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
0.11/0.35	% Computer : n022.cluster.edu
0.11/0.35	% Model    : x86_64 x86_64
0.11/0.35	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.35	% Memory   : 8046.5625MB
0.11/0.35	% OS       : Linux 6.8.0-71-generic
0.11/0.35	% CPULimit : 1440
0.11/0.35	% WCLimit  : 180
0.11/0.35	% DateTime : Mon Jul 27 12:24:43 UTC 2026
0.11/0.35	% CPUTime  : 
0.11/0.36	Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.14/0.40	Running higher-order theorem proving
0.14/0.43	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.cjGwKrkbEx/E---3.1_884544.p
123.15/18.32	% Version: 3.5.1-ho
123.15/18.32	% Preprocessing class: HSLMSLSSLLLCHFA.
123.15/18.32	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
123.15/18.32	% Starting ehoh_best5 with 180s (1) cores
123.15/18.32	% Starting almost_fo_3_lam with 180s (1) cores
123.15/18.32	% Starting new_bool_5 with 180s (1) cores
123.15/18.32	% Starting pre_casc_3 with 180s (1) cores
123.15/18.32	% Starting ho_unfolding_8 with 180s (1) cores
123.15/18.32	% Starting new_ho_10_cnf2 with 180s (1) cores
123.15/18.32	% Starting new_bool_3 with 180s (1) cores
123.15/18.32	% Starting new_ho_5 with 180s (1) cores
123.15/18.32	% new_bool_5 with pid 884573 completed with status 0
123.15/18.32	% Result found by new_bool_5
123.15/18.32	% Preprocessing class: HSLMSLSSLLLCHFA.
123.15/18.32	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
123.15/18.32	% Starting ehoh_best5 with 180s (1) cores
123.15/18.32	% Starting almost_fo_3_lam with 180s (1) cores
123.15/18.32	% Starting new_bool_5 with 180s (1) cores
123.15/18.32	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
123.15/18.32	% SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
123.15/18.32	% Search class: HGHSM-FSLM32-MHFMMSBN
123.15/18.32	% Scheduled 11 strats onto 1 cores with 180 seconds (180 total)
123.15/18.32	% Starting SubtermCWHack with 17s (1) cores
123.15/18.32	% SubtermCWHack with pid 884585 completed with status 8
123.15/18.32	% Starting new_bool_5 with 19s (1) cores
123.15/18.32	% new_bool_5 with pid 884665 completed with status 0
123.15/18.32	% Result found by new_bool_5
123.15/18.32	% Preprocessing class: HSLMSLSSLLLCHFA.
123.15/18.32	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
123.15/18.32	% Starting ehoh_best5 with 180s (1) cores
123.15/18.32	% Starting almost_fo_3_lam with 180s (1) cores
123.15/18.32	% Starting new_bool_5 with 180s (1) cores
123.15/18.32	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
123.15/18.32	% SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
123.15/18.32	% Search class: HGHSM-FSLM32-MHFMMSBN
123.15/18.32	% Scheduled 11 strats onto 1 cores with 180 seconds (180 total)
123.15/18.32	% Starting SubtermCWHack with 17s (1) cores
123.15/18.32	% SubtermCWHack with pid 884585 completed with status 8
123.15/18.32	% Starting new_bool_5 with 19s (1) cores
123.15/18.32	% Preprocessing time       : 0.010 s
123.15/18.32	% Presaturation interreduction done
123.15/18.32	
123.15/18.32	% Proof found!
123.15/18.32	% SZS status Theorem
123.15/18.32	% SZS output start CNFRefutation
123.15/18.32	thf(decl_23, type, in: $i > $i > $o).
123.15/18.32	thf(decl_24, type, exu: ($i > $o) > $o).
123.15/18.32	thf(decl_25, type, setextAx: $o).
123.15/18.32	thf(decl_26, type, emptyset: $i).
123.15/18.32	thf(decl_27, type, emptysetAx: $o).
123.15/18.32	thf(decl_28, type, setadjoin: $i > $i > $i).
123.15/18.32	thf(decl_29, type, setadjoinAx: $o).
123.15/18.32	thf(decl_30, type, powerset: $i > $i).
123.15/18.32	thf(decl_31, type, powersetAx: $o).
123.15/18.32	thf(decl_32, type, setunion: $i > $i).
123.15/18.32	thf(decl_33, type, setunionAx: $o).
123.15/18.32	thf(decl_34, type, omega: $i).
123.15/18.32	thf(decl_35, type, omega0Ax: $o).
123.15/18.32	thf(decl_36, type, omegaSAx: $o).
123.15/18.32	thf(decl_37, type, omegaIndAx: $o).
123.15/18.32	thf(decl_38, type, replAx: $o).
123.15/18.32	thf(decl_39, type, foundationAx: $o).
123.15/18.32	thf(decl_40, type, wellorderingAx: $o).
123.15/18.32	thf(decl_41, type, descr: ($i > $o) > $i).
123.15/18.32	thf(decl_42, type, descrp: $o).
123.15/18.32	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_44, type, dsetconstrI: $o).
123.15/18.32	thf(decl_45, type, dsetconstrEL: $o).
123.15/18.32	thf(decl_46, type, dsetconstrER: $o).
123.15/18.32	thf(decl_47, type, exuE1: $o).
123.15/18.32	thf(decl_48, type, prop2set: $o > $i).
123.15/18.32	thf(decl_49, type, prop2setE: $o).
123.15/18.32	thf(decl_50, type, emptysetE: $o).
123.15/18.32	thf(decl_51, type, emptysetimpfalse: $o).
123.15/18.32	thf(decl_52, type, notinemptyset: $o).
123.15/18.32	thf(decl_53, type, exuE3e: $o).
123.15/18.32	thf(decl_54, type, setext: $o).
123.15/18.32	thf(decl_55, type, emptyI: $o).
123.15/18.32	thf(decl_56, type, noeltsimpempty: $o).
123.15/18.32	thf(decl_57, type, setbeta: $o).
123.15/18.32	thf(decl_58, type, nonempty: $i > $o).
123.15/18.32	thf(decl_59, type, nonemptyE1: $o).
123.15/18.32	thf(decl_60, type, nonemptyI: $o).
123.15/18.32	thf(decl_61, type, nonemptyI1: $o).
123.15/18.32	thf(decl_62, type, setadjoinIL: $o).
123.15/18.32	thf(decl_63, type, emptyinunitempty: $o).
123.15/18.32	thf(decl_64, type, setadjoinIR: $o).
123.15/18.32	thf(decl_65, type, setadjoinE: $o).
123.15/18.32	thf(decl_66, type, setadjoinOr: $o).
123.15/18.32	thf(decl_67, type, setoftrueEq: $o).
123.15/18.32	thf(decl_68, type, powersetI: $o).
123.15/18.32	thf(decl_69, type, emptyinPowerset: $o).
123.15/18.32	thf(decl_70, type, emptyInPowerset: $o).
123.15/18.32	thf(decl_71, type, powersetE: $o).
123.15/18.32	thf(decl_72, type, setunionI: $o).
123.15/18.32	thf(decl_73, type, setunionE: $o).
123.15/18.32	thf(decl_74, type, subPowSU: $o).
123.15/18.32	thf(decl_75, type, exuE2: $o).
123.15/18.32	thf(decl_76, type, nonemptyImpWitness: $o).
123.15/18.32	thf(decl_77, type, uniqinunit: $o).
123.15/18.32	thf(decl_78, type, notinsingleton: $o).
123.15/18.32	thf(decl_79, type, eqinunit: $o).
123.15/18.32	thf(decl_80, type, singletonsswitch: $o).
123.15/18.32	thf(decl_81, type, upairsetE: $o).
123.15/18.32	thf(decl_82, type, upairsetIL: $o).
123.15/18.32	thf(decl_83, type, upairsetIR: $o).
123.15/18.32	thf(decl_84, type, emptyE1: $o).
123.15/18.32	thf(decl_85, type, vacuousDall: $o).
123.15/18.32	thf(decl_86, type, quantDeMorgan1: $o).
123.15/18.32	thf(decl_87, type, quantDeMorgan2: $o).
123.15/18.32	thf(decl_88, type, quantDeMorgan3: $o).
123.15/18.32	thf(decl_89, type, quantDeMorgan4: $o).
123.15/18.32	thf(decl_90, type, prop2setI: $o).
123.15/18.32	thf(decl_92, type, prop2set2propI: $o).
123.15/18.32	thf(decl_93, type, notdexE: $o).
123.15/18.32	thf(decl_94, type, notdallE: $o).
123.15/18.32	thf(decl_95, type, exuI1: $o).
123.15/18.32	thf(decl_96, type, exuI3: $o).
123.15/18.32	thf(decl_97, type, exuI2: $o).
123.15/18.32	thf(decl_98, type, inCongP: $o).
123.15/18.32	thf(decl_99, type, in__Cong: $o).
123.15/18.32	thf(decl_100, type, exuE3u: $o).
123.15/18.32	thf(decl_101, type, exu__Cong: $o).
123.15/18.32	thf(decl_102, type, emptyset__Cong: $o).
123.15/18.32	thf(decl_103, type, setadjoin__Cong: $o).
123.15/18.32	thf(decl_104, type, powerset__Cong: $o).
123.15/18.32	thf(decl_105, type, setunion__Cong: $o).
123.15/18.32	thf(decl_106, type, omega__Cong: $o).
123.15/18.32	thf(decl_107, type, exuEu: $o).
123.15/18.32	thf(decl_108, type, descr__Cong: $o).
123.15/18.32	thf(decl_109, type, dsetconstr__Cong: $o).
123.15/18.32	thf(decl_110, type, subset: $i > $i > $o).
123.15/18.32	thf(decl_113, type, subsetI1: $o).
123.15/18.32	thf(decl_114, type, eqimpsubset2: $o).
123.15/18.32	thf(decl_115, type, eqimpsubset1: $o).
123.15/18.32	thf(decl_116, type, subsetI2: $o).
123.15/18.32	thf(decl_117, type, emptysetsubset: $o).
123.15/18.32	thf(decl_118, type, subsetE: $o).
123.15/18.32	thf(decl_119, type, subsetE2: $o).
123.15/18.32	thf(decl_120, type, notsubsetI: $o).
123.15/18.32	thf(decl_121, type, notequalI1: $o).
123.15/18.32	thf(decl_122, type, notequalI2: $o).
123.15/18.32	thf(decl_123, type, subsetRefl: $o).
123.15/18.32	thf(decl_124, type, subsetTrans: $o).
123.15/18.32	thf(decl_125, type, setadjoinSub: $o).
123.15/18.32	thf(decl_126, type, setadjoinSub2: $o).
123.15/18.32	thf(decl_127, type, subset2powerset: $o).
123.15/18.32	thf(decl_128, type, setextsub: $o).
123.15/18.32	thf(decl_129, type, subsetemptysetimpeq: $o).
123.15/18.32	thf(decl_130, type, powersetI1: $o).
123.15/18.32	thf(decl_131, type, powersetE1: $o).
123.15/18.32	thf(decl_132, type, inPowerset: $o).
123.15/18.32	thf(decl_133, type, powersetsubset: $o).
123.15/18.32	thf(decl_134, type, sepInPowerset: $o).
123.15/18.32	thf(decl_135, type, sepSubset: $o).
123.15/18.32	thf(decl_136, type, binunion: $i > $i > $i).
123.15/18.32	thf(decl_137, type, binunionIL: $o).
123.15/18.32	thf(decl_138, type, upairset2IR: $o).
123.15/18.32	thf(decl_139, type, binunionIR: $o).
123.15/18.32	thf(decl_140, type, binunionEcases: $o).
123.15/18.32	thf(decl_141, type, binunionE: $o).
123.15/18.32	thf(decl_142, type, binunionLsub: $o).
123.15/18.32	thf(decl_143, type, binunionRsub: $o).
123.15/18.32	thf(decl_144, type, binintersect: $i > $i > $i).
123.15/18.32	thf(decl_145, type, binintersectI: $o).
123.15/18.32	thf(decl_146, type, binintersectSubset5: $o).
123.15/18.32	thf(decl_147, type, binintersectEL: $o).
123.15/18.32	thf(decl_148, type, binintersectLsub: $o).
123.15/18.32	thf(decl_149, type, binintersectSubset2: $o).
123.15/18.32	thf(decl_150, type, binintersectSubset3: $o).
123.15/18.32	thf(decl_151, type, binintersectER: $o).
123.15/18.32	thf(decl_152, type, disjointsetsI1: $o).
123.15/18.32	thf(decl_153, type, binintersectRsub: $o).
123.15/18.32	thf(decl_154, type, binintersectSubset4: $o).
123.15/18.32	thf(decl_155, type, binintersectSubset1: $o).
123.15/18.32	thf(decl_156, type, bs114d: $o).
123.15/18.32	thf(decl_158, type, setminus: $i > $i > $i).
123.15/18.32	thf(decl_159, type, setminusI: $o).
123.15/18.32	thf(decl_160, type, setminusEL: $o).
123.15/18.32	thf(decl_161, type, setminusER: $o).
123.15/18.32	thf(decl_162, type, setminusSubset2: $o).
123.15/18.32	thf(decl_163, type, setminusERneg: $o).
123.15/18.32	thf(decl_164, type, setminusELneg: $o).
123.15/18.32	thf(decl_165, type, setminusILneg: $o).
123.15/18.32	thf(decl_166, type, setminusIRneg: $o).
123.15/18.32	thf(decl_167, type, setminusLsub: $o).
123.15/18.32	thf(decl_168, type, setminusSubset1: $o).
123.15/18.32	thf(decl_169, type, symdiff: $i > $i > $i).
123.15/18.32	thf(decl_170, type, symdiffE: $o).
123.15/18.32	thf(decl_171, type, symdiffI1: $o).
123.15/18.32	thf(decl_172, type, symdiffI2: $o).
123.15/18.32	thf(decl_173, type, symdiffIneg1: $o).
123.15/18.32	thf(decl_174, type, symdiffIneg2: $o).
123.15/18.32	thf(decl_175, type, iskpair: $i > $o).
123.15/18.32	thf(decl_176, type, secondinupair: $o).
123.15/18.32	thf(decl_177, type, setukpairIL: $o).
123.15/18.32	thf(decl_178, type, setukpairIR: $o).
123.15/18.32	thf(decl_179, type, kpairiskpair: $o).
123.15/18.32	thf(decl_180, type, kpair: $i > $i > $i).
123.15/18.32	thf(decl_181, type, kpairp: $o).
123.15/18.32	thf(decl_182, type, cartprod: $i > $i > $i).
123.15/18.32	thf(decl_183, type, singletonsubset: $o).
123.15/18.32	thf(decl_184, type, singletoninpowerset: $o).
123.15/18.32	thf(decl_185, type, singletoninpowunion: $o).
123.15/18.32	thf(decl_186, type, upairset2E: $o).
123.15/18.32	thf(decl_187, type, upairsubunion: $o).
123.15/18.32	thf(decl_188, type, upairinpowunion: $o).
123.15/18.32	thf(decl_189, type, ubforcartprodlem1: $o).
123.15/18.32	thf(decl_190, type, ubforcartprodlem2: $o).
123.15/18.32	thf(decl_191, type, ubforcartprodlem3: $o).
123.15/18.32	thf(decl_192, type, cartprodpairin: $o).
123.15/18.32	thf(decl_193, type, cartprodmempair1: $o).
123.15/18.32	thf(decl_194, type, cartprodmempair: $o).
123.15/18.32	thf(decl_195, type, setunionE2: $o).
123.15/18.32	thf(decl_196, type, setunionsingleton1: $o).
123.15/18.32	thf(decl_197, type, setunionsingleton2: $o).
123.15/18.32	thf(decl_198, type, setunionsingleton: $o).
123.15/18.32	thf(decl_199, type, singleton: $i > $o).
123.15/18.32	thf(decl_200, type, singletonprop: $o).
123.15/18.32	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
123.15/18.32	thf(decl_202, type, ex1E1: $o).
123.15/18.32	thf(decl_203, type, ex1I: $o).
123.15/18.32	thf(decl_204, type, ex1I2: $o).
123.15/18.32	thf(decl_205, type, singletonsuniq: $o).
123.15/18.32	thf(decl_210, type, setukpairinjL1: $o).
123.15/18.32	thf(decl_211, type, kfstsingleton: $o).
123.15/18.32	thf(decl_212, type, theprop: $o).
123.15/18.32	thf(decl_213, type, kfst: $i > $i).
123.15/18.32	thf(decl_214, type, kfstpairEq: $o).
123.15/18.32	thf(decl_215, type, cartprodfstin: $o).
123.15/18.32	thf(decl_216, type, setukpairinjL2: $o).
123.15/18.32	thf(decl_217, type, setukpairinjL: $o).
123.15/18.32	thf(decl_218, type, setukpairinjR11: $o).
123.15/18.32	thf(decl_219, type, setukpairinjR12: $o).
123.15/18.32	thf(decl_220, type, setukpairinjR1: $o).
123.15/18.32	thf(decl_221, type, upairequniteq: $o).
123.15/18.32	thf(decl_222, type, setukpairinjR2: $o).
123.15/18.32	thf(decl_223, type, setukpairinjR: $o).
123.15/18.32	thf(decl_224, type, ksndsingleton: $o).
123.15/18.32	thf(decl_225, type, ksnd: $i > $i).
123.15/18.32	thf(decl_226, type, ksndpairEq: $o).
123.15/18.32	thf(decl_227, type, kpairsurjEq: $o).
123.15/18.32	thf(decl_228, type, cartprodsndin: $o).
123.15/18.32	thf(decl_229, type, cartprodpairmemEL: $o).
123.15/18.32	thf(decl_230, type, cartprodpairmemER: $o).
123.15/18.32	thf(decl_231, type, cartprodmempaircEq: $o).
123.15/18.32	thf(decl_232, type, cartprodfstpairEq: $o).
123.15/18.32	thf(decl_233, type, cartprodsndpairEq: $o).
123.15/18.32	thf(decl_234, type, cartprodpairsurjEq: $o).
123.15/18.32	thf(decl_235, type, breln: $i > $i > $i > $o).
123.15/18.32	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
123.15/18.32	thf(decl_237, type, dpsetconstrI: $o).
123.15/18.32	thf(decl_238, type, dpsetconstrSub: $o).
123.15/18.32	thf(decl_239, type, setOfPairsIsBReln: $o).
123.15/18.32	thf(decl_240, type, dpsetconstrERa: $o).
123.15/18.32	thf(decl_241, type, dpsetconstrEL1: $o).
123.15/18.32	thf(decl_242, type, dpsetconstrEL2: $o).
123.15/18.32	thf(decl_243, type, dpsetconstrER: $o).
123.15/18.32	thf(decl_244, type, func: $i > $i > $i > $o).
123.15/18.32	thf(decl_245, type, funcSet: $i > $i > $i).
123.15/18.32	thf(decl_246, type, funcImageSingleton: $o).
123.15/18.32	thf(decl_247, type, apProp: $o).
123.15/18.32	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
123.15/18.32	thf(decl_249, type, app: $o).
123.15/18.32	thf(decl_250, type, infuncsetfunc: $o).
123.15/18.32	thf(decl_251, type, ap2p: $o).
123.15/18.32	thf(decl_252, type, funcinfuncset: $o).
123.15/18.32	thf(decl_253, type, lamProp: $o).
123.15/18.32	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
123.15/18.32	thf(decl_255, type, lamp: $o).
123.15/18.32	thf(decl_256, type, lam2p: $o).
123.15/18.32	thf(decl_257, type, brelnall1: $o).
123.15/18.32	thf(decl_258, type, brelnall2: $o).
123.15/18.32	thf(decl_259, type, ex1E2: $o).
123.15/18.32	thf(decl_260, type, funcGraphProp1: $o).
123.15/18.32	thf(decl_261, type, funcGraphProp3: $o).
123.15/18.32	thf(decl_262, type, funcGraphProp2: $o).
123.15/18.32	thf(decl_263, type, funcextLem: $o).
123.15/18.32	thf(decl_264, type, funcGraphProp4: $o).
123.15/18.32	thf(decl_265, type, subbreln: $o).
123.15/18.32	thf(decl_266, type, eqbreln: $o).
123.15/18.32	thf(decl_267, type, funcext: $o).
123.15/18.32	thf(decl_268, type, funcext2: $o).
123.15/18.32	thf(decl_269, type, ap2apEq1: $o).
123.15/18.32	thf(decl_270, type, ap2apEq2: $o).
123.15/18.32	thf(decl_271, type, beta1: $o).
123.15/18.32	thf(decl_272, type, eta1: $o).
123.15/18.32	thf(decl_273, type, lam2lamEq: $o).
123.15/18.32	thf(decl_274, type, beta2: $o).
123.15/18.32	thf(decl_275, type, eta2: $o).
123.15/18.32	thf(decl_276, type, iffalseProp1: $o).
123.15/18.32	thf(decl_277, type, iffalseProp2: $o).
123.15/18.32	thf(decl_278, type, iftrueProp1: $o).
123.15/18.32	thf(decl_279, type, iftrueProp2: $o).
123.15/18.32	thf(decl_280, type, ifSingleton: $o).
123.15/18.32	thf(decl_281, type, if: $i > $o > $i > $i > $i).
123.15/18.32	thf(decl_282, type, ifp: $o).
123.15/18.32	thf(decl_283, type, theeq: $o).
123.15/18.32	thf(decl_284, type, iftrue: $o).
123.15/18.32	thf(decl_285, type, iffalse: $o).
123.15/18.32	thf(decl_286, type, iftrueorfalse: $o).
123.15/18.32	thf(decl_287, type, binintersectT_lem: $o).
123.15/18.32	thf(decl_288, type, binunionT_lem: $o).
123.15/18.32	thf(decl_289, type, powersetT_lem: $o).
123.15/18.32	thf(decl_290, type, setminusT_lem: $o).
123.15/18.32	thf(decl_291, type, complementT_lem: $o).
123.15/18.32	thf(decl_292, type, setextT: $o).
123.15/18.32	thf(decl_293, type, subsetTI: $o).
123.15/18.32	thf(decl_294, type, powersetTI1: $o).
123.15/18.32	thf(decl_295, type, powersetTE1: $o).
123.15/18.32	thf(decl_296, type, complementTI1: $o).
123.15/18.32	thf(decl_297, type, complementTE1: $o).
123.15/18.32	thf(decl_298, type, binintersectTELcontra: $o).
123.15/18.32	thf(decl_299, type, binintersectTERcontra: $o).
123.15/18.32	thf(decl_300, type, contrasubsetT: $o).
123.15/18.32	thf(decl_301, type, contrasubsetT1: $o).
123.15/18.32	thf(decl_302, type, contrasubsetT2: $o).
123.15/18.32	thf(decl_303, type, contrasubsetT3: $o).
123.15/18.32	thf(decl_304, type, doubleComplementI1: $o).
123.15/18.32	thf(decl_305, type, doubleComplementE1: $o).
123.15/18.32	thf(decl_306, type, doubleComplementSub1: $o).
123.15/18.32	thf(decl_307, type, doubleComplementSub2: $o).
123.15/18.32	thf(decl_308, type, doubleComplementEq: $o).
123.15/18.32	thf(decl_309, type, complementTnotintersectT: $o).
123.15/18.32	thf(decl_310, type, complementImpComplementIntersect: $o).
123.15/18.32	thf(decl_311, type, complementSubsetComplementIntersect: $o).
123.15/18.32	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
123.15/18.32	thf(decl_313, type, contraSubsetComplement: $o).
123.15/18.32	thf(decl_314, type, complementTcontraSubset: $o).
123.15/18.32	thf(decl_315, type, binunionTILcontra: $o).
123.15/18.32	thf(decl_316, type, binunionTIRcontra: $o).
123.15/18.32	thf(decl_317, type, inIntersectImpInUnion: $o).
123.15/18.32	thf(decl_318, type, inIntersectImpInUnion2: $o).
123.15/18.32	thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
123.15/18.32	thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
123.15/18.32	thf(decl_321, type, inComplementUnionImpNotIn1: $o).
123.15/18.32	thf(decl_322, type, inComplementUnionImpInComplement1: $o).
123.15/18.32	thf(decl_323, type, binunionTE: $o).
123.15/18.32	thf(decl_324, type, binunionTEcontra: $o).
123.15/18.32	thf(decl_325, type, demorgan2a1: $o).
123.15/18.32	thf(decl_326, type, epred1_0: $o).
123.15/18.32	thf(decl_327, type, esk1_2: $i > $i > $i).
123.15/18.32	thf(decl_328, type, esk2_2: $i > $i > $i).
123.15/18.32	thf(decl_329, type, esk3_2: $i > $i > $i).
123.15/18.32	thf(decl_330, type, esk4_1: $i > $i).
123.15/18.32	thf(decl_331, type, esk5_2: ($i > $i > $o) > $i > $i).
123.15/18.32	thf(decl_332, type, esk6_2: ($i > $i > $o) > $i > $i).
123.15/18.32	thf(decl_333, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
123.15/18.32	thf(decl_334, type, esk8_1: $i > $i).
123.15/18.32	thf(decl_335, type, esk9_1: ($i > $o) > $i).
123.15/18.32	thf(decl_336, type, esk10_1: ($i > $o) > $i).
123.15/18.32	thf(decl_337, type, esk11_2: $i > $i > $i).
123.15/18.32	thf(decl_338, type, esk12_2: $i > $i > $i).
123.15/18.32	thf(decl_339, type, esk13_1: $i > $i).
123.15/18.32	thf(decl_340, type, esk14_1: $i > $i).
123.15/18.32	thf(decl_341, type, esk15_1: $i > $i).
123.15/18.32	thf(decl_342, type, esk16_2: $i > $i > $i).
123.15/18.32	thf(decl_343, type, esk17_3: $i > $i > $o > $i).
123.15/18.32	thf(decl_344, type, esk18_1: ($i > $o) > $i).
123.15/18.32	thf(decl_345, type, esk19_1: $i > $i).
123.15/18.32	thf(decl_346, type, esk20_2: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_347, type, esk21_2: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_348, type, esk22_2: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_349, type, esk23_2: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_350, type, esk24_2: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_351, type, esk25_2: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_352, type, esk26_2: ($i > $o) > $i > $i).
123.15/18.32	thf(decl_353, type, esk27_1: ($i > $o) > $i).
123.15/18.32	thf(decl_354, type, esk28_1: ($i > $o) > $i).
123.15/18.32	thf(decl_355, type, esk29_2: ($i > $o) > $i > $i).
123.15/18.32	thf(decl_356, type, esk30_2: ($i > $o) > ($i > $o) > $i).
123.15/18.32	thf(decl_357, type, esk31_2: ($i > $o) > ($i > $o) > $i).
123.15/18.32	thf(decl_358, type, esk32_2: ($i > $o) > ($i > $o) > $i).
123.15/18.32	thf(decl_359, type, esk33_2: ($i > $o) > ($i > $o) > $i).
123.15/18.32	thf(decl_360, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
123.15/18.32	thf(decl_361, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
123.15/18.32	thf(decl_362, type, esk36_2: $i > $i > $i).
123.15/18.32	thf(decl_363, type, esk37_2: $i > $i > $i).
123.15/18.32	thf(decl_364, type, esk38_2: $i > $i > $i).
123.15/18.32	thf(decl_365, type, esk39_3: $i > $i > $i > $i).
123.15/18.32	thf(decl_366, type, esk40_3: $i > $i > $i > $i).
123.15/18.32	thf(decl_367, type, esk41_2: $i > $i > $i).
123.15/18.32	thf(decl_368, type, esk42_2: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_369, type, esk43_2: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_370, type, esk44_2: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_371, type, esk45_3: $i > ($i > $o) > $i > $i).
123.15/18.32	thf(decl_372, type, esk46_2: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_373, type, esk47_2: $i > ($i > $o) > $i).
123.15/18.32	thf(decl_374, type, esk48_3: $i > $i > ($i > $i) > $i).
123.15/18.32	thf(decl_375, type, esk49_3: $i > $i > ($i > $i) > $i).
123.15/18.32	thf(decl_376, type, esk50_3: $i > $i > ($i > $i) > $i).
123.15/18.32	thf(decl_377, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
123.15/18.32	thf(decl_378, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
123.15/18.32	thf(decl_379, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
123.15/18.32	thf(decl_380, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
123.15/18.32	thf(decl_381, type, esk55_4: $i > $i > $i > $i > $i).
123.15/18.32	thf(decl_382, type, esk56_4: $i > $i > $i > $i > $i).
123.15/18.32	thf(decl_383, type, esk57_4: $i > $i > $i > $i > $i).
123.15/18.32	thf(decl_384, type, esk58_4: $i > $i > $i > $i > $i).
123.15/18.32	thf(decl_385, type, esk59_4: $i > $i > $i > $i > $i).
123.15/18.32	thf(decl_386, type, esk60_4: $i > $i > $i > $i > $i).
123.15/18.32	thf(decl_387, type, esk61_4: $i > $i > $i > $i > $i).
123.15/18.32	thf(decl_388, type, esk62_4: $i > $i > $i > $i > $i).
123.15/18.32	thf(decl_389, type, esk63_4: $i > $i > $i > $i > $i).
123.15/18.32	thf(decl_390, type, esk64_3: $i > $i > ($i > $i) > $i).
123.15/18.32	thf(decl_391, type, esk65_3: $i > $i > ($i > $i) > $i).
123.15/18.32	thf(decl_392, type, esk66_3: $i > $i > ($i > $i) > $i).
123.15/18.32	thf(decl_393, type, esk67_3: $i > $i > $i > $i).
123.15/18.32	thf(decl_394, type, esk68_3: $i > $i > $i > $i).
123.15/18.32	thf(decl_395, type, esk69_3: $i > $i > $i > $i).
123.15/18.32	thf(decl_396, type, esk70_3: $i > $i > $i > $i).
123.15/18.32	thf(decl_397, type, esk71_0: $i).
123.15/18.32	thf(decl_398, type, esk72_0: $i).
123.15/18.32	thf(decl_399, type, esk73_0: $i).
123.15/18.32	thf(complementUnionInPowersetComplement, conjecture, ((((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>(((((foundationAx)=>((wellorderingAx)=>(((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>(((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((((setbeta)=>((nonemptyE1)=>(((nonemptyI1)=>((setadjoinIL)=>(((setadjoinIR)=>((((setoftrueEq)=>(((emptyinPowerset)=>(((powersetE)=>((((subPowSU)=>((((uniqinunit)=>((notinsingleton)=>((eqinunit)=>(((upairsetE)=>(((upairsetIR)=>((emptyE1)=>(((quantDeMorgan1)=>(((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>((notdexE)=>(((exuI1)=>(((exuI2)=>((inCongP)=>(((exuE3u)=>((((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((((dsetconstr__Cong)=>((subsetI1)=>(((((emptysetsubset)=>((((((notequalI2)=>((subsetRefl)=>(((((((subsetemptysetimpeq)=>((powersetI1)=>((((powersetsubset)=>((sepInPowerset)=>(((((((binunionE)=>((binunionLsub)=>((((((binintersectLsub)=>((binintersectSubset2)=>(((binintersectER)=>((((binintersectSubset4)=>(((bs114d)=>((setminusI)=>((setminusEL)=>(((((setminusELneg)=>((setminusILneg)=>(((setminusLsub)=>((setminusSubset1)=>(((symdiffI1)=>((symdiffI2)=>(((symdiffIneg2)=>(((((kpairiskpair)=>((((singletoninpowerset)=>((((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>(((((((setunionsingleton)=>((singletonprop)=>(((ex1I)=>((ex1I2)=>((singletonsuniq)=>(((((kfstpairEq)=>((((setukpairinjL)=>((setukpairinjR11)=>((((upairequniteq)=>((setukpairinjR2)=>(((((kpairsurjEq)=>((((((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((((setOfPairsIsBReln)=>((((dpsetconstrEL2)=>(((((app)=>(((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>(((brelnall2)=>((((funcGraphProp3)=>(((funcextLem)=>(((subbreln)=>((((((ap2apEq2)=>((beta1)=>(((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>(((iftrueProp1)=>(((ifSingleton)=>((ifp)=>(((iftrue)=>((iffalse)=>(((binintersectT_lem)=>(((powersetT_lem)=>((setminusT_lem)=>((((((powersetTE1)=>((complementTI1)=>(((binintersectTELcontra)=>((binintersectTERcontra)=>((((contrasubsetT2)=>((contrasubsetT3)=>((((doubleComplementSub1)=>((doubleComplementSub2)=>((((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>(((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))))))<=(inComplementUnionImpNotIn1))<=(intersectInPowersetIntersectUnions))))<=(inIntersectImpInUnion)))))))))<=(complementTnotintersectT))<=(doubleComplementEq))))<=(doubleComplementE1))<=(doubleComplementI1))))<=(contrasubsetT1))<=(contrasubsetT))))<=(complementTE1))))<=(powersetTI1))<=(subsetTI))<=(setextT))<=(complementT_lem))))<=(binunionT_lem)))<=(iftrueorfalse))))<=(theeq))))<=(iftrueProp2)))<=(iffalseProp2))))))<=(eta1))))<=(ap2apEq1))<=(funcext2))<=(funcext))<=(eqbreln)))<=(funcGraphProp4)))<=(funcGraphProp2)))<=(funcGraphProp1))<=(ex1E2)))<=(brelnall1)))))))<=(infuncsetfunc)))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER)))<=(dpsetconstrEL1))<=(dpsetconstrERa)))<=(dpsetconstrSub))<=(dpsetconstrI)))))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin)))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))))<=(setukpairinjR1))<=(setukpairinjR12))))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1)))))<=(ex1E1))))<=(setunionsingleton2))<=(setunionsingleton1))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))))))))<=(upairset2E))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp)))<=(setukpairIR))<=(setukpairIL))<=(secondinupair)))<=(symdiffIneg1))))<=(symdiffE))))<=(setminusIRneg))))<=(setminusERneg))<=(setminusSubset2))<=(setminusER)))))<=(binintersectSubset1)))<=(binintersectRsub))<=(disjointsetsI1)))<=(binintersectSubset3))))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))))<=(binunionEcases))<=(binunionIR))<=(upairset2IR))<=(binunionIL))<=(sepSubset))))<=(inPowerset))<=(powersetE1))))<=(setextsub))<=(subset2powerset))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans))))<=(notequalI1))<=(notsubsetI))<=(subsetE2))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2))))<=(descr__Cong))<=(exuEu))))))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong))))<=(exuI3)))<=(notdallE)))))<=(quantDeMorgan4)))<=(quantDeMorgan2)))<=(vacuousDall))))<=(upairsetIL)))<=(singletonsswitch)))))<=(nonemptyImpWitness))<=(exuE2)))<=(setunionE))<=(setunionI)))<=(emptyInPowerset)))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE)))<=(emptyinunitempty))))<=(nonemptyI))))<=(noeltsimpempty))<=(emptyI))))))<=(emptysetE)))))))<=(descrp))))<=(replAx))<=(omegaIndAx))<=(omegaSAx))))))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', complementUnionInPowersetComplement)).
123.15/18.32	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', descr__Cong)).
123.15/18.32	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', exuEu)).
123.15/18.32	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', exu__Cong)).
123.15/18.32	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', exuI3)).
123.15/18.32	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', exuE2)).
123.15/18.32	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', nonemptyI)).
123.15/18.32	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', descrp)).
123.15/18.32	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', replAx)).
123.15/18.32	thf(ex1I, axiom, ((ex1I)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', ex1I)).
123.15/18.32	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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', singletonprop)).
123.15/18.32	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', ex1I2)).
123.15/18.32	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', dpsetconstrEL2)).
123.15/18.32	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setOfPairsIsBReln)).
123.15/18.32	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', lamProp)).
123.15/18.32	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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', lam2p)).
123.15/18.32	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', lamp)).
123.15/18.32	thf(beta1, axiom, ((beta1)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', beta1)).
123.15/18.32	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', ifSingleton)).
123.15/18.32	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', iftrueProp1)).
123.15/18.32	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', iffalseProp1)).
123.15/18.32	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', eta2)).
123.15/18.32	thf(beta2, axiom, ((beta2)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', beta2)).
123.15/18.32	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.cjGwKrkbEx/E---3.1_884544.p', lam2lamEq)).
123.15/18.32	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.cjGwKrkbEx/E---3.1_884544.p', eta1)).
123.15/18.32	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', iffalseProp2)).
123.15/18.32	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', iftrueProp2)).
123.15/18.32	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.cjGwKrkbEx/E---3.1_884544.p', ex1E2)).
123.15/18.32	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', apProp)).
123.15/18.32	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', dpsetconstrI)).
123.15/18.32	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', dpsetconstrSub)).
123.15/18.32	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', dpsetconstrERa)).
123.15/18.32	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', dpsetconstrEL1)).
123.15/18.32	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', dpsetconstrER)).
123.15/18.32	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', funcImageSingleton)).
123.15/18.32	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.cjGwKrkbEx/E---3.1_884544.p', ksndsingleton)).
123.15/18.32	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', ex1E1)).
123.15/18.32	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', kfstsingleton)).
123.15/18.32	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', sepSubset)).
123.15/18.32	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', sepInPowerset)).
123.15/18.32	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', dsetconstr__Cong)).
123.15/18.32	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', exuE3u)).
123.15/18.32	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.cjGwKrkbEx/E---3.1_884544.p', exuI2)).
123.15/18.32	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.cjGwKrkbEx/E---3.1_884544.p', exuI1)).
123.15/18.32	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.cjGwKrkbEx/E---3.1_884544.p', emptyE1)).
123.15/18.32	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setoftrueEq)).
123.15/18.32	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setbeta)).
123.15/18.32	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', exuE3e)).
123.15/18.32	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', exuE1)).
123.15/18.32	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', dsetconstrER)).
123.15/18.32	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', dsetconstrEL)).
123.15/18.32	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', dsetconstrI)).
123.15/18.32	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', powersetE1)).
123.15/18.32	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', inPowerset)).
123.15/18.32	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setextsub)).
123.15/18.32	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', subset2powerset)).
123.15/18.32	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setadjoinSub2)).
123.15/18.32	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setadjoinSub)).
123.15/18.32	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', subsetTrans)).
123.15/18.32	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setminusILneg)).
123.15/18.32	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', notequalI1)).
123.15/18.32	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setminusELneg)).
123.15/18.32	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', notsubsetI)).
123.15/18.32	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setminusEL)).
123.15/18.32	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', subsetE2)).
123.15/18.32	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setminusI)).
123.15/18.32	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', subsetE)).
123.15/18.32	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', bs114d)).
123.15/18.32	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', subsetI2)).
123.15/18.32	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectSubset4)).
123.15/18.32	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', eqimpsubset1)).
123.15/18.32	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectER)).
123.15/18.32	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', eqimpsubset2)).
123.15/18.32	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setminusLsub)).
123.15/18.32	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', emptyset__Cong)).
123.15/18.32	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.cjGwKrkbEx/E---3.1_884544.p', in__Cong)).
123.15/18.32	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', notdallE)).
123.15/18.32	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', quantDeMorgan4)).
123.15/18.32	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', quantDeMorgan2)).
123.15/18.32	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', vacuousDall)).
123.15/18.32	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', upairsetIL)).
123.15/18.32	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', singletonsswitch)).
123.15/18.32	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', nonemptyImpWitness)).
123.15/18.32	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', upairsubunion)).
123.15/18.32	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setunionE)).
123.15/18.32	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', singletoninpowerset)).
123.15/18.32	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setunionI)).
123.15/18.32	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.cjGwKrkbEx/E---3.1_884544.p', kpairiskpair)).
123.15/18.32	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', emptyInPowerset)).
123.15/18.32	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', symdiffIneg2)).
123.15/18.32	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', powersetI)).
123.15/18.32	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', symdiffI2)).
123.15/18.32	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setadjoinOr)).
123.15/18.32	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', symdiffI1)).
123.15/18.32	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.cjGwKrkbEx/E---3.1_884544.p', setadjoinE)).
123.15/18.32	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setminusSubset1)).
123.15/18.32	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', emptyinunitempty)).
123.15/18.32	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.cjGwKrkbEx/E---3.1_884544.p', upairinpowunion)).
123.15/18.32	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', noeltsimpempty)).
123.15/18.32	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', emptyI)).
123.15/18.32	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', emptysetE)).
123.15/18.32	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', omegaIndAx)).
123.15/18.32	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', omegaSAx)).
123.15/18.32	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', emptysetAx)).
123.15/18.32	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setextAx)).
123.15/18.32	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setunionsingleton)).
123.15/18.32	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', cartprodpairin)).
123.15/18.32	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', ubforcartprodlem3)).
123.15/18.33	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', ubforcartprodlem2)).
123.15/18.33	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', ubforcartprodlem1)).
123.15/18.33	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', kpairsurjEq)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', setukpairinjR2)).
123.15/18.33	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', upairequniteq)).
123.15/18.33	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setukpairinjR11)).
123.15/18.33	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setukpairinjL)).
123.15/18.33	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', kfstpairEq)).
123.15/18.33	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', singletonsuniq)).
123.15/18.33	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', cartprodfstpairEq)).
123.15/18.33	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', funcinfuncset)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', ap2p)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', app)).
123.15/18.33	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', cartprodpairsurjEq)).
123.15/18.33	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', cartprodsndpairEq)).
123.15/18.33	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', ap2apEq2)).
123.15/18.33	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', subbreln)).
123.15/18.33	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', funcextLem)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', funcGraphProp3)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', brelnall2)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', ifp)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', iftrue)).
123.15/18.33	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectSubset5)).
123.15/18.33	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectEL)).
123.15/18.33	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectSubset3)).
123.15/18.33	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', disjointsetsI1)).
123.15/18.33	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectRsub)).
123.15/18.33	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binunionIR)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', binintersectTELcontra)).
123.15/18.33	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', complementTI1)).
123.15/18.33	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', powersetTE1)).
123.15/18.33	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', setminusT_lem)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', powersetT_lem)).
123.15/18.33	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectT_lem)).
123.15/18.33	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', iffalse)).
123.15/18.33	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectTERcontra)).
123.15/18.33	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', complementInPowersetComplementIntersect)).
123.15/18.33	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', complementSubsetComplementIntersect)).
123.15/18.33	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', complementImpComplementIntersect)).
123.15/18.33	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', doubleComplementSub2)).
123.15/18.33	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', doubleComplementSub1)).
123.15/18.33	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', contrasubsetT3)).
123.15/18.33	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', contrasubsetT2)).
123.15/18.33	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', contraSubsetComplement)).
123.15/18.33	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', binunionTE)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', inComplementUnionImpInComplement1)).
123.15/18.33	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', inIntersectImpInIntersectUnions)).
123.15/18.33	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', inIntersectImpInUnion2)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', binunionTIRcontra)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', binunionTILcontra)).
123.15/18.33	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', complementTcontraSubset)).
123.15/18.33	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binunionTEcontra)).
123.15/18.33	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', doubleComplementE1)).
123.15/18.33	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', doubleComplementEq)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', complementTnotintersectT)).
123.15/18.33	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', inIntersectImpInUnion)).
123.15/18.33	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', intersectInPowersetIntersectUnions)).
123.15/18.33	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', inComplementUnionImpNotIn1)).
123.15/18.33	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', demorgan2a1)).
123.15/18.33	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', doubleComplementI1)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', complementT_lem)).
123.15/18.33	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setextT)).
123.15/18.33	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', subsetTI)).
123.15/18.33	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', powersetTI1)).
123.15/18.33	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', complementTE1)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', contrasubsetT)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', contrasubsetT1)).
123.15/18.33	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binunionT_lem)).
123.15/18.33	thf(funcext2, axiom, ((funcext2)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', funcext2)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', ap2apEq1)).
123.15/18.33	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', theeq)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', iftrueorfalse)).
123.15/18.33	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', funcext)).
123.15/18.33	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', infuncsetfunc)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', brelnall1)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', funcGraphProp1)).
123.15/18.33	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', funcGraphProp2)).
123.15/18.33	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', funcGraphProp4)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', eqbreln)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', cartprodmempaircEq)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', cartprodpairmemER)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', setukpairinjR12)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', setukpairinjR1)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', setukpairinjR)).
123.15/18.33	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', ksndpairEq)).
123.15/18.33	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', cartprodsndin)).
123.15/18.33	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', cartprodpairmemEL)).
123.15/18.33	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setukpairinjL2)).
123.15/18.33	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setunionsingleton1)).
123.15/18.33	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setunionsingleton2)).
123.15/18.33	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.cjGwKrkbEx/E---3.1_884544.p', setukpairinjL1)).
123.15/18.33	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', theprop)).
123.15/18.33	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', cartprodfstin)).
123.15/18.33	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setunionE2)).
123.15/18.33	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setukpairIR)).
123.15/18.33	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', kpairp)).
123.15/18.33	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', singletonsubset)).
123.15/18.33	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', singletoninpowunion)).
123.15/18.33	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', upairset2E)).
123.15/18.33	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.cjGwKrkbEx/E---3.1_884544.p', cartprodmempair1)).
123.15/18.33	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', cartprodmempair)).
123.15/18.33	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setukpairIL)).
123.15/18.33	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setminusER)).
123.15/18.33	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setminusSubset2)).
123.15/18.33	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setminusERneg)).
123.15/18.33	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setminusIRneg)).
123.15/18.33	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.cjGwKrkbEx/E---3.1_884544.p', symdiffE)).
123.15/18.33	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', symdiffIneg1)).
123.15/18.33	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', secondinupair)).
123.15/18.33	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectSubset1)).
123.15/18.33	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binunionRsub)).
123.15/18.33	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectI)).
123.15/18.33	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', upairset2IR)).
123.15/18.33	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binunionIL)).
123.15/18.33	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binunionEcases)).
123.15/18.33	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectSubset2)).
123.15/18.33	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binintersectLsub)).
123.15/18.33	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binunionLsub)).
123.15/18.33	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', binunionE)).
123.15/18.33	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', powersetsubset)).
123.15/18.33	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', powersetI1)).
123.15/18.33	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', subsetemptysetimpeq)).
123.15/18.33	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', subsetRefl)).
123.15/18.33	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', notequalI2)).
123.15/18.33	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', emptysetsubset)).
123.15/18.33	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', subsetI1)).
123.15/18.33	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', omega__Cong)).
123.15/18.33	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setunion__Cong)).
123.15/18.33	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', powerset__Cong)).
123.15/18.33	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setadjoin__Cong)).
123.15/18.33	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', inCongP)).
123.15/18.33	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', notdexE)).
123.15/18.33	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', prop2setI)).
123.15/18.33	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', quantDeMorgan3)).
123.15/18.33	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', quantDeMorgan1)).
123.15/18.33	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', upairsetIR)).
123.15/18.33	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', upairsetE)).
123.15/18.33	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', eqinunit)).
123.15/18.33	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', notinsingleton)).
123.15/18.33	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', uniqinunit)).
123.15/18.33	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', subPowSU)).
123.15/18.33	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', powersetE)).
123.15/18.33	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', emptyinPowerset)).
123.15/18.33	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setadjoinIR)).
123.15/18.33	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setadjoinIL)).
123.15/18.33	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', nonemptyI1)).
123.15/18.33	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', nonemptyE1)).
123.15/18.33	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setext)).
123.15/18.33	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', notinemptyset)).
123.15/18.33	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', emptysetimpfalse)).
123.15/18.33	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', prop2setE)).
123.15/18.33	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', wellorderingAx)).
123.15/18.33	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', foundationAx)).
123.15/18.33	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', omega0Ax)).
123.15/18.33	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setunionAx)).
123.15/18.33	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', powersetAx)).
123.15/18.33	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.cjGwKrkbEx/E---3.1_884544.p', setadjoinAx)).
123.15/18.33	thf(c_0_265, negated_conjecture, ~(((((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>(((((foundationAx)=>((wellorderingAx)=>(((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>(((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((((setbeta)=>((nonemptyE1)=>(((nonemptyI1)=>((setadjoinIL)=>(((setadjoinIR)=>((((setoftrueEq)=>(((emptyinPowerset)=>(((powersetE)=>((((subPowSU)=>((((uniqinunit)=>((notinsingleton)=>((eqinunit)=>(((upairsetE)=>(((upairsetIR)=>((emptyE1)=>(((quantDeMorgan1)=>(((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>((notdexE)=>(((exuI1)=>(((exuI2)=>((inCongP)=>(((exuE3u)=>((((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((((dsetconstr__Cong)=>((subsetI1)=>(((((emptysetsubset)=>((((((notequalI2)=>((subsetRefl)=>(((((((subsetemptysetimpeq)=>((powersetI1)=>((((powersetsubset)=>((sepInPowerset)=>(((((((binunionE)=>((binunionLsub)=>((((((binintersectLsub)=>((binintersectSubset2)=>(((binintersectER)=>((((binintersectSubset4)=>(((bs114d)=>((setminusI)=>((setminusEL)=>(((((setminusELneg)=>((setminusILneg)=>(((setminusLsub)=>((setminusSubset1)=>(((symdiffI1)=>((symdiffI2)=>(((symdiffIneg2)=>(((((kpairiskpair)=>((((singletoninpowerset)=>((((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>(((((((setunionsingleton)=>((singletonprop)=>(((ex1I)=>((ex1I2)=>((singletonsuniq)=>(((((kfstpairEq)=>((((setukpairinjL)=>((setukpairinjR11)=>((((upairequniteq)=>((setukpairinjR2)=>(((((kpairsurjEq)=>((((((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((((setOfPairsIsBReln)=>((((dpsetconstrEL2)=>(((((app)=>(((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>(((brelnall2)=>((((funcGraphProp3)=>(((funcextLem)=>(((subbreln)=>((((((ap2apEq2)=>((beta1)=>(((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>(((iftrueProp1)=>(((ifSingleton)=>((ifp)=>(((iftrue)=>((iffalse)=>(((binintersectT_lem)=>(((powersetT_lem)=>((setminusT_lem)=>((((((powersetTE1)=>((complementTI1)=>(((binintersectTELcontra)=>((binintersectTERcontra)=>((((contrasubsetT2)=>((contrasubsetT3)=>((((doubleComplementSub1)=>((doubleComplementSub2)=>((((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>(((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))))))<=(inComplementUnionImpNotIn1))<=(intersectInPowersetIntersectUnions))))<=(inIntersectImpInUnion)))))))))<=(complementTnotintersectT))<=(doubleComplementEq))))<=(doubleComplementE1))<=(doubleComplementI1))))<=(contrasubsetT1))<=(contrasubsetT))))<=(complementTE1))))<=(powersetTI1))<=(subsetTI))<=(setextT))<=(complementT_lem))))<=(binunionT_lem)))<=(iftrueorfalse))))<=(theeq))))<=(iftrueProp2)))<=(iffalseProp2))))))<=(eta1))))<=(ap2apEq1))<=(funcext2))<=(funcext))<=(eqbreln)))<=(funcGraphProp4)))<=(funcGraphProp2)))<=(funcGraphProp1))<=(ex1E2)))<=(brelnall1)))))))<=(infuncsetfunc)))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER)))<=(dpsetconstrEL1))<=(dpsetconstrERa)))<=(dpsetconstrSub))<=(dpsetconstrI)))))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin)))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))))<=(setukpairinjR1))<=(setukpairinjR12))))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1)))))<=(ex1E1))))<=(setunionsingleton2))<=(setunionsingleton1))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))))))))<=(upairset2E))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp)))<=(setukpairIR))<=(setukpairIL))<=(secondinupair)))<=(symdiffIneg1))))<=(symdiffE))))<=(setminusIRneg))))<=(setminusERneg))<=(setminusSubset2))<=(setminusER)))))<=(binintersectSubset1)))<=(binintersectRsub))<=(disjointsetsI1)))<=(binintersectSubset3))))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))))<=(binunionEcases))<=(binunionIR))<=(upairset2IR))<=(binunionIL))<=(sepSubset))))<=(inPowerset))<=(powersetE1))))<=(setextsub))<=(subset2powerset))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans))))<=(notequalI1))<=(notsubsetI))<=(subsetE2))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2))))<=(descr__Cong))<=(exuEu))))))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong))))<=(exuI3)))<=(notdallE)))))<=(quantDeMorgan4)))<=(quantDeMorgan2)))<=(vacuousDall))))<=(upairsetIL)))<=(singletonsswitch)))))<=(nonemptyImpWitness))<=(exuE2)))<=(setunionE))<=(setunionI)))<=(emptyInPowerset)))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE)))<=(emptyinunitempty))))<=(nonemptyI))))<=(noeltsimpempty))<=(emptyI))))))<=(emptysetE)))))))<=(descrp))))<=(replAx))<=(omegaIndAx))<=(omegaSAx))))))<=(emptysetAx))<=(setextAx))), inference(assume_negation,[status(cth)],[complementUnionInPowersetComplement])).
123.15/18.33	thf(c_0_266, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
123.15/18.33	thf(c_0_267, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
123.15/18.33	thf(c_0_268, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
123.15/18.33	thf(c_0_269, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
123.15/18.33	thf(c_0_270, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
123.15/18.33	thf(c_0_271, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
123.15/18.33	thf(c_0_272, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
123.15/18.33	thf(c_0_273, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
123.15/18.33	thf(c_0_274, plain, ((ex1I)<=>![X4:$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])).
123.15/18.33	thf(c_0_275, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
123.15/18.33	thf(c_0_276, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
123.15/18.33	thf(c_0_277, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
123.15/18.33	thf(c_0_278, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
123.15/18.33	thf(c_0_279, plain, ((lamProp)<=>![X4:$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])).
123.15/18.33	thf(c_0_280, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
123.15/18.33	thf(c_0_281, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
123.15/18.33	thf(c_0_282, plain, ((beta1)<=>![X4:$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])).
123.15/18.33	thf(c_0_283, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
123.15/18.33	thf(c_0_284, plain, ((iftrueProp1)<=>![X4:$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])).
123.15/18.33	thf(c_0_285, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
123.15/18.33	thf(c_0_286, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
123.15/18.33	thf(c_0_287, plain, ((beta2)<=>![X4:$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])).
123.15/18.33	thf(c_0_288, 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])).
123.15/18.33	thf(c_0_289, 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])).
123.15/18.33	thf(c_0_290, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
123.15/18.33	thf(c_0_291, plain, ((iftrueProp2)<=>![X4:$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])).
123.15/18.33	thf(c_0_292, 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])).
123.15/18.33	thf(c_0_293, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
123.15/18.33	thf(c_0_294, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
123.15/18.33	thf(c_0_295, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
123.15/18.33	thf(c_0_296, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
123.15/18.33	thf(c_0_297, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
123.15/18.33	thf(c_0_298, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
123.15/18.33	thf(c_0_299, plain, ((funcImageSingleton)<=>![X4:$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])).
123.15/18.33	thf(c_0_300, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
123.15/18.33	thf(c_0_301, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
123.15/18.33	thf(c_0_302, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
123.15/18.33	thf(c_0_303, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
123.15/18.33	thf(c_0_304, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
123.15/18.33	thf(c_0_305, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
123.15/18.33	thf(c_0_306, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
123.15/18.33	thf(c_0_307, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
123.15/18.33	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])).
123.15/18.33	thf(c_0_309, 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])).
123.15/18.33	thf(c_0_310, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
123.15/18.33	thf(c_0_311, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
123.15/18.33	thf(c_0_312, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
123.15/18.33	thf(c_0_313, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
123.15/18.33	thf(c_0_314, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
123.15/18.33	thf(c_0_315, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
123.15/18.33	thf(c_0_316, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
123.15/18.33	thf(c_0_317, plain, ((epred1_0)<=>![X901:$i]:(?[X902:$i]:((((![X903:$i]:(((in @ X903 @ X902)=>![X904:$i]:(((in @ X904 @ X903)=>(in @ X904 @ X901)))))&![X905:$i, X906:$i]:((((in @ X905 @ X901)&(in @ X906 @ X901))=>(![X907:$i]:(((in @ X907 @ X902)=>((in @ X905 @ X907)<=>(in @ X906 @ X907))))=>((X905)=(X906))))))&![X908:$i, X909:$i]:((((in @ X908 @ X902)&(in @ X909 @ X902))=>(![X910:$i]:(((in @ X910 @ X908)=>(in @ X910 @ X909)))|![X911:$i]:(((in @ X911 @ X909)=>(in @ X911 @ X908)))))))&![X912:$i]:(((![X913:$i]:(((in @ X913 @ X912)=>(in @ X913 @ X901)))&?[X914:$i]:((in @ X914 @ X912)))=>?[X915:$i, X916:$i]:(((((in @ X915 @ X902)&(in @ X916 @ X912))&~(?[X917:$i]:(((in @ X917 @ X915)&(in @ X917 @ X912)))))&![X918:$i]:(((in @ X918 @ X902)=>(![X919:$i]:(((in @ X919 @ X918)=>(in @ X919 @ X915)))|(in @ X916 @ X918)))))))))))), introduced(definition)).
123.15/18.33	thf(c_0_318, negated_conjecture, ~((![X1719:$i, X1720:$i]:((![X1721:$i]:(((in @ X1721 @ X1719)<=>(in @ X1721 @ X1720)))=>((X1719)=(X1720))))=>(![X1718:$i]:(~(in @ X1718 @ emptyset))=>(![X888:$i, X889:$i, X890:$i]:(((in @ X890 @ (setadjoin @ X888 @ X889))<=>(((X890)=(X888))|(in @ X890 @ X889))))=>(![X891:$i, X892:$i]:(((in @ X892 @ (powerset @ X891))<=>![X893:$i]:(((in @ X893 @ X892)=>(in @ X893 @ X891)))))=>(![X894:$i, X895:$i]:(((in @ X895 @ (setunion @ X894))<=>?[X896:$i]:(((in @ X895 @ X896)&(in @ X896 @ X894)))))=>((in @ emptyset @ omega)=>(![X1717:$i]:(((in @ X1717 @ omega)=>(in @ (setadjoin @ X1717 @ X1717) @ omega)))=>(![X1714:$i]:((((in @ emptyset @ X1714)&![X1715:$i]:((((in @ X1715 @ omega)&(in @ X1715 @ X1714))=>(in @ (setadjoin @ X1715 @ X1715) @ X1714))))=>![X1716:$i]:(((in @ X1716 @ omega)=>(in @ X1716 @ X1714)))))=>(![X1708:$i > $i > $o, X1709:$i]:((![X1710:$i]:(((in @ X1710 @ X1709)=>(exu @ (X1708 @ X1710))))=>?[X1711:$i]:(![X1712:$i]:(((in @ X1712 @ X1711)<=>?[X1713:$i]:(((in @ X1713 @ X1709)&(X1708 @ X1713 @ X1712))))))))=>(![X897:$i]:((?[X898:$i]:((in @ X898 @ X897))=>?[X899:$i]:(((in @ X899 @ X897)&~(?[X900:$i]:(((in @ X900 @ X899)&(in @ X900 @ X897))))))))=>((epred1_0)=>(![X1707:$i > $o]:(((exu @ X1707)=>(X1707 @ (descr @ (^[Z0:$i]:(X1707 @ Z0))))))=>(![X920:$i, X921:$i > $o, X922:$i]:(((in @ X922 @ X920)=>((X921 @ X922)=>(in @ X922 @ (dsetconstr @ X920 @ X921)))))=>(![X923:$i, X924:$i > $o, X925:$i]:(((in @ X925 @ (dsetconstr @ X923 @ X924))=>(in @ X925 @ X923)))=>(![X926:$i, X927:$i > $o, X928:$i]:(((in @ X928 @ (dsetconstr @ X926 @ X927))=>(X927 @ X928)))=>(![X929:$i > $o]:(((exu @ X929)=>?[X930:$i]:(((X929 @ X930)&![X931:$i]:(((X929 @ X931)=>((X930)=(X931))))))))=>(![X932:$o, X933:$i]:(((in @ X933 @ (prop2set @ ((X932))))=>(X932)))=>(![X1705:$i]:(((in @ X1705 @ emptyset)=>![X1706:$o]:((X1706))))=>(![X934:$i]:(((in @ X934 @ emptyset)=>~($true)))=>(![X935:$i]:(~(in @ X935 @ emptyset))=>(![X936:$i > $o]:(((exu @ X936)=>?[X937:$i]:((X936 @ X937))))=>(![X938:$i, X939:$i]:((![X940:$i]:(((in @ X940 @ X938)=>(in @ X940 @ X939)))=>(![X941:$i]:(((in @ X941 @ X939)=>(in @ X941 @ X938)))=>((X938)=(X939)))))=>(![X1703:$i]:((![X1704:$i]:(~(in @ X1704 @ X1703))=>((X1703)=(emptyset))))=>(![X1701:$i]:((![X1702:$i]:(~(in @ X1702 @ X1701))=>((X1701)=(emptyset))))=>(![X942:$i, X943:$i > $o, X944:$i]:(((in @ X944 @ X942)=>((in @ X944 @ (dsetconstr @ X942 @ X943))<=>(X943 @ X944))))=>(![X945:$i]:(((nonempty @ X945)=>?[X946:$i]:((in @ X946 @ X945))))=>(![X1698:$i, X1699:$i > $o, X1700:$i]:(((in @ X1700 @ X1698)=>((X1699 @ X1700)=>(nonempty @ (dsetconstr @ X1698 @ X1699)))))=>(![X947:$i]:((?[X948:$i]:((in @ X948 @ X947))=>(nonempty @ X947)))=>(![X949:$i, X950:$i]:((in @ X949 @ (setadjoin @ X949 @ X950)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X951:$i, X952:$i, X953:$i]:(((in @ X953 @ X952)=>(in @ X953 @ (setadjoin @ X951 @ X952))))=>(![X1694:$i, X1695:$i, X1696:$i]:(((in @ X1696 @ (setadjoin @ X1694 @ X1695))=>![X1697:$o]:(((((X1696)=(X1694))=>(X1697))=>(((in @ X1696 @ X1695)=>(X1697))=>(X1697))))))=>(![X1691:$i, X1692:$i, X1693:$i]:(((in @ X1693 @ (setadjoin @ X1691 @ X1692))=>(((X1693)=(X1691))|(in @ X1693 @ X1692))))=>(![X954:$i]:(((dsetconstr @ X954 @ (^[Z0:$i]:($true)))=(X954)))=>(![X1688:$i, X1689:$i]:((![X1690:$i]:(((in @ X1690 @ X1689)=>(in @ X1690 @ X1688)))=>(in @ X1689 @ (powerset @ X1688))))=>(![X955:$i]:((in @ emptyset @ (powerset @ X955)))=>(![X1687:$i]:((in @ emptyset @ (powerset @ X1687)))=>(![X956:$i, X957:$i, X958:$i]:(((in @ X957 @ (powerset @ X956))=>((in @ X958 @ X957)=>(in @ X958 @ X956))))=>(![X1684:$i, X1685:$i, X1686:$i]:(((in @ X1685 @ X1686)=>((in @ X1686 @ X1684)=>(in @ X1685 @ (setunion @ X1684)))))=>(![X1680:$i, X1681:$i]:(((in @ X1681 @ (setunion @ X1680))=>![X1682:$o]:((![X1683:$i]:(((in @ X1681 @ X1683)=>((in @ X1683 @ X1680)=>(X1682))))=>(X1682)))))=>(![X959:$i, X960:$i]:(((in @ X960 @ X959)=>(in @ X960 @ (powerset @ (setunion @ X959)))))=>(![X1677:$i > $o]:(((exu @ X1677)=>?[X1678:$i]:(![X1679:$i]:(((X1677 @ X1679)<=>((X1679)=(X1678)))))))=>(![X1675:$i]:(((nonempty @ X1675)=>?[X1676:$i]:(((in @ X1676 @ X1675)&$true))))=>(![X961:$i, X962:$i]:(((in @ X961 @ (setadjoin @ X962 @ emptyset))=>((X961)=(X962))))=>(![X963:$i, X964:$i]:((((X963)!=(X964))=>~(in @ X964 @ (setadjoin @ X963 @ emptyset))))=>(![X965:$i, X966:$i]:((((X965)=(X966))=>(in @ X965 @ (setadjoin @ X966 @ emptyset))))=>(![X1673:$i, X1674:$i]:(((in @ X1673 @ (setadjoin @ X1674 @ emptyset))=>(in @ X1674 @ (setadjoin @ X1673 @ emptyset))))=>(![X967:$i, X968:$i, X969:$i]:(((in @ X969 @ (setadjoin @ X967 @ (setadjoin @ X968 @ emptyset)))=>(((X969)=(X967))|((X969)=(X968)))))=>(![X1671:$i, X1672:$i]:((in @ X1671 @ (setadjoin @ X1671 @ (setadjoin @ X1672 @ emptyset))))=>(![X970:$i, X971:$i]:((in @ X971 @ (setadjoin @ X970 @ (setadjoin @ X971 @ emptyset))))=>(![X972:$i, X973:$i > $o]:((?[X974:$i]:(((in @ X974 @ X972)&(X973 @ X974)))=>(((dsetconstr @ X972 @ X973)=(emptyset))=>~($true))))=>(![X1669:$i > $o, X1670:$i]:(((in @ X1670 @ emptyset)=>(X1669 @ X1670)))=>(![X975:$i, X976:$i > $o]:((~(![X977:$i]:(((in @ X977 @ X975)=>(X976 @ X977))))=>?[X978:$i]:(((in @ X978 @ X975)&~((X976 @ X978))))))=>(![X1665:$i, X1666:$i > $o]:((![X1667:$i]:(((in @ X1667 @ X1665)=>~((X1666 @ X1667))))=>~(?[X1668:$i]:(((in @ X1668 @ X1665)&(X1666 @ X1668))))))=>(![X979:$i, X980:$i > $o]:((~(?[X981:$i]:(((in @ X981 @ X979)&(X980 @ X981))))=>![X982:$i]:(((in @ X982 @ X979)=>~((X980 @ X982))))))=>(![X1661:$i, X1662:$i > $o]:((?[X1663:$i]:(((in @ X1663 @ X1661)&~((X1662 @ X1663))))=>~(![X1664:$i]:(((in @ X1664 @ X1661)=>(X1662 @ X1664))))))=>(![X983:$o]:(((X983)=>(in @ emptyset @ (prop2set @ ((X983))))))=>((prop2set2propI)=>(![X984:$i, X985:$i > $o]:((~(?[X986:$i]:(((in @ X986 @ X984)&(X985 @ X986))))=>![X987:$i]:(((in @ X987 @ X984)=>~((X985 @ X987))))))=>(![X1657:$i, X1658:$i > $o]:((~(![X1659:$i]:(((in @ X1659 @ X1657)=>(X1658 @ X1659))))=>?[X1660:$i]:(((in @ X1660 @ X1657)&~((X1658 @ X1660))))))=>(![X988:$i > $o]:((?[X989:$i]:(((X988 @ X989)&![X990:$i]:(((X988 @ X990)=>((X989)=(X990))))))=>(exu @ X988)))=>(![X1653:$i > $o]:((?[X1654:$i]:((X1653 @ X1654))=>(![X1655:$i, X1656:$i]:(((X1653 @ X1655)=>((X1653 @ X1656)=>((X1655)=(X1656)))))=>(exu @ X1653))))=>(![X991:$i > $o]:((?[X992:$i]:(![X993:$i]:(((X991 @ X993)<=>((X993)=(X992)))))=>(exu @ X991)))=>(![X994:$i, X995:$i]:((((X994)=(X995))=>![X996:$i, X997:$i]:((((X996)=(X997))=>((in @ X996 @ X994)=>(in @ X997 @ X995))))))=>(![X1649:$i, X1650:$i]:((((X1649)=(X1650))=>![X1651:$i, X1652:$i]:((((X1651)=(X1652))=>((in @ X1651 @ X1649)<=>(in @ X1652 @ X1650))))))=>(![X998:$i > $o]:(((exu @ X998)=>![X999:$i, X1000:$i]:(((X998 @ X999)=>((X998 @ X1000)=>((X999)=(X1000)))))))=>(![X1645:$i > $o, X1646:$i > $o]:((![X1647:$i, X1648:$i]:((((X1647)=(X1648))=>((X1645 @ X1647)<=>(X1646 @ X1648))))=>((exu @ X1645)<=>(exu @ X1646))))=>(((emptyset)=(emptyset))=>(![X1001:$i, 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@ X1289)=>(in @ X1290 @ (setminus @ X1287 @ X1288))))))))))=>(![X1291:$i, X1292:$i]:(((in @ X1292 @ (powerset @ X1291))=>![X1293:$i]:(((in @ X1293 @ (powerset @ X1291))=>((subset @ X1292 @ (setminus @ X1291 @ X1293))=>(subset @ X1293 @ (setminus @ X1291 @ X1292)))))))=>(![X1294:$i, X1295:$i]:(((in @ X1295 @ (powerset @ X1294))=>![X1296:$i]:(((in @ X1296 @ (powerset @ X1294))=>![X1297:$i]:(((in @ X1297 @ X1294)=>(~(in @ X1297 @ (binunion @ X1295 @ X1296))=>~(in @ X1297 @ X1295))))))))=>(![X1298:$i, X1299:$i]:(((in @ X1299 @ (powerset @ X1298))=>![X1300:$i]:(((in @ X1300 @ (powerset @ X1298))=>![X1301:$i]:(((in @ X1301 @ X1298)=>(~(in @ X1301 @ (binunion @ X1299 @ X1300))=>~(in @ X1301 @ X1300))))))))=>(![X1337:$i, X1338:$i]:(((in @ X1338 @ (powerset @ X1337))=>![X1339:$i]:(((in @ X1339 @ (powerset @ X1337))=>![X1340:$i]:(((in @ X1340 @ (powerset @ X1337))=>![X1341:$i]:(((in @ X1341 @ X1337)=>((in @ X1341 @ (binintersect @ X1338 @ X1339))=>(in @ X1341 @ (binunion @ X1338 @ X1340)))))))))))=>(![X1302:$i, X1303:$i]:(((in @ X1303 @ (powerset @ X1302))=>![X1304:$i]:(((in @ X1304 @ (powerset @ X1302))=>![X1305:$i]:(((in @ X1305 @ (powerset @ X1302))=>![X1306:$i]:(((in @ X1306 @ X1302)=>((in @ X1306 @ (binintersect @ X1303 @ X1304))=>(in @ X1306 @ (binunion @ X1304 @ X1305)))))))))))=>(![X1307:$i, X1308:$i]:(((in @ X1308 @ (powerset @ X1307))=>![X1309:$i]:(((in @ X1309 @ (powerset @ X1307))=>![X1310:$i]:(((in @ X1310 @ (powerset @ X1307))=>![X1311:$i]:(((in @ X1311 @ X1307)=>((in @ X1311 @ (binintersect @ X1308 @ X1309))=>(in @ X1311 @ (binintersect @ (binunion @ X1308 @ X1310) @ (binunion @ X1309 @ X1310))))))))))))=>(![X1333:$i, X1334:$i]:(((in @ X1334 @ (powerset @ X1333))=>![X1335:$i]:(((in @ X1335 @ (powerset @ X1333))=>![X1336:$i]:(((in @ X1336 @ (powerset @ X1333))=>(in @ (binintersect @ X1334 @ X1335) @ (powerset @ (binintersect @ (binunion @ X1334 @ X1336) @ (binunion @ X1335 @ X1336))))))))))=>(![X1329:$i, X1330:$i]:(((in @ X1330 @ (powerset @ X1329))=>![X1331:$i]:(((in @ X1331 @ (powerset @ X1329))=>![X1332:$i]:(((in @ X1332 @ X1329)=>((in @ X1332 @ (setminus @ X1329 @ (binunion @ X1330 @ X1331)))=>~(in @ X1332 @ X1330))))))))=>(![X1312:$i, X1313:$i]:(((in @ X1313 @ (powerset @ X1312))=>![X1314:$i]:(((in @ X1314 @ (powerset @ X1312))=>![X1315:$i]:(((in @ X1315 @ X1312)=>((in @ X1315 @ (setminus @ X1312 @ (binunion @ X1313 @ X1314)))=>(in @ X1315 @ (setminus @ X1312 @ X1313)))))))))=>(![X1316:$i, X1317:$i]:(((in @ X1317 @ (powerset @ X1316))=>![X1318:$i]:(((in @ X1318 @ (powerset @ X1316))=>![X1319:$o, X1320:$i]:(((in @ X1320 @ X1316)=>((in @ X1320 @ (binunion @ X1317 @ X1318))=>(((in @ X1320 @ X1317)=>(X1319))=>(((in @ X1320 @ X1318)=>(X1319))=>(X1319))))))))))=>(![X1321:$i, X1322:$i]:(((in @ X1322 @ (powerset @ X1321))=>![X1323:$i]:(((in @ X1323 @ (powerset @ X1321))=>![X1324:$i]:(((in @ X1324 @ X1321)=>(~(in @ X1324 @ X1322)=>(~(in @ X1324 @ X1323)=>~(in @ X1324 @ (binunion @ X1322 @ X1323))))))))))=>(![X1325:$i, X1326:$i]:(((in @ X1326 @ (powerset @ X1325))=>![X1327:$i]:(((in @ X1327 @ (powerset @ X1325))=>![X1328:$i]:(((in @ X1328 @ X1325)=>((in @ X1328 @ (setminus @ X1325 @ (binunion @ X1326 @ X1327)))=>(in @ X1328 @ (setminus @ X1325 @ X1326)))))))))=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_265, powersetE1]), inPowerset]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), setminusILneg]), notequalI1]), setminusELneg]), notsubsetI]), setminusEL]), subsetE2]), setminusI]), subsetE]), bs114d]), subsetI2]), binintersectSubset4]), eqimpsubset1]), binintersectER]), eqimpsubset2]), setminusLsub]), c_0_266]), c_0_267]), emptyset__Cong]), c_0_268]), in__Cong]), c_0_269]), notdallE]), quantDeMorgan4]), quantDeMorgan2]), vacuousDall]), upairsetIL]), singletonsswitch]), nonemptyImpWitness]), c_0_270]), upairsubunion]), setunionE]), singletoninpowerset]), setunionI]), kpairiskpair]), emptyInPowerset]), symdiffIneg2]), powersetI]), symdiffI2]), setadjoinOr]), symdiffI1]), setadjoinE]), setminusSubset1]), emptyinunitempty]), upairinpowunion]), c_0_271]), noeltsimpempty]), emptyI]), emptysetE]), c_0_272]), c_0_273]), omegaIndAx]), omegaSAx]), emptysetAx]), setextAx]), c_0_274]), c_0_275]), setunionsingleton]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), c_0_276]), kpairsurjEq]), setukpairinjR2]), upairequniteq]), setukpairinjR11]), setukpairinjL]), kfstpairEq]), singletonsuniq]), cartprodfstpairEq]), funcinfuncset]), ap2p]), app]), c_0_277]), c_0_278]), cartprodpairsurjEq]), cartprodsndpairEq]), c_0_279]), ap2apEq2]), subbreln]), funcextLem]), funcGraphProp3]), brelnall2]), c_0_280]), c_0_281]), c_0_282]), ifp]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), iftrue]), binintersectSubset5]), binintersectEL]), binintersectSubset3]), disjointsetsI1]), binintersectRsub]), binunionIR]), binintersectTELcontra]), complementTI1]), powersetTE1]), setminusT_lem]), powersetT_lem]), binintersectT_lem]), iffalse]), binintersectTERcontra]), complementInPowersetComplementIntersect]), complementSubsetComplementIntersect]), complementImpComplementIntersect]), doubleComplementSub2]), doubleComplementSub1]), contrasubsetT3]), contrasubsetT2]), contraSubsetComplement]), binunionTE]), inComplementUnionImpInComplement1]), inIntersectImpInIntersectUnions]), inIntersectImpInUnion2]), binunionTIRcontra]), binunionTILcontra]), complementTcontraSubset]), binunionTEcontra]), doubleComplementE1]), doubleComplementEq]), complementTnotintersectT]), inIntersectImpInUnion]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), demorgan2a1]), doubleComplementI1]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), complementTE1]), contrasubsetT]), contrasubsetT1]), binunionT_lem]), funcext2]), ap2apEq1]), c_0_289]), c_0_290]), c_0_291]), theeq]), iftrueorfalse]), funcext]), infuncsetfunc]), brelnall1]), c_0_292]), funcGraphProp1]), funcGraphProp2]), funcGraphProp4]), eqbreln]), c_0_293]), cartprodmempaircEq]), c_0_294]), c_0_295]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), cartprodpairmemER]), setukpairinjR12]), setukpairinjR1]), setukpairinjR]), c_0_300]), ksndpairEq]), cartprodsndin]), cartprodpairmemEL]), setukpairinjL2]), setunionsingleton1]), setunionsingleton2]), c_0_301]), setukpairinjL1]), c_0_302]), theprop]), cartprodfstin]), setunionE2]), setukpairIR]), kpairp]), singletonsubset]), singletoninpowunion]), upairset2E]), cartprodmempair1]), cartprodmempair]), setukpairIL]), setminusER]), setminusSubset2]), setminusERneg]), setminusIRneg]), symdiffE]), symdiffIneg1]), secondinupair]), binintersectSubset1]), binunionRsub]), binintersectI]), upairset2IR]), binunionIL]), c_0_303]), binunionEcases]), binintersectSubset2]), binintersectLsub]), binunionLsub]), binunionE]), c_0_304]), powersetsubset]), powersetI1]), subsetemptysetimpeq]), subsetRefl]), notequalI2]), emptysetsubset]), subsetI1]), c_0_305]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), c_0_306]), inCongP]), c_0_307]), c_0_308]), notdexE]), prop2setI]), quantDeMorgan3]), quantDeMorgan1]), c_0_309]), upairsetIR]), upairsetE]), eqinunit]), notinsingleton]), uniqinunit]), subPowSU]), powersetE]), emptyinPowerset]), c_0_310]), setadjoinIR]), setadjoinIL]), nonemptyI1]), nonemptyE1]), c_0_311]), setext]), c_0_312]), notinemptyset]), emptysetimpfalse]), prop2setE]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), wellorderingAx]), foundationAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx])])]), c_0_317])).
123.15/18.33	thf(c_0_319, negated_conjecture, ![X1722:$i, X1723:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1735:$i, X1736:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1744:$i, X1745:$i > $i > $o, X1746:$i, X1749:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1756:$i, X1757:$i > $o, X1758:$i, X1759:$i > $o, X1760:$i, X1761:$i, X1762:$i > $o, X1763:$i, X1764:$i, X1765:$i > $o, X1766:$i, X1767:$i > $o, X1769:$i, X1770:$o, X1771:$i, X1772:$i, X1773:$o, X1774:$i, X1775:$i, X1776:$i > $o, X1778:$i, X1779:$i, X1782:$i, X1784:$i, X1786:$i, X1787:$i > $o, X1788:$i, X1789:$i, X1791:$i, X1792:$i > $o, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$o, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$o, X1824:$i, X1825:$i, X1826:$i > $o, X1828:$i, X1829:$i, X1830:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i > $o, X1849:$i, X1850:$i > $o, X1851:$i, X1852:$i, X1853:$i > $o, X1854:$i, X1856:$i, X1857:$i > $o, X1859:$i, X1860:$i, X1861:$i > $o, X1863:$i, X1864:$i, X1865:$i > $o, X1866:$i, X1868:$o, X1869:$i, X1870:$i > $o, X1872:$i, X1873:$i, X1874:$i > $o, X1875:$i, X1877:$i > $o, X1878:$i, X1880:$i > $o, X1881:$i, X1884:$i > $o, X1885:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i > $o, X1896:$i, X1897:$i, X1898:$i > $o, X1899:$i > $o, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i > $o, X1911:$i, X1912:$i, X1913:$i > $o, X1914:$i > $o, X1917:$i, X1918:$i, X1919:$i > $o, X1920:$i > $o, X1923:$i, X1924:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i > $o, X1971:$i, X1972:$i > $o, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$o, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$o, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i > $o, X2127:$i, X2128:$i, X2129:$i > $o, X2131:$i, X2132:$i > $o, X2133:$i, X2135:$i, X2136:$i > $o, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i > $i > $o, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i > $i > $o, X2217:$i, X2218:$i, X2219:$i > $i > $o, X2220:$i, X2221:$i, X2222:$i > $i > $o, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i > $i > $o, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i > $i > $o, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i > $i > $o, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$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 > $i, X2266:$i, X2267:$i, X2268:$i > $i, X2270:$i, X2271:$i, X2272:$i > $i, X2274:$i, X2275:$i, X2276:$i, X2277:$i > $o, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i > $o, X2287:$i, X2288:$i, X2289:$i > $o, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i > $i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i > $i, X2361:$i, X2362:$i, X2363:$i > $i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$o, X2371:$i, X2372:$i, X2373:$i, X2374:$o, X2375:$i, X2376:$i, X2377:$i, X2378:$o, X2379:$i, X2380:$i, X2381:$i, X2382:$o, X2383:$i, X2384:$i, X2385:$i, X2386:$o, X2387:$i, X2388:$i, X2389:$i, X2390:$o, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$o, X2397:$i, X2398:$i, X2399:$i, X2400:$o, X2401:$i, X2402:$i, X2403:$i, X2404:$o, X2405:$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:$i, X2425:$i, X2426:$i, X2427:$i, X2429:$i, X2430:$i, X2431:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, 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, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$o, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i]:((((~(in @ (esk1_2 @ X1722 @ X1723) @ X1722)|~(in @ (esk1_2 @ X1722 @ X1723) @ X1723)|((X1722)=(X1723)))&((in @ (esk1_2 @ X1722 @ X1723) @ X1722)|(in @ (esk1_2 @ X1722 @ X1723) @ X1723)|((X1722)=(X1723))))&(~(in @ X1725 @ emptyset)&(((~(in @ X1728 @ (setadjoin @ X1726 @ X1727))|(((X1728)=(X1726))|(in @ X1728 @ X1727)))&((((X1728)!=(X1726))|(in @ X1728 @ (setadjoin @ X1726 @ X1727)))&(~(in @ X1728 @ X1727)|(in @ X1728 @ (setadjoin @ X1726 @ X1727)))))&(((~(in @ X1730 @ (powerset @ X1729))|(~(in @ X1731 @ X1730)|(in @ X1731 @ X1729)))&(((in @ (esk2_2 @ X1732 @ X1733) @ X1733)|(in @ X1733 @ (powerset @ X1732)))&(~(in @ (esk2_2 @ X1732 @ X1733) @ X1732)|(in @ X1733 @ (powerset @ X1732)))))&(((((in @ X1736 @ (esk3_2 @ X1735 @ X1736))|~(in @ X1736 @ (setunion @ X1735)))&((in @ (esk3_2 @ X1735 @ X1736) @ X1735)|~(in @ X1736 @ (setunion @ X1735))))&(~(in @ X1739 @ X1740)|~(in @ X1740 @ X1738)|(in @ X1739 @ (setunion @ X1738))))&((in @ emptyset @ omega)&((~(in @ X1741 @ omega)|(in @ (setadjoin @ X1741 @ X1741) @ omega))&(((((in @ (esk4_1 @ X1742) @ omega)|~(in @ emptyset @ X1742)|(~(in @ X1744 @ omega)|(in @ X1744 @ X1742)))&((in @ (esk4_1 @ X1742) @ X1742)|~(in @ emptyset @ X1742)|(~(in @ X1744 @ omega)|(in @ X1744 @ X1742))))&(~(in @ (setadjoin @ (esk4_1 @ X1742) @ (esk4_1 @ X1742)) @ X1742)|~(in @ emptyset @ X1742)|(~(in @ X1744 @ omega)|(in @ X1744 @ X1742))))&((((((in @ (esk7_3 @ X1745 @ X1746 @ X1749) @ X1746)|~(in @ X1749 @ (esk6_2 @ X1745 @ X1746))|(in @ (esk5_2 @ X1745 @ X1746) @ X1746))&((X1745 @ (esk7_3 @ X1745 @ X1746 @ X1749) @ X1749)|~(in @ X1749 @ (esk6_2 @ X1745 @ X1746))|(in @ (esk5_2 @ X1745 @ X1746) @ X1746)))&(~(in @ X1752 @ X1746)|~(X1745 @ X1752 @ X1751)|(in @ X1751 @ (esk6_2 @ X1745 @ X1746))|(in @ (esk5_2 @ X1745 @ X1746) @ X1746)))&((((in @ (esk7_3 @ X1745 @ X1746 @ X1749) @ X1746)|~(in @ X1749 @ (esk6_2 @ X1745 @ X1746))|~(exu @ (X1745 @ (esk5_2 @ X1745 @ X1746))))&((X1745 @ (esk7_3 @ X1745 @ X1746 @ X1749) @ X1749)|~(in @ X1749 @ (esk6_2 @ X1745 @ X1746))|~(exu @ (X1745 @ (esk5_2 @ X1745 @ X1746)))))&(~(in @ X1752 @ X1746)|~(X1745 @ X1752 @ X1751)|(in @ X1751 @ (esk6_2 @ X1745 @ X1746))|~(exu @ (X1745 @ (esk5_2 @ X1745 @ X1746))))))&((((in @ (esk8_1 @ X1753) @ X1753)|~(in @ X1754 @ X1753))&(~(in @ X1756 @ (esk8_1 @ X1753))|~(in @ X1756 @ X1753)|~(in @ X1754 @ X1753)))&((epred1_0)&((~(exu @ X1757)|(X1757 @ (descr @ X1757)))&((~(in @ X1760 @ X1758)|(~(X1759 @ X1760)|(in @ X1760 @ (dsetconstr @ X1758 @ X1759))))&((~(in @ X1763 @ (dsetconstr @ X1761 @ X1762))|(in @ X1763 @ X1761))&((~(in @ X1766 @ (dsetconstr @ X1764 @ X1765))|(X1765 @ X1766))&((((X1767 @ (esk9_1 @ X1767))|~(exu @ X1767))&(~(X1767 @ X1769)|((esk9_1 @ X1767)=(X1769))|~(exu @ X1767)))&((~(in @ X1771 @ (prop2set @ ((X1770))))|(X1770))&((~(in @ X1772 @ emptyset)|(X1773))&((~(in @ X1774 @ emptyset)|~($true))&(~(in @ X1775 @ emptyset)&((~(exu @ X1776)|(X1776 @ (esk10_1 @ X1776)))&(((((in @ (esk12_2 @ X1778 @ X1779) @ X1779)|((X1778)=(X1779))|(in @ (esk11_2 @ X1778 @ X1779) @ X1778))&(~(in @ (esk12_2 @ X1778 @ X1779) @ X1778)|((X1778)=(X1779))|(in @ (esk11_2 @ X1778 @ X1779) @ X1778)))&(((in @ (esk12_2 @ X1778 @ X1779) @ X1779)|((X1778)=(X1779))|~(in @ (esk11_2 @ X1778 @ X1779) @ X1779))&(~(in @ (esk12_2 @ X1778 @ X1779) @ X1778)|((X1778)=(X1779))|~(in @ (esk11_2 @ X1778 @ X1779) @ X1779))))&(((in @ (esk13_1 @ X1782) @ X1782)|((X1782)=(emptyset)))&(((in @ (esk14_1 @ X1784) @ X1784)|((X1784)=(emptyset)))&(((~(in @ X1788 @ (dsetconstr @ X1786 @ X1787))|(X1787 @ X1788)|~(in @ X1788 @ X1786))&(~(X1787 @ X1788)|(in @ X1788 @ (dsetconstr @ X1786 @ X1787))|~(in @ X1788 @ X1786)))&((~(nonempty @ X1789)|(in @ (esk15_1 @ X1789) @ X1789))&((~(in @ X1793 @ X1791)|(~(X1792 @ X1793)|(nonempty @ (dsetconstr @ X1791 @ X1792))))&((~(in @ X1795 @ X1794)|(nonempty @ X1794))&((in @ X1796 @ (setadjoin @ X1796 @ X1797))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1800 @ X1799)|(in @ X1800 @ (setadjoin @ X1798 @ X1799)))&(((((in @ X1803 @ X1802)|(X1804)|((X1803)=(X1801))|~(in @ X1803 @ (setadjoin @ X1801 @ X1802)))&(~(X1804)|(X1804)|((X1803)=(X1801))|~(in @ X1803 @ (setadjoin @ X1801 @ X1802))))&(((in @ X1803 @ X1802)|(X1804)|~(X1804)|~(in @ X1803 @ (setadjoin @ X1801 @ X1802)))&(~(X1804)|(X1804)|~(X1804)|~(in @ X1803 @ (setadjoin @ X1801 @ X1802)))))&((~(in @ X1807 @ (setadjoin @ X1805 @ X1806))|(((X1807)=(X1805))|(in @ X1807 @ X1806)))&(((dsetconstr @ X1808 @ (^[Z0:$i]:($true)))=(X1808))&((((in @ (esk16_2 @ X1809 @ X1810) @ X1810)|(in @ X1810 @ (powerset @ X1809)))&(~(in @ (esk16_2 @ X1809 @ X1810) @ X1809)|(in @ X1810 @ (powerset @ X1809))))&((in @ emptyset @ (powerset @ X1812))&((in @ emptyset @ (powerset @ X1813))&((~(in @ X1815 @ (powerset @ X1814))|(~(in @ X1816 @ X1815)|(in @ X1816 @ X1814)))&((~(in @ X1818 @ X1819)|(~(in @ X1819 @ X1817)|(in @ X1818 @ (setunion @ X1817))))&((((in @ X1821 @ (esk17_3 @ X1820 @ X1821 @ X1822))|(X1822)|~(in @ X1821 @ (setunion @ X1820)))&(((in @ (esk17_3 @ X1820 @ X1821 @ X1822) @ X1820)|(X1822)|~(in @ X1821 @ (setunion @ X1820)))&(~(X1822)|(X1822)|~(in @ X1821 @ (setunion @ X1820)))))&((~(in @ X1825 @ X1824)|(in @ X1825 @ (powerset @ (setunion @ X1824))))&(((~(X1826 @ X1828)|((X1828)=(esk18_1 @ X1826))|~(exu @ X1826))&(((X1829)!=(esk18_1 @ X1826))|(X1826 @ X1829)|~(exu @ X1826)))&((((in @ (esk19_1 @ X1830) @ X1830)|~(nonempty @ X1830))&(($true)|~(nonempty @ X1830)))&((~(in @ X1832 @ (setadjoin @ X1833 @ emptyset))|((X1832)=(X1833)))&((((X1834)=(X1835))|~(in @ X1835 @ (setadjoin @ X1834 @ emptyset)))&((((X1836)!=(X1837))|(in @ X1836 @ (setadjoin @ X1837 @ emptyset)))&((~(in @ X1838 @ (setadjoin @ X1839 @ emptyset))|(in @ X1839 @ (setadjoin @ X1838 @ emptyset)))&((~(in @ X1842 @ (setadjoin @ X1840 @ (setadjoin @ X1841 @ emptyset)))|(((X1842)=(X1840))|((X1842)=(X1841))))&((in @ X1843 @ (setadjoin @ X1843 @ (setadjoin @ X1844 @ emptyset)))&((in @ X1846 @ (setadjoin @ X1845 @ (setadjoin @ X1846 @ emptyset)))&((~(in @ X1849 @ X1847)|~(X1848 @ X1849)|(((dsetconstr @ X1847 @ 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@ X2339 @ (funcSet @ X2336 @ X2337))|~(in @ X2338 @ (funcSet @ X2336 @ X2337))))&((~(in @ X2343 @ (funcSet @ X2341 @ X2342))|(~(in @ X2344 @ X2341)|((ap @ X2341 @ X2342 @ X2343 @ X2344)=(ap @ X2341 @ X2342 @ X2343 @ X2344))))&((~(func @ X2345 @ X2346 @ X2347)|(~(in @ X2348 @ X2345)|((ap @ X2345 @ X2346 @ X2347 @ X2348)=(ap @ X2345 @ X2346 @ X2347 @ X2348))))&((((in @ (esk64_3 @ X2349 @ X2350 @ X2351) @ X2349)|(~(in @ X2353 @ X2349)|((ap @ X2349 @ X2350 @ (lam @ X2349 @ X2350 @ X2351) @ X2353)=(X2351 @ X2353))))&(~(in @ (X2351 @ (esk64_3 @ X2349 @ X2350 @ X2351)) @ X2350)|(~(in @ X2353 @ X2349)|((ap @ X2349 @ X2350 @ (lam @ X2349 @ X2350 @ X2351) @ X2353)=(X2351 @ X2353)))))&((~(func @ X2354 @ X2355 @ X2356)|((lam @ X2354 @ X2355 @ (ap @ X2354 @ X2355 @ X2356))=(X2356)))&((((in @ (esk65_3 @ X2357 @ X2358 @ X2359) @ X2357)|((lam @ X2357 @ X2358 @ X2359)=(lam @ X2357 @ X2358 @ X2359)))&(~(in @ (X2359 @ (esk65_3 @ X2357 @ X2358 @ X2359)) @ X2358)|((lam @ X2357 @ X2358 @ X2359)=(lam @ X2357 @ X2358 @ X2359))))&((((in @ (esk66_3 @ X2361 @ X2362 @ X2363) @ X2361)|(~(in @ X2365 @ X2361)|((ap @ X2361 @ X2362 @ (lam @ X2361 @ X2362 @ X2363) @ X2365)=(X2363 @ X2365))))&(~(in @ (X2363 @ (esk66_3 @ X2361 @ X2362 @ X2363)) @ X2362)|(~(in @ X2365 @ X2361)|((ap @ X2361 @ X2362 @ (lam @ X2361 @ X2362 @ X2363) @ X2365)=(X2363 @ X2365)))))&((~(in @ X2368 @ (funcSet @ X2366 @ X2367))|((lam @ X2366 @ X2367 @ (ap @ X2366 @ X2367 @ X2368))=(X2368)))&((~(in @ X2371 @ X2369)|(~(in @ X2372 @ X2369)|((X2370)|(in @ X2372 @ (dsetconstr @ X2369 @ (^[Z0:$i]:((((((X2370))&(((Z0)=(X2371)))))|(((~((X2370)))&(((Z0)=(X2372)))))))))))))&((~(in @ X2375 @ X2373)|(~(in @ X2376 @ X2373)|((X2374)|((dsetconstr @ X2373 @ (^[Z0:$i]:((((((X2374))&(((Z0)=(X2375)))))|(((~((X2374)))&(((Z0)=(X2376)))))))))=(setadjoin @ X2376 @ emptyset)))))&((~(in @ X2379 @ X2377)|(~(in @ X2380 @ X2377)|(~(X2378)|(in @ X2379 @ (dsetconstr @ X2377 @ (^[Z0:$i]:((((((X2378))&(((Z0)=(X2379)))))|(((~((X2378)))&(((Z0)=(X2380)))))))))))))&((~(in @ X2383 @ X2381)|(~(in @ X2384 @ X2381)|(~(X2382)|((dsetconstr @ X2381 @ (^[Z0:$i]:((((((X2382))&(((Z0)=(X2383)))))|(((~((X2382)))&(((Z0)=(X2384)))))))))=(setadjoin @ X2383 @ emptyset)))))&((~(in @ X2387 @ X2385)|(~(in @ X2388 @ X2385)|(singleton @ (dsetconstr @ X2385 @ (^[Z0:$i]:((((((X2386))&(((Z0)=(X2387)))))|(((~((X2386)))&(((Z0)=(X2388))))))))))))&((~(in @ X2391 @ X2389)|(~(in @ X2392 @ X2389)|(in @ (if @ X2389 @ ((X2390)) @ X2391 @ X2392) @ X2389)))&((~(singleton @ X2393)|(~(in @ X2394 @ X2393)|((setunion @ X2393)=(X2394))))&((~(in @ X2397 @ X2395)|(~(in @ X2398 @ X2395)|(~(X2396)|((if @ X2395 @ ((X2396)) @ X2397 @ X2398)=(X2397)))))&((~(in @ X2401 @ X2399)|(~(in @ X2402 @ X2399)|((X2400)|((if @ X2399 @ ((X2400)) @ X2401 @ X2402)=(X2402)))))&((~(in @ X2405 @ X2403)|(~(in @ X2406 @ X2403)|(in @ (if @ X2403 @ ((X2404)) @ X2405 @ X2406) @ (setadjoin @ X2405 @ (setadjoin @ X2406 @ emptyset)))))&((~(in @ X2408 @ (powerset @ X2407))|(~(in @ X2409 @ (powerset @ X2407))|(in @ (binintersect @ X2408 @ X2409) @ (powerset @ X2407))))&((~(in @ X2411 @ (powerset @ X2410))|(~(in @ X2412 @ (powerset @ X2410))|(in @ (binunion @ X2411 @ X2412) @ (powerset @ X2410))))&((~(in @ X2414 @ (powerset @ X2413))|(in @ (powerset @ X2414) @ (powerset @ (powerset @ X2413))))&((~(in @ X2416 @ (powerset @ X2415))|(~(in @ X2417 @ (powerset @ X2415))|(in @ (setminus @ X2416 @ X2417) @ (powerset @ X2415))))&((~(in @ X2419 @ (powerset @ X2418))|(in @ (setminus @ X2418 @ X2419) @ (powerset @ X2418)))&(((((in @ (esk68_3 @ X2420 @ X2421 @ X2422) @ X2420)|((X2421)=(X2422))|(in @ (esk67_3 @ X2420 @ X2421 @ X2422) @ X2420)|~(in @ X2422 @ (powerset @ X2420))|~(in @ X2421 @ (powerset @ X2420)))&(((in @ (esk68_3 @ X2420 @ X2421 @ X2422) @ X2422)|((X2421)=(X2422))|(in @ (esk67_3 @ X2420 @ X2421 @ X2422) @ X2420)|~(in @ X2422 @ (powerset @ X2420))|~(in @ X2421 @ (powerset @ X2420)))&(~(in @ (esk68_3 @ X2420 @ X2421 @ X2422) @ X2421)|((X2421)=(X2422))|(in @ (esk67_3 @ X2420 @ X2421 @ X2422) @ X2420)|~(in @ X2422 @ (powerset @ X2420))|~(in @ X2421 @ (powerset @ X2420)))))&((((in @ (esk68_3 @ X2420 @ X2421 @ X2422) @ X2420)|((X2421)=(X2422))|(in @ (esk67_3 @ X2420 @ X2421 @ X2422) @ X2421)|~(in @ X2422 @ (powerset @ X2420))|~(in @ X2421 @ (powerset @ X2420)))&(((in @ (esk68_3 @ X2420 @ X2421 @ X2422) @ X2422)|((X2421)=(X2422))|(in @ (esk67_3 @ X2420 @ X2421 @ X2422) @ X2421)|~(in @ X2422 @ (powerset @ X2420))|~(in @ X2421 @ (powerset @ X2420)))&(~(in @ (esk68_3 @ X2420 @ X2421 @ X2422) @ X2421)|((X2421)=(X2422))|(in @ (esk67_3 @ X2420 @ X2421 @ X2422) @ X2421)|~(in @ X2422 @ (powerset @ X2420))|~(in @ X2421 @ (powerset @ X2420)))))&(((in @ (esk68_3 @ X2420 @ X2421 @ X2422) @ X2420)|((X2421)=(X2422))|~(in @ (esk67_3 @ X2420 @ X2421 @ X2422) @ X2422)|~(in @ X2422 @ (powerset @ X2420))|~(in @ X2421 @ (powerset @ X2420)))&(((in @ (esk68_3 @ X2420 @ X2421 @ X2422) @ X2422)|((X2421)=(X2422))|~(in @ (esk67_3 @ X2420 @ X2421 @ X2422) @ X2422)|~(in @ X2422 @ (powerset @ X2420))|~(in @ X2421 @ (powerset @ X2420)))&(~(in @ (esk68_3 @ X2420 @ X2421 @ X2422) @ X2421)|((X2421)=(X2422))|~(in @ (esk67_3 @ X2420 @ X2421 @ X2422) @ X2422)|~(in @ X2422 @ (powerset @ X2420))|~(in @ X2421 @ (powerset @ X2420)))))))&((((in @ (esk69_3 @ X2425 @ X2426 @ X2427) @ X2425)|(subset @ X2426 @ X2427)|~(in @ X2427 @ (powerset @ X2425))|~(in @ X2426 @ (powerset @ X2425)))&(((in @ (esk69_3 @ X2425 @ X2426 @ X2427) @ X2426)|(subset @ X2426 @ X2427)|~(in @ X2427 @ (powerset @ X2425))|~(in @ X2426 @ (powerset @ X2425)))&(~(in @ (esk69_3 @ X2425 @ X2426 @ X2427) @ X2427)|(subset @ X2426 @ X2427)|~(in @ X2427 @ (powerset @ X2425))|~(in @ X2426 @ (powerset @ X2425)))))&((((in @ (esk70_3 @ X2429 @ X2430 @ X2431) @ X2429)|(in @ X2430 @ (powerset @ X2431))|~(in @ X2431 @ (powerset @ X2429))|~(in @ X2430 @ (powerset @ X2429)))&(((in @ (esk70_3 @ X2429 @ X2430 @ X2431) @ X2430)|(in @ X2430 @ (powerset @ X2431))|~(in @ X2431 @ (powerset @ X2429))|~(in @ X2430 @ (powerset @ X2429)))&(~(in @ (esk70_3 @ X2429 @ X2430 @ X2431) @ X2431)|(in @ X2430 @ (powerset @ X2431))|~(in @ X2431 @ (powerset @ X2429))|~(in @ X2430 @ (powerset @ X2429)))))&((~(in @ X2434 @ (powerset @ X2433))|(~(in @ X2435 @ (powerset @ X2433))|(~(in @ X2436 @ X2433)|(~(in @ X2434 @ (powerset @ X2435))|(~(in @ X2436 @ X2434)|(in @ X2436 @ X2435))))))&((~(in @ X2438 @ (powerset @ X2437))|(~(in @ X2439 @ X2437)|(~(in @ X2439 @ X2438)|~(in @ X2439 @ (setminus @ X2437 @ X2438)))))&((~(in @ X2441 @ (powerset @ X2440))|(~(in @ X2442 @ X2440)|((in @ X2442 @ (setminus @ X2440 @ X2441))|(in @ X2442 @ X2441))))&((~(in @ X2444 @ (powerset @ X2443))|(~(in @ X2445 @ (powerset @ X2443))|(~(in @ X2446 @ X2443)|((in @ X2446 @ X2444)|~(in @ X2446 @ (binintersect @ X2444 @ X2445))))))&((~(in @ X2448 @ (powerset @ X2447))|(~(in @ X2449 @ (powerset @ X2447))|(~(in @ X2450 @ X2447)|((in @ X2450 @ X2449)|~(in @ X2450 @ (binintersect @ X2448 @ X2449))))))&((~(in @ X2452 @ (powerset @ X2451))|(~(in @ X2453 @ (powerset @ X2451))|(~(in @ X2454 @ X2451)|(~(subset @ X2452 @ (setminus @ X2451 @ X2453))|(~(in @ X2454 @ X2453)|~(in @ X2454 @ X2452))))))&((~(in @ X2456 @ (powerset @ X2455))|(~(in @ X2457 @ (powerset @ X2455))|(~(in @ X2458 @ X2455)|(~(subset @ X2456 @ X2457)|((in @ X2458 @ X2457)|~(in @ X2458 @ X2456))))))&((~(in @ X2460 @ (powerset @ X2459))|(~(in @ X2461 @ (powerset @ X2459))|(~(subset @ X2460 @ X2461)|(subset @ (setminus @ X2459 @ X2461) @ (setminus @ X2459 @ X2460)))))&((~(in @ X2463 @ (powerset @ X2462))|(~(in @ X2464 @ (powerset @ X2462))|(~(subset @ (setminus @ X2462 @ X2464) @ (setminus @ X2462 @ X2463))|(subset @ X2463 @ X2464))))&((~(in @ X2466 @ (powerset @ X2465))|(~(in @ X2467 @ X2465)|(~(in @ X2467 @ X2466)|(in @ X2467 @ (setminus @ X2465 @ (setminus @ X2465 @ X2466))))))&((~(in @ X2469 @ (powerset @ X2468))|(~(in @ X2470 @ X2468)|(~(in @ X2470 @ (setminus @ X2468 @ (setminus @ X2468 @ X2469)))|(in @ X2470 @ X2469))))&((~(in @ X2472 @ (powerset @ X2471))|(subset @ X2472 @ (setminus @ X2471 @ (setminus @ X2471 @ X2472))))&((~(in @ X2474 @ (powerset @ X2473))|(subset @ (setminus @ X2473 @ (setminus @ X2473 @ X2474)) @ X2474))&((~(in @ X2476 @ (powerset @ X2475))|((X2476)=(setminus @ X2475 @ (setminus @ X2475 @ X2476))))&((~(in @ X2478 @ (powerset @ X2477))|(~(in @ X2479 @ (powerset @ X2477))|(~(in @ X2480 @ X2477)|(~(in @ X2480 @ (setminus @ X2477 @ X2478))|~(in @ X2480 @ (binintersect @ X2478 @ X2479))))))&((~(in @ X2482 @ (powerset @ X2481))|(~(in @ X2483 @ (powerset @ X2481))|(~(in @ X2484 @ X2481)|(~(in @ X2484 @ (setminus @ X2481 @ X2482))|(in @ X2484 @ (setminus @ X2481 @ (binintersect @ X2482 @ X2483)))))))&((~(in @ X2486 @ (powerset @ X2485))|(~(in @ X2487 @ (powerset @ X2485))|(subset @ (setminus @ X2485 @ X2486) @ (setminus @ X2485 @ (binintersect @ X2486 @ X2487)))))&((~(in @ X2489 @ (powerset @ X2488))|(~(in @ X2490 @ (powerset @ X2488))|(in @ (setminus @ X2488 @ X2489) @ (powerset @ (setminus @ X2488 @ (binintersect @ X2489 @ X2490))))))&((~(in @ X2492 @ (powerset @ X2491))|(~(in @ X2493 @ (powerset @ X2491))|(~(subset @ X2492 @ (setminus @ X2491 @ X2493))|(~(in @ X2494 @ X2491)|(~(in @ X2494 @ X2493)|(in @ X2494 @ (setminus @ X2491 @ X2492)))))))&((~(in @ X2496 @ (powerset @ X2495))|(~(in @ X2497 @ (powerset @ X2495))|(~(subset @ X2496 @ (setminus @ X2495 @ X2497))|(subset @ X2497 @ (setminus @ X2495 @ X2496)))))&((~(in @ X2499 @ (powerset @ X2498))|(~(in @ X2500 @ (powerset @ X2498))|(~(in @ X2501 @ X2498)|((in @ X2501 @ (binunion @ X2499 @ X2500))|~(in @ X2501 @ X2499)))))&((~(in @ X2503 @ (powerset @ X2502))|(~(in @ X2504 @ (powerset @ X2502))|(~(in @ X2505 @ X2502)|((in @ X2505 @ (binunion @ X2503 @ X2504))|~(in @ X2505 @ X2504)))))&((~(in @ X2507 @ (powerset @ X2506))|(~(in @ X2508 @ (powerset @ X2506))|(~(in @ X2509 @ (powerset @ X2506))|(~(in @ X2510 @ X2506)|(~(in @ X2510 @ (binintersect @ X2507 @ X2508))|(in @ X2510 @ (binunion @ X2507 @ X2509)))))))&((~(in @ X2512 @ (powerset @ X2511))|(~(in @ X2513 @ (powerset @ X2511))|(~(in @ X2514 @ (powerset @ X2511))|(~(in @ X2515 @ X2511)|(~(in @ X2515 @ (binintersect @ X2512 @ X2513))|(in @ X2515 @ (binunion @ X2513 @ X2514)))))))&((~(in @ X2517 @ (powerset @ X2516))|(~(in @ X2518 @ (powerset @ X2516))|(~(in @ X2519 @ (powerset @ X2516))|(~(in @ X2520 @ X2516)|(~(in @ X2520 @ (binintersect @ X2517 @ X2518))|(in @ X2520 @ (binintersect @ (binunion @ X2517 @ X2519) @ (binunion @ X2518 @ X2519))))))))&((~(in @ X2522 @ (powerset @ X2521))|(~(in @ X2523 @ (powerset @ X2521))|(~(in @ X2524 @ (powerset @ X2521))|(in @ (binintersect @ X2522 @ X2523) @ (powerset @ (binintersect @ (binunion @ X2522 @ X2524) @ (binunion @ X2523 @ X2524)))))))&((~(in @ X2526 @ (powerset @ X2525))|(~(in @ X2527 @ (powerset @ X2525))|(~(in @ X2528 @ X2525)|(~(in @ X2528 @ (setminus @ X2525 @ (binunion @ X2526 @ X2527)))|~(in @ X2528 @ X2526)))))&((~(in @ X2530 @ (powerset @ X2529))|(~(in @ X2531 @ (powerset @ X2529))|(~(in @ X2532 @ X2529)|(~(in @ X2532 @ (setminus @ X2529 @ (binunion @ X2530 @ X2531)))|(in @ X2532 @ (setminus @ X2529 @ X2530))))))&(((((in @ X2537 @ X2535)|(X2536)|(in @ X2537 @ X2534)|~(in @ X2537 @ (binunion @ X2534 @ X2535))|~(in @ X2537 @ X2533)|~(in @ X2535 @ (powerset @ X2533))|~(in @ X2534 @ (powerset @ X2533)))&(~(X2536)|(X2536)|(in @ X2537 @ X2534)|~(in @ X2537 @ (binunion @ X2534 @ X2535))|~(in @ X2537 @ X2533)|~(in @ X2535 @ (powerset @ X2533))|~(in @ X2534 @ (powerset @ X2533))))&(((in @ X2537 @ X2535)|(X2536)|~(X2536)|~(in @ X2537 @ (binunion @ X2534 @ X2535))|~(in @ X2537 @ X2533)|~(in @ X2535 @ (powerset @ X2533))|~(in @ X2534 @ (powerset @ X2533)))&(~(X2536)|(X2536)|~(X2536)|~(in @ X2537 @ (binunion @ X2534 @ X2535))|~(in @ X2537 @ X2533)|~(in @ X2535 @ (powerset @ X2533))|~(in @ X2534 @ (powerset @ X2533)))))&((~(in @ X2539 @ (powerset @ X2538))|(~(in @ X2540 @ (powerset @ X2538))|(~(in @ X2541 @ X2538)|((in @ X2541 @ X2539)|((in @ X2541 @ X2540)|~(in @ X2541 @ (binunion @ X2539 @ X2540)))))))&((~(in @ X2543 @ (powerset @ X2542))|(~(in @ X2544 @ (powerset @ X2542))|(~(in @ X2545 @ X2542)|(~(in @ X2545 @ (setminus @ X2542 @ (binunion @ X2543 @ X2544)))|(in @ X2545 @ (setminus @ X2542 @ X2543))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&~(in @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)) @ (powerset @ (setminus @ esk71_0 @ esk72_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_318])])])])])])])).
123.15/18.33	thf(c_0_320, negated_conjecture, ~((in @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)) @ (powerset @ (setminus @ esk71_0 @ esk72_0)))), inference(split_conjunct,[status(thm)],[c_0_319])).
123.15/18.33	thf(c_0_321, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_319])).
123.15/18.33	thf(c_0_322, negated_conjecture, ~((subset @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)) @ (setminus @ esk71_0 @ esk72_0))), inference(spm,[status(thm)],[c_0_320, c_0_321])).
123.15/18.33	thf(c_0_323, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ (setminus @ X3 @ X4) @ (setminus @ X3 @ X2))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((subset @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_319])).
123.15/18.33	thf(c_0_324, negated_conjecture, (in @ esk72_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_319])).
123.15/18.33	thf(c_0_325, negated_conjecture, ![X2:$i, X3:$i]:((subset @ X2 @ (binunion @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_319])).
123.15/18.33	thf(c_0_326, negated_conjecture, ~((in @ (binunion @ esk72_0 @ esk73_0) @ (powerset @ esk71_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_322, c_0_323]), c_0_324]), c_0_325])])).
123.15/18.33	thf(c_0_327, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ (binunion @ X2 @ X4) @ (powerset @ X3))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_319])).
123.15/18.33	thf(c_0_328, negated_conjecture, (in @ esk73_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_319])).
123.15/18.33	thf(c_0_329, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_326, c_0_327]), c_0_328]), c_0_324])]), ['proof']).
123.15/18.33	% SZS output end CNFRefutation
123.15/18.33	% Parsed axioms                        : 573
123.15/18.33	% Removed by relevancy pruning/SinE    : 308
123.15/18.33	% Initial clauses                      : 428
123.15/18.33	% Removed in clause preprocessing      : 37
123.15/18.33	% Initial clauses in saturation        : 391
123.15/18.33	% Processed clauses                    : 829
123.15/18.33	% ...of these trivial                  : 13
123.15/18.33	% ...subsumed                          : 117
123.15/18.33	% ...remaining for further processing  : 699
123.15/18.33	% Other redundant clauses eliminated   : 53
123.15/18.33	% Clauses deleted for lack of memory   : 0
123.15/18.33	% Backward-subsumed                    : 1
123.15/18.33	% Backward-rewritten                   : 12
123.15/18.33	% Generated clauses                    : 5487
123.15/18.33	% ...of the previous two non-redundant : 5201
123.15/18.33	% ...aggressively subsumed             : 0
123.15/18.33	% Contextual simplify-reflections      : 8
123.15/18.33	% Paramodulations                      : 5401
123.15/18.33	% Factorizations                       : 2
123.15/18.33	% NegExts                              : 0
123.15/18.33	% Equation resolutions                 : 58
123.15/18.33	% Disequality decompositions           : 0
123.15/18.33	% Total rewrite steps                  : 302
123.15/18.33	% ...of those cached                   : 205
123.15/18.33	% Propositional unsat checks           : 0
123.15/18.33	%    Propositional check models        : 0
123.15/18.33	%    Propositional check unsatisfiable : 0
123.15/18.33	%    Propositional clauses             : 0
123.15/18.33	%    Propositional clauses after purity: 0
123.15/18.33	%    Propositional unsat core size     : 0
123.15/18.33	%    Propositional preprocessing time  : 0.000
123.15/18.33	%    Propositional encoding time       : 0.000
123.15/18.33	%    Propositional solver time         : 0.000
123.15/18.33	%    Success case prop preproc time    : 0.000
123.15/18.33	%    Success case prop encoding time   : 0.000
123.15/18.33	%    Success case prop solver time     : 0.000
123.15/18.33	% Current number of processed clauses  : 331
123.15/18.33	%    Positive orientable unit clauses  : 58
123.15/18.33	%    Positive unorientable unit clauses: 0
123.15/18.33	%    Negative unit clauses             : 14
123.15/18.33	%    Non-unit-clauses                  : 259
123.15/18.33	% Current number of unprocessed clauses: 5067
123.15/18.33	% ...number of literals in the above   : 17210
123.15/18.33	% Current number of archived formulas  : 0
123.15/18.33	% Current number of archived clauses   : 352
123.15/18.33	% Clause-clause subsumption calls (NU) : 37826
123.15/18.33	% Rec. Clause-clause subsumption calls : 19819
123.15/18.33	% Non-unit clause-clause subsumptions  : 77
123.15/18.33	% Unit Clause-clause subsumption calls : 508
123.15/18.33	% Rewrite failures with RHS unbound    : 0
123.15/18.33	% BW rewrite match attempts            : 37
123.15/18.33	% BW rewrite match successes           : 8
123.15/18.33	% Condensation attempts                : 829
123.15/18.33	% Condensation successes               : 8
123.15/18.33	% Termbank termtop insertions          : 149615
123.15/18.33	% Search garbage collected termcells   : 26936
123.15/18.33	
123.15/18.33	% -------------------------------------------------
123.15/18.33	% User time                : 16.891 s
123.15/18.33	% System time              : 0.532 s
123.15/18.33	% Total time               : 17.423 s
123.15/18.33	% Maximum resident set size: 10156 pages
123.15/18.33	
123.15/18.33	% -------------------------------------------------
123.15/18.33	% User time                : 16.901 s
123.15/18.33	% System time              : 0.538 s
123.15/18.33	% Total time               : 17.439 s
123.15/18.33	% Maximum resident set size: 5632 pages
123.15/18.33	% E exiting
123.15/18.33	EOF