%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU819^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:25:45 AM UTC 2026
% Result : Theorem 1.36s 0.52s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU819^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n001.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 14:40:20 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.23/0.29 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=300 /export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p
% 1.36/0.52 % Version: 3.5.1-ho
% 1.36/0.52 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.36/0.52 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.52 % Starting ehoh_best5 with 300s (1) cores
% 1.36/0.52 % Starting almost_fo_3_lam with 300s (1) cores
% 1.36/0.52 % Starting new_bool_5 with 300s (1) cores
% 1.36/0.52 % Starting pre_casc_3 with 300s (1) cores
% 1.36/0.52 % Starting ho_unfolding_8 with 300s (1) cores
% 1.36/0.52 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.36/0.52 % Starting new_bool_3 with 300s (1) cores
% 1.36/0.52 % Starting new_ho_5 with 300s (1) cores
% 1.36/0.52 % pre_casc_3 with pid 1334429 completed with status 0
% 1.36/0.52 % Result found by pre_casc_3
% 1.36/0.52 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.36/0.52 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.52 % Starting ehoh_best5 with 300s (1) cores
% 1.36/0.52 % Starting almost_fo_3_lam with 300s (1) cores
% 1.36/0.52 % Starting new_bool_5 with 300s (1) cores
% 1.36/0.52 % Starting pre_casc_3 with 300s (1) cores
% 1.36/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 1.36/0.52 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 1.36/0.52 % Search class: HGHSF-FMLM31-SHFMMFBN
% 1.36/0.52 % partial match(3): HGHSM-FSLM31-SHFMMSBN
% 1.36/0.52 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.36/0.52 % Starting SubtermCWHack with 28s (1) cores
% 1.36/0.52 % SubtermCWHack with pid 1334441 completed with status 0
% 1.36/0.52 % Result found by SubtermCWHack
% 1.36/0.52 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.36/0.52 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.52 % Starting ehoh_best5 with 300s (1) cores
% 1.36/0.52 % Starting almost_fo_3_lam with 300s (1) cores
% 1.36/0.52 % Starting new_bool_5 with 300s (1) cores
% 1.36/0.52 % Starting pre_casc_3 with 300s (1) cores
% 1.36/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 1.36/0.52 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 1.36/0.52 % Search class: HGHSF-FMLM31-SHFMMFBN
% 1.36/0.52 % partial match(3): HGHSM-FSLM31-SHFMMSBN
% 1.36/0.52 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.36/0.52 % Starting SubtermCWHack with 28s (1) cores
% 1.36/0.52 % Preprocessing time : 0.008 s
% 1.36/0.52
% 1.36/0.52 % Proof found!
% 1.36/0.52 % SZS status Theorem
% 1.36/0.52 % SZS output start CNFRefutation
% 1.36/0.52 thf(decl_23, type, in: $i > $i > $o).
% 1.36/0.52 thf(decl_25, type, setextAx: $o).
% 1.36/0.52 thf(decl_26, type, emptyset: $i).
% 1.36/0.52 thf(decl_27, type, emptysetAx: $o).
% 1.36/0.52 thf(decl_29, type, setadjoinAx: $o).
% 1.36/0.52 thf(decl_30, type, powerset: $i > $i).
% 1.36/0.52 thf(decl_31, type, powersetAx: $o).
% 1.36/0.52 thf(decl_32, type, setunion: $i > $i).
% 1.36/0.52 thf(decl_33, type, setunionAx: $o).
% 1.36/0.52 thf(decl_35, type, omega0Ax: $o).
% 1.36/0.52 thf(decl_36, type, omegaSAx: $o).
% 1.36/0.52 thf(decl_37, type, omegaIndAx: $o).
% 1.36/0.52 thf(decl_38, type, replAx: $o).
% 1.36/0.52 thf(decl_39, type, foundationAx: $o).
% 1.36/0.52 thf(decl_40, type, wellorderingAx: $o).
% 1.36/0.52 thf(decl_42, type, descrp: $o).
% 1.36/0.52 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 1.36/0.52 thf(decl_44, type, dsetconstrI: $o).
% 1.36/0.52 thf(decl_45, type, dsetconstrEL: $o).
% 1.36/0.52 thf(decl_46, type, dsetconstrER: $o).
% 1.36/0.52 thf(decl_47, type, exuE1: $o).
% 1.36/0.52 thf(decl_49, type, prop2setE: $o).
% 1.36/0.52 thf(decl_50, type, emptysetE: $o).
% 1.36/0.52 thf(decl_51, type, emptysetimpfalse: $o).
% 1.36/0.52 thf(decl_52, type, notinemptyset: $o).
% 1.36/0.52 thf(decl_53, type, exuE3e: $o).
% 1.36/0.52 thf(decl_54, type, setext: $o).
% 1.36/0.52 thf(decl_55, type, emptyI: $o).
% 1.36/0.52 thf(decl_56, type, noeltsimpempty: $o).
% 1.36/0.52 thf(decl_57, type, setbeta: $o).
% 1.36/0.52 thf(decl_58, type, nonempty: $i > $o).
% 1.36/0.52 thf(decl_59, type, nonemptyE1: $o).
% 1.36/0.52 thf(decl_60, type, nonemptyI: $o).
% 1.36/0.52 thf(decl_61, type, nonemptyI1: $o).
% 1.36/0.52 thf(decl_62, type, setadjoinIL: $o).
% 1.36/0.52 thf(decl_63, type, emptyinunitempty: $o).
% 1.36/0.52 thf(decl_64, type, setadjoinIR: $o).
% 1.36/0.52 thf(decl_65, type, setadjoinE: $o).
% 1.36/0.52 thf(decl_66, type, setadjoinOr: $o).
% 1.36/0.52 thf(decl_67, type, setoftrueEq: $o).
% 1.36/0.52 thf(decl_68, type, powersetI: $o).
% 1.36/0.52 thf(decl_69, type, emptyinPowerset: $o).
% 1.36/0.52 thf(decl_70, type, emptyInPowerset: $o).
% 1.36/0.52 thf(decl_71, type, powersetE: $o).
% 1.36/0.52 thf(decl_72, type, setunionI: $o).
% 1.36/0.52 thf(decl_73, type, setunionE: $o).
% 1.36/0.52 thf(decl_74, type, subPowSU: $o).
% 1.36/0.52 thf(decl_75, type, exuE2: $o).
% 1.36/0.52 thf(decl_76, type, nonemptyImpWitness: $o).
% 1.36/0.52 thf(decl_77, type, uniqinunit: $o).
% 1.36/0.52 thf(decl_78, type, notinsingleton: $o).
% 1.36/0.52 thf(decl_79, type, eqinunit: $o).
% 1.36/0.52 thf(decl_80, type, singletonsswitch: $o).
% 1.36/0.52 thf(decl_81, type, upairsetE: $o).
% 1.36/0.52 thf(decl_82, type, upairsetIL: $o).
% 1.36/0.52 thf(decl_83, type, upairsetIR: $o).
% 1.36/0.52 thf(decl_84, type, emptyE1: $o).
% 1.36/0.52 thf(decl_85, type, vacuousDall: $o).
% 1.36/0.52 thf(decl_86, type, quantDeMorgan1: $o).
% 1.36/0.52 thf(decl_87, type, quantDeMorgan2: $o).
% 1.36/0.52 thf(decl_88, type, quantDeMorgan3: $o).
% 1.36/0.52 thf(decl_89, type, quantDeMorgan4: $o).
% 1.36/0.52 thf(decl_90, type, prop2setI: $o).
% 1.36/0.52 thf(decl_92, type, prop2set2propI: $o).
% 1.36/0.52 thf(decl_93, type, notdexE: $o).
% 1.36/0.52 thf(decl_94, type, notdallE: $o).
% 1.36/0.52 thf(decl_95, type, exuI1: $o).
% 1.36/0.52 thf(decl_96, type, exuI3: $o).
% 1.36/0.52 thf(decl_97, type, exuI2: $o).
% 1.36/0.52 thf(decl_98, type, inCongP: $o).
% 1.36/0.52 thf(decl_99, type, in__Cong: $o).
% 1.36/0.52 thf(decl_100, type, exuE3u: $o).
% 1.36/0.52 thf(decl_101, type, exu__Cong: $o).
% 1.36/0.52 thf(decl_102, type, emptyset__Cong: $o).
% 1.36/0.52 thf(decl_103, type, setadjoin__Cong: $o).
% 1.36/0.52 thf(decl_104, type, powerset__Cong: $o).
% 1.36/0.52 thf(decl_105, type, setunion__Cong: $o).
% 1.36/0.52 thf(decl_106, type, omega__Cong: $o).
% 1.36/0.52 thf(decl_107, type, exuEu: $o).
% 1.36/0.52 thf(decl_108, type, descr__Cong: $o).
% 1.36/0.52 thf(decl_109, type, dsetconstr__Cong: $o).
% 1.36/0.52 thf(decl_110, type, subset: $i > $i > $o).
% 1.36/0.52 thf(decl_113, type, subsetI1: $o).
% 1.36/0.52 thf(decl_114, type, eqimpsubset2: $o).
% 1.36/0.52 thf(decl_115, type, eqimpsubset1: $o).
% 1.36/0.52 thf(decl_116, type, subsetI2: $o).
% 1.36/0.52 thf(decl_117, type, emptysetsubset: $o).
% 1.36/0.52 thf(decl_118, type, subsetE: $o).
% 1.36/0.52 thf(decl_119, type, subsetE2: $o).
% 1.36/0.52 thf(decl_120, type, notsubsetI: $o).
% 1.36/0.52 thf(decl_121, type, notequalI1: $o).
% 1.36/0.52 thf(decl_122, type, notequalI2: $o).
% 1.36/0.52 thf(decl_123, type, subsetRefl: $o).
% 1.36/0.52 thf(decl_124, type, subsetTrans: $o).
% 1.36/0.52 thf(decl_125, type, setadjoinSub: $o).
% 1.36/0.52 thf(decl_126, type, setadjoinSub2: $o).
% 1.36/0.52 thf(decl_127, type, subset2powerset: $o).
% 1.36/0.52 thf(decl_128, type, setextsub: $o).
% 1.36/0.52 thf(decl_129, type, subsetemptysetimpeq: $o).
% 1.36/0.52 thf(decl_130, type, powersetI1: $o).
% 1.36/0.52 thf(decl_131, type, powersetE1: $o).
% 1.36/0.52 thf(decl_132, type, inPowerset: $o).
% 1.36/0.52 thf(decl_133, type, powersetsubset: $o).
% 1.36/0.52 thf(decl_134, type, sepInPowerset: $o).
% 1.36/0.52 thf(decl_135, type, sepSubset: $o).
% 1.36/0.52 thf(decl_137, type, binunionIL: $o).
% 1.36/0.52 thf(decl_138, type, upairset2IR: $o).
% 1.36/0.52 thf(decl_139, type, binunionIR: $o).
% 1.36/0.52 thf(decl_140, type, binunionEcases: $o).
% 1.36/0.52 thf(decl_141, type, binunionE: $o).
% 1.36/0.52 thf(decl_142, type, binunionLsub: $o).
% 1.36/0.52 thf(decl_143, type, binunionRsub: $o).
% 1.36/0.52 thf(decl_144, type, binintersect: $i > $i > $i).
% 1.36/0.52 thf(decl_145, type, binintersectI: $o).
% 1.36/0.52 thf(decl_146, type, binintersectSubset5: $o).
% 1.36/0.52 thf(decl_147, type, binintersectEL: $o).
% 1.36/0.52 thf(decl_148, type, binintersectLsub: $o).
% 1.36/0.52 thf(decl_149, type, binintersectSubset2: $o).
% 1.36/0.52 thf(decl_150, type, binintersectSubset3: $o).
% 1.36/0.52 thf(decl_151, type, binintersectER: $o).
% 1.36/0.52 thf(decl_152, type, disjointsetsI1: $o).
% 1.36/0.52 thf(decl_153, type, binintersectRsub: $o).
% 1.36/0.52 thf(decl_154, type, binintersectSubset4: $o).
% 1.36/0.52 thf(decl_155, type, binintersectSubset1: $o).
% 1.36/0.52 thf(decl_156, type, bs114d: $o).
% 1.36/0.52 thf(decl_159, type, setminusI: $o).
% 1.36/0.52 thf(decl_160, type, setminusEL: $o).
% 1.36/0.52 thf(decl_161, type, setminusER: $o).
% 1.36/0.52 thf(decl_162, type, setminusSubset2: $o).
% 1.36/0.52 thf(decl_163, type, setminusERneg: $o).
% 1.36/0.52 thf(decl_164, type, setminusELneg: $o).
% 1.36/0.52 thf(decl_165, type, setminusILneg: $o).
% 1.36/0.52 thf(decl_166, type, setminusIRneg: $o).
% 1.36/0.52 thf(decl_167, type, setminusLsub: $o).
% 1.36/0.52 thf(decl_168, type, setminusSubset1: $o).
% 1.36/0.52 thf(decl_170, type, symdiffE: $o).
% 1.36/0.52 thf(decl_171, type, symdiffI1: $o).
% 1.36/0.52 thf(decl_172, type, symdiffI2: $o).
% 1.36/0.52 thf(decl_173, type, symdiffIneg1: $o).
% 1.36/0.52 thf(decl_174, type, symdiffIneg2: $o).
% 1.36/0.52 thf(decl_176, type, secondinupair: $o).
% 1.36/0.52 thf(decl_177, type, setukpairIL: $o).
% 1.36/0.52 thf(decl_178, type, setukpairIR: $o).
% 1.36/0.52 thf(decl_179, type, kpairiskpair: $o).
% 1.36/0.52 thf(decl_181, type, kpairp: $o).
% 1.36/0.52 thf(decl_183, type, singletonsubset: $o).
% 1.36/0.52 thf(decl_184, type, singletoninpowerset: $o).
% 1.36/0.52 thf(decl_185, type, singletoninpowunion: $o).
% 1.36/0.52 thf(decl_186, type, upairset2E: $o).
% 1.36/0.52 thf(decl_187, type, upairsubunion: $o).
% 1.36/0.52 thf(decl_188, type, upairinpowunion: $o).
% 1.36/0.52 thf(decl_189, type, ubforcartprodlem1: $o).
% 1.36/0.52 thf(decl_190, type, ubforcartprodlem2: $o).
% 1.36/0.52 thf(decl_191, type, ubforcartprodlem3: $o).
% 1.36/0.52 thf(decl_192, type, cartprodpairin: $o).
% 1.36/0.52 thf(decl_193, type, cartprodmempair1: $o).
% 1.36/0.52 thf(decl_194, type, cartprodmempair: $o).
% 1.36/0.52 thf(decl_195, type, setunionE2: $o).
% 1.36/0.52 thf(decl_196, type, setunionsingleton1: $o).
% 1.36/0.52 thf(decl_197, type, setunionsingleton2: $o).
% 1.36/0.52 thf(decl_198, type, setunionsingleton: $o).
% 1.36/0.52 thf(decl_200, type, singletonprop: $o).
% 1.36/0.52 thf(decl_202, type, ex1E1: $o).
% 1.36/0.52 thf(decl_203, type, ex1I: $o).
% 1.36/0.52 thf(decl_204, type, ex1I2: $o).
% 1.36/0.52 thf(decl_205, type, singletonsuniq: $o).
% 1.36/0.52 thf(decl_210, type, setukpairinjL1: $o).
% 1.36/0.52 thf(decl_211, type, kfstsingleton: $o).
% 1.36/0.52 thf(decl_212, type, theprop: $o).
% 1.36/0.52 thf(decl_214, type, kfstpairEq: $o).
% 1.36/0.52 thf(decl_215, type, cartprodfstin: $o).
% 1.36/0.52 thf(decl_216, type, setukpairinjL2: $o).
% 1.36/0.52 thf(decl_217, type, setukpairinjL: $o).
% 1.36/0.52 thf(decl_218, type, setukpairinjR11: $o).
% 1.36/0.52 thf(decl_219, type, setukpairinjR12: $o).
% 1.36/0.52 thf(decl_220, type, setukpairinjR1: $o).
% 1.36/0.52 thf(decl_221, type, upairequniteq: $o).
% 1.36/0.52 thf(decl_222, type, setukpairinjR2: $o).
% 1.36/0.52 thf(decl_223, type, setukpairinjR: $o).
% 1.36/0.52 thf(decl_224, type, ksndsingleton: $o).
% 1.36/0.52 thf(decl_226, type, ksndpairEq: $o).
% 1.36/0.52 thf(decl_227, type, kpairsurjEq: $o).
% 1.36/0.52 thf(decl_228, type, cartprodsndin: $o).
% 1.36/0.52 thf(decl_229, type, cartprodpairmemEL: $o).
% 1.36/0.52 thf(decl_230, type, cartprodpairmemER: $o).
% 1.36/0.52 thf(decl_231, type, cartprodmempaircEq: $o).
% 1.36/0.52 thf(decl_232, type, cartprodfstpairEq: $o).
% 1.36/0.52 thf(decl_233, type, cartprodsndpairEq: $o).
% 1.36/0.52 thf(decl_234, type, cartprodpairsurjEq: $o).
% 1.36/0.52 thf(decl_237, type, dpsetconstrI: $o).
% 1.36/0.52 thf(decl_238, type, dpsetconstrSub: $o).
% 1.36/0.52 thf(decl_239, type, setOfPairsIsBReln: $o).
% 1.36/0.52 thf(decl_240, type, dpsetconstrERa: $o).
% 1.36/0.52 thf(decl_241, type, dpsetconstrEL1: $o).
% 1.36/0.52 thf(decl_242, type, dpsetconstrEL2: $o).
% 1.36/0.52 thf(decl_243, type, dpsetconstrER: $o).
% 1.36/0.52 thf(decl_246, type, funcImageSingleton: $o).
% 1.36/0.52 thf(decl_247, type, apProp: $o).
% 1.36/0.52 thf(decl_249, type, app: $o).
% 1.36/0.52 thf(decl_250, type, infuncsetfunc: $o).
% 1.36/0.52 thf(decl_251, type, ap2p: $o).
% 1.36/0.52 thf(decl_252, type, funcinfuncset: $o).
% 1.36/0.52 thf(decl_253, type, lamProp: $o).
% 1.36/0.52 thf(decl_255, type, lamp: $o).
% 1.36/0.52 thf(decl_256, type, lam2p: $o).
% 1.36/0.52 thf(decl_257, type, brelnall1: $o).
% 1.36/0.52 thf(decl_258, type, brelnall2: $o).
% 1.36/0.52 thf(decl_259, type, ex1E2: $o).
% 1.36/0.52 thf(decl_260, type, funcGraphProp1: $o).
% 1.36/0.52 thf(decl_261, type, funcGraphProp3: $o).
% 1.36/0.52 thf(decl_262, type, funcGraphProp2: $o).
% 1.36/0.52 thf(decl_263, type, funcextLem: $o).
% 1.36/0.52 thf(decl_264, type, funcGraphProp4: $o).
% 1.36/0.52 thf(decl_265, type, subbreln: $o).
% 1.36/0.52 thf(decl_266, type, eqbreln: $o).
% 1.36/0.52 thf(decl_267, type, funcext: $o).
% 1.36/0.52 thf(decl_268, type, funcext2: $o).
% 1.36/0.52 thf(decl_269, type, ap2apEq1: $o).
% 1.36/0.52 thf(decl_270, type, ap2apEq2: $o).
% 1.36/0.52 thf(decl_271, type, beta1: $o).
% 1.36/0.52 thf(decl_272, type, eta1: $o).
% 1.36/0.52 thf(decl_273, type, lam2lamEq: $o).
% 1.36/0.52 thf(decl_274, type, beta2: $o).
% 1.36/0.52 thf(decl_275, type, eta2: $o).
% 1.36/0.52 thf(decl_276, type, iffalseProp1: $o).
% 1.36/0.52 thf(decl_277, type, iffalseProp2: $o).
% 1.36/0.52 thf(decl_278, type, iftrueProp1: $o).
% 1.36/0.52 thf(decl_279, type, iftrueProp2: $o).
% 1.36/0.52 thf(decl_280, type, ifSingleton: $o).
% 1.36/0.52 thf(decl_282, type, ifp: $o).
% 1.36/0.52 thf(decl_283, type, theeq: $o).
% 1.36/0.52 thf(decl_284, type, iftrue: $o).
% 1.36/0.52 thf(decl_285, type, iffalse: $o).
% 1.36/0.52 thf(decl_286, type, iftrueorfalse: $o).
% 1.36/0.52 thf(decl_287, type, binintersectT_lem: $o).
% 1.36/0.52 thf(decl_288, type, binunionT_lem: $o).
% 1.36/0.52 thf(decl_289, type, powersetT_lem: $o).
% 1.36/0.52 thf(decl_290, type, setminusT_lem: $o).
% 1.36/0.52 thf(decl_291, type, complementT_lem: $o).
% 1.36/0.52 thf(decl_292, type, setextT: $o).
% 1.36/0.52 thf(decl_293, type, subsetTI: $o).
% 1.36/0.52 thf(decl_294, type, powersetTI1: $o).
% 1.36/0.52 thf(decl_295, type, powersetTE1: $o).
% 1.36/0.52 thf(decl_296, type, complementTI1: $o).
% 1.36/0.52 thf(decl_297, type, complementTE1: $o).
% 1.36/0.52 thf(decl_298, type, binintersectTELcontra: $o).
% 1.36/0.52 thf(decl_299, type, binintersectTERcontra: $o).
% 1.36/0.52 thf(decl_300, type, contrasubsetT: $o).
% 1.36/0.52 thf(decl_301, type, contrasubsetT1: $o).
% 1.36/0.52 thf(decl_302, type, contrasubsetT2: $o).
% 1.36/0.52 thf(decl_303, type, contrasubsetT3: $o).
% 1.36/0.52 thf(decl_304, type, doubleComplementI1: $o).
% 1.36/0.52 thf(decl_305, type, doubleComplementE1: $o).
% 1.36/0.52 thf(decl_306, type, doubleComplementSub1: $o).
% 1.36/0.52 thf(decl_307, type, doubleComplementSub2: $o).
% 1.36/0.52 thf(decl_308, type, doubleComplementEq: $o).
% 1.36/0.52 thf(decl_309, type, complementTnotintersectT: $o).
% 1.36/0.52 thf(decl_310, type, complementImpComplementIntersect: $o).
% 1.36/0.52 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 1.36/0.52 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 1.36/0.52 thf(decl_313, type, contraSubsetComplement: $o).
% 1.36/0.52 thf(decl_314, type, complementTcontraSubset: $o).
% 1.36/0.52 thf(decl_315, type, binunionTILcontra: $o).
% 1.36/0.52 thf(decl_316, type, binunionTIRcontra: $o).
% 1.36/0.52 thf(decl_317, type, inIntersectImpInUnion: $o).
% 1.36/0.52 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 1.36/0.52 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 1.36/0.52 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 1.36/0.52 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 1.36/0.52 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 1.36/0.52 thf(decl_323, type, binunionTE: $o).
% 1.36/0.52 thf(decl_324, type, binunionTEcontra: $o).
% 1.36/0.52 thf(decl_325, type, demorgan2a1: $o).
% 1.36/0.52 thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 1.36/0.52 thf(decl_327, type, demorgan2a2: $o).
% 1.36/0.52 thf(decl_328, type, demorgan1a: $o).
% 1.36/0.52 thf(decl_329, type, demorgan1b: $o).
% 1.36/0.52 thf(decl_330, type, demorgan1: $o).
% 1.36/0.52 thf(decl_331, type, demorgan2a: $o).
% 1.36/0.52 thf(decl_332, type, demorgan2b2: $o).
% 1.36/0.52 thf(decl_333, type, demorgan2b: $o).
% 1.36/0.52 thf(decl_334, type, demorgan2: $o).
% 1.36/0.52 thf(decl_335, type, woz13rule0: $o).
% 1.36/0.52 thf(decl_336, type, woz13rule1: $o).
% 1.36/0.52 thf(decl_337, type, woz13rule2: $o).
% 1.36/0.52 thf(decl_338, type, woz13rule3: $o).
% 1.36/0.52 thf(decl_339, type, woz13rule4: $o).
% 1.36/0.52 thf(decl_340, type, woz1_1: $o).
% 1.36/0.52 thf(decl_341, type, woz1_2: $o).
% 1.36/0.52 thf(decl_342, type, woz1_3: $o).
% 1.36/0.52 thf(decl_343, type, woz1_4: $o).
% 1.36/0.52 thf(decl_344, type, woz1_5: $o).
% 1.36/0.52 thf(decl_346, type, breln1all2: $o).
% 1.36/0.52 thf(decl_348, type, breln1SetBreln1: $o).
% 1.36/0.52 thf(decl_355, type, choice2fnsingleton: $o).
% 1.36/0.52 thf(decl_356, type, setOfPairsIsBReln1: $o).
% 1.36/0.52 thf(decl_357, type, breln1all1: $o).
% 1.36/0.52 thf(decl_358, type, subbreln1: $o).
% 1.36/0.52 thf(decl_359, type, eqbreln1: $o).
% 1.36/0.52 thf(decl_361, type, breln1invprop: $o).
% 1.36/0.52 thf(decl_362, type, breln1invI: $o).
% 1.36/0.52 thf(decl_363, type, breln1invE: $o).
% 1.36/0.52 thf(decl_365, type, breln1compprop: $o).
% 1.36/0.52 thf(decl_366, type, breln1compI: $o).
% 1.36/0.52 thf(decl_367, type, breln1compE: $o).
% 1.36/0.52 thf(decl_368, type, breln1compEex: $o).
% 1.36/0.52 thf(decl_369, type, breln1unionprop: $o).
% 1.36/0.52 thf(decl_370, type, breln1unionIL: $o).
% 1.36/0.52 thf(decl_371, type, breln1unionIR: $o).
% 1.36/0.52 thf(decl_372, type, breln1unionI: $o).
% 1.36/0.52 thf(decl_373, type, breln1unionE: $o).
% 1.36/0.52 thf(decl_374, type, breln1unionEcases: $o).
% 1.36/0.52 thf(decl_375, type, breln1unionCommutes: $o).
% 1.36/0.52 thf(decl_376, type, woz2Ex: $o).
% 1.36/0.52 thf(decl_377, type, woz2W: $o).
% 1.36/0.52 thf(decl_378, type, woz2A: $o).
% 1.36/0.52 thf(decl_379, type, woz2B: $o).
% 1.36/0.52 thf(decl_380, type, image1Ex: $o).
% 1.36/0.52 thf(decl_381, type, image1Ex1: $o).
% 1.36/0.52 thf(decl_383, type, image1Equiv: $o).
% 1.36/0.52 thf(decl_384, type, image1E: $o).
% 1.36/0.52 thf(decl_385, type, image1I: $o).
% 1.36/0.52 thf(decl_388, type, injFuncInInjFuncSet: $o).
% 1.36/0.52 thf(decl_389, type, injFuncSetFuncIn: $o).
% 1.36/0.52 thf(decl_390, type, injFuncSetFuncInj: $o).
% 1.36/0.52 thf(decl_393, type, surjFuncSetFuncIn: $o).
% 1.36/0.52 thf(decl_394, type, surjFuncSetFuncSurj: $o).
% 1.36/0.52 thf(decl_395, type, leftInvIsSurj: $o).
% 1.36/0.52 thf(decl_396, type, surjCantorThm: $o).
% 1.36/0.52 thf(decl_397, type, foundation2: $o).
% 1.36/0.52 thf(decl_398, type, notinself: $o).
% 1.36/0.52 thf(decl_399, type, notinself2: $o).
% 1.36/0.52 thf(decl_401, type, omegaSp: $o).
% 1.36/0.52 thf(decl_402, type, omegaSclos: $o).
% 1.36/0.52 thf(decl_403, type, peano0notS: $o).
% 1.36/0.52 thf(decl_407, type, peanoSinj: $o).
% 1.36/0.52 thf(decl_409, type, transitiveset: $i > $o).
% 1.36/0.52 thf(decl_410, type, transitivesetOp1: $o).
% 1.36/0.52 thf(decl_411, type, binintTransitive: $o).
% 1.36/0.52 thf(decl_412, type, transitivesetOp2: $o).
% 1.36/0.52 thf(decl_413, type, setunionTransitive: $o).
% 1.36/0.52 thf(decl_414, type, stricttotalorderedByIn: $i > $o).
% 1.36/0.52 thf(decl_415, type, wellorderedByIn: $i > $o).
% 1.36/0.52 thf(decl_416, type, ordinal: $i > $o).
% 1.36/0.52 thf(decl_418, type, ordinalMinLem1: $o).
% 1.36/0.52 thf(decl_419, type, ordinalTransSet: $o).
% 1.36/0.52 thf(decl_420, type, ordinalTransSet1: $o).
% 1.36/0.52 thf(decl_421, type, epred1_1: $i > $o).
% 1.36/0.52 thf(decl_422, type, epred2_1: $i > $o).
% 1.36/0.52 thf(decl_423, type, epred3_1: $i > $o).
% 1.36/0.52 thf(decl_424, type, epred4_1: $i > $o).
% 1.36/0.52 thf(decl_425, type, epred5_1: $i > $o).
% 1.36/0.52 thf(decl_426, type, esk1_1: $i > $i).
% 1.36/0.52 thf(decl_427, type, esk2_1: $i > $i).
% 1.36/0.52 thf(decl_428, type, esk3_1: $i > $i).
% 1.36/0.52 thf(decl_429, type, esk4_1: $i > $i).
% 1.36/0.52 thf(decl_430, type, esk5_1: $i > $i).
% 1.36/0.52 thf(decl_431, type, esk6_2: $i > $i > $i).
% 1.36/0.52 thf(decl_432, type, esk7_1: $i > $i).
% 1.36/0.52 thf(decl_433, type, esk8_1: $i > $i).
% 1.36/0.52 thf(decl_434, type, esk9_1: $i > $i).
% 1.36/0.52 thf(decl_435, type, esk10_1: $i > $i).
% 1.36/0.52 thf(decl_436, type, esk11_1: $i > $i).
% 1.36/0.52 thf(decl_437, type, esk12_1: $i > $i).
% 1.36/0.52 thf(decl_438, type, esk13_2: $i > $i > $i).
% 1.36/0.52 thf(decl_439, type, esk14_2: $i > $i > $i).
% 1.36/0.52 thf(decl_440, type, esk15_2: $i > $i > $i).
% 1.36/0.52 thf(decl_441, type, esk16_2: $i > $i > $i).
% 1.36/0.52 thf(decl_442, type, esk17_3: $i > $i > $i > $i).
% 1.36/0.52 thf(decl_443, type, esk18_1: $i > $i).
% 1.36/0.52 thf(decl_444, type, esk19_1: $i > $i).
% 1.36/0.52 thf(decl_445, type, esk20_1: $i > $i).
% 1.36/0.52 thf(decl_446, type, esk21_2: $i > $i > $i).
% 1.36/0.52 thf(decl_447, type, esk22_1: $i > $i).
% 1.36/0.52 thf(decl_448, type, esk23_1: $i > $i).
% 1.36/0.52 thf(decl_449, type, esk24_1: $i > $i).
% 1.36/0.52 thf(decl_450, type, esk25_2: $i > $i > $i).
% 1.36/0.52 thf(decl_451, type, esk26_0: $i).
% 1.36/0.52 thf(decl_452, type, esk27_0: $i).
% 1.36/0.52 thf(decl_473, type, esk48_2: $i > $i > $i).
% 1.36/0.52 thf(wellorderedByIn, axiom, ((wellorderedByIn)=(^[X4:$i]:((((stricttotalorderedByIn @ X4))&(![X21:$i]:((((in @ X21 @ (powerset @ X4)))=>((((nonempty @ X21))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', wellorderedByIn)).
% 1.36/0.52 thf(stricttotalorderedByIn, axiom, ((stricttotalorderedByIn)=(^[X4:$i]:(((((![X2:$i]:((((in @ X2 @ X4))=>(![X21:$i]:((((in @ X21 @ X4))=>(![X48:$i]:((((in @ X48 @ X4))=>((((((in @ X2 @ X21))&((in @ X21 @ X48))))=>((in @ X2 @ X48)))))))))))))&(![X21:$i]:((((in @ X21 @ X4))=>(![X48:$i]:((((in @ X48 @ X4))=>(((((((X21)=(X48)))|((in @ X21 @ X48))))|((in @ X48 @ X21))))))))))))&(![X21:$i]:((((in @ X21 @ X4))=>(~((in @ X21 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', stricttotalorderedByIn)).
% 1.36/0.52 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', nonempty)).
% 1.36/0.52 thf(ordinal, axiom, ((ordinal)=(^[X2:$i]:((((transitiveset @ X2))&((wellorderedByIn @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', ordinal)).
% 1.36/0.52 thf(transitiveset, axiom, ((transitiveset)=(^[X4:$i]:(![X21:$i]:((((in @ X21 @ X4))=>((subset @ X21 @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', transitiveset)).
% 1.36/0.52 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.uuCIDe0kxA/E---3.1_1334370.p', nonemptyI)).
% 1.36/0.52 thf(setunionOrdinalLem1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>((breln1compprop)=>((breln1compI)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>((breln1unionIR)=>((breln1unionI)=>((breln1unionE)=>((breln1unionEcases)=>((breln1unionCommutes)=>((woz2Ex)=>((woz2W)=>((woz2A)=>((woz2B)=>((image1Ex)=>((image1Ex1)=>((image1Equiv)=>((image1E)=>((image1I)=>((injFuncInInjFuncSet)=>((injFuncSetFuncIn)=>((injFuncSetFuncInj)=>((surjFuncSetFuncIn)=>((surjFuncSetFuncSurj)=>((leftInvIsSurj)=>((surjCantorThm)=>((foundation2)=>((notinself)=>((notinself2)=>((omegaSp)=>((omegaSclos)=>((peano0notS)=>((peanoSinj)=>((transitivesetOp1)=>((binintTransitive)=>((transitivesetOp2)=>((setunionTransitive)=>((ordinalMinLem1)=>((ordinalTransSet)=>((ordinalTransSet1)=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(ordinal @ X2)))=>(transitiveset @ (setunion @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', setunionOrdinalLem1)).
% 1.36/0.52 thf(foundation2, axiom, ((foundation2)<=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', foundation2)).
% 1.36/0.52 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', nonemptyImpWitness)).
% 1.36/0.52 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', nonemptyI1)).
% 1.36/0.52 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', nonemptyE1)).
% 1.36/0.52 thf(ordinalTransSet1, axiom, ((ordinalTransSet1)<=>![X21:$i]:(((ordinal @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', ordinalTransSet1)).
% 1.36/0.52 thf(ordinalTransSet, axiom, ((ordinalTransSet)<=>![X21:$i]:(((ordinal @ X21)=>![X2:$i, X4:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', ordinalTransSet)).
% 1.36/0.52 thf(ordinalMinLem1, axiom, ((ordinalMinLem1)<=>![X21:$i]:(((ordinal @ X21)=>![X48:$i]:(((ordinal @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', ordinalMinLem1)).
% 1.36/0.52 thf(setunionTransitive, axiom, ((setunionTransitive)<=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(transitiveset @ X2)))=>(transitiveset @ (setunion @ X21))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', setunionTransitive)).
% 1.36/0.52 thf(transitivesetOp2, axiom, ((transitivesetOp2)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i, X2:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', transitivesetOp2)).
% 1.36/0.52 thf(binintTransitive, axiom, ((binintTransitive)<=>![X21:$i]:(((transitiveset @ X21)=>![X48:$i]:(((transitiveset @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', binintTransitive)).
% 1.36/0.52 thf(transitivesetOp1, axiom, ((transitivesetOp1)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.uuCIDe0kxA/E---3.1_1334370.p', transitivesetOp1)).
% 1.36/0.52 thf(c_0_18, plain, ((wellorderedByIn)=(^[Z0:$i]:((((((((![X99:$i]:((((in @ X99 @ Z0))=>(![X100:$i]:((((in @ X100 @ Z0))=>(![X101:$i]:((((in @ X101 @ Z0))=>((((((in @ X99 @ X100))&((in @ X100 @ X101))))=>((in @ X99 @ X101)))))))))))))&(![X102:$i]:((((in @ X102 @ Z0))=>(![X103:$i]:((((in @ X103 @ Z0))=>(((((((X102)=(X103)))|((in @ X102 @ X103))))|((in @ X103 @ X102))))))))))))&(![X104:$i]:((((in @ X104 @ Z0))=>(~((in @ X104 @ X104)))))))))&(![X21:$i]:((((in @ X21 @ (powerset @ Z0)))=>((((((X21)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), inference(fof_simplification,[status(thm)],[wellorderedByIn])).
% 1.36/0.52 thf(c_0_19, plain, ((stricttotalorderedByIn)=(^[Z0:$i]:(((((![X2:$i]:((((in @ X2 @ Z0))=>(![X21:$i]:((((in @ X21 @ Z0))=>(![X48:$i]:((((in @ X48 @ Z0))=>((((((in @ X2 @ X21))&((in @ X21 @ X48))))=>((in @ X2 @ X48)))))))))))))&(![X21:$i]:((((in @ X21 @ Z0))=>(![X48:$i]:((((in @ X48 @ Z0))=>(((((((X21)=(X48)))|((in @ X21 @ X48))))|((in @ X48 @ X21))))))))))))&(![X21:$i]:((((in @ X21 @ Z0))=>(~((in @ X21 @ X21)))))))))), inference(fof_simplification,[status(thm)],[stricttotalorderedByIn])).
% 1.36/0.52 thf(c_0_20, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 1.36/0.52 thf(c_0_21, plain, ((ordinal)=(^[Z0:$i]:((((![X105:$i]:((((in @ X105 @ Z0))=>((subset @ X105 @ Z0))))))&(((((((((![X106:$i]:((((in @ X106 @ Z0))=>(![X107:$i]:((((in @ X107 @ Z0))=>(![X108:$i]:((((in @ X108 @ Z0))=>((((((in @ X106 @ X107))&((in @ X107 @ X108))))=>((in @ X106 @ X108)))))))))))))&(![X109:$i]:((((in @ X109 @ Z0))=>(![X110:$i]:((((in @ X110 @ Z0))=>(((((((X109)=(X110)))|((in @ X109 @ X110))))|((in @ X110 @ X109))))))))))))&(![X111:$i]:((((in @ X111 @ Z0))=>(~((in @ X111 @ X111)))))))))&(![X112:$i]:((((in @ X112 @ (powerset @ Z0)))=>((((((X112)!=(emptyset))))=>(?[X113:$i]:((((in @ X113 @ X112))&(![X114:$i]:((((in @ X114 @ X112))=>(((((X113)=(X114)))|((in @ X113 @ X114)))))))))))))))))))))), inference(fof_simplification,[status(thm)],[ordinal])).
% 1.36/0.52 thf(c_0_22, plain, ((wellorderedByIn)=(^[Z0:$i]:((((((((![X99:$i]:((((in @ X99 @ Z0))=>(![X100:$i]:((((in @ X100 @ Z0))=>(![X101:$i]:((((in @ X101 @ Z0))=>((((((in @ X99 @ X100))&((in @ X100 @ X101))))=>((in @ X99 @ X101)))))))))))))&(![X102:$i]:((((in @ X102 @ Z0))=>(![X103:$i]:((((in @ X103 @ Z0))=>(((((((X102)=(X103)))|((in @ X102 @ X103))))|((in @ X103 @ X102))))))))))))&(![X104:$i]:((((in @ X104 @ Z0))=>(~((in @ X104 @ X104)))))))))&(![X21:$i]:((((in @ X21 @ (powerset @ Z0)))=>((((((X21)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18, c_0_19]), c_0_20])).
% 1.36/0.52 thf(c_0_23, plain, ((transitiveset)=(^[Z0:$i]:(![X21:$i]:((((in @ X21 @ Z0))=>((subset @ X21 @ Z0))))))), inference(fof_simplification,[status(thm)],[transitiveset])).
% 1.36/0.52 thf(c_0_24, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.36/0.52 thf(c_0_25, plain, ((ordinal)=(^[Z0:$i]:((((![X105:$i]:((((in @ X105 @ Z0))=>((subset @ X105 @ Z0))))))&(((((((((![X106:$i]:((((in @ X106 @ Z0))=>(![X107:$i]:((((in @ X107 @ Z0))=>(![X108:$i]:((((in @ X108 @ Z0))=>((((((in @ X106 @ X107))&((in @ X107 @ X108))))=>((in @ X106 @ X108)))))))))))))&(![X109:$i]:((((in @ X109 @ Z0))=>(![X110:$i]:((((in @ X110 @ Z0))=>(((((((X109)=(X110)))|((in @ X109 @ X110))))|((in @ X110 @ X109))))))))))))&(![X111:$i]:((((in @ X111 @ Z0))=>(~((in @ X111 @ X111)))))))))&(![X112:$i]:((((in @ X112 @ (powerset @ Z0)))=>((((((X112)!=(emptyset))))=>(?[X113:$i]:((((in @ X113 @ X112))&(![X114:$i]:((((in @ X114 @ X112))=>(((((X113)=(X114)))|((in @ X113 @ X114)))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21, c_0_22]), c_0_23])).
% 1.36/0.52 thf(c_0_26, plain, ![X2:$i]:(((epred5_1 @ X2)<=>(![X231:$i]:(((in @ X231 @ X2)=>(subset @ X231 @ X2)))&(((![X232:$i]:(((in @ X232 @ X2)=>![X233:$i]:(((in @ X233 @ X2)=>![X234:$i]:(((in @ X234 @ X2)=>(((in @ X232 @ X233)&(in @ X233 @ X234))=>(in @ X232 @ X234))))))))&![X235:$i]:(((in @ X235 @ X2)=>![X236:$i]:(((in @ X236 @ X2)=>(((X235)=(X236))|(in @ X235 @ X236)|(in @ X236 @ X235)))))))&![X237:$i]:(((in @ X237 @ X2)=>~(in @ X237 @ X237))))&![X238:$i]:(((in @ X238 @ (powerset @ X2))=>(((X238)!=(emptyset))=>?[X239:$i]:(((in @ X239 @ X238)&![X240:$i]:(((in @ X240 @ X238)=>(((X239)=(X240))|(in @ X239 @ X240))))))))))))), introduced(definition)).
% 1.36/0.52 thf(c_0_27, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>((breln1compprop)=>((breln1compI)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>((breln1unionIR)=>((breln1unionI)=>((breln1unionE)=>((breln1unionEcases)=>((breln1unionCommutes)=>((woz2Ex)=>((woz2W)=>((woz2A)=>((woz2B)=>((image1Ex)=>((image1Ex1)=>((image1Equiv)=>((image1E)=>((image1I)=>((injFuncInInjFuncSet)=>((injFuncSetFuncIn)=>((injFuncSetFuncInj)=>((surjFuncSetFuncIn)=>((surjFuncSetFuncSurj)=>((leftInvIsSurj)=>((surjCantorThm)=>((foundation2)=>((notinself)=>((notinself2)=>((omegaSp)=>((omegaSclos)=>((peano0notS)=>((peanoSinj)=>((transitivesetOp1)=>((binintTransitive)=>((transitivesetOp2)=>((setunionTransitive)=>((ordinalMinLem1)=>((ordinalTransSet)=>((ordinalTransSet1)=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(ordinal @ X2)))=>(transitiveset @ (setunion @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setunionOrdinalLem1])).
% 1.36/0.52 thf(c_0_28, axiom, ((foundation2)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X21:$i]:((((in @ X21 @ X4))&(((binintersect @ X21 @ X4)=(emptyset)))))))))), inference(apply_def,[status(thm)],[foundation2, c_0_20])).
% 1.36/0.52 thf(c_0_29, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_20])).
% 1.36/0.52 thf(c_0_30, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_20])).
% 1.36/0.52 thf(c_0_31, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_24, c_0_20])).
% 1.36/0.52 thf(c_0_32, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_20])).
% 1.36/0.52 thf(c_0_33, axiom, ((ordinalTransSet1)=(![X21:$i]:(((((((![X146:$i]:((((in @ X146 @ X21))=>((subset @ X146 @ X21))))))&(((((((((![X147:$i]:((((in @ X147 @ X21))=>(![X148:$i]:((((in @ X148 @ X21))=>(![X149:$i]:((((in @ X149 @ X21))=>((((((in @ X147 @ X148))&((in @ X148 @ X149))))=>((in @ X147 @ X149)))))))))))))&(![X150:$i]:((((in @ X150 @ X21))=>(![X151:$i]:((((in @ X151 @ X21))=>(((((((X150)=(X151)))|((in @ X150 @ X151))))|((in @ X151 @ X150))))))))))))&(![X152:$i]:((((in @ X152 @ X21))=>(~((in @ X152 @ X152)))))))))&(![X153:$i]:((((in @ X153 @ (powerset @ X21)))=>((((((X153)!=(emptyset))))=>(?[X154:$i]:((((in @ X154 @ X153))&(![X155:$i]:((((in @ X155 @ X153))=>(((((X154)=(X155)))|((in @ X154 @ X155)))))))))))))))))))))=>(![X4:$i]:((((in @ X4 @ X21))=>((subset @ X4 @ X21))))))))), inference(apply_def,[status(thm)],[ordinalTransSet1, c_0_25])).
% 1.36/0.52 thf(c_0_34, axiom, ((ordinalTransSet)=(![X21:$i]:(((((((![X136:$i]:((((in @ X136 @ X21))=>((subset @ X136 @ X21))))))&(((((((((![X137:$i]:((((in @ X137 @ X21))=>(![X138:$i]:((((in @ X138 @ X21))=>(![X139:$i]:((((in @ X139 @ X21))=>((((((in @ X137 @ X138))&((in @ X138 @ X139))))=>((in @ X137 @ X139)))))))))))))&(![X140:$i]:((((in @ X140 @ X21))=>(![X141:$i]:((((in @ X141 @ X21))=>(((((((X140)=(X141)))|((in @ X140 @ X141))))|((in @ X141 @ X140))))))))))))&(![X142:$i]:((((in @ X142 @ X21))=>(~((in @ X142 @ X142)))))))))&(![X143:$i]:((((in @ X143 @ (powerset @ X21)))=>((((((X143)!=(emptyset))))=>(?[X144:$i]:((((in @ X144 @ X143))&(![X145:$i]:((((in @ X145 @ X143))=>(((((X144)=(X145)))|((in @ X144 @ X145)))))))))))))))))))))=>(![X2:$i, X4:$i]:((((in @ X4 @ X21))=>((((in @ X2 @ X4))=>((in @ X2 @ X21))))))))))), inference(apply_def,[status(thm)],[ordinalTransSet, c_0_25])).
% 1.36/0.52 thf(c_0_35, axiom, ((ordinalMinLem1)=(![X21:$i]:(((((((![X115:$i]:((((in @ X115 @ X21))=>((subset @ X115 @ X21))))))&(((((((((![X116:$i]:((((in @ X116 @ X21))=>(![X117:$i]:((((in @ X117 @ X21))=>(![X118:$i]:((((in @ X118 @ X21))=>((((((in @ X116 @ X117))&((in @ X117 @ X118))))=>((in @ X116 @ X118)))))))))))))&(![X119:$i]:((((in @ X119 @ X21))=>(![X120:$i]:((((in @ X120 @ X21))=>(((((((X119)=(X120)))|((in @ X119 @ X120))))|((in @ X120 @ X119))))))))))))&(![X121:$i]:((((in @ X121 @ X21))=>(~((in @ X121 @ X121)))))))))&(![X122:$i]:((((in @ X122 @ (powerset @ X21)))=>((((((X122)!=(emptyset))))=>(?[X123:$i]:((((in @ X123 @ X122))&(![X124:$i]:((((in @ X124 @ X122))=>(((((X123)=(X124)))|((in @ X123 @ X124)))))))))))))))))))))=>(![X48:$i]:(((((((![X125:$i]:((((in @ X125 @ X48))=>((subset @ X125 @ X48))))))&(((((((((![X126:$i]:((((in @ X126 @ X48))=>(![X127:$i]:((((in @ X127 @ X48))=>(![X128:$i]:((((in @ X128 @ X48))=>((((((in @ X126 @ X127))&((in @ X127 @ X128))))=>((in @ X126 @ X128)))))))))))))&(![X129:$i]:((((in @ X129 @ X48))=>(![X130:$i]:((((in @ X130 @ X48))=>(((((((X129)=(X130)))|((in @ X129 @ X130))))|((in @ X130 @ X129))))))))))))&(![X131:$i]:((((in @ X131 @ X48))=>(~((in @ X131 @ X131)))))))))&(![X132:$i]:((((in @ X132 @ (powerset @ X48)))=>((((((X132)!=(emptyset))))=>(?[X133:$i]:((((in @ X133 @ X132))&(![X134:$i]:((((in @ X134 @ X132))=>(((((X133)=(X134)))|((in @ X133 @ X134)))))))))))))))))))))=>((![X135:$i]:((((in @ X135 @ (binintersect @ X21 @ X48)))=>((subset @ X135 @ (binintersect @ X21 @ X48)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ordinalMinLem1, c_0_25]), c_0_23])).
% 1.36/0.52 thf(c_0_36, axiom, ((setunionTransitive)=(![X21:$i]:(((![X2:$i]:((((in @ X2 @ X21))=>((![X97:$i]:((((in @ X97 @ X2))=>((subset @ X97 @ X2)))))))))=>((![X98:$i]:((((in @ X98 @ (setunion @ X21)))=>((subset @ X98 @ (setunion @ X21))))))))))), inference(apply_def,[status(thm)],[setunionTransitive, c_0_23])).
% 1.36/0.52 thf(c_0_37, axiom, ((transitivesetOp2)=(![X21:$i]:((((![X96:$i]:((((in @ X96 @ X21))=>((subset @ X96 @ X21))))))=>(![X4:$i, X2:$i]:((((in @ X4 @ X21))=>((((in @ X2 @ X4))=>((in @ X2 @ X21))))))))))), inference(apply_def,[status(thm)],[transitivesetOp2, c_0_23])).
% 1.36/0.52 thf(c_0_38, axiom, ((binintTransitive)=(![X21:$i]:((((![X93:$i]:((((in @ X93 @ X21))=>((subset @ X93 @ X21))))))=>(![X48:$i]:((((![X94:$i]:((((in @ X94 @ X48))=>((subset @ X94 @ X48))))))=>((![X95:$i]:((((in @ X95 @ (binintersect @ X21 @ X48)))=>((subset @ X95 @ (binintersect @ X21 @ X48)))))))))))))), inference(apply_def,[status(thm)],[binintTransitive, c_0_23])).
% 1.36/0.52 thf(c_0_39, axiom, ((transitivesetOp1)=(![X21:$i]:((((![X92:$i]:((((in @ X92 @ X21))=>((subset @ X92 @ X21))))))=>(![X4:$i]:((((in @ X4 @ X21))=>((subset @ X4 @ X21))))))))), inference(apply_def,[status(thm)],[transitivesetOp1, c_0_23])).
% 1.36/0.52 thf(c_0_40, plain, ![X183:$i]:(((epred1_1 @ X183)<=>(![X185:$i]:(((in @ X185 @ X183)=>![X186:$i]:(((in @ X186 @ X183)=>![X187:$i]:(((in @ X187 @ X183)=>(((in @ X185 @ X186)&(in @ X186 @ X187))=>(in @ X185 @ X187))))))))&![X188:$i]:(((in @ X188 @ X183)=>![X189:$i]:(((in @ X189 @ X183)=>(((X188)=(X189))|(in @ X188 @ X189)|(in @ X189 @ X188))))))))), introduced(definition)).
% 1.36/0.52 thf(c_0_41, plain, ![X194:$i]:(((epred2_1 @ X194)<=>(![X196:$i]:(((in @ X196 @ X194)=>![X197:$i]:(((in @ X197 @ X194)=>![X198:$i]:(((in @ X198 @ X194)=>(((in @ X196 @ X197)&(in @ X197 @ X198))=>(in @ X196 @ X198))))))))&![X199:$i]:(((in @ X199 @ X194)=>![X200:$i]:(((in @ X200 @ X194)=>(((X199)=(X200))|(in @ X199 @ X200)|(in @ X200 @ X199))))))))), introduced(definition)).
% 1.36/0.52 thf(c_0_42, plain, ![X206:$i]:(((epred3_1 @ X206)<=>(![X208:$i]:(((in @ X208 @ X206)=>![X209:$i]:(((in @ X209 @ X206)=>![X210:$i]:(((in @ X210 @ X206)=>(((in @ X208 @ X209)&(in @ X209 @ X210))=>(in @ X208 @ X210))))))))&![X211:$i]:(((in @ X211 @ X206)=>![X212:$i]:(((in @ X212 @ X206)=>(((X211)=(X212))|(in @ X211 @ X212)|(in @ X212 @ X211))))))))), introduced(definition)).
% 1.36/0.52 thf(c_0_43, plain, ![X219:$i]:(((epred4_1 @ X219)<=>(![X221:$i]:(((in @ X221 @ X219)=>![X222:$i]:(((in @ X222 @ X219)=>![X223:$i]:(((in @ X223 @ X219)=>(((in @ X221 @ X222)&(in @ X222 @ X223))=>(in @ X221 @ X223))))))))&![X224:$i]:(((in @ X224 @ X219)=>![X225:$i]:(((in @ X225 @ X219)=>(((X224)=(X225))|(in @ X224 @ X225)|(in @ X225 @ X224))))))))), introduced(definition)).
% 1.36/0.52 thf(c_0_44, plain, ![X2:$i]:(((epred5_1 @ X2)=>(![X231:$i]:(((in @ X231 @ X2)=>(subset @ X231 @ X2)))&(((![X232:$i]:(((in @ X232 @ X2)=>![X233:$i]:(((in @ X233 @ X2)=>![X234:$i]:(((in @ X234 @ X2)=>(((in @ X232 @ X233)&(in @ X233 @ X234))=>(in @ X232 @ X234))))))))&![X235:$i]:(((in @ X235 @ X2)=>![X236:$i]:(((in @ X236 @ X2)=>(((X235)=(X236))|(in @ X235 @ X236)|(in @ X236 @ X235)))))))&![X237:$i]:(((in @ X237 @ X2)=>~(in @ X237 @ X237))))&![X238:$i]:(((in @ X238 @ (powerset @ X2))=>(((X238)!=(emptyset))=>?[X239:$i]:(((in @ X239 @ X238)&![X240:$i]:(((in @ X240 @ X238)=>(((X239)=(X240))|(in @ X239 @ X240))))))))))))), inference(split_equiv,[status(thm)],[c_0_26])).
% 1.36/0.52 thf(c_0_45, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>(![X156:$i]:((((X156)!=(emptyset))=>?[X157:$i]:((in @ X157 @ X156))))=>(![X158:$i, X159:$i > $o, X160:$i]:(((in @ X160 @ X158)=>((X159 @ X160)=>((dsetconstr @ X158 @ X159)!=(emptyset)))))=>(![X161:$i]:((?[X162:$i]:((in @ X162 @ X161))=>((X161)!=(emptyset))))=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>(![X163:$i]:((((X163)!=(emptyset))=>?[X164:$i]:(((in @ X164 @ X163)&$true))))=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>((breln1compprop)=>((breln1compI)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>((breln1unionIR)=>((breln1unionI)=>((breln1unionE)=>((breln1unionEcases)=>((breln1unionCommutes)=>((woz2Ex)=>((woz2W)=>((woz2A)=>((woz2B)=>((image1Ex)=>((image1Ex1)=>((image1Equiv)=>((image1E)=>((image1I)=>((injFuncInInjFuncSet)=>((injFuncSetFuncIn)=>((injFuncSetFuncInj)=>((surjFuncSetFuncIn)=>((surjFuncSetFuncSurj)=>((leftInvIsSurj)=>((surjCantorThm)=>(![X165:$i]:((((X165)!=(emptyset))=>?[X166:$i]:(((in @ X166 @ X165)&((binintersect @ X166 @ X165)=(emptyset))))))=>((notinself)=>((notinself2)=>((omegaSp)=>((omegaSclos)=>((peano0notS)=>((peanoSinj)=>(![X167:$i]:((![X168:$i]:(((in @ X168 @ X167)=>(subset @ X168 @ X167)))=>![X169:$i]:(((in @ X169 @ X167)=>(subset @ X169 @ X167)))))=>(![X170:$i]:((![X171:$i]:(((in @ X171 @ X170)=>(subset @ X171 @ X170)))=>![X172:$i]:((![X173:$i]:(((in @ X173 @ X172)=>(subset @ X173 @ X172)))=>![X174:$i]:(((in @ X174 @ (binintersect @ X170 @ X172))=>(subset @ X174 @ (binintersect @ X170 @ X172))))))))=>(![X175:$i]:((![X176:$i]:(((in @ X176 @ X175)=>(subset @ X176 @ X175)))=>![X177:$i, X178:$i]:(((in @ X177 @ X175)=>((in @ X178 @ X177)=>(in @ X178 @ X175))))))=>(![X179:$i]:((![X180:$i]:(((in @ X180 @ X179)=>![X181:$i]:(((in @ X181 @ X180)=>(subset @ X181 @ X180)))))=>![X182:$i]:(((in @ X182 @ (setunion @ X179))=>(subset @ X182 @ (setunion @ X179))))))=>(![X183:$i]:(((![X184:$i]:(((in @ X184 @ X183)=>(subset @ X184 @ X183)))&(((epred1_1 @ X183)&![X190:$i]:(((in @ X190 @ X183)=>~(in @ X190 @ X190))))&![X191:$i]:(((in @ X191 @ (powerset @ X183))=>(((X191)!=(emptyset))=>?[X192:$i]:(((in @ X192 @ X191)&![X193:$i]:(((in @ X193 @ X191)=>(((X192)=(X193))|(in @ X192 @ X193)))))))))))=>![X194:$i]:(((![X195:$i]:(((in @ X195 @ X194)=>(subset @ X195 @ X194)))&(((epred2_1 @ X194)&![X201:$i]:(((in @ X201 @ X194)=>~(in @ X201 @ X201))))&![X202:$i]:(((in @ X202 @ (powerset @ X194))=>(((X202)!=(emptyset))=>?[X203:$i]:(((in @ X203 @ X202)&![X204:$i]:(((in @ X204 @ X202)=>(((X203)=(X204))|(in @ X203 @ X204)))))))))))=>![X205:$i]:(((in @ X205 @ (binintersect @ X183 @ X194))=>(subset @ X205 @ (binintersect @ X183 @ X194))))))))=>(![X206:$i]:(((![X207:$i]:(((in @ X207 @ X206)=>(subset @ X207 @ X206)))&(((epred3_1 @ X206)&![X213:$i]:(((in @ X213 @ X206)=>~(in @ X213 @ X213))))&![X214:$i]:(((in @ X214 @ (powerset @ X206))=>(((X214)!=(emptyset))=>?[X215:$i]:(((in @ X215 @ X214)&![X216:$i]:(((in @ X216 @ X214)=>(((X215)=(X216))|(in @ X215 @ X216)))))))))))=>![X217:$i, X218:$i]:(((in @ X218 @ X206)=>((in @ X217 @ X218)=>(in @ X217 @ X206))))))=>(![X219:$i]:(((![X220:$i]:(((in @ X220 @ X219)=>(subset @ X220 @ X219)))&(((epred4_1 @ X219)&![X226:$i]:(((in @ X226 @ X219)=>~(in @ X226 @ X226))))&![X227:$i]:(((in @ X227 @ (powerset @ X219))=>(((X227)!=(emptyset))=>?[X228:$i]:(((in @ X228 @ X227)&![X229:$i]:(((in @ X229 @ X227)=>(((X228)=(X229))|(in @ X228 @ X229)))))))))))=>![X230:$i]:(((in @ X230 @ X219)=>(subset @ X230 @ X219)))))=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(epred5_1 @ X2)))=>![X241:$i]:(((in @ X241 @ (setunion @ X21))=>(subset @ X241 @ (setunion @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[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)],[c_0_27, c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_32]), c_0_33]), c_0_34]), c_0_35]), c_0_25]), c_0_36]), c_0_37]), c_0_38]), c_0_39]), c_0_23])])]), c_0_40]), c_0_41]), c_0_42]), c_0_43]), c_0_26])).
% 1.36/0.52 thf(c_0_46, plain, ![X324:$i, X325:$i, X326:$i, X327:$i, X328:$i, X329:$i, X330:$i, X331:$i, X332:$i, X334:$i]:(((~(in @ X325 @ X324)|(subset @ X325 @ X324)|~(epred5_1 @ X324))&((((~(in @ X326 @ X324)|(~(in @ X327 @ X324)|(~(in @ X328 @ X324)|(~(in @ X326 @ X327)|~(in @ X327 @ X328)|(in @ X326 @ X328))))|~(epred5_1 @ X324))&(~(in @ X329 @ X324)|(~(in @ X330 @ X324)|(((X329)=(X330))|(in @ X329 @ X330)|(in @ X330 @ X329)))|~(epred5_1 @ X324)))&(~(in @ X331 @ X324)|~(in @ X331 @ X331)|~(epred5_1 @ X324)))&(((in @ (esk48_2 @ X324 @ X332) @ X332)|((X332)=(emptyset))|~(in @ X332 @ (powerset @ X324))|~(epred5_1 @ X324))&(~(in @ X334 @ X332)|(((esk48_2 @ X324 @ X332)=(X334))|(in @ (esk48_2 @ X324 @ X332) @ X334))|((X332)=(emptyset))|~(in @ X332 @ (powerset @ X324))|~(epred5_1 @ X324)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])])])])).
% 1.36/0.52 thf(c_0_47, negated_conjecture, ![X242:$i, X244:$i, X245:$i > $o, X246:$i, X247:$i, X248:$i, X249:$i, X251:$i, X253:$i, X255:$i, X256:$i, X258:$i, X260:$i, X261:$i, X263:$i, X264:$i, X265:$i, X268:$i, X269:$i, X273:$i, X275:$i, X279:$i, X281:$i, X282:$i, X286:$i, X288:$i, X289:$i, X290:$i, X294:$i, X296:$i, X298:$i]:(((setextAx)&((emptysetAx)&((setadjoinAx)&((powersetAx)&((setunionAx)&((omega0Ax)&((omegaSAx)&((omegaIndAx)&((replAx)&((foundationAx)&((wellorderingAx)&((descrp)&((dsetconstrI)&((dsetconstrEL)&((dsetconstrER)&((exuE1)&((prop2setE)&((emptysetE)&((emptysetimpfalse)&((notinemptyset)&((exuE3e)&((setext)&((emptyI)&((noeltsimpempty)&((setbeta)&((((X242)=(emptyset))|(in @ (esk1_1 @ X242) @ X242))&((~(in @ X246 @ X244)|(~(X245 @ X246)|((dsetconstr @ X244 @ X245)!=(emptyset))))&((~(in @ X248 @ X247)|((X247)!=(emptyset)))&((setadjoinIL)&((emptyinunitempty)&((setadjoinIR)&((setadjoinE)&((setadjoinOr)&((setoftrueEq)&((powersetI)&((emptyinPowerset)&((emptyInPowerset)&((powersetE)&((setunionI)&((setunionE)&((subPowSU)&((exuE2)&((((in @ (esk2_1 @ X249) @ X249)|((X249)=(emptyset)))&(($true)|((X249)=(emptyset))))&((uniqinunit)&((notinsingleton)&((eqinunit)&((singletonsswitch)&((upairsetE)&((upairsetIL)&((upairsetIR)&((emptyE1)&((vacuousDall)&((quantDeMorgan1)&((quantDeMorgan2)&((quantDeMorgan3)&((quantDeMorgan4)&((prop2setI)&((prop2set2propI)&((notdexE)&((notdallE)&((exuI1)&((exuI3)&((exuI2)&((inCongP)&((in__Cong)&((exuE3u)&((exu__Cong)&((emptyset__Cong)&((setadjoin__Cong)&((powerset__Cong)&((setunion__Cong)&((omega__Cong)&((exuEu)&((descr__Cong)&((dsetconstr__Cong)&((subsetI1)&((eqimpsubset2)&((eqimpsubset1)&((subsetI2)&((emptysetsubset)&((subsetE)&((subsetE2)&((notsubsetI)&((notequalI1)&((notequalI2)&((subsetRefl)&((subsetTrans)&((setadjoinSub)&((setadjoinSub2)&((subset2powerset)&((setextsub)&((subsetemptysetimpeq)&((powersetI1)&((powersetE1)&((inPowerset)&((powersetsubset)&((sepInPowerset)&((sepSubset)&((binunionIL)&((upairset2IR)&((binunionIR)&((binunionEcases)&((binunionE)&((binunionLsub)&((binunionRsub)&((binintersectI)&((binintersectSubset5)&((binintersectEL)&((binintersectLsub)&((binintersectSubset2)&((binintersectSubset3)&((binintersectER)&((disjointsetsI1)&((binintersectRsub)&((binintersectSubset4)&((binintersectSubset1)&((bs114d)&((setminusI)&((setminusEL)&((setminusER)&((setminusSubset2)&((setminusERneg)&((setminusELneg)&((setminusILneg)&((setminusIRneg)&((setminusLsub)&((setminusSubset1)&((symdiffE)&((symdiffI1)&((symdiffI2)&((symdiffIneg1)&((symdiffIneg2)&((secondinupair)&((setukpairIL)&((setukpairIR)&((kpairiskpair)&((kpairp)&((singletonsubset)&((singletoninpowerset)&((singletoninpowunion)&((upairset2E)&((upairsubunion)&((upairinpowunion)&((ubforcartprodlem1)&((ubforcartprodlem2)&((ubforcartprodlem3)&((cartprodpairin)&((cartprodmempair1)&((cartprodmempair)&((setunionE2)&((setunionsingleton1)&((setunionsingleton2)&((setunionsingleton)&((singletonprop)&((ex1E1)&((ex1I)&((ex1I2)&((singletonsuniq)&((setukpairinjL1)&((kfstsingleton)&((theprop)&((kfstpairEq)&((cartprodfstin)&((setukpairinjL2)&((setukpairinjL)&((setukpairinjR11)&((setukpairinjR12)&((setukpairinjR1)&((upairequniteq)&((setukpairinjR2)&((setukpairinjR)&((ksndsingleton)&((ksndpairEq)&((kpairsurjEq)&((cartprodsndin)&((cartprodpairmemEL)&((cartprodpairmemER)&((cartprodmempaircEq)&((cartprodfstpairEq)&((cartprodsndpairEq)&((cartprodpairsurjEq)&((dpsetconstrI)&((dpsetconstrSub)&((setOfPairsIsBReln)&((dpsetconstrERa)&((dpsetconstrEL1)&((dpsetconstrEL2)&((dpsetconstrER)&((funcImageSingleton)&((apProp)&((app)&((infuncsetfunc)&((ap2p)&((funcinfuncset)&((lamProp)&((lamp)&((lam2p)&((brelnall1)&((brelnall2)&((ex1E2)&((funcGraphProp1)&((funcGraphProp3)&((funcGraphProp2)&((funcextLem)&((funcGraphProp4)&((subbreln)&((eqbreln)&((funcext)&((funcext2)&((ap2apEq1)&((ap2apEq2)&((beta1)&((eta1)&((lam2lamEq)&((beta2)&((eta2)&((iffalseProp1)&((iffalseProp2)&((iftrueProp1)&((iftrueProp2)&((ifSingleton)&((ifp)&((theeq)&((iftrue)&((iffalse)&((iftrueorfalse)&((binintersectT_lem)&((binunionT_lem)&((powersetT_lem)&((setminusT_lem)&((complementT_lem)&((setextT)&((subsetTI)&((powersetTI1)&((powersetTE1)&((complementTI1)&((complementTE1)&((binintersectTELcontra)&((binintersectTERcontra)&((contrasubsetT)&((contrasubsetT1)&((contrasubsetT2)&((contrasubsetT3)&((doubleComplementI1)&((doubleComplementE1)&((doubleComplementSub1)&((doubleComplementSub2)&((doubleComplementEq)&((complementTnotintersectT)&((complementImpComplementIntersect)&((complementSubsetComplementIntersect)&((complementInPowersetComplementIntersect)&((contraSubsetComplement)&((complementTcontraSubset)&((binunionTILcontra)&((binunionTIRcontra)&((inIntersectImpInUnion)&((inIntersectImpInUnion2)&((inIntersectImpInIntersectUnions)&((intersectInPowersetIntersectUnions)&((inComplementUnionImpNotIn1)&((inComplementUnionImpInComplement1)&((binunionTE)&((binunionTEcontra)&((demorgan2a1)&((complementUnionInPowersetComplement)&((demorgan2a2)&((demorgan1a)&((demorgan1b)&((demorgan1)&((demorgan2a)&((demorgan2b2)&((demorgan2b)&((demorgan2)&((woz13rule0)&((woz13rule1)&((woz13rule2)&((woz13rule3)&((woz13rule4)&((woz1_1)&((woz1_2)&((woz1_3)&((woz1_4)&((woz1_5)&((breln1all2)&((breln1SetBreln1)&((choice2fnsingleton)&((setOfPairsIsBReln1)&((breln1all1)&((subbreln1)&((eqbreln1)&((breln1invprop)&((breln1invI)&((breln1invE)&((breln1compprop)&((breln1compI)&((breln1compE)&((breln1compEex)&((breln1unionprop)&((breln1unionIL)&((breln1unionIR)&((breln1unionI)&((breln1unionE)&((breln1unionEcases)&((breln1unionCommutes)&((woz2Ex)&((woz2W)&((woz2A)&((woz2B)&((image1Ex)&((image1Ex1)&((image1Equiv)&((image1E)&((image1I)&((injFuncInInjFuncSet)&((injFuncSetFuncIn)&((injFuncSetFuncInj)&((surjFuncSetFuncIn)&((surjFuncSetFuncSurj)&((leftInvIsSurj)&((surjCantorThm)&((((in @ (esk3_1 @ X251) @ X251)|((X251)=(emptyset)))&(((binintersect @ (esk3_1 @ X251) @ X251)=(emptyset))|((X251)=(emptyset))))&((notinself)&((notinself2)&((omegaSp)&((omegaSclos)&((peano0notS)&((peanoSinj)&((((in @ (esk4_1 @ X253) @ X253)|(~(in @ X255 @ X253)|(subset @ X255 @ X253)))&(~(subset @ (esk4_1 @ X253) @ X253)|(~(in @ X255 @ X253)|(subset @ X255 @ X253))))&(((((in @ (esk6_2 @ X256 @ X258) @ X258)|(~(in @ X260 @ (binintersect @ X256 @ X258))|(subset @ X260 @ (binintersect @ X256 @ X258)))|(in @ (esk5_1 @ X256) @ X256))&(~(subset @ (esk6_2 @ X256 @ X258) @ X258)|(~(in @ X260 @ (binintersect @ X256 @ X258))|(subset @ X260 @ (binintersect @ X256 @ X258)))|(in @ (esk5_1 @ X256) @ X256)))&(((in @ (esk6_2 @ X256 @ X258) @ X258)|(~(in @ X260 @ (binintersect @ X256 @ X258))|(subset @ X260 @ (binintersect @ X256 @ X258)))|~(subset @ (esk5_1 @ X256) @ X256))&(~(subset @ (esk6_2 @ X256 @ X258) @ X258)|(~(in @ X260 @ (binintersect @ X256 @ X258))|(subset @ X260 @ (binintersect @ X256 @ X258)))|~(subset @ (esk5_1 @ X256) @ X256))))&((((in @ (esk7_1 @ X261) @ X261)|(~(in @ X263 @ X261)|(~(in @ X264 @ X263)|(in @ X264 @ X261))))&(~(subset @ (esk7_1 @ X261) @ X261)|(~(in @ X263 @ X261)|(~(in @ X264 @ X263)|(in @ X264 @ X261)))))&((((in @ (esk8_1 @ X265) @ X265)|(~(in @ X268 @ (setunion @ X265))|(subset @ X268 @ (setunion @ X265))))&(((in @ (esk9_1 @ X265) @ (esk8_1 @ X265))|(~(in @ X268 @ (setunion @ X265))|(subset @ X268 @ (setunion @ X265))))&(~(subset @ (esk9_1 @ X265) @ (esk8_1 @ X265))|(~(in @ X268 @ (setunion @ X265))|(subset @ X268 @ (setunion @ X265))))))&(((((((((in @ (esk16_2 @ X269 @ X275) @ (powerset @ X275))|((in @ (esk15_2 @ X269 @ X275) @ X275)|~(epred2_1 @ X275))|(in @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&((((esk16_2 @ X269 @ X275)!=(emptyset))|((in @ (esk15_2 @ X269 @ X275) @ X275)|~(epred2_1 @ X275))|(in @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&(((in @ (esk17_3 @ X269 @ X275 @ X279) @ (esk16_2 @ X269 @ X275))|~(in @ X279 @ (esk16_2 @ X269 @ X275))|((in @ (esk15_2 @ X269 @ X275) @ X275)|~(epred2_1 @ X275))|(in @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&((((X279)!=(esk17_3 @ X269 @ X275 @ X279))|~(in @ X279 @ (esk16_2 @ X269 @ X275))|((in @ (esk15_2 @ X269 @ X275) @ X275)|~(epred2_1 @ X275))|(in @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&(~(in @ X279 @ (esk17_3 @ X269 @ X275 @ X279))|~(in @ X279 @ (esk16_2 @ X269 @ X275))|((in @ (esk15_2 @ X269 @ X275) @ X275)|~(epred2_1 @ X275))|(in @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))))))&(((in @ (esk16_2 @ X269 @ X275) @ (powerset @ X275))|((in @ (esk15_2 @ X269 @ X275) @ (esk15_2 @ X269 @ X275))|~(epred2_1 @ X275))|(in @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&((((esk16_2 @ X269 @ X275)!=(emptyset))|((in @ (esk15_2 @ X269 @ X275) @ (esk15_2 @ X269 @ X275))|~(epred2_1 @ X275))|(in @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&(((in @ (esk17_3 @ X269 @ X275 @ X279) @ (esk16_2 @ X269 @ X275))|~(in @ X279 @ (esk16_2 @ X269 @ X275))|((in @ (esk15_2 @ X269 @ X275) @ (esk15_2 @ X269 @ X275))|~(epred2_1 @ X275))|(in @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&((((X279)!=(esk17_3 @ X269 @ X275 @ X279))|~(in @ X279 @ (esk16_2 @ X269 @ X275))|((in @ (esk15_2 @ X269 @ X275) @ (esk15_2 @ X269 @ X275))|~(epred2_1 @ X275))|(in @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&(~(in @ X279 @ (esk17_3 @ X269 @ X275 @ X279))|~(in @ X279 @ (esk16_2 @ X269 @ X275))|((in @ (esk15_2 @ X269 @ X275) @ (esk15_2 @ X269 @ X275))|~(epred2_1 @ X275))|(in @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269))))))))&((((in @ (esk16_2 @ X269 @ X275) @ (powerset @ X275))|((in @ (esk15_2 @ X269 @ X275) @ X275)|~(epred2_1 @ X275))|~(subset @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&((((esk16_2 @ X269 @ X275)!=(emptyset))|((in @ (esk15_2 @ X269 @ X275) @ X275)|~(epred2_1 @ X275))|~(subset @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&(((in @ (esk17_3 @ X269 @ X275 @ X279) @ (esk16_2 @ X269 @ X275))|~(in @ X279 @ (esk16_2 @ X269 @ X275))|((in @ (esk15_2 @ X269 @ X275) @ X275)|~(epred2_1 @ X275))|~(subset @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&((((X279)!=(esk17_3 @ X269 @ X275 @ X279))|~(in @ X279 @ (esk16_2 @ X269 @ X275))|((in @ (esk15_2 @ X269 @ X275) @ X275)|~(epred2_1 @ X275))|~(subset @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))&(~(in @ X279 @ (esk17_3 @ X269 @ X275 @ X279))|~(in @ X279 @ (esk16_2 @ X269 @ X275))|((in @ (esk15_2 @ X269 @ X275) @ X275)|~(epred2_1 @ X275))|~(subset @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ X269)|~(epred1_1 @ X269))|(in @ (esk10_1 @ X269) @ X269)))))))&(((in @ (esk16_2 @ X269 @ X275) @ (powerset @ X275))|((in @ (esk15_2 @ X269 @ X275) @ (esk15_2 @ X269 @ X275))|~(epred2_1 @ X275))|~(subset @ (esk14_2 @ X269 @ X275) @ X275)|(~(in @ X281 @ (binintersect @ X269 @ X275))|(subset @ X281 @ (binintersect @ X269 @ X275)))|((in @ (esk12_1 @ X269) @ (powerset @ X269))|((in @ (esk11_1 @ X269) @ 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X273 @ (esk12_1 @ X269))|((in @ (esk11_1 @ X269) @ (esk11_1 @ X269))|~(epred1_1 @ X269))|~(subset @ (esk10_1 @ X269) @ X269)))))))))))))))&((((((in @ (esk20_1 @ X282) @ (powerset @ X282))|((in @ (esk19_1 @ X282) @ X282)|~(epred3_1 @ X282))|(in @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&((((esk20_1 @ X282)!=(emptyset))|((in @ (esk19_1 @ X282) @ X282)|~(epred3_1 @ X282))|(in @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&(((in @ (esk21_2 @ X282 @ X286) @ (esk20_1 @ X282))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ X282)|~(epred3_1 @ X282))|(in @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&((((X286)!=(esk21_2 @ X282 @ X286))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ X282)|~(epred3_1 @ X282))|(in @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&(~(in @ X286 @ (esk21_2 @ X282 @ X286))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ X282)|~(epred3_1 @ X282))|(in @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))))))&(((in @ (esk20_1 @ X282) @ (powerset @ X282))|((in @ (esk19_1 @ X282) @ (esk19_1 @ X282))|~(epred3_1 @ X282))|(in @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&((((esk20_1 @ X282)!=(emptyset))|((in @ (esk19_1 @ X282) @ (esk19_1 @ X282))|~(epred3_1 @ X282))|(in @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&(((in @ (esk21_2 @ X282 @ X286) @ (esk20_1 @ X282))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ (esk19_1 @ X282))|~(epred3_1 @ X282))|(in @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&((((X286)!=(esk21_2 @ X282 @ X286))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ (esk19_1 @ X282))|~(epred3_1 @ X282))|(in @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&(~(in @ X286 @ (esk21_2 @ X282 @ X286))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ (esk19_1 @ X282))|~(epred3_1 @ X282))|(in @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282)))))))))&((((in @ (esk20_1 @ X282) @ (powerset @ X282))|((in @ (esk19_1 @ X282) @ X282)|~(epred3_1 @ X282))|~(subset @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&((((esk20_1 @ X282)!=(emptyset))|((in @ (esk19_1 @ X282) @ X282)|~(epred3_1 @ X282))|~(subset @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&(((in @ (esk21_2 @ X282 @ X286) @ (esk20_1 @ X282))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ X282)|~(epred3_1 @ X282))|~(subset @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&((((X286)!=(esk21_2 @ X282 @ X286))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ X282)|~(epred3_1 @ X282))|~(subset @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&(~(in @ X286 @ (esk21_2 @ X282 @ X286))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ X282)|~(epred3_1 @ X282))|~(subset @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))))))&(((in @ (esk20_1 @ X282) @ (powerset @ X282))|((in @ (esk19_1 @ X282) @ (esk19_1 @ X282))|~(epred3_1 @ X282))|~(subset @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&((((esk20_1 @ X282)!=(emptyset))|((in @ (esk19_1 @ X282) @ (esk19_1 @ X282))|~(epred3_1 @ X282))|~(subset @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&(((in @ (esk21_2 @ X282 @ X286) @ (esk20_1 @ X282))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ (esk19_1 @ X282))|~(epred3_1 @ X282))|~(subset @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&((((X286)!=(esk21_2 @ X282 @ X286))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ (esk19_1 @ X282))|~(epred3_1 @ X282))|~(subset @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))&(~(in @ X286 @ (esk21_2 @ X282 @ X286))|~(in @ X286 @ (esk20_1 @ X282))|((in @ (esk19_1 @ X282) @ (esk19_1 @ X282))|~(epred3_1 @ X282))|~(subset @ (esk18_1 @ X282) @ X282)|(~(in @ X289 @ X282)|(~(in @ X288 @ X289)|(in @ X288 @ X282))))))))))&((((((in @ (esk24_1 @ X290) @ (powerset @ X290))|((in @ (esk23_1 @ X290) @ X290)|~(epred4_1 @ X290))|(in @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&((((esk24_1 @ X290)!=(emptyset))|((in @ (esk23_1 @ X290) @ X290)|~(epred4_1 @ X290))|(in @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&(((in @ (esk25_2 @ X290 @ X294) @ (esk24_1 @ X290))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ X290)|~(epred4_1 @ X290))|(in @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&((((X294)!=(esk25_2 @ X290 @ X294))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ X290)|~(epred4_1 @ X290))|(in @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&(~(in @ X294 @ (esk25_2 @ X290 @ X294))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ X290)|~(epred4_1 @ X290))|(in @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))))))&(((in @ (esk24_1 @ X290) @ (powerset @ X290))|((in @ (esk23_1 @ X290) @ (esk23_1 @ X290))|~(epred4_1 @ X290))|(in @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&((((esk24_1 @ X290)!=(emptyset))|((in @ (esk23_1 @ X290) @ (esk23_1 @ X290))|~(epred4_1 @ X290))|(in @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&(((in @ (esk25_2 @ X290 @ X294) @ (esk24_1 @ X290))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ (esk23_1 @ X290))|~(epred4_1 @ X290))|(in @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&((((X294)!=(esk25_2 @ X290 @ X294))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ (esk23_1 @ X290))|~(epred4_1 @ X290))|(in @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&(~(in @ X294 @ (esk25_2 @ X290 @ X294))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ (esk23_1 @ X290))|~(epred4_1 @ X290))|(in @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290))))))))&((((in @ (esk24_1 @ X290) @ (powerset @ X290))|((in @ (esk23_1 @ X290) @ X290)|~(epred4_1 @ X290))|~(subset @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&((((esk24_1 @ X290)!=(emptyset))|((in @ (esk23_1 @ X290) @ X290)|~(epred4_1 @ X290))|~(subset @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&(((in @ (esk25_2 @ X290 @ X294) @ (esk24_1 @ X290))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ X290)|~(epred4_1 @ X290))|~(subset @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&((((X294)!=(esk25_2 @ X290 @ X294))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ X290)|~(epred4_1 @ X290))|~(subset @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&(~(in @ X294 @ (esk25_2 @ X290 @ X294))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ X290)|~(epred4_1 @ X290))|~(subset @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))))))&(((in @ (esk24_1 @ X290) @ (powerset @ X290))|((in @ (esk23_1 @ X290) @ (esk23_1 @ X290))|~(epred4_1 @ X290))|~(subset @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&((((esk24_1 @ X290)!=(emptyset))|((in @ (esk23_1 @ X290) @ (esk23_1 @ X290))|~(epred4_1 @ X290))|~(subset @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&(((in @ (esk25_2 @ X290 @ X294) @ (esk24_1 @ X290))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ (esk23_1 @ X290))|~(epred4_1 @ X290))|~(subset @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&((((X294)!=(esk25_2 @ X290 @ X294))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ (esk23_1 @ X290))|~(epred4_1 @ X290))|~(subset @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))&(~(in @ X294 @ (esk25_2 @ X290 @ X294))|~(in @ X294 @ (esk24_1 @ X290))|((in @ (esk23_1 @ X290) @ (esk23_1 @ X290))|~(epred4_1 @ X290))|~(subset @ (esk22_1 @ X290) @ X290)|(~(in @ X296 @ X290)|(subset @ X296 @ X290)))))))))&((~(in @ X298 @ esk26_0)|(epred5_1 @ X298))&((in @ esk27_0 @ (setunion @ esk26_0))&~(subset @ esk27_0 @ (setunion @ esk26_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_45])])])])])])])).
% 1.36/0.52 thf(c_0_48, plain, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ X3))|~((epred5_1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_46])).
% 1.36/0.52 thf(c_0_49, negated_conjecture, ![X2:$i]:(((epred5_1 @ X2)|~((in @ X2 @ esk26_0)))), inference(split_conjunct,[status(thm)],[c_0_47])).
% 1.36/0.52 thf(c_0_50, negated_conjecture, ![X3:$i, X2:$i]:(((subset @ X3 @ (setunion @ X2))|~((subset @ (esk9_1 @ X2) @ (esk8_1 @ X2)))|~((in @ X3 @ (setunion @ X2))))), inference(split_conjunct,[status(thm)],[c_0_47])).
% 1.36/0.52 thf(c_0_51, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X3 @ esk26_0))|~((in @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_48, c_0_49])).
% 1.36/0.52 thf(c_0_52, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk9_1 @ X2) @ (esk8_1 @ X2))|(subset @ X3 @ (setunion @ X2))|~((in @ X3 @ (setunion @ X2))))), inference(split_conjunct,[status(thm)],[c_0_47])).
% 1.36/0.52 thf(c_0_53, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk8_1 @ X2) @ X2)|(subset @ X3 @ (setunion @ X2))|~((in @ X3 @ (setunion @ X2))))), inference(split_conjunct,[status(thm)],[c_0_47])).
% 1.36/0.52 thf(c_0_54, negated_conjecture, (in @ esk27_0 @ (setunion @ esk26_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
% 1.36/0.52 thf(c_0_55, negated_conjecture, ~((subset @ esk27_0 @ (setunion @ esk26_0))), inference(split_conjunct,[status(thm)],[c_0_47])).
% 1.36/0.52 thf(c_0_56, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ (setunion @ X3))|~((in @ (esk8_1 @ X3) @ esk26_0))|~((in @ X2 @ (setunion @ X3))))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_52])).
% 1.36/0.52 thf(c_0_57, negated_conjecture, (in @ (esk8_1 @ esk26_0) @ esk26_0), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_55])).
% 1.36/0.52 thf(c_0_58, negated_conjecture, ![X2:$i]:(((subset @ X2 @ (setunion @ esk26_0))|~((in @ X2 @ (setunion @ esk26_0))))), inference(spm,[status(thm)],[c_0_56, c_0_57])).
% 1.36/0.52 thf(c_0_59, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_58]), c_0_54])]), ['proof']).
% 1.36/0.52 % SZS output end CNFRefutation
% 1.36/0.52 % Parsed axioms : 740
% 1.36/0.52 % Removed by relevancy pruning/SinE : 722
% 1.36/0.52 % Initial clauses : 910
% 1.36/0.52 % Removed in clause preprocessing : 1
% 1.36/0.52 % Initial clauses in saturation : 909
% 1.36/0.52 % Processed clauses : 801
% 1.36/0.52 % ...of these trivial : 2
% 1.36/0.52 % ...subsumed : 8
% 1.36/0.52 % ...remaining for further processing : 791
% 1.36/0.52 % Other redundant clauses eliminated : 1
% 1.36/0.52 % Clauses deleted for lack of memory : 0
% 1.36/0.52 % Backward-subsumed : 1
% 1.36/0.52 % Backward-rewritten : 0
% 1.36/0.52 % Generated clauses : 11960
% 1.36/0.52 % ...of the previous two non-redundant : 11799
% 1.36/0.52 % ...aggressively subsumed : 0
% 1.36/0.52 % Contextual simplify-reflections : 2
% 1.36/0.52 % Paramodulations : 11959
% 1.36/0.52 % Factorizations : 0
% 1.36/0.52 % NegExts : 0
% 1.36/0.52 % Equation resolutions : 1
% 1.36/0.52 % Disequality decompositions : 0
% 1.36/0.52 % Total rewrite steps : 85
% 1.36/0.52 % ...of those cached : 77
% 1.36/0.52 % Propositional unsat checks : 0
% 1.36/0.52 % Propositional check models : 0
% 1.36/0.52 % Propositional check unsatisfiable : 0
% 1.36/0.52 % Propositional clauses : 0
% 1.36/0.52 % Propositional clauses after purity: 0
% 1.36/0.52 % Propositional unsat core size : 0
% 1.36/0.52 % Propositional preprocessing time : 0.000
% 1.36/0.52 % Propositional encoding time : 0.000
% 1.36/0.52 % Propositional solver time : 0.000
% 1.36/0.52 % Success case prop preproc time : 0.000
% 1.36/0.52 % Success case prop encoding time : 0.000
% 1.36/0.52 % Success case prop solver time : 0.000
% 1.36/0.52 % Current number of processed clauses : 789
% 1.36/0.52 % Positive orientable unit clauses : 331
% 1.36/0.52 % Positive unorientable unit clauses: 0
% 1.36/0.52 % Negative unit clauses : 3
% 1.36/0.52 % Non-unit-clauses : 455
% 1.36/0.52 % Current number of unprocessed clauses: 11907
% 1.36/0.52 % ...number of literals in the above : 76890
% 1.36/0.52 % Current number of archived formulas : 0
% 1.36/0.52 % Current number of archived clauses : 1
% 1.36/0.52 % Clause-clause subsumption calls (NU) : 14358
% 1.36/0.52 % Rec. Clause-clause subsumption calls : 4310
% 1.36/0.52 % Non-unit clause-clause subsumptions : 7
% 1.36/0.52 % Unit Clause-clause subsumption calls : 7
% 1.36/0.52 % Rewrite failures with RHS unbound : 0
% 1.36/0.52 % BW rewrite match attempts : 0
% 1.36/0.52 % BW rewrite match successes : 0
% 1.36/0.52 % Condensation attempts : 0
% 1.36/0.52 % Condensation successes : 0
% 1.36/0.52 % Termbank termtop insertions : 335647
% 1.36/0.52 % Search garbage collected termcells : 13872
% 1.36/0.52
% 1.36/0.52 % -------------------------------------------------
% 1.36/0.52 % User time : 0.167 s
% 1.36/0.52 % System time : 0.011 s
% 1.36/0.52 % Total time : 0.178 s
% 1.36/0.52 % Maximum resident set size: 7556 pages
% 1.36/0.52
% 1.36/0.52 % -------------------------------------------------
% 1.36/0.52 % User time : 0.186 s
% 1.36/0.52 % System time : 0.021 s
% 1.36/0.52 % Total time : 0.207 s
% 1.36/0.52 % Maximum resident set size: 5888 pages
% 1.36/0.52 % E exiting
%------------------------------------------------------------------------------