%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU824^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:25:47 AM UTC 2026
% Result : Theorem 3.53s 0.94s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU824^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n011.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 14:35:01 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.26 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p
% 3.53/0.94 % Version: 3.5.1-ho
% 3.53/0.94 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.53/0.94 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.53/0.94 % Starting ehoh_best5 with 300s (1) cores
% 3.53/0.94 % Starting almost_fo_3_lam with 300s (1) cores
% 3.53/0.94 % Starting new_bool_5 with 300s (1) cores
% 3.53/0.94 % Starting pre_casc_3 with 300s (1) cores
% 3.53/0.94 % Starting ho_unfolding_8 with 300s (1) cores
% 3.53/0.94 % Starting new_ho_10_cnf2 with 300s (1) cores
% 3.53/0.94 % Starting new_bool_3 with 300s (1) cores
% 3.53/0.94 % Starting new_ho_5 with 300s (1) cores
% 3.53/0.94 % new_ho_5 with pid 170729 completed with status 0
% 3.53/0.94 % Result found by new_ho_5
% 3.53/0.94 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.53/0.94 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.53/0.94 % Starting ehoh_best5 with 300s (1) cores
% 3.53/0.94 % Starting almost_fo_3_lam with 300s (1) cores
% 3.53/0.94 % Starting new_bool_5 with 300s (1) cores
% 3.53/0.94 % Starting pre_casc_3 with 300s (1) cores
% 3.53/0.94 % Starting ho_unfolding_8 with 300s (1) cores
% 3.53/0.94 % Starting new_ho_10_cnf2 with 300s (1) cores
% 3.53/0.94 % Starting new_bool_3 with 300s (1) cores
% 3.53/0.94 % Starting new_ho_5 with 300s (1) cores
% 3.53/0.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
% 3.53/0.94 % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 3.53/0.94 % Search class: HGHSF-FSLM31-SHFMMFBN
% 3.53/0.94 % partial match(2): HGHSM-FSLM31-SHFMMSBN
% 3.53/0.94 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.53/0.94 % Starting SubtermCWHack with 28s (1) cores
% 3.53/0.94 % SubtermCWHack with pid 170731 completed with status 0
% 3.53/0.94 % Result found by SubtermCWHack
% 3.53/0.94 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.53/0.94 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.53/0.94 % Starting ehoh_best5 with 300s (1) cores
% 3.53/0.94 % Starting almost_fo_3_lam with 300s (1) cores
% 3.53/0.94 % Starting new_bool_5 with 300s (1) cores
% 3.53/0.94 % Starting pre_casc_3 with 300s (1) cores
% 3.53/0.94 % Starting ho_unfolding_8 with 300s (1) cores
% 3.53/0.94 % Starting new_ho_10_cnf2 with 300s (1) cores
% 3.53/0.94 % Starting new_bool_3 with 300s (1) cores
% 3.53/0.94 % Starting new_ho_5 with 300s (1) cores
% 3.53/0.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
% 3.53/0.94 % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 3.53/0.94 % Search class: HGHSF-FSLM31-SHFMMFBN
% 3.53/0.94 % partial match(2): HGHSM-FSLM31-SHFMMSBN
% 3.53/0.94 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.53/0.94 % Starting SubtermCWHack with 28s (1) cores
% 3.53/0.94 % Preprocessing time : 0.007 s
% 3.53/0.94
% 3.53/0.94 % Proof found!
% 3.53/0.94 % SZS status Theorem
% 3.53/0.94 % SZS output start CNFRefutation
% 3.53/0.94 thf(decl_23, type, in: $i > $i > $o).
% 3.53/0.94 thf(decl_25, type, setextAx: $o).
% 3.53/0.94 thf(decl_26, type, emptyset: $i).
% 3.53/0.94 thf(decl_27, type, emptysetAx: $o).
% 3.53/0.94 thf(decl_29, type, setadjoinAx: $o).
% 3.53/0.94 thf(decl_30, type, powerset: $i > $i).
% 3.53/0.94 thf(decl_31, type, powersetAx: $o).
% 3.53/0.94 thf(decl_32, type, setunion: $i > $i).
% 3.53/0.94 thf(decl_33, type, setunionAx: $o).
% 3.53/0.94 thf(decl_35, type, omega0Ax: $o).
% 3.53/0.94 thf(decl_36, type, omegaSAx: $o).
% 3.53/0.94 thf(decl_37, type, omegaIndAx: $o).
% 3.53/0.94 thf(decl_38, type, replAx: $o).
% 3.53/0.94 thf(decl_39, type, foundationAx: $o).
% 3.53/0.94 thf(decl_40, type, wellorderingAx: $o).
% 3.53/0.94 thf(decl_42, type, descrp: $o).
% 3.53/0.94 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 3.53/0.94 thf(decl_44, type, dsetconstrI: $o).
% 3.53/0.94 thf(decl_45, type, dsetconstrEL: $o).
% 3.53/0.94 thf(decl_46, type, dsetconstrER: $o).
% 3.53/0.94 thf(decl_47, type, exuE1: $o).
% 3.53/0.94 thf(decl_49, type, prop2setE: $o).
% 3.53/0.94 thf(decl_50, type, emptysetE: $o).
% 3.53/0.94 thf(decl_51, type, emptysetimpfalse: $o).
% 3.53/0.94 thf(decl_52, type, notinemptyset: $o).
% 3.53/0.94 thf(decl_53, type, exuE3e: $o).
% 3.53/0.94 thf(decl_54, type, setext: $o).
% 3.53/0.94 thf(decl_55, type, emptyI: $o).
% 3.53/0.94 thf(decl_56, type, noeltsimpempty: $o).
% 3.53/0.94 thf(decl_57, type, setbeta: $o).
% 3.53/0.94 thf(decl_58, type, nonempty: $i > $o).
% 3.53/0.94 thf(decl_59, type, nonemptyE1: $o).
% 3.53/0.94 thf(decl_60, type, nonemptyI: $o).
% 3.53/0.94 thf(decl_61, type, nonemptyI1: $o).
% 3.53/0.94 thf(decl_62, type, setadjoinIL: $o).
% 3.53/0.94 thf(decl_63, type, emptyinunitempty: $o).
% 3.53/0.94 thf(decl_64, type, setadjoinIR: $o).
% 3.53/0.94 thf(decl_65, type, setadjoinE: $o).
% 3.53/0.94 thf(decl_66, type, setadjoinOr: $o).
% 3.53/0.94 thf(decl_67, type, setoftrueEq: $o).
% 3.53/0.94 thf(decl_68, type, powersetI: $o).
% 3.53/0.94 thf(decl_69, type, emptyinPowerset: $o).
% 3.53/0.94 thf(decl_70, type, emptyInPowerset: $o).
% 3.53/0.94 thf(decl_71, type, powersetE: $o).
% 3.53/0.94 thf(decl_72, type, setunionI: $o).
% 3.53/0.94 thf(decl_73, type, setunionE: $o).
% 3.53/0.94 thf(decl_74, type, subPowSU: $o).
% 3.53/0.94 thf(decl_75, type, exuE2: $o).
% 3.53/0.94 thf(decl_76, type, nonemptyImpWitness: $o).
% 3.53/0.94 thf(decl_77, type, uniqinunit: $o).
% 3.53/0.94 thf(decl_78, type, notinsingleton: $o).
% 3.53/0.94 thf(decl_79, type, eqinunit: $o).
% 3.53/0.94 thf(decl_80, type, singletonsswitch: $o).
% 3.53/0.94 thf(decl_81, type, upairsetE: $o).
% 3.53/0.94 thf(decl_82, type, upairsetIL: $o).
% 3.53/0.94 thf(decl_83, type, upairsetIR: $o).
% 3.53/0.94 thf(decl_84, type, emptyE1: $o).
% 3.53/0.94 thf(decl_85, type, vacuousDall: $o).
% 3.53/0.94 thf(decl_86, type, quantDeMorgan1: $o).
% 3.53/0.94 thf(decl_87, type, quantDeMorgan2: $o).
% 3.53/0.94 thf(decl_88, type, quantDeMorgan3: $o).
% 3.53/0.94 thf(decl_89, type, quantDeMorgan4: $o).
% 3.53/0.94 thf(decl_90, type, prop2setI: $o).
% 3.53/0.94 thf(decl_92, type, prop2set2propI: $o).
% 3.53/0.94 thf(decl_93, type, notdexE: $o).
% 3.53/0.94 thf(decl_94, type, notdallE: $o).
% 3.53/0.94 thf(decl_95, type, exuI1: $o).
% 3.53/0.94 thf(decl_96, type, exuI3: $o).
% 3.53/0.94 thf(decl_97, type, exuI2: $o).
% 3.53/0.94 thf(decl_98, type, inCongP: $o).
% 3.53/0.94 thf(decl_99, type, in__Cong: $o).
% 3.53/0.94 thf(decl_100, type, exuE3u: $o).
% 3.53/0.94 thf(decl_101, type, exu__Cong: $o).
% 3.53/0.94 thf(decl_102, type, emptyset__Cong: $o).
% 3.53/0.94 thf(decl_103, type, setadjoin__Cong: $o).
% 3.53/0.94 thf(decl_104, type, powerset__Cong: $o).
% 3.53/0.94 thf(decl_105, type, setunion__Cong: $o).
% 3.53/0.94 thf(decl_106, type, omega__Cong: $o).
% 3.53/0.94 thf(decl_107, type, exuEu: $o).
% 3.53/0.94 thf(decl_108, type, descr__Cong: $o).
% 3.53/0.94 thf(decl_109, type, dsetconstr__Cong: $o).
% 3.53/0.94 thf(decl_110, type, subset: $i > $i > $o).
% 3.53/0.94 thf(decl_113, type, subsetI1: $o).
% 3.53/0.94 thf(decl_114, type, eqimpsubset2: $o).
% 3.53/0.94 thf(decl_115, type, eqimpsubset1: $o).
% 3.53/0.94 thf(decl_116, type, subsetI2: $o).
% 3.53/0.94 thf(decl_117, type, emptysetsubset: $o).
% 3.53/0.94 thf(decl_118, type, subsetE: $o).
% 3.53/0.94 thf(decl_119, type, subsetE2: $o).
% 3.53/0.94 thf(decl_120, type, notsubsetI: $o).
% 3.53/0.94 thf(decl_121, type, notequalI1: $o).
% 3.53/0.94 thf(decl_122, type, notequalI2: $o).
% 3.53/0.94 thf(decl_123, type, subsetRefl: $o).
% 3.53/0.94 thf(decl_124, type, subsetTrans: $o).
% 3.53/0.94 thf(decl_125, type, setadjoinSub: $o).
% 3.53/0.94 thf(decl_126, type, setadjoinSub2: $o).
% 3.53/0.94 thf(decl_127, type, subset2powerset: $o).
% 3.53/0.94 thf(decl_128, type, setextsub: $o).
% 3.53/0.94 thf(decl_129, type, subsetemptysetimpeq: $o).
% 3.53/0.94 thf(decl_130, type, powersetI1: $o).
% 3.53/0.94 thf(decl_131, type, powersetE1: $o).
% 3.53/0.94 thf(decl_132, type, inPowerset: $o).
% 3.53/0.94 thf(decl_133, type, powersetsubset: $o).
% 3.53/0.94 thf(decl_134, type, sepInPowerset: $o).
% 3.53/0.94 thf(decl_135, type, sepSubset: $o).
% 3.53/0.94 thf(decl_137, type, binunionIL: $o).
% 3.53/0.94 thf(decl_138, type, upairset2IR: $o).
% 3.53/0.94 thf(decl_139, type, binunionIR: $o).
% 3.53/0.94 thf(decl_140, type, binunionEcases: $o).
% 3.53/0.94 thf(decl_141, type, binunionE: $o).
% 3.53/0.94 thf(decl_142, type, binunionLsub: $o).
% 3.53/0.94 thf(decl_143, type, binunionRsub: $o).
% 3.53/0.94 thf(decl_144, type, binintersect: $i > $i > $i).
% 3.53/0.94 thf(decl_145, type, binintersectI: $o).
% 3.53/0.94 thf(decl_146, type, binintersectSubset5: $o).
% 3.53/0.94 thf(decl_147, type, binintersectEL: $o).
% 3.53/0.94 thf(decl_148, type, binintersectLsub: $o).
% 3.53/0.94 thf(decl_149, type, binintersectSubset2: $o).
% 3.53/0.94 thf(decl_150, type, binintersectSubset3: $o).
% 3.53/0.94 thf(decl_151, type, binintersectER: $o).
% 3.53/0.94 thf(decl_152, type, disjointsetsI1: $o).
% 3.53/0.94 thf(decl_153, type, binintersectRsub: $o).
% 3.53/0.94 thf(decl_154, type, binintersectSubset4: $o).
% 3.53/0.94 thf(decl_155, type, binintersectSubset1: $o).
% 3.53/0.94 thf(decl_156, type, bs114d: $o).
% 3.53/0.94 thf(decl_159, type, setminusI: $o).
% 3.53/0.94 thf(decl_160, type, setminusEL: $o).
% 3.53/0.94 thf(decl_161, type, setminusER: $o).
% 3.53/0.94 thf(decl_162, type, setminusSubset2: $o).
% 3.53/0.94 thf(decl_163, type, setminusERneg: $o).
% 3.53/0.94 thf(decl_164, type, setminusELneg: $o).
% 3.53/0.94 thf(decl_165, type, setminusILneg: $o).
% 3.53/0.94 thf(decl_166, type, setminusIRneg: $o).
% 3.53/0.94 thf(decl_167, type, setminusLsub: $o).
% 3.53/0.94 thf(decl_168, type, setminusSubset1: $o).
% 3.53/0.94 thf(decl_170, type, symdiffE: $o).
% 3.53/0.94 thf(decl_171, type, symdiffI1: $o).
% 3.53/0.94 thf(decl_172, type, symdiffI2: $o).
% 3.53/0.94 thf(decl_173, type, symdiffIneg1: $o).
% 3.53/0.94 thf(decl_174, type, symdiffIneg2: $o).
% 3.53/0.94 thf(decl_176, type, secondinupair: $o).
% 3.53/0.94 thf(decl_177, type, setukpairIL: $o).
% 3.53/0.94 thf(decl_178, type, setukpairIR: $o).
% 3.53/0.94 thf(decl_179, type, kpairiskpair: $o).
% 3.53/0.94 thf(decl_181, type, kpairp: $o).
% 3.53/0.94 thf(decl_183, type, singletonsubset: $o).
% 3.53/0.94 thf(decl_184, type, singletoninpowerset: $o).
% 3.53/0.94 thf(decl_185, type, singletoninpowunion: $o).
% 3.53/0.94 thf(decl_186, type, upairset2E: $o).
% 3.53/0.94 thf(decl_187, type, upairsubunion: $o).
% 3.53/0.94 thf(decl_188, type, upairinpowunion: $o).
% 3.53/0.94 thf(decl_189, type, ubforcartprodlem1: $o).
% 3.53/0.94 thf(decl_190, type, ubforcartprodlem2: $o).
% 3.53/0.94 thf(decl_191, type, ubforcartprodlem3: $o).
% 3.53/0.94 thf(decl_192, type, cartprodpairin: $o).
% 3.53/0.94 thf(decl_193, type, cartprodmempair1: $o).
% 3.53/0.94 thf(decl_194, type, cartprodmempair: $o).
% 3.53/0.94 thf(decl_195, type, setunionE2: $o).
% 3.53/0.94 thf(decl_196, type, setunionsingleton1: $o).
% 3.53/0.94 thf(decl_197, type, setunionsingleton2: $o).
% 3.53/0.94 thf(decl_198, type, setunionsingleton: $o).
% 3.53/0.94 thf(decl_200, type, singletonprop: $o).
% 3.53/0.94 thf(decl_202, type, ex1E1: $o).
% 3.53/0.94 thf(decl_203, type, ex1I: $o).
% 3.53/0.94 thf(decl_204, type, ex1I2: $o).
% 3.53/0.94 thf(decl_205, type, singletonsuniq: $o).
% 3.53/0.94 thf(decl_210, type, setukpairinjL1: $o).
% 3.53/0.94 thf(decl_211, type, kfstsingleton: $o).
% 3.53/0.94 thf(decl_212, type, theprop: $o).
% 3.53/0.94 thf(decl_214, type, kfstpairEq: $o).
% 3.53/0.94 thf(decl_215, type, cartprodfstin: $o).
% 3.53/0.94 thf(decl_216, type, setukpairinjL2: $o).
% 3.53/0.94 thf(decl_217, type, setukpairinjL: $o).
% 3.53/0.94 thf(decl_218, type, setukpairinjR11: $o).
% 3.53/0.94 thf(decl_219, type, setukpairinjR12: $o).
% 3.53/0.94 thf(decl_220, type, setukpairinjR1: $o).
% 3.53/0.94 thf(decl_221, type, upairequniteq: $o).
% 3.53/0.94 thf(decl_222, type, setukpairinjR2: $o).
% 3.53/0.94 thf(decl_223, type, setukpairinjR: $o).
% 3.53/0.94 thf(decl_224, type, ksndsingleton: $o).
% 3.53/0.94 thf(decl_226, type, ksndpairEq: $o).
% 3.53/0.94 thf(decl_227, type, kpairsurjEq: $o).
% 3.53/0.94 thf(decl_228, type, cartprodsndin: $o).
% 3.53/0.94 thf(decl_229, type, cartprodpairmemEL: $o).
% 3.53/0.94 thf(decl_230, type, cartprodpairmemER: $o).
% 3.53/0.94 thf(decl_231, type, cartprodmempaircEq: $o).
% 3.53/0.94 thf(decl_232, type, cartprodfstpairEq: $o).
% 3.53/0.94 thf(decl_233, type, cartprodsndpairEq: $o).
% 3.53/0.94 thf(decl_234, type, cartprodpairsurjEq: $o).
% 3.53/0.94 thf(decl_237, type, dpsetconstrI: $o).
% 3.53/0.94 thf(decl_238, type, dpsetconstrSub: $o).
% 3.53/0.94 thf(decl_239, type, setOfPairsIsBReln: $o).
% 3.53/0.94 thf(decl_240, type, dpsetconstrERa: $o).
% 3.53/0.94 thf(decl_241, type, dpsetconstrEL1: $o).
% 3.53/0.94 thf(decl_242, type, dpsetconstrEL2: $o).
% 3.53/0.94 thf(decl_243, type, dpsetconstrER: $o).
% 3.53/0.94 thf(decl_246, type, funcImageSingleton: $o).
% 3.53/0.94 thf(decl_247, type, apProp: $o).
% 3.53/0.94 thf(decl_249, type, app: $o).
% 3.53/0.94 thf(decl_250, type, infuncsetfunc: $o).
% 3.53/0.94 thf(decl_251, type, ap2p: $o).
% 3.53/0.94 thf(decl_252, type, funcinfuncset: $o).
% 3.53/0.94 thf(decl_253, type, lamProp: $o).
% 3.53/0.94 thf(decl_255, type, lamp: $o).
% 3.53/0.94 thf(decl_256, type, lam2p: $o).
% 3.53/0.94 thf(decl_257, type, brelnall1: $o).
% 3.53/0.94 thf(decl_258, type, brelnall2: $o).
% 3.53/0.94 thf(decl_259, type, ex1E2: $o).
% 3.53/0.94 thf(decl_260, type, funcGraphProp1: $o).
% 3.53/0.94 thf(decl_261, type, funcGraphProp3: $o).
% 3.53/0.94 thf(decl_262, type, funcGraphProp2: $o).
% 3.53/0.94 thf(decl_263, type, funcextLem: $o).
% 3.53/0.94 thf(decl_264, type, funcGraphProp4: $o).
% 3.53/0.94 thf(decl_265, type, subbreln: $o).
% 3.53/0.94 thf(decl_266, type, eqbreln: $o).
% 3.53/0.94 thf(decl_267, type, funcext: $o).
% 3.53/0.94 thf(decl_268, type, funcext2: $o).
% 3.53/0.94 thf(decl_269, type, ap2apEq1: $o).
% 3.53/0.94 thf(decl_270, type, ap2apEq2: $o).
% 3.53/0.94 thf(decl_271, type, beta1: $o).
% 3.53/0.94 thf(decl_272, type, eta1: $o).
% 3.53/0.94 thf(decl_273, type, lam2lamEq: $o).
% 3.53/0.94 thf(decl_274, type, beta2: $o).
% 3.53/0.94 thf(decl_275, type, eta2: $o).
% 3.53/0.94 thf(decl_276, type, iffalseProp1: $o).
% 3.53/0.94 thf(decl_277, type, iffalseProp2: $o).
% 3.53/0.94 thf(decl_278, type, iftrueProp1: $o).
% 3.53/0.94 thf(decl_279, type, iftrueProp2: $o).
% 3.53/0.94 thf(decl_280, type, ifSingleton: $o).
% 3.53/0.94 thf(decl_282, type, ifp: $o).
% 3.53/0.94 thf(decl_283, type, theeq: $o).
% 3.53/0.94 thf(decl_284, type, iftrue: $o).
% 3.53/0.94 thf(decl_285, type, iffalse: $o).
% 3.53/0.94 thf(decl_286, type, iftrueorfalse: $o).
% 3.53/0.94 thf(decl_287, type, binintersectT_lem: $o).
% 3.53/0.94 thf(decl_288, type, binunionT_lem: $o).
% 3.53/0.94 thf(decl_289, type, powersetT_lem: $o).
% 3.53/0.94 thf(decl_290, type, setminusT_lem: $o).
% 3.53/0.94 thf(decl_291, type, complementT_lem: $o).
% 3.53/0.94 thf(decl_292, type, setextT: $o).
% 3.53/0.94 thf(decl_293, type, subsetTI: $o).
% 3.53/0.94 thf(decl_294, type, powersetTI1: $o).
% 3.53/0.94 thf(decl_295, type, powersetTE1: $o).
% 3.53/0.94 thf(decl_296, type, complementTI1: $o).
% 3.53/0.94 thf(decl_297, type, complementTE1: $o).
% 3.53/0.94 thf(decl_298, type, binintersectTELcontra: $o).
% 3.53/0.94 thf(decl_299, type, binintersectTERcontra: $o).
% 3.53/0.94 thf(decl_300, type, contrasubsetT: $o).
% 3.53/0.94 thf(decl_301, type, contrasubsetT1: $o).
% 3.53/0.94 thf(decl_302, type, contrasubsetT2: $o).
% 3.53/0.94 thf(decl_303, type, contrasubsetT3: $o).
% 3.53/0.94 thf(decl_304, type, doubleComplementI1: $o).
% 3.53/0.94 thf(decl_305, type, doubleComplementE1: $o).
% 3.53/0.94 thf(decl_306, type, doubleComplementSub1: $o).
% 3.53/0.94 thf(decl_307, type, doubleComplementSub2: $o).
% 3.53/0.94 thf(decl_308, type, doubleComplementEq: $o).
% 3.53/0.94 thf(decl_309, type, complementTnotintersectT: $o).
% 3.53/0.94 thf(decl_310, type, complementImpComplementIntersect: $o).
% 3.53/0.94 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 3.53/0.94 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 3.53/0.94 thf(decl_313, type, contraSubsetComplement: $o).
% 3.53/0.94 thf(decl_314, type, complementTcontraSubset: $o).
% 3.53/0.94 thf(decl_315, type, binunionTILcontra: $o).
% 3.53/0.94 thf(decl_316, type, binunionTIRcontra: $o).
% 3.53/0.94 thf(decl_317, type, inIntersectImpInUnion: $o).
% 3.53/0.94 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 3.53/0.94 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 3.53/0.94 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 3.53/0.94 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 3.53/0.94 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 3.53/0.94 thf(decl_323, type, binunionTE: $o).
% 3.53/0.94 thf(decl_324, type, binunionTEcontra: $o).
% 3.53/0.94 thf(decl_325, type, demorgan2a1: $o).
% 3.53/0.94 thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 3.53/0.94 thf(decl_327, type, demorgan2a2: $o).
% 3.53/0.94 thf(decl_328, type, demorgan1a: $o).
% 3.53/0.94 thf(decl_329, type, demorgan1b: $o).
% 3.53/0.94 thf(decl_330, type, demorgan1: $o).
% 3.53/0.94 thf(decl_331, type, demorgan2a: $o).
% 3.53/0.94 thf(decl_332, type, demorgan2b2: $o).
% 3.53/0.94 thf(decl_333, type, demorgan2b: $o).
% 3.53/0.94 thf(decl_334, type, demorgan2: $o).
% 3.53/0.94 thf(decl_335, type, woz13rule0: $o).
% 3.53/0.94 thf(decl_336, type, woz13rule1: $o).
% 3.53/0.94 thf(decl_337, type, woz13rule2: $o).
% 3.53/0.94 thf(decl_338, type, woz13rule3: $o).
% 3.53/0.94 thf(decl_339, type, woz13rule4: $o).
% 3.53/0.94 thf(decl_340, type, woz1_1: $o).
% 3.53/0.94 thf(decl_341, type, woz1_2: $o).
% 3.53/0.94 thf(decl_342, type, woz1_3: $o).
% 3.53/0.94 thf(decl_343, type, woz1_4: $o).
% 3.53/0.94 thf(decl_344, type, woz1_5: $o).
% 3.53/0.94 thf(decl_346, type, breln1all2: $o).
% 3.53/0.94 thf(decl_348, type, breln1SetBreln1: $o).
% 3.53/0.94 thf(decl_355, type, choice2fnsingleton: $o).
% 3.53/0.94 thf(decl_356, type, setOfPairsIsBReln1: $o).
% 3.53/0.94 thf(decl_357, type, breln1all1: $o).
% 3.53/0.94 thf(decl_358, type, subbreln1: $o).
% 3.53/0.94 thf(decl_359, type, eqbreln1: $o).
% 3.53/0.94 thf(decl_361, type, breln1invprop: $o).
% 3.53/0.94 thf(decl_362, type, breln1invI: $o).
% 3.53/0.94 thf(decl_363, type, breln1invE: $o).
% 3.53/0.94 thf(decl_365, type, breln1compprop: $o).
% 3.53/0.94 thf(decl_366, type, breln1compI: $o).
% 3.53/0.94 thf(decl_367, type, breln1compE: $o).
% 3.53/0.94 thf(decl_368, type, breln1compEex: $o).
% 3.53/0.94 thf(decl_369, type, breln1unionprop: $o).
% 3.53/0.94 thf(decl_370, type, breln1unionIL: $o).
% 3.53/0.94 thf(decl_371, type, breln1unionIR: $o).
% 3.53/0.94 thf(decl_372, type, breln1unionI: $o).
% 3.53/0.94 thf(decl_373, type, breln1unionE: $o).
% 3.53/0.94 thf(decl_374, type, breln1unionEcases: $o).
% 3.53/0.94 thf(decl_375, type, breln1unionCommutes: $o).
% 3.53/0.94 thf(decl_376, type, woz2Ex: $o).
% 3.53/0.94 thf(decl_377, type, woz2W: $o).
% 3.53/0.94 thf(decl_378, type, woz2A: $o).
% 3.53/0.94 thf(decl_379, type, woz2B: $o).
% 3.53/0.94 thf(decl_380, type, image1Ex: $o).
% 3.53/0.94 thf(decl_381, type, image1Ex1: $o).
% 3.53/0.94 thf(decl_383, type, image1Equiv: $o).
% 3.53/0.94 thf(decl_384, type, image1E: $o).
% 3.53/0.94 thf(decl_385, type, image1I: $o).
% 3.53/0.94 thf(decl_388, type, injFuncInInjFuncSet: $o).
% 3.53/0.94 thf(decl_389, type, injFuncSetFuncIn: $o).
% 3.53/0.94 thf(decl_390, type, injFuncSetFuncInj: $o).
% 3.53/0.94 thf(decl_393, type, surjFuncSetFuncIn: $o).
% 3.53/0.94 thf(decl_394, type, surjFuncSetFuncSurj: $o).
% 3.53/0.94 thf(decl_395, type, leftInvIsSurj: $o).
% 3.53/0.94 thf(decl_396, type, surjCantorThm: $o).
% 3.53/0.94 thf(decl_397, type, foundation2: $o).
% 3.53/0.94 thf(decl_398, type, notinself: $o).
% 3.53/0.94 thf(decl_399, type, notinself2: $o).
% 3.53/0.94 thf(decl_401, type, omegaSp: $o).
% 3.53/0.94 thf(decl_402, type, omegaSclos: $o).
% 3.53/0.94 thf(decl_403, type, peano0notS: $o).
% 3.53/0.94 thf(decl_407, type, peanoSinj: $o).
% 3.53/0.94 thf(decl_409, type, transitiveset: $i > $o).
% 3.53/0.94 thf(decl_410, type, transitivesetOp1: $o).
% 3.53/0.94 thf(decl_411, type, binintTransitive: $o).
% 3.53/0.94 thf(decl_412, type, transitivesetOp2: $o).
% 3.53/0.94 thf(decl_413, type, setunionTransitive: $o).
% 3.53/0.94 thf(decl_414, type, stricttotalorderedByIn: $i > $o).
% 3.53/0.94 thf(decl_415, type, wellorderedByIn: $i > $o).
% 3.53/0.94 thf(decl_416, type, ordinal: $i > $o).
% 3.53/0.94 thf(decl_418, type, ordinalMinLem1: $o).
% 3.53/0.94 thf(decl_419, type, ordinalTransSet: $o).
% 3.53/0.94 thf(decl_420, type, ordinalTransSet1: $o).
% 3.53/0.94 thf(decl_421, type, setunionOrdinalLem1: $o).
% 3.53/0.94 thf(decl_423, type, emptysetOrdinal: $o).
% 3.53/0.94 thf(decl_424, type, ordinalIrrefl: $o).
% 3.53/0.94 thf(decl_425, type, ordinalIrrefl2: $o).
% 3.53/0.94 thf(decl_426, type, ordinalNoCycle: $o).
% 3.53/0.94 thf(decl_427, type, epred1_1: $i > $o).
% 3.53/0.94 thf(decl_428, type, epred2_1: $i > $o).
% 3.53/0.94 thf(decl_429, type, epred3_1: $i > $o).
% 3.53/0.94 thf(decl_430, type, epred4_1: $i > $o).
% 3.53/0.94 thf(decl_431, type, esk1_1: $i > $i).
% 3.53/0.94 thf(decl_432, type, esk2_1: $i > $i).
% 3.53/0.94 thf(decl_433, type, esk3_1: $i > $i).
% 3.53/0.94 thf(decl_434, type, esk4_1: $i > $i).
% 3.53/0.94 thf(decl_435, type, esk5_1: $i > $i).
% 3.53/0.94 thf(decl_436, type, esk6_1: $i > $i).
% 3.53/0.94 thf(decl_437, type, esk7_2: $i > $i > $i).
% 3.53/0.94 thf(decl_438, type, esk8_2: $i > $i > $i).
% 3.53/0.94 thf(decl_439, type, esk9_2: $i > $i > $i).
% 3.53/0.94 thf(decl_440, type, esk10_3: $i > $i > $i > $i).
% 3.53/0.94 thf(decl_441, type, esk11_1: $i > $i).
% 3.53/0.94 thf(decl_442, type, esk12_1: $i > $i).
% 3.53/0.94 thf(decl_443, type, esk13_1: $i > $i).
% 3.53/0.94 thf(decl_444, type, esk14_2: $i > $i > $i).
% 3.53/0.94 thf(decl_445, type, esk15_0: $i).
% 3.53/0.94 thf(decl_446, type, esk16_0: $i).
% 3.53/0.94 thf(decl_447, type, esk17_0: $i).
% 3.53/0.94 thf(decl_448, type, esk18_0: $i).
% 3.53/0.94 thf(decl_464, type, esk34_2: $i > $i > $i).
% 3.53/0.94 thf(wellorderedByIn, axiom, ((wellorderedByIn)=(^[X4:$i]:((((stricttotalorderedByIn @ X4))&(![X21:$i]:((((in @ X21 @ (powerset @ X4)))=>((((nonempty @ X21))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', wellorderedByIn)).
% 3.53/0.94 thf(stricttotalorderedByIn, axiom, ((stricttotalorderedByIn)=(^[X4:$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/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', stricttotalorderedByIn)).
% 3.53/0.94 thf(ordinal, axiom, ((ordinal)=(^[X2:$i]:((((transitiveset @ X2))&((wellorderedByIn @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', ordinal)).
% 3.53/0.94 thf(ordinalTransIn, 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)=>((setunionOrdinalLem1)=>((emptysetOrdinal)=>((ordinalIrrefl)=>((ordinalIrrefl2)=>((ordinalNoCycle)=>![X21:$i]:(((ordinal @ X21)=>![X2:$i, X4:$i, X5:$i]:(((in @ X2 @ X4)=>((in @ X4 @ X5)=>((in @ X5 @ X21)=>(in @ X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', ordinalTransIn)).
% 3.53/0.94 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', nonemptyI)).
% 3.53/0.94 thf(setunionOrdinalLem1, axiom, ((setunionOrdinalLem1)<=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(ordinal @ X2)))=>(transitiveset @ (setunion @ X21))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', setunionOrdinalLem1)).
% 3.53/0.94 thf(ordinalMinLem1, axiom, ((ordinalMinLem1)<=>![X21:$i]:(((ordinal @ X21)=>![X48:$i]:(((ordinal @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', ordinalMinLem1)).
% 3.53/0.94 thf(foundation2, axiom, ((foundation2)<=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', foundation2)).
% 3.53/0.94 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', nonemptyImpWitness)).
% 3.53/0.94 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', nonemptyI1)).
% 3.53/0.94 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', nonemptyE1)).
% 3.53/0.94 thf(setunionTransitive, axiom, ((setunionTransitive)<=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(transitiveset @ X2)))=>(transitiveset @ (setunion @ X21))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', setunionTransitive)).
% 3.53/0.94 thf(transitivesetOp2, axiom, ((transitivesetOp2)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i, X2:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', transitivesetOp2)).
% 3.53/0.94 thf(binintTransitive, axiom, ((binintTransitive)<=>![X21:$i]:(((transitiveset @ X21)=>![X48:$i]:(((transitiveset @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', binintTransitive)).
% 3.53/0.94 thf(transitivesetOp1, axiom, ((transitivesetOp1)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.Gldj3VpHLv/E---3.1_170709.p', transitivesetOp1)).
% 3.53/0.94 thf(c_0_15, plain, ((wellorderedByIn)=(^[Z0:$i]:((((((((![X91:$i]:((((in @ X91 @ Z0))=>(![X92:$i]:((((in @ X92 @ Z0))=>(![X93:$i]:((((in @ X93 @ Z0))=>((((((in @ X91 @ X92))&((in @ X92 @ X93))))=>((in @ X91 @ X93)))))))))))))&(![X94:$i]:((((in @ X94 @ Z0))=>(![X95:$i]:((((in @ X95 @ Z0))=>(((((((X94)=(X95)))|((in @ X94 @ X95))))|((in @ X95 @ X94))))))))))))&(![X96:$i]:((((in @ X96 @ Z0))=>(~((in @ X96 @ X96)))))))))&(![X21:$i]:((((in @ X21 @ (powerset @ Z0)))=>((((nonempty @ X21))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), inference(fof_simplification,[status(thm)],[wellorderedByIn])).
% 3.53/0.94 thf(c_0_16, plain, ((stricttotalorderedByIn)=(^[Z0:$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])).
% 3.53/0.94 thf(c_0_17, plain, ((ordinal)=(^[Z0:$i]:((((transitiveset @ Z0))&(((((((((![X97:$i]:((((in @ X97 @ Z0))=>(![X98:$i]:((((in @ X98 @ Z0))=>(![X99:$i]:((((in @ X99 @ Z0))=>((((((in @ X97 @ X98))&((in @ X98 @ X99))))=>((in @ X97 @ X99)))))))))))))&(![X100:$i]:((((in @ X100 @ Z0))=>(![X101:$i]:((((in @ X101 @ Z0))=>(((((((X100)=(X101)))|((in @ X100 @ X101))))|((in @ X101 @ X100))))))))))))&(![X102:$i]:((((in @ X102 @ Z0))=>(~((in @ X102 @ X102)))))))))&(![X103:$i]:((((in @ X103 @ (powerset @ Z0)))=>((((nonempty @ X103))=>(?[X104:$i]:((((in @ X104 @ X103))&(![X105:$i]:((((in @ X105 @ X103))=>(((((X104)=(X105)))|((in @ X104 @ X105)))))))))))))))))))))), inference(fof_simplification,[status(thm)],[ordinal])).
% 3.53/0.94 thf(c_0_18, plain, ((wellorderedByIn)=(^[Z0:$i]:((((((((![X91:$i]:((((in @ X91 @ Z0))=>(![X92:$i]:((((in @ X92 @ Z0))=>(![X93:$i]:((((in @ X93 @ Z0))=>((((((in @ X91 @ X92))&((in @ X92 @ X93))))=>((in @ X91 @ X93)))))))))))))&(![X94:$i]:((((in @ X94 @ Z0))=>(![X95:$i]:((((in @ X95 @ Z0))=>(((((((X94)=(X95)))|((in @ X94 @ X95))))|((in @ X95 @ X94))))))))))))&(![X96:$i]:((((in @ X96 @ Z0))=>(~((in @ X96 @ X96)))))))))&(![X21:$i]:((((in @ X21 @ (powerset @ Z0)))=>((((nonempty @ X21))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), inference(apply_def,[status(thm)],[c_0_15, c_0_16])).
% 3.53/0.94 thf(c_0_19, plain, ((ordinal)=(^[Z0:$i]:((((transitiveset @ Z0))&(((((((((![X97:$i]:((((in @ X97 @ Z0))=>(![X98:$i]:((((in @ X98 @ Z0))=>(![X99:$i]:((((in @ X99 @ Z0))=>((((((in @ X97 @ X98))&((in @ X98 @ X99))))=>((in @ X97 @ X99)))))))))))))&(![X100:$i]:((((in @ X100 @ Z0))=>(![X101:$i]:((((in @ X101 @ Z0))=>(((((((X100)=(X101)))|((in @ X100 @ X101))))|((in @ X101 @ X100))))))))))))&(![X102:$i]:((((in @ X102 @ Z0))=>(~((in @ X102 @ X102)))))))))&(![X103:$i]:((((in @ X103 @ (powerset @ Z0)))=>((((nonempty @ X103))=>(?[X104:$i]:((((in @ X104 @ X103))&(![X105:$i]:((((in @ X105 @ X103))=>(((((X104)=(X105)))|((in @ X104 @ X105)))))))))))))))))))))), inference(apply_def,[status(thm)],[c_0_17, c_0_18])).
% 3.53/0.94 thf(c_0_20, 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)=>((setunionOrdinalLem1)=>((emptysetOrdinal)=>((ordinalIrrefl)=>((ordinalIrrefl2)=>((ordinalNoCycle)=>![X21:$i]:(((ordinal @ X21)=>![X2:$i, X4:$i, X5:$i]:(((in @ X2 @ X4)=>((in @ X4 @ X5)=>((in @ X5 @ X21)=>(in @ X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[ordinalTransIn])).
% 3.53/0.94 thf(c_0_21, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 3.53/0.94 thf(c_0_22, axiom, ((setunionOrdinalLem1)=(![X21:$i]:(((![X2:$i]:((((in @ X2 @ X21))=>(((((transitiveset @ X2))&(((((((((![X124:$i]:((((in @ X124 @ X2))=>(![X125:$i]:((((in @ X125 @ X2))=>(![X126:$i]:((((in @ X126 @ X2))=>((((((in @ X124 @ X125))&((in @ X125 @ X126))))=>((in @ X124 @ X126)))))))))))))&(![X127:$i]:((((in @ X127 @ X2))=>(![X128:$i]:((((in @ X128 @ X2))=>(((((((X127)=(X128)))|((in @ X127 @ X128))))|((in @ X128 @ X127))))))))))))&(![X129:$i]:((((in @ X129 @ X2))=>(~((in @ X129 @ X129)))))))))&(![X130:$i]:((((in @ X130 @ (powerset @ X2)))=>((((nonempty @ X130))=>(?[X131:$i]:((((in @ X131 @ X130))&(![X132:$i]:((((in @ X132 @ X130))=>(((((X131)=(X132)))|((in @ X131 @ X132))))))))))))))))))))))))=>((transitiveset @ (setunion @ X21))))))), inference(apply_def,[status(thm)],[setunionOrdinalLem1, c_0_19])).
% 3.53/0.94 thf(c_0_23, axiom, ((ordinalMinLem1)=(![X21:$i]:(((((((transitiveset @ X21))&(((((((((![X106:$i]:((((in @ X106 @ X21))=>(![X107:$i]:((((in @ X107 @ X21))=>(![X108:$i]:((((in @ X108 @ X21))=>((((((in @ X106 @ X107))&((in @ X107 @ X108))))=>((in @ X106 @ X108)))))))))))))&(![X109:$i]:((((in @ X109 @ X21))=>(![X110:$i]:((((in @ X110 @ X21))=>(((((((X109)=(X110)))|((in @ X109 @ X110))))|((in @ X110 @ X109))))))))))))&(![X111:$i]:((((in @ X111 @ X21))=>(~((in @ X111 @ X111)))))))))&(![X112:$i]:((((in @ X112 @ (powerset @ X21)))=>((((nonempty @ X112))=>(?[X113:$i]:((((in @ X113 @ X112))&(![X114:$i]:((((in @ X114 @ X112))=>(((((X113)=(X114)))|((in @ X113 @ X114)))))))))))))))))))))=>(![X48:$i]:(((((((transitiveset @ X48))&(((((((((![X115:$i]:((((in @ X115 @ X48))=>(![X116:$i]:((((in @ X116 @ X48))=>(![X117:$i]:((((in @ X117 @ X48))=>((((((in @ X115 @ X116))&((in @ X116 @ X117))))=>((in @ X115 @ X117)))))))))))))&(![X118:$i]:((((in @ X118 @ X48))=>(![X119:$i]:((((in @ X119 @ X48))=>(((((((X118)=(X119)))|((in @ X118 @ X119))))|((in @ X119 @ X118))))))))))))&(![X120:$i]:((((in @ X120 @ X48))=>(~((in @ X120 @ X120)))))))))&(![X121:$i]:((((in @ X121 @ (powerset @ X48)))=>((((nonempty @ X121))=>(?[X122:$i]:((((in @ X122 @ X121))&(![X123:$i]:((((in @ X123 @ X121))=>(((((X122)=(X123)))|((in @ X122 @ X123)))))))))))))))))))))=>((transitiveset @ (binintersect @ X21 @ X48)))))))))), inference(apply_def,[status(thm)],[ordinalMinLem1, c_0_19])).
% 3.53/0.94 thf(c_0_24, plain, ![X153:$i]:(((epred1_1 @ X153)<=>(![X154:$i]:(((in @ X154 @ X153)=>![X155:$i]:(((in @ X155 @ X153)=>![X156:$i]:(((in @ X156 @ X153)=>(((in @ X154 @ X155)&(in @ X155 @ X156))=>(in @ X154 @ X156))))))))&![X157:$i]:(((in @ X157 @ X153)=>![X158:$i]:(((in @ X158 @ X153)=>(((X157)=(X158))|(in @ X157 @ X158)|(in @ X158 @ X157))))))))), introduced(definition)).
% 3.53/0.94 thf(c_0_25, plain, ![X163:$i]:(((epred2_1 @ X163)<=>(![X164:$i]:(((in @ X164 @ X163)=>![X165:$i]:(((in @ X165 @ X163)=>![X166:$i]:(((in @ X166 @ X163)=>(((in @ X164 @ X165)&(in @ X165 @ X166))=>(in @ X164 @ X166))))))))&![X167:$i]:(((in @ X167 @ X163)=>![X168:$i]:(((in @ X168 @ X163)=>(((X167)=(X168))|(in @ X167 @ X168)|(in @ X168 @ X167))))))))), introduced(definition)).
% 3.53/0.94 thf(c_0_26, plain, ![X174:$i]:(((epred3_1 @ X174)<=>(![X175:$i]:(((in @ X175 @ X174)=>![X176:$i]:(((in @ X176 @ X174)=>![X177:$i]:(((in @ X177 @ X174)=>(((in @ X175 @ X176)&(in @ X176 @ X177))=>(in @ X175 @ X177))))))))&![X178:$i]:(((in @ X178 @ X174)=>![X179:$i]:(((in @ X179 @ X174)=>(((X178)=(X179))|(in @ X178 @ X179)|(in @ X179 @ X178))))))))), introduced(definition)).
% 3.53/0.94 thf(c_0_27, plain, ![X21:$i]:(((epred4_1 @ X21)<=>((transitiveset @ X21)&(((![X184:$i]:(((in @ X184 @ X21)=>![X185:$i]:(((in @ X185 @ X21)=>![X186:$i]:(((in @ X186 @ X21)=>(((in @ X184 @ X185)&(in @ X185 @ X186))=>(in @ X184 @ X186))))))))&![X187:$i]:(((in @ X187 @ X21)=>![X188:$i]:(((in @ X188 @ X21)=>(((X187)=(X188))|(in @ X187 @ X188)|(in @ X188 @ X187)))))))&![X189:$i]:(((in @ X189 @ X21)=>~(in @ X189 @ X189))))&![X190:$i]:(((in @ X190 @ (powerset @ X21))=>((nonempty @ X190)=>?[X191:$i]:(((in @ X191 @ X190)&![X192:$i]:(((in @ X192 @ X190)=>(((X191)=(X192))|(in @ X191 @ X192))))))))))))), introduced(definition)).
% 3.53/0.94 thf(c_0_28, 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)=>(![X133:$i]:(((nonempty @ X133)=>?[X134:$i]:((in @ X134 @ X133))))=>(![X135:$i, X136:$i > $o, X137:$i]:(((in @ X137 @ X135)=>((X136 @ X137)=>(nonempty @ (dsetconstr @ X135 @ X136)))))=>(![X138:$i]:((?[X139:$i]:((in @ X139 @ X138))=>(nonempty @ X138)))=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>(![X140:$i]:(((nonempty @ X140)=>?[X141:$i]:(((in @ X141 @ X140)&$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)=>(![X142:$i]:(((nonempty @ X142)=>?[X143:$i]:(((in @ X143 @ X142)&((binintersect @ X143 @ X142)=(emptyset))))))=>((notinself)=>((notinself2)=>((omegaSp)=>((omegaSclos)=>((peano0notS)=>((peanoSinj)=>(![X144:$i]:(((transitiveset @ X144)=>![X145:$i]:(((in @ X145 @ X144)=>(subset @ X145 @ X144)))))=>(![X146:$i]:(((transitiveset @ X146)=>![X147:$i]:(((transitiveset @ X147)=>(transitiveset @ (binintersect @ X146 @ X147))))))=>(![X148:$i]:(((transitiveset @ X148)=>![X149:$i, X150:$i]:(((in @ X149 @ X148)=>((in @ X150 @ X149)=>(in @ X150 @ X148))))))=>(![X151:$i]:((![X152:$i]:(((in @ X152 @ X151)=>(transitiveset @ X152)))=>(transitiveset @ (setunion @ X151))))=>(![X153:$i]:((((transitiveset @ X153)&(((epred1_1 @ X153)&![X159:$i]:(((in @ X159 @ X153)=>~(in @ X159 @ X159))))&![X160:$i]:(((in @ X160 @ (powerset @ X153))=>((nonempty @ X160)=>?[X161:$i]:(((in @ X161 @ X160)&![X162:$i]:(((in @ X162 @ X160)=>(((X161)=(X162))|(in @ X161 @ X162)))))))))))=>![X163:$i]:((((transitiveset @ X163)&(((epred2_1 @ X163)&![X169:$i]:(((in @ X169 @ X163)=>~(in @ X169 @ X169))))&![X170:$i]:(((in @ X170 @ (powerset @ X163))=>((nonempty @ X170)=>?[X171:$i]:(((in @ X171 @ X170)&![X172:$i]:(((in @ X172 @ X170)=>(((X171)=(X172))|(in @ X171 @ X172)))))))))))=>(transitiveset @ (binintersect @ X153 @ X163))))))=>((ordinalTransSet)=>((ordinalTransSet1)=>(![X173:$i]:((![X174:$i]:(((in @ X174 @ X173)=>((transitiveset @ X174)&(((epred3_1 @ X174)&![X180:$i]:(((in @ X180 @ X174)=>~(in @ X180 @ X180))))&![X181:$i]:(((in @ X181 @ (powerset @ X174))=>((nonempty @ X181)=>?[X182:$i]:(((in @ X182 @ X181)&![X183:$i]:(((in @ X183 @ X181)=>(((X182)=(X183))|(in @ X182 @ X183)))))))))))))=>(transitiveset @ (setunion @ X173))))=>((emptysetOrdinal)=>((ordinalIrrefl)=>((ordinalIrrefl2)=>((ordinalNoCycle)=>![X21:$i]:(((epred4_1 @ X21)=>![X2:$i, X4:$i, X5:$i]:(((in @ X2 @ X4)=>((in @ X4 @ X5)=>((in @ X5 @ X21)=>(in @ X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_20, foundation2]), nonemptyImpWitness]), nonemptyI1]), c_0_21]), nonemptyE1]), c_0_22]), c_0_23]), setunionTransitive]), transitivesetOp2]), binintTransitive]), transitivesetOp1]), c_0_19])])]), c_0_24]), c_0_25]), c_0_26]), c_0_27])).
% 3.53/0.94 thf(c_0_29, plain, ![X21:$i]:(((epred4_1 @ X21)=>((transitiveset @ X21)&(((![X184:$i]:(((in @ X184 @ X21)=>![X185:$i]:(((in @ X185 @ X21)=>![X186:$i]:(((in @ X186 @ X21)=>(((in @ X184 @ X185)&(in @ X185 @ X186))=>(in @ X184 @ X186))))))))&![X187:$i]:(((in @ X187 @ X21)=>![X188:$i]:(((in @ X188 @ X21)=>(((X187)=(X188))|(in @ X187 @ X188)|(in @ X188 @ X187)))))))&![X189:$i]:(((in @ X189 @ X21)=>~(in @ X189 @ X189))))&![X190:$i]:(((in @ X190 @ (powerset @ X21))=>((nonempty @ X190)=>?[X191:$i]:(((in @ X191 @ X190)&![X192:$i]:(((in @ X192 @ X190)=>(((X191)=(X192))|(in @ X191 @ X192))))))))))))), inference(split_equiv,[status(thm)],[c_0_27])).
% 3.53/0.94 thf(c_0_30, negated_conjecture, ![X193:$i, X195:$i, X196:$i > $o, X197:$i, X198:$i, X199:$i, X200:$i, X202:$i, X204:$i, X205:$i, X206:$i, X207:$i, X208:$i, X209:$i, X210:$i, X211:$i, X213:$i, X216:$i, X218:$i, X221:$i, X223:$i, X227:$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)&((~(nonempty @ X193)|(in @ (esk1_1 @ X193) @ X193))&((~(in @ X197 @ X195)|(~(X196 @ X197)|(nonempty @ (dsetconstr @ X195 @ X196))))&((~(in @ X199 @ X198)|(nonempty @ X198))&((setadjoinIL)&((emptyinunitempty)&((setadjoinIR)&((setadjoinE)&((setadjoinOr)&((setoftrueEq)&((powersetI)&((emptyinPowerset)&((emptyInPowerset)&((powersetE)&((setunionI)&((setunionE)&((subPowSU)&((exuE2)&((((in @ (esk2_1 @ X200) @ X200)|~(nonempty @ X200))&(($true)|~(nonempty @ X200)))&((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 @ X202) @ X202)|~(nonempty @ X202))&(((binintersect @ (esk3_1 @ X202) @ X202)=(emptyset))|~(nonempty @ X202)))&((notinself)&((notinself2)&((omegaSp)&((omegaSclos)&((peano0notS)&((peanoSinj)&((~(transitiveset @ X204)|(~(in @ X205 @ X204)|(subset @ X205 @ X204)))&((~(transitiveset @ X206)|(~(transitiveset @ X207)|(transitiveset @ (binintersect @ X206 @ X207))))&((~(transitiveset @ X208)|(~(in @ X209 @ X208)|(~(in @ X210 @ X209)|(in @ X210 @ X208))))&((((in @ (esk4_1 @ X211) @ X211)|(transitiveset @ (setunion @ X211)))&(~(transitiveset @ (esk4_1 @ X211))|(transitiveset @ (setunion @ X211))))&(((((((in @ (esk9_2 @ X213 @ X218) @ (powerset @ X218))|((in @ (esk8_2 @ X213 @ X218) @ X218)|~(epred2_1 @ X218))|~(transitiveset @ X218)|(transitiveset @ (binintersect @ X213 @ X218))|((in @ (esk6_1 @ X213) @ (powerset @ X213))|((in @ (esk5_1 @ X213) @ X213)|~(epred1_1 @ X213))|~(transitiveset @ X213)))&(((nonempty @ (esk9_2 @ X213 @ X218))|((in @ (esk8_2 @ X213 @ X218) @ X218)|~(epred2_1 @ 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X218))|(((X216)!=(esk7_2 @ X213 @ X216))|~(in @ X216 @ (esk6_1 @ X213))|((in @ (esk5_1 @ X213) @ (esk5_1 @ X213))|~(epred1_1 @ X213))|~(transitiveset @ X213))))))))&((((in @ (esk9_2 @ X213 @ X218) @ (powerset @ X218))|((in @ (esk8_2 @ X213 @ X218) @ X218)|~(epred2_1 @ X218))|~(transitiveset @ X218)|(transitiveset @ (binintersect @ X213 @ X218))|(~(in @ X216 @ (esk7_2 @ X213 @ X216))|~(in @ X216 @ (esk6_1 @ X213))|((in @ (esk5_1 @ X213) @ (esk5_1 @ X213))|~(epred1_1 @ X213))|~(transitiveset @ X213)))&(((nonempty @ (esk9_2 @ X213 @ X218))|((in @ (esk8_2 @ X213 @ X218) @ X218)|~(epred2_1 @ X218))|~(transitiveset @ X218)|(transitiveset @ (binintersect @ X213 @ X218))|(~(in @ X216 @ (esk7_2 @ X213 @ X216))|~(in @ X216 @ (esk6_1 @ X213))|((in @ (esk5_1 @ X213) @ (esk5_1 @ X213))|~(epred1_1 @ X213))|~(transitiveset @ X213)))&(((in @ (esk10_3 @ X213 @ X218 @ X221) @ (esk9_2 @ X213 @ X218))|~(in @ X221 @ (esk9_2 @ X213 @ X218))|((in @ (esk8_2 @ X213 @ X218) @ X218)|~(epred2_1 @ X218))|~(transitiveset @ X218)|(transitiveset @ (binintersect @ X213 @ X218))|(~(in @ X216 @ (esk7_2 @ X213 @ X216))|~(in @ X216 @ (esk6_1 @ X213))|((in @ (esk5_1 @ X213) @ (esk5_1 @ X213))|~(epred1_1 @ X213))|~(transitiveset @ X213)))&((((X221)!=(esk10_3 @ X213 @ X218 @ X221))|~(in @ X221 @ (esk9_2 @ X213 @ X218))|((in @ (esk8_2 @ X213 @ X218) @ X218)|~(epred2_1 @ X218))|~(transitiveset @ X218)|(transitiveset @ (binintersect @ X213 @ X218))|(~(in @ X216 @ (esk7_2 @ X213 @ X216))|~(in @ X216 @ (esk6_1 @ X213))|((in @ (esk5_1 @ X213) @ (esk5_1 @ X213))|~(epred1_1 @ X213))|~(transitiveset @ X213)))&(~(in @ X221 @ (esk10_3 @ X213 @ X218 @ X221))|~(in @ X221 @ (esk9_2 @ X213 @ X218))|((in @ (esk8_2 @ X213 @ X218) @ X218)|~(epred2_1 @ X218))|~(transitiveset @ X218)|(transitiveset @ (binintersect @ X213 @ X218))|(~(in @ X216 @ (esk7_2 @ X213 @ X216))|~(in @ X216 @ (esk6_1 @ X213))|((in @ (esk5_1 @ X213) @ (esk5_1 @ X213))|~(epred1_1 @ X213))|~(transitiveset @ X213)))))))&(((in @ (esk9_2 @ X213 @ X218) @ (powerset @ X218))|((in @ (esk8_2 @ X213 @ X218) @ (esk8_2 @ X213 @ X218))|~(epred2_1 @ X218))|~(transitiveset @ X218)|(transitiveset @ (binintersect @ X213 @ X218))|(~(in @ X216 @ (esk7_2 @ X213 @ X216))|~(in @ X216 @ (esk6_1 @ X213))|((in @ (esk5_1 @ X213) @ (esk5_1 @ X213))|~(epred1_1 @ X213))|~(transitiveset @ X213)))&(((nonempty @ (esk9_2 @ X213 @ X218))|((in @ (esk8_2 @ X213 @ X218) @ (esk8_2 @ X213 @ X218))|~(epred2_1 @ X218))|~(transitiveset @ X218)|(transitiveset @ (binintersect @ X213 @ X218))|(~(in @ X216 @ (esk7_2 @ X213 @ X216))|~(in @ X216 @ (esk6_1 @ X213))|((in @ (esk5_1 @ X213) @ (esk5_1 @ X213))|~(epred1_1 @ X213))|~(transitiveset @ X213)))&(((in @ (esk10_3 @ X213 @ X218 @ X221) @ (esk9_2 @ X213 @ X218))|~(in @ X221 @ (esk9_2 @ X213 @ X218))|((in @ (esk8_2 @ X213 @ X218) @ (esk8_2 @ X213 @ X218))|~(epred2_1 @ X218))|~(transitiveset @ X218)|(transitiveset @ (binintersect @ X213 @ X218))|(~(in @ X216 @ (esk7_2 @ X213 @ X216))|~(in @ X216 @ (esk6_1 @ X213))|((in @ (esk5_1 @ X213) @ (esk5_1 @ X213))|~(epred1_1 @ X213))|~(transitiveset @ X213)))&((((X221)!=(esk10_3 @ X213 @ X218 @ X221))|~(in @ X221 @ (esk9_2 @ X213 @ X218))|((in @ (esk8_2 @ X213 @ X218) @ (esk8_2 @ X213 @ X218))|~(epred2_1 @ X218))|~(transitiveset @ X218)|(transitiveset @ (binintersect @ X213 @ X218))|(~(in @ X216 @ (esk7_2 @ X213 @ X216))|~(in @ X216 @ (esk6_1 @ X213))|((in @ (esk5_1 @ X213) @ (esk5_1 @ X213))|~(epred1_1 @ X213))|~(transitiveset @ X213)))&(~(in @ X221 @ (esk10_3 @ X213 @ X218 @ X221))|~(in @ X221 @ (esk9_2 @ X213 @ X218))|((in @ (esk8_2 @ X213 @ X218) @ (esk8_2 @ X213 @ X218))|~(epred2_1 @ X218))|~(transitiveset @ X218)|(transitiveset @ (binintersect @ X213 @ X218))|(~(in @ X216 @ (esk7_2 @ X213 @ X216))|~(in @ X216 @ (esk6_1 @ X213))|((in @ (esk5_1 @ X213) @ (esk5_1 @ X213))|~(epred1_1 @ X213))|~(transitiveset @ X213)))))))))))))&((ordinalTransSet)&((ordinalTransSet1)&((((in @ (esk11_1 @ X223) @ X223)|(transitiveset @ (setunion @ X223)))&((((in @ (esk13_1 @ X223) @ (powerset @ (esk11_1 @ X223)))|((in @ (esk12_1 @ X223) @ (esk11_1 @ X223))|~(epred3_1 @ (esk11_1 @ X223)))|~(transitiveset @ (esk11_1 @ X223))|(transitiveset @ (setunion @ X223)))&(((nonempty @ (esk13_1 @ X223))|((in @ (esk12_1 @ X223) @ (esk11_1 @ X223))|~(epred3_1 @ (esk11_1 @ X223)))|~(transitiveset @ (esk11_1 @ X223))|(transitiveset @ (setunion @ X223)))&(((in @ (esk14_2 @ X223 @ X227) @ (esk13_1 @ X223))|~(in @ X227 @ (esk13_1 @ X223))|((in @ (esk12_1 @ X223) @ (esk11_1 @ X223))|~(epred3_1 @ (esk11_1 @ X223)))|~(transitiveset @ (esk11_1 @ X223))|(transitiveset @ (setunion @ X223)))&((((X227)!=(esk14_2 @ X223 @ X227))|~(in @ X227 @ (esk13_1 @ X223))|((in @ (esk12_1 @ X223) @ (esk11_1 @ X223))|~(epred3_1 @ (esk11_1 @ X223)))|~(transitiveset @ (esk11_1 @ X223))|(transitiveset @ (setunion @ X223)))&(~(in @ X227 @ (esk14_2 @ X223 @ X227))|~(in @ X227 @ (esk13_1 @ X223))|((in @ (esk12_1 @ X223) @ (esk11_1 @ X223))|~(epred3_1 @ (esk11_1 @ X223)))|~(transitiveset @ (esk11_1 @ X223))|(transitiveset @ (setunion @ X223)))))))&(((in @ (esk13_1 @ X223) @ (powerset @ (esk11_1 @ X223)))|((in @ (esk12_1 @ X223) @ (esk12_1 @ X223))|~(epred3_1 @ (esk11_1 @ X223)))|~(transitiveset @ (esk11_1 @ X223))|(transitiveset @ (setunion @ X223)))&(((nonempty @ (esk13_1 @ X223))|((in @ (esk12_1 @ X223) @ (esk12_1 @ X223))|~(epred3_1 @ (esk11_1 @ X223)))|~(transitiveset @ (esk11_1 @ X223))|(transitiveset @ (setunion @ X223)))&(((in @ (esk14_2 @ X223 @ X227) @ (esk13_1 @ X223))|~(in @ X227 @ (esk13_1 @ X223))|((in @ (esk12_1 @ X223) @ (esk12_1 @ X223))|~(epred3_1 @ (esk11_1 @ X223)))|~(transitiveset @ (esk11_1 @ X223))|(transitiveset @ (setunion @ X223)))&((((X227)!=(esk14_2 @ X223 @ X227))|~(in @ X227 @ (esk13_1 @ X223))|((in @ (esk12_1 @ X223) @ (esk12_1 @ X223))|~(epred3_1 @ (esk11_1 @ X223)))|~(transitiveset @ (esk11_1 @ X223))|(transitiveset @ (setunion @ X223)))&(~(in @ X227 @ (esk14_2 @ X223 @ X227))|~(in @ X227 @ (esk13_1 @ X223))|((in @ (esk12_1 @ X223) @ (esk12_1 @ X223))|~(epred3_1 @ (esk11_1 @ X223)))|~(transitiveset @ (esk11_1 @ X223))|(transitiveset @ (setunion @ X223)))))))))&((emptysetOrdinal)&((ordinalIrrefl)&((ordinalIrrefl2)&((ordinalNoCycle)&((epred4_1 @ esk15_0)&((in @ esk16_0 @ esk17_0)&((in @ esk17_0 @ esk18_0)&((in @ esk18_0 @ esk15_0)&~(in @ esk16_0 @ esk18_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_28])])])])])])])).
% 3.53/0.94 thf(c_0_31, plain, ![X251:$i, X252:$i, X253:$i, X254:$i, X255:$i, X256:$i, X257:$i, X258:$i, X260:$i]:((((transitiveset @ X251)|~(epred4_1 @ X251))&((((~(in @ X252 @ X251)|(~(in @ X253 @ X251)|(~(in @ X254 @ X251)|(~(in @ X252 @ X253)|~(in @ X253 @ X254)|(in @ X252 @ X254))))|~(epred4_1 @ X251))&(~(in @ X255 @ X251)|(~(in @ X256 @ X251)|(((X255)=(X256))|(in @ X255 @ X256)|(in @ X256 @ X255)))|~(epred4_1 @ X251)))&(~(in @ X257 @ X251)|~(in @ X257 @ X257)|~(epred4_1 @ X251)))&(((in @ (esk34_2 @ X251 @ X258) @ X258)|~(nonempty @ X258)|~(in @ X258 @ (powerset @ X251))|~(epred4_1 @ X251))&(~(in @ X260 @ X258)|(((esk34_2 @ X251 @ X258)=(X260))|(in @ (esk34_2 @ X251 @ X258) @ X260))|~(nonempty @ X258)|~(in @ X258 @ (powerset @ X251))|~(epred4_1 @ X251)))))), 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_29])])])])])])).
% 3.53/0.94 thf(c_0_32, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X4 @ X2)|~((transitiveset @ X2))|~((in @ X3 @ X2))|~((in @ X4 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_30])).
% 3.53/0.94 thf(c_0_33, negated_conjecture, (in @ esk17_0 @ esk18_0), inference(split_conjunct,[status(thm)],[c_0_30])).
% 3.53/0.94 thf(c_0_34, plain, ![X2:$i]:(((transitiveset @ X2)|~((epred4_1 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_31])).
% 3.53/0.94 thf(c_0_35, negated_conjecture, (epred4_1 @ esk15_0), inference(split_conjunct,[status(thm)],[c_0_30])).
% 3.53/0.94 thf(c_0_36, plain, ![X2:$i, X5:$i, X4:$i, X3:$i]:(((in @ X2 @ X5)|~((in @ X2 @ X3))|~((in @ X4 @ X3))|~((in @ X5 @ X3))|~((in @ X2 @ X4))|~((in @ X4 @ X5))|~((epred4_1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_31])).
% 3.53/0.94 thf(c_0_37, negated_conjecture, (in @ esk18_0 @ esk15_0), inference(split_conjunct,[status(thm)],[c_0_30])).
% 3.53/0.94 thf(c_0_38, negated_conjecture, ![X2:$i]:(((in @ esk17_0 @ X2)|~((in @ esk18_0 @ X2))|~((transitiveset @ X2)))), inference(spm,[status(thm)],[c_0_32, c_0_33])).
% 3.53/0.94 thf(c_0_39, negated_conjecture, (transitiveset @ esk15_0), inference(spm,[status(thm)],[c_0_34, c_0_35])).
% 3.53/0.94 thf(c_0_40, negated_conjecture, (in @ esk16_0 @ esk17_0), inference(split_conjunct,[status(thm)],[c_0_30])).
% 3.53/0.94 thf(c_0_41, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ esk18_0)|~((in @ X3 @ esk18_0))|~((in @ X3 @ esk15_0))|~((in @ X2 @ esk15_0))|~((in @ X2 @ X3)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37]), c_0_35])])).
% 3.53/0.94 thf(c_0_42, negated_conjecture, (in @ esk17_0 @ esk15_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_37])])).
% 3.53/0.94 thf(c_0_43, negated_conjecture, ![X2:$i]:(((in @ esk16_0 @ X2)|~((in @ esk17_0 @ X2))|~((transitiveset @ X2)))), inference(spm,[status(thm)],[c_0_32, c_0_40])).
% 3.53/0.94 thf(c_0_44, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk18_0)|~((in @ X2 @ esk15_0))|~((in @ X2 @ esk17_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_33])])).
% 3.53/0.94 thf(c_0_45, negated_conjecture, (in @ esk16_0 @ esk15_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_39]), c_0_42])])).
% 3.53/0.94 thf(c_0_46, negated_conjecture, ~((in @ esk16_0 @ esk18_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
% 3.53/0.94 thf(c_0_47, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_40]), c_0_45])]), c_0_46]), ['proof']).
% 3.53/0.94 % SZS output end CNFRefutation
% 3.53/0.94 % Parsed axioms : 749
% 3.53/0.94 % Removed by relevancy pruning/SinE : 734
% 3.53/0.94 % Initial clauses : 553
% 3.53/0.94 % Removed in clause preprocessing : 1
% 3.53/0.94 % Initial clauses in saturation : 552
% 3.53/0.94 % Processed clauses : 1673
% 3.53/0.94 % ...of these trivial : 0
% 3.53/0.94 % ...subsumed : 411
% 3.53/0.94 % ...remaining for further processing : 1262
% 3.53/0.94 % Other redundant clauses eliminated : 0
% 3.53/0.94 % Clauses deleted for lack of memory : 0
% 3.53/0.94 % Backward-subsumed : 4
% 3.53/0.94 % Backward-rewritten : 0
% 3.53/0.94 % Generated clauses : 16871
% 3.53/0.94 % ...of the previous two non-redundant : 16681
% 3.53/0.94 % ...aggressively subsumed : 0
% 3.53/0.94 % Contextual simplify-reflections : 9
% 3.53/0.94 % Paramodulations : 16871
% 3.53/0.94 % Factorizations : 0
% 3.53/0.94 % NegExts : 0
% 3.53/0.94 % Equation resolutions : 0
% 3.53/0.94 % Disequality decompositions : 0
% 3.53/0.94 % Total rewrite steps : 2359
% 3.53/0.94 % ...of those cached : 2349
% 3.53/0.94 % Propositional unsat checks : 0
% 3.53/0.94 % Propositional check models : 0
% 3.53/0.94 % Propositional check unsatisfiable : 0
% 3.53/0.94 % Propositional clauses : 0
% 3.53/0.94 % Propositional clauses after purity: 0
% 3.53/0.94 % Propositional unsat core size : 0
% 3.53/0.94 % Propositional preprocessing time : 0.000
% 3.53/0.94 % Propositional encoding time : 0.000
% 3.53/0.94 % Propositional solver time : 0.000
% 3.53/0.94 % Success case prop preproc time : 0.000
% 3.53/0.94 % Success case prop encoding time : 0.000
% 3.53/0.94 % Success case prop solver time : 0.000
% 3.53/0.94 % Current number of processed clauses : 1258
% 3.53/0.94 % Positive orientable unit clauses : 339
% 3.53/0.94 % Positive unorientable unit clauses: 0
% 3.53/0.94 % Negative unit clauses : 4
% 3.53/0.94 % Non-unit-clauses : 915
% 3.53/0.94 % Current number of unprocessed clauses: 15513
% 3.53/0.94 % ...number of literals in the above : 89431
% 3.53/0.94 % Current number of archived formulas : 0
% 3.53/0.94 % Current number of archived clauses : 4
% 3.53/0.94 % Clause-clause subsumption calls (NU) : 84013
% 3.53/0.94 % Rec. Clause-clause subsumption calls : 29069
% 3.53/0.94 % Non-unit clause-clause subsumptions : 402
% 3.53/0.94 % Unit Clause-clause subsumption calls : 119
% 3.53/0.94 % Rewrite failures with RHS unbound : 0
% 3.53/0.94 % BW rewrite match attempts : 0
% 3.53/0.94 % BW rewrite match successes : 0
% 3.53/0.94 % Condensation attempts : 0
% 3.53/0.94 % Condensation successes : 0
% 3.53/0.94 % Termbank termtop insertions : 384978
% 3.53/0.94 % Search garbage collected termcells : 11401
% 3.53/0.94
% 3.53/0.94 % -------------------------------------------------
% 3.53/0.94 % User time : 0.427 s
% 3.53/0.94 % System time : 0.025 s
% 3.53/0.94 % Total time : 0.452 s
% 3.53/0.94 % Maximum resident set size: 6232 pages
% 3.53/0.94
% 3.53/0.94 % -------------------------------------------------
% 3.53/0.94 % User time : 0.448 s
% 3.53/0.94 % System time : 0.032 s
% 3.53/0.94 % Total time : 0.480 s
% 3.53/0.94 % Maximum resident set size: 5632 pages
% 3.53/0.94 % E exiting
%------------------------------------------------------------------------------