0.00/0.03	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.05	% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.11/0.39	% Computer : n026.cluster.edu
0.11/0.39	% Model    : x86_64 x86_64
0.11/0.39	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.39	% Memory   : 8046.5625MB
0.11/0.39	% OS       : Linux 6.8.0-71-generic
0.11/0.39	% CPULimit : 1440
0.11/0.40	% WCLimit  : 180
0.11/0.40	% DateTime : Mon Jul 27 12:39:04 UTC 2026
0.11/0.40	% CPUTime  : 
0.11/0.40	Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.11/0.47	Running higher-order theorem proving
0.20/0.55	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.Om7go5tdiW/E---3.1_2684583.p
10.59/2.19	% Version: 3.5.1-ho
10.59/2.19	% Preprocessing class: HSLMSLSSLLLCHFA.
10.59/2.19	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
10.59/2.19	% Starting ehoh_best5 with 180s (1) cores
10.59/2.19	% Starting almost_fo_3_lam with 180s (1) cores
10.59/2.19	% Starting new_bool_5 with 180s (1) cores
10.59/2.19	% Starting pre_casc_3 with 180s (1) cores
10.59/2.19	% Starting ho_unfolding_8 with 180s (1) cores
10.59/2.19	% Starting new_ho_10_cnf2 with 180s (1) cores
10.59/2.19	% Starting new_bool_3 with 180s (1) cores
10.59/2.19	% Starting new_ho_5 with 180s (1) cores
10.59/2.19	% ho_unfolding_8 with pid 2684600 completed with status 0
10.59/2.19	% Result found by ho_unfolding_8
10.59/2.19	% Preprocessing class: HSLMSLSSLLLCHFA.
10.59/2.19	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
10.59/2.19	% Starting ehoh_best5 with 180s (1) cores
10.59/2.19	% Starting almost_fo_3_lam with 180s (1) cores
10.59/2.19	% Starting new_bool_5 with 180s (1) cores
10.59/2.19	% Starting pre_casc_3 with 180s (1) cores
10.59/2.19	% Starting ho_unfolding_8 with 180s (1) cores
10.59/2.19	% (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
10.59/2.19	% No SInE strategy applied
10.59/2.19	% Search class: HGHSM-FSLM32-DHFMMSBN
10.59/2.19	% partial match(1): HGHSM-FSLM32-MHFMMSBN
10.59/2.19	% Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
10.59/2.19	% Starting SubtermCWHack with 19s (1) cores
10.59/2.19	% SubtermCWHack with pid 2684611 completed with status 0
10.59/2.19	% Result found by SubtermCWHack
10.59/2.19	% Preprocessing class: HSLMSLSSLLLCHFA.
10.59/2.19	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
10.59/2.19	% Starting ehoh_best5 with 180s (1) cores
10.59/2.19	% Starting almost_fo_3_lam with 180s (1) cores
10.59/2.19	% Starting new_bool_5 with 180s (1) cores
10.59/2.19	% Starting pre_casc_3 with 180s (1) cores
10.59/2.19	% Starting ho_unfolding_8 with 180s (1) cores
10.59/2.19	% (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
10.59/2.19	% No SInE strategy applied
10.59/2.19	% Search class: HGHSM-FSLM32-DHFMMSBN
10.59/2.19	% partial match(1): HGHSM-FSLM32-MHFMMSBN
10.59/2.19	% Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
10.59/2.19	% Starting SubtermCWHack with 19s (1) cores
10.59/2.19	% Preprocessing time       : 0.009 s
10.59/2.19	
10.59/2.19	% Proof found!
10.59/2.19	% SZS status Theorem
10.59/2.19	% SZS output start CNFRefutation
10.59/2.19	thf(decl_23, type, in: $i > $i > $o).
10.59/2.19	thf(decl_24, type, exu: ($i > $o) > $o).
10.59/2.19	thf(decl_25, type, setextAx: $o).
10.59/2.19	thf(decl_26, type, emptyset: $i).
10.59/2.19	thf(decl_27, type, emptysetAx: $o).
10.59/2.19	thf(decl_28, type, setadjoin: $i > $i > $i).
10.59/2.19	thf(decl_29, type, setadjoinAx: $o).
10.59/2.19	thf(decl_30, type, powerset: $i > $i).
10.59/2.19	thf(decl_31, type, powersetAx: $o).
10.59/2.19	thf(decl_32, type, setunion: $i > $i).
10.59/2.19	thf(decl_33, type, setunionAx: $o).
10.59/2.19	thf(decl_34, type, omega: $i).
10.59/2.19	thf(decl_35, type, omega0Ax: $o).
10.59/2.19	thf(decl_36, type, omegaSAx: $o).
10.59/2.19	thf(decl_37, type, omegaIndAx: $o).
10.59/2.19	thf(decl_38, type, replAx: $o).
10.59/2.19	thf(decl_39, type, foundationAx: $o).
10.59/2.19	thf(decl_40, type, wellorderingAx: $o).
10.59/2.19	thf(decl_41, type, descr: ($i > $o) > $i).
10.59/2.19	thf(decl_42, type, descrp: $o).
10.59/2.19	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_44, type, dsetconstrI: $o).
10.59/2.19	thf(decl_45, type, dsetconstrEL: $o).
10.59/2.19	thf(decl_46, type, dsetconstrER: $o).
10.59/2.19	thf(decl_47, type, exuE1: $o).
10.59/2.19	thf(decl_48, type, prop2set: $o > $i).
10.59/2.19	thf(decl_49, type, prop2setE: $o).
10.59/2.19	thf(decl_50, type, emptysetE: $o).
10.59/2.19	thf(decl_51, type, emptysetimpfalse: $o).
10.59/2.19	thf(decl_52, type, notinemptyset: $o).
10.59/2.19	thf(decl_53, type, exuE3e: $o).
10.59/2.19	thf(decl_54, type, setext: $o).
10.59/2.19	thf(decl_55, type, emptyI: $o).
10.59/2.19	thf(decl_56, type, noeltsimpempty: $o).
10.59/2.19	thf(decl_57, type, setbeta: $o).
10.59/2.19	thf(decl_58, type, nonempty: $i > $o).
10.59/2.19	thf(decl_59, type, nonemptyE1: $o).
10.59/2.19	thf(decl_60, type, nonemptyI: $o).
10.59/2.19	thf(decl_61, type, nonemptyI1: $o).
10.59/2.19	thf(decl_62, type, setadjoinIL: $o).
10.59/2.19	thf(decl_63, type, emptyinunitempty: $o).
10.59/2.19	thf(decl_64, type, setadjoinIR: $o).
10.59/2.19	thf(decl_65, type, setadjoinE: $o).
10.59/2.19	thf(decl_66, type, setadjoinOr: $o).
10.59/2.19	thf(decl_67, type, setoftrueEq: $o).
10.59/2.19	thf(decl_68, type, powersetI: $o).
10.59/2.19	thf(decl_69, type, emptyinPowerset: $o).
10.59/2.19	thf(decl_70, type, emptyInPowerset: $o).
10.59/2.19	thf(decl_71, type, powersetE: $o).
10.59/2.19	thf(decl_72, type, setunionI: $o).
10.59/2.19	thf(decl_73, type, setunionE: $o).
10.59/2.19	thf(decl_74, type, subPowSU: $o).
10.59/2.19	thf(decl_75, type, exuE2: $o).
10.59/2.19	thf(decl_76, type, nonemptyImpWitness: $o).
10.59/2.19	thf(decl_77, type, uniqinunit: $o).
10.59/2.19	thf(decl_78, type, notinsingleton: $o).
10.59/2.19	thf(decl_79, type, eqinunit: $o).
10.59/2.19	thf(decl_80, type, singletonsswitch: $o).
10.59/2.19	thf(decl_81, type, upairsetE: $o).
10.59/2.19	thf(decl_82, type, upairsetIL: $o).
10.59/2.19	thf(decl_83, type, upairsetIR: $o).
10.59/2.19	thf(decl_84, type, emptyE1: $o).
10.59/2.19	thf(decl_85, type, vacuousDall: $o).
10.59/2.19	thf(decl_86, type, quantDeMorgan1: $o).
10.59/2.19	thf(decl_87, type, quantDeMorgan2: $o).
10.59/2.19	thf(decl_88, type, quantDeMorgan3: $o).
10.59/2.19	thf(decl_89, type, quantDeMorgan4: $o).
10.59/2.19	thf(decl_90, type, prop2setI: $o).
10.59/2.19	thf(decl_91, type, set2prop: $i > $o).
10.59/2.19	thf(decl_92, type, prop2set2propI: $o).
10.59/2.19	thf(decl_93, type, notdexE: $o).
10.59/2.19	thf(decl_94, type, notdallE: $o).
10.59/2.19	thf(decl_95, type, exuI1: $o).
10.59/2.19	thf(decl_96, type, exuI3: $o).
10.59/2.19	thf(decl_97, type, exuI2: $o).
10.59/2.19	thf(decl_98, type, inCongP: $o).
10.59/2.19	thf(decl_99, type, in__Cong: $o).
10.59/2.19	thf(decl_100, type, exuE3u: $o).
10.59/2.19	thf(decl_101, type, exu__Cong: $o).
10.59/2.19	thf(decl_102, type, emptyset__Cong: $o).
10.59/2.19	thf(decl_103, type, setadjoin__Cong: $o).
10.59/2.19	thf(decl_104, type, powerset__Cong: $o).
10.59/2.19	thf(decl_105, type, setunion__Cong: $o).
10.59/2.19	thf(decl_106, type, omega__Cong: $o).
10.59/2.19	thf(decl_107, type, exuEu: $o).
10.59/2.19	thf(decl_108, type, descr__Cong: $o).
10.59/2.19	thf(decl_109, type, dsetconstr__Cong: $o).
10.59/2.19	thf(decl_110, type, subset: $i > $i > $o).
10.59/2.19	thf(decl_113, type, subsetI1: $o).
10.59/2.19	thf(decl_114, type, eqimpsubset2: $o).
10.59/2.19	thf(decl_115, type, eqimpsubset1: $o).
10.59/2.19	thf(decl_116, type, subsetI2: $o).
10.59/2.19	thf(decl_117, type, emptysetsubset: $o).
10.59/2.19	thf(decl_118, type, subsetE: $o).
10.59/2.19	thf(decl_119, type, subsetE2: $o).
10.59/2.19	thf(decl_120, type, notsubsetI: $o).
10.59/2.19	thf(decl_121, type, notequalI1: $o).
10.59/2.19	thf(decl_122, type, notequalI2: $o).
10.59/2.19	thf(decl_123, type, subsetRefl: $o).
10.59/2.19	thf(decl_124, type, subsetTrans: $o).
10.59/2.19	thf(decl_125, type, setadjoinSub: $o).
10.59/2.19	thf(decl_126, type, setadjoinSub2: $o).
10.59/2.19	thf(decl_127, type, subset2powerset: $o).
10.59/2.19	thf(decl_128, type, setextsub: $o).
10.59/2.19	thf(decl_129, type, subsetemptysetimpeq: $o).
10.59/2.19	thf(decl_130, type, powersetI1: $o).
10.59/2.19	thf(decl_131, type, powersetE1: $o).
10.59/2.19	thf(decl_132, type, inPowerset: $o).
10.59/2.19	thf(decl_133, type, powersetsubset: $o).
10.59/2.19	thf(decl_134, type, sepInPowerset: $o).
10.59/2.19	thf(decl_135, type, sepSubset: $o).
10.59/2.19	thf(decl_136, type, binunion: $i > $i > $i).
10.59/2.19	thf(decl_137, type, binunionIL: $o).
10.59/2.19	thf(decl_138, type, upairset2IR: $o).
10.59/2.19	thf(decl_139, type, binunionIR: $o).
10.59/2.19	thf(decl_140, type, binunionEcases: $o).
10.59/2.19	thf(decl_141, type, binunionE: $o).
10.59/2.19	thf(decl_142, type, binunionLsub: $o).
10.59/2.19	thf(decl_143, type, binunionRsub: $o).
10.59/2.19	thf(decl_144, type, binintersect: $i > $i > $i).
10.59/2.19	thf(decl_145, type, binintersectI: $o).
10.59/2.19	thf(decl_146, type, binintersectSubset5: $o).
10.59/2.19	thf(decl_147, type, binintersectEL: $o).
10.59/2.19	thf(decl_148, type, binintersectLsub: $o).
10.59/2.19	thf(decl_149, type, binintersectSubset2: $o).
10.59/2.19	thf(decl_150, type, binintersectSubset3: $o).
10.59/2.19	thf(decl_151, type, binintersectER: $o).
10.59/2.19	thf(decl_152, type, disjointsetsI1: $o).
10.59/2.19	thf(decl_153, type, binintersectRsub: $o).
10.59/2.19	thf(decl_154, type, binintersectSubset4: $o).
10.59/2.19	thf(decl_155, type, binintersectSubset1: $o).
10.59/2.19	thf(decl_156, type, bs114d: $o).
10.59/2.19	thf(decl_158, type, setminus: $i > $i > $i).
10.59/2.19	thf(decl_159, type, setminusI: $o).
10.59/2.19	thf(decl_160, type, setminusEL: $o).
10.59/2.19	thf(decl_161, type, setminusER: $o).
10.59/2.19	thf(decl_162, type, setminusSubset2: $o).
10.59/2.19	thf(decl_163, type, setminusERneg: $o).
10.59/2.19	thf(decl_164, type, setminusELneg: $o).
10.59/2.19	thf(decl_165, type, setminusILneg: $o).
10.59/2.19	thf(decl_166, type, setminusIRneg: $o).
10.59/2.19	thf(decl_167, type, setminusLsub: $o).
10.59/2.19	thf(decl_168, type, setminusSubset1: $o).
10.59/2.19	thf(decl_169, type, symdiff: $i > $i > $i).
10.59/2.19	thf(decl_170, type, symdiffE: $o).
10.59/2.19	thf(decl_171, type, symdiffI1: $o).
10.59/2.19	thf(decl_172, type, symdiffI2: $o).
10.59/2.19	thf(decl_173, type, symdiffIneg1: $o).
10.59/2.19	thf(decl_174, type, symdiffIneg2: $o).
10.59/2.19	thf(decl_175, type, iskpair: $i > $o).
10.59/2.19	thf(decl_176, type, secondinupair: $o).
10.59/2.19	thf(decl_177, type, setukpairIL: $o).
10.59/2.19	thf(decl_178, type, setukpairIR: $o).
10.59/2.19	thf(decl_179, type, kpairiskpair: $o).
10.59/2.19	thf(decl_180, type, kpair: $i > $i > $i).
10.59/2.19	thf(decl_181, type, kpairp: $o).
10.59/2.19	thf(decl_182, type, cartprod: $i > $i > $i).
10.59/2.19	thf(decl_183, type, singletonsubset: $o).
10.59/2.19	thf(decl_184, type, singletoninpowerset: $o).
10.59/2.19	thf(decl_185, type, singletoninpowunion: $o).
10.59/2.19	thf(decl_186, type, upairset2E: $o).
10.59/2.19	thf(decl_187, type, upairsubunion: $o).
10.59/2.19	thf(decl_188, type, upairinpowunion: $o).
10.59/2.19	thf(decl_189, type, ubforcartprodlem1: $o).
10.59/2.19	thf(decl_190, type, ubforcartprodlem2: $o).
10.59/2.19	thf(decl_191, type, ubforcartprodlem3: $o).
10.59/2.19	thf(decl_192, type, cartprodpairin: $o).
10.59/2.19	thf(decl_193, type, cartprodmempair1: $o).
10.59/2.19	thf(decl_194, type, cartprodmempair: $o).
10.59/2.19	thf(decl_195, type, setunionE2: $o).
10.59/2.19	thf(decl_196, type, setunionsingleton1: $o).
10.59/2.19	thf(decl_197, type, setunionsingleton2: $o).
10.59/2.19	thf(decl_198, type, setunionsingleton: $o).
10.59/2.19	thf(decl_199, type, singleton: $i > $o).
10.59/2.19	thf(decl_200, type, singletonprop: $o).
10.59/2.19	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
10.59/2.19	thf(decl_202, type, ex1E1: $o).
10.59/2.19	thf(decl_203, type, ex1I: $o).
10.59/2.19	thf(decl_204, type, ex1I2: $o).
10.59/2.19	thf(decl_205, type, singletonsuniq: $o).
10.59/2.19	thf(decl_210, type, setukpairinjL1: $o).
10.59/2.19	thf(decl_211, type, kfstsingleton: $o).
10.59/2.19	thf(decl_212, type, theprop: $o).
10.59/2.19	thf(decl_213, type, kfst: $i > $i).
10.59/2.19	thf(decl_214, type, kfstpairEq: $o).
10.59/2.19	thf(decl_215, type, cartprodfstin: $o).
10.59/2.19	thf(decl_216, type, setukpairinjL2: $o).
10.59/2.19	thf(decl_217, type, setukpairinjL: $o).
10.59/2.19	thf(decl_218, type, setukpairinjR11: $o).
10.59/2.19	thf(decl_219, type, setukpairinjR12: $o).
10.59/2.19	thf(decl_220, type, setukpairinjR1: $o).
10.59/2.19	thf(decl_221, type, upairequniteq: $o).
10.59/2.19	thf(decl_222, type, setukpairinjR2: $o).
10.59/2.19	thf(decl_223, type, setukpairinjR: $o).
10.59/2.19	thf(decl_224, type, ksndsingleton: $o).
10.59/2.19	thf(decl_225, type, ksnd: $i > $i).
10.59/2.19	thf(decl_226, type, ksndpairEq: $o).
10.59/2.19	thf(decl_227, type, kpairsurjEq: $o).
10.59/2.19	thf(decl_228, type, cartprodsndin: $o).
10.59/2.19	thf(decl_229, type, cartprodpairmemEL: $o).
10.59/2.19	thf(decl_230, type, cartprodpairmemER: $o).
10.59/2.19	thf(decl_231, type, cartprodmempaircEq: $o).
10.59/2.19	thf(decl_232, type, cartprodfstpairEq: $o).
10.59/2.19	thf(decl_233, type, cartprodsndpairEq: $o).
10.59/2.19	thf(decl_234, type, cartprodpairsurjEq: $o).
10.59/2.19	thf(decl_235, type, breln: $i > $i > $i > $o).
10.59/2.19	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
10.59/2.19	thf(decl_237, type, dpsetconstrI: $o).
10.59/2.19	thf(decl_238, type, dpsetconstrSub: $o).
10.59/2.19	thf(decl_239, type, setOfPairsIsBReln: $o).
10.59/2.19	thf(decl_240, type, dpsetconstrERa: $o).
10.59/2.19	thf(decl_241, type, dpsetconstrEL1: $o).
10.59/2.19	thf(decl_242, type, dpsetconstrEL2: $o).
10.59/2.19	thf(decl_243, type, dpsetconstrER: $o).
10.59/2.19	thf(decl_244, type, func: $i > $i > $i > $o).
10.59/2.19	thf(decl_245, type, funcSet: $i > $i > $i).
10.59/2.19	thf(decl_246, type, funcImageSingleton: $o).
10.59/2.19	thf(decl_247, type, apProp: $o).
10.59/2.19	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
10.59/2.19	thf(decl_249, type, app: $o).
10.59/2.19	thf(decl_250, type, infuncsetfunc: $o).
10.59/2.19	thf(decl_251, type, ap2p: $o).
10.59/2.19	thf(decl_252, type, funcinfuncset: $o).
10.59/2.19	thf(decl_253, type, lamProp: $o).
10.59/2.19	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
10.59/2.19	thf(decl_255, type, lamp: $o).
10.59/2.19	thf(decl_256, type, lam2p: $o).
10.59/2.19	thf(decl_257, type, brelnall1: $o).
10.59/2.19	thf(decl_258, type, brelnall2: $o).
10.59/2.19	thf(decl_259, type, ex1E2: $o).
10.59/2.19	thf(decl_260, type, funcGraphProp1: $o).
10.59/2.19	thf(decl_261, type, funcGraphProp3: $o).
10.59/2.19	thf(decl_262, type, funcGraphProp2: $o).
10.59/2.19	thf(decl_263, type, funcextLem: $o).
10.59/2.19	thf(decl_264, type, funcGraphProp4: $o).
10.59/2.19	thf(decl_265, type, subbreln: $o).
10.59/2.19	thf(decl_266, type, eqbreln: $o).
10.59/2.19	thf(decl_267, type, funcext: $o).
10.59/2.19	thf(decl_268, type, funcext2: $o).
10.59/2.19	thf(decl_269, type, ap2apEq1: $o).
10.59/2.19	thf(decl_270, type, ap2apEq2: $o).
10.59/2.19	thf(decl_271, type, beta1: $o).
10.59/2.19	thf(decl_272, type, eta1: $o).
10.59/2.19	thf(decl_273, type, lam2lamEq: $o).
10.59/2.19	thf(decl_274, type, beta2: $o).
10.59/2.19	thf(decl_275, type, eta2: $o).
10.59/2.19	thf(decl_276, type, iffalseProp1: $o).
10.59/2.19	thf(decl_277, type, iffalseProp2: $o).
10.59/2.19	thf(decl_278, type, iftrueProp1: $o).
10.59/2.19	thf(decl_279, type, iftrueProp2: $o).
10.59/2.19	thf(decl_280, type, ifSingleton: $o).
10.59/2.19	thf(decl_281, type, if: $i > $o > $i > $i > $i).
10.59/2.19	thf(decl_282, type, ifp: $o).
10.59/2.19	thf(decl_283, type, theeq: $o).
10.59/2.19	thf(decl_284, type, iftrue: $o).
10.59/2.19	thf(decl_285, type, iffalse: $o).
10.59/2.19	thf(decl_286, type, iftrueorfalse: $o).
10.59/2.19	thf(decl_287, type, binintersectT_lem: $o).
10.59/2.19	thf(decl_288, type, binunionT_lem: $o).
10.59/2.19	thf(decl_289, type, powersetT_lem: $o).
10.59/2.19	thf(decl_290, type, setminusT_lem: $o).
10.59/2.19	thf(decl_291, type, complementT_lem: $o).
10.59/2.19	thf(decl_292, type, setextT: $o).
10.59/2.19	thf(decl_293, type, subsetTI: $o).
10.59/2.19	thf(decl_294, type, powersetTI1: $o).
10.59/2.19	thf(decl_295, type, powersetTE1: $o).
10.59/2.19	thf(decl_296, type, complementTI1: $o).
10.59/2.19	thf(decl_297, type, complementTE1: $o).
10.59/2.19	thf(decl_298, type, binintersectTELcontra: $o).
10.59/2.19	thf(decl_299, type, binintersectTERcontra: $o).
10.59/2.19	thf(decl_300, type, contrasubsetT: $o).
10.59/2.19	thf(decl_301, type, contrasubsetT1: $o).
10.59/2.19	thf(decl_302, type, contrasubsetT2: $o).
10.59/2.19	thf(decl_303, type, contrasubsetT3: $o).
10.59/2.19	thf(decl_304, type, doubleComplementI1: $o).
10.59/2.19	thf(decl_305, type, doubleComplementE1: $o).
10.59/2.19	thf(decl_306, type, doubleComplementSub1: $o).
10.59/2.19	thf(decl_307, type, doubleComplementSub2: $o).
10.59/2.19	thf(decl_308, type, doubleComplementEq: $o).
10.59/2.19	thf(decl_309, type, complementTnotintersectT: $o).
10.59/2.19	thf(decl_310, type, complementImpComplementIntersect: $o).
10.59/2.19	thf(decl_311, type, complementSubsetComplementIntersect: $o).
10.59/2.19	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
10.59/2.19	thf(decl_313, type, contraSubsetComplement: $o).
10.59/2.19	thf(decl_314, type, complementTcontraSubset: $o).
10.59/2.19	thf(decl_315, type, binunionTILcontra: $o).
10.59/2.19	thf(decl_316, type, binunionTIRcontra: $o).
10.59/2.19	thf(decl_317, type, inIntersectImpInUnion: $o).
10.59/2.19	thf(decl_318, type, inIntersectImpInUnion2: $o).
10.59/2.19	thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
10.59/2.19	thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
10.59/2.19	thf(decl_321, type, inComplementUnionImpNotIn1: $o).
10.59/2.19	thf(decl_322, type, inComplementUnionImpInComplement1: $o).
10.59/2.19	thf(decl_323, type, binunionTE: $o).
10.59/2.19	thf(decl_324, type, binunionTEcontra: $o).
10.59/2.19	thf(decl_325, type, demorgan2a1: $o).
10.59/2.19	thf(decl_326, type, complementUnionInPowersetComplement: $o).
10.59/2.19	thf(decl_327, type, demorgan2a2: $o).
10.59/2.19	thf(decl_328, type, demorgan1a: $o).
10.59/2.19	thf(decl_329, type, demorgan1b: $o).
10.59/2.19	thf(decl_330, type, demorgan1: $o).
10.59/2.19	thf(decl_331, type, demorgan2a: $o).
10.59/2.19	thf(decl_332, type, demorgan2b2: $o).
10.59/2.19	thf(decl_333, type, demorgan2b: $o).
10.59/2.19	thf(decl_334, type, demorgan2: $o).
10.59/2.19	thf(decl_335, type, woz13rule0: $o).
10.59/2.19	thf(decl_336, type, woz13rule1: $o).
10.59/2.19	thf(decl_337, type, woz13rule2: $o).
10.59/2.19	thf(decl_338, type, woz13rule3: $o).
10.59/2.19	thf(decl_339, type, woz13rule4: $o).
10.59/2.19	thf(decl_340, type, woz1_1: $o).
10.59/2.19	thf(decl_341, type, woz1_2: $o).
10.59/2.19	thf(decl_342, type, woz1_3: $o).
10.59/2.19	thf(decl_343, type, woz1_4: $o).
10.59/2.19	thf(decl_344, type, woz1_5: $o).
10.59/2.19	thf(decl_345, type, breln1: $i > $i > $o).
10.59/2.19	thf(decl_346, type, breln1all2: $o).
10.59/2.19	thf(decl_347, type, breln1Set: $i > $i).
10.59/2.19	thf(decl_348, type, breln1SetBreln1: $o).
10.59/2.19	thf(decl_354, type, reflwellordering: $i > $i > $o).
10.59/2.19	thf(decl_355, type, choice2fnsingleton: $o).
10.59/2.19	thf(decl_356, type, setOfPairsIsBReln1: $o).
10.59/2.19	thf(decl_357, type, breln1all1: $o).
10.59/2.19	thf(decl_358, type, subbreln1: $o).
10.59/2.19	thf(decl_359, type, eqbreln1: $o).
10.59/2.19	thf(decl_360, type, breln1invset: $i > $i > $i).
10.59/2.19	thf(decl_361, type, breln1invprop: $o).
10.59/2.19	thf(decl_362, type, epred1_0: $o).
10.59/2.19	thf(decl_363, type, esk1_2: $i > $i > $i).
10.59/2.19	thf(decl_364, type, esk2_2: $i > $i > $i).
10.59/2.19	thf(decl_365, type, esk3_2: $i > $i > $i).
10.59/2.19	thf(decl_366, type, esk4_1: $i > $i).
10.59/2.19	thf(decl_367, type, esk5_2: ($i > $i > $o) > $i > $i).
10.59/2.19	thf(decl_368, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
10.59/2.19	thf(decl_369, type, esk7_2: ($i > $i > $o) > $i > $i).
10.59/2.19	thf(decl_370, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
10.59/2.19	thf(decl_371, type, esk9_1: $i > $i).
10.59/2.19	thf(decl_372, type, esk10_2: ($i > $o) > $i > $i).
10.59/2.19	thf(decl_373, type, esk11_2: ($i > $o) > $i > $i).
10.59/2.19	thf(decl_374, type, esk12_1: ($i > $o) > $i).
10.59/2.19	thf(decl_375, type, esk13_2: ($i > $o) > $i > $i).
10.59/2.19	thf(decl_376, type, esk14_1: ($i > $o) > $i).
10.59/2.19	thf(decl_377, type, esk15_2: $i > $i > $i).
10.59/2.19	thf(decl_378, type, esk16_2: $i > $i > $i).
10.59/2.19	thf(decl_379, type, esk17_1: $i > $i).
10.59/2.19	thf(decl_380, type, esk18_1: $i > $i).
10.59/2.19	thf(decl_381, type, esk19_1: $i > $i).
10.59/2.19	thf(decl_382, type, esk20_2: $i > $i > $i).
10.59/2.19	thf(decl_383, type, esk21_3: $i > $i > $o > $i).
10.59/2.19	thf(decl_384, type, esk22_2: ($i > $o) > $i > $i).
10.59/2.19	thf(decl_385, type, esk23_1: ($i > $o) > $i).
10.59/2.19	thf(decl_386, type, esk24_1: $i > $i).
10.59/2.19	thf(decl_387, type, esk25_2: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_388, type, esk26_2: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_389, type, esk27_2: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_390, type, esk28_2: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_391, type, esk29_2: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_392, type, esk30_2: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_393, type, esk31_2: ($i > $o) > $i > $i).
10.59/2.19	thf(decl_394, type, esk32_1: ($i > $o) > $i).
10.59/2.19	thf(decl_395, type, esk33_1: ($i > $o) > $i).
10.59/2.19	thf(decl_396, type, esk34_1: ($i > $o) > $i).
10.59/2.19	thf(decl_397, type, esk35_1: ($i > $o) > $i).
10.59/2.19	thf(decl_398, type, esk36_2: ($i > $o) > $i > $i).
10.59/2.19	thf(decl_399, type, esk37_1: ($i > $o) > $i).
10.59/2.19	thf(decl_400, type, esk38_2: ($i > $o) > $i > $i).
10.59/2.19	thf(decl_401, type, esk39_2: ($i > $o) > ($i > $o) > $i).
10.59/2.19	thf(decl_402, type, esk40_2: ($i > $o) > ($i > $o) > $i).
10.59/2.19	thf(decl_403, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
10.59/2.19	thf(decl_404, type, esk42_2: ($i > $o) > ($i > $o) > $i).
10.59/2.19	thf(decl_405, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
10.59/2.19	thf(decl_406, type, esk44_2: ($i > $o) > ($i > $o) > $i).
10.59/2.19	thf(decl_407, type, esk45_2: ($i > $o) > $i > $i).
10.59/2.19	thf(decl_408, type, esk46_2: ($i > $o) > ($i > $o) > $i).
10.59/2.19	thf(decl_409, type, esk47_2: ($i > $o) > ($i > $o) > $i).
10.59/2.19	thf(decl_410, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
10.59/2.19	thf(decl_411, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
10.59/2.19	thf(decl_412, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
10.59/2.19	thf(decl_413, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
10.59/2.19	thf(decl_414, type, esk52_2: $i > $i > $i).
10.59/2.19	thf(decl_415, type, esk53_2: $i > $i > $i).
10.59/2.19	thf(decl_416, type, esk54_2: $i > $i > $i).
10.59/2.19	thf(decl_417, type, esk55_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_418, type, esk56_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_419, type, esk57_2: $i > $i > $i).
10.59/2.19	thf(decl_420, type, esk58_2: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_421, type, esk59_2: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_422, type, esk60_2: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_423, type, esk61_3: $i > ($i > $o) > $i > $i).
10.59/2.19	thf(decl_424, type, esk62_2: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_425, type, esk63_2: $i > ($i > $o) > $i).
10.59/2.19	thf(decl_426, type, esk64_3: $i > $i > ($i > $i) > $i).
10.59/2.19	thf(decl_427, type, esk65_3: $i > $i > ($i > $i) > $i).
10.59/2.19	thf(decl_428, type, esk66_3: $i > $i > ($i > $i) > $i).
10.59/2.19	thf(decl_429, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
10.59/2.19	thf(decl_430, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
10.59/2.19	thf(decl_431, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
10.59/2.19	thf(decl_432, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
10.59/2.19	thf(decl_433, type, esk71_4: $i > $i > $i > $i > $i).
10.59/2.19	thf(decl_434, type, esk72_4: $i > $i > $i > $i > $i).
10.59/2.19	thf(decl_435, type, esk73_4: $i > $i > $i > $i > $i).
10.59/2.19	thf(decl_436, type, esk74_4: $i > $i > $i > $i > $i).
10.59/2.19	thf(decl_437, type, esk75_4: $i > $i > $i > $i > $i).
10.59/2.19	thf(decl_438, type, esk76_4: $i > $i > $i > $i > $i).
10.59/2.19	thf(decl_439, type, esk77_4: $i > $i > $i > $i > $i).
10.59/2.19	thf(decl_440, type, esk78_4: $i > $i > $i > $i > $i).
10.59/2.19	thf(decl_441, type, esk79_4: $i > $i > $i > $i > $i).
10.59/2.19	thf(decl_442, type, esk80_3: $i > $i > ($i > $i) > $i).
10.59/2.19	thf(decl_443, type, esk81_3: $i > $i > ($i > $i) > $i).
10.59/2.19	thf(decl_444, type, esk82_3: $i > $i > ($i > $i) > $i).
10.59/2.19	thf(decl_445, type, esk83_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_446, type, esk84_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_447, type, esk85_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_448, type, esk86_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_449, type, esk87_3: $i > $i > ($i > $o) > $i).
10.59/2.19	thf(decl_450, type, esk88_3: $i > $i > ($i > $o) > $i).
10.59/2.19	thf(decl_451, type, esk89_3: $i > $i > ($i > $i > $o) > $i).
10.59/2.19	thf(decl_452, type, esk90_3: $i > $i > ($i > $o) > $i).
10.59/2.19	thf(decl_453, type, esk91_3: $i > $i > ($i > $o) > $i).
10.59/2.19	thf(decl_454, type, esk92_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_455, type, esk93_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_456, type, esk94_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_457, type, esk95_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_458, type, esk96_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_459, type, esk97_3: $i > $i > $i > $i).
10.59/2.19	thf(decl_460, type, esk98_0: $i).
10.59/2.19	thf(decl_461, type, esk99_0: $i).
10.59/2.19	thf(decl_462, type, esk100_0: $i).
10.59/2.19	thf(decl_463, type, esk101_0: $i).
10.59/2.19	thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', breln1)).
10.59/2.19	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', breln)).
10.59/2.19	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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', replAx)).
10.59/2.19	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', exu)).
10.59/2.19	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', descrp)).
10.59/2.19	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', exuE1)).
10.59/2.19	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', exuE3e)).
10.59/2.19	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', nonempty)).
10.59/2.19	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', nonemptyI)).
10.59/2.19	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', exuE2)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', exuI1)).
10.59/2.19	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', exuI3)).
10.59/2.19	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', exuI2)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', exuE3u)).
10.59/2.19	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', exu__Cong)).
10.59/2.19	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', exuEu)).
10.59/2.19	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', descr__Cong)).
10.59/2.19	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setOfPairsIsBReln)).
10.59/2.19	thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setOfPairsIsBReln1)).
10.59/2.19	thf(breln1invI, conjecture, ((((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>(((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((((emptysetE)=>((emptysetimpfalse)=>(((exuE3e)=>((setext)=>((emptyI)=>((((((nonemptyI1)=>((setadjoinIL)=>((((((((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((((exuE2)=>((nonemptyImpWitness)=>(((notinsingleton)=>((eqinunit)=>(((upairsetE)=>((((emptyE1)=>((((((((prop2set2propI)=>((((exuI1)=>((((((exuE3u)=>((exu__Cong)=>(((setadjoin__Cong)=>((powerset__Cong)=>(((((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>(((subsetI2)=>((emptysetsubset)=>((subsetE)=>(((notsubsetI)=>((notequalI1)=>(((((setadjoinSub)=>(((subset2powerset)=>((((powersetI1)=>((((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((((binunionRsub)=>(((binintersectSubset5)=>((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>(((bs114d)=>((((setminusER)=>(((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>((symdiffE)=>((((((secondinupair)=>((setukpairIL)=>((((kpairp)=>(((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>(((upairinpowunion)=>(((ubforcartprodlem2)=>(((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((((setunionsingleton)=>(((ex1E1)=>((ex1I)=>(((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((((((setukpairinjL)=>((setukpairinjR11)=>((((((setukpairinjR)=>((((((cartprodpairmemEL)=>((((cartprodfstpairEq)=>(((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>(((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((((((infuncsetfunc)=>((((lamProp)=>((lamp)=>(((brelnall1)=>((((funcGraphProp1)=>(((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(((eqbreln)=>((funcext)=>(((ap2apEq1)=>((ap2apEq2)=>(((eta1)=>((lam2lamEq)=>((((iffalseProp1)=>(((iftrueProp1)=>(((((theeq)=>(((iffalse)=>((iftrueorfalse)=>((((powersetT_lem)=>(((((((powersetTE1)=>((complementTI1)=>((complementTE1)=>((((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((((doubleComplementE1)=>((doubleComplementSub1)=>(((((complementImpComplementIntersect)=>(((complementInPowersetComplementIntersect)=>(((complementTcontraSubset)=>((((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((((demorgan2a1)=>(((demorgan2a2)=>((demorgan1a)=>((((demorgan2a)=>(((demorgan2b)=>(((woz13rule0)=>((((woz13rule3)=>(((((((woz1_5)=>((breln1all2)=>(((choice2fnsingleton)=>(((breln1all1)=>((subbreln1)=>(((breln1invprop)=>![X4:$i, X33:$i]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:((((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))<=(in @ X3 @ X4)))))<=(breln1 @ X4 @ X33))))<=(eqbreln1))))<=(setOfPairsIsBReln1)))<=(breln1SetBreln1))))<=(woz1_4))<=(woz1_3))<=(woz1_2))<=(woz1_1))<=(woz13rule4)))<=(woz13rule2))<=(woz13rule1)))<=(demorgan2)))<=(demorgan2b2)))<=(demorgan1))<=(demorgan1b))))<=(complementUnionInPowersetComplement)))<=(binunionTEcontra))<=(binunionTE))))))))<=(binunionTIRcontra))<=(binunionTILcontra)))<=(contraSubsetComplement)))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT))<=(doubleComplementEq))<=(doubleComplementSub2))))<=(doubleComplementI1))<=(contrasubsetT3)))))<=(binintersectTERcontra))<=(binintersectTELcontra)))))<=(powersetTI1))<=(subsetTI))<=(setextT))<=(complementT_lem))<=(setminusT_lem)))<=(binunionT_lem))<=(binintersectT_lem))))<=(iftrue)))<=(ifp))<=(ifSingleton))<=(iftrueProp2)))<=(iffalseProp2)))<=(eta2))<=(beta2))))<=(beta1))))<=(funcext2))))<=(subbreln)))))<=(funcGraphProp3)))<=(ex1E2))<=(brelnall2)))<=(lam2p))))<=(funcinfuncset))<=(ap2p)))<=(app))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER)))))<=(setOfPairsIsBReln)))))<=(cartprodsndpairEq)))<=(cartprodmempaircEq))<=(cartprodpairmemER)))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton)))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1))<=(setukpairinjR12))))<=(setukpairinjL2))<=(cartprodfstin))<=(kfstpairEq))<=(theprop)))))<=(ex1I2))))<=(singletonprop)))<=(setunionsingleton2))<=(setunionsingleton1))))))<=(ubforcartprodlem3)))<=(ubforcartprodlem1)))<=(upairsubunion)))))<=(singletonsubset)))<=(kpairiskpair))<=(setukpairIR))))<=(symdiffIneg2))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1))))<=(setminusLsub))))))<=(setminusSubset2)))<=(setminusEL))<=(setminusI)))<=(binintersectSubset1))))))))<=(binintersectLsub))))<=(binintersectI)))<=(binunionLsub))<=(binunionE)))))))))<=(inPowerset))<=(powersetE1)))<=(subsetemptysetimpeq))<=(setextsub)))<=(setadjoinSub2)))<=(subsetTrans))<=(subsetRefl))<=(notequalI2))))<=(subsetE2)))))<=(eqimpsubset1))))))<=(exuEu))<=(omega__Cong))<=(setunion__Cong))))<=(emptyset__Cong))))<=(in__Cong))<=(inCongP))<=(exuI2))<=(exuI3)))<=(notdallE))<=(notdexE)))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL)))<=(singletonsswitch))))<=(uniqinunit))))<=(subPowSU))<=(setunionE)))<=(powersetE))))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty))))<=(nonemptyI))<=(nonemptyE1))<=(setbeta))<=(noeltsimpempty)))))<=(notinemptyset))))<=(prop2setE))<=(exuE1)))))))<=(foundationAx)))))))))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', breln1invI)).
10.59/2.19	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', dsetconstrI)).
10.59/2.19	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', dsetconstrEL)).
10.59/2.19	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', dsetconstrER)).
10.59/2.19	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setbeta)).
10.59/2.19	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', nonemptyE1)).
10.59/2.19	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', nonemptyI1)).
10.59/2.19	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setoftrueEq)).
10.59/2.19	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', nonemptyImpWitness)).
10.59/2.19	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', emptyE1)).
10.59/2.19	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', dsetconstr__Cong)).
10.59/2.19	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', sepInPowerset)).
10.59/2.19	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', sepSubset)).
10.59/2.19	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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', singletonprop)).
10.59/2.19	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ex1E1)).
10.59/2.19	thf(ex1I, axiom, ((ex1I)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', ex1I)).
10.59/2.19	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ex1I2)).
10.59/2.19	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', kfstsingleton)).
10.59/2.19	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ksndsingleton)).
10.59/2.19	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', dpsetconstrI)).
10.59/2.19	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', dpsetconstrSub)).
10.59/2.19	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', dpsetconstrERa)).
10.59/2.19	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', dpsetconstrEL1)).
10.59/2.19	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', dpsetconstrEL2)).
10.59/2.19	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', dpsetconstrER)).
10.59/2.19	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', funcImageSingleton)).
10.59/2.19	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', apProp)).
10.59/2.19	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', lamProp)).
10.59/2.19	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', lamp)).
10.59/2.19	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', lam2p)).
10.59/2.19	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', brelnall1)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', brelnall2)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', ex1E2)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', subbreln)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', eqbreln)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', beta1)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', eta1)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', lam2lamEq)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', beta2)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', eta2)).
10.59/2.19	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', iffalseProp1)).
10.59/2.19	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', iffalseProp2)).
10.59/2.19	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', iftrueProp1)).
10.59/2.19	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', iftrueProp2)).
10.59/2.19	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ifSingleton)).
10.59/2.19	thf(breln1all2, axiom, ((breln1all2)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', breln1all2)).
10.59/2.19	thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', breln1SetBreln1)).
10.59/2.19	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:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ X3 @ X14) @ X33)))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', choice2fnsingleton)).
10.59/2.19	thf(breln1all1, axiom, ((breln1all1)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', breln1all1)).
10.59/2.19	thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', subbreln1)).
10.59/2.19	thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', eqbreln1)).
10.59/2.19	thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', breln1invprop)).
10.59/2.19	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setextAx)).
10.59/2.19	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', emptysetAx)).
10.59/2.19	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setadjoinAx)).
10.59/2.19	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', powersetAx)).
10.59/2.19	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setunionAx)).
10.59/2.19	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', omega0Ax)).
10.59/2.19	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', omegaSAx)).
10.59/2.19	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', omegaIndAx)).
10.59/2.19	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', foundationAx)).
10.59/2.19	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', wellorderingAx)).
10.59/2.19	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', prop2setE)).
10.59/2.19	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', emptysetE)).
10.59/2.19	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', emptysetimpfalse)).
10.59/2.19	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', notinemptyset)).
10.59/2.19	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setext)).
10.59/2.19	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', emptyI)).
10.59/2.19	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', noeltsimpempty)).
10.59/2.19	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setadjoinIL)).
10.59/2.19	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', emptyinunitempty)).
10.59/2.19	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setadjoinIR)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', setadjoinE)).
10.59/2.19	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setadjoinOr)).
10.59/2.19	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', powersetI)).
10.59/2.19	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', emptyinPowerset)).
10.59/2.19	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', emptyInPowerset)).
10.59/2.19	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', powersetE)).
10.59/2.19	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setunionI)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', setunionE)).
10.59/2.19	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', subPowSU)).
10.59/2.19	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', uniqinunit)).
10.59/2.19	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', notinsingleton)).
10.59/2.19	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', eqinunit)).
10.59/2.19	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', singletonsswitch)).
10.59/2.19	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', upairsetE)).
10.59/2.19	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', upairsetIL)).
10.59/2.19	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', upairsetIR)).
10.59/2.19	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', vacuousDall)).
10.59/2.19	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', quantDeMorgan1)).
10.59/2.19	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', quantDeMorgan2)).
10.59/2.19	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', quantDeMorgan3)).
10.59/2.19	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', quantDeMorgan4)).
10.59/2.19	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', prop2setI)).
10.59/2.19	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', prop2set2propI)).
10.59/2.19	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', notdexE)).
10.59/2.19	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', notdallE)).
10.59/2.19	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', inCongP)).
10.59/2.19	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', in__Cong)).
10.59/2.19	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', emptyset__Cong)).
10.59/2.19	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setadjoin__Cong)).
10.59/2.19	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', powerset__Cong)).
10.59/2.19	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setunion__Cong)).
10.59/2.19	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', omega__Cong)).
10.59/2.19	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', subsetI1)).
10.59/2.19	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', eqimpsubset2)).
10.59/2.19	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', eqimpsubset1)).
10.59/2.19	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', subsetI2)).
10.59/2.19	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', emptysetsubset)).
10.59/2.19	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', subsetE)).
10.59/2.19	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', subsetE2)).
10.59/2.19	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', notsubsetI)).
10.59/2.19	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', notequalI1)).
10.59/2.19	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', notequalI2)).
10.59/2.19	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', subsetRefl)).
10.59/2.19	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', subsetTrans)).
10.59/2.19	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setadjoinSub)).
10.59/2.19	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setadjoinSub2)).
10.59/2.19	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', subset2powerset)).
10.59/2.19	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setextsub)).
10.59/2.19	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', subsetemptysetimpeq)).
10.59/2.19	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', powersetI1)).
10.59/2.19	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', powersetE1)).
10.59/2.19	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', inPowerset)).
10.59/2.19	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', powersetsubset)).
10.59/2.19	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binunionIL)).
10.59/2.19	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', upairset2IR)).
10.59/2.19	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binunionIR)).
10.59/2.19	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binunionEcases)).
10.59/2.19	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binunionE)).
10.59/2.19	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binunionLsub)).
10.59/2.19	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binunionRsub)).
10.59/2.19	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectI)).
10.59/2.19	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectSubset5)).
10.59/2.19	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectEL)).
10.59/2.19	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectLsub)).
10.59/2.19	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectSubset2)).
10.59/2.19	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectSubset3)).
10.59/2.19	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectER)).
10.59/2.19	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', disjointsetsI1)).
10.59/2.19	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectRsub)).
10.59/2.19	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectSubset4)).
10.59/2.19	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectSubset1)).
10.59/2.19	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', bs114d)).
10.59/2.19	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setminusI)).
10.59/2.19	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setminusEL)).
10.59/2.19	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setminusER)).
10.59/2.19	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setminusSubset2)).
10.59/2.19	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setminusERneg)).
10.59/2.19	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setminusELneg)).
10.59/2.19	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setminusILneg)).
10.59/2.19	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setminusIRneg)).
10.59/2.19	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setminusLsub)).
10.59/2.19	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setminusSubset1)).
10.59/2.19	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', symdiffE)).
10.59/2.19	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', symdiffI1)).
10.59/2.19	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', symdiffI2)).
10.59/2.19	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', symdiffIneg1)).
10.59/2.19	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', symdiffIneg2)).
10.59/2.19	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', secondinupair)).
10.59/2.19	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setukpairIL)).
10.59/2.19	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setukpairIR)).
10.59/2.19	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', kpairiskpair)).
10.59/2.19	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', kpairp)).
10.59/2.19	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', singletonsubset)).
10.59/2.19	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', singletoninpowerset)).
10.59/2.19	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', singletoninpowunion)).
10.59/2.19	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', upairset2E)).
10.59/2.19	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', upairsubunion)).
10.59/2.19	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', upairinpowunion)).
10.59/2.19	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ubforcartprodlem1)).
10.59/2.19	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ubforcartprodlem2)).
10.59/2.19	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ubforcartprodlem3)).
10.59/2.19	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', cartprodpairin)).
10.59/2.19	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', cartprodmempair1)).
10.59/2.19	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', cartprodmempair)).
10.59/2.19	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setunionE2)).
10.59/2.19	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setunionsingleton1)).
10.59/2.19	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setunionsingleton2)).
10.59/2.19	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setunionsingleton)).
10.59/2.19	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', singletonsuniq)).
10.59/2.19	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.Om7go5tdiW/E---3.1_2684583.p', setukpairinjL1)).
10.59/2.19	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', theprop)).
10.59/2.19	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', kfstpairEq)).
10.59/2.19	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', cartprodfstin)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', setukpairinjL2)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', setukpairinjL)).
10.59/2.19	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setukpairinjR11)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', setukpairinjR12)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', setukpairinjR1)).
10.59/2.19	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', upairequniteq)).
10.59/2.19	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setukpairinjR2)).
10.59/2.19	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setukpairinjR)).
10.59/2.19	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ksndpairEq)).
10.59/2.19	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', kpairsurjEq)).
10.59/2.19	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', cartprodsndin)).
10.59/2.19	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', cartprodpairmemEL)).
10.59/2.19	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', cartprodpairmemER)).
10.59/2.19	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', cartprodmempaircEq)).
10.59/2.19	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', cartprodfstpairEq)).
10.59/2.19	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', cartprodsndpairEq)).
10.59/2.19	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', cartprodpairsurjEq)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', app)).
10.59/2.19	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', infuncsetfunc)).
10.59/2.19	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ap2p)).
10.59/2.19	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', funcinfuncset)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', funcGraphProp1)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', funcGraphProp3)).
10.59/2.19	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', funcGraphProp2)).
10.59/2.19	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', funcextLem)).
10.59/2.19	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', funcGraphProp4)).
10.59/2.19	thf(funcext, axiom, ((funcext)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', funcext)).
10.59/2.19	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', funcext2)).
10.59/2.19	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ap2apEq1)).
10.59/2.19	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ap2apEq2)).
10.59/2.19	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', ifp)).
10.59/2.19	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', theeq)).
10.59/2.19	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', iftrue)).
10.59/2.19	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', iffalse)).
10.59/2.19	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', iftrueorfalse)).
10.59/2.19	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', binintersectT_lem)).
10.59/2.19	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binunionT_lem)).
10.59/2.19	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', powersetT_lem)).
10.59/2.19	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', setminusT_lem)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', complementT_lem)).
10.59/2.19	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', setextT)).
10.59/2.19	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', subsetTI)).
10.59/2.19	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', powersetTI1)).
10.59/2.19	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', powersetTE1)).
10.59/2.19	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', complementTI1)).
10.59/2.19	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', complementTE1)).
10.59/2.19	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectTELcontra)).
10.59/2.19	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', binintersectTERcontra)).
10.59/2.19	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', contrasubsetT)).
10.59/2.19	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', contrasubsetT1)).
10.59/2.19	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', contrasubsetT2)).
10.59/2.19	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', contrasubsetT3)).
10.59/2.19	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', doubleComplementI1)).
10.59/2.19	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', doubleComplementE1)).
10.59/2.19	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', doubleComplementSub1)).
10.59/2.19	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', doubleComplementSub2)).
10.59/2.19	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', doubleComplementEq)).
10.59/2.19	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', complementTnotintersectT)).
10.59/2.19	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', complementImpComplementIntersect)).
10.59/2.19	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', complementSubsetComplementIntersect)).
10.59/2.19	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', complementInPowersetComplementIntersect)).
10.59/2.19	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', contraSubsetComplement)).
10.59/2.19	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', complementTcontraSubset)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', binunionTILcontra)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', binunionTIRcontra)).
10.59/2.19	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', inIntersectImpInUnion)).
10.59/2.19	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', inIntersectImpInUnion2)).
10.59/2.19	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', inIntersectImpInIntersectUnions)).
10.59/2.19	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', intersectInPowersetIntersectUnions)).
10.59/2.19	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', inComplementUnionImpNotIn1)).
10.59/2.19	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', inComplementUnionImpInComplement1)).
10.59/2.19	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', binunionTE)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', binunionTEcontra)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', demorgan2a1)).
10.59/2.19	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', complementUnionInPowersetComplement)).
10.59/2.19	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', demorgan2a2)).
10.59/2.19	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', demorgan1a)).
10.59/2.19	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', demorgan1b)).
10.59/2.19	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', demorgan1)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', demorgan2a)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', demorgan2b2)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', demorgan2b)).
10.59/2.19	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', demorgan2)).
10.59/2.19	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', woz13rule0)).
10.59/2.19	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', woz13rule1)).
10.59/2.19	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', woz13rule2)).
10.59/2.19	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', woz13rule3)).
10.59/2.19	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', woz13rule4)).
10.59/2.19	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', woz1_1)).
10.59/2.19	thf(woz1_2, axiom, ((woz1_2)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', woz1_2)).
10.59/2.19	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.Om7go5tdiW/E---3.1_2684583.p', woz1_3)).
10.59/2.19	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', woz1_4)).
10.59/2.19	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$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.Om7go5tdiW/E---3.1_2684583.p', woz1_5)).
10.59/2.19	thf(breln1invset, axiom, ((breln1invset)=(^[X4:$i, X33:$i]:(dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((in @ (kpair @ X3 @ X2) @ X33)))))), file('/export/starexec/sandbox/tmp/tmp.Om7go5tdiW/E---3.1_2684583.p', breln1invset)).
10.59/2.19	thf(c_0_298, plain, ((breln1)=(^[Z0:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
10.59/2.19	thf(c_0_299, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
10.59/2.19	thf(c_0_300, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
10.59/2.19	thf(c_0_301, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
10.59/2.19	thf(c_0_302, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
10.59/2.19	thf(c_0_303, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
10.59/2.19	thf(c_0_304, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
10.59/2.19	thf(c_0_305, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
10.59/2.19	thf(c_0_306, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
10.59/2.19	thf(c_0_307, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
10.59/2.19	thf(c_0_308, 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])).
10.59/2.19	thf(c_0_309, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
10.59/2.19	thf(c_0_310, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
10.59/2.19	thf(c_0_311, 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])).
10.59/2.19	thf(c_0_312, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
10.59/2.19	thf(c_0_313, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
10.59/2.19	thf(c_0_314, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
10.59/2.19	thf(c_0_315, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
10.59/2.19	thf(c_0_316, plain, ((breln1)=(^[Z0:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_298, c_0_299])).
10.59/2.19	thf(c_0_317, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
10.59/2.19	thf(c_0_318, negated_conjecture, ~(((((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>(((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((((emptysetE)=>((emptysetimpfalse)=>(((exuE3e)=>((setext)=>((emptyI)=>((((((nonemptyI1)=>((setadjoinIL)=>((((((((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((((exuE2)=>((nonemptyImpWitness)=>(((notinsingleton)=>((eqinunit)=>(((upairsetE)=>((((emptyE1)=>((((((((prop2set2propI)=>((((exuI1)=>((((((exuE3u)=>((exu__Cong)=>(((setadjoin__Cong)=>((powerset__Cong)=>(((((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>(((subsetI2)=>((emptysetsubset)=>((subsetE)=>(((notsubsetI)=>((notequalI1)=>(((((setadjoinSub)=>(((subset2powerset)=>((((powersetI1)=>((((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((((binunionRsub)=>(((binintersectSubset5)=>((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>(((bs114d)=>((((setminusER)=>(((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>((symdiffE)=>((((((secondinupair)=>((setukpairIL)=>((((kpairp)=>(((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>(((upairinpowunion)=>(((ubforcartprodlem2)=>(((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((((setunionsingleton)=>(((ex1E1)=>((ex1I)=>(((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((((((setukpairinjL)=>((setukpairinjR11)=>((((((setukpairinjR)=>((((((cartprodpairmemEL)=>((((cartprodfstpairEq)=>(((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>(((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((((((infuncsetfunc)=>((((lamProp)=>((lamp)=>(((brelnall1)=>((((funcGraphProp1)=>(((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(((eqbreln)=>((funcext)=>(((ap2apEq1)=>((ap2apEq2)=>(((eta1)=>((lam2lamEq)=>((((iffalseProp1)=>(((iftrueProp1)=>(((((theeq)=>(((iffalse)=>((iftrueorfalse)=>((((powersetT_lem)=>(((((((powersetTE1)=>((complementTI1)=>((complementTE1)=>((((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((((doubleComplementE1)=>((doubleComplementSub1)=>(((((complementImpComplementIntersect)=>(((complementInPowersetComplementIntersect)=>(((complementTcontraSubset)=>((((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((((demorgan2a1)=>(((demorgan2a2)=>((demorgan1a)=>((((demorgan2a)=>(((demorgan2b)=>(((woz13rule0)=>((((woz13rule3)=>(((((((woz1_5)=>((breln1all2)=>(((choice2fnsingleton)=>(((breln1all1)=>((subbreln1)=>(((breln1invprop)=>![X4:$i, X33:$i]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:((((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))<=(in @ X3 @ X4)))))<=(breln1 @ X4 @ X33))))<=(eqbreln1))))<=(setOfPairsIsBReln1)))<=(breln1SetBreln1))))<=(woz1_4))<=(woz1_3))<=(woz1_2))<=(woz1_1))<=(woz13rule4)))<=(woz13rule2))<=(woz13rule1)))<=(demorgan2)))<=(demorgan2b2)))<=(demorgan1))<=(demorgan1b))))<=(complementUnionInPowersetComplement)))<=(binunionTEcontra))<=(binunionTE))))))))<=(binunionTIRcontra))<=(binunionTILcontra)))<=(contraSubsetComplement)))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT))<=(doubleComplementEq))<=(doubleComplementSub2))))<=(doubleComplementI1))<=(contrasubsetT3)))))<=(binintersectTERcontra))<=(binintersectTELcontra)))))<=(powersetTI1))<=(subsetTI))<=(setextT))<=(complementT_lem))<=(setminusT_lem)))<=(binunionT_lem))<=(binintersectT_lem))))<=(iftrue)))<=(ifp))<=(ifSingleton))<=(iftrueProp2)))<=(iffalseProp2)))<=(eta2))<=(beta2))))<=(beta1))))<=(funcext2))))<=(subbreln)))))<=(funcGraphProp3)))<=(ex1E2))<=(brelnall2)))<=(lam2p))))<=(funcinfuncset))<=(ap2p)))<=(app))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER)))))<=(setOfPairsIsBReln)))))<=(cartprodsndpairEq)))<=(cartprodmempaircEq))<=(cartprodpairmemER)))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton)))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1))<=(setukpairinjR12))))<=(setukpairinjL2))<=(cartprodfstin))<=(kfstpairEq))<=(theprop)))))<=(ex1I2))))<=(singletonprop)))<=(setunionsingleton2))<=(setunionsingleton1))))))<=(ubforcartprodlem3)))<=(ubforcartprodlem1)))<=(upairsubunion)))))<=(singletonsubset)))<=(kpairiskpair))<=(setukpairIR))))<=(symdiffIneg2))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1))))<=(setminusLsub))))))<=(setminusSubset2)))<=(setminusEL))<=(setminusI)))<=(binintersectSubset1))))))))<=(binintersectLsub))))<=(binintersectI)))<=(binunionLsub))<=(binunionE)))))))))<=(inPowerset))<=(powersetE1)))<=(subsetemptysetimpeq))<=(setextsub)))<=(setadjoinSub2)))<=(subsetTrans))<=(subsetRefl))<=(notequalI2))))<=(subsetE2)))))<=(eqimpsubset1))))))<=(exuEu))<=(omega__Cong))<=(setunion__Cong))))<=(emptyset__Cong))))<=(in__Cong))<=(inCongP))<=(exuI2))<=(exuI3)))<=(notdallE))<=(notdexE)))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL)))<=(singletonsswitch))))<=(uniqinunit))))<=(subPowSU))<=(setunionE)))<=(powersetE))))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty))))<=(nonemptyI))<=(nonemptyE1))<=(setbeta))<=(noeltsimpempty)))))<=(notinemptyset))))<=(prop2setE))<=(exuE1)))))))<=(foundationAx)))))))))<=(emptysetAx))<=(setextAx))), inference(assume_negation,[status(cth)],[breln1invI])).
10.59/2.19	thf(c_0_319, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X1002:$i]:(((((X6 @ X2 @ X1002)))&(![X1003:$i]:(((((X6 @ X2 @ X1003)))=>(((X1002)=(X1003)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_300, c_0_301])).
10.59/2.19	thf(c_0_320, plain, ((descrp)=(![X1:$i > $o]:((((?[X1004:$i]:(((((X1 @ X1004)))&(![X1005:$i]:(((((X1 @ X1005)))=>(((X1004)=(X1005))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_302, c_0_301])).
10.59/2.19	thf(c_0_321, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
10.59/2.19	thf(c_0_322, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
10.59/2.19	thf(c_0_323, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
10.59/2.19	thf(c_0_324, plain, ((exuE1)=(![X1:$i > $o]:((((?[X1006:$i]:(((((X1 @ X1006)))&(![X1007:$i]:(((((X1 @ X1007)))=>(((X1006)=(X1007))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_303, c_0_301])).
10.59/2.19	thf(c_0_325, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X1008:$i]:(((((X1 @ X1008)))&(![X1009:$i]:(((((X1 @ X1009)))=>(((X1008)=(X1009))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_301])).
10.59/2.19	thf(c_0_326, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
10.59/2.19	thf(c_0_327, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_305])).
10.59/2.19	thf(c_0_328, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_306, c_0_305])).
10.59/2.19	thf(c_0_329, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_305])).
10.59/2.19	thf(c_0_330, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
10.59/2.19	thf(c_0_331, plain, ((exuE2)=(![X1:$i > $o]:((((?[X1010:$i]:(((((X1 @ X1010)))&(![X1011:$i]:(((((X1 @ X1011)))=>(((X1010)=(X1011))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_301])).
10.59/2.19	thf(c_0_332, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_305])).
10.59/2.19	thf(c_0_333, 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])).
10.59/2.19	thf(c_0_334, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X1012:$i]:(((((X1 @ X1012)))&(![X1013:$i]:(((((X1 @ X1013)))=>(((X1012)=(X1013)))))))))))))), inference(apply_def,[status(thm)],[c_0_308, c_0_301])).
10.59/2.19	thf(c_0_335, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X1014:$i]:(((((X1 @ X1014)))&(![X1015:$i]:(((((X1 @ X1015)))=>(((X1014)=(X1015)))))))))))))))), inference(apply_def,[status(thm)],[c_0_309, c_0_301])).
10.59/2.19	thf(c_0_336, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X1016:$i]:(((((X1 @ X1016)))&(![X1017:$i]:(((((X1 @ X1017)))=>(((X1016)=(X1017)))))))))))))), inference(apply_def,[status(thm)],[c_0_310, c_0_301])).
10.59/2.19	thf(c_0_337, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X1018:$i]:(((((X1 @ X1018)))&(![X1019:$i]:(((((X1 @ X1019)))=>(((X1018)=(X1019))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_311, c_0_301])).
10.59/2.19	thf(c_0_338, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1020:$i]:(((((X1 @ X1020)))&(![X1021:$i]:(((((X1 @ X1021)))=>(((X1020)=(X1021))))))))))<=>((?[X1022:$i]:(((((X17 @ X1022)))&(![X1023:$i]:(((((X17 @ X1023)))=>(((X1022)=(X1023)))))))))))))))), inference(apply_def,[status(thm)],[c_0_312, c_0_301])).
10.59/2.19	thf(c_0_339, plain, ((exuEu)=(![X1:$i > $o]:((((?[X1024:$i]:(((((X1 @ X1024)))&(![X1025:$i]:(((((X1 @ X1025)))=>(((X1024)=(X1025))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_313, c_0_301])).
10.59/2.19	thf(c_0_340, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1026:$i]:(((((X1 @ X1026)))&(![X1027:$i]:(((((X1 @ X1027)))=>(((X1026)=(X1027))))))))))=>((((?[X1028:$i]:(((((X17 @ X1028)))&(![X1029:$i]:(((((X17 @ X1029)))=>(((X1028)=(X1029))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_314, c_0_301])).
10.59/2.19	thf(c_0_341, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
10.59/2.19	thf(c_0_342, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
10.59/2.19	thf(c_0_343, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
10.59/2.19	thf(c_0_344, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
10.59/2.19	thf(c_0_345, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
10.59/2.19	thf(c_0_346, plain, ((ex1I)<=>![X4:$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])).
10.59/2.19	thf(c_0_347, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
10.59/2.19	thf(c_0_348, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
10.59/2.19	thf(c_0_349, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
10.59/2.19	thf(c_0_350, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
10.59/2.19	thf(c_0_351, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
10.59/2.19	thf(c_0_352, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_315, c_0_299])).
10.59/2.19	thf(c_0_353, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
10.59/2.19	thf(c_0_354, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
10.59/2.19	thf(c_0_355, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
10.59/2.19	thf(c_0_356, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
10.59/2.19	thf(c_0_357, plain, ((funcImageSingleton)<=>![X4:$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])).
10.59/2.19	thf(c_0_358, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
10.59/2.19	thf(c_0_359, plain, ((lamProp)<=>![X4:$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])).
10.59/2.19	thf(c_0_360, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
10.59/2.19	thf(c_0_361, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
10.59/2.19	thf(c_0_362, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_299])).
10.59/2.19	thf(c_0_363, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_299])).
10.59/2.19	thf(c_0_364, 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])).
10.59/2.19	thf(c_0_365, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_299])).
10.59/2.19	thf(c_0_366, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_299])).
10.59/2.19	thf(c_0_367, 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])).
10.59/2.19	thf(c_0_368, 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])).
10.59/2.19	thf(c_0_369, 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])).
10.59/2.19	thf(c_0_370, 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])).
10.59/2.19	thf(c_0_371, 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])).
10.59/2.19	thf(c_0_372, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
10.59/2.19	thf(c_0_373, plain, ((iffalseProp2)<=>![X4:$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])).
10.59/2.19	thf(c_0_374, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
10.59/2.19	thf(c_0_375, plain, ((iftrueProp2)<=>![X4:$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])).
10.59/2.19	thf(c_0_376, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
10.59/2.19	thf(c_0_377, axiom, ((breln1all2)=(![X4:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X4))))=>(![X1:$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)))))))))))), inference(apply_def,[status(thm)],[breln1all2, c_0_316])).
10.59/2.19	thf(c_0_378, axiom, ((breln1SetBreln1)=(![X4:$i, X33:$i]:((((in @ X33 @ (breln1Set @ X4)))=>(((subset @ X33 @ (cartprod @ X4 @ X4)))))))), inference(apply_def,[status(thm)],[breln1SetBreln1, c_0_316])).
10.59/2.19	thf(c_0_379, 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:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ Z0 @ X14) @ X33)))))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])).
10.59/2.19	thf(c_0_380, plain, ((setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X4)))))), inference(apply_def,[status(thm)],[c_0_317, c_0_316])).
10.59/2.19	thf(c_0_381, axiom, ((breln1all1)=(![X4:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X4))))=>(![X1:$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)))))))))))), inference(apply_def,[status(thm)],[breln1all1, c_0_316])).
10.59/2.19	thf(c_0_382, axiom, ((subbreln1)=(![X4:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X4))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X4))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln1, c_0_316])).
10.59/2.19	thf(c_0_383, axiom, ((eqbreln1)=(![X4:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X4))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X4))))=>(((![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)))))))))))))), inference(apply_def,[status(thm)],[eqbreln1, c_0_316])).
10.59/2.19	thf(c_0_384, axiom, ((breln1invprop)=(![X4:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X4))))=>(((subset @ (breln1invset @ X4 @ X33) @ (cartprod @ X4 @ X4)))))))), inference(apply_def,[status(thm)],[breln1invprop, c_0_316])).
10.59/2.19	thf(c_0_385, plain, ((epred1_0)<=>![X1051:$i]:(?[X1052:$i]:((((![X1053:$i]:(((in @ X1053 @ X1052)=>![X1054:$i]:(((in @ X1054 @ X1053)=>(in @ X1054 @ X1051)))))&![X1055:$i, X1056:$i]:((((in @ X1055 @ X1051)&(in @ X1056 @ X1051))=>(![X1057:$i]:(((in @ X1057 @ X1052)=>((in @ X1055 @ X1057)<=>(in @ X1056 @ X1057))))=>((X1055)=(X1056))))))&![X1058:$i, X1059:$i]:((((in @ X1058 @ X1052)&(in @ X1059 @ X1052))=>(![X1060:$i]:(((in @ X1060 @ X1058)=>(in @ X1060 @ X1059)))|![X1061:$i]:(((in @ X1061 @ X1059)=>(in @ X1061 @ X1058)))))))&![X1062:$i]:(((![X1063:$i]:(((in @ X1063 @ X1062)=>(in @ X1063 @ X1051)))&?[X1064:$i]:((in @ X1064 @ X1062)))=>?[X1065:$i, X1066:$i]:(((((in @ X1065 @ X1052)&(in @ X1066 @ X1062))&~(?[X1067:$i]:(((in @ X1067 @ X1065)&(in @ X1067 @ X1062)))))&![X1068:$i]:(((in @ X1068 @ X1052)=>(![X1069:$i]:(((in @ X1069 @ X1068)=>(in @ X1069 @ X1065)))|(in @ X1066 @ X1068)))))))))))), introduced(definition)).
10.59/2.19	thf(c_0_386, negated_conjecture, ~((![X2000:$i, X2001:$i]:((![X2002:$i]:(((in @ X2002 @ X2000)<=>(in @ X2002 @ X2001)))=>((X2000)=(X2001))))=>(![X1999:$i]:(~(in @ X1999 @ emptyset))=>(![X1030:$i, X1031:$i, X1032:$i]:(((in @ X1032 @ (setadjoin @ X1030 @ X1031))<=>(((X1032)=(X1030))|(in @ X1032 @ X1031))))=>(![X1033:$i, X1034:$i]:(((in @ X1034 @ (powerset @ X1033))<=>![X1035:$i]:(((in @ X1035 @ X1034)=>(in @ X1035 @ X1033)))))=>(![X1036:$i, X1037:$i]:(((in @ X1037 @ (setunion @ X1036))<=>?[X1038:$i]:(((in @ X1037 @ X1038)&(in @ X1038 @ X1036)))))=>((in @ emptyset @ omega)=>(![X1039:$i]:(((in @ X1039 @ omega)=>(in @ (setadjoin @ X1039 @ X1039) @ omega)))=>(![X1040:$i]:((((in @ emptyset @ X1040)&![X1041:$i]:((((in @ X1041 @ omega)&(in @ X1041 @ X1040))=>(in @ (setadjoin @ X1041 @ X1041) @ X1040))))=>![X1042:$i]:(((in @ X1042 @ omega)=>(in @ X1042 @ X1040)))))=>(![X1043:$i > $i > $o, X1044:$i]:((![X1045:$i]:(((in @ X1045 @ X1044)=>?[X1046:$i]:(((X1043 @ X1045 @ X1046)&![X1047:$i]:(((X1043 @ X1045 @ X1047)=>((X1046)=(X1047))))))))=>?[X1048:$i]:(![X1049:$i]:(((in @ X1049 @ X1048)<=>?[X1050:$i]:(((in @ X1050 @ X1044)&(X1043 @ X1050 @ X1049))))))))=>(![X1995:$i]:((?[X1996:$i]:((in @ X1996 @ X1995))=>?[X1997:$i]:(((in @ X1997 @ X1995)&~(?[X1998:$i]:(((in @ X1998 @ X1997)&(in @ X1998 @ X1995))))))))=>((epred1_0)=>(![X1070:$i > $o]:((?[X1071:$i]:(((X1070 @ X1071)&![X1072:$i]:(((X1070 @ X1072)=>((X1071)=(X1072))))))=>(X1070 @ (descr @ (^[Z0:$i]:(X1070 @ Z0))))))=>(![X1073:$i, X1074:$i > $o, X1075:$i]:(((in @ X1075 @ X1073)=>((X1074 @ X1075)=>(in @ X1075 @ (dsetconstr @ X1073 @ X1074)))))=>(![X1076:$i, X1077:$i > $o, X1078:$i]:(((in @ X1078 @ (dsetconstr @ X1076 @ X1077))=>(in @ X1078 @ X1076)))=>(![X1079:$i, X1080:$i > $o, X1081:$i]:(((in @ X1081 @ (dsetconstr @ X1079 @ X1080))=>(X1080 @ X1081)))=>(![X1990:$i > $o]:((?[X1991:$i]:(((X1990 @ X1991)&![X1992:$i]:(((X1990 @ X1992)=>((X1991)=(X1992))))))=>?[X1993:$i]:(((X1990 @ X1993)&![X1994:$i]:(((X1990 @ X1994)=>((X1993)=(X1994))))))))=>(![X1988:$o, X1989:$i]:(((in @ X1989 @ (prop2set @ ((X1988))))=>(X1988)))=>(![X1082:$i]:(((in @ X1082 @ emptyset)=>![X1083:$o]:((X1083))))=>(![X1084:$i]:(((in @ X1084 @ emptyset)=>~($true)))=>(![X1987:$i]:(~(in @ X1987 @ emptyset))=>(![X1085:$i > $o]:((?[X1086:$i]:(((X1085 @ X1086)&![X1087:$i]:(((X1085 @ X1087)=>((X1086)=(X1087))))))=>?[X1088:$i]:((X1085 @ X1088))))=>(![X1089:$i, X1090:$i]:((![X1091:$i]:(((in @ X1091 @ X1089)=>(in @ X1091 @ X1090)))=>(![X1092:$i]:(((in @ X1092 @ X1090)=>(in @ X1092 @ X1089)))=>((X1089)=(X1090)))))=>(![X1093:$i]:((![X1094:$i]:(~(in @ X1094 @ X1093))=>((X1093)=(emptyset))))=>(![X1985:$i]:((![X1986:$i]:(~(in @ X1986 @ X1985))=>((X1985)=(emptyset))))=>(![X1982:$i, X1983:$i > $o, X1984:$i]:(((in @ X1984 @ X1982)=>((in @ X1984 @ (dsetconstr @ X1982 @ X1983))<=>(X1983 @ X1984))))=>(![X1980:$i]:((((X1980)!=(emptyset))=>?[X1981:$i]:((in @ X1981 @ X1980))))=>(![X1977:$i, X1978:$i > $o, X1979:$i]:(((in @ X1979 @ X1977)=>((X1978 @ X1979)=>((dsetconstr @ X1977 @ X1978)!=(emptyset)))))=>(![X1095:$i]:((?[X1096:$i]:((in @ X1096 @ X1095))=>((X1095)!=(emptyset))))=>(![X1097:$i, X1098:$i]:((in @ X1097 @ (setadjoin @ X1097 @ X1098)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1974:$i, X1975:$i, X1976:$i]:(((in @ X1976 @ X1975)=>(in @ X1976 @ (setadjoin @ X1974 @ X1975))))=>(![X1970:$i, X1971:$i, X1972:$i]:(((in @ X1972 @ (setadjoin @ X1970 @ X1971))=>![X1973:$o]:(((((X1972)=(X1970))=>(X1973))=>(((in @ X1972 @ X1971)=>(X1973))=>(X1973))))))=>(![X1967:$i, X1968:$i, X1969:$i]:(((in @ X1969 @ (setadjoin @ X1967 @ X1968))=>(((X1969)=(X1967))|(in @ X1969 @ X1968))))=>(![X1966:$i]:(((dsetconstr @ X1966 @ (^[Z0:$i]:($true)))=(X1966)))=>(![X1963:$i, X1964:$i]:((![X1965:$i]:(((in @ X1965 @ X1964)=>(in @ X1965 @ X1963)))=>(in @ X1964 @ (powerset @ X1963))))=>(![X1099:$i]:((in @ emptyset @ (powerset @ X1099)))=>(![X1100:$i]:((in @ emptyset @ (powerset @ X1100)))=>(![X1960:$i, X1961:$i, X1962:$i]:(((in @ X1961 @ (powerset @ X1960))=>((in @ X1962 @ X1961)=>(in @ X1962 @ X1960))))=>(![X1101:$i, X1102:$i, X1103:$i]:(((in @ X1102 @ X1103)=>((in @ X1103 @ X1101)=>(in @ X1102 @ (setunion @ X1101)))))=>(![X1956:$i, X1957:$i]:(((in @ X1957 @ (setunion @ X1956))=>![X1958:$o]:((![X1959:$i]:(((in @ X1957 @ X1959)=>((in @ X1959 @ X1956)=>(X1958))))=>(X1958)))))=>(![X1954:$i, X1955:$i]:(((in @ X1955 @ X1954)=>(in @ X1955 @ (powerset @ (setunion @ X1954)))))=>(![X1104:$i > $o]:((?[X1105:$i]:(((X1104 @ X1105)&![X1106:$i]:(((X1104 @ X1106)=>((X1105)=(X1106))))))=>?[X1107:$i]:(![X1108:$i]:(((X1104 @ X1108)<=>((X1108)=(X1107)))))))=>(![X1109:$i]:((((X1109)!=(emptyset))=>?[X1110:$i]:(((in @ X1110 @ X1109)&$true))))=>(![X1952:$i, X1953:$i]:(((in @ X1952 @ (setadjoin @ X1953 @ emptyset))=>((X1952)=(X1953))))=>(![X1111:$i, X1112:$i]:((((X1111)!=(X1112))=>~(in @ X1112 @ (setadjoin @ X1111 @ emptyset))))=>(![X1113:$i, X1114:$i]:((((X1113)=(X1114))=>(in @ X1113 @ (setadjoin @ X1114 @ emptyset))))=>(![X1950:$i, X1951:$i]:(((in @ X1950 @ (setadjoin @ X1951 @ emptyset))=>(in @ X1951 @ (setadjoin @ X1950 @ emptyset))))=>(![X1115:$i, X1116:$i, X1117:$i]:(((in @ X1117 @ (setadjoin @ X1115 @ (setadjoin @ X1116 @ emptyset)))=>(((X1117)=(X1115))|((X1117)=(X1116)))))=>(![X1948:$i, X1949:$i]:((in @ X1948 @ (setadjoin @ X1948 @ (setadjoin @ X1949 @ emptyset))))=>(![X1946:$i, X1947:$i]:((in @ X1947 @ (setadjoin @ X1946 @ (setadjoin @ X1947 @ emptyset))))=>(![X1118:$i, X1119:$i > $o]:((?[X1120:$i]:(((in @ X1120 @ X1118)&(X1119 @ X1120)))=>(((dsetconstr @ X1118 @ X1119)=(emptyset))=>~($true))))=>(![X1944:$i > $o, X1945:$i]:(((in @ X1945 @ emptyset)=>(X1944 @ X1945)))=>(![X1940:$i, X1941:$i > $o]:((~(![X1942:$i]:(((in @ X1942 @ X1940)=>(X1941 @ X1942))))=>?[X1943:$i]:(((in @ X1943 @ X1940)&~((X1941 @ X1943))))))=>(![X1936:$i, X1937:$i > $o]:((![X1938:$i]:(((in @ X1938 @ X1936)=>~((X1937 @ X1938))))=>~(?[X1939:$i]:(((in @ X1939 @ X1936)&(X1937 @ X1939))))))=>(![X1932:$i, X1933:$i > $o]:((~(?[X1934:$i]:(((in @ X1934 @ X1932)&(X1933 @ X1934))))=>![X1935:$i]:(((in @ X1935 @ X1932)=>~((X1933 @ X1935))))))=>(![X1928:$i, X1929:$i > $o]:((?[X1930:$i]:(((in @ X1930 @ X1928)&~((X1929 @ X1930))))=>~(![X1931:$i]:(((in @ X1931 @ X1928)=>(X1929 @ X1931))))))=>(![X1927:$o]:(((X1927)=>(in @ emptyset @ (prop2set @ ((X1927))))))=>(![X1121:$o]:(((X1121)=>(set2prop @ (prop2set @ ((X1121))))))=>(![X1923:$i, X1924:$i > $o]:((~(?[X1925:$i]:(((in @ X1925 @ X1923)&(X1924 @ X1925))))=>![X1926:$i]:(((in @ X1926 @ X1923)=>~((X1924 @ X1926))))))=>(![X1919:$i, X1920:$i > $o]:((~(![X1921:$i]:(((in @ X1921 @ X1919)=>(X1920 @ X1921))))=>?[X1922:$i]:(((in @ X1922 @ X1919)&~((X1920 @ X1922))))))=>(![X1122:$i > $o]:((?[X1123:$i]:(((X1122 @ X1123)&![X1124:$i]:(((X1122 @ X1124)=>((X1123)=(X1124))))))=>?[X1125:$i]:(((X1122 @ X1125)&![X1126:$i]:(((X1122 @ X1126)=>((X1125)=(X1126))))))))=>(![X1913:$i > $o]:((?[X1914:$i]:((X1913 @ X1914))=>(![X1915:$i, X1916:$i]:(((X1913 @ X1915)=>((X1913 @ X1916)=>((X1915)=(X1916)))))=>?[X1917:$i]:(((X1913 @ X1917)&![X1918:$i]:(((X1913 @ X1918)=>((X1917)=(X1918)))))))))=>(![X1908:$i > $o]:((?[X1909:$i]:(![X1910:$i]:(((X1908 @ X1910)<=>((X1910)=(X1909)))))=>?[X1911:$i]:(((X1908 @ X1911)&![X1912:$i]:(((X1908 @ X1912)=>((X1911)=(X1912))))))))=>(![X1904:$i, X1905:$i]:((((X1904)=(X1905))=>![X1906:$i, X1907:$i]:((((X1906)=(X1907))=>((in @ X1906 @ X1904)=>(in @ X1907 @ X1905))))))=>(![X1900:$i, X1901:$i]:((((X1900)=(X1901))=>![X1902:$i, X1903:$i]:((((X1902)=(X1903))=>((in @ X1902 @ X1900)<=>(in @ X1903 @ X1901))))))=>(![X1127:$i > $o]:((?[X1128:$i]:(((X1127 @ X1128)&![X1129:$i]:(((X1127 @ X1129)=>((X1128)=(X1129))))))=>![X1130:$i, X1131:$i]:(((X1127 @ X1130)=>((X1127 @ X1131)=>((X1130)=(X1131)))))))=>(![X1132:$i > $o, X1133:$i > $o]:((![X1134:$i, X1135:$i]:((((X1134)=(X1135))=>((X1132 @ X1134)<=>(X1133 @ X1135))))=>(?[X1136:$i]:(((X1132 @ X1136)&![X1137:$i]:(((X1132 @ X1137)=>((X1136)=(X1137))))))<=>?[X1138:$i]:(((X1133 @ X1138)&![X1139:$i]:(((X1133 @ X1139)=>((X1138)=(X1139)))))))))=>(((emptyset)=(emptyset))=>(![X1140:$i, X1141:$i]:((((X1140)=(X1141))=>![X1142:$i, X1143:$i]:((((X1142)=(X1143))=>((setadjoin @ X1140 @ X1142)=(setadjoin @ X1141 @ X1143))))))=>(![X1144:$i, X1145:$i]:((((X1144)=(X1145))=>((powerset @ X1144)=(powerset @ X1145))))=>(![X1898:$i, X1899:$i]:((((X1898)=(X1899))=>((setunion @ X1898)=(setunion @ X1899))))=>(((omega)=(omega))=>(![X1893:$i > $o]:((?[X1894:$i]:(((X1893 @ X1894)&![X1895:$i]:(((X1893 @ X1895)=>((X1894)=(X1895))))))=>![X1896:$i, X1897:$i]:(((X1893 @ X1896)=>((X1893 @ X1897)=>((X1896)=(X1897)))))))=>(![X1146:$i > $o, X1147:$i > $o]:((![X1148:$i, X1149:$i]:((((X1148)=(X1149))=>((X1146 @ X1148)<=>(X1147 @ X1149))))=>(?[X1150:$i]:(((X1146 @ X1150)&![X1151:$i]:(((X1146 @ X1151)=>((X1150)=(X1151))))))=>(?[X1152:$i]:(((X1147 @ X1152)&![X1153:$i]:(((X1147 @ X1153)=>((X1152)=(X1153))))))=>((descr @ X1146)=(descr @ X1147))))))=>(![X1154:$i, X1155:$i]:((((X1154)=(X1155))=>![X1156:$i > $o, X1157:$i > $o]:((![X1158:$i]:(((in @ X1158 @ X1154)=>![X1159:$i]:(((in @ X1159 @ X1155)=>(((X1158)=(X1159))=>((X1156 @ X1158)<=>(X1157 @ X1159)))))))=>((dsetconstr @ X1154 @ X1156)=(dsetconstr @ X1155 @ X1157))))))=>(![X1160:$i, X1161:$i]:((![X1162:$i]:(((in @ X1162 @ X1160)=>(in @ X1162 @ X1161)))=>(subset @ X1160 @ X1161)))=>(![X1163:$i, X1164:$i]:((((X1163)=(X1164))=>(subset @ X1164 @ X1163)))=>(![X1891:$i, X1892:$i]:((((X1891)=(X1892))=>(subset @ X1891 @ X1892)))=>(![X1165:$i, X1166:$i]:((![X1167:$i]:(((in @ X1167 @ X1165)=>(in @ X1167 @ X1166)))=>(subset @ X1165 @ X1166)))=>(![X1168:$i]:((subset @ emptyset @ X1168))=>(![X1169:$i, X1170:$i, X1171:$i]:(((subset @ X1169 @ X1170)=>((in @ X1171 @ X1169)=>(in @ X1171 @ X1170))))=>(![X1888:$i, X1889:$i, X1890:$i]:(((subset @ X1888 @ X1889)=>(~(in @ X1890 @ X1889)=>~(in @ X1890 @ X1888))))=>(![X1172:$i, X1173:$i, X1174:$i]:(((in @ X1174 @ X1172)=>(~(in @ X1174 @ X1173)=>~(subset @ X1172 @ X1173))))=>(![X1175:$i, X1176:$i]:((~(subset @ X1175 @ X1176)=>((X1175)!=(X1176))))=>(![X1885:$i, X1886:$i, X1887:$i]:(((in @ X1887 @ X1885)=>(~(in @ X1887 @ X1886)=>((X1885)!=(X1886)))))=>(![X1884:$i]:((subset @ X1884 @ X1884))=>(![X1881:$i, X1882:$i, X1883:$i]:(((subset @ X1881 @ X1882)=>((subset @ X1882 @ X1883)=>(subset @ X1881 @ X1883))))=>(![X1177:$i, X1178:$i]:((subset @ X1178 @ (setadjoin @ X1177 @ X1178)))=>(![X1878:$i, X1879:$i, X1880:$i]:(((subset @ X1878 @ X1880)=>(subset @ X1878 @ (setadjoin @ X1879 @ X1880))))=>(![X1179:$i, X1180:$i]:(((subset @ X1179 @ X1180)=>(in @ X1179 @ (powerset @ X1180))))=>(![X1876:$i, X1877:$i]:(((subset @ X1876 @ X1877)=>((subset @ X1877 @ X1876)=>((X1876)=(X1877)))))=>(![X1875:$i]:(((subset @ X1875 @ emptyset)=>((X1875)=(emptyset))))=>(![X1181:$i, X1182:$i]:(((subset @ X1182 @ X1181)=>(in @ X1182 @ (powerset @ X1181))))=>(![X1873:$i, X1874:$i]:(((in @ X1874 @ (powerset @ X1873))=>(subset @ X1874 @ X1873)))=>(![X1872:$i]:((in @ X1872 @ (powerset @ X1872)))=>(![X1183:$i, X1184:$i]:(((subset @ X1183 @ X1184)=>(subset @ (powerset @ X1183) @ (powerset @ X1184))))=>(![X1185:$i, X1186:$i > $o]:((in @ (dsetconstr @ X1185 @ X1186) @ (powerset @ X1185)))=>(![X1187:$i, X1188:$i > $o]:((subset @ (dsetconstr @ X1187 @ X1188) @ X1187))=>(![X1189:$i, X1190:$i, X1191:$i]:(((in @ X1191 @ X1189)=>(in @ X1191 @ (binunion @ X1189 @ X1190))))=>(![X1192:$i, X1193:$i]:((in @ X1193 @ (setadjoin @ X1192 @ (setadjoin @ X1193 @ emptyset))))=>(![X1194:$i, X1195:$i, X1196:$i]:(((in @ X1196 @ X1195)=>(in @ X1196 @ (binunion @ X1194 @ X1195))))=>(![X1197:$i, X1198:$i, X1199:$i, X1200:$o]:(((in @ X1199 @ (binunion @ X1197 @ X1198))=>(((in @ X1199 @ X1197)=>(X1200))=>(((in @ X1199 @ X1198)=>(X1200))=>(X1200)))))=>(![X1869:$i, X1870:$i, X1871:$i]:(((in @ X1871 @ (binunion @ X1869 @ X1870))=>((in @ X1871 @ X1869)|(in @ X1871 @ X1870))))=>(![X1867:$i, X1868:$i]:((subset @ X1867 @ (binunion @ X1867 @ X1868)))=>(![X1201:$i, X1202:$i]:((subset @ X1202 @ (binunion @ X1201 @ X1202)))=>(![X1864:$i, X1865:$i, X1866:$i]:(((in @ X1866 @ X1864)=>((in @ X1866 @ X1865)=>(in @ X1866 @ (binintersect @ X1864 @ X1865)))))=>(![X1203:$i, X1204:$i, X1205:$i]:(((subset @ X1205 @ X1203)=>((subset @ X1205 @ X1204)=>(subset @ X1205 @ (binintersect @ X1203 @ X1204)))))=>(![X1206:$i, X1207:$i, X1208:$i]:(((in @ X1208 @ (binintersect @ X1206 @ X1207))=>(in @ X1208 @ X1206)))=>(![X1862:$i, X1863:$i]:((subset @ (binintersect @ X1862 @ X1863) @ X1862))=>(![X1209:$i, X1210:$i]:(((subset @ X1209 @ X1210)=>((binintersect @ X1209 @ X1210)=(X1209))))=>(![X1211:$i, X1212:$i]:((((binintersect @ X1211 @ X1212)=(X1212))=>(subset @ X1212 @ X1211)))=>(![X1213:$i, X1214:$i, X1215:$i]:(((in @ X1215 @ (binintersect @ X1213 @ X1214))=>(in @ X1215 @ X1214)))=>(![X1216:$i, X1217:$i]:((~(?[X1218:$i]:(((in @ X1218 @ X1216)&(in @ X1218 @ X1217))))=>((binintersect @ X1216 @ X1217)=(emptyset))))=>(![X1219:$i, X1220:$i]:((subset @ (binintersect @ X1219 @ X1220) @ X1220))=>(![X1221:$i, 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_319]), foundationAx]), wellorderingAx]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), c_0_324]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_325]), setext]), emptyI]), noeltsimpempty]), c_0_326]), c_0_327]), c_0_328]), c_0_329]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_330]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_331]), c_0_332]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_333]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_334]), c_0_335]), c_0_336]), inCongP]), in__Cong]), c_0_337]), c_0_338]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_339]), c_0_340]), c_0_341]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_342]), c_0_343]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), singletonsuniq]), setukpairinjL1]), c_0_348]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_349]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_350]), c_0_351]), c_0_352]), c_0_353]), c_0_354]), c_0_355]), c_0_356]), c_0_357]), c_0_358]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_359]), c_0_360]), c_0_361]), c_0_362]), c_0_363]), c_0_364]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_365]), c_0_366]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_367]), c_0_368]), c_0_369]), c_0_370]), c_0_371]), c_0_372]), c_0_373]), c_0_374]), c_0_375]), c_0_376]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3]), woz1_4]), woz1_5]), c_0_316]), c_0_377]), c_0_378]), c_0_379]), c_0_380]), c_0_381]), c_0_382]), c_0_383]), c_0_384])])]), c_0_385])).
10.59/2.19	thf(c_0_387, plain, ![X2003:$i, X2004:$i]:(((breln1invset @ X2003 @ X2004)=(dpsetconstr @ X2003 @ X2003 @ (^[Z0:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X2004)))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[breln1invset])])).
10.59/2.19	thf(c_0_388, negated_conjecture, ![X2007:$i, X2008:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2020:$i, X2021:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2029:$i, X2030:$i > $i > $o, X2031:$i, X2033:$i, X2036:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2043:$i, X2044:$i > $o, X2045:$i, X2047:$i, X2048:$i > $o, X2049:$i, X2050:$i, X2051:$i > $o, X2052:$i, X2053:$i, X2054:$i > $o, X2055:$i, X2056:$i > $o, X2057:$i, X2060:$i, X2061:$o, X2062:$i, X2063:$i, X2064:$o, X2065:$i, X2066:$i, X2067:$i > $o, X2068:$i, X2071:$i, X2072:$i, X2075:$i, X2077:$i, X2079:$i, X2080:$i > $o, X2081:$i, X2082:$i, X2084:$i, X2085:$i > $o, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$o, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$o, X2117:$i, X2118:$i, X2119:$i > $o, X2120:$i, X2123:$i, X2124:$i, X2125:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i > $o, X2144:$i, X2145:$i > $o, X2146:$i, X2147:$i, X2148:$i > $o, X2149:$i, X2151:$i, X2152:$i > $o, X2154:$i, X2155:$i, X2156:$i > $o, X2158:$i, X2159:$i, X2160:$i > $o, X2161:$i, X2163:$o, X2164:$o, X2165:$i, X2166:$i > $o, X2168:$i, X2169:$i, X2170:$i > $o, X2171:$i, X2173:$i > $o, X2174:$i, X2177:$i, X2178:$i > $o, X2179:$i, X2183:$i, X2184:$i > $o, X2185:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i > $o, X2198:$i, X2200:$i, X2201:$i, X2202:$i > $o, X2203:$i > $o, X2206:$i, X2209:$i, X2210:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i > $o, X2223:$i, X2225:$i, X2226:$i, X2227:$i > $o, X2228:$i > $o, X2231:$i, X2233:$i, X2235:$i, X2236:$i, X2237:$i > $o, X2238:$i > $o, X2241:$i, X2242:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i > $o, X2289:$i, X2290:$i > $o, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$o, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$o, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i > $o, X2445:$i, X2446:$i, X2447:$i > $o, X2449:$i, X2450:$i > $o, X2451:$i, X2453:$i, X2454:$i > $o, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i > $i > $o, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i > $i > $o, X2535:$i, X2536:$i, X2537:$i > $i > $o, X2538:$i, X2539:$i, X2540:$i > $i > $o, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i > $i > $o, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i > $i > $o, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i > $i > $o, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i > $i, X2584:$i, X2585:$i, X2586:$i > $i, X2588:$i, X2589:$i, X2590:$i > $i, X2592:$i, X2593:$i, X2594:$i, X2595:$i > $o, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i > $o, X2605:$i, X2606:$i, X2607:$i > $o, X2608:$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, X2628:$i, X2629:$i, X2630:$i, X2631:$i, X2632:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i > $i, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$i > $i, X2679:$i, X2680:$i, X2681:$i > $i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$o, X2689:$i, X2690:$i, X2691:$i, X2692:$o, X2693:$i, X2694:$i, X2695:$i, X2696:$o, X2697:$i, X2698:$i, X2699:$i, X2700:$o, X2701:$i, X2702:$i, X2703:$i, X2704:$o, X2705:$i, X2706:$i, X2707:$i, X2708:$o, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$o, X2715:$i, X2716:$i, X2717:$i, X2718:$o, X2719:$i, X2720:$i, X2721:$i, X2722:$o, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2743:$i, X2744:$i, X2745:$i, X2747:$i, X2748:$i, X2749:$i, X2751:$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, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, 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:$o, X2855:$i, X2856:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i, X2871:$i, X2872:$i, X2873:$i, X2874:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$i, X2885:$i, X2886:$i, X2887:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2901:$i, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i > $o, X2941:$i, X2942:$i, X2943:$i, X2944:$i, X2945:$i, X2946:$i > $i > $o, X2948:$i, X2949:$i, X2950:$i, X2951:$i, X2952:$i > $i > $o, X2953:$i, X2954:$i, X2955:$i > $o, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2964:$i, X2965:$i, X2966:$i, X2971:$i, X2972:$i]:((((~(in @ (esk1_2 @ X2007 @ X2008) @ X2007)|~(in @ (esk1_2 @ X2007 @ X2008) @ X2008)|((X2007)=(X2008)))&((in @ (esk1_2 @ X2007 @ X2008) @ X2007)|(in @ (esk1_2 @ X2007 @ X2008) @ X2008)|((X2007)=(X2008))))&(~(in @ X2010 @ emptyset)&(((~(in @ X2013 @ (setadjoin @ X2011 @ X2012))|(((X2013)=(X2011))|(in @ X2013 @ X2012)))&((((X2013)!=(X2011))|(in @ X2013 @ (setadjoin @ X2011 @ X2012)))&(~(in @ X2013 @ X2012)|(in @ X2013 @ (setadjoin @ X2011 @ X2012)))))&(((~(in @ X2015 @ (powerset @ X2014))|(~(in @ X2016 @ X2015)|(in @ X2016 @ X2014)))&(((in @ (esk2_2 @ X2017 @ X2018) @ X2018)|(in @ X2018 @ (powerset @ X2017)))&(~(in @ (esk2_2 @ X2017 @ X2018) @ X2017)|(in @ X2018 @ (powerset @ X2017)))))&(((((in @ X2021 @ (esk3_2 @ X2020 @ X2021))|~(in @ X2021 @ (setunion @ X2020)))&((in @ (esk3_2 @ X2020 @ X2021) @ X2020)|~(in @ X2021 @ (setunion @ X2020))))&(~(in @ X2024 @ X2025)|~(in @ X2025 @ X2023)|(in @ X2024 @ (setunion @ X2023))))&((in @ emptyset @ omega)&((~(in @ X2026 @ omega)|(in @ (setadjoin @ X2026 @ X2026) @ omega))&(((((in @ (esk4_1 @ X2027) @ omega)|~(in @ emptyset @ X2027)|(~(in @ X2029 @ omega)|(in @ X2029 @ X2027)))&((in @ (esk4_1 @ X2027) @ X2027)|~(in @ emptyset @ X2027)|(~(in @ X2029 @ omega)|(in @ X2029 @ X2027))))&(~(in @ (setadjoin @ (esk4_1 @ X2027) @ (esk4_1 @ X2027)) @ X2027)|~(in @ emptyset @ X2027)|(~(in @ X2029 @ omega)|(in @ X2029 @ X2027))))&((((((in @ (esk8_3 @ X2030 @ X2031 @ X2036) @ X2031)|~(in @ X2036 @ (esk7_2 @ X2030 @ X2031))|(in @ (esk5_2 @ X2030 @ X2031) @ X2031))&((X2030 @ (esk8_3 @ X2030 @ X2031 @ X2036) @ X2036)|~(in @ X2036 @ (esk7_2 @ X2030 @ X2031))|(in @ (esk5_2 @ X2030 @ X2031) @ X2031)))&(~(in @ X2039 @ X2031)|~(X2030 @ X2039 @ X2038)|(in @ X2038 @ (esk7_2 @ X2030 @ X2031))|(in @ (esk5_2 @ X2030 @ X2031) @ X2031)))&(((((in @ (esk8_3 @ X2030 @ X2031 @ X2036) @ X2031)|~(in @ X2036 @ (esk7_2 @ X2030 @ X2031))|((X2030 @ (esk5_2 @ X2030 @ X2031) @ (esk6_3 @ X2030 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X2945 @ X2949)|(~(in @ X2950 @ X2944)|(singleton @ (dsetconstr @ X2945 @ (^[Z0:$i]:(((X2946 @ X2950 @ Z0)&(![X1536:$i]:((((in @ X1536 @ X2945))=>(((X2946 @ X2950 @ X1536)=>((in @ (kpair @ Z0 @ X1536) @ X2949))))))))))))))))&(~(in @ X2948 @ X2945)|~(X2946 @ (esk89_3 @ X2944 @ X2945 @ X2946) @ X2948)|(~(in @ X2949 @ (breln1Set @ X2945))|(~(reflwellordering @ X2945 @ X2949)|(~(in @ X2950 @ X2944)|(singleton @ (dsetconstr @ X2945 @ (^[Z0:$i]:(((X2946 @ X2950 @ Z0)&(![X1536:$i]:((((in @ X1536 @ X2945))=>(((X2946 @ X2950 @ X1536)=>((in @ (kpair @ Z0 @ X1536) @ X2949)))))))))))))))))&((subset @ (dpsetconstr @ X2951 @ X2951 @ X2952) @ (cartprod @ X2951 @ X2951))&((((in @ (esk90_3 @ X2953 @ X2954 @ X2955) @ X2953)|(~(in @ X2958 @ X2954)|(X2955 @ X2958))|~(subset @ X2954 @ (cartprod @ X2953 @ X2953)))&(((in @ (esk91_3 @ X2953 @ X2954 @ X2955) @ X2953)|(~(in @ X2958 @ X2954)|(X2955 @ X2958))|~(subset @ X2954 @ (cartprod @ X2953 @ X2953)))&(((in @ (kpair @ (esk90_3 @ X2953 @ X2954 @ X2955) @ (esk91_3 @ X2953 @ X2954 @ X2955)) @ X2954)|(~(in @ X2958 @ X2954)|(X2955 @ X2958))|~(subset @ X2954 @ (cartprod @ X2953 @ X2953)))&(~(X2955 @ (kpair @ (esk90_3 @ X2953 @ X2954 @ X2955) @ (esk91_3 @ X2953 @ X2954 @ X2955)))|(~(in @ X2958 @ X2954)|(X2955 @ X2958))|~(subset @ X2954 @ (cartprod @ X2953 @ X2953))))))&((((in @ (esk92_3 @ X2959 @ X2960 @ X2961) @ X2959)|(subset @ X2960 @ X2961)|~(subset @ X2961 @ (cartprod @ X2959 @ X2959))|~(subset @ X2960 @ (cartprod @ X2959 @ X2959)))&(((in @ (esk93_3 @ X2959 @ X2960 @ X2961) @ X2959)|(subset @ X2960 @ X2961)|~(subset @ X2961 @ (cartprod @ X2959 @ X2959))|~(subset @ X2960 @ (cartprod @ X2959 @ X2959)))&(((in @ (kpair @ (esk92_3 @ X2959 @ X2960 @ X2961) @ (esk93_3 @ X2959 @ X2960 @ X2961)) @ X2960)|(subset @ X2960 @ X2961)|~(subset @ X2961 @ (cartprod @ X2959 @ X2959))|~(subset @ X2960 @ (cartprod @ X2959 @ X2959)))&(~(in @ (kpair @ (esk92_3 @ X2959 @ X2960 @ X2961) @ (esk93_3 @ X2959 @ X2960 @ X2961)) @ X2961)|(subset @ X2960 @ X2961)|~(subset @ X2961 @ (cartprod @ X2959 @ X2959))|~(subset @ X2960 @ (cartprod @ X2959 @ X2959))))))&(((((in @ (esk96_3 @ X2964 @ X2965 @ X2966) @ X2964)|((X2965)=(X2966))|(in @ (esk94_3 @ X2964 @ X2965 @ X2966) @ X2964)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(((in @ (esk97_3 @ X2964 @ X2965 @ X2966) @ X2964)|((X2965)=(X2966))|(in @ (esk94_3 @ X2964 @ X2965 @ X2966) @ X2964)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(((in @ (kpair @ (esk96_3 @ X2964 @ X2965 @ X2966) @ (esk97_3 @ X2964 @ X2965 @ X2966)) @ X2966)|((X2965)=(X2966))|(in @ (esk94_3 @ X2964 @ X2965 @ X2966) @ X2964)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(~(in @ (kpair @ (esk96_3 @ X2964 @ X2965 @ X2966) @ (esk97_3 @ X2964 @ X2965 @ X2966)) @ X2965)|((X2965)=(X2966))|(in @ (esk94_3 @ X2964 @ X2965 @ X2966) @ X2964)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964))))))&((((in @ (esk96_3 @ X2964 @ X2965 @ X2966) @ X2964)|((X2965)=(X2966))|(in @ (esk95_3 @ X2964 @ X2965 @ X2966) @ X2964)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(((in @ (esk97_3 @ X2964 @ X2965 @ X2966) @ X2964)|((X2965)=(X2966))|(in @ (esk95_3 @ X2964 @ X2965 @ X2966) @ X2964)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(((in @ (kpair @ (esk96_3 @ X2964 @ X2965 @ X2966) @ (esk97_3 @ X2964 @ X2965 @ X2966)) @ X2966)|((X2965)=(X2966))|(in @ (esk95_3 @ X2964 @ X2965 @ X2966) @ X2964)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(~(in @ (kpair @ (esk96_3 @ X2964 @ X2965 @ X2966) @ (esk97_3 @ X2964 @ X2965 @ X2966)) @ X2965)|((X2965)=(X2966))|(in @ (esk95_3 @ X2964 @ X2965 @ X2966) @ X2964)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964))))))&((((in @ (esk96_3 @ X2964 @ X2965 @ X2966) @ X2964)|((X2965)=(X2966))|(in @ (kpair @ (esk94_3 @ X2964 @ X2965 @ X2966) @ (esk95_3 @ X2964 @ X2965 @ X2966)) @ X2965)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(((in @ (esk97_3 @ X2964 @ X2965 @ X2966) @ X2964)|((X2965)=(X2966))|(in @ (kpair @ (esk94_3 @ X2964 @ X2965 @ X2966) @ (esk95_3 @ X2964 @ X2965 @ X2966)) @ X2965)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(((in @ (kpair @ (esk96_3 @ X2964 @ X2965 @ X2966) @ (esk97_3 @ X2964 @ X2965 @ X2966)) @ X2966)|((X2965)=(X2966))|(in @ (kpair @ (esk94_3 @ X2964 @ X2965 @ X2966) @ (esk95_3 @ X2964 @ X2965 @ X2966)) @ X2965)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(~(in @ (kpair @ (esk96_3 @ X2964 @ X2965 @ X2966) @ (esk97_3 @ X2964 @ X2965 @ X2966)) @ X2965)|((X2965)=(X2966))|(in @ (kpair @ (esk94_3 @ X2964 @ X2965 @ X2966) @ (esk95_3 @ X2964 @ X2965 @ X2966)) @ X2965)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964))))))&(((in @ (esk96_3 @ X2964 @ X2965 @ X2966) @ X2964)|((X2965)=(X2966))|~(in @ (kpair @ (esk94_3 @ X2964 @ X2965 @ X2966) @ (esk95_3 @ X2964 @ X2965 @ X2966)) @ X2966)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(((in @ (esk97_3 @ X2964 @ X2965 @ X2966) @ X2964)|((X2965)=(X2966))|~(in @ (kpair @ (esk94_3 @ X2964 @ X2965 @ X2966) @ (esk95_3 @ X2964 @ X2965 @ X2966)) @ X2966)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(((in @ (kpair @ (esk96_3 @ X2964 @ X2965 @ X2966) @ (esk97_3 @ X2964 @ X2965 @ X2966)) @ X2966)|((X2965)=(X2966))|~(in @ (kpair @ (esk94_3 @ X2964 @ X2965 @ X2966) @ (esk95_3 @ X2964 @ X2965 @ X2966)) @ X2966)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))&(~(in @ (kpair @ (esk96_3 @ X2964 @ X2965 @ X2966) @ (esk97_3 @ X2964 @ X2965 @ X2966)) @ X2965)|((X2965)=(X2966))|~(in @ (kpair @ (esk94_3 @ X2964 @ X2965 @ X2966) @ (esk95_3 @ X2964 @ X2965 @ X2966)) @ X2966)|~(subset @ X2966 @ (cartprod @ X2964 @ X2964))|~(subset @ X2965 @ (cartprod @ X2964 @ X2964)))))))))&((~(subset @ X2972 @ (cartprod @ X2971 @ X2971))|(subset @ (breln1invset @ X2971 @ X2972) @ (cartprod @ X2971 @ X2971)))&((subset @ esk99_0 @ (cartprod @ esk98_0 @ esk98_0))&((in @ esk100_0 @ esk98_0)&((in @ esk101_0 @ esk98_0)&((in @ (kpair @ esk100_0 @ esk101_0) @ esk99_0)&~(in @ (kpair @ esk101_0 @ esk100_0) @ (breln1invset @ esk98_0 @ esk99_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_386])])])])])])])).
10.59/2.19	thf(c_0_389, plain, ![X2005:$i, X2006:$i]:(((breln1invset @ X2005 @ X2006)=(dpsetconstr @ X2005 @ X2005 @ (^[Z0:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X2006)))))), inference(variable_rename,[status(thm)],[c_0_387])).
10.59/2.19	thf(c_0_390, negated_conjecture, ~((in @ (kpair @ esk101_0 @ esk100_0) @ (breln1invset @ esk98_0 @ esk99_0))), inference(split_conjunct,[status(thm)],[c_0_388])).
10.59/2.19	thf(c_0_391, plain, ![X2:$i, X3:$i]:(((breln1invset @ X2 @ X3)=(dpsetconstr @ X2 @ X2 @ (^[Z0:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X3)))))), inference(split_conjunct,[status(thm)],[c_0_389])).
10.59/2.19	thf(c_0_392, negated_conjecture, ~((in @ (kpair @ esk101_0 @ esk100_0) @ (dpsetconstr @ esk98_0 @ esk98_0 @ (^[Z0:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ esk99_0)))))), inference(rw,[status(thm)],[c_0_390, c_0_391])).
10.59/2.19	thf(c_0_393, negated_conjecture, ![X3:$i, X2:$i, X6:$i > $i > $o, X5:$i, X4:$i]:(((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X5 @ X6))|~((in @ X2 @ X3))|~((in @ X4 @ X5))|~((X6 @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_388])).
10.59/2.19	thf(c_0_394, negated_conjecture, (in @ esk100_0 @ esk98_0), inference(split_conjunct,[status(thm)],[c_0_388])).
10.59/2.19	thf(c_0_395, negated_conjecture, (in @ esk101_0 @ esk98_0), inference(split_conjunct,[status(thm)],[c_0_388])).
10.59/2.19	thf(c_0_396, negated_conjecture, (in @ (kpair @ esk100_0 @ esk101_0) @ esk99_0), inference(split_conjunct,[status(thm)],[c_0_388])).
10.59/2.19	thf(c_0_397, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_392, c_0_393]), c_0_394]), c_0_395]), c_0_396])]), ['proof']).
10.59/2.19	% SZS output end CNFRefutation
10.59/2.19	% Parsed axioms                        : 637
10.59/2.19	% Removed by relevancy pruning/SinE    : 0
10.59/2.19	% Initial clauses                      : 846
10.59/2.19	% Removed in clause preprocessing      : 372
10.59/2.19	% Initial clauses in saturation        : 474
10.59/2.19	% Processed clauses                    : 3663
10.59/2.19	% ...of these trivial                  : 20
10.59/2.19	% ...subsumed                          : 2618
10.59/2.19	% ...remaining for further processing  : 1025
10.59/2.19	% Other redundant clauses eliminated   : 227
10.59/2.19	% Clauses deleted for lack of memory   : 0
10.59/2.19	% Backward-subsumed                    : 32
10.59/2.19	% Backward-rewritten                   : 19
10.59/2.19	% Generated clauses                    : 51787
10.59/2.19	% ...of the previous two non-redundant : 47574
10.59/2.19	% ...aggressively subsumed             : 0
10.59/2.19	% Contextual simplify-reflections      : 16
10.59/2.19	% Paramodulations                      : 51549
10.59/2.19	% Factorizations                       : 6
10.59/2.19	% NegExts                              : 0
10.59/2.19	% Equation resolutions                 : 232
10.59/2.19	% Disequality decompositions           : 0
10.59/2.19	% Total rewrite steps                  : 10962
10.59/2.19	% ...of those cached                   : 10618
10.59/2.19	% Propositional unsat checks           : 0
10.59/2.19	%    Propositional check models        : 0
10.59/2.19	%    Propositional check unsatisfiable : 0
10.59/2.19	%    Propositional clauses             : 0
10.59/2.19	%    Propositional clauses after purity: 0
10.59/2.19	%    Propositional unsat core size     : 0
10.59/2.19	%    Propositional preprocessing time  : 0.000
10.59/2.19	%    Propositional encoding time       : 0.000
10.59/2.19	%    Propositional solver time         : 0.000
10.59/2.19	%    Success case prop preproc time    : 0.000
10.59/2.19	%    Success case prop encoding time   : 0.000
10.59/2.19	%    Success case prop solver time     : 0.000
10.59/2.19	% Current number of processed clauses  : 960
10.59/2.19	%    Positive orientable unit clauses  : 214
10.59/2.19	%    Positive unorientable unit clauses: 0
10.59/2.19	%    Negative unit clauses             : 5
10.59/2.19	%    Non-unit-clauses                  : 741
10.59/2.19	% Current number of unprocessed clauses: 40710
10.59/2.19	% ...number of literals in the above   : 158581
10.59/2.19	% Current number of archived formulas  : 0
10.59/2.19	% Current number of archived clauses   : 52
10.59/2.19	% Clause-clause subsumption calls (NU) : 109470
10.59/2.19	% Rec. Clause-clause subsumption calls : 57785
10.59/2.19	% Non-unit clause-clause subsumptions  : 1783
10.59/2.19	% Unit Clause-clause subsumption calls : 531
10.59/2.19	% Rewrite failures with RHS unbound    : 0
10.59/2.19	% BW rewrite match attempts            : 968
10.59/2.19	% BW rewrite match successes           : 15
10.59/2.19	% Condensation attempts                : 0
10.59/2.19	% Condensation successes               : 0
10.59/2.19	% Termbank termtop insertions          : 929355
10.59/2.19	% Search garbage collected termcells   : 32098
10.59/2.19	
10.59/2.19	% -------------------------------------------------
10.59/2.19	% User time                : 1.280 s
10.59/2.19	% System time              : 0.057 s
10.59/2.19	% Total time               : 1.337 s
10.59/2.19	% Maximum resident set size: 11256 pages
10.59/2.19	
10.59/2.19	% -------------------------------------------------
10.59/2.19	% User time                : 1.300 s
10.59/2.19	% System time              : 0.065 s
10.59/2.19	% Total time               : 1.365 s
10.59/2.19	% Maximum resident set size: 5888 pages
10.59/2.19	% E exiting
10.59/2.20	EOF