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E---3.5.1.THM-CRf.s

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Problem Process solution in
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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SEU822^1 : 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 : n003.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 08:25:46 AM UTC 2026

% Result   : Theorem 0.22s 0.35s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU822^1 : 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 : n003.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
% 0.07/0.18  % CPULimit : 300
% 0.07/0.18  % WCLimit  : 300
% 0.07/0.18  % DateTime : Tue Sep 29 14:36:28 UTC 2026
% 0.07/0.18  % CPUTime  : 
% 0.07/0.18  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22  Running higher-order theorem proving
% 0.07/0.26  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.vlUndA7UJh/E---3.1_2592797.p
% 0.22/0.35  % Version: 3.5.1-ho
% 0.22/0.35  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.35  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.35  % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.35  % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.35  % Starting new_bool_5 with 300s (1) cores
% 0.22/0.35  % Starting pre_casc_3 with 300s (1) cores
% 0.22/0.35  % Starting ho_unfolding_8 with 300s (1) cores
% 0.22/0.35  % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.22/0.35  % Starting new_bool_3 with 300s (1) cores
% 0.22/0.35  % Starting new_ho_5 with 300s (1) cores
% 0.22/0.35  % new_ho_5 with pid 2592817 completed with status 0
% 0.22/0.35  % Result found by new_ho_5
% 0.22/0.35  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.35  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.35  % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.35  % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.35  % Starting new_bool_5 with 300s (1) cores
% 0.22/0.35  % Starting pre_casc_3 with 300s (1) cores
% 0.22/0.35  % Starting ho_unfolding_8 with 300s (1) cores
% 0.22/0.35  % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.22/0.35  % Starting new_bool_3 with 300s (1) cores
% 0.22/0.35  % Starting new_ho_5 with 300s (1) cores
% 0.22/0.35  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
% 0.22/0.35  % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.22/0.35  % Search class: HGHSF-FSLM31-SHFMMFBN
% 0.22/0.35  % partial match(2): HGHSM-FSLM31-SHFMMSBN
% 0.22/0.35  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.35  % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.35  % SubtermCWHack with pid 2592818 completed with status 0
% 0.22/0.35  % Result found by SubtermCWHack
% 0.22/0.35  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.35  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.35  % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.35  % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.35  % Starting new_bool_5 with 300s (1) cores
% 0.22/0.35  % Starting pre_casc_3 with 300s (1) cores
% 0.22/0.35  % Starting ho_unfolding_8 with 300s (1) cores
% 0.22/0.35  % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.22/0.35  % Starting new_bool_3 with 300s (1) cores
% 0.22/0.35  % Starting new_ho_5 with 300s (1) cores
% 0.22/0.35  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
% 0.22/0.35  % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.22/0.35  % Search class: HGHSF-FSLM31-SHFMMFBN
% 0.22/0.35  % partial match(2): HGHSM-FSLM31-SHFMMSBN
% 0.22/0.35  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.35  % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.35  % Preprocessing time       : 0.007 s
% 0.22/0.35  
% 0.22/0.35  % Proof found!
% 0.22/0.35  % SZS status Theorem
% 0.22/0.35  % SZS output start CNFRefutation
% 0.22/0.35  thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.35  thf(decl_25, type, setextAx: $o).
% 0.22/0.35  thf(decl_26, type, emptyset: $i).
% 0.22/0.35  thf(decl_27, type, emptysetAx: $o).
% 0.22/0.35  thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.35  thf(decl_30, type, powerset: $i > $i).
% 0.22/0.35  thf(decl_31, type, powersetAx: $o).
% 0.22/0.35  thf(decl_32, type, setunion: $i > $i).
% 0.22/0.35  thf(decl_33, type, setunionAx: $o).
% 0.22/0.35  thf(decl_35, type, omega0Ax: $o).
% 0.22/0.35  thf(decl_36, type, omegaSAx: $o).
% 0.22/0.35  thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.35  thf(decl_38, type, replAx: $o).
% 0.22/0.35  thf(decl_39, type, foundationAx: $o).
% 0.22/0.35  thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.35  thf(decl_42, type, descrp: $o).
% 0.22/0.35  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.35  thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.35  thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.36  thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.36  thf(decl_47, type, exuE1: $o).
% 0.22/0.36  thf(decl_49, type, prop2setE: $o).
% 0.22/0.36  thf(decl_50, type, emptysetE: $o).
% 0.22/0.36  thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.36  thf(decl_52, type, notinemptyset: $o).
% 0.22/0.36  thf(decl_53, type, exuE3e: $o).
% 0.22/0.36  thf(decl_54, type, setext: $o).
% 0.22/0.36  thf(decl_55, type, emptyI: $o).
% 0.22/0.36  thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.36  thf(decl_57, type, setbeta: $o).
% 0.22/0.36  thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.36  thf(decl_59, type, nonemptyE1: $o).
% 0.22/0.36  thf(decl_60, type, nonemptyI: $o).
% 0.22/0.36  thf(decl_61, type, nonemptyI1: $o).
% 0.22/0.36  thf(decl_62, type, setadjoinIL: $o).
% 0.22/0.36  thf(decl_63, type, emptyinunitempty: $o).
% 0.22/0.36  thf(decl_64, type, setadjoinIR: $o).
% 0.22/0.36  thf(decl_65, type, setadjoinE: $o).
% 0.22/0.36  thf(decl_66, type, setadjoinOr: $o).
% 0.22/0.36  thf(decl_67, type, setoftrueEq: $o).
% 0.22/0.36  thf(decl_68, type, powersetI: $o).
% 0.22/0.36  thf(decl_69, type, emptyinPowerset: $o).
% 0.22/0.36  thf(decl_70, type, emptyInPowerset: $o).
% 0.22/0.36  thf(decl_71, type, powersetE: $o).
% 0.22/0.36  thf(decl_72, type, setunionI: $o).
% 0.22/0.36  thf(decl_73, type, setunionE: $o).
% 0.22/0.36  thf(decl_74, type, subPowSU: $o).
% 0.22/0.36  thf(decl_75, type, exuE2: $o).
% 0.22/0.36  thf(decl_76, type, nonemptyImpWitness: $o).
% 0.22/0.36  thf(decl_77, type, uniqinunit: $o).
% 0.22/0.36  thf(decl_78, type, notinsingleton: $o).
% 0.22/0.36  thf(decl_79, type, eqinunit: $o).
% 0.22/0.36  thf(decl_80, type, singletonsswitch: $o).
% 0.22/0.36  thf(decl_81, type, upairsetE: $o).
% 0.22/0.36  thf(decl_82, type, upairsetIL: $o).
% 0.22/0.36  thf(decl_83, type, upairsetIR: $o).
% 0.22/0.36  thf(decl_84, type, emptyE1: $o).
% 0.22/0.36  thf(decl_85, type, vacuousDall: $o).
% 0.22/0.36  thf(decl_86, type, quantDeMorgan1: $o).
% 0.22/0.36  thf(decl_87, type, quantDeMorgan2: $o).
% 0.22/0.36  thf(decl_88, type, quantDeMorgan3: $o).
% 0.22/0.36  thf(decl_89, type, quantDeMorgan4: $o).
% 0.22/0.36  thf(decl_90, type, prop2setI: $o).
% 0.22/0.36  thf(decl_92, type, prop2set2propI: $o).
% 0.22/0.36  thf(decl_93, type, notdexE: $o).
% 0.22/0.36  thf(decl_94, type, notdallE: $o).
% 0.22/0.36  thf(decl_95, type, exuI1: $o).
% 0.22/0.36  thf(decl_96, type, exuI3: $o).
% 0.22/0.36  thf(decl_97, type, exuI2: $o).
% 0.22/0.36  thf(decl_98, type, inCongP: $o).
% 0.22/0.36  thf(decl_99, type, in__Cong: $o).
% 0.22/0.36  thf(decl_100, type, exuE3u: $o).
% 0.22/0.36  thf(decl_101, type, exu__Cong: $o).
% 0.22/0.36  thf(decl_102, type, emptyset__Cong: $o).
% 0.22/0.36  thf(decl_103, type, setadjoin__Cong: $o).
% 0.22/0.36  thf(decl_104, type, powerset__Cong: $o).
% 0.22/0.36  thf(decl_105, type, setunion__Cong: $o).
% 0.22/0.36  thf(decl_106, type, omega__Cong: $o).
% 0.22/0.36  thf(decl_107, type, exuEu: $o).
% 0.22/0.36  thf(decl_108, type, descr__Cong: $o).
% 0.22/0.36  thf(decl_109, type, dsetconstr__Cong: $o).
% 0.22/0.36  thf(decl_110, type, subset: $i > $i > $o).
% 0.22/0.36  thf(decl_113, type, subsetI1: $o).
% 0.22/0.36  thf(decl_114, type, eqimpsubset2: $o).
% 0.22/0.36  thf(decl_115, type, eqimpsubset1: $o).
% 0.22/0.36  thf(decl_116, type, subsetI2: $o).
% 0.22/0.36  thf(decl_117, type, emptysetsubset: $o).
% 0.22/0.36  thf(decl_118, type, subsetE: $o).
% 0.22/0.36  thf(decl_119, type, subsetE2: $o).
% 0.22/0.36  thf(decl_120, type, notsubsetI: $o).
% 0.22/0.36  thf(decl_121, type, notequalI1: $o).
% 0.22/0.36  thf(decl_122, type, notequalI2: $o).
% 0.22/0.36  thf(decl_123, type, subsetRefl: $o).
% 0.22/0.36  thf(decl_124, type, subsetTrans: $o).
% 0.22/0.36  thf(decl_125, type, setadjoinSub: $o).
% 0.22/0.36  thf(decl_126, type, setadjoinSub2: $o).
% 0.22/0.36  thf(decl_127, type, subset2powerset: $o).
% 0.22/0.36  thf(decl_128, type, setextsub: $o).
% 0.22/0.36  thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.22/0.36  thf(decl_130, type, powersetI1: $o).
% 0.22/0.36  thf(decl_131, type, powersetE1: $o).
% 0.22/0.36  thf(decl_132, type, inPowerset: $o).
% 0.22/0.36  thf(decl_133, type, powersetsubset: $o).
% 0.22/0.36  thf(decl_134, type, sepInPowerset: $o).
% 0.22/0.36  thf(decl_135, type, sepSubset: $o).
% 0.22/0.36  thf(decl_137, type, binunionIL: $o).
% 0.22/0.36  thf(decl_138, type, upairset2IR: $o).
% 0.22/0.36  thf(decl_139, type, binunionIR: $o).
% 0.22/0.36  thf(decl_140, type, binunionEcases: $o).
% 0.22/0.36  thf(decl_141, type, binunionE: $o).
% 0.22/0.36  thf(decl_142, type, binunionLsub: $o).
% 0.22/0.36  thf(decl_143, type, binunionRsub: $o).
% 0.22/0.36  thf(decl_144, type, binintersect: $i > $i > $i).
% 0.22/0.36  thf(decl_145, type, binintersectI: $o).
% 0.22/0.36  thf(decl_146, type, binintersectSubset5: $o).
% 0.22/0.36  thf(decl_147, type, binintersectEL: $o).
% 0.22/0.36  thf(decl_148, type, binintersectLsub: $o).
% 0.22/0.36  thf(decl_149, type, binintersectSubset2: $o).
% 0.22/0.36  thf(decl_150, type, binintersectSubset3: $o).
% 0.22/0.36  thf(decl_151, type, binintersectER: $o).
% 0.22/0.36  thf(decl_152, type, disjointsetsI1: $o).
% 0.22/0.36  thf(decl_153, type, binintersectRsub: $o).
% 0.22/0.36  thf(decl_154, type, binintersectSubset4: $o).
% 0.22/0.36  thf(decl_155, type, binintersectSubset1: $o).
% 0.22/0.36  thf(decl_156, type, bs114d: $o).
% 0.22/0.36  thf(decl_159, type, setminusI: $o).
% 0.22/0.36  thf(decl_160, type, setminusEL: $o).
% 0.22/0.36  thf(decl_161, type, setminusER: $o).
% 0.22/0.36  thf(decl_162, type, setminusSubset2: $o).
% 0.22/0.36  thf(decl_163, type, setminusERneg: $o).
% 0.22/0.36  thf(decl_164, type, setminusELneg: $o).
% 0.22/0.36  thf(decl_165, type, setminusILneg: $o).
% 0.22/0.36  thf(decl_166, type, setminusIRneg: $o).
% 0.22/0.36  thf(decl_167, type, setminusLsub: $o).
% 0.22/0.36  thf(decl_168, type, setminusSubset1: $o).
% 0.22/0.36  thf(decl_170, type, symdiffE: $o).
% 0.22/0.36  thf(decl_171, type, symdiffI1: $o).
% 0.22/0.36  thf(decl_172, type, symdiffI2: $o).
% 0.22/0.36  thf(decl_173, type, symdiffIneg1: $o).
% 0.22/0.36  thf(decl_174, type, symdiffIneg2: $o).
% 0.22/0.36  thf(decl_176, type, secondinupair: $o).
% 0.22/0.36  thf(decl_177, type, setukpairIL: $o).
% 0.22/0.36  thf(decl_178, type, setukpairIR: $o).
% 0.22/0.36  thf(decl_179, type, kpairiskpair: $o).
% 0.22/0.36  thf(decl_181, type, kpairp: $o).
% 0.22/0.36  thf(decl_183, type, singletonsubset: $o).
% 0.22/0.36  thf(decl_184, type, singletoninpowerset: $o).
% 0.22/0.36  thf(decl_185, type, singletoninpowunion: $o).
% 0.22/0.36  thf(decl_186, type, upairset2E: $o).
% 0.22/0.36  thf(decl_187, type, upairsubunion: $o).
% 0.22/0.36  thf(decl_188, type, upairinpowunion: $o).
% 0.22/0.36  thf(decl_189, type, ubforcartprodlem1: $o).
% 0.22/0.36  thf(decl_190, type, ubforcartprodlem2: $o).
% 0.22/0.36  thf(decl_191, type, ubforcartprodlem3: $o).
% 0.22/0.36  thf(decl_192, type, cartprodpairin: $o).
% 0.22/0.36  thf(decl_193, type, cartprodmempair1: $o).
% 0.22/0.36  thf(decl_194, type, cartprodmempair: $o).
% 0.22/0.36  thf(decl_195, type, setunionE2: $o).
% 0.22/0.36  thf(decl_196, type, setunionsingleton1: $o).
% 0.22/0.36  thf(decl_197, type, setunionsingleton2: $o).
% 0.22/0.36  thf(decl_198, type, setunionsingleton: $o).
% 0.22/0.36  thf(decl_200, type, singletonprop: $o).
% 0.22/0.36  thf(decl_202, type, ex1E1: $o).
% 0.22/0.36  thf(decl_203, type, ex1I: $o).
% 0.22/0.36  thf(decl_204, type, ex1I2: $o).
% 0.22/0.36  thf(decl_205, type, singletonsuniq: $o).
% 0.22/0.36  thf(decl_210, type, setukpairinjL1: $o).
% 0.22/0.36  thf(decl_211, type, kfstsingleton: $o).
% 0.22/0.36  thf(decl_212, type, theprop: $o).
% 0.22/0.36  thf(decl_214, type, kfstpairEq: $o).
% 0.22/0.36  thf(decl_215, type, cartprodfstin: $o).
% 0.22/0.36  thf(decl_216, type, setukpairinjL2: $o).
% 0.22/0.36  thf(decl_217, type, setukpairinjL: $o).
% 0.22/0.36  thf(decl_218, type, setukpairinjR11: $o).
% 0.22/0.36  thf(decl_219, type, setukpairinjR12: $o).
% 0.22/0.36  thf(decl_220, type, setukpairinjR1: $o).
% 0.22/0.36  thf(decl_221, type, upairequniteq: $o).
% 0.22/0.36  thf(decl_222, type, setukpairinjR2: $o).
% 0.22/0.36  thf(decl_223, type, setukpairinjR: $o).
% 0.22/0.36  thf(decl_224, type, ksndsingleton: $o).
% 0.22/0.36  thf(decl_226, type, ksndpairEq: $o).
% 0.22/0.36  thf(decl_227, type, kpairsurjEq: $o).
% 0.22/0.36  thf(decl_228, type, cartprodsndin: $o).
% 0.22/0.36  thf(decl_229, type, cartprodpairmemEL: $o).
% 0.22/0.36  thf(decl_230, type, cartprodpairmemER: $o).
% 0.22/0.36  thf(decl_231, type, cartprodmempaircEq: $o).
% 0.22/0.36  thf(decl_232, type, cartprodfstpairEq: $o).
% 0.22/0.36  thf(decl_233, type, cartprodsndpairEq: $o).
% 0.22/0.36  thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.22/0.36  thf(decl_237, type, dpsetconstrI: $o).
% 0.22/0.36  thf(decl_238, type, dpsetconstrSub: $o).
% 0.22/0.36  thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.22/0.36  thf(decl_240, type, dpsetconstrERa: $o).
% 0.22/0.36  thf(decl_241, type, dpsetconstrEL1: $o).
% 0.22/0.36  thf(decl_242, type, dpsetconstrEL2: $o).
% 0.22/0.36  thf(decl_243, type, dpsetconstrER: $o).
% 0.22/0.36  thf(decl_246, type, funcImageSingleton: $o).
% 0.22/0.36  thf(decl_247, type, apProp: $o).
% 0.22/0.36  thf(decl_249, type, app: $o).
% 0.22/0.36  thf(decl_250, type, infuncsetfunc: $o).
% 0.22/0.36  thf(decl_251, type, ap2p: $o).
% 0.22/0.36  thf(decl_252, type, funcinfuncset: $o).
% 0.22/0.36  thf(decl_253, type, lamProp: $o).
% 0.22/0.36  thf(decl_255, type, lamp: $o).
% 0.22/0.36  thf(decl_256, type, lam2p: $o).
% 0.22/0.36  thf(decl_257, type, brelnall1: $o).
% 0.22/0.36  thf(decl_258, type, brelnall2: $o).
% 0.22/0.36  thf(decl_259, type, ex1E2: $o).
% 0.22/0.36  thf(decl_260, type, funcGraphProp1: $o).
% 0.22/0.36  thf(decl_261, type, funcGraphProp3: $o).
% 0.22/0.36  thf(decl_262, type, funcGraphProp2: $o).
% 0.22/0.36  thf(decl_263, type, funcextLem: $o).
% 0.22/0.36  thf(decl_264, type, funcGraphProp4: $o).
% 0.22/0.36  thf(decl_265, type, subbreln: $o).
% 0.22/0.36  thf(decl_266, type, eqbreln: $o).
% 0.22/0.36  thf(decl_267, type, funcext: $o).
% 0.22/0.36  thf(decl_268, type, funcext2: $o).
% 0.22/0.36  thf(decl_269, type, ap2apEq1: $o).
% 0.22/0.36  thf(decl_270, type, ap2apEq2: $o).
% 0.22/0.36  thf(decl_271, type, beta1: $o).
% 0.22/0.36  thf(decl_272, type, eta1: $o).
% 0.22/0.36  thf(decl_273, type, lam2lamEq: $o).
% 0.22/0.36  thf(decl_274, type, beta2: $o).
% 0.22/0.36  thf(decl_275, type, eta2: $o).
% 0.22/0.36  thf(decl_276, type, iffalseProp1: $o).
% 0.22/0.36  thf(decl_277, type, iffalseProp2: $o).
% 0.22/0.36  thf(decl_278, type, iftrueProp1: $o).
% 0.22/0.36  thf(decl_279, type, iftrueProp2: $o).
% 0.22/0.36  thf(decl_280, type, ifSingleton: $o).
% 0.22/0.36  thf(decl_282, type, ifp: $o).
% 0.22/0.36  thf(decl_283, type, theeq: $o).
% 0.22/0.36  thf(decl_284, type, iftrue: $o).
% 0.22/0.36  thf(decl_285, type, iffalse: $o).
% 0.22/0.36  thf(decl_286, type, iftrueorfalse: $o).
% 0.22/0.36  thf(decl_287, type, binintersectT_lem: $o).
% 0.22/0.36  thf(decl_288, type, binunionT_lem: $o).
% 0.22/0.36  thf(decl_289, type, powersetT_lem: $o).
% 0.22/0.36  thf(decl_290, type, setminusT_lem: $o).
% 0.22/0.36  thf(decl_291, type, complementT_lem: $o).
% 0.22/0.36  thf(decl_292, type, setextT: $o).
% 0.22/0.36  thf(decl_293, type, subsetTI: $o).
% 0.22/0.36  thf(decl_294, type, powersetTI1: $o).
% 0.22/0.36  thf(decl_295, type, powersetTE1: $o).
% 0.22/0.36  thf(decl_296, type, complementTI1: $o).
% 0.22/0.36  thf(decl_297, type, complementTE1: $o).
% 0.22/0.36  thf(decl_298, type, binintersectTELcontra: $o).
% 0.22/0.36  thf(decl_299, type, binintersectTERcontra: $o).
% 0.22/0.36  thf(decl_300, type, contrasubsetT: $o).
% 0.22/0.36  thf(decl_301, type, contrasubsetT1: $o).
% 0.22/0.36  thf(decl_302, type, contrasubsetT2: $o).
% 0.22/0.36  thf(decl_303, type, contrasubsetT3: $o).
% 0.22/0.36  thf(decl_304, type, doubleComplementI1: $o).
% 0.22/0.36  thf(decl_305, type, doubleComplementE1: $o).
% 0.22/0.36  thf(decl_306, type, doubleComplementSub1: $o).
% 0.22/0.36  thf(decl_307, type, doubleComplementSub2: $o).
% 0.22/0.36  thf(decl_308, type, doubleComplementEq: $o).
% 0.22/0.36  thf(decl_309, type, complementTnotintersectT: $o).
% 0.22/0.36  thf(decl_310, type, complementImpComplementIntersect: $o).
% 0.22/0.36  thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 0.22/0.36  thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 0.22/0.36  thf(decl_313, type, contraSubsetComplement: $o).
% 0.22/0.36  thf(decl_314, type, complementTcontraSubset: $o).
% 0.22/0.36  thf(decl_315, type, binunionTILcontra: $o).
% 0.22/0.36  thf(decl_316, type, binunionTIRcontra: $o).
% 0.22/0.36  thf(decl_317, type, inIntersectImpInUnion: $o).
% 0.22/0.36  thf(decl_318, type, inIntersectImpInUnion2: $o).
% 0.22/0.36  thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 0.22/0.36  thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 0.22/0.36  thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 0.22/0.36  thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 0.22/0.36  thf(decl_323, type, binunionTE: $o).
% 0.22/0.36  thf(decl_324, type, binunionTEcontra: $o).
% 0.22/0.36  thf(decl_325, type, demorgan2a1: $o).
% 0.22/0.36  thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 0.22/0.36  thf(decl_327, type, demorgan2a2: $o).
% 0.22/0.36  thf(decl_328, type, demorgan1a: $o).
% 0.22/0.36  thf(decl_329, type, demorgan1b: $o).
% 0.22/0.36  thf(decl_330, type, demorgan1: $o).
% 0.22/0.36  thf(decl_331, type, demorgan2a: $o).
% 0.22/0.36  thf(decl_332, type, demorgan2b2: $o).
% 0.22/0.36  thf(decl_333, type, demorgan2b: $o).
% 0.22/0.36  thf(decl_334, type, demorgan2: $o).
% 0.22/0.36  thf(decl_335, type, woz13rule0: $o).
% 0.22/0.36  thf(decl_336, type, woz13rule1: $o).
% 0.22/0.36  thf(decl_337, type, woz13rule2: $o).
% 0.22/0.36  thf(decl_338, type, woz13rule3: $o).
% 0.22/0.36  thf(decl_339, type, woz13rule4: $o).
% 0.22/0.36  thf(decl_340, type, woz1_1: $o).
% 0.22/0.36  thf(decl_341, type, woz1_2: $o).
% 0.22/0.36  thf(decl_342, type, woz1_3: $o).
% 0.22/0.36  thf(decl_343, type, woz1_4: $o).
% 0.22/0.36  thf(decl_344, type, woz1_5: $o).
% 0.22/0.36  thf(decl_346, type, breln1all2: $o).
% 0.22/0.36  thf(decl_348, type, breln1SetBreln1: $o).
% 0.22/0.36  thf(decl_355, type, choice2fnsingleton: $o).
% 0.22/0.36  thf(decl_356, type, setOfPairsIsBReln1: $o).
% 0.22/0.36  thf(decl_357, type, breln1all1: $o).
% 0.22/0.36  thf(decl_358, type, subbreln1: $o).
% 0.22/0.36  thf(decl_359, type, eqbreln1: $o).
% 0.22/0.36  thf(decl_361, type, breln1invprop: $o).
% 0.22/0.36  thf(decl_362, type, breln1invI: $o).
% 0.22/0.36  thf(decl_363, type, breln1invE: $o).
% 0.22/0.36  thf(decl_365, type, breln1compprop: $o).
% 0.22/0.36  thf(decl_366, type, breln1compI: $o).
% 0.22/0.36  thf(decl_367, type, breln1compE: $o).
% 0.22/0.36  thf(decl_368, type, breln1compEex: $o).
% 0.22/0.36  thf(decl_369, type, breln1unionprop: $o).
% 0.22/0.36  thf(decl_370, type, breln1unionIL: $o).
% 0.22/0.36  thf(decl_371, type, breln1unionIR: $o).
% 0.22/0.36  thf(decl_372, type, breln1unionI: $o).
% 0.22/0.36  thf(decl_373, type, breln1unionE: $o).
% 0.22/0.36  thf(decl_374, type, breln1unionEcases: $o).
% 0.22/0.36  thf(decl_375, type, breln1unionCommutes: $o).
% 0.22/0.36  thf(decl_376, type, woz2Ex: $o).
% 0.22/0.36  thf(decl_377, type, woz2W: $o).
% 0.22/0.36  thf(decl_378, type, woz2A: $o).
% 0.22/0.36  thf(decl_379, type, woz2B: $o).
% 0.22/0.36  thf(decl_380, type, image1Ex: $o).
% 0.22/0.36  thf(decl_381, type, image1Ex1: $o).
% 0.22/0.36  thf(decl_383, type, image1Equiv: $o).
% 0.22/0.36  thf(decl_384, type, image1E: $o).
% 0.22/0.36  thf(decl_385, type, image1I: $o).
% 0.22/0.36  thf(decl_388, type, injFuncInInjFuncSet: $o).
% 0.22/0.36  thf(decl_389, type, injFuncSetFuncIn: $o).
% 0.22/0.36  thf(decl_390, type, injFuncSetFuncInj: $o).
% 0.22/0.36  thf(decl_393, type, surjFuncSetFuncIn: $o).
% 0.22/0.36  thf(decl_394, type, surjFuncSetFuncSurj: $o).
% 0.22/0.36  thf(decl_395, type, leftInvIsSurj: $o).
% 0.22/0.36  thf(decl_396, type, surjCantorThm: $o).
% 0.22/0.36  thf(decl_397, type, foundation2: $o).
% 0.22/0.36  thf(decl_398, type, notinself: $o).
% 0.22/0.36  thf(decl_399, type, notinself2: $o).
% 0.22/0.36  thf(decl_401, type, omegaSp: $o).
% 0.22/0.36  thf(decl_402, type, omegaSclos: $o).
% 0.22/0.36  thf(decl_403, type, peano0notS: $o).
% 0.22/0.36  thf(decl_407, type, peanoSinj: $o).
% 0.22/0.36  thf(decl_409, type, transitiveset: $i > $o).
% 0.22/0.36  thf(decl_410, type, transitivesetOp1: $o).
% 0.22/0.36  thf(decl_411, type, binintTransitive: $o).
% 0.22/0.36  thf(decl_412, type, transitivesetOp2: $o).
% 0.22/0.36  thf(decl_413, type, setunionTransitive: $o).
% 0.22/0.36  thf(decl_414, type, stricttotalorderedByIn: $i > $o).
% 0.22/0.36  thf(decl_415, type, wellorderedByIn: $i > $o).
% 0.22/0.36  thf(decl_416, type, ordinal: $i > $o).
% 0.22/0.36  thf(decl_418, type, ordinalMinLem1: $o).
% 0.22/0.36  thf(decl_419, type, ordinalTransSet: $o).
% 0.22/0.36  thf(decl_420, type, ordinalTransSet1: $o).
% 0.22/0.36  thf(decl_421, type, setunionOrdinalLem1: $o).
% 0.22/0.36  thf(decl_423, type, emptysetOrdinal: $o).
% 0.22/0.36  thf(decl_424, type, ordinalIrrefl: $o).
% 0.22/0.36  thf(decl_425, type, epred1_1: $i > $o).
% 0.22/0.36  thf(decl_426, type, epred2_1: $i > $o).
% 0.22/0.36  thf(decl_427, type, epred3_1: $i > $o).
% 0.22/0.36  thf(decl_428, type, epred4_1: $i > $o).
% 0.22/0.36  thf(decl_429, type, esk1_1: $i > $i).
% 0.22/0.36  thf(decl_430, type, esk2_1: $i > $i).
% 0.22/0.36  thf(decl_431, type, esk3_1: $i > $i).
% 0.22/0.36  thf(decl_432, type, esk4_1: $i > $i).
% 0.22/0.36  thf(decl_433, type, esk5_1: $i > $i).
% 0.22/0.36  thf(decl_434, type, esk6_1: $i > $i).
% 0.22/0.36  thf(decl_435, type, esk7_2: $i > $i > $i).
% 0.22/0.36  thf(decl_436, type, esk8_2: $i > $i > $i).
% 0.22/0.36  thf(decl_437, type, esk9_2: $i > $i > $i).
% 0.22/0.36  thf(decl_438, type, esk10_3: $i > $i > $i > $i).
% 0.22/0.36  thf(decl_439, type, esk11_1: $i > $i).
% 0.22/0.36  thf(decl_440, type, esk12_1: $i > $i).
% 0.22/0.36  thf(decl_441, type, esk13_1: $i > $i).
% 0.22/0.36  thf(decl_442, type, esk14_2: $i > $i > $i).
% 0.22/0.36  thf(decl_443, type, esk15_0: $i).
% 0.22/0.36  thf(decl_459, type, esk31_2: $i > $i > $i).
% 0.22/0.36  thf(wellorderedByIn, axiom, ((wellorderedByIn)=(^[X4:$i]:((((stricttotalorderedByIn @ X4))&(![X21:$i]:((((in @ X21 @ (powerset @ X4)))=>((((nonempty @ X21))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', wellorderedByIn)).
% 0.22/0.36  thf(stricttotalorderedByIn, axiom, ((stricttotalorderedByIn)=(^[X4:$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.vlUndA7UJh/E---3.1_2592797.p', stricttotalorderedByIn)).
% 0.22/0.36  thf(ordinal, axiom, ((ordinal)=(^[X2:$i]:((((transitiveset @ X2))&((wellorderedByIn @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', ordinal)).
% 0.22/0.36  thf(ordinalIrrefl2, 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)=>![X21:$i]:(((ordinal @ X21)=>~((in @ X21 @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', ordinalIrrefl2)).
% 0.22/0.36  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', nonemptyI)).
% 0.22/0.36  thf(setunionOrdinalLem1, axiom, ((setunionOrdinalLem1)<=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(ordinal @ X2)))=>(transitiveset @ (setunion @ X21))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', setunionOrdinalLem1)).
% 0.22/0.36  thf(ordinalMinLem1, axiom, ((ordinalMinLem1)<=>![X21:$i]:(((ordinal @ X21)=>![X48:$i]:(((ordinal @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', ordinalMinLem1)).
% 0.22/0.36  thf(foundation2, axiom, ((foundation2)<=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', foundation2)).
% 0.22/0.36  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', nonemptyImpWitness)).
% 0.22/0.36  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', nonemptyI1)).
% 0.22/0.36  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', nonemptyE1)).
% 0.22/0.36  thf(setunionTransitive, axiom, ((setunionTransitive)<=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(transitiveset @ X2)))=>(transitiveset @ (setunion @ X21))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', setunionTransitive)).
% 0.22/0.36  thf(transitivesetOp2, axiom, ((transitivesetOp2)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i, X2:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', transitivesetOp2)).
% 0.22/0.36  thf(binintTransitive, axiom, ((binintTransitive)<=>![X21:$i]:(((transitiveset @ X21)=>![X48:$i]:(((transitiveset @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', binintTransitive)).
% 0.22/0.36  thf(transitivesetOp1, axiom, ((transitivesetOp1)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.vlUndA7UJh/E---3.1_2592797.p', transitivesetOp1)).
% 0.22/0.36  thf(c_0_15, plain, ((wellorderedByIn)=(^[Z0:$i]:((((((((![X88:$i]:((((in @ X88 @ Z0))=>(![X89:$i]:((((in @ X89 @ Z0))=>(![X90:$i]:((((in @ X90 @ Z0))=>((((((in @ X88 @ X89))&((in @ X89 @ X90))))=>((in @ X88 @ X90)))))))))))))&(![X91:$i]:((((in @ X91 @ Z0))=>(![X92:$i]:((((in @ X92 @ Z0))=>(((((((X91)=(X92)))|((in @ X91 @ X92))))|((in @ X92 @ X91))))))))))))&(![X93:$i]:((((in @ X93 @ Z0))=>(~((in @ X93 @ X93)))))))))&(![X21:$i]:((((in @ X21 @ (powerset @ Z0)))=>((((nonempty @ X21))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), inference(fof_simplification,[status(thm)],[wellorderedByIn])).
% 0.22/0.36  thf(c_0_16, plain, ((stricttotalorderedByIn)=(^[Z0:$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])).
% 0.22/0.36  thf(c_0_17, plain, ((ordinal)=(^[Z0:$i]:((((transitiveset @ Z0))&(((((((((![X94:$i]:((((in @ X94 @ Z0))=>(![X95:$i]:((((in @ X95 @ Z0))=>(![X96:$i]:((((in @ X96 @ Z0))=>((((((in @ X94 @ X95))&((in @ X95 @ X96))))=>((in @ X94 @ X96)))))))))))))&(![X97:$i]:((((in @ X97 @ Z0))=>(![X98:$i]:((((in @ X98 @ Z0))=>(((((((X97)=(X98)))|((in @ X97 @ X98))))|((in @ X98 @ X97))))))))))))&(![X99:$i]:((((in @ X99 @ Z0))=>(~((in @ X99 @ X99)))))))))&(![X100:$i]:((((in @ X100 @ (powerset @ Z0)))=>((((nonempty @ X100))=>(?[X101:$i]:((((in @ X101 @ X100))&(![X102:$i]:((((in @ X102 @ X100))=>(((((X101)=(X102)))|((in @ X101 @ X102)))))))))))))))))))))), inference(fof_simplification,[status(thm)],[ordinal])).
% 0.22/0.36  thf(c_0_18, plain, ((wellorderedByIn)=(^[Z0:$i]:((((((((![X88:$i]:((((in @ X88 @ Z0))=>(![X89:$i]:((((in @ X89 @ Z0))=>(![X90:$i]:((((in @ X90 @ Z0))=>((((((in @ X88 @ X89))&((in @ X89 @ X90))))=>((in @ X88 @ X90)))))))))))))&(![X91:$i]:((((in @ X91 @ Z0))=>(![X92:$i]:((((in @ X92 @ Z0))=>(((((((X91)=(X92)))|((in @ X91 @ X92))))|((in @ X92 @ X91))))))))))))&(![X93:$i]:((((in @ X93 @ Z0))=>(~((in @ X93 @ X93)))))))))&(![X21:$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])).
% 0.22/0.36  thf(c_0_19, plain, ((ordinal)=(^[Z0:$i]:((((transitiveset @ Z0))&(((((((((![X94:$i]:((((in @ X94 @ Z0))=>(![X95:$i]:((((in @ X95 @ Z0))=>(![X96:$i]:((((in @ X96 @ Z0))=>((((((in @ X94 @ X95))&((in @ X95 @ X96))))=>((in @ X94 @ X96)))))))))))))&(![X97:$i]:((((in @ X97 @ Z0))=>(![X98:$i]:((((in @ X98 @ Z0))=>(((((((X97)=(X98)))|((in @ X97 @ X98))))|((in @ X98 @ X97))))))))))))&(![X99:$i]:((((in @ X99 @ Z0))=>(~((in @ X99 @ X99)))))))))&(![X100:$i]:((((in @ X100 @ (powerset @ Z0)))=>((((nonempty @ X100))=>(?[X101:$i]:((((in @ X101 @ X100))&(![X102:$i]:((((in @ X102 @ X100))=>(((((X101)=(X102)))|((in @ X101 @ X102)))))))))))))))))))))), inference(apply_def,[status(thm)],[c_0_17, c_0_18])).
% 0.22/0.36  thf(c_0_20, plain, ![X21:$i]:(((epred4_1 @ X21)<=>((transitiveset @ X21)&(((![X181:$i]:(((in @ X181 @ X21)=>![X182:$i]:(((in @ X182 @ X21)=>![X183:$i]:(((in @ X183 @ X21)=>(((in @ X181 @ X182)&(in @ X182 @ X183))=>(in @ X181 @ X183))))))))&![X184:$i]:(((in @ X184 @ X21)=>![X185:$i]:(((in @ X185 @ X21)=>(((X184)=(X185))|(in @ X184 @ X185)|(in @ X185 @ X184)))))))&![X186:$i]:(((in @ X186 @ X21)=>~(in @ X186 @ X186))))&![X187:$i]:(((in @ X187 @ (powerset @ X21))=>((nonempty @ X187)=>?[X188:$i]:(((in @ X188 @ X187)&![X189:$i]:(((in @ X189 @ X187)=>(((X188)=(X189))|(in @ X188 @ X189))))))))))))), introduced(definition)).
% 0.22/0.36  thf(c_0_21, 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)=>![X21:$i]:(((ordinal @ X21)=>~((in @ X21 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[ordinalIrrefl2])).
% 0.22/0.36  thf(c_0_22, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.36  thf(c_0_23, axiom, ((setunionOrdinalLem1)=(![X21:$i]:(((![X2:$i]:((((in @ X2 @ X21))=>(((((transitiveset @ X2))&(((((((((![X121:$i]:((((in @ X121 @ X2))=>(![X122:$i]:((((in @ X122 @ X2))=>(![X123:$i]:((((in @ X123 @ X2))=>((((((in @ X121 @ X122))&((in @ X122 @ X123))))=>((in @ X121 @ X123)))))))))))))&(![X124:$i]:((((in @ X124 @ X2))=>(![X125:$i]:((((in @ X125 @ X2))=>(((((((X124)=(X125)))|((in @ X124 @ X125))))|((in @ X125 @ X124))))))))))))&(![X126:$i]:((((in @ X126 @ X2))=>(~((in @ X126 @ X126)))))))))&(![X127:$i]:((((in @ X127 @ (powerset @ X2)))=>((((nonempty @ X127))=>(?[X128:$i]:((((in @ X128 @ X127))&(![X129:$i]:((((in @ X129 @ X127))=>(((((X128)=(X129)))|((in @ X128 @ X129))))))))))))))))))))))))=>((transitiveset @ (setunion @ X21))))))), inference(apply_def,[status(thm)],[setunionOrdinalLem1, c_0_19])).
% 0.22/0.36  thf(c_0_24, axiom, ((ordinalMinLem1)=(![X21:$i]:(((((((transitiveset @ X21))&(((((((((![X103:$i]:((((in @ X103 @ X21))=>(![X104:$i]:((((in @ X104 @ X21))=>(![X105:$i]:((((in @ X105 @ X21))=>((((((in @ X103 @ X104))&((in @ X104 @ X105))))=>((in @ X103 @ X105)))))))))))))&(![X106:$i]:((((in @ X106 @ X21))=>(![X107:$i]:((((in @ X107 @ X21))=>(((((((X106)=(X107)))|((in @ X106 @ X107))))|((in @ X107 @ X106))))))))))))&(![X108:$i]:((((in @ X108 @ X21))=>(~((in @ X108 @ X108)))))))))&(![X109:$i]:((((in @ X109 @ (powerset @ X21)))=>((((nonempty @ X109))=>(?[X110:$i]:((((in @ X110 @ X109))&(![X111:$i]:((((in @ X111 @ X109))=>(((((X110)=(X111)))|((in @ X110 @ X111)))))))))))))))))))))=>(![X48:$i]:(((((((transitiveset @ X48))&(((((((((![X112:$i]:((((in @ X112 @ X48))=>(![X113:$i]:((((in @ X113 @ X48))=>(![X114:$i]:((((in @ X114 @ X48))=>((((((in @ X112 @ X113))&((in @ X113 @ X114))))=>((in @ X112 @ X114)))))))))))))&(![X115:$i]:((((in @ X115 @ X48))=>(![X116:$i]:((((in @ X116 @ X48))=>(((((((X115)=(X116)))|((in @ X115 @ X116))))|((in @ X116 @ X115))))))))))))&(![X117:$i]:((((in @ X117 @ X48))=>(~((in @ X117 @ X117)))))))))&(![X118:$i]:((((in @ X118 @ (powerset @ X48)))=>((((nonempty @ X118))=>(?[X119:$i]:((((in @ X119 @ X118))&(![X120:$i]:((((in @ X120 @ X118))=>(((((X119)=(X120)))|((in @ X119 @ X120)))))))))))))))))))))=>((transitiveset @ (binintersect @ X21 @ X48)))))))))), inference(apply_def,[status(thm)],[ordinalMinLem1, c_0_19])).
% 0.22/0.36  thf(c_0_25, plain, ![X150:$i]:(((epred1_1 @ X150)<=>(![X151:$i]:(((in @ X151 @ X150)=>![X152:$i]:(((in @ X152 @ X150)=>![X153:$i]:(((in @ X153 @ X150)=>(((in @ X151 @ X152)&(in @ X152 @ X153))=>(in @ X151 @ X153))))))))&![X154:$i]:(((in @ X154 @ X150)=>![X155:$i]:(((in @ X155 @ X150)=>(((X154)=(X155))|(in @ X154 @ X155)|(in @ X155 @ X154))))))))), introduced(definition)).
% 0.22/0.36  thf(c_0_26, plain, ![X160:$i]:(((epred2_1 @ X160)<=>(![X161:$i]:(((in @ X161 @ X160)=>![X162:$i]:(((in @ X162 @ X160)=>![X163:$i]:(((in @ X163 @ X160)=>(((in @ X161 @ X162)&(in @ X162 @ X163))=>(in @ X161 @ X163))))))))&![X164:$i]:(((in @ X164 @ X160)=>![X165:$i]:(((in @ X165 @ X160)=>(((X164)=(X165))|(in @ X164 @ X165)|(in @ X165 @ X164))))))))), introduced(definition)).
% 0.22/0.36  thf(c_0_27, plain, ![X171:$i]:(((epred3_1 @ X171)<=>(![X172:$i]:(((in @ X172 @ X171)=>![X173:$i]:(((in @ X173 @ X171)=>![X174:$i]:(((in @ X174 @ X171)=>(((in @ X172 @ X173)&(in @ X173 @ X174))=>(in @ X172 @ X174))))))))&![X175:$i]:(((in @ X175 @ X171)=>![X176:$i]:(((in @ X176 @ X171)=>(((X175)=(X176))|(in @ X175 @ X176)|(in @ X176 @ X175))))))))), introduced(definition)).
% 0.22/0.36  thf(c_0_28, plain, ![X21:$i]:(((epred4_1 @ X21)=>((transitiveset @ X21)&(((![X181:$i]:(((in @ X181 @ X21)=>![X182:$i]:(((in @ X182 @ X21)=>![X183:$i]:(((in @ X183 @ X21)=>(((in @ X181 @ X182)&(in @ X182 @ X183))=>(in @ X181 @ X183))))))))&![X184:$i]:(((in @ X184 @ X21)=>![X185:$i]:(((in @ X185 @ X21)=>(((X184)=(X185))|(in @ X184 @ X185)|(in @ X185 @ X184)))))))&![X186:$i]:(((in @ X186 @ X21)=>~(in @ X186 @ X186))))&![X187:$i]:(((in @ X187 @ (powerset @ X21))=>((nonempty @ X187)=>?[X188:$i]:(((in @ X188 @ X187)&![X189:$i]:(((in @ X189 @ X187)=>(((X188)=(X189))|(in @ X188 @ X189))))))))))))), inference(split_equiv,[status(thm)],[c_0_20])).
% 0.22/0.36  thf(c_0_29, 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)=>(![X130:$i]:(((nonempty @ X130)=>?[X131:$i]:((in @ X131 @ X130))))=>(![X132:$i, X133:$i > $o, X134:$i]:(((in @ X134 @ X132)=>((X133 @ X134)=>(nonempty @ (dsetconstr @ X132 @ X133)))))=>(![X135:$i]:((?[X136:$i]:((in @ X136 @ X135))=>(nonempty @ X135)))=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>(![X137:$i]:(((nonempty @ X137)=>?[X138:$i]:(((in @ X138 @ X137)&$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)=>(![X139:$i]:(((nonempty @ X139)=>?[X140:$i]:(((in @ X140 @ X139)&((binintersect @ X140 @ X139)=(emptyset))))))=>((notinself)=>((notinself2)=>((omegaSp)=>((omegaSclos)=>((peano0notS)=>((peanoSinj)=>(![X141:$i]:(((transitiveset @ X141)=>![X142:$i]:(((in @ X142 @ X141)=>(subset @ X142 @ X141)))))=>(![X143:$i]:(((transitiveset @ X143)=>![X144:$i]:(((transitiveset @ X144)=>(transitiveset @ (binintersect @ X143 @ X144))))))=>(![X145:$i]:(((transitiveset @ X145)=>![X146:$i, X147:$i]:(((in @ X146 @ X145)=>((in @ X147 @ X146)=>(in @ X147 @ X145))))))=>(![X148:$i]:((![X149:$i]:(((in @ X149 @ X148)=>(transitiveset @ X149)))=>(transitiveset @ (setunion @ X148))))=>(![X150:$i]:((((transitiveset @ X150)&(((epred1_1 @ X150)&![X156:$i]:(((in @ X156 @ X150)=>~(in @ X156 @ X156))))&![X157:$i]:(((in @ X157 @ (powerset @ X150))=>((nonempty @ X157)=>?[X158:$i]:(((in @ X158 @ X157)&![X159:$i]:(((in @ X159 @ X157)=>(((X158)=(X159))|(in @ X158 @ X159)))))))))))=>![X160:$i]:((((transitiveset @ X160)&(((epred2_1 @ X160)&![X166:$i]:(((in @ X166 @ X160)=>~(in @ X166 @ X166))))&![X167:$i]:(((in @ X167 @ (powerset @ X160))=>((nonempty @ X167)=>?[X168:$i]:(((in @ X168 @ X167)&![X169:$i]:(((in @ X169 @ X167)=>(((X168)=(X169))|(in @ X168 @ X169)))))))))))=>(transitiveset @ (binintersect @ X150 @ X160))))))=>((ordinalTransSet)=>((ordinalTransSet1)=>(![X170:$i]:((![X171:$i]:(((in @ X171 @ X170)=>((transitiveset @ X171)&(((epred3_1 @ X171)&![X177:$i]:(((in @ X177 @ X171)=>~(in @ X177 @ X177))))&![X178:$i]:(((in @ X178 @ (powerset @ X171))=>((nonempty @ X178)=>?[X179:$i]:(((in @ X179 @ X178)&![X180:$i]:(((in @ X180 @ X178)=>(((X179)=(X180))|(in @ X179 @ X180)))))))))))))=>(transitiveset @ (setunion @ X170))))=>((emptysetOrdinal)=>((ordinalIrrefl)=>![X21:$i]:(((epred4_1 @ X21)=>~(in @ X21 @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21, foundation2]), nonemptyImpWitness]), nonemptyI1]), c_0_22]), nonemptyE1]), c_0_23]), c_0_24]), setunionTransitive]), transitivesetOp2]), binintTransitive]), transitivesetOp1]), c_0_19])])]), c_0_25]), c_0_26]), c_0_27]), c_0_20])).
% 0.22/0.36  thf(c_0_30, plain, ![X245:$i, X246:$i, X247:$i, X248:$i, X249:$i, X250:$i, X251:$i, X252:$i, X254:$i]:((((transitiveset @ X245)|~(epred4_1 @ X245))&((((~(in @ X246 @ X245)|(~(in @ X247 @ X245)|(~(in @ X248 @ X245)|(~(in @ X246 @ X247)|~(in @ X247 @ X248)|(in @ X246 @ X248))))|~(epred4_1 @ X245))&(~(in @ X249 @ X245)|(~(in @ X250 @ X245)|(((X249)=(X250))|(in @ X249 @ X250)|(in @ X250 @ X249)))|~(epred4_1 @ X245)))&(~(in @ X251 @ X245)|~(in @ X251 @ X251)|~(epred4_1 @ X245)))&(((in @ (esk31_2 @ X245 @ X252) @ X252)|~(nonempty @ X252)|~(in @ X252 @ (powerset @ X245))|~(epred4_1 @ X245))&(~(in @ X254 @ X252)|(((esk31_2 @ X245 @ X252)=(X254))|(in @ (esk31_2 @ X245 @ X252) @ X254))|~(nonempty @ X252)|~(in @ X252 @ (powerset @ X245))|~(epred4_1 @ X245)))))), 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_28])])])])])])).
% 0.22/0.36  thf(c_0_31, negated_conjecture, ![X190:$i, X192:$i, X193:$i > $o, X194:$i, X195:$i, X196:$i, X197:$i, X199:$i, X201:$i, X202:$i, X203:$i, X204:$i, X205:$i, X206:$i, X207:$i, X208:$i, X210:$i, X213:$i, X215:$i, X218:$i, X220:$i, X224:$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 @ X190)|(in @ (esk1_1 @ X190) @ X190))&((~(in @ X194 @ X192)|(~(X193 @ X194)|(nonempty @ (dsetconstr @ X192 @ X193))))&((~(in @ X196 @ X195)|(nonempty @ X195))&((setadjoinIL)&((emptyinunitempty)&((setadjoinIR)&((setadjoinE)&((setadjoinOr)&((setoftrueEq)&((powersetI)&((emptyinPowerset)&((emptyInPowerset)&((powersetE)&((setunionI)&((setunionE)&((subPowSU)&((exuE2)&((((in @ (esk2_1 @ X197) @ X197)|~(nonempty @ X197))&(($true)|~(nonempty @ X197)))&((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 @ X199) @ X199)|~(nonempty @ X199))&(((binintersect @ (esk3_1 @ X199) @ X199)=(emptyset))|~(nonempty @ X199)))&((notinself)&((notinself2)&((omegaSp)&((omegaSclos)&((peano0notS)&((peanoSinj)&((~(transitiveset @ X201)|(~(in @ X202 @ X201)|(subset @ X202 @ X201)))&((~(transitiveset @ X203)|(~(transitiveset @ X204)|(transitiveset @ (binintersect @ X203 @ X204))))&((~(transitiveset @ X205)|(~(in @ X206 @ X205)|(~(in @ X207 @ X206)|(in @ X207 @ X205))))&((((in @ (esk4_1 @ X208) @ X208)|(transitiveset @ (setunion @ X208)))&(~(transitiveset @ (esk4_1 @ X208))|(transitiveset @ (setunion @ X208))))&(((((((in @ (esk9_2 @ X210 @ X215) @ (powerset @ X215))|((in @ (esk8_2 @ X210 @ X215) @ X215)|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|((in @ (esk6_1 @ X210) @ (powerset @ X210))|((in @ (esk5_1 @ X210) @ X210)|~(epred1_1 @ X210))|~(transitiveset @ X210)))&(((nonempty @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ X215)|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|((in @ (esk6_1 @ X210) @ (powerset @ X210))|((in @ (esk5_1 @ X210) @ X210)|~(epred1_1 @ X210))|~(transitiveset @ X210)))&(((in @ (esk10_3 @ X210 @ X215 @ X218) @ (esk9_2 @ X210 @ X215))|~(in @ X218 @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ X215)|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|((in @ (esk6_1 @ X210) @ (powerset @ X210))|((in @ (esk5_1 @ X210) @ X210)|~(epred1_1 @ X210))|~(transitiveset @ X210)))&((((X218)!=(esk10_3 @ X210 @ X215 @ X218))|~(in @ X218 @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ X215)|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|((in @ (esk6_1 @ X210) @ (powerset @ X210))|((in @ (esk5_1 @ X210) @ X210)|~(epred1_1 @ X210))|~(transitiveset @ X210)))&(~(in @ X218 @ (esk10_3 @ X210 @ X215 @ X218))|~(in @ X218 @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ 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X215))|(((X213)!=(esk7_2 @ X210 @ X213))|~(in @ X213 @ (esk6_1 @ X210))|((in @ (esk5_1 @ X210) @ (esk5_1 @ X210))|~(epred1_1 @ X210))|~(transitiveset @ X210))))))))&((((in @ (esk9_2 @ X210 @ X215) @ (powerset @ X215))|((in @ (esk8_2 @ X210 @ X215) @ X215)|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|(~(in @ X213 @ (esk7_2 @ X210 @ X213))|~(in @ X213 @ (esk6_1 @ X210))|((in @ (esk5_1 @ X210) @ (esk5_1 @ X210))|~(epred1_1 @ X210))|~(transitiveset @ X210)))&(((nonempty @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ X215)|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|(~(in @ X213 @ (esk7_2 @ X210 @ X213))|~(in @ X213 @ (esk6_1 @ X210))|((in @ (esk5_1 @ X210) @ (esk5_1 @ X210))|~(epred1_1 @ X210))|~(transitiveset @ X210)))&(((in @ (esk10_3 @ X210 @ X215 @ X218) @ (esk9_2 @ X210 @ X215))|~(in @ X218 @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ X215)|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|(~(in @ X213 @ (esk7_2 @ X210 @ X213))|~(in @ X213 @ (esk6_1 @ X210))|((in @ (esk5_1 @ X210) @ (esk5_1 @ X210))|~(epred1_1 @ X210))|~(transitiveset @ X210)))&((((X218)!=(esk10_3 @ X210 @ X215 @ X218))|~(in @ X218 @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ X215)|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|(~(in @ X213 @ (esk7_2 @ X210 @ X213))|~(in @ X213 @ (esk6_1 @ X210))|((in @ (esk5_1 @ X210) @ (esk5_1 @ X210))|~(epred1_1 @ X210))|~(transitiveset @ X210)))&(~(in @ X218 @ (esk10_3 @ X210 @ X215 @ X218))|~(in @ X218 @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ X215)|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|(~(in @ X213 @ (esk7_2 @ X210 @ X213))|~(in @ X213 @ (esk6_1 @ X210))|((in @ (esk5_1 @ X210) @ (esk5_1 @ X210))|~(epred1_1 @ X210))|~(transitiveset @ X210)))))))&(((in @ (esk9_2 @ X210 @ X215) @ (powerset @ X215))|((in @ (esk8_2 @ X210 @ X215) @ (esk8_2 @ X210 @ X215))|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|(~(in @ X213 @ (esk7_2 @ X210 @ X213))|~(in @ X213 @ (esk6_1 @ X210))|((in @ (esk5_1 @ X210) @ (esk5_1 @ X210))|~(epred1_1 @ X210))|~(transitiveset @ X210)))&(((nonempty @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ (esk8_2 @ X210 @ X215))|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|(~(in @ X213 @ (esk7_2 @ X210 @ X213))|~(in @ X213 @ (esk6_1 @ X210))|((in @ (esk5_1 @ X210) @ (esk5_1 @ X210))|~(epred1_1 @ X210))|~(transitiveset @ X210)))&(((in @ (esk10_3 @ X210 @ X215 @ X218) @ (esk9_2 @ X210 @ X215))|~(in @ X218 @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ (esk8_2 @ X210 @ X215))|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|(~(in @ X213 @ (esk7_2 @ X210 @ X213))|~(in @ X213 @ (esk6_1 @ X210))|((in @ (esk5_1 @ X210) @ (esk5_1 @ X210))|~(epred1_1 @ X210))|~(transitiveset @ X210)))&((((X218)!=(esk10_3 @ X210 @ X215 @ X218))|~(in @ X218 @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ (esk8_2 @ X210 @ X215))|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|(~(in @ X213 @ (esk7_2 @ X210 @ X213))|~(in @ X213 @ (esk6_1 @ X210))|((in @ (esk5_1 @ X210) @ (esk5_1 @ X210))|~(epred1_1 @ X210))|~(transitiveset @ X210)))&(~(in @ X218 @ (esk10_3 @ X210 @ X215 @ X218))|~(in @ X218 @ (esk9_2 @ X210 @ X215))|((in @ (esk8_2 @ X210 @ X215) @ (esk8_2 @ X210 @ X215))|~(epred2_1 @ X215))|~(transitiveset @ X215)|(transitiveset @ (binintersect @ X210 @ X215))|(~(in @ X213 @ (esk7_2 @ X210 @ X213))|~(in @ X213 @ (esk6_1 @ X210))|((in @ (esk5_1 @ X210) @ (esk5_1 @ X210))|~(epred1_1 @ X210))|~(transitiveset @ X210)))))))))))))&((ordinalTransSet)&((ordinalTransSet1)&((((in @ (esk11_1 @ X220) @ X220)|(transitiveset @ (setunion @ X220)))&((((in @ (esk13_1 @ X220) @ (powerset @ (esk11_1 @ X220)))|((in @ (esk12_1 @ X220) @ (esk11_1 @ X220))|~(epred3_1 @ (esk11_1 @ X220)))|~(transitiveset @ (esk11_1 @ X220))|(transitiveset @ (setunion @ X220)))&(((nonempty @ (esk13_1 @ X220))|((in @ (esk12_1 @ X220) @ (esk11_1 @ X220))|~(epred3_1 @ (esk11_1 @ X220)))|~(transitiveset @ (esk11_1 @ X220))|(transitiveset @ (setunion @ X220)))&(((in @ (esk14_2 @ X220 @ X224) @ (esk13_1 @ X220))|~(in @ X224 @ (esk13_1 @ X220))|((in @ (esk12_1 @ X220) @ (esk11_1 @ X220))|~(epred3_1 @ (esk11_1 @ X220)))|~(transitiveset @ (esk11_1 @ X220))|(transitiveset @ (setunion @ X220)))&((((X224)!=(esk14_2 @ X220 @ X224))|~(in @ X224 @ (esk13_1 @ X220))|((in @ (esk12_1 @ X220) @ (esk11_1 @ X220))|~(epred3_1 @ (esk11_1 @ X220)))|~(transitiveset @ (esk11_1 @ X220))|(transitiveset @ (setunion @ X220)))&(~(in @ X224 @ (esk14_2 @ X220 @ X224))|~(in @ X224 @ (esk13_1 @ X220))|((in @ (esk12_1 @ X220) @ (esk11_1 @ X220))|~(epred3_1 @ (esk11_1 @ X220)))|~(transitiveset @ (esk11_1 @ X220))|(transitiveset @ (setunion @ X220)))))))&(((in @ (esk13_1 @ X220) @ (powerset @ (esk11_1 @ X220)))|((in @ (esk12_1 @ X220) @ (esk12_1 @ X220))|~(epred3_1 @ (esk11_1 @ X220)))|~(transitiveset @ (esk11_1 @ X220))|(transitiveset @ (setunion @ X220)))&(((nonempty @ (esk13_1 @ X220))|((in @ (esk12_1 @ X220) @ (esk12_1 @ X220))|~(epred3_1 @ (esk11_1 @ X220)))|~(transitiveset @ (esk11_1 @ X220))|(transitiveset @ (setunion @ X220)))&(((in @ (esk14_2 @ X220 @ X224) @ (esk13_1 @ X220))|~(in @ X224 @ (esk13_1 @ X220))|((in @ (esk12_1 @ X220) @ (esk12_1 @ X220))|~(epred3_1 @ (esk11_1 @ X220)))|~(transitiveset @ (esk11_1 @ X220))|(transitiveset @ (setunion @ X220)))&((((X224)!=(esk14_2 @ X220 @ X224))|~(in @ X224 @ (esk13_1 @ X220))|((in @ (esk12_1 @ X220) @ (esk12_1 @ X220))|~(epred3_1 @ (esk11_1 @ X220)))|~(transitiveset @ (esk11_1 @ X220))|(transitiveset @ (setunion @ X220)))&(~(in @ X224 @ (esk14_2 @ X220 @ X224))|~(in @ X224 @ (esk13_1 @ X220))|((in @ (esk12_1 @ X220) @ (esk12_1 @ X220))|~(epred3_1 @ (esk11_1 @ X220)))|~(transitiveset @ (esk11_1 @ X220))|(transitiveset @ (setunion @ X220)))))))))&((emptysetOrdinal)&((ordinalIrrefl)&((epred4_1 @ esk15_0)&(in @ esk15_0 @ esk15_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_29])])])])])])])).
% 0.22/0.36  thf(c_0_32, plain, ![X2:$i, X3:$i]:((~((in @ X2 @ X3))|~((in @ X2 @ X2))|~((epred4_1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_30])).
% 0.22/0.36  thf(c_0_33, negated_conjecture, (in @ esk15_0 @ esk15_0), inference(split_conjunct,[status(thm)],[c_0_31])).
% 0.22/0.36  thf(c_0_34, negated_conjecture, (epred4_1 @ esk15_0), inference(split_conjunct,[status(thm)],[c_0_31])).
% 0.22/0.36  thf(c_0_35, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33]), c_0_33]), c_0_34])]), ['proof']).
% 0.22/0.36  % SZS output end CNFRefutation
% 0.22/0.36  % Parsed axioms                        : 745
% 0.22/0.36  % Removed by relevancy pruning/SinE    : 730
% 0.22/0.36  % Initial clauses                      : 548
% 0.22/0.36  % Removed in clause preprocessing      : 1
% 0.22/0.36  % Initial clauses in saturation        : 547
% 0.22/0.36  % Processed clauses                    : 345
% 0.22/0.36  % ...of these trivial                  : 0
% 0.22/0.36  % ...subsumed                          : 1
% 0.22/0.36  % ...remaining for further processing  : 344
% 0.22/0.36  % Other redundant clauses eliminated   : 0
% 0.22/0.36  % Clauses deleted for lack of memory   : 0
% 0.22/0.36  % Backward-subsumed                    : 0
% 0.22/0.36  % Backward-rewritten                   : 0
% 0.22/0.36  % Generated clauses                    : 14
% 0.22/0.36  % ...of the previous two non-redundant : 5
% 0.22/0.36  % ...aggressively subsumed             : 0
% 0.22/0.36  % Contextual simplify-reflections      : 0
% 0.22/0.36  % Paramodulations                      : 14
% 0.22/0.36  % Factorizations                       : 0
% 0.22/0.36  % NegExts                              : 0
% 0.22/0.36  % Equation resolutions                 : 0
% 0.22/0.36  % Disequality decompositions           : 0
% 0.22/0.36  % Total rewrite steps                  : 2
% 0.22/0.36  % ...of those cached                   : 0
% 0.22/0.36  % Propositional unsat checks           : 0
% 0.22/0.36  %    Propositional check models        : 0
% 0.22/0.36  %    Propositional check unsatisfiable : 0
% 0.22/0.36  %    Propositional clauses             : 0
% 0.22/0.36  %    Propositional clauses after purity: 0
% 0.22/0.36  %    Propositional unsat core size     : 0
% 0.22/0.36  %    Propositional preprocessing time  : 0.000
% 0.22/0.36  %    Propositional encoding time       : 0.000
% 0.22/0.36  %    Propositional solver time         : 0.000
% 0.22/0.36  %    Success case prop preproc time    : 0.000
% 0.22/0.36  %    Success case prop encoding time   : 0.000
% 0.22/0.36  %    Success case prop solver time     : 0.000
% 0.22/0.36  % Current number of processed clauses  : 344
% 0.22/0.36  %    Positive orientable unit clauses  : 331
% 0.22/0.36  %    Positive unorientable unit clauses: 0
% 0.22/0.36  %    Negative unit clauses             : 0
% 0.22/0.36  %    Non-unit-clauses                  : 13
% 0.22/0.36  % Current number of unprocessed clauses: 207
% 0.22/0.36  % ...number of literals in the above   : 1380
% 0.22/0.36  % Current number of archived formulas  : 0
% 0.22/0.36  % Current number of archived clauses   : 0
% 0.22/0.36  % Clause-clause subsumption calls (NU) : 25
% 0.22/0.36  % Rec. Clause-clause subsumption calls : 25
% 0.22/0.36  % Non-unit clause-clause subsumptions  : 1
% 0.22/0.36  % Unit Clause-clause subsumption calls : 0
% 0.22/0.36  % Rewrite failures with RHS unbound    : 0
% 0.22/0.36  % BW rewrite match attempts            : 0
% 0.22/0.36  % BW rewrite match successes           : 0
% 0.22/0.36  % Condensation attempts                : 0
% 0.22/0.36  % Condensation successes               : 0
% 0.22/0.36  % Termbank termtop insertions          : 34422
% 0.22/0.36  % Search garbage collected termcells   : 11300
% 0.22/0.36  
% 0.22/0.36  % -------------------------------------------------
% 0.22/0.36  % User time                : 0.043 s
% 0.22/0.36  % System time              : 0.010 s
% 0.22/0.36  % Total time               : 0.053 s
% 0.22/0.36  % Maximum resident set size: 6536 pages
% 0.22/0.36  
% 0.22/0.36  % -------------------------------------------------
% 0.22/0.36  % User time                : 0.066 s
% 0.22/0.36  % System time              : 0.015 s
% 0.22/0.36  % Total time               : 0.081 s
% 0.22/0.36  % Maximum resident set size: 5888 pages
% 0.22/0.36  % E exiting
%------------------------------------------------------------------------------