=>![X4:$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])).
2.09/0.83	thf(c_0_390, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
2.09/0.83	thf(c_0_391, plain, ((ifSingleton)<=>![X4:$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])).
2.09/0.83	thf(c_0_392, 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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
2.09/0.83	thf(c_0_393, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
2.09/0.83	thf(c_0_394, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
2.09/0.83	thf(c_0_395, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
2.09/0.83	thf(c_0_396, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
2.09/0.83	thf(c_0_397, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
2.09/0.83	thf(c_0_398, plain, ((ex1I)<=>![X4:$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])).
2.09/0.83	thf(c_0_399, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
2.09/0.83	thf(c_0_400, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
2.09/0.83	thf(c_0_401, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
2.09/0.83	thf(c_0_402, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
2.09/0.83	thf(c_0_403, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1162:$i]:(((((X1 @ X1162)))&(![X1163:$i]:(((((X1 @ X1163)))=>(((X1162)=(X1163))))))))))=>((((?[X1164:$i]:(((((X17 @ X1164)))&(![X1165:$i]:(((((X17 @ X1165)))=>(((X1164)=(X1165))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_343, c_0_334])).
2.09/0.83	thf(c_0_404, plain, ((exuEu)=(![X1:$i > $o]:((((?[X1160:$i]:(((((X1 @ X1160)))&(![X1161:$i]:(((((X1 @ X1161)))=>(((X1160)=(X1161))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_344, c_0_334])).
2.09/0.83	thf(c_0_405, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X1152:$i]:(((((X1 @ X1152)))&(![X1153:$i]:(((((X1 @ X1153)))=>(((X1152)=(X1153)))))))))))))), inference(apply_def,[status(thm)],[c_0_345, c_0_334])).
2.09/0.83	thf(c_0_406, plain, ((exuE2)=(![X1:$i > $o]:((((?[X1146:$i]:(((((X1 @ X1146)))&(![X1147:$i]:(((((X1 @ X1147)))=>(((X1146)=(X1147))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_346, c_0_334])).
2.09/0.83	thf(c_0_407, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_347, c_0_338])).
2.09/0.83	thf(c_0_408, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_338])).
2.09/0.83	thf(c_0_409, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
2.09/0.83	thf(c_0_410, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X1144:$i]:(((((X1 @ X1144)))&(![X1145:$i]:(((((X1 @ X1145)))=>(((X1144)=(X1145))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_348, c_0_334])).
2.09/0.83	thf(c_0_411, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
2.09/0.83	thf(c_0_412, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X1138:$i]:(((((X6 @ X2 @ X1138)))&(![X1139:$i]:(((((X6 @ X2 @ X1139)))=>(((X1138)=(X1139)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_349, c_0_334])).
2.09/0.83	thf(c_0_413, plain, ((epred1_0)<=>![X2252:$i]:(?[X2253:$i]:((((![X2254:$i]:(((in @ X2254 @ X2253)=>![X2255:$i]:(((in @ X2255 @ X2254)=>(in @ X2255 @ X2252)))))&![X2256:$i, X2257:$i]:((((in @ X2256 @ X2252)&(in @ X2257 @ X2252))=>(![X2258:$i]:(((in @ X2258 @ X2253)=>((in @ X2256 @ X2258)<=>(in @ X2257 @ X2258))))=>((X2256)=(X2257))))))&![X2259:$i, X2260:$i]:((((in @ X2259 @ X2253)&(in @ X2260 @ X2253))=>(![X2261:$i]:(((in @ X2261 @ X2259)=>(in @ X2261 @ X2260)))|![X2262:$i]:(((in @ X2262 @ X2260)=>(in @ X2262 @ X2259)))))))&![X2263:$i]:(((![X2264:$i]:(((in @ X2264 @ X2263)=>(in @ X2264 @ X2252)))&?[X2265:$i]:((in @ X2265 @ X2263)))=>?[X2266:$i, X2267:$i]:(((((in @ X2266 @ X2253)&(in @ X2267 @ X2263))&~(?[X2268:$i]:(((in @ X2268 @ X2266)&(in @ X2268 @ X2263)))))&![X2269:$i]:(((in @ X2269 @ X2253)=>(![X2270:$i]:(((in @ X2270 @ X2269)=>(in @ X2270 @ X2266)))|(in @ X2267 @ X2269)))))))))))), introduced(definition)).
2.09/0.83	thf(c_0_414, negated_conjecture, ~((![X1169:$i, X1170:$i]:((![X1171:$i]:(((in @ X1171 @ X1169)<=>(in @ X1171 @ X1170)))=>((X1169)=(X1170))))=>(![X1172:$i]:(~(in @ X1172 @ emptyset))=>(![X1173:$i, X1174:$i, X1175:$i]:(((in @ X1175 @ (setadjoin @ X1173 @ X1174))<=>(((X1175)=(X1173))|(in @ X1175 @ X1174))))=>(![X1176:$i, X1177:$i]:(((in @ X1177 @ (powerset @ X1176))<=>![X1178:$i]:(((in @ X1178 @ X1177)=>(in @ X1178 @ X1176)))))=>(![X2278:$i, X2279:$i]:(((in @ X2279 @ (setunion @ X2278))<=>?[X2280:$i]:(((in @ X2279 @ X2280)&(in @ X2280 @ X2278)))))=>((in @ emptyset @ omega)=>(![X1179:$i]:(((in @ X1179 @ omega)=>(in @ (setadjoin @ X1179 @ X1179) @ omega)))=>(![X2275:$i]:((((in @ emptyset @ X2275)&![X2276:$i]:((((in @ X2276 @ omega)&(in @ X2276 @ X2275))=>(in @ (setadjoin @ X2276 @ X2276) @ X2275))))=>![X2277:$i]:(((in @ X2277 @ omega)=>(in @ X2277 @ X2275)))))=>(![X1180:$i > $i > $o, X1181:$i]:((![X1182:$i]:(((in @ X1182 @ X1181)=>?[X1183:$i]:(((X1180 @ X1182 @ X1183)&![X1184:$i]:(((X1180 @ X1182 @ X1184)=>((X1183)=(X1184))))))))=>?[X1185:$i]:(![X1186:$i]:(((in @ X1186 @ X1185)<=>?[X1187:$i]:(((in @ X1187 @ X1181)&(X1180 @ X1187 @ X1186))))))))=>(![X2271:$i]:((?[X2272:$i]:((in @ X2272 @ X2271))=>?[X2273:$i]:(((in @ X2273 @ X2271)&~(?[X2274:$i]:(((in @ X2274 @ X2273)&(in @ X2274 @ X2271))))))))=>((epred1_0)=>(![X2249:$i > $o]:((?[X2250:$i]:(((X2249 @ X2250)&![X2251:$i]:(((X2249 @ X2251)=>((X2250)=(X2251))))))=>(X2249 @ (descr @ (^[Z0:$i]:(X2249 @ Z0))))))=>(![X2246:$i, X2247:$i > $o, X2248:$i]:(((in @ X2248 @ X2246)=>((X2247 @ X2248)=>(in @ X2248 @ (dsetconstr @ X2246 @ X2247)))))=>(![X2243:$i, X2244:$i > $o, X2245:$i]:(((in @ X2245 @ (dsetconstr @ X2243 @ X2244))=>(in @ X2245 @ X2243)))=>(![X1188:$i, X1189:$i > $o, X1190:$i]:(((in @ X1190 @ (dsetconstr @ X1188 @ X1189))=>(X1189 @ X1190)))=>(![X2238:$i > $o]:((?[X2239:$i]:(((X2238 @ X2239)&![X2240:$i]:(((X2238 @ X2240)=>((X2239)=(X2240))))))=>?[X2241:$i]:(((X2238 @ X2241)&![X2242:$i]:(((X2238 @ X2242)=>((X2241)=(X2242))))))))=>(![X2236:$o, X2237:$i]:(((in @ X2237 @ (prop2set @ ((X2236))))=>(X2236)))=>(![X2234:$i]:(((in @ X2234 @ emptyset)=>![X2235:$o]:((X2235))))=>(![X2233:$i]:(((in @ X2233 @ emptyset)=>~($true)))=>(![X2232:$i]:(~(in @ X2232 @ emptyset))=>(![X1191:$i > $o]:((?[X1192:$i]:(((X1191 @ X1192)&![X1193:$i]:(((X1191 @ X1193)=>((X1192)=(X1193))))))=>?[X1194:$i]:((X1191 @ X1194))))=>(![X1195:$i, X1196:$i]:((![X1197:$i]:(((in @ X1197 @ X1195)=>(in @ X1197 @ X1196)))=>(![X1198:$i]:(((in @ X1198 @ X1196)=>(in @ X1198 @ X1195)))=>((X1195)=(X1196)))))=>(![X2230:$i]:((![X2231:$i]:(~(in @ X2231 @ X2230))=>((X2230)=(emptyset))))=>(![X1199:$i]:((![X1200:$i]:(~(in @ X1200 @ X1199))=>((X1199)=(emptyset))))=>(![X1201:$i, X1202:$i > $o, X1203:$i]:(((in @ X1203 @ X1201)=>((in @ X1203 @ (dsetconstr @ X1201 @ X1202))<=>(X1202 @ X1203))))=>(![X1204:$i]:((((X1204)!=(emptyset))=>?[X1205:$i]:((in @ X1205 @ X1204))))=>(![X1206:$i, X1207:$i > $o, X1208:$i]:(((in @ X1208 @ X1206)=>((X1207 @ X1208)=>((dsetconstr @ X1206 @ X1207)!=(emptyset)))))=>(![X2228:$i]:((?[X2229:$i]:((in @ X2229 @ X2228))=>((X2228)!=(emptyset))))=>(![X1209:$i, X1210:$i]:((in @ X1209 @ (setadjoin @ X1209 @ X1210)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1211:$i, X1212:$i, X1213:$i]:(((in @ X1213 @ X1212)=>(in @ X1213 @ (setadjoin @ X1211 @ X1212))))=>(![X1214:$i, X1215:$i, X1216:$i]:(((in @ X1216 @ (setadjoin @ X1214 @ X1215))=>![X1217:$o]:(((((X1216)=(X1214))=>(X1217))=>(((in @ X1216 @ X1215)=>(X1217))=>(X1217))))))=>(![X1218:$i, X1219:$i, X1220:$i]:(((in @ X1220 @ (setadjoin @ X1218 @ X1219))=>(((X1220)=(X1218))|(in @ X1220 @ X1219))))=>(![X2227:$i]:(((dsetconstr @ X2227 @ (^[Z0:$i]:($true)))=(X2227)))=>(![X1221:$i, X1222:$i]:((![X1223:$i]:(((in @ X1223 @ X1222)=>(in @ X1223 @ X1221)))=>(in @ X1222 @ (powerset @ X1221))))=>(![X1224:$i]:((in @ emptyset @ (powerset @ X1224)))=>(![X1225:$i]:((in @ emptyset @ (powerset @ X1225)))=>(![X1226:$i, X1227:$i, X1228:$i]:(((in @ X1227 @ (powerset @ X1226))=>((in @ X1228 @ X1227)=>(in @ X1228 @ X1226))))=>(![X2224:$i, X2225:$i, X2226:$i]:(((in @ X2225 @ X2226)=>((in @ X2226 @ X2224)=>(in @ X2225 @ (setunion @ X2224)))))=>(![X2220:$i, X2221:$i]:(((in @ X2221 @ (setunion @ X2220))=>![X2222:$o]:((![X2223:$i]:(((in @ X2221 @ X2223)=>((in @ X2223 @ X2220)=>(X2222))))=>(X2222)))))=>(![X1229:$i, X1230:$i]:(((in @ X1230 @ X1229)=>(in @ X1230 @ (powerset @ (setunion @ X1229)))))=>(![X1231:$i > $o]:((?[X1232:$i]:(((X1231 @ X1232)&![X1233:$i]:(((X1231 @ X1233)=>((X1232)=(X1233))))))=>?[X1234:$i]:(![X1235:$i]:(((X1231 @ X1235)<=>((X1235)=(X1234)))))))=>(![X2218:$i]:((((X2218)!=(emptyset))=>?[X2219:$i]:(((in @ X2219 @ X2218)&$true))))=>(![X1236:$i, X1237:$i]:(((in @ X1236 @ (setadjoin @ X1237 @ emptyset))=>((X1236)=(X1237))))=>(![X1238:$i, X1239:$i]:((((X1238)!=(X1239))=>~(in @ X1239 @ (setadjoin @ X1238 @ emptyset))))=>(![X2216:$i, X2217:$i]:((((X2216)=(X2217))=>(in @ X2216 @ (setadjoin @ X2217 @ emptyset))))=>(![X1240:$i, X1241:$i]:(((in @ X1240 @ (setadjoin @ X1241 @ emptyset))=>(in @ X1241 @ (setadjoin @ X1240 @ emptyset))))=>(![X1242:$i, X1243:$i, X1244:$i]:(((in @ X1244 @ (setadjoin @ X1242 @ (setadjoin @ X1243 @ emptyset)))=>(((X1244)=(X1242))|((X1244)=(X1243)))))=>(![X2214:$i, X2215:$i]:((in @ X2214 @ (setadjoin @ X2214 @ (setadjoin @ X2215 @ emptyset))))=>(![X1245:$i, X1246:$i]:((in @ X1246 @ (setadjoin @ X1245 @ (setadjoin @ X1246 @ emptyset))))=>(![X2211:$i, X2212:$i > $o]:((?[X2213:$i]:(((in @ X2213 @ X2211)&(X2212 @ X2213)))=>(((dsetconstr @ X2211 @ X2212)=(emptyset))=>~($true))))=>(![X2209:$i > $o, X2210:$i]:(((in @ X2210 @ emptyset)=>(X2209 @ X2210)))=>(![X1247:$i, X1248:$i > $o]:((~(![X1249:$i]:(((in @ X1249 @ X1247)=>(X1248 @ X1249))))=>?[X1250:$i]:(((in @ X1250 @ X1247)&~((X1248 @ X1250))))))=>(![X2205:$i, X2206:$i > $o]:((![X2207:$i]:(((in @ X2207 @ X2205)=>~((X2206 @ X2207))))=>~(?[X2208:$i]:(((in @ X2208 @ X2205)&(X2206 @ X2208))))))=>(![X1251:$i, X1252:$i > $o]:((~(?[X1253:$i]:(((in @ X1253 @ X1251)&(X1252 @ X1253))))=>![X1254:$i]:(((in @ X1254 @ X1251)=>~((X1252 @ X1254))))))=>(![X2201:$i, X2202:$i > $o]:((?[X2203:$i]:(((in @ X2203 @ X2201)&~((X2202 @ X2203))))=>~(![X2204:$i]:(((in @ X2204 @ X2201)=>(X2202 @ X2204))))))=>(![X1255:$o]:(((X1255)=>(in @ emptyset @ (prop2set @ ((X1255))))))=>(![X1256:$o]:(((X1256)=>(set2prop @ (prop2set @ ((X1256))))))=>(![X2197:$i, X2198:$i > $o]:((~(?[X2199:$i]:(((in @ X2199 @ X2197)&(X2198 @ X2199))))=>![X2200:$i]:(((in @ X2200 @ X2197)=>~((X2198 @ X2200))))))=>(![X2193:$i, X2194:$i > $o]:((~(![X2195:$i]:(((in @ X2195 @ X2193)=>(X2194 @ X2195))))=>?[X2196:$i]:(((in @ X2196 @ X2193)&~((X2194 @ X2196))))))=>(![X2188:$i > $o]:((?[X2189:$i]:(((X2188 @ X2189)&![X2190:$i]:(((X2188 @ X2190)=>((X2189)=(X2190))))))=>?[X2191:$i]:(((X2188 @ X2191)&![X2192:$i]:(((X2188 @ X2192)=>((X2191)=(X2192))))))))=>(![X2182:$i > $o]:((?[X2183:$i]:((X2182 @ X2183))=>(![X2184:$i, X2185:$i]:(((X2182 @ X2184)=>((X2182 @ X2185)=>((X2184)=(X2185)))))=>?[X2186:$i]:(((X2182 @ X2186)&![X2187:$i]:(((X2182 @ X2187)=>((X2186)=(X2187)))))))))=>(![X1257:$i > $o]:((?[X1258:$i]:(![X1259:$i]:(((X1257 @ X1259)<=>((X1259)=(X1258)))))=>?[X1260:$i]:(((X1257 @ X1260)&![X1261:$i]:(((X1257 @ X1261)=>((X1260)=(X1261))))))))=>(![X1262:$i, X1263:$i]:((((X1262)=(X1263))=>![X1264:$i, X1265:$i]:((((X1264)=(X1265))=>((in @ X1264 @ X1262)=>(in @ X1265 @ X1263))))))=>(![X2178:$i, X2179:$i]:((((X2178)=(X2179))=>![X2180:$i, X2181:$i]:((((X2180)=(X2181))=>((in @ X2180 @ X2178)<=>(in @ X2181 @ X2179))))))=>(![X2173:$i > $o]:((?[X2174:$i]:(((X2173 @ X2174)&![X2175:$i]:(((X2173 @ X2175)=>((X2174)=(X2175))))))=>![X2176:$i, X2177:$i]:(((X2173 @ X2176)=>((X2173 @ X2177)=>((X2176)=(X2177)))))))=>(![X2165:$i > $o, X2166:$i > $o]:((![X2167:$i, X2168:$i]:((((X2167)=(X2168))=>((X2165 @ X2167)<=>(X2166 @ X2168))))=>(?[X2169:$i]:(((X2165 @ X2169)&![X2170:$i]:(((X2165 @ X2170)=>((X2169)=(X2170))))))<=>?[X2171:$i]:(((X2166 @ X2171)&![X2172:$i]:(((X2166 @ X2172)=>((X2171)=(X2172)))))))))=>(((emptyset)=(emptyset))=>(![X1266:$i, X1267:$i]:((((X1266)=(X1267))=>![X1268:$i, X1269:$i]:((((X1268)=(X1269))=>((setadjoin @ X1266 @ X1268)=(setadjoin @ X1267 @ X1269))))))=>(![X2163:$i, X2164:$i]:((((X2163)=(X2164))=>((powerset @ X2163)=(powerset @ X2164))))=>(![X1270:$i, X1271:$i]:((((X1270)=(X1271))=>((setunion @ X1270)=(setunion @ X1271))))=>(((omega)=(omega))=>(![X1272:$i > $o]:((?[X1273:$i]:(((X1272 @ X1273)&![X1274:$i]:(((X1272 @ X1274)=>((X1273)=(X1274))))))=>![X1275:$i, X1276:$i]:(((X1272 @ X1275)=>((X1272 @ X1276)=>((X1275)=(X1276)))))))=>(![X1277:$i > $o, X1278:$i > $o]:((![X1279:$i, X1280:$i]:((((X1279)=(X1280))=>((X1277 @ X1279)<=>(X1278 @ X1280))))=>(?[X1281:$i]:(((X1277 @ X1281)&![X1282:$i]:(((X1277 @ X1282)=>((X1281)=(X1282))))))=>(?[X1283:$i]:(((X1278 @ X1283)&![X1284:$i]:(((X1278 @ X1284)=>((X1283)=(X1284))))))=>((descr @ X1277)=(descr @ X1278))))))=>(![X1285:$i, X1286:$i]:((((X1285)=(X1286))=>![X1287:$i > $o, X1288:$i > $o]:((![X1289:$i]:(((in @ X1289 @ X1285)=>![X1290:$i]:(((in @ X1290 @ X1286)=>(((X1289)=(X1290))=>((X1287 @ X1289)<=>(X1288 @ X1290)))))))=>((dsetconstr @ X1285 @ X1287)=(dsetconstr @ X1286 @ X1288))))))=>(![X1291:$i, X1292:$i]:((![X1293:$i]:(((in @ X1293 @ X1291)=>(in @ X1293 @ X1292)))=>(subset @ X1291 @ X1292)))=>(![X2161:$i, X2162:$i]:((((X2161)=(X2162))=>(subset @ X2162 @ X2161)))=>(![X2159:$i, X2160:$i]:((((X2159)=(X2160))=>(subset @ X2159 @ X2160)))=>(![X1294:$i, X1295:$i]:((![X1296:$i]:(((in @ X1296 @ X1294)=>(in @ X1296 @ X1295)))=>(subset @ X1294 @ X1295)))=>(![X1297:$i]:((subset @ emptyset @ X1297))=>(![X1298:$i, X1299:$i, X1300:$i]:(((subset @ X1298 @ X1299)=>((in @ X1300 @ X1298)=>(in @ X1300 @ X1299))))=>(![X1301:$i, X1302:$i, X1303:$i]:(((subset @ X1301 @ X1302)=>(~(in @ X1303 @ X1302)=>~(in @ X1303 @ X1301))))=>(![X2156:$i, X2157:$i, X2158:$i]:(((in @ X2158 @ X2156)=>(~(in @ X2158 @ X2157)=>~(subset @ X2156 @ X2157))))=>(![X2154:$i, X2155:$i]:((~(subset @ X2154 @ X2155)=>((X2154)!=(X2155))))=>(![X1304:$i, X1305:$i, X1306:$i]:(((in @ X1306 @ X1304)=>(~(in @ X1306 @ X1305)=>((X1304)!=(X1305)))))=>(![X1307:$i]:((subset @ X1307 @ X1307))=>(![X1308:$i, X1309:$i, X1310:$i]:(((subset @ X1308 @ X1309)=>((subset @ X1309 @ X1310)=>(subset @ X1308 @ X1310))))=>(![X2152:$i, X2153:$i]:((subset @ X2153 @ (setadjoin @ X2152 @ X2153)))=>(![X2149:$i, X2150:$i, X2151:$i]:(((subset @ X2149 @ X2151)=>(subset @ X2149 @ (setadjoin @ X2150 @ X2151))))=>(![X1311:$i, X1312:$i]:(((subset @ X1311 @ X1312)=>(in @ X1311 @ (powerset @ X1312))))=>(![X2147:$i, X2148:$i]:(((subset @ X2147 @ X2148)=>((subset @ X2148 @ X2147)=>((X2147)=(X2148)))))=>(![X2146:$i]:(((subset @ X2146 @ emptyset)=>((X2146)=(emptyset))))=>(![X1313:$i, X1314:$i]:(((subset @ X1314 @ X1313)=>(in @ X1314 @ (powerset @ X1313))))=>(![X2144:$i, X2145:$i]:(((in @ X2145 @ (powerset @ X2144))=>(subset @ X2145 @ X2144)))=>(![X2143:$i]:((in @ X2143 @ (powerset @ X2143)))=>(![X2141:$i, X2142:$i]:(((subset @ X2141 @ X2142)=>(subset @ (powerset @ X2141) @ (powerset @ X2142))))=>(![X2139:$i, X2140:$i > $o]:((in @ (dsetconstr @ X2139 @ X2140) @ (powerset @ X2139)))=>(![X1315:$i, X1316:$i > $o]:((subset @ (dsetconstr @ X1315 @ X1316) @ X1315))=>(![X2136:$i, X2137:$i, X2138:$i]:(((in @ X2138 @ X2136)=>(in @ X2138 @ (binunion @ X2136 @ X2137))))=>(![X2134:$i, X2135:$i]:((in @ X2135 @ (setadjoin @ X2134 @ (setadjoin @ X2135 @ emptyset))))=>(![X1317:$i, X1318:$i, X1319:$i]:(((in @ X1319 @ X1318)=>(in @ X1319 @ (binunion @ X1317 @ X1318))))=>(![X1320:$i, X1321:$i, X1322:$i, X1323:$o]:(((in @ X1322 @ (binunion @ X1320 @ X1321))=>(((in @ X1322 @ X1320)=>(X1323))=>(((in @ X1322 @ X1321)=>(X1323))=>(X1323)))))=>(![X1324:$i, X1325:$i, X1326:$i]:(((in @ X1326 @ (binunion @ X1324 @ X1325))=>((in @ X1326 @ X1324)|(in @ X1326 @ X1325))))=>(![X1327:$i, X1328:$i]:((subset @ X1327 @ (binunion @ X1327 @ X1328)))=>(![X1329:$i, X1330:$i]:((subset @ X1330 @ (binunion @ X1329 @ X1330)))=>(![X1331:$i, X1332:$i, X1333:$i]:(((in @ X1333 @ X1331)=>((in @ X1333 @ X1332)=>(in @ X1333 @ (binintersect @ X1331 @ X1332)))))=>(![X2131:$i, X2132:$i, X2133:$i]:(((subset @ X2133 @ X2131)=>((subset @ X2133 @ X2132)=>(subset @ X2133 @ (binintersect @ X2131 @ X2132)))))=>(![X2128:$i, X2129:$i, X2130:$i]:(((in @ X2130 @ (binintersect @ X2128 @ X2129))=>(in @ X2130 @ X2128)))=>(![X2126:$i, X2127:$i]:((subset @ (binintersect @ X2126 @ X2127) @ X2126))=>(![X1334:$i, X1335:$i]:(((subset @ X1334 @ X1335)=>((binintersect @ X1334 @ X1335)=(X1334))))=>(![X2124:$i, X2125:$i]:((((binintersect @ X2124 @ X2125)=(X2125))=>(subset @ X2125 @ X2124)))=>(![X2121:$i, X2122:$i, X2123:$i]:(((in @ X2123 @ (binintersect @ X2121 @ X2122))=>(in @ X2123 @ X2122)))=>(![X1336:$i, X1337:$i]:((~(?[X1338:$i]:(((in @ X1338 @ X1336)&(in @ X1338 @ X1337))))=>((binintersect @ X1336 @ X1337)=(emptyset))))=>(![X2119:$i, X2120:$i]:((subset @ (binintersect @ X2119 @ X2120) @ X2120))=>(![X2117:$i, X2118:$i]:(((subset @ X2118 @ X2117)=>((binintersect @ X2117 @ X2118)=(X2118))))=>(![X2115:$i, X2116:$i]:((((binintersect @ X2115 @ X2116)=(X2115))=>(subset @ X2115 @ X2116)))=>(![X1339:$i, X1340:$i, X1341:$i]:(((binintersect @ X1339 @ (binunion @ X1340 @ X1341))=(binunion @ (binintersect @ X1339 @ X1340) @ (binintersect @ X1339 @ X1341))))=>(![X1342:$i, X1343:$i, X1344:$i]:(((in @ X1344 @ X1342)=>(~(in @ X1344 @ X1343)=>(in @ X1344 @ (setminus @ X1342 @ X1343)))))=>(![X1345:$i, X1346:$i, X1347:$i]:(((in @ X1347 @ (setminus @ X1345 @ X1346))=>(in @ X1347 @ X1345)))=>(![X1348:$i, X1349:$i, X1350:$i]:(((in @ X1350 @ (setminus @ X1348 @ X1349))=>~(in @ X1350 @ X1349)))=>(![X1351:$i, X1352:$i]:(((subset @ X1351 @ X1352)=>((setminus @ X1351 @ X1352)=(emptyset))))=>(![X1353:$i, X1354:$i, X1355:$i]:((~(in @ X1355 @ (setminus @ X1353 @ X1354))=>((in @ X1355 @ X1353)=>(in @ X1355 @ X1354))))=>(![X1356:$i, X1357:$i, X1358:$i]:((~(in @ X1358 @ (setminus @ X1356 @ X1357))=>(~(in @ X1358 @ 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binintersectSubset4]), binintersectRsub]), binintersectER]), binintersectSubset3]), binintersectLsub]), binintersectEL]), binintersectSubset5]), upairset2IR]), binunionIL]), symdiffE]), c_0_351]), setminusSubset1]), powersetsubset]), setminusILneg]), inPowerset]), setminusELneg]), powersetE1]), setminusERneg]), subsetemptysetimpeq]), setminusEL]), setextsub]), setminusSubset2]), setadjoinSub2]), setminusER]), setadjoinSub]), symdiffIneg2]), notequalI1]), notsubsetI]), eqimpsubset1]), eqimpsubset2]), powerset__Cong]), emptyset__Cong]), c_0_352]), c_0_353]), in__Cong]), c_0_354]), c_0_355]), notdallE]), notdexE]), ubforcartprodlem2]), quantDeMorgan4]), ubforcartprodlem1]), quantDeMorgan2]), upairinpowunion]), vacuousDall]), upairsubunion]), c_0_356]), upairset2E]), upairsetIL]), singletoninpowerset]), eqinunit]), setukpairIL]), c_0_357]), cartprodmempair1]), setunionE]), setunionI]), c_0_358]), emptyinunitempty]), c_0_359]), emptyI]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_360]), c_0_361]), c_0_362]), c_0_363]), theprop]), wellorderingAx]), singletonsuniq]), foundationAx]), c_0_364]), omegaIndAx]), setunionsingleton]), omega0Ax]), setunionsingleton1]), setunionAx]), setunionE2]), cartprodmempair]), setukpairinjL2]), c_0_365]), powersetTE1]), c_0_366]), cartprodsndpairEq]), cartprodpairmemEL]), setukpairinjR2]), setukpairinjR1]), setukpairinjR12]), setukpairinjL]), c_0_367]), c_0_368]), c_0_369]), ap2p]), app]), c_0_370]), c_0_371]), c_0_372]), c_0_373]), ap2apEq1]), funcext2]), funcext]), funcGraphProp4]), funcGraphProp2]), c_0_374]), brelnall1]), c_0_375]), setextT]), binunionT_lem]), iftrueorfalse]), iftrue]), c_0_376]), c_0_377]), breln1unionE]), breln1invprop]), woz13rule4]), woz1_1]), woz1_2]), woz1_4]), c_0_378]), breln1all1]), doubleComplementSub2]), doubleComplementSub1]), doubleComplementI1]), contrasubsetT3]), contrasubsetT2]), contrasubsetT1]), complementTI1]), doubleComplementEq]), binunionTE]), inComplementUnionImpInComplement1]), inComplementUnionImpNotIn1]), inIntersectImpInIntersectUnions]), inIntersectImpInUnion2]), binunionTILcontra]), complementImpComplementIntersect]), demorgan1a]), breln1SetBreln1]), breln1all2]), woz1_5]), woz1_3]), woz13rule0]), demorgan2]), demorgan1]), c_0_379]), woz2W]), breln1unionEcases]), breln1unionprop]), breln1compEex]), breln1compE]), breln1compprop]), subbreln1]), woz2B]), c_0_342]), peanoSinj]), c_0_380]), leftInvIsSurj]), injFuncSetFuncIn]), c_0_381]), c_0_382]), c_0_383]), surjFuncSetFuncSurj]), surjCantorThm]), notinself]), notinself2]), omegaSp]), omegaSclos]), peano0notS]), surjFuncSetFuncIn]), woz2Ex]), woz2A]), image1Ex]), c_0_384]), c_0_385]), injFuncInInjFuncSet]), injFuncSetFuncInj]), breln1unionCommutes]), breln1invI]), breln1invE]), breln1compI]), breln1unionIL]), breln1unionIR]), breln1unionI]), eqbreln1]), woz13rule3]), demorgan2a2]), demorgan1b]), demorgan2a]), demorgan2b2]), demorgan2b]), woz13rule1]), woz13rule2]), 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2.09/0.83	thf(c_0_415, negated_conjecture, ![X2281:$i, X2282:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2294:$i, X2295:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2303:$i, X2304:$i > $i > $o, X2305:$i, X2307:$i, X2310:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2317:$i, X2318:$i > $o, X2319:$i, X2321:$i, X2322:$i > $o, X2323:$i, X2324:$i, X2325:$i > $o, X2326:$i, X2327:$i, X2328:$i > $o, X2329:$i, X2330:$i > $o, X2331:$i, X2334:$i, X2335:$o, X2336:$i, X2337:$i, X2338:$o, X2339:$i, X2340:$i, X2341:$i > $o, X2342:$i, X2345:$i, X2346:$i, X2349:$i, X2351:$i, X2353:$i, X2354:$i > $o, X2355:$i, X2356:$i, X2358:$i, X2359:$i > $o, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$o, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$o, X2391:$i, X2392:$i, X2393:$i > $o, X2394:$i, X2397:$i, X2398:$i, X2399:$i, X2401:$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, X2414:$i, X2415:$i, X2416:$i, X2417:$i > $o, X2418:$i, X2419:$i > $o, X2420:$i, X2421:$i, X2422:$i > $o, X2423:$i, X2425:$i, X2426:$i > $o, X2428:$i, X2429:$i, X2430:$i > $o, X2432:$i, X2433:$i, X2434:$i > $o, X2435:$i, X2437:$o, X2438:$o, X2439:$i, X2440:$i > $o, X2442:$i, X2443:$i, X2444:$i > $o, X2445:$i, X2447:$i > $o, X2448:$i, X2451:$i, X2452:$i > $o, X2453:$i, X2457:$i, X2458:$i > $o, X2459:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i > $o, X2472:$i, X2474:$i, X2475:$i, X2476:$i > $o, X2477:$i > $o, X2480:$i, X2483:$i, X2484:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i > $o, X2497:$i, X2499:$i, X2500:$i, X2501:$i > $o, X2502:$i > $o, X2505:$i, X2507:$i, X2509:$i, X2510:$i, X2511:$i > $o, X2512:$i > $o, X2515:$i, X2516:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$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 > $o, X2563:$i, X2564:$i > $o, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$o, X2577:$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, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2623:$i, X2624:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i, X2630:$i, X2631:$i, X2632:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$o, 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, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i > $o, X2719:$i, X2720:$i, X2721:$i > $o, X2723:$i, X2724:$i > $o, X2725:$i, X2727:$i, X2728:$i > $o, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i > $i > $o, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i > $i > $o, X2809:$i, X2810:$i, X2811:$i > $i > $o, X2812:$i, X2813:$i, X2814:$i > $i > $o, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i > $i > $o, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i > $i > $o, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i > $i > $o, X2830:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$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 > $i, X2858:$i, X2859:$i, X2860:$i > $i, X2862:$i, X2863:$i, X2864:$i > $i, X2866:$i, X2867:$i, X2868:$i, X2869:$i > $o, X2872:$i, X2873:$i, X2874:$i, X2875:$i, X2876:$i > $o, X2879:$i, X2880:$i, X2881:$i > $o, X2882:$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, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i > $i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$i, X2951:$i > $i, X2953:$i, X2954:$i, X2955:$i > $i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$o, X2963:$i, X2964:$i, X2965:$i, X2966:$o, X2967:$i, X2968:$i, X2969:$i, X2970:$o, X2971:$i, X2972:$i, X2973:$i, X2974:$o, X2975:$i, X2976:$i, X2977:$i, X2978:$o, X2979:$i, X2980:$i, X2981:$i, X2982:$o, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$o, X2989:$i, X2990:$i, X2991:$i, X2992:$o, X2993:$i, X2994:$i, X2995:$i, X2996:$o, X2997:$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:$i, X3017:$i, X3018:$i, X3019:$i, X3021:$i, X3022:$i, X3023:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i, X3037:$i, X3038:$i, X3039:$i, X3040:$i, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3047:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3059:$i, X3060:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i, X3068:$i, X3069:$i, X3070:$i, X3071:$i, X3072:$i, X3073:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i, X3079:$i, X3080:$i, X3081:$i, X3082:$i, X3083:$i, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i, X3090:$i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$i, X3115:$i, X3116:$i, X3117:$i, X3118:$i, X3119:$i, X3120:$i, X3121:$i, X3122:$i, X3123:$i, X3124:$i, X3125:$i, X3126:$i, X3127:$i, X3128:$o, X3129:$i, X3130:$i, X3131:$i, X3132:$i, X3133:$i, X3134:$i, X3135:$i, X3136:$i, X3137:$i, X3138:$i, X3139:$i, X3140:$i, X3141:$i, X3142:$i, X3143:$i, X3144:$i, X3145:$i, X3146:$i, X3147:$i, X3148:$i, X3149:$i, X3150:$i, X3151:$i, X3152:$i, X3153:$i, X3154:$i, X3155:$i, X3156:$i, X3157:$i, X3158:$i, X3159:$i, X3160:$i, X3161:$i, X3162:$i, X3163:$i, X3164:$i, X3165:$i, X3166:$i, X3167:$i, X3168:$i, X3169:$i, X3170:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i, X3176:$i, X3177:$i, X3178:$i, X3179:$i, X3180:$i, X3181:$i, X3182:$i, X3183:$i, X3184:$i, X3185:$i, X3186:$i, X3187:$i, X3188:$i, X3189:$i, X3190:$i, X3191:$i, X3192:$i, X3193:$i, X3194:$i, X3195:$i, X3196:$i, X3197:$i, X3198:$i, X3199:$i, X3200:$i, X3201:$i, X3202:$i, X3203:$i, X3204:$i, X3205:$i, X3206:$i, X3207:$i, X3208:$i, X3209:$i, X3210:$i, X3211:$i, X3212:$i > $o, X3215:$i, X3216:$i, X3217:$i, X3218:$i, X3219:$i, X3220:$i > $i > $o, X3222:$i, X3223:$i, X3224:$i, X3225:$i, X3226:$i > $i > $o, X3227:$i, X3228:$i, X3229:$i > $o, X3232:$i, X3233:$i, X3234:$i, X3235:$i, X3238:$i, X3239:$i, X3240:$i, X3245:$i, X3246:$i, X3247:$i, X3248:$i, X3249:$i, X3250:$i, X3251:$i, X3252:$i, X3253:$i, X3254:$i, X3255:$i, X3256:$i, X3257:$i, X3258:$i, X3259:$i, X3260:$i, X3261:$i, X3262:$i, X3263:$i, X3264:$i, X3265:$i, X3266:$i, X3267:$i, X3268:$i, X3270:$i, X3271:$i, X3272:$i, X3273:$i, X3274:$i, X3275:$o, X3277:$i, X3278:$i, X3279:$i, X3280:$i, X3281:$i, X3282:$i, X3283:$i, X3284:$i, X3285:$i, X3286:$i, X3287:$i, X3288:$i, X3289:$i, X3290:$i, X3291:$i, X3292:$i, X3293:$i, X3294:$i, X3295:$i, X3296:$i, X3297:$i, X3298:$i, X3299:$i, X3300:$i, X3301:$i, X3302:$i, X3303:$i, X3304:$i, X3305:$o, X3306:$i, X3307:$i, X3308:$i, X3309:$i, X3310:$i, X3311:$i, X3312:$i, X3313:$i, X3314:$i, X3315:$i, X3316:$i, X3317:$i, X3318:$i, X3319:$i, X3320:$i, X3321:$i, X3322:$i, X3323:$i > $i, X3325:$i, X3327:$i, X3328:$i, X3329:$i, X3330:$i > $i, X3332:$i, X3334:$i, X3335:$i, X3336:$i, X3338:$i, X3340:$i, X3341:$i > $i, X3342:$i, X3344:$i, X3345:$i > $i, X3346:$i, X3347:$i, X3348:$i, X3349:$i > $i, X3350:$i, X3352:$i, X3353:$i > $i, X3354:$i, X3355:$i, X3356:$i, X3357:$i, X3358:$i, X3359:$i, X3360:$i, X3361:$i, X3362:$i, X3363:$i, X3364:$i, X3365:$i, X3366:$i, X3367:$i, X3368:$i, X3369:$i, X3370:$i, X3371:$i, X3372:$i, X3373:$i > $i, X3375:$i, X3377:$i, X3378:$i, X3379:$i, X3381:$i, X3382:$i, X3383:$i, X3384:$i, X3385:$i, X3386:$i, X3387:$i, X3388:$i, X3389:$i, X3391:$i, X3393:$i, X3395:$i]:((((~(in @ (esk1_2 @ X2281 @ X2282) @ X2281)|~(in @ (esk1_2 @ X2281 @ X2282) @ X2282)|((X2281)=(X2282)))&((in @ (esk1_2 @ X2281 @ X2282) @ X2281)|(in @ (esk1_2 @ X2281 @ X2282) @ X2282)|((X2281)=(X2282))))&(~(in @ X2284 @ emptyset)&(((~(in @ X2287 @ (setadjoin @ X2285 @ X2286))|(((X2287)=(X2285))|(in @ X2287 @ X2286)))&((((X2287)!=(X2285))|(in @ X2287 @ (setadjoin @ X2285 @ X2286)))&(~(in @ X2287 @ X2286)|(in @ X2287 @ (setadjoin @ X2285 @ X2286)))))&(((~(in @ X2289 @ (powerset @ X2288))|(~(in @ X2290 @ X2289)|(in @ X2290 @ X2288)))&(((in @ (esk2_2 @ X2291 @ X2292) @ X2292)|(in @ X2292 @ (powerset @ X2291)))&(~(in @ (esk2_2 @ X2291 @ X2292) @ X2291)|(in @ X2292 @ (powerset @ X2291)))))&(((((in @ X2295 @ (esk3_2 @ X2294 @ X2295))|~(in @ X2295 @ (setunion @ X2294)))&((in @ (esk3_2 @ X2294 @ X2295) @ X2294)|~(in @ X2295 @ (setunion @ X2294))))&(~(in @ X2298 @ X2299)|~(in @ X2299 @ X2297)|(in @ X2298 @ (setunion @ X2297))))&((in @ emptyset @ omega)&((~(in @ X2300 @ omega)|(in @ (setadjoin @ X2300 @ X2300) @ omega))&(((((in @ (esk4_1 @ X2301) @ omega)|~(in @ emptyset @ X2301)|(~(in @ X2303 @ omega)|(in @ X2303 @ X2301)))&((in @ (esk4_1 @ X2301) @ X2301)|~(in @ emptyset @ X2301)|(~(in @ X2303 @ omega)|(in @ X2303 @ X2301))))&(~(in @ (setadjoin @ (esk4_1 @ X2301) @ (esk4_1 @ X2301)) @ X2301)|~(in @ emptyset @ X2301)|(~(in @ X2303 @ omega)|(in @ X2303 @ X2301))))&((((((in @ (esk8_3 @ X2304 @ X2305 @ X2310) @ X2305)|~(in @ X2310 @ (esk7_2 @ X2304 @ X2305))|(in @ (esk5_2 @ X2304 @ X2305) @ X2305))&((X2304 @ (esk8_3 @ X2304 @ X2305 @ X2310) @ X2310)|~(in @ X2310 @ (esk7_2 @ X2304 @ X2305))|(in @ (esk5_2 @ X2304 @ X2305) @ X2305)))&(~(in @ X2313 @ X2305)|~(X2304 @ X2313 @ X2312)|(in @ X2312 @ (esk7_2 @ X2304 @ X2305))|(in @ (esk5_2 @ X2304 @ X2305) @ X2305)))&(((((in @ (esk8_3 @ X2304 @ X2305 @ X2310) @ X2305)|~(in @ X2310 @ (esk7_2 @ X2304 @ X2305))|((X2304 @ (esk5_2 @ X2304 @ X2305) @ (esk6_3 @ X2304 @ X2305 @ X2307))|~(X2304 @ (esk5_2 @ X2304 @ X2305) @ X2307)))&((X2304 @ (esk8_3 @ X2304 @ X2305 @ X2310) @ X2310)|~(in @ X2310 @ (esk7_2 @ X2304 @ X2305))|((X2304 @ (esk5_2 @ X2304 @ X2305) @ (esk6_3 @ X2304 @ X2305 @ X2307))|~(X2304 @ (esk5_2 @ X2304 @ X2305) @ X2307))))&(~(in @ X2313 @ X2305)|~(X2304 @ X2313 @ X2312)|(in @ X2312 @ (esk7_2 @ X2304 @ X2305))|((X2304 @ (esk5_2 @ X2304 @ X2305) @ (esk6_3 @ X2304 @ X2305 @ X2307))|~(X2304 @ (esk5_2 @ X2304 @ X2305) @ X2307))))&((((in @ (esk8_3 @ X2304 @ X2305 @ X2310) @ X2305)|~(in @ X2310 @ (esk7_2 @ X2304 @ X2305))|(((X2307)!=(esk6_3 @ X2304 @ X2305 @ X2307))|~(X2304 @ 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@ X3235) @ X3233)|(subset @ X3234 @ X3235)|~(breln1 @ X3233 @ X3235)|~(breln1 @ X3233 @ X3234))&(((in @ (kpair @ (esk92_3 @ X3233 @ X3234 @ X3235) @ (esk93_3 @ X3233 @ X3234 @ X3235)) @ X3234)|(subset @ X3234 @ X3235)|~(breln1 @ X3233 @ X3235)|~(breln1 @ X3233 @ X3234))&(~(in @ (kpair @ (esk92_3 @ X3233 @ X3234 @ X3235) @ (esk93_3 @ X3233 @ X3234 @ X3235)) @ X3235)|(subset @ X3234 @ X3235)|~(breln1 @ X3233 @ X3235)|~(breln1 @ X3233 @ X3234)))))&(((((in @ (esk96_3 @ X3238 @ X3239 @ X3240) @ X3238)|((X3239)=(X3240))|(in @ (esk94_3 @ X3238 @ X3239 @ X3240) @ X3238)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(((in @ (esk97_3 @ X3238 @ X3239 @ X3240) @ X3238)|((X3239)=(X3240))|(in @ (esk94_3 @ X3238 @ X3239 @ X3240) @ X3238)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(((in @ (kpair @ (esk96_3 @ X3238 @ X3239 @ X3240) @ (esk97_3 @ X3238 @ X3239 @ X3240)) @ X3240)|((X3239)=(X3240))|(in @ (esk94_3 @ X3238 @ X3239 @ X3240) @ X3238)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(~(in @ (kpair @ (esk96_3 @ X3238 @ X3239 @ X3240) @ (esk97_3 @ X3238 @ X3239 @ X3240)) @ X3239)|((X3239)=(X3240))|(in @ (esk94_3 @ X3238 @ X3239 @ X3240) @ X3238)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239)))))&((((in @ (esk96_3 @ X3238 @ X3239 @ X3240) @ X3238)|((X3239)=(X3240))|(in @ (esk95_3 @ X3238 @ X3239 @ X3240) @ X3238)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(((in @ (esk97_3 @ X3238 @ X3239 @ X3240) @ X3238)|((X3239)=(X3240))|(in @ (esk95_3 @ X3238 @ X3239 @ X3240) @ X3238)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(((in @ (kpair @ (esk96_3 @ X3238 @ X3239 @ X3240) @ (esk97_3 @ X3238 @ X3239 @ X3240)) @ X3240)|((X3239)=(X3240))|(in @ (esk95_3 @ X3238 @ X3239 @ X3240) @ X3238)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(~(in @ (kpair @ (esk96_3 @ X3238 @ X3239 @ X3240) @ (esk97_3 @ X3238 @ X3239 @ X3240)) @ X3239)|((X3239)=(X3240))|(in @ (esk95_3 @ X3238 @ X3239 @ X3240) @ X3238)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239)))))&((((in @ (esk96_3 @ X3238 @ X3239 @ X3240) @ X3238)|((X3239)=(X3240))|(in @ (kpair @ (esk94_3 @ X3238 @ X3239 @ X3240) @ (esk95_3 @ X3238 @ X3239 @ X3240)) @ X3239)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(((in @ (esk97_3 @ X3238 @ X3239 @ X3240) @ X3238)|((X3239)=(X3240))|(in @ (kpair @ (esk94_3 @ X3238 @ X3239 @ X3240) @ (esk95_3 @ X3238 @ X3239 @ X3240)) @ X3239)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(((in @ (kpair @ (esk96_3 @ X3238 @ X3239 @ X3240) @ (esk97_3 @ X3238 @ X3239 @ X3240)) @ X3240)|((X3239)=(X3240))|(in @ (kpair @ (esk94_3 @ X3238 @ X3239 @ X3240) @ (esk95_3 @ X3238 @ X3239 @ X3240)) @ X3239)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(~(in @ (kpair @ (esk96_3 @ X3238 @ X3239 @ X3240) @ (esk97_3 @ X3238 @ X3239 @ X3240)) @ X3239)|((X3239)=(X3240))|(in @ (kpair @ (esk94_3 @ X3238 @ X3239 @ X3240) @ (esk95_3 @ X3238 @ X3239 @ X3240)) @ X3239)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239)))))&(((in @ (esk96_3 @ X3238 @ X3239 @ X3240) @ X3238)|((X3239)=(X3240))|~(in @ (kpair @ (esk94_3 @ X3238 @ X3239 @ X3240) @ (esk95_3 @ X3238 @ X3239 @ X3240)) @ X3240)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(((in @ (esk97_3 @ X3238 @ X3239 @ X3240) @ X3238)|((X3239)=(X3240))|~(in @ (kpair @ (esk94_3 @ X3238 @ X3239 @ X3240) @ (esk95_3 @ X3238 @ X3239 @ X3240)) @ X3240)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(((in @ (kpair @ (esk96_3 @ X3238 @ X3239 @ X3240) @ (esk97_3 @ X3238 @ X3239 @ X3240)) @ X3240)|((X3239)=(X3240))|~(in @ (kpair @ (esk94_3 @ X3238 @ X3239 @ X3240) @ (esk95_3 @ X3238 @ X3239 @ X3240)) @ X3240)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))&(~(in @ (kpair @ (esk96_3 @ X3238 @ X3239 @ X3240) @ (esk97_3 @ X3238 @ X3239 @ X3240)) @ X3239)|((X3239)=(X3240))|~(in @ (kpair @ (esk94_3 @ X3238 @ X3239 @ X3240) @ (esk95_3 @ X3238 @ X3239 @ X3240)) @ X3240)|~(breln1 @ X3238 @ X3240)|~(breln1 @ X3238 @ X3239))))))))&((~(breln1 @ X3245 @ X3246)|(breln1 @ X3245 @ (breln1invset @ X3245 @ X3246)))&((~(breln1 @ X3247 @ X3248)|(~(in @ X3249 @ X3247)|(~(in @ X3250 @ X3247)|(~(in @ (kpair @ X3249 @ X3250) @ X3248)|(in @ (kpair @ X3250 @ X3249) @ (breln1invset @ X3247 @ X3248))))))&((~(breln1 @ X3251 @ X3252)|(~(in @ X3253 @ X3251)|(~(in @ X3254 @ X3251)|(~(in @ (kpair @ X3254 @ X3253) @ (breln1invset @ X3251 @ X3252))|(in @ (kpair @ X3253 @ X3254) @ X3252)))))&((~(breln1 @ X3255 @ X3256)|(~(breln1 @ X3255 @ X3257)|(breln1 @ X3255 @ (breln1compset @ X3255 @ X3256 @ X3257))))&((~(breln1 @ X3258 @ X3259)|(~(breln1 @ X3258 @ X3260)|(~(in @ X3261 @ X3258)|(~(in @ X3262 @ X3258)|(~(in @ X3263 @ X3258)|(~(in @ (kpair @ X3261 @ X3263) @ X3259)|(~(in @ (kpair @ X3263 @ X3262) @ X3260)|(in @ (kpair @ X3261 @ X3262) @ (breln1compset @ X3258 @ X3259 @ X3260)))))))))&(((((in @ (esk98_5 @ X3264 @ X3265 @ X3266 @ X3267 @ X3268) @ X3264)|~(in @ (kpair @ X3267 @ X3268) @ (breln1compset @ X3264 @ X3265 @ X3266))|~(in @ X3268 @ X3264)|~(in @ X3267 @ X3264)|~(breln1 @ X3264 @ X3266)|~(breln1 @ X3264 @ X3265))&((in @ (kpair @ X3267 @ (esk98_5 @ X3264 @ X3265 @ X3266 @ X3267 @ X3268)) @ X3265)|~(in @ (kpair @ X3267 @ X3268) @ (breln1compset @ X3264 @ X3265 @ X3266))|~(in @ X3268 @ X3264)|~(in @ X3267 @ X3264)|~(breln1 @ X3264 @ X3266)|~(breln1 @ X3264 @ X3265)))&((in @ (kpair @ (esk98_5 @ X3264 @ X3265 @ X3266 @ X3267 @ X3268) @ X3268) @ X3266)|~(in @ (kpair @ X3267 @ X3268) @ (breln1compset @ X3264 @ X3265 @ X3266))|~(in @ X3268 @ X3264)|~(in @ X3267 @ X3264)|~(breln1 @ X3264 @ X3266)|~(breln1 @ X3264 @ X3265)))&((((in @ (esk99_6 @ X3270 @ X3271 @ X3272 @ X3273 @ X3274 @ X3275) @ X3270)|(X3275)|~(in @ (kpair @ X3273 @ X3274) @ (breln1compset @ X3270 @ X3271 @ X3272))|~(in @ X3274 @ X3270)|~(in @ X3273 @ X3270)|~(breln1 @ X3270 @ X3272)|~(breln1 @ X3270 @ X3271))&(((in @ (kpair @ X3273 @ (esk99_6 @ X3270 @ X3271 @ X3272 @ X3273 @ X3274 @ X3275)) @ X3271)|(X3275)|~(in @ (kpair @ X3273 @ X3274) @ (breln1compset @ X3270 @ X3271 @ X3272))|~(in @ X3274 @ X3270)|~(in @ X3273 @ X3270)|~(breln1 @ X3270 @ X3272)|~(breln1 @ X3270 @ X3271))&(((in @ (kpair @ (esk99_6 @ X3270 @ X3271 @ X3272 @ X3273 @ X3274 @ X3275) @ X3274) @ X3272)|(X3275)|~(in @ (kpair @ X3273 @ X3274) @ (breln1compset @ X3270 @ X3271 @ X3272))|~(in @ X3274 @ X3270)|~(in @ X3273 @ X3270)|~(breln1 @ X3270 @ X3272)|~(breln1 @ X3270 @ X3271))&(~(X3275)|(X3275)|~(in @ (kpair @ X3273 @ X3274) @ (breln1compset @ X3270 @ X3271 @ X3272))|~(in @ X3274 @ X3270)|~(in @ X3273 @ X3270)|~(breln1 @ X3270 @ X3272)|~(breln1 @ X3270 @ X3271)))))&((~(breln1 @ X3277 @ X3278)|(~(breln1 @ X3277 @ X3279)|(breln1 @ X3277 @ (binunion @ X3278 @ X3279))))&((~(breln1 @ X3280 @ X3281)|(~(breln1 @ X3280 @ X3282)|(~(in @ X3283 @ X3280)|(~(in @ X3284 @ X3280)|(~(in @ (kpair @ X3283 @ X3284) @ X3281)|(in @ (kpair @ X3283 @ X3284) @ (binunion @ X3281 @ X3282)))))))&((~(breln1 @ X3285 @ X3286)|(~(breln1 @ X3285 @ X3287)|(~(in @ X3288 @ X3285)|(~(in @ X3289 @ X3285)|(~(in @ (kpair @ X3288 @ X3289) @ X3287)|(in @ (kpair @ X3288 @ X3289) @ (binunion @ X3286 @ X3287)))))))&(((~(in @ (kpair @ X3293 @ X3294) @ X3291)|(in @ (kpair @ X3293 @ X3294) @ (binunion @ X3291 @ X3292))|~(in @ X3294 @ X3290)|~(in @ X3293 @ X3290)|~(breln1 @ X3290 @ X3292)|~(breln1 @ X3290 @ X3291))&(~(in @ (kpair @ X3293 @ X3294) @ X3292)|(in @ (kpair @ X3293 @ X3294) @ (binunion @ X3291 @ X3292))|~(in @ X3294 @ X3290)|~(in @ X3293 @ X3290)|~(breln1 @ X3290 @ X3292)|~(breln1 @ X3290 @ X3291)))&((~(breln1 @ X3295 @ X3296)|(~(breln1 @ X3295 @ X3297)|(~(in @ X3298 @ X3295)|(~(in @ X3299 @ X3295)|(~(in @ (kpair @ X3298 @ X3299) @ (binunion @ X3296 @ X3297))|((in @ (kpair @ X3298 @ X3299) @ X3296)|(in @ (kpair @ X3298 @ X3299) @ X3297)))))))&(((((in @ (kpair @ X3303 @ X3304) @ X3302)|(X3305)|(in @ (kpair @ X3303 @ X3304) @ X3301)|~(in @ (kpair @ X3303 @ X3304) @ (binunion @ X3301 @ X3302))|~(in @ X3304 @ X3300)|~(in @ X3303 @ X3300)|~(breln1 @ X3300 @ X3302)|~(breln1 @ X3300 @ X3301))&(~(X3305)|(X3305)|(in @ (kpair @ X3303 @ X3304) @ X3301)|~(in @ (kpair @ X3303 @ X3304) @ (binunion @ X3301 @ X3302))|~(in @ X3304 @ X3300)|~(in @ X3303 @ X3300)|~(breln1 @ X3300 @ X3302)|~(breln1 @ X3300 @ X3301)))&(((in @ (kpair @ X3303 @ X3304) @ X3302)|(X3305)|~(X3305)|~(in @ (kpair @ X3303 @ X3304) @ (binunion @ X3301 @ X3302))|~(in @ X3304 @ X3300)|~(in @ X3303 @ X3300)|~(breln1 @ X3300 @ X3302)|~(breln1 @ X3300 @ X3301))&(~(X3305)|(X3305)|~(X3305)|~(in @ (kpair @ X3303 @ X3304) @ (binunion @ X3301 @ X3302))|~(in @ X3304 @ X3300)|~(in @ X3303 @ X3300)|~(breln1 @ X3300 @ X3302)|~(breln1 @ X3300 @ X3301))))&((~(breln1 @ X3306 @ X3307)|(~(breln1 @ X3306 @ X3308)|((binunion @ X3307 @ X3308)=(binunion @ X3308 @ X3307))))&((~(breln1 @ X3309 @ X3310)|((X3310)=(breln1invset @ X3309 @ (breln1invset @ X3309 @ X3310))))&((~(breln1 @ X3311 @ X3312)|(~(breln1 @ X3311 @ X3313)|((breln1invset @ X3311 @ (breln1compset @ X3311 @ X3312 @ X3313))=(breln1compset @ X3311 @ (breln1invset @ X3311 @ X3313) @ (breln1invset @ X3311 @ X3312)))))&((~(breln1 @ X3314 @ X3315)|(~(breln1 @ X3314 @ X3316)|(~(breln1 @ X3314 @ X3317)|((breln1compset @ X3314 @ (binunion @ X3315 @ X3316) @ X3317)=(binunion @ (breln1compset @ X3314 @ X3315 @ X3317) @ (breln1compset @ X3314 @ X3316 @ X3317))))))&((~(breln1 @ X3318 @ X3319)|(~(breln1 @ X3318 @ X3320)|(~(breln1 @ X3318 @ X3321)|((breln1compset @ X3318 @ (binunion @ X3319 @ X3320) @ X3321)=(binunion @ (breln1invset @ X3318 @ (breln1compset @ X3318 @ (breln1invset @ X3318 @ X3321) @ (breln1invset @ X3318 @ X3320))) @ (breln1invset @ X3318 @ (breln1compset @ X3318 @ (breln1invset @ X3318 @ X3321) @ (breln1invset @ X3318 @ X3319))))))))&(((((in @ (esk101_3 @ X3322 @ X3323 @ X3325) @ X3322)|~(in @ X3325 @ (esk100_2 @ X3322 @ X3323)))&(((X3325)=(X3323 @ (esk101_3 @ X3322 @ X3323 @ X3325)))|~(in @ X3325 @ (esk100_2 @ X3322 @ X3323))))&(~(in @ X3328 @ X3322)|((X3327)!=(X3323 @ X3328))|(in @ X3327 @ (esk100_2 @ X3322 @ X3323))))&((((((in @ (esk103_3 @ X3329 @ X3330 @ X3332) @ X3329)|~(in @ X3332 @ (esk102_2 @ X3329 @ X3330)))&(((X3332)=(X3330 @ (esk103_3 @ X3329 @ X3330 @ X3332)))|~(in @ X3332 @ (esk102_2 @ X3329 @ X3330))))&(~(in @ X3335 @ X3329)|((X3334)!=(X3330 @ X3335))|(in @ X3334 @ (esk102_2 @ X3329 @ X3330))))&((~(in @ (esk104_3 @ X3329 @ X3330 @ X3336) @ X3336)|(~(in @ X3338 @ X3329)|((esk104_3 @ X3329 @ X3330 @ X3336)!=(X3330 @ X3338)))|((esk102_2 @ X3329 @ X3330)=(X3336)))&(((in @ (esk105_3 @ X3329 @ X3330 @ X3336) @ X3329)|(in @ (esk104_3 @ X3329 @ X3330 @ X3336) @ X3336)|((esk102_2 @ X3329 @ X3330)=(X3336)))&(((esk104_3 @ X3329 @ X3330 @ X3336)=(X3330 @ (esk105_3 @ X3329 @ X3330 @ X3336)))|(in @ (esk104_3 @ X3329 @ X3330 @ X3336) @ X3336)|((esk102_2 @ X3329 @ X3330)=(X3336))))))&(((((in @ (esk106_3 @ X3340 @ X3341 @ X3342) @ X3340)|~(in @ X3342 @ (image1 @ X3340 @ X3341)))&(((X3342)=(X3341 @ (esk106_3 @ X3340 @ X3341 @ X3342)))|~(in @ X3342 @ (image1 @ X3340 @ X3341))))&(~(in @ X3347 @ X3344)|((X3346)!=(X3345 @ X3347))|(in @ X3346 @ (image1 @ X3344 @ X3345))))&((((in @ (esk107_3 @ X3348 @ X3349 @ X3350) @ X3348)|~(in @ X3350 @ (image1 @ X3348 @ X3349)))&(((X3350)=(X3349 @ (esk107_3 @ X3348 @ X3349 @ X3350)))|~(in @ X3350 @ (image1 @ X3348 @ X3349))))&((~(in @ X3355 @ X3352)|((X3354)!=(X3353 @ X3355))|(in @ X3354 @ (image1 @ X3352 @ X3353)))&((~(in @ X3358 @ (funcSet @ X3356 @ X3357))|(~(injective @ X3356 @ X3357 @ X3358)|(in @ X3358 @ (injFuncSet @ X3356 @ X3357))))&((~(in @ X3361 @ (injFuncSet @ X3359 @ X3360))|(in @ X3361 @ (funcSet @ X3359 @ X3360)))&((~(in @ X3364 @ (injFuncSet @ X3362 @ X3363))|(injective @ X3362 @ X3363 @ X3364))&((~(in @ X3367 @ (surjFuncSet @ X3365 @ X3366))|(in @ X3367 @ (funcSet @ X3365 @ X3366)))&((~(in @ X3370 @ (surjFuncSet @ X3368 @ X3369))|(surjective @ X3368 @ X3369 @ X3370))&(((((in @ (esk109_4 @ X3371 @ X3372 @ X3373 @ X3375) @ X3371)|(surjective @ X3372 @ X3371 @ X3375)|~(in @ X3375 @ (funcSet @ X3372 @ X3371))|(in @ (esk108_3 @ X3371 @ X3372 @ X3373) @ X3371))&(((ap @ X3372 @ X3371 @ X3375 @ (X3373 @ (esk109_4 @ X3371 @ X3372 @ X3373 @ X3375)))!=(esk109_4 @ X3371 @ X3372 @ X3373 @ X3375))|(surjective @ X3372 @ X3371 @ X3375)|~(in @ X3375 @ (funcSet @ X3372 @ X3371))|(in @ (esk108_3 @ X3371 @ X3372 @ X3373) @ X3371)))&(((in @ (esk109_4 @ X3371 @ X3372 @ X3373 @ X3375) @ X3371)|(surjective @ X3372 @ X3371 @ X3375)|~(in @ X3375 @ (funcSet @ X3372 @ X3371))|~(in @ (X3373 @ (esk108_3 @ X3371 @ X3372 @ X3373)) @ X3372))&(((ap @ X3372 @ X3371 @ X3375 @ (X3373 @ (esk109_4 @ X3371 @ X3372 @ X3373 @ X3375)))!=(esk109_4 @ X3371 @ X3372 @ X3373 @ X3375))|(surjective @ X3372 @ X3371 @ X3375)|~(in @ X3375 @ (funcSet @ X3372 @ X3371))|~(in @ (X3373 @ (esk108_3 @ X3371 @ X3372 @ X3373)) @ X3372))))&((~(in @ X3378 @ (funcSet @ X3377 @ (powerset @ X3377)))|~(surjective @ X3377 @ (powerset @ X3377) @ X3378))&((((in @ (esk110_1 @ X3379) @ X3379)|((X3379)=(emptyset)))&(((binintersect @ (esk110_1 @ X3379) @ X3379)=(emptyset))|((X3379)=(emptyset))))&(~(in @ X3381 @ X3381)&((~(in @ X3382 @ X3383)|~(in @ X3383 @ X3382))&((~(in @ X3384 @ omega)|(in @ (omegaS @ X3384) @ omega))&((~(in @ X3385 @ omega)|(in @ (setadjoin @ X3385 @ X3385) @ omega))&((~(in @ X3386 @ omega)|((omegaS @ X3386)!=(emptyset)))&((~(in @ X3387 @ omega)|(~(in @ X3388 @ omega)|(((omegaS @ X3387)!=(omegaS @ X3388))|((X3387)=(X3388)))))&((((in @ (esk111_1 @ X3389) @ X3389)|(~(in @ X3391 @ X3389)|(subset @ X3391 @ X3389)))&(~(subset @ (esk111_1 @ X3389) @ X3389)|(~(in @ X3391 @ X3389)|(subset @ X3391 @ X3389))))&((~(in @ X3393 @ esk112_0)|(subset @ X3393 @ esk112_0))&((~(in @ X3395 @ esk113_0)|(subset @ X3395 @ esk113_0))&((in @ esk114_0 @ (binintersect @ esk112_0 @ esk113_0))&~(subset @ esk114_0 @ (binintersect @ esk112_0 @ esk113_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_414])])])])])])])).
2.09/0.83	thf(c_0_416, negated_conjecture, ~((subset @ esk114_0 @ (binintersect @ esk112_0 @ esk113_0))), inference(split_conjunct,[status(thm)],[c_0_415])).
2.09/0.83	thf(c_0_417, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X2 @ (binintersect @ X3 @ X4))|~((subset @ X2 @ X3))|~((subset @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_415])).
2.09/0.83	thf(c_0_418, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X4)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_415])).
2.09/0.83	thf(c_0_419, negated_conjecture, (in @ esk114_0 @ (binintersect @ esk112_0 @ esk113_0)), inference(split_conjunct,[status(thm)],[c_0_415])).
2.09/0.83	thf(c_0_420, negated_conjecture, (~((subset @ esk114_0 @ esk113_0))|~((subset @ esk114_0 @ esk112_0))), inference(spm,[status(thm)],[c_0_416, c_0_417])).
2.09/0.83	thf(c_0_421, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk113_0)|~((in @ X2 @ esk113_0)))), inference(split_conjunct,[status(thm)],[c_0_415])).
2.09/0.83	thf(c_0_422, negated_conjecture, (in @ esk114_0 @ esk113_0), inference(spm,[status(thm)],[c_0_418, c_0_419])).
2.09/0.83	thf(c_0_423, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_415])).
2.09/0.83	thf(c_0_424, negated_conjecture, ~((subset @ esk114_0 @ esk112_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_420, c_0_421]), c_0_422])])).
2.09/0.83	thf(c_0_425, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk112_0)|~((in @ X2 @ esk112_0)))), inference(split_conjunct,[status(thm)],[c_0_415])).
2.09/0.83	thf(c_0_426, negated_conjecture, (in @ esk114_0 @ esk112_0), inference(spm,[status(thm)],[c_0_423, c_0_419])).
2.09/0.83	thf(c_0_427, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_424, c_0_425]), c_0_426])]), ['proof']).
2.09/0.83	% SZS output end CNFRefutation
2.09/0.83	% Parsed axioms                        : 721
2.09/0.83	% Removed by relevancy pruning/SinE    : 388
2.09/0.83	% Initial clauses                      : 592
2.09/0.83	% Removed in clause preprocessing      : 41
2.09/0.83	% Initial clauses in saturation        : 551
2.09/0.83	% Processed clauses                    : 1125
2.09/0.83	% ...of these trivial                  : 15
2.09/0.83	% ...subsumed                          : 428
2.09/0.83	% ...remaining for further processing  : 682
2.09/0.83	% Other redundant clauses eliminated   : 26
2.09/0.83	% Clauses deleted for lack of memory   : 0
2.09/0.83	% Backward-subsumed                    : 20
2.09/0.83	% Backward-rewritten                   : 4
2.09/0.83	% Generated clauses                    : 6943
2.09/0.83	% ...of the previous two non-redundant : 6426
2.09/0.83	% ...aggressively subsumed             : 0
2.09/0.83	% Contextual simplify-reflections      : 2
2.09/0.83	% Paramodulations                      : 6909
2.09/0.83	% Factorizations                       : 2
2.09/0.83	% NegExts                              : 0
2.09/0.83	% Equation resolutions                 : 30
2.09/0.83	% Disequality decompositions           : 0
2.09/0.83	% Total rewrite steps                  : 737
2.09/0.83	% ...of those cached                   : 640
2.09/0.83	% Propositional unsat checks           : 0
2.09/0.83	%    Propositional check models        : 0
2.09/0.83	%    Propositional check unsatisfiable : 0
2.09/0.83	%    Propositional clauses             : 0
2.09/0.83	%    Propositional clauses after purity: 0
2.09/0.83	%    Propositional unsat core size     : 0
2.09/0.83	%    Propositional preprocessing time  : 0.000
2.09/0.83	%    Propositional encoding time       : 0.000
2.09/0.83	%    Propositional solver time         : 0.000
2.09/0.83	%    Success case prop preproc time    : 0.000
2.09/0.83	%    Success case prop encoding time   : 0.000
2.09/0.83	%    Success case prop solver time     : 0.000
2.09/0.83	% Current number of processed clauses  : 646
2.09/0.83	%    Positive orientable unit clauses  : 92
2.09/0.83	%    Positive unorientable unit clauses: 0
2.09/0.83	%    Negative unit clauses             : 280
2.09/0.83	%    Non-unit-clauses                  : 274
2.09/0.83	% Current number of unprocessed clauses: 5822
2.09/0.83	% ...number of literals in the above   : 15140
2.09/0.83	% Current number of archived formulas  : 0
2.09/0.83	% Current number of archived clauses   : 25
2.09/0.83	% Clause-clause subsumption calls (NU) : 13241
2.09/0.83	% Rec. Clause-clause subsumption calls : 11333
2.09/0.83	% Non-unit clause-clause subsumptions  : 133
2.09/0.83	% Unit Clause-clause subsumption calls : 16902
2.09/0.83	% Rewrite failures with RHS unbound    : 0
2.09/0.83	% BW rewrite match attempts            : 23
2.09/0.83	% BW rewrite match successes           : 4
2.09/0.83	% Condensation attempts                : 0
2.09/0.83	% Condensation successes               : 0
2.09/0.83	% Termbank termtop insertions          : 185210
2.09/0.83	% Search garbage collected termcells   : 37417
2.09/0.83	
2.09/0.83	% -------------------------------------------------
2.09/0.83	% User time                : 0.212 s
2.09/0.83	% System time              : 0.021 s
2.09/0.83	% Total time               : 0.233 s
2.09/0.83	% Maximum resident set size: 12648 pages
2.09/0.83	
2.09/0.83	% -------------------------------------------------
2.09/0.83	% User time                : 0.233 s
2.09/0.83	% System time              : 0.028 s
2.09/0.83	% Total time               : 0.261 s
2.09/0.83	% Maximum resident set size: 5888 pages
2.09/0.83	% E exiting
2.09/0.83	EOF