E---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SEU823^1 : 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 : n007.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 0.30s 0.46s
% Output   : CNFRefutation 0.98s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU823^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18  % Computer : n007.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 14:32:55 UTC 2026
% 0.10/0.19  % CPUTime  : 
% 0.10/0.19  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23  Running higher-order theorem proving
% 0.23/0.32  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.5hk0wYH06C/E---3.1_3450233.p
% 0.30/0.46  % Version: 3.5.1-ho
% 0.30/0.46  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.30/0.46  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.46  % Starting ehoh_best5 with 300s (1) cores
% 0.30/0.46  % Starting almost_fo_3_lam with 300s (1) cores
% 0.30/0.46  % Starting new_bool_5 with 300s (1) cores
% 0.30/0.46  % Starting pre_casc_3 with 300s (1) cores
% 0.30/0.46  % Starting ho_unfolding_8 with 300s (1) cores
% 0.30/0.46  % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.30/0.46  % Starting new_bool_3 with 300s (1) cores
% 0.30/0.46  % Starting new_ho_5 with 300s (1) cores
% 0.30/0.46  % pre_casc_3 with pid 3450249 completed with status 0
% 0.30/0.46  % Result found by pre_casc_3
% 0.30/0.46  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.30/0.46  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.46  % Starting ehoh_best5 with 300s (1) cores
% 0.30/0.46  % Starting almost_fo_3_lam with 300s (1) cores
% 0.30/0.46  % Starting new_bool_5 with 300s (1) cores
% 0.30/0.46  % Starting pre_casc_3 with 300s (1) cores
% 0.30/0.46  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.30/0.46  % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.30/0.46  % Search class: HGHSF-FSLM31-SHFMMFBN
% 0.30/0.46  % partial match(2): HGHSM-FSLM31-SHFMMSBN
% 0.30/0.46  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.30/0.46  % Starting SubtermCWHack with 28s (1) cores
% 0.30/0.46  % SubtermCWHack with pid 3450254 completed with status 0
% 0.30/0.46  % Result found by SubtermCWHack
% 0.30/0.46  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.30/0.46  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.46  % Starting ehoh_best5 with 300s (1) cores
% 0.30/0.46  % Starting almost_fo_3_lam with 300s (1) cores
% 0.30/0.46  % Starting new_bool_5 with 300s (1) cores
% 0.30/0.46  % Starting pre_casc_3 with 300s (1) cores
% 0.30/0.46  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.30/0.46  % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.30/0.46  % Search class: HGHSF-FSLM31-SHFMMFBN
% 0.30/0.46  % partial match(2): HGHSM-FSLM31-SHFMMSBN
% 0.30/0.46  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.30/0.46  % Starting SubtermCWHack with 28s (1) cores
% 0.30/0.46  % Preprocessing time       : 0.009 s
% 0.30/0.46  
% 0.30/0.46  % Proof found!
% 0.30/0.46  % SZS status Theorem
% 0.30/0.46  % SZS output start CNFRefutation
% 0.30/0.46  thf(decl_23, type, in: $i > $i > $o).
% 0.30/0.46  thf(decl_25, type, setextAx: $o).
% 0.30/0.46  thf(decl_26, type, emptyset: $i).
% 0.30/0.46  thf(decl_27, type, emptysetAx: $o).
% 0.30/0.46  thf(decl_29, type, setadjoinAx: $o).
% 0.30/0.46  thf(decl_30, type, powerset: $i > $i).
% 0.30/0.46  thf(decl_31, type, powersetAx: $o).
% 0.30/0.46  thf(decl_32, type, setunion: $i > $i).
% 0.30/0.46  thf(decl_33, type, setunionAx: $o).
% 0.30/0.46  thf(decl_35, type, omega0Ax: $o).
% 0.30/0.46  thf(decl_36, type, omegaSAx: $o).
% 0.30/0.46  thf(decl_37, type, omegaIndAx: $o).
% 0.30/0.46  thf(decl_38, type, replAx: $o).
% 0.30/0.46  thf(decl_39, type, foundationAx: $o).
% 0.30/0.46  thf(decl_40, type, wellorderingAx: $o).
% 0.30/0.46  thf(decl_42, type, descrp: $o).
% 0.30/0.46  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.30/0.46  thf(decl_44, type, dsetconstrI: $o).
% 0.30/0.46  thf(decl_45, type, dsetconstrEL: $o).
% 0.30/0.46  thf(decl_46, type, dsetconstrER: $o).
% 0.30/0.46  thf(decl_47, type, exuE1: $o).
% 0.30/0.46  thf(decl_49, type, prop2setE: $o).
% 0.30/0.46  thf(decl_50, type, emptysetE: $o).
% 0.30/0.46  thf(decl_51, type, emptysetimpfalse: $o).
% 0.30/0.46  thf(decl_52, type, notinemptyset: $o).
% 0.30/0.46  thf(decl_53, type, exuE3e: $o).
% 0.30/0.46  thf(decl_54, type, setext: $o).
% 0.30/0.46  thf(decl_55, type, emptyI: $o).
% 0.30/0.46  thf(decl_56, type, noeltsimpempty: $o).
% 0.30/0.46  thf(decl_57, type, setbeta: $o).
% 0.30/0.46  thf(decl_58, type, nonempty: $i > $o).
% 0.30/0.46  thf(decl_59, type, nonemptyE1: $o).
% 0.30/0.46  thf(decl_60, type, nonemptyI: $o).
% 0.30/0.46  thf(decl_61, type, nonemptyI1: $o).
% 0.30/0.46  thf(decl_62, type, setadjoinIL: $o).
% 0.30/0.46  thf(decl_63, type, emptyinunitempty: $o).
% 0.30/0.46  thf(decl_64, type, setadjoinIR: $o).
% 0.30/0.46  thf(decl_65, type, setadjoinE: $o).
% 0.30/0.46  thf(decl_66, type, setadjoinOr: $o).
% 0.30/0.46  thf(decl_67, type, setoftrueEq: $o).
% 0.30/0.46  thf(decl_68, type, powersetI: $o).
% 0.30/0.46  thf(decl_69, type, emptyinPowerset: $o).
% 0.30/0.46  thf(decl_70, type, emptyInPowerset: $o).
% 0.30/0.46  thf(decl_71, type, powersetE: $o).
% 0.30/0.46  thf(decl_72, type, setunionI: $o).
% 0.30/0.46  thf(decl_73, type, setunionE: $o).
% 0.30/0.46  thf(decl_74, type, subPowSU: $o).
% 0.30/0.46  thf(decl_75, type, exuE2: $o).
% 0.30/0.46  thf(decl_76, type, nonemptyImpWitness: $o).
% 0.30/0.46  thf(decl_77, type, uniqinunit: $o).
% 0.30/0.46  thf(decl_78, type, notinsingleton: $o).
% 0.30/0.46  thf(decl_79, type, eqinunit: $o).
% 0.30/0.46  thf(decl_80, type, singletonsswitch: $o).
% 0.30/0.46  thf(decl_81, type, upairsetE: $o).
% 0.30/0.46  thf(decl_82, type, upairsetIL: $o).
% 0.30/0.46  thf(decl_83, type, upairsetIR: $o).
% 0.30/0.46  thf(decl_84, type, emptyE1: $o).
% 0.30/0.46  thf(decl_85, type, vacuousDall: $o).
% 0.30/0.46  thf(decl_86, type, quantDeMorgan1: $o).
% 0.30/0.46  thf(decl_87, type, quantDeMorgan2: $o).
% 0.30/0.46  thf(decl_88, type, quantDeMorgan3: $o).
% 0.30/0.46  thf(decl_89, type, quantDeMorgan4: $o).
% 0.30/0.46  thf(decl_90, type, prop2setI: $o).
% 0.30/0.46  thf(decl_92, type, prop2set2propI: $o).
% 0.30/0.46  thf(decl_93, type, notdexE: $o).
% 0.30/0.46  thf(decl_94, type, notdallE: $o).
% 0.30/0.46  thf(decl_95, type, exuI1: $o).
% 0.30/0.46  thf(decl_96, type, exuI3: $o).
% 0.30/0.46  thf(decl_97, type, exuI2: $o).
% 0.30/0.46  thf(decl_98, type, inCongP: $o).
% 0.30/0.46  thf(decl_99, type, in__Cong: $o).
% 0.30/0.46  thf(decl_100, type, exuE3u: $o).
% 0.30/0.46  thf(decl_101, type, exu__Cong: $o).
% 0.30/0.46  thf(decl_102, type, emptyset__Cong: $o).
% 0.30/0.46  thf(decl_103, type, setadjoin__Cong: $o).
% 0.30/0.46  thf(decl_104, type, powerset__Cong: $o).
% 0.30/0.46  thf(decl_105, type, setunion__Cong: $o).
% 0.30/0.46  thf(decl_106, type, omega__Cong: $o).
% 0.30/0.46  thf(decl_107, type, exuEu: $o).
% 0.30/0.46  thf(decl_108, type, descr__Cong: $o).
% 0.30/0.46  thf(decl_109, type, dsetconstr__Cong: $o).
% 0.30/0.46  thf(decl_110, type, subset: $i > $i > $o).
% 0.30/0.46  thf(decl_113, type, subsetI1: $o).
% 0.30/0.46  thf(decl_114, type, eqimpsubset2: $o).
% 0.30/0.46  thf(decl_115, type, eqimpsubset1: $o).
% 0.30/0.46  thf(decl_116, type, subsetI2: $o).
% 0.30/0.46  thf(decl_117, type, emptysetsubset: $o).
% 0.30/0.46  thf(decl_118, type, subsetE: $o).
% 0.30/0.46  thf(decl_119, type, subsetE2: $o).
% 0.30/0.46  thf(decl_120, type, notsubsetI: $o).
% 0.30/0.46  thf(decl_121, type, notequalI1: $o).
% 0.30/0.46  thf(decl_122, type, notequalI2: $o).
% 0.30/0.46  thf(decl_123, type, subsetRefl: $o).
% 0.30/0.46  thf(decl_124, type, subsetTrans: $o).
% 0.30/0.46  thf(decl_125, type, setadjoinSub: $o).
% 0.30/0.46  thf(decl_126, type, setadjoinSub2: $o).
% 0.30/0.46  thf(decl_127, type, subset2powerset: $o).
% 0.30/0.46  thf(decl_128, type, setextsub: $o).
% 0.30/0.46  thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.30/0.46  thf(decl_130, type, powersetI1: $o).
% 0.30/0.46  thf(decl_131, type, powersetE1: $o).
% 0.30/0.46  thf(decl_132, type, inPowerset: $o).
% 0.30/0.46  thf(decl_133, type, powersetsubset: $o).
% 0.30/0.46  thf(decl_134, type, sepInPowerset: $o).
% 0.30/0.46  thf(decl_135, type, sepSubset: $o).
% 0.30/0.46  thf(decl_137, type, binunionIL: $o).
% 0.30/0.46  thf(decl_138, type, upairset2IR: $o).
% 0.30/0.46  thf(decl_139, type, binunionIR: $o).
% 0.30/0.46  thf(decl_140, type, binunionEcases: $o).
% 0.30/0.46  thf(decl_141, type, binunionE: $o).
% 0.30/0.46  thf(decl_142, type, binunionLsub: $o).
% 0.30/0.46  thf(decl_143, type, binunionRsub: $o).
% 0.30/0.46  thf(decl_144, type, binintersect: $i > $i > $i).
% 0.30/0.46  thf(decl_145, type, binintersectI: $o).
% 0.30/0.46  thf(decl_146, type, binintersectSubset5: $o).
% 0.30/0.46  thf(decl_147, type, binintersectEL: $o).
% 0.30/0.46  thf(decl_148, type, binintersectLsub: $o).
% 0.30/0.46  thf(decl_149, type, binintersectSubset2: $o).
% 0.30/0.46  thf(decl_150, type, binintersectSubset3: $o).
% 0.30/0.46  thf(decl_151, type, binintersectER: $o).
% 0.30/0.46  thf(decl_152, type, disjointsetsI1: $o).
% 0.30/0.46  thf(decl_153, type, binintersectRsub: $o).
% 0.30/0.46  thf(decl_154, type, binintersectSubset4: $o).
% 0.30/0.46  thf(decl_155, type, binintersectSubset1: $o).
% 0.30/0.46  thf(decl_156, type, bs114d: $o).
% 0.30/0.46  thf(decl_159, type, setminusI: $o).
% 0.30/0.46  thf(decl_160, type, setminusEL: $o).
% 0.30/0.46  thf(decl_161, type, setminusER: $o).
% 0.30/0.46  thf(decl_162, type, setminusSubset2: $o).
% 0.30/0.46  thf(decl_163, type, setminusERneg: $o).
% 0.30/0.46  thf(decl_164, type, setminusELneg: $o).
% 0.30/0.46  thf(decl_165, type, setminusILneg: $o).
% 0.30/0.46  thf(decl_166, type, setminusIRneg: $o).
% 0.30/0.46  thf(decl_167, type, setminusLsub: $o).
% 0.30/0.46  thf(decl_168, type, setminusSubset1: $o).
% 0.30/0.46  thf(decl_170, type, symdiffE: $o).
% 0.30/0.46  thf(decl_171, type, symdiffI1: $o).
% 0.30/0.46  thf(decl_172, type, symdiffI2: $o).
% 0.30/0.46  thf(decl_173, type, symdiffIneg1: $o).
% 0.30/0.46  thf(decl_174, type, symdiffIneg2: $o).
% 0.30/0.46  thf(decl_176, type, secondinupair: $o).
% 0.30/0.46  thf(decl_177, type, setukpairIL: $o).
% 0.30/0.46  thf(decl_178, type, setukpairIR: $o).
% 0.30/0.46  thf(decl_179, type, kpairiskpair: $o).
% 0.30/0.46  thf(decl_181, type, kpairp: $o).
% 0.30/0.46  thf(decl_183, type, singletonsubset: $o).
% 0.30/0.46  thf(decl_184, type, singletoninpowerset: $o).
% 0.30/0.46  thf(decl_185, type, singletoninpowunion: $o).
% 0.30/0.46  thf(decl_186, type, upairset2E: $o).
% 0.30/0.46  thf(decl_187, type, upairsubunion: $o).
% 0.30/0.46  thf(decl_188, type, upairinpowunion: $o).
% 0.30/0.46  thf(decl_189, type, ubforcartprodlem1: $o).
% 0.30/0.46  thf(decl_190, type, ubforcartprodlem2: $o).
% 0.30/0.46  thf(decl_191, type, ubforcartprodlem3: $o).
% 0.30/0.46  thf(decl_192, type, cartprodpairin: $o).
% 0.30/0.46  thf(decl_193, type, cartprodmempair1: $o).
% 0.30/0.46  thf(decl_194, type, cartprodmempair: $o).
% 0.30/0.46  thf(decl_195, type, setunionE2: $o).
% 0.30/0.46  thf(decl_196, type, setunionsingleton1: $o).
% 0.30/0.46  thf(decl_197, type, setunionsingleton2: $o).
% 0.30/0.46  thf(decl_198, type, setunionsingleton: $o).
% 0.30/0.46  thf(decl_200, type, singletonprop: $o).
% 0.30/0.46  thf(decl_202, type, ex1E1: $o).
% 0.30/0.46  thf(decl_203, type, ex1I: $o).
% 0.30/0.46  thf(decl_204, type, ex1I2: $o).
% 0.30/0.46  thf(decl_205, type, singletonsuniq: $o).
% 0.30/0.46  thf(decl_210, type, setukpairinjL1: $o).
% 0.30/0.46  thf(decl_211, type, kfstsingleton: $o).
% 0.30/0.46  thf(decl_212, type, theprop: $o).
% 0.30/0.46  thf(decl_214, type, kfstpairEq: $o).
% 0.30/0.46  thf(decl_215, type, cartprodfstin: $o).
% 0.30/0.46  thf(decl_216, type, setukpairinjL2: $o).
% 0.30/0.46  thf(decl_217, type, setukpairinjL: $o).
% 0.30/0.46  thf(decl_218, type, setukpairinjR11: $o).
% 0.30/0.46  thf(decl_219, type, setukpairinjR12: $o).
% 0.30/0.46  thf(decl_220, type, setukpairinjR1: $o).
% 0.30/0.46  thf(decl_221, type, upairequniteq: $o).
% 0.30/0.46  thf(decl_222, type, setukpairinjR2: $o).
% 0.30/0.46  thf(decl_223, type, setukpairinjR: $o).
% 0.30/0.46  thf(decl_224, type, ksndsingleton: $o).
% 0.30/0.46  thf(decl_226, type, ksndpairEq: $o).
% 0.30/0.46  thf(decl_227, type, kpairsurjEq: $o).
% 0.30/0.46  thf(decl_228, type, cartprodsndin: $o).
% 0.30/0.46  thf(decl_229, type, cartprodpairmemEL: $o).
% 0.30/0.46  thf(decl_230, type, cartprodpairmemER: $o).
% 0.30/0.46  thf(decl_231, type, cartprodmempaircEq: $o).
% 0.30/0.46  thf(decl_232, type, cartprodfstpairEq: $o).
% 0.30/0.46  thf(decl_233, type, cartprodsndpairEq: $o).
% 0.30/0.46  thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.30/0.46  thf(decl_237, type, dpsetconstrI: $o).
% 0.30/0.46  thf(decl_238, type, dpsetconstrSub: $o).
% 0.30/0.46  thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.30/0.46  thf(decl_240, type, dpsetconstrERa: $o).
% 0.30/0.46  thf(decl_241, type, dpsetconstrEL1: $o).
% 0.30/0.46  thf(decl_242, type, dpsetconstrEL2: $o).
% 0.30/0.46  thf(decl_243, type, dpsetconstrER: $o).
% 0.30/0.46  thf(decl_246, type, funcImageSingleton: $o).
% 0.30/0.46  thf(decl_247, type, apProp: $o).
% 0.30/0.46  thf(decl_249, type, app: $o).
% 0.30/0.46  thf(decl_250, type, infuncsetfunc: $o).
% 0.30/0.46  thf(decl_251, type, ap2p: $o).
% 0.30/0.46  thf(decl_252, type, funcinfuncset: $o).
% 0.30/0.46  thf(decl_253, type, lamProp: $o).
% 0.30/0.46  thf(decl_255, type, lamp: $o).
% 0.30/0.46  thf(decl_256, type, lam2p: $o).
% 0.30/0.46  thf(decl_257, type, brelnall1: $o).
% 0.30/0.46  thf(decl_258, type, brelnall2: $o).
% 0.30/0.46  thf(decl_259, type, ex1E2: $o).
% 0.30/0.46  thf(decl_260, type, funcGraphProp1: $o).
% 0.30/0.46  thf(decl_261, type, funcGraphProp3: $o).
% 0.30/0.46  thf(decl_262, type, funcGraphProp2: $o).
% 0.30/0.46  thf(decl_263, type, funcextLem: $o).
% 0.30/0.46  thf(decl_264, type, funcGraphProp4: $o).
% 0.30/0.46  thf(decl_265, type, subbreln: $o).
% 0.30/0.46  thf(decl_266, type, eqbreln: $o).
% 0.30/0.46  thf(decl_267, type, funcext: $o).
% 0.30/0.46  thf(decl_268, type, funcext2: $o).
% 0.30/0.46  thf(decl_269, type, ap2apEq1: $o).
% 0.30/0.46  thf(decl_270, type, ap2apEq2: $o).
% 0.30/0.46  thf(decl_271, type, beta1: $o).
% 0.30/0.46  thf(decl_272, type, eta1: $o).
% 0.30/0.46  thf(decl_273, type, lam2lamEq: $o).
% 0.30/0.46  thf(decl_274, type, beta2: $o).
% 0.30/0.46  thf(decl_275, type, eta2: $o).
% 0.30/0.46  thf(decl_276, type, iffalseProp1: $o).
% 0.30/0.46  thf(decl_277, type, iffalseProp2: $o).
% 0.30/0.46  thf(decl_278, type, iftrueProp1: $o).
% 0.30/0.46  thf(decl_279, type, iftrueProp2: $o).
% 0.30/0.46  thf(decl_280, type, ifSingleton: $o).
% 0.30/0.46  thf(decl_282, type, ifp: $o).
% 0.30/0.46  thf(decl_283, type, theeq: $o).
% 0.30/0.46  thf(decl_284, type, iftrue: $o).
% 0.30/0.46  thf(decl_285, type, iffalse: $o).
% 0.30/0.46  thf(decl_286, type, iftrueorfalse: $o).
% 0.30/0.46  thf(decl_287, type, binintersectT_lem: $o).
% 0.30/0.46  thf(decl_288, type, binunionT_lem: $o).
% 0.30/0.46  thf(decl_289, type, powersetT_lem: $o).
% 0.30/0.46  thf(decl_290, type, setminusT_lem: $o).
% 0.30/0.46  thf(decl_291, type, complementT_lem: $o).
% 0.30/0.46  thf(decl_292, type, setextT: $o).
% 0.30/0.46  thf(decl_293, type, subsetTI: $o).
% 0.30/0.46  thf(decl_294, type, powersetTI1: $o).
% 0.30/0.46  thf(decl_295, type, powersetTE1: $o).
% 0.30/0.46  thf(decl_296, type, complementTI1: $o).
% 0.30/0.46  thf(decl_297, type, complementTE1: $o).
% 0.30/0.46  thf(decl_298, type, binintersectTELcontra: $o).
% 0.30/0.46  thf(decl_299, type, binintersectTERcontra: $o).
% 0.30/0.46  thf(decl_300, type, contrasubsetT: $o).
% 0.30/0.46  thf(decl_301, type, contrasubsetT1: $o).
% 0.30/0.46  thf(decl_302, type, contrasubsetT2: $o).
% 0.30/0.46  thf(decl_303, type, contrasubsetT3: $o).
% 0.30/0.46  thf(decl_304, type, doubleComplementI1: $o).
% 0.30/0.46  thf(decl_305, type, doubleComplementE1: $o).
% 0.30/0.46  thf(decl_306, type, doubleComplementSub1: $o).
% 0.30/0.46  thf(decl_307, type, doubleComplementSub2: $o).
% 0.30/0.46  thf(decl_308, type, doubleComplementEq: $o).
% 0.30/0.46  thf(decl_309, type, complementTnotintersectT: $o).
% 0.30/0.46  thf(decl_310, type, complementImpComplementIntersect: $o).
% 0.30/0.46  thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 0.30/0.46  thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 0.30/0.46  thf(decl_313, type, contraSubsetComplement: $o).
% 0.30/0.46  thf(decl_314, type, complementTcontraSubset: $o).
% 0.30/0.46  thf(decl_315, type, binunionTILcontra: $o).
% 0.30/0.46  thf(decl_316, type, binunionTIRcontra: $o).
% 0.30/0.46  thf(decl_317, type, inIntersectImpInUnion: $o).
% 0.30/0.46  thf(decl_318, type, inIntersectImpInUnion2: $o).
% 0.30/0.46  thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 0.30/0.46  thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 0.30/0.46  thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 0.30/0.46  thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 0.30/0.46  thf(decl_323, type, binunionTE: $o).
% 0.30/0.46  thf(decl_324, type, binunionTEcontra: $o).
% 0.30/0.46  thf(decl_325, type, demorgan2a1: $o).
% 0.30/0.46  thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 0.30/0.46  thf(decl_327, type, demorgan2a2: $o).
% 0.30/0.46  thf(decl_328, type, demorgan1a: $o).
% 0.30/0.46  thf(decl_329, type, demorgan1b: $o).
% 0.30/0.46  thf(decl_330, type, demorgan1: $o).
% 0.30/0.46  thf(decl_331, type, demorgan2a: $o).
% 0.30/0.46  thf(decl_332, type, demorgan2b2: $o).
% 0.30/0.46  thf(decl_333, type, demorgan2b: $o).
% 0.30/0.46  thf(decl_334, type, demorgan2: $o).
% 0.30/0.46  thf(decl_335, type, woz13rule0: $o).
% 0.30/0.46  thf(decl_336, type, woz13rule1: $o).
% 0.30/0.46  thf(decl_337, type, woz13rule2: $o).
% 0.30/0.46  thf(decl_338, type, woz13rule3: $o).
% 0.30/0.46  thf(decl_339, type, woz13rule4: $o).
% 0.30/0.46  thf(decl_340, type, woz1_1: $o).
% 0.30/0.46  thf(decl_341, type, woz1_2: $o).
% 0.30/0.46  thf(decl_342, type, woz1_3: $o).
% 0.30/0.46  thf(decl_343, type, woz1_4: $o).
% 0.30/0.46  thf(decl_344, type, woz1_5: $o).
% 0.30/0.46  thf(decl_346, type, breln1all2: $o).
% 0.30/0.46  thf(decl_348, type, breln1SetBreln1: $o).
% 0.30/0.46  thf(decl_355, type, choice2fnsingleton: $o).
% 0.30/0.46  thf(decl_356, type, setOfPairsIsBReln1: $o).
% 0.30/0.46  thf(decl_357, type, breln1all1: $o).
% 0.30/0.46  thf(decl_358, type, subbreln1: $o).
% 0.30/0.46  thf(decl_359, type, eqbreln1: $o).
% 0.30/0.46  thf(decl_361, type, breln1invprop: $o).
% 0.30/0.46  thf(decl_362, type, breln1invI: $o).
% 0.30/0.46  thf(decl_363, type, breln1invE: $o).
% 0.30/0.46  thf(decl_365, type, breln1compprop: $o).
% 0.30/0.46  thf(decl_366, type, breln1compI: $o).
% 0.30/0.46  thf(decl_367, type, breln1compE: $o).
% 0.30/0.46  thf(decl_368, type, breln1compEex: $o).
% 0.30/0.46  thf(decl_369, type, breln1unionprop: $o).
% 0.30/0.46  thf(decl_370, type, breln1unionIL: $o).
% 0.30/0.46  thf(decl_371, type, breln1unionIR: $o).
% 0.30/0.46  thf(decl_372, type, breln1unionI: $o).
% 0.30/0.46  thf(decl_373, type, breln1unionE: $o).
% 0.30/0.46  thf(decl_374, type, breln1unionEcases: $o).
% 0.30/0.46  thf(decl_375, type, breln1unionCommutes: $o).
% 0.30/0.46  thf(decl_376, type, woz2Ex: $o).
% 0.30/0.46  thf(decl_377, type, woz2W: $o).
% 0.30/0.46  thf(decl_378, type, woz2A: $o).
% 0.30/0.46  thf(decl_379, type, woz2B: $o).
% 0.30/0.46  thf(decl_380, type, image1Ex: $o).
% 0.30/0.46  thf(decl_381, type, image1Ex1: $o).
% 0.30/0.46  thf(decl_383, type, image1Equiv: $o).
% 0.30/0.46  thf(decl_384, type, image1E: $o).
% 0.30/0.46  thf(decl_385, type, image1I: $o).
% 0.30/0.46  thf(decl_388, type, injFuncInInjFuncSet: $o).
% 0.30/0.46  thf(decl_389, type, injFuncSetFuncIn: $o).
% 0.30/0.46  thf(decl_390, type, injFuncSetFuncInj: $o).
% 0.30/0.46  thf(decl_393, type, surjFuncSetFuncIn: $o).
% 0.30/0.46  thf(decl_394, type, surjFuncSetFuncSurj: $o).
% 0.30/0.46  thf(decl_395, type, leftInvIsSurj: $o).
% 0.30/0.46  thf(decl_396, type, surjCantorThm: $o).
% 0.30/0.46  thf(decl_397, type, foundation2: $o).
% 0.30/0.46  thf(decl_398, type, notinself: $o).
% 0.30/0.46  thf(decl_399, type, notinself2: $o).
% 0.30/0.46  thf(decl_401, type, omegaSp: $o).
% 0.30/0.46  thf(decl_402, type, omegaSclos: $o).
% 0.30/0.46  thf(decl_403, type, peano0notS: $o).
% 0.30/0.46  thf(decl_407, type, peanoSinj: $o).
% 0.30/0.46  thf(decl_409, type, transitiveset: $i > $o).
% 0.30/0.46  thf(decl_410, type, transitivesetOp1: $o).
% 0.30/0.46  thf(decl_411, type, binintTransitive: $o).
% 0.30/0.46  thf(decl_412, type, transitivesetOp2: $o).
% 0.30/0.46  thf(decl_413, type, setunionTransitive: $o).
% 0.98/0.46  thf(decl_414, type, stricttotalorderedByIn: $i > $o).
% 0.98/0.46  thf(decl_415, type, wellorderedByIn: $i > $o).
% 0.98/0.46  thf(decl_416, type, ordinal: $i > $o).
% 0.98/0.46  thf(decl_418, type, ordinalMinLem1: $o).
% 0.98/0.46  thf(decl_419, type, ordinalTransSet: $o).
% 0.98/0.46  thf(decl_420, type, ordinalTransSet1: $o).
% 0.98/0.46  thf(decl_421, type, setunionOrdinalLem1: $o).
% 0.98/0.46  thf(decl_423, type, emptysetOrdinal: $o).
% 0.98/0.46  thf(decl_424, type, ordinalIrrefl: $o).
% 0.98/0.46  thf(decl_425, type, ordinalIrrefl2: $o).
% 0.98/0.46  thf(decl_426, type, epred1_1: $i > $o).
% 0.98/0.46  thf(decl_427, type, epred2_1: $i > $o).
% 0.98/0.46  thf(decl_428, type, epred3_1: $i > $o).
% 0.98/0.46  thf(decl_429, type, epred4_1: $i > $o).
% 0.98/0.46  thf(decl_430, type, epred5_1: $i > $o).
% 0.98/0.46  thf(decl_431, type, epred6_0: $o).
% 0.98/0.46  thf(decl_432, type, epred7_1: $i > $o).
% 0.98/0.46  thf(decl_433, type, epred8_1: $i > $o).
% 0.98/0.46  thf(decl_434, type, epred9_1: $i > $o).
% 0.98/0.46  thf(decl_435, type, esk1_1: $i > $i).
% 0.98/0.46  thf(decl_436, type, esk2_1: $i > $i).
% 0.98/0.46  thf(decl_437, type, esk3_1: $i > $i).
% 0.98/0.46  thf(decl_438, type, esk4_1: $i > $i).
% 0.98/0.46  thf(decl_439, type, esk5_1: $i > $i).
% 0.98/0.46  thf(decl_440, type, esk6_1: $i > $i).
% 0.98/0.46  thf(decl_441, type, esk7_2: $i > $i > $i).
% 0.98/0.46  thf(decl_442, type, esk8_2: $i > $i > $i).
% 0.98/0.46  thf(decl_443, type, esk9_2: $i > $i > $i).
% 0.98/0.46  thf(decl_444, type, esk10_3: $i > $i > $i > $i).
% 0.98/0.46  thf(decl_445, type, esk11_1: $i > $i).
% 0.98/0.46  thf(decl_446, type, esk12_1: $i > $i).
% 0.98/0.46  thf(decl_447, type, esk13_2: $i > $i > $i).
% 0.98/0.46  thf(decl_448, type, esk14_1: $i > $i).
% 0.98/0.46  thf(decl_449, type, esk15_1: $i > $i).
% 0.98/0.46  thf(decl_450, type, esk16_2: $i > $i > $i).
% 0.98/0.46  thf(decl_451, type, esk17_1: $i > $i).
% 0.98/0.46  thf(decl_452, type, esk18_1: $i > $i).
% 0.98/0.46  thf(decl_453, type, esk19_1: $i > $i).
% 0.98/0.46  thf(decl_454, type, esk20_2: $i > $i > $i).
% 0.98/0.46  thf(decl_455, type, esk21_1: $i > $i).
% 0.98/0.46  thf(decl_456, type, esk22_1: $i > $i).
% 0.98/0.46  thf(decl_457, type, esk23_2: $i > $i > $i).
% 0.98/0.46  thf(decl_458, type, esk24_1: $i > $i).
% 0.98/0.46  thf(decl_459, type, esk25_1: $i > $i).
% 0.98/0.46  thf(decl_460, type, esk26_2: $i > $i > $i).
% 0.98/0.46  thf(decl_461, type, esk27_0: $i).
% 0.98/0.46  thf(decl_462, type, esk28_0: $i).
% 0.98/0.46  thf(decl_499, type, esk65_2: $i > $i > $i).
% 0.98/0.46  thf(wellorderedByIn, axiom, ((wellorderedByIn)=(^[X4:$i]:((((stricttotalorderedByIn @ X4))&(![X21:$i]:((((in @ X21 @ (powerset @ X4)))=>((((nonempty @ X21))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', wellorderedByIn)).
% 0.98/0.46  thf(stricttotalorderedByIn, axiom, ((stricttotalorderedByIn)=(^[X4:$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.5hk0wYH06C/E---3.1_3450233.p', stricttotalorderedByIn)).
% 0.98/0.46  thf(ordinal, axiom, ((ordinal)=(^[X2:$i]:((((transitiveset @ X2))&((wellorderedByIn @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', ordinal)).
% 0.98/0.46  thf(ordinalNoCycle, 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)=>![X21:$i]:(((ordinal @ X21)=>![X4:$i]:(((in @ X21 @ X4)=>~((in @ X4 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', ordinalNoCycle)).
% 0.98/0.46  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', nonemptyI)).
% 0.98/0.46  thf(ordinalIrrefl2, axiom, ((ordinalIrrefl2)<=>![X21:$i]:(((ordinal @ X21)=>~((in @ X21 @ X21))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', ordinalIrrefl2)).
% 0.98/0.46  thf(ordinalIrrefl, axiom, ((ordinalIrrefl)<=>![X21:$i]:(((ordinal @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>~((in @ X4 @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', ordinalIrrefl)).
% 0.98/0.46  thf(emptysetOrdinal, axiom, ((emptysetOrdinal)<=>(ordinal @ emptyset)), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', emptysetOrdinal)).
% 0.98/0.46  thf(setunionOrdinalLem1, axiom, ((setunionOrdinalLem1)<=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(ordinal @ X2)))=>(transitiveset @ (setunion @ X21))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', setunionOrdinalLem1)).
% 0.98/0.46  thf(ordinalTransSet1, axiom, ((ordinalTransSet1)<=>![X21:$i]:(((ordinal @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', ordinalTransSet1)).
% 0.98/0.46  thf(ordinalTransSet, axiom, ((ordinalTransSet)<=>![X21:$i]:(((ordinal @ X21)=>![X2:$i, X4:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', ordinalTransSet)).
% 0.98/0.46  thf(ordinalMinLem1, axiom, ((ordinalMinLem1)<=>![X21:$i]:(((ordinal @ X21)=>![X48:$i]:(((ordinal @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', ordinalMinLem1)).
% 0.98/0.46  thf(foundation2, axiom, ((foundation2)<=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', foundation2)).
% 0.98/0.46  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', nonemptyImpWitness)).
% 0.98/0.46  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', nonemptyI1)).
% 0.98/0.46  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', nonemptyE1)).
% 0.98/0.46  thf(setunionTransitive, axiom, ((setunionTransitive)<=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(transitiveset @ X2)))=>(transitiveset @ (setunion @ X21))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', setunionTransitive)).
% 0.98/0.46  thf(transitivesetOp2, axiom, ((transitivesetOp2)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i, X2:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', transitivesetOp2)).
% 0.98/0.46  thf(binintTransitive, axiom, ((binintTransitive)<=>![X21:$i]:(((transitiveset @ X21)=>![X48:$i]:(((transitiveset @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', binintTransitive)).
% 0.98/0.46  thf(transitivesetOp1, axiom, ((transitivesetOp1)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.5hk0wYH06C/E---3.1_3450233.p', transitivesetOp1)).
% 0.98/0.46  thf(c_0_20, plain, ((wellorderedByIn)=(^[Z0:$i]:((((((((![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)))))))))&(![X21:$i]:((((in @ X21 @ (powerset @ Z0)))=>((((nonempty @ X21))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), inference(fof_simplification,[status(thm)],[wellorderedByIn])).
% 0.98/0.46  thf(c_0_21, plain, ((stricttotalorderedByIn)=(^[Z0:$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])).
% 0.98/0.46  thf(c_0_22, plain, ((ordinal)=(^[Z0:$i]:((((transitiveset @ Z0))&(((((((((![X103:$i]:((((in @ X103 @ Z0))=>(![X104:$i]:((((in @ X104 @ Z0))=>(![X105:$i]:((((in @ X105 @ Z0))=>((((((in @ X103 @ X104))&((in @ X104 @ X105))))=>((in @ X103 @ X105)))))))))))))&(![X106:$i]:((((in @ X106 @ Z0))=>(![X107:$i]:((((in @ X107 @ Z0))=>(((((((X106)=(X107)))|((in @ X106 @ X107))))|((in @ X107 @ X106))))))))))))&(![X108:$i]:((((in @ X108 @ Z0))=>(~((in @ X108 @ X108)))))))))&(![X109:$i]:((((in @ X109 @ (powerset @ Z0)))=>((((nonempty @ X109))=>(?[X110:$i]:((((in @ X110 @ X109))&(![X111:$i]:((((in @ X111 @ X109))=>(((((X110)=(X111)))|((in @ X110 @ X111)))))))))))))))))))))), inference(fof_simplification,[status(thm)],[ordinal])).
% 0.98/0.46  thf(c_0_23, plain, ((wellorderedByIn)=(^[Z0:$i]:((((((((![X97:$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:$i]:((((in @ X102 @ Z0))=>(~((in @ X102 @ X102)))))))))&(![X21:$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_20, c_0_21])).
% 0.98/0.46  thf(c_0_24, plain, ((ordinal)=(^[Z0:$i]:((((transitiveset @ Z0))&(((((((((![X103:$i]:((((in @ X103 @ Z0))=>(![X104:$i]:((((in @ X104 @ Z0))=>(![X105:$i]:((((in @ X105 @ Z0))=>((((((in @ X103 @ X104))&((in @ X104 @ X105))))=>((in @ X103 @ X105)))))))))))))&(![X106:$i]:((((in @ X106 @ Z0))=>(![X107:$i]:((((in @ X107 @ Z0))=>(((((((X106)=(X107)))|((in @ X106 @ X107))))|((in @ X107 @ X106))))))))))))&(![X108:$i]:((((in @ X108 @ Z0))=>(~((in @ X108 @ X108)))))))))&(![X109:$i]:((((in @ X109 @ (powerset @ Z0)))=>((((nonempty @ X109))=>(?[X110:$i]:((((in @ X110 @ X109))&(![X111:$i]:((((in @ X111 @ X109))=>(((((X110)=(X111)))|((in @ X110 @ X111)))))))))))))))))))))), inference(apply_def,[status(thm)],[c_0_22, c_0_23])).
% 0.98/0.46  thf(c_0_25, 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)=>![X21:$i]:(((ordinal @ X21)=>![X4:$i]:(((in @ X21 @ X4)=>~((in @ X4 @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[ordinalNoCycle])).
% 0.98/0.46  thf(c_0_26, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.98/0.46  thf(c_0_27, axiom, ((ordinalIrrefl2)=(![X21:$i]:(((((((transitiveset @ X21))&(((((((((![X175:$i]:((((in @ X175 @ X21))=>(![X176:$i]:((((in @ X176 @ X21))=>(![X177:$i]:((((in @ X177 @ X21))=>((((((in @ X175 @ X176))&((in @ X176 @ X177))))=>((in @ X175 @ X177)))))))))))))&(![X178:$i]:((((in @ X178 @ X21))=>(![X179:$i]:((((in @ X179 @ X21))=>(((((((X178)=(X179)))|((in @ X178 @ X179))))|((in @ X179 @ X178))))))))))))&(![X180:$i]:((((in @ X180 @ X21))=>(~((in @ X180 @ X180)))))))))&(![X181:$i]:((((in @ X181 @ (powerset @ X21)))=>((((nonempty @ X181))=>(?[X182:$i]:((((in @ X182 @ X181))&(![X183:$i]:((((in @ X183 @ X181))=>(((((X182)=(X183)))|((in @ X182 @ X183)))))))))))))))))))))=>(~((in @ X21 @ X21))))))), inference(apply_def,[status(thm)],[ordinalIrrefl2, c_0_24])).
% 0.98/0.46  thf(c_0_28, axiom, ((ordinalIrrefl)=(![X21:$i]:(((((((transitiveset @ X21))&(((((((((![X166:$i]:((((in @ X166 @ X21))=>(![X167:$i]:((((in @ X167 @ X21))=>(![X168:$i]:((((in @ X168 @ X21))=>((((((in @ X166 @ X167))&((in @ X167 @ X168))))=>((in @ X166 @ X168)))))))))))))&(![X169:$i]:((((in @ X169 @ X21))=>(![X170:$i]:((((in @ X170 @ X21))=>(((((((X169)=(X170)))|((in @ X169 @ X170))))|((in @ X170 @ X169))))))))))))&(![X171:$i]:((((in @ X171 @ X21))=>(~((in @ X171 @ X171)))))))))&(![X172:$i]:((((in @ X172 @ (powerset @ X21)))=>((((nonempty @ X172))=>(?[X173:$i]:((((in @ X173 @ X172))&(![X174:$i]:((((in @ X174 @ X172))=>(((((X173)=(X174)))|((in @ X173 @ X174)))))))))))))))))))))=>(![X4:$i]:((((in @ X4 @ X21))=>(~((in @ X4 @ X4)))))))))), inference(apply_def,[status(thm)],[ordinalIrrefl, c_0_24])).
% 0.98/0.46  thf(c_0_29, axiom, ((emptysetOrdinal)=(((((transitiveset @ emptyset))&(((((((((![X157:$i]:((((in @ X157 @ emptyset))=>(![X158:$i]:((((in @ X158 @ emptyset))=>(![X159:$i]:((((in @ X159 @ emptyset))=>((((((in @ X157 @ X158))&((in @ X158 @ X159))))=>((in @ X157 @ X159)))))))))))))&(![X160:$i]:((((in @ X160 @ emptyset))=>(![X161:$i]:((((in @ X161 @ emptyset))=>(((((((X160)=(X161)))|((in @ X160 @ X161))))|((in @ X161 @ X160))))))))))))&(![X162:$i]:((((in @ X162 @ emptyset))=>(~((in @ X162 @ X162)))))))))&(![X163:$i]:((((in @ X163 @ (powerset @ emptyset)))=>((((nonempty @ X163))=>(?[X164:$i]:((((in @ X164 @ X163))&(![X165:$i]:((((in @ X165 @ X163))=>(((((X164)=(X165)))|((in @ X164 @ X165)))))))))))))))))))))), inference(apply_def,[status(thm)],[emptysetOrdinal, c_0_24])).
% 0.98/0.46  thf(c_0_30, axiom, ((setunionOrdinalLem1)=(![X21:$i]:(((![X2:$i]:((((in @ X2 @ X21))=>(((((transitiveset @ X2))&(((((((((![X148:$i]:((((in @ X148 @ X2))=>(![X149:$i]:((((in @ X149 @ X2))=>(![X150:$i]:((((in @ X150 @ X2))=>((((((in @ X148 @ X149))&((in @ X149 @ X150))))=>((in @ X148 @ X150)))))))))))))&(![X151:$i]:((((in @ X151 @ X2))=>(![X152:$i]:((((in @ X152 @ X2))=>(((((((X151)=(X152)))|((in @ X151 @ X152))))|((in @ X152 @ X151))))))))))))&(![X153:$i]:((((in @ X153 @ X2))=>(~((in @ X153 @ X153)))))))))&(![X154:$i]:((((in @ X154 @ (powerset @ X2)))=>((((nonempty @ X154))=>(?[X155:$i]:((((in @ X155 @ X154))&(![X156:$i]:((((in @ X156 @ X154))=>(((((X155)=(X156)))|((in @ X155 @ X156))))))))))))))))))))))))=>((transitiveset @ (setunion @ X21))))))), inference(apply_def,[status(thm)],[setunionOrdinalLem1, c_0_24])).
% 0.98/0.46  thf(c_0_31, axiom, ((ordinalTransSet1)=(![X21:$i]:(((((((transitiveset @ X21))&(((((((((![X139:$i]:((((in @ X139 @ X21))=>(![X140:$i]:((((in @ X140 @ X21))=>(![X141:$i]:((((in @ X141 @ X21))=>((((((in @ X139 @ X140))&((in @ X140 @ X141))))=>((in @ X139 @ X141)))))))))))))&(![X142:$i]:((((in @ X142 @ X21))=>(![X143:$i]:((((in @ X143 @ X21))=>(((((((X142)=(X143)))|((in @ X142 @ X143))))|((in @ X143 @ X142))))))))))))&(![X144:$i]:((((in @ X144 @ X21))=>(~((in @ X144 @ X144)))))))))&(![X145:$i]:((((in @ X145 @ (powerset @ X21)))=>((((nonempty @ X145))=>(?[X146:$i]:((((in @ X146 @ X145))&(![X147:$i]:((((in @ X147 @ X145))=>(((((X146)=(X147)))|((in @ X146 @ X147)))))))))))))))))))))=>(![X4:$i]:((((in @ X4 @ X21))=>((subset @ X4 @ X21))))))))), inference(apply_def,[status(thm)],[ordinalTransSet1, c_0_24])).
% 0.98/0.46  thf(c_0_32, axiom, ((ordinalTransSet)=(![X21:$i]:(((((((transitiveset @ X21))&(((((((((![X130:$i]:((((in @ X130 @ X21))=>(![X131:$i]:((((in @ X131 @ X21))=>(![X132:$i]:((((in @ X132 @ X21))=>((((((in @ X130 @ X131))&((in @ X131 @ X132))))=>((in @ X130 @ X132)))))))))))))&(![X133:$i]:((((in @ X133 @ X21))=>(![X134:$i]:((((in @ X134 @ X21))=>(((((((X133)=(X134)))|((in @ X133 @ X134))))|((in @ X134 @ X133))))))))))))&(![X135:$i]:((((in @ X135 @ X21))=>(~((in @ X135 @ X135)))))))))&(![X136:$i]:((((in @ X136 @ (powerset @ X21)))=>((((nonempty @ X136))=>(?[X137:$i]:((((in @ X137 @ X136))&(![X138:$i]:((((in @ X138 @ X136))=>(((((X137)=(X138)))|((in @ X137 @ X138)))))))))))))))))))))=>(![X2:$i, X4:$i]:((((in @ X4 @ X21))=>((((in @ X2 @ X4))=>((in @ X2 @ X21))))))))))), inference(apply_def,[status(thm)],[ordinalTransSet, c_0_24])).
% 0.98/0.46  thf(c_0_33, axiom, ((ordinalMinLem1)=(![X21:$i]:(((((((transitiveset @ X21))&(((((((((![X112:$i]:((((in @ X112 @ X21))=>(![X113:$i]:((((in @ X113 @ X21))=>(![X114:$i]:((((in @ X114 @ X21))=>((((((in @ X112 @ X113))&((in @ X113 @ X114))))=>((in @ X112 @ X114)))))))))))))&(![X115:$i]:((((in @ X115 @ X21))=>(![X116:$i]:((((in @ X116 @ X21))=>(((((((X115)=(X116)))|((in @ X115 @ X116))))|((in @ X116 @ X115))))))))))))&(![X117:$i]:((((in @ X117 @ X21))=>(~((in @ X117 @ X117)))))))))&(![X118:$i]:((((in @ X118 @ (powerset @ X21)))=>((((nonempty @ X118))=>(?[X119:$i]:((((in @ X119 @ X118))&(![X120:$i]:((((in @ X120 @ X118))=>(((((X119)=(X120)))|((in @ X119 @ X120)))))))))))))))))))))=>(![X48:$i]:(((((((transitiveset @ X48))&(((((((((![X121:$i]:((((in @ X121 @ X48))=>(![X122:$i]:((((in @ X122 @ X48))=>(![X123:$i]:((((in @ X123 @ X48))=>((((((in @ X121 @ X122))&((in @ X122 @ X123))))=>((in @ X121 @ X123)))))))))))))&(![X124:$i]:((((in @ X124 @ X48))=>(![X125:$i]:((((in @ X125 @ X48))=>(((((((X124)=(X125)))|((in @ X124 @ X125))))|((in @ X125 @ X124))))))))))))&(![X126:$i]:((((in @ X126 @ X48))=>(~((in @ X126 @ X126)))))))))&(![X127:$i]:((((in @ X127 @ (powerset @ X48)))=>((((nonempty @ X127))=>(?[X128:$i]:((((in @ X128 @ X127))&(![X129:$i]:((((in @ X129 @ X127))=>(((((X128)=(X129)))|((in @ X128 @ X129)))))))))))))))))))))=>((transitiveset @ (binintersect @ X21 @ X48)))))))))), inference(apply_def,[status(thm)],[ordinalMinLem1, c_0_24])).
% 0.98/0.46  thf(c_0_34, plain, ![X204:$i]:(((epred1_1 @ X204)<=>(![X205:$i]:(((in @ X205 @ X204)=>![X206:$i]:(((in @ X206 @ X204)=>![X207:$i]:(((in @ X207 @ X204)=>(((in @ X205 @ X206)&(in @ X206 @ X207))=>(in @ X205 @ X207))))))))&![X208:$i]:(((in @ X208 @ X204)=>![X209:$i]:(((in @ X209 @ X204)=>(((X208)=(X209))|(in @ X208 @ X209)|(in @ X209 @ X208))))))))), introduced(definition)).
% 0.98/0.46  thf(c_0_35, plain, ![X214:$i]:(((epred2_1 @ X214)<=>(![X215:$i]:(((in @ X215 @ X214)=>![X216:$i]:(((in @ X216 @ X214)=>![X217:$i]:(((in @ X217 @ X214)=>(((in @ X215 @ X216)&(in @ X216 @ X217))=>(in @ X215 @ X217))))))))&![X218:$i]:(((in @ X218 @ X214)=>![X219:$i]:(((in @ X219 @ X214)=>(((X218)=(X219))|(in @ X218 @ X219)|(in @ X219 @ X218))))))))), introduced(definition)).
% 0.98/0.46  thf(c_0_36, plain, ![X224:$i]:(((epred3_1 @ X224)<=>(![X225:$i]:(((in @ X225 @ X224)=>![X226:$i]:(((in @ X226 @ X224)=>![X227:$i]:(((in @ X227 @ X224)=>(((in @ X225 @ X226)&(in @ X226 @ X227))=>(in @ X225 @ X227))))))))&![X228:$i]:(((in @ X228 @ X224)=>![X229:$i]:(((in @ X229 @ X224)=>(((X228)=(X229))|(in @ X228 @ X229)|(in @ X229 @ X228))))))))), introduced(definition)).
% 0.98/0.46  thf(c_0_37, plain, ![X236:$i]:(((epred4_1 @ X236)<=>(![X237:$i]:(((in @ X237 @ X236)=>![X238:$i]:(((in @ X238 @ X236)=>![X239:$i]:(((in @ X239 @ X236)=>(((in @ X237 @ X238)&(in @ X238 @ X239))=>(in @ X237 @ X239))))))))&![X240:$i]:(((in @ X240 @ X236)=>![X241:$i]:(((in @ X241 @ X236)=>(((X240)=(X241))|(in @ X240 @ X241)|(in @ X241 @ X240))))))))), introduced(definition)).
% 0.98/0.46  thf(c_0_38, plain, ![X248:$i]:(((epred5_1 @ X248)<=>(![X249:$i]:(((in @ X249 @ X248)=>![X250:$i]:(((in @ X250 @ X248)=>![X251:$i]:(((in @ X251 @ X248)=>(((in @ X249 @ X250)&(in @ X250 @ X251))=>(in @ X249 @ X251))))))))&![X252:$i]:(((in @ X252 @ X248)=>![X253:$i]:(((in @ X253 @ X248)=>(((X252)=(X253))|(in @ X252 @ X253)|(in @ X253 @ X252))))))))), introduced(definition)).
% 0.98/0.46  thf(c_0_39, plain, ((epred6_0)<=>((transitiveset @ emptyset)&(((![X258:$i]:(((in @ X258 @ emptyset)=>![X259:$i]:(((in @ X259 @ emptyset)=>![X260:$i]:(((in @ X260 @ emptyset)=>(((in @ X258 @ X259)&(in @ X259 @ X260))=>(in @ X258 @ X260))))))))&![X261:$i]:(((in @ X261 @ emptyset)=>![X262:$i]:(((in @ X262 @ emptyset)=>(((X261)=(X262))|(in @ X261 @ X262)|(in @ X262 @ X261)))))))&![X263:$i]:(((in @ X263 @ emptyset)=>~(in @ X263 @ X263))))&![X264:$i]:(((in @ X264 @ (powerset @ emptyset))=>((nonempty @ X264)=>?[X265:$i]:(((in @ X265 @ X264)&![X266:$i]:(((in @ X266 @ X264)=>(((X265)=(X266))|(in @ X265 @ X266)))))))))))), introduced(definition)).
% 0.98/0.46  thf(c_0_40, plain, ![X267:$i]:(((epred7_1 @ X267)<=>(![X268:$i]:(((in @ X268 @ X267)=>![X269:$i]:(((in @ X269 @ X267)=>![X270:$i]:(((in @ X270 @ X267)=>(((in @ X268 @ X269)&(in @ X269 @ X270))=>(in @ X268 @ X270))))))))&![X271:$i]:(((in @ X271 @ X267)=>![X272:$i]:(((in @ X272 @ X267)=>(((X271)=(X272))|(in @ X271 @ X272)|(in @ X272 @ X271))))))))), introduced(definition)).
% 0.98/0.46  thf(c_0_41, plain, ![X278:$i]:(((epred8_1 @ X278)<=>(![X279:$i]:(((in @ X279 @ X278)=>![X280:$i]:(((in @ X280 @ X278)=>![X281:$i]:(((in @ X281 @ X278)=>(((in @ X279 @ X280)&(in @ X280 @ X281))=>(in @ X279 @ X281))))))))&![X282:$i]:(((in @ X282 @ X278)=>![X283:$i]:(((in @ X283 @ X278)=>(((X282)=(X283))|(in @ X282 @ X283)|(in @ X283 @ X282))))))))), introduced(definition)).
% 0.98/0.46  thf(c_0_42, plain, ![X21:$i]:(((epred9_1 @ X21)<=>((transitiveset @ X21)&(((![X288:$i]:(((in @ X288 @ X21)=>![X289:$i]:(((in @ X289 @ X21)=>![X290:$i]:(((in @ X290 @ X21)=>(((in @ X288 @ X289)&(in @ X289 @ X290))=>(in @ X288 @ X290))))))))&![X291:$i]:(((in @ X291 @ X21)=>![X292:$i]:(((in @ X292 @ X21)=>(((X291)=(X292))|(in @ X291 @ X292)|(in @ X292 @ X291)))))))&![X293:$i]:(((in @ X293 @ X21)=>~(in @ X293 @ X293))))&![X294:$i]:(((in @ X294 @ (powerset @ X21))=>((nonempty @ X294)=>?[X295:$i]:(((in @ X295 @ X294)&![X296:$i]:(((in @ X296 @ X294)=>(((X295)=(X296))|(in @ X295 @ X296))))))))))))), introduced(definition)).
% 0.98/0.46  thf(c_0_43, 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)=>(![X184:$i]:(((nonempty @ X184)=>?[X185:$i]:((in @ X185 @ X184))))=>(![X186:$i, X187:$i > $o, X188:$i]:(((in @ X188 @ X186)=>((X187 @ X188)=>(nonempty @ (dsetconstr @ X186 @ X187)))))=>(![X189:$i]:((?[X190:$i]:((in @ X190 @ X189))=>(nonempty @ X189)))=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>(![X191:$i]:(((nonempty @ X191)=>?[X192:$i]:(((in @ X192 @ X191)&$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)=>(![X193:$i]:(((nonempty @ X193)=>?[X194:$i]:(((in @ X194 @ X193)&((binintersect @ X194 @ X193)=(emptyset))))))=>((notinself)=>((notinself2)=>((omegaSp)=>((omegaSclos)=>((peano0notS)=>((peanoSinj)=>(![X195:$i]:(((transitiveset @ X195)=>![X196:$i]:(((in @ X196 @ X195)=>(subset @ X196 @ X195)))))=>(![X197:$i]:(((transitiveset @ X197)=>![X198:$i]:(((transitiveset @ X198)=>(transitiveset @ (binintersect @ X197 @ X198))))))=>(![X199:$i]:(((transitiveset @ X199)=>![X200:$i, X201:$i]:(((in @ X200 @ X199)=>((in @ X201 @ X200)=>(in @ X201 @ X199))))))=>(![X202:$i]:((![X203:$i]:(((in @ X203 @ X202)=>(transitiveset @ X203)))=>(transitiveset @ (setunion @ X202))))=>(![X204:$i]:((((transitiveset @ X204)&(((epred1_1 @ X204)&![X210:$i]:(((in @ X210 @ X204)=>~(in @ X210 @ X210))))&![X211:$i]:(((in @ X211 @ (powerset @ X204))=>((nonempty @ X211)=>?[X212:$i]:(((in @ X212 @ X211)&![X213:$i]:(((in @ X213 @ X211)=>(((X212)=(X213))|(in @ X212 @ X213)))))))))))=>![X214:$i]:((((transitiveset @ X214)&(((epred2_1 @ X214)&![X220:$i]:(((in @ X220 @ X214)=>~(in @ X220 @ X220))))&![X221:$i]:(((in @ X221 @ (powerset @ X214))=>((nonempty @ X221)=>?[X222:$i]:(((in @ X222 @ X221)&![X223:$i]:(((in @ X223 @ X221)=>(((X222)=(X223))|(in @ X222 @ X223)))))))))))=>(transitiveset @ (binintersect @ X204 @ X214))))))=>(![X224:$i]:((((transitiveset @ X224)&(((epred3_1 @ X224)&![X230:$i]:(((in @ X230 @ X224)=>~(in @ X230 @ X230))))&![X231:$i]:(((in @ X231 @ (powerset @ X224))=>((nonempty @ X231)=>?[X232:$i]:(((in @ X232 @ X231)&![X233:$i]:(((in @ X233 @ X231)=>(((X232)=(X233))|(in @ X232 @ X233)))))))))))=>![X234:$i, X235:$i]:(((in @ X235 @ X224)=>((in @ X234 @ X235)=>(in @ X234 @ X224))))))=>(![X236:$i]:((((transitiveset @ X236)&(((epred4_1 @ X236)&![X242:$i]:(((in @ X242 @ X236)=>~(in @ X242 @ X242))))&![X243:$i]:(((in @ X243 @ (powerset @ X236))=>((nonempty @ X243)=>?[X244:$i]:(((in @ X244 @ X243)&![X245:$i]:(((in @ X245 @ X243)=>(((X244)=(X245))|(in @ X244 @ X245)))))))))))=>![X246:$i]:(((in @ X246 @ X236)=>(subset @ X246 @ X236)))))=>(![X247:$i]:((![X248:$i]:(((in @ X248 @ X247)=>((transitiveset @ X248)&(((epred5_1 @ X248)&![X254:$i]:(((in @ X254 @ X248)=>~(in @ X254 @ X254))))&![X255:$i]:(((in @ X255 @ (powerset @ X248))=>((nonempty @ X255)=>?[X256:$i]:(((in @ X256 @ X255)&![X257:$i]:(((in @ X257 @ X255)=>(((X256)=(X257))|(in @ X256 @ X257)))))))))))))=>(transitiveset @ (setunion @ X247))))=>((epred6_0)=>(![X267:$i]:((((transitiveset @ X267)&(((epred7_1 @ X267)&![X273:$i]:(((in @ X273 @ X267)=>~(in @ X273 @ X273))))&![X274:$i]:(((in @ X274 @ (powerset @ X267))=>((nonempty @ X274)=>?[X275:$i]:(((in @ X275 @ X274)&![X276:$i]:(((in @ X276 @ X274)=>(((X275)=(X276))|(in @ X275 @ X276)))))))))))=>![X277:$i]:(((in @ X277 @ X267)=>~(in @ X277 @ X277)))))=>(![X278:$i]:((((transitiveset @ X278)&(((epred8_1 @ X278)&![X284:$i]:(((in @ X284 @ X278)=>~(in @ X284 @ X284))))&![X285:$i]:(((in @ X285 @ (powerset @ X278))=>((nonempty @ X285)=>?[X286:$i]:(((in @ X286 @ X285)&![X287:$i]:(((in @ X287 @ X285)=>(((X286)=(X287))|(in @ X286 @ X287)))))))))))=>~(in @ X278 @ X278)))=>![X21:$i]:(((epred9_1 @ X21)=>![X4:$i]:(((in @ X21 @ X4)=>~(in @ X4 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_25, foundation2]), nonemptyImpWitness]), nonemptyI1]), c_0_26]), nonemptyE1]), setunionTransitive]), transitivesetOp2]), binintTransitive]), transitivesetOp1]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_32]), c_0_33]), c_0_24])])]), c_0_34]), c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_39]), c_0_40]), c_0_41]), c_0_42])).
% 0.98/0.46  thf(c_0_44, plain, ![X21:$i]:(((epred9_1 @ X21)=>((transitiveset @ X21)&(((![X288:$i]:(((in @ X288 @ X21)=>![X289:$i]:(((in @ X289 @ X21)=>![X290:$i]:(((in @ X290 @ X21)=>(((in @ X288 @ X289)&(in @ X289 @ X290))=>(in @ X288 @ X290))))))))&![X291:$i]:(((in @ X291 @ X21)=>![X292:$i]:(((in @ X292 @ X21)=>(((X291)=(X292))|(in @ X291 @ X292)|(in @ X292 @ X291)))))))&![X293:$i]:(((in @ X293 @ X21)=>~(in @ X293 @ X293))))&![X294:$i]:(((in @ X294 @ (powerset @ X21))=>((nonempty @ X294)=>?[X295:$i]:(((in @ X295 @ X294)&![X296:$i]:(((in @ X296 @ X294)=>(((X295)=(X296))|(in @ X295 @ X296))))))))))))), inference(split_equiv,[status(thm)],[c_0_42])).
% 0.98/0.46  thf(c_0_45, negated_conjecture, ![X297:$i, X299:$i, X300:$i > $o, X301:$i, X302:$i, X303:$i, X304:$i, X306:$i, X308:$i, X309:$i, X310:$i, X311:$i, X312:$i, X313:$i, X314:$i, X315:$i, X317:$i, X320:$i, X322:$i, X325:$i, X327:$i, X330:$i, X332:$i, X333:$i, X334:$i, X337:$i, X339:$i, X340:$i, X344:$i, X346:$i, X349:$i, X351:$i, X352:$i, X355:$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 @ X297)|(in @ (esk1_1 @ X297) @ X297))&((~(in @ X301 @ X299)|(~(X300 @ X301)|(nonempty @ (dsetconstr @ X299 @ X300))))&((~(in @ X303 @ X302)|(nonempty @ X302))&((setadjoinIL)&((emptyinunitempty)&((setadjoinIR)&((setadjoinE)&((setadjoinOr)&((setoftrueEq)&((powersetI)&((emptyinPowerset)&((emptyInPowerset)&((powersetE)&((setunionI)&((setunionE)&((subPowSU)&((exuE2)&((((in @ (esk2_1 @ X304) @ X304)|~(nonempty @ X304))&(($true)|~(nonempty @ 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X340)))))))&(((in @ (esk19_1 @ X340) @ (powerset @ (esk17_1 @ X340)))|((in @ (esk18_1 @ X340) @ (esk18_1 @ X340))|~(epred5_1 @ (esk17_1 @ X340)))|~(transitiveset @ (esk17_1 @ X340))|(transitiveset @ (setunion @ X340)))&(((nonempty @ (esk19_1 @ X340))|((in @ (esk18_1 @ X340) @ (esk18_1 @ X340))|~(epred5_1 @ (esk17_1 @ X340)))|~(transitiveset @ (esk17_1 @ X340))|(transitiveset @ (setunion @ X340)))&(((in @ (esk20_2 @ X340 @ X344) @ (esk19_1 @ X340))|~(in @ X344 @ (esk19_1 @ X340))|((in @ (esk18_1 @ X340) @ (esk18_1 @ X340))|~(epred5_1 @ (esk17_1 @ X340)))|~(transitiveset @ (esk17_1 @ X340))|(transitiveset @ (setunion @ X340)))&((((X344)!=(esk20_2 @ X340 @ X344))|~(in @ X344 @ (esk19_1 @ X340))|((in @ (esk18_1 @ X340) @ (esk18_1 @ X340))|~(epred5_1 @ (esk17_1 @ X340)))|~(transitiveset @ (esk17_1 @ X340))|(transitiveset @ (setunion @ X340)))&(~(in @ X344 @ (esk20_2 @ X340 @ X344))|~(in @ X344 @ (esk19_1 @ X340))|((in @ (esk18_1 @ X340) @ (esk18_1 @ X340))|~(epred5_1 @ (esk17_1 @ X340)))|~(transitiveset @ (esk17_1 @ X340))|(transitiveset @ (setunion @ X340)))))))))&((epred6_0)&(((((in @ (esk22_1 @ X346) @ (powerset @ X346))|((in @ (esk21_1 @ X346) @ X346)|~(epred7_1 @ X346))|~(transitiveset @ X346)|(~(in @ X351 @ X346)|~(in @ X351 @ X351)))&(((nonempty @ (esk22_1 @ X346))|((in @ (esk21_1 @ X346) @ X346)|~(epred7_1 @ X346))|~(transitiveset @ X346)|(~(in @ X351 @ X346)|~(in @ X351 @ X351)))&(((in @ (esk23_2 @ X346 @ X349) @ (esk22_1 @ X346))|~(in @ X349 @ (esk22_1 @ X346))|((in @ (esk21_1 @ X346) @ X346)|~(epred7_1 @ X346))|~(transitiveset @ X346)|(~(in @ X351 @ X346)|~(in @ X351 @ X351)))&((((X349)!=(esk23_2 @ X346 @ X349))|~(in @ X349 @ (esk22_1 @ X346))|((in @ (esk21_1 @ X346) @ X346)|~(epred7_1 @ X346))|~(transitiveset @ X346)|(~(in @ X351 @ X346)|~(in @ X351 @ X351)))&(~(in @ X349 @ (esk23_2 @ X346 @ X349))|~(in @ X349 @ (esk22_1 @ X346))|((in @ (esk21_1 @ X346) @ X346)|~(epred7_1 @ X346))|~(transitiveset @ X346)|(~(in @ X351 @ X346)|~(in @ X351 @ X351)))))))&(((in @ (esk22_1 @ X346) @ (powerset @ X346))|((in @ (esk21_1 @ X346) @ (esk21_1 @ X346))|~(epred7_1 @ X346))|~(transitiveset @ X346)|(~(in @ X351 @ X346)|~(in @ X351 @ X351)))&(((nonempty @ (esk22_1 @ X346))|((in @ (esk21_1 @ X346) @ (esk21_1 @ X346))|~(epred7_1 @ X346))|~(transitiveset @ X346)|(~(in @ X351 @ X346)|~(in @ X351 @ X351)))&(((in @ (esk23_2 @ X346 @ X349) @ (esk22_1 @ X346))|~(in @ X349 @ (esk22_1 @ X346))|((in @ (esk21_1 @ X346) @ (esk21_1 @ X346))|~(epred7_1 @ X346))|~(transitiveset @ X346)|(~(in @ X351 @ X346)|~(in @ X351 @ X351)))&((((X349)!=(esk23_2 @ X346 @ X349))|~(in @ X349 @ (esk22_1 @ X346))|((in @ (esk21_1 @ X346) @ (esk21_1 @ X346))|~(epred7_1 @ X346))|~(transitiveset @ X346)|(~(in @ X351 @ X346)|~(in @ X351 @ X351)))&(~(in @ X349 @ (esk23_2 @ X346 @ X349))|~(in @ X349 @ (esk22_1 @ X346))|((in @ (esk21_1 @ X346) @ (esk21_1 @ X346))|~(epred7_1 @ X346))|~(transitiveset @ X346)|(~(in @ X351 @ X346)|~(in @ X351 @ X351))))))))&(((((in @ (esk25_1 @ X352) @ (powerset @ X352))|((in @ (esk24_1 @ X352) @ X352)|~(epred8_1 @ X352))|~(transitiveset @ X352)|~(in @ X352 @ X352))&(((nonempty @ (esk25_1 @ X352))|((in @ (esk24_1 @ X352) @ X352)|~(epred8_1 @ X352))|~(transitiveset @ X352)|~(in @ X352 @ X352))&(((in @ (esk26_2 @ X352 @ X355) @ (esk25_1 @ X352))|~(in @ X355 @ (esk25_1 @ X352))|((in @ (esk24_1 @ X352) @ X352)|~(epred8_1 @ X352))|~(transitiveset @ X352)|~(in @ X352 @ X352))&((((X355)!=(esk26_2 @ X352 @ X355))|~(in @ X355 @ (esk25_1 @ X352))|((in @ (esk24_1 @ X352) @ X352)|~(epred8_1 @ X352))|~(transitiveset @ X352)|~(in @ X352 @ X352))&(~(in @ X355 @ (esk26_2 @ X352 @ X355))|~(in @ X355 @ (esk25_1 @ X352))|((in @ (esk24_1 @ X352) @ X352)|~(epred8_1 @ X352))|~(transitiveset @ X352)|~(in @ X352 @ X352))))))&(((in @ (esk25_1 @ X352) @ (powerset @ X352))|((in @ (esk24_1 @ X352) @ (esk24_1 @ X352))|~(epred8_1 @ X352))|~(transitiveset @ X352)|~(in @ X352 @ X352))&(((nonempty @ (esk25_1 @ X352))|((in @ (esk24_1 @ X352) @ (esk24_1 @ X352))|~(epred8_1 @ X352))|~(transitiveset @ X352)|~(in @ X352 @ X352))&(((in @ (esk26_2 @ X352 @ X355) @ (esk25_1 @ X352))|~(in @ X355 @ (esk25_1 @ X352))|((in @ (esk24_1 @ X352) @ (esk24_1 @ X352))|~(epred8_1 @ X352))|~(transitiveset @ X352)|~(in @ X352 @ X352))&((((X355)!=(esk26_2 @ X352 @ X355))|~(in @ X355 @ (esk25_1 @ X352))|((in @ (esk24_1 @ X352) @ (esk24_1 @ X352))|~(epred8_1 @ X352))|~(transitiveset @ X352)|~(in @ X352 @ X352))&(~(in @ X355 @ (esk26_2 @ X352 @ X355))|~(in @ X355 @ (esk25_1 @ X352))|((in @ (esk24_1 @ X352) @ (esk24_1 @ X352))|~(epred8_1 @ X352))|~(transitiveset @ X352)|~(in @ X352 @ X352)))))))&((epred9_1 @ esk27_0)&((in @ esk27_0 @ esk28_0)&(in @ esk28_0 @ esk27_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_43])])])])])])])).
% 0.98/0.47  thf(c_0_46, plain, ![X410:$i, X411:$i, X412:$i, X413:$i, X414:$i, X415:$i, X416:$i, X417:$i, X419:$i]:((((transitiveset @ X410)|~(epred9_1 @ X410))&((((~(in @ X411 @ X410)|(~(in @ X412 @ X410)|(~(in @ X413 @ X410)|(~(in @ X411 @ X412)|~(in @ X412 @ X413)|(in @ X411 @ X413))))|~(epred9_1 @ X410))&(~(in @ X414 @ X410)|(~(in @ X415 @ X410)|(((X414)=(X415))|(in @ X414 @ X415)|(in @ X415 @ X414)))|~(epred9_1 @ X410)))&(~(in @ X416 @ X410)|~(in @ X416 @ X416)|~(epred9_1 @ X410)))&(((in @ (esk65_2 @ X410 @ X417) @ X417)|~(nonempty @ X417)|~(in @ X417 @ (powerset @ X410))|~(epred9_1 @ X410))&(~(in @ X419 @ X417)|(((esk65_2 @ X410 @ X417)=(X419))|(in @ (esk65_2 @ X410 @ X417) @ X419))|~(nonempty @ X417)|~(in @ X417 @ (powerset @ X410))|~(epred9_1 @ X410)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])])])])).
% 0.98/0.47  thf(c_0_47, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X4 @ X2)|~((transitiveset @ X2))|~((in @ X3 @ X2))|~((in @ X4 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_45])).
% 0.98/0.47  thf(c_0_48, negated_conjecture, (in @ esk27_0 @ esk28_0), inference(split_conjunct,[status(thm)],[c_0_45])).
% 0.98/0.47  thf(c_0_49, plain, ![X2:$i]:(((transitiveset @ X2)|~((epred9_1 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_46])).
% 0.98/0.47  thf(c_0_50, negated_conjecture, (epred9_1 @ esk27_0), inference(split_conjunct,[status(thm)],[c_0_45])).
% 0.98/0.47  thf(c_0_51, negated_conjecture, ![X2:$i]:(((in @ esk27_0 @ X2)|~((in @ esk28_0 @ X2))|~((transitiveset @ X2)))), inference(spm,[status(thm)],[c_0_47, c_0_48])).
% 0.98/0.47  thf(c_0_52, negated_conjecture, (transitiveset @ esk27_0), inference(spm,[status(thm)],[c_0_49, c_0_50])).
% 0.98/0.47  thf(c_0_53, negated_conjecture, (in @ esk28_0 @ esk27_0), inference(split_conjunct,[status(thm)],[c_0_45])).
% 0.98/0.47  thf(c_0_54, plain, ![X2:$i, X3:$i]:((~((in @ X2 @ X3))|~((in @ X2 @ X2))|~((epred9_1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_46])).
% 0.98/0.47  thf(c_0_55, negated_conjecture, (in @ esk27_0 @ esk27_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52]), c_0_53])])).
% 0.98/0.47  thf(c_0_56, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_55]), c_0_50])]), ['proof']).
% 0.98/0.47  % SZS output end CNFRefutation
% 0.98/0.47  % Parsed axioms                        : 747
% 0.98/0.47  % Removed by relevancy pruning/SinE    : 727
% 0.98/0.47  % Initial clauses                      : 712
% 0.98/0.47  % Removed in clause preprocessing      : 1
% 0.98/0.47  % Initial clauses in saturation        : 711
% 0.98/0.47  % Processed clauses                    : 669
% 0.98/0.47  % ...of these trivial                  : 0
% 0.98/0.47  % ...subsumed                          : 86
% 0.98/0.47  % ...remaining for further processing  : 583
% 0.98/0.47  % Other redundant clauses eliminated   : 0
% 0.98/0.47  % Clauses deleted for lack of memory   : 0
% 0.98/0.47  % Backward-subsumed                    : 1
% 0.98/0.47  % Backward-rewritten                   : 1
% 0.98/0.47  % Generated clauses                    : 653
% 0.98/0.47  % ...of the previous two non-redundant : 645
% 0.98/0.47  % ...aggressively subsumed             : 0
% 0.98/0.47  % Contextual simplify-reflections      : 7
% 0.98/0.47  % Paramodulations                      : 653
% 0.98/0.47  % Factorizations                       : 0
% 0.98/0.47  % NegExts                              : 0
% 0.98/0.47  % Equation resolutions                 : 0
% 0.98/0.47  % Disequality decompositions           : 0
% 0.98/0.47  % Total rewrite steps                  : 11
% 0.98/0.47  % ...of those cached                   : 5
% 0.98/0.47  % Propositional unsat checks           : 0
% 0.98/0.47  %    Propositional check models        : 0
% 0.98/0.47  %    Propositional check unsatisfiable : 0
% 0.98/0.47  %    Propositional clauses             : 0
% 0.98/0.47  %    Propositional clauses after purity: 0
% 0.98/0.47  %    Propositional unsat core size     : 0
% 0.98/0.47  %    Propositional preprocessing time  : 0.000
% 0.98/0.47  %    Propositional encoding time       : 0.000
% 0.98/0.47  %    Propositional solver time         : 0.000
% 0.98/0.47  %    Success case prop preproc time    : 0.000
% 0.98/0.47  %    Success case prop encoding time   : 0.000
% 0.98/0.47  %    Success case prop solver time     : 0.000
% 0.98/0.47  % Current number of processed clauses  : 581
% 0.98/0.47  %    Positive orientable unit clauses  : 332
% 0.98/0.47  %    Positive unorientable unit clauses: 0
% 0.98/0.47  %    Negative unit clauses             : 1
% 0.98/0.47  %    Non-unit-clauses                  : 248
% 0.98/0.47  % Current number of unprocessed clauses: 685
% 0.98/0.47  % ...number of literals in the above   : 3509
% 0.98/0.47  % Current number of archived formulas  : 0
% 0.98/0.47  % Current number of archived clauses   : 2
% 0.98/0.47  % Clause-clause subsumption calls (NU) : 6445
% 0.98/0.47  % Rec. Clause-clause subsumption calls : 4276
% 0.98/0.47  % Non-unit clause-clause subsumptions  : 93
% 0.98/0.47  % Unit Clause-clause subsumption calls : 209
% 0.98/0.47  % Rewrite failures with RHS unbound    : 0
% 0.98/0.47  % BW rewrite match attempts            : 1
% 0.98/0.47  % BW rewrite match successes           : 1
% 0.98/0.47  % Condensation attempts                : 0
% 0.98/0.47  % Condensation successes               : 0
% 0.98/0.47  % Termbank termtop insertions          : 53811
% 0.98/0.47  % Search garbage collected termcells   : 14231
% 0.98/0.47  
% 0.98/0.47  % -------------------------------------------------
% 0.98/0.47  % User time                : 0.078 s
% 0.98/0.47  % System time              : 0.013 s
% 0.98/0.47  % Total time               : 0.091 s
% 0.98/0.47  % Maximum resident set size: 6792 pages
% 0.98/0.47  
% 0.98/0.47  % -------------------------------------------------
% 0.98/0.47  % User time                : 0.098 s
% 0.98/0.47  % System time              : 0.024 s
% 0.98/0.47  % Total time               : 0.122 s
% 0.98/0.47  % Maximum resident set size: 5376 pages
% 0.98/0.47  % E exiting
%------------------------------------------------------------------------------