%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU778^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:25:35 AM UTC 2026
% Result : Theorem 0.44s 0.39s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU778^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n018.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 14:30:11 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.21/0.30 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p
% 0.44/0.39 % Version: 3.5.1-ho
% 0.44/0.39 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.44/0.39 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.39 % Starting ehoh_best5 with 300s (1) cores
% 0.44/0.39 % Starting almost_fo_3_lam with 300s (1) cores
% 0.44/0.39 % Starting new_bool_5 with 300s (1) cores
% 0.44/0.39 % Starting pre_casc_3 with 300s (1) cores
% 0.44/0.39 % Starting ho_unfolding_8 with 300s (1) cores
% 0.44/0.39 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.44/0.39 % Starting new_bool_3 with 300s (1) cores
% 0.44/0.39 % Starting new_ho_5 with 300s (1) cores
% 0.44/0.39 % pre_casc_3 with pid 156493 completed with status 0
% 0.44/0.39 % Result found by pre_casc_3
% 0.44/0.39 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.44/0.39 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.39 % Starting ehoh_best5 with 300s (1) cores
% 0.44/0.39 % Starting almost_fo_3_lam with 300s (1) cores
% 0.44/0.39 % Starting new_bool_5 with 300s (1) cores
% 0.44/0.39 % Starting pre_casc_3 with 300s (1) cores
% 0.44/0.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.44/0.39 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.44/0.39 % Search class: HGUSM-FSLM33-MHFMMFBN
% 0.44/0.39 % partial match(3): HGHSM-FSLM32-MHFMMSBN
% 0.44/0.39 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 0.44/0.39 % Starting SubtermCWHack with 31s (1) cores
% 0.44/0.39 % SubtermCWHack with pid 156506 completed with status 0
% 0.44/0.39 % Result found by SubtermCWHack
% 0.44/0.39 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.44/0.39 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.39 % Starting ehoh_best5 with 300s (1) cores
% 0.44/0.39 % Starting almost_fo_3_lam with 300s (1) cores
% 0.44/0.39 % Starting new_bool_5 with 300s (1) cores
% 0.44/0.39 % Starting pre_casc_3 with 300s (1) cores
% 0.44/0.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.44/0.39 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.44/0.39 % Search class: HGUSM-FSLM33-MHFMMFBN
% 0.44/0.39 % partial match(3): HGHSM-FSLM32-MHFMMSBN
% 0.44/0.39 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 0.44/0.39 % Starting SubtermCWHack with 31s (1) cores
% 0.44/0.39 % Preprocessing time : 0.005 s
% 0.44/0.39
% 0.44/0.39 % Proof found!
% 0.44/0.39 % SZS status Theorem
% 0.44/0.39 % SZS output start CNFRefutation
% 0.44/0.39 thf(decl_23, type, in: $i > $i > $o).
% 0.44/0.39 thf(decl_25, type, setextAx: $o).
% 0.44/0.39 thf(decl_26, type, emptyset: $i).
% 0.44/0.39 thf(decl_27, type, emptysetAx: $o).
% 0.44/0.39 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.44/0.39 thf(decl_29, type, setadjoinAx: $o).
% 0.44/0.39 thf(decl_31, type, powersetAx: $o).
% 0.44/0.39 thf(decl_32, type, setunion: $i > $i).
% 0.44/0.39 thf(decl_33, type, setunionAx: $o).
% 0.44/0.39 thf(decl_35, type, omega0Ax: $o).
% 0.44/0.39 thf(decl_36, type, omegaSAx: $o).
% 0.44/0.39 thf(decl_37, type, omegaIndAx: $o).
% 0.44/0.39 thf(decl_38, type, replAx: $o).
% 0.44/0.39 thf(decl_39, type, foundationAx: $o).
% 0.44/0.39 thf(decl_40, type, wellorderingAx: $o).
% 0.44/0.39 thf(decl_42, type, descrp: $o).
% 0.44/0.39 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.44/0.39 thf(decl_44, type, dsetconstrI: $o).
% 0.44/0.39 thf(decl_45, type, dsetconstrEL: $o).
% 0.44/0.39 thf(decl_46, type, dsetconstrER: $o).
% 0.44/0.39 thf(decl_47, type, exuE1: $o).
% 0.44/0.39 thf(decl_49, type, prop2setE: $o).
% 0.44/0.39 thf(decl_50, type, emptysetE: $o).
% 0.44/0.39 thf(decl_51, type, emptysetimpfalse: $o).
% 0.44/0.39 thf(decl_52, type, notinemptyset: $o).
% 0.44/0.39 thf(decl_53, type, exuE3e: $o).
% 0.44/0.39 thf(decl_54, type, setext: $o).
% 0.44/0.39 thf(decl_55, type, emptyI: $o).
% 0.44/0.39 thf(decl_56, type, noeltsimpempty: $o).
% 0.44/0.39 thf(decl_57, type, setbeta: $o).
% 0.44/0.39 thf(decl_59, type, nonemptyE1: $o).
% 0.44/0.39 thf(decl_60, type, nonemptyI: $o).
% 0.44/0.39 thf(decl_61, type, nonemptyI1: $o).
% 0.44/0.39 thf(decl_62, type, setadjoinIL: $o).
% 0.44/0.39 thf(decl_63, type, emptyinunitempty: $o).
% 0.44/0.39 thf(decl_64, type, setadjoinIR: $o).
% 0.44/0.39 thf(decl_65, type, setadjoinE: $o).
% 0.44/0.39 thf(decl_66, type, setadjoinOr: $o).
% 0.44/0.39 thf(decl_67, type, setoftrueEq: $o).
% 0.44/0.39 thf(decl_68, type, powersetI: $o).
% 0.44/0.39 thf(decl_69, type, emptyinPowerset: $o).
% 0.44/0.39 thf(decl_70, type, emptyInPowerset: $o).
% 0.44/0.39 thf(decl_71, type, powersetE: $o).
% 0.44/0.39 thf(decl_72, type, setunionI: $o).
% 0.44/0.39 thf(decl_73, type, setunionE: $o).
% 0.44/0.39 thf(decl_74, type, subPowSU: $o).
% 0.44/0.39 thf(decl_75, type, exuE2: $o).
% 0.44/0.39 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.44/0.39 thf(decl_77, type, uniqinunit: $o).
% 0.44/0.39 thf(decl_78, type, notinsingleton: $o).
% 0.44/0.39 thf(decl_79, type, eqinunit: $o).
% 0.44/0.39 thf(decl_80, type, singletonsswitch: $o).
% 0.44/0.39 thf(decl_81, type, upairsetE: $o).
% 0.44/0.39 thf(decl_82, type, upairsetIL: $o).
% 0.44/0.39 thf(decl_83, type, upairsetIR: $o).
% 0.44/0.39 thf(decl_84, type, emptyE1: $o).
% 0.44/0.39 thf(decl_85, type, vacuousDall: $o).
% 0.44/0.39 thf(decl_86, type, quantDeMorgan1: $o).
% 0.44/0.39 thf(decl_87, type, quantDeMorgan2: $o).
% 0.44/0.39 thf(decl_88, type, quantDeMorgan3: $o).
% 0.44/0.39 thf(decl_89, type, quantDeMorgan4: $o).
% 0.44/0.39 thf(decl_90, type, prop2setI: $o).
% 0.44/0.39 thf(decl_92, type, prop2set2propI: $o).
% 0.44/0.39 thf(decl_93, type, notdexE: $o).
% 0.44/0.39 thf(decl_94, type, notdallE: $o).
% 0.44/0.39 thf(decl_95, type, exuI1: $o).
% 0.44/0.39 thf(decl_96, type, exuI3: $o).
% 0.44/0.39 thf(decl_97, type, exuI2: $o).
% 0.44/0.39 thf(decl_98, type, inCongP: $o).
% 0.44/0.39 thf(decl_99, type, in__Cong: $o).
% 0.44/0.39 thf(decl_100, type, exuE3u: $o).
% 0.44/0.39 thf(decl_101, type, exu__Cong: $o).
% 0.44/0.39 thf(decl_102, type, emptyset__Cong: $o).
% 0.44/0.39 thf(decl_103, type, setadjoin__Cong: $o).
% 0.44/0.39 thf(decl_104, type, powerset__Cong: $o).
% 0.44/0.39 thf(decl_105, type, setunion__Cong: $o).
% 0.44/0.39 thf(decl_106, type, omega__Cong: $o).
% 0.44/0.39 thf(decl_107, type, exuEu: $o).
% 0.44/0.39 thf(decl_108, type, descr__Cong: $o).
% 0.44/0.39 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.44/0.39 thf(decl_110, type, subset: $i > $i > $o).
% 0.44/0.39 thf(decl_113, type, subsetI1: $o).
% 0.44/0.39 thf(decl_114, type, eqimpsubset2: $o).
% 0.44/0.39 thf(decl_115, type, eqimpsubset1: $o).
% 0.44/0.39 thf(decl_116, type, subsetI2: $o).
% 0.44/0.39 thf(decl_117, type, emptysetsubset: $o).
% 0.44/0.39 thf(decl_118, type, subsetE: $o).
% 0.44/0.39 thf(decl_119, type, subsetE2: $o).
% 0.44/0.39 thf(decl_120, type, notsubsetI: $o).
% 0.44/0.39 thf(decl_121, type, notequalI1: $o).
% 0.44/0.39 thf(decl_122, type, notequalI2: $o).
% 0.44/0.39 thf(decl_123, type, subsetRefl: $o).
% 0.44/0.39 thf(decl_124, type, subsetTrans: $o).
% 0.44/0.39 thf(decl_125, type, setadjoinSub: $o).
% 0.44/0.39 thf(decl_126, type, setadjoinSub2: $o).
% 0.44/0.39 thf(decl_127, type, subset2powerset: $o).
% 0.44/0.39 thf(decl_128, type, setextsub: $o).
% 0.44/0.39 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.44/0.39 thf(decl_130, type, powersetI1: $o).
% 0.44/0.39 thf(decl_131, type, powersetE1: $o).
% 0.44/0.39 thf(decl_132, type, inPowerset: $o).
% 0.44/0.39 thf(decl_133, type, powersetsubset: $o).
% 0.44/0.39 thf(decl_134, type, sepInPowerset: $o).
% 0.44/0.39 thf(decl_135, type, sepSubset: $o).
% 0.44/0.39 thf(decl_137, type, binunionIL: $o).
% 0.44/0.39 thf(decl_138, type, upairset2IR: $o).
% 0.44/0.39 thf(decl_139, type, binunionIR: $o).
% 0.44/0.39 thf(decl_140, type, binunionEcases: $o).
% 0.44/0.39 thf(decl_141, type, binunionE: $o).
% 0.44/0.39 thf(decl_142, type, binunionLsub: $o).
% 0.44/0.39 thf(decl_143, type, binunionRsub: $o).
% 0.44/0.39 thf(decl_145, type, binintersectI: $o).
% 0.44/0.39 thf(decl_146, type, binintersectSubset5: $o).
% 0.44/0.39 thf(decl_147, type, binintersectEL: $o).
% 0.44/0.39 thf(decl_148, type, binintersectLsub: $o).
% 0.44/0.39 thf(decl_149, type, binintersectSubset2: $o).
% 0.44/0.39 thf(decl_150, type, binintersectSubset3: $o).
% 0.44/0.39 thf(decl_151, type, binintersectER: $o).
% 0.44/0.39 thf(decl_152, type, disjointsetsI1: $o).
% 0.44/0.39 thf(decl_153, type, binintersectRsub: $o).
% 0.44/0.39 thf(decl_154, type, binintersectSubset4: $o).
% 0.44/0.39 thf(decl_155, type, binintersectSubset1: $o).
% 0.44/0.39 thf(decl_156, type, bs114d: $o).
% 0.44/0.39 thf(decl_159, type, setminusI: $o).
% 0.44/0.39 thf(decl_160, type, setminusEL: $o).
% 0.44/0.39 thf(decl_161, type, setminusER: $o).
% 0.44/0.39 thf(decl_162, type, setminusSubset2: $o).
% 0.44/0.39 thf(decl_163, type, setminusERneg: $o).
% 0.44/0.39 thf(decl_164, type, setminusELneg: $o).
% 0.44/0.39 thf(decl_165, type, setminusILneg: $o).
% 0.44/0.39 thf(decl_166, type, setminusIRneg: $o).
% 0.44/0.39 thf(decl_167, type, setminusLsub: $o).
% 0.44/0.39 thf(decl_168, type, setminusSubset1: $o).
% 0.44/0.39 thf(decl_170, type, symdiffE: $o).
% 0.44/0.39 thf(decl_171, type, symdiffI1: $o).
% 0.44/0.39 thf(decl_172, type, symdiffI2: $o).
% 0.44/0.39 thf(decl_173, type, symdiffIneg1: $o).
% 0.44/0.39 thf(decl_174, type, symdiffIneg2: $o).
% 0.44/0.39 thf(decl_175, type, iskpair: $i > $o).
% 0.44/0.39 thf(decl_176, type, secondinupair: $o).
% 0.44/0.39 thf(decl_177, type, setukpairIL: $o).
% 0.44/0.39 thf(decl_178, type, setukpairIR: $o).
% 0.44/0.39 thf(decl_179, type, kpairiskpair: $o).
% 0.44/0.39 thf(decl_180, type, kpair: $i > $i > $i).
% 0.44/0.39 thf(decl_181, type, kpairp: $o).
% 0.44/0.39 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.44/0.39 thf(decl_183, type, singletonsubset: $o).
% 0.44/0.39 thf(decl_184, type, singletoninpowerset: $o).
% 0.44/0.39 thf(decl_185, type, singletoninpowunion: $o).
% 0.44/0.39 thf(decl_186, type, upairset2E: $o).
% 0.44/0.39 thf(decl_187, type, upairsubunion: $o).
% 0.44/0.39 thf(decl_188, type, upairinpowunion: $o).
% 0.44/0.39 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.44/0.39 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.44/0.39 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.44/0.39 thf(decl_192, type, cartprodpairin: $o).
% 0.44/0.39 thf(decl_193, type, cartprodmempair1: $o).
% 0.44/0.39 thf(decl_194, type, cartprodmempair: $o).
% 0.44/0.39 thf(decl_195, type, setunionE2: $o).
% 0.44/0.39 thf(decl_196, type, setunionsingleton1: $o).
% 0.44/0.39 thf(decl_197, type, setunionsingleton2: $o).
% 0.44/0.39 thf(decl_198, type, setunionsingleton: $o).
% 0.44/0.39 thf(decl_199, type, singleton: $i > $o).
% 0.44/0.39 thf(decl_200, type, singletonprop: $o).
% 0.44/0.39 thf(decl_202, type, ex1E1: $o).
% 0.44/0.39 thf(decl_203, type, ex1I: $o).
% 0.44/0.39 thf(decl_204, type, ex1I2: $o).
% 0.44/0.39 thf(decl_205, type, singletonsuniq: $o).
% 0.44/0.39 thf(decl_210, type, setukpairinjL1: $o).
% 0.44/0.39 thf(decl_211, type, kfstsingleton: $o).
% 0.44/0.39 thf(decl_212, type, theprop: $o).
% 0.44/0.39 thf(decl_213, type, kfst: $i > $i).
% 0.44/0.39 thf(decl_214, type, kfstpairEq: $o).
% 0.44/0.39 thf(decl_215, type, cartprodfstin: $o).
% 0.44/0.39 thf(decl_216, type, setukpairinjL2: $o).
% 0.44/0.39 thf(decl_217, type, setukpairinjL: $o).
% 0.44/0.39 thf(decl_218, type, setukpairinjR11: $o).
% 0.44/0.39 thf(decl_219, type, setukpairinjR12: $o).
% 0.44/0.39 thf(decl_220, type, setukpairinjR1: $o).
% 0.44/0.39 thf(decl_221, type, upairequniteq: $o).
% 0.44/0.39 thf(decl_222, type, setukpairinjR2: $o).
% 0.44/0.39 thf(decl_223, type, setukpairinjR: $o).
% 0.44/0.39 thf(decl_224, type, ksndsingleton: $o).
% 0.44/0.39 thf(decl_225, type, ksnd: $i > $i).
% 0.44/0.39 thf(decl_226, type, ksndpairEq: $o).
% 0.44/0.39 thf(decl_227, type, kpairsurjEq: $o).
% 0.44/0.39 thf(decl_228, type, cartprodsndin: $o).
% 0.44/0.39 thf(decl_229, type, cartprodpairmemEL: $o).
% 0.44/0.39 thf(decl_230, type, cartprodpairmemER: $o).
% 0.44/0.39 thf(decl_231, type, cartprodmempaircEq: $o).
% 0.44/0.39 thf(decl_232, type, cartprodfstpairEq: $o).
% 0.44/0.39 thf(decl_233, type, cartprodsndpairEq: $o).
% 0.44/0.39 thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.44/0.39 thf(decl_235, type, breln: $i > $i > $i > $o).
% 0.44/0.39 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.44/0.39 thf(decl_237, type, dpsetconstrI: $o).
% 0.44/0.39 thf(decl_238, type, dpsetconstrSub: $o).
% 0.44/0.39 thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.44/0.39 thf(decl_240, type, dpsetconstrERa: $o).
% 0.44/0.39 thf(decl_241, type, dpsetconstrEL1: $o).
% 0.44/0.39 thf(decl_242, type, dpsetconstrEL2: $o).
% 0.44/0.39 thf(decl_243, type, dpsetconstrER: $o).
% 0.44/0.39 thf(decl_244, type, func: $i > $i > $i > $o).
% 0.44/0.39 thf(decl_246, type, funcImageSingleton: $o).
% 0.44/0.39 thf(decl_247, type, apProp: $o).
% 0.44/0.39 thf(decl_249, type, app: $o).
% 0.44/0.39 thf(decl_250, type, infuncsetfunc: $o).
% 0.44/0.39 thf(decl_251, type, ap2p: $o).
% 0.44/0.39 thf(decl_252, type, funcinfuncset: $o).
% 0.44/0.39 thf(decl_253, type, lamProp: $o).
% 0.44/0.39 thf(decl_255, type, lamp: $o).
% 0.44/0.39 thf(decl_256, type, lam2p: $o).
% 0.44/0.39 thf(decl_257, type, brelnall1: $o).
% 0.44/0.39 thf(decl_258, type, brelnall2: $o).
% 0.44/0.39 thf(decl_259, type, ex1E2: $o).
% 0.44/0.39 thf(decl_260, type, funcGraphProp1: $o).
% 0.44/0.39 thf(decl_261, type, funcGraphProp3: $o).
% 0.44/0.39 thf(decl_262, type, funcGraphProp2: $o).
% 0.44/0.39 thf(decl_263, type, funcextLem: $o).
% 0.44/0.39 thf(decl_264, type, funcGraphProp4: $o).
% 0.44/0.39 thf(decl_265, type, subbreln: $o).
% 0.44/0.39 thf(decl_266, type, eqbreln: $o).
% 0.44/0.39 thf(decl_267, type, funcext: $o).
% 0.44/0.39 thf(decl_268, type, funcext2: $o).
% 0.44/0.39 thf(decl_269, type, ap2apEq1: $o).
% 0.44/0.39 thf(decl_270, type, ap2apEq2: $o).
% 0.44/0.39 thf(decl_271, type, beta1: $o).
% 0.44/0.39 thf(decl_272, type, eta1: $o).
% 0.44/0.39 thf(decl_273, type, lam2lamEq: $o).
% 0.44/0.39 thf(decl_274, type, beta2: $o).
% 0.44/0.39 thf(decl_275, type, eta2: $o).
% 0.44/0.39 thf(decl_276, type, iffalseProp1: $o).
% 0.44/0.39 thf(decl_277, type, iffalseProp2: $o).
% 0.44/0.39 thf(decl_278, type, iftrueProp1: $o).
% 0.44/0.39 thf(decl_279, type, iftrueProp2: $o).
% 0.44/0.39 thf(decl_280, type, ifSingleton: $o).
% 0.44/0.39 thf(decl_282, type, ifp: $o).
% 0.44/0.39 thf(decl_283, type, theeq: $o).
% 0.44/0.39 thf(decl_284, type, iftrue: $o).
% 0.44/0.39 thf(decl_285, type, iffalse: $o).
% 0.44/0.39 thf(decl_286, type, iftrueorfalse: $o).
% 0.44/0.39 thf(decl_287, type, binintersectT_lem: $o).
% 0.44/0.39 thf(decl_288, type, binunionT_lem: $o).
% 0.44/0.39 thf(decl_289, type, powersetT_lem: $o).
% 0.44/0.39 thf(decl_290, type, setminusT_lem: $o).
% 0.44/0.39 thf(decl_291, type, complementT_lem: $o).
% 0.44/0.39 thf(decl_292, type, setextT: $o).
% 0.44/0.39 thf(decl_293, type, subsetTI: $o).
% 0.44/0.39 thf(decl_294, type, powersetTI1: $o).
% 0.44/0.39 thf(decl_295, type, powersetTE1: $o).
% 0.44/0.39 thf(decl_296, type, complementTI1: $o).
% 0.44/0.39 thf(decl_297, type, complementTE1: $o).
% 0.44/0.39 thf(decl_298, type, binintersectTELcontra: $o).
% 0.44/0.39 thf(decl_299, type, binintersectTERcontra: $o).
% 0.44/0.39 thf(decl_300, type, contrasubsetT: $o).
% 0.44/0.39 thf(decl_301, type, contrasubsetT1: $o).
% 0.44/0.39 thf(decl_302, type, contrasubsetT2: $o).
% 0.44/0.39 thf(decl_303, type, contrasubsetT3: $o).
% 0.44/0.39 thf(decl_304, type, doubleComplementI1: $o).
% 0.44/0.39 thf(decl_305, type, doubleComplementE1: $o).
% 0.44/0.39 thf(decl_306, type, doubleComplementSub1: $o).
% 0.44/0.39 thf(decl_307, type, doubleComplementSub2: $o).
% 0.44/0.39 thf(decl_308, type, doubleComplementEq: $o).
% 0.44/0.39 thf(decl_309, type, complementTnotintersectT: $o).
% 0.44/0.39 thf(decl_310, type, complementImpComplementIntersect: $o).
% 0.44/0.39 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 0.44/0.39 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 0.44/0.39 thf(decl_313, type, contraSubsetComplement: $o).
% 0.44/0.39 thf(decl_314, type, complementTcontraSubset: $o).
% 0.44/0.39 thf(decl_315, type, binunionTILcontra: $o).
% 0.44/0.39 thf(decl_316, type, binunionTIRcontra: $o).
% 0.44/0.39 thf(decl_317, type, inIntersectImpInUnion: $o).
% 0.44/0.39 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 0.44/0.39 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 0.44/0.39 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 0.44/0.39 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 0.44/0.39 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 0.44/0.39 thf(decl_323, type, binunionTE: $o).
% 0.44/0.39 thf(decl_324, type, binunionTEcontra: $o).
% 0.44/0.39 thf(decl_325, type, demorgan2a1: $o).
% 0.44/0.39 thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 0.44/0.39 thf(decl_327, type, demorgan2a2: $o).
% 0.44/0.39 thf(decl_328, type, demorgan1a: $o).
% 0.44/0.39 thf(decl_329, type, demorgan1b: $o).
% 0.44/0.39 thf(decl_330, type, demorgan1: $o).
% 0.44/0.39 thf(decl_331, type, demorgan2a: $o).
% 0.44/0.39 thf(decl_332, type, demorgan2b2: $o).
% 0.44/0.39 thf(decl_333, type, demorgan2b: $o).
% 0.44/0.39 thf(decl_334, type, demorgan2: $o).
% 0.44/0.39 thf(decl_335, type, woz13rule0: $o).
% 0.44/0.39 thf(decl_336, type, woz13rule1: $o).
% 0.44/0.39 thf(decl_337, type, woz13rule2: $o).
% 0.44/0.39 thf(decl_338, type, woz13rule3: $o).
% 0.44/0.39 thf(decl_339, type, woz13rule4: $o).
% 0.44/0.39 thf(decl_340, type, woz1_1: $o).
% 0.44/0.39 thf(decl_341, type, woz1_2: $o).
% 0.44/0.39 thf(decl_342, type, woz1_3: $o).
% 0.44/0.39 thf(decl_343, type, woz1_4: $o).
% 0.44/0.39 thf(decl_344, type, woz1_5: $o).
% 0.44/0.39 thf(decl_345, type, breln1: $i > $i > $o).
% 0.44/0.39 thf(decl_346, type, breln1all2: $o).
% 0.44/0.39 thf(decl_347, type, breln1Set: $i > $i).
% 0.44/0.39 thf(decl_348, type, breln1SetBreln1: $o).
% 0.44/0.39 thf(decl_354, type, reflwellordering: $i > $i > $o).
% 0.44/0.39 thf(decl_355, type, choice2fnsingleton: $o).
% 0.44/0.39 thf(decl_356, type, setOfPairsIsBReln1: $o).
% 0.44/0.39 thf(decl_357, type, breln1all1: $o).
% 0.44/0.39 thf(decl_358, type, subbreln1: $o).
% 0.44/0.39 thf(decl_359, type, eqbreln1: $o).
% 0.44/0.39 thf(decl_361, type, breln1invprop: $o).
% 0.44/0.39 thf(decl_362, type, breln1invI: $o).
% 0.44/0.39 thf(decl_363, type, breln1invE: $o).
% 0.44/0.39 thf(decl_364, type, breln1compset: $i > $i > $i > $i).
% 0.44/0.39 thf(decl_365, type, esk1_3: $i > $i > $i > $i).
% 0.44/0.39 thf(decl_366, type, esk2_3: $i > $i > $i > $i).
% 0.44/0.39 thf(decl_367, type, esk3_2: $i > ($i > $o) > $i).
% 0.44/0.39 thf(decl_368, type, esk4_2: $i > ($i > $o) > $i).
% 0.44/0.39 thf(decl_369, type, esk5_3: $i > $i > ($i > $i) > $i).
% 0.44/0.39 thf(decl_370, type, esk6_4: $i > $i > $i > ($i > $o) > $i).
% 0.44/0.39 thf(decl_371, type, esk7_4: $i > $i > $i > ($i > $o) > $i).
% 0.44/0.39 thf(decl_372, type, esk8_4: $i > $i > $i > ($i > $o) > $i).
% 0.44/0.39 thf(decl_373, type, esk9_4: $i > $i > $i > ($i > $o) > $i).
% 0.44/0.39 thf(decl_374, type, esk10_4: $i > $i > $i > $i > $i).
% 0.44/0.39 thf(decl_375, type, esk11_4: $i > $i > $i > $i > $i).
% 0.44/0.39 thf(decl_376, type, esk12_4: $i > $i > $i > $i > $i).
% 0.44/0.39 thf(decl_377, type, esk13_4: $i > $i > $i > $i > $i).
% 0.44/0.39 thf(decl_378, type, esk14_4: $i > $i > $i > $i > $i).
% 0.44/0.39 thf(decl_379, type, esk15_4: $i > $i > $i > $i > $i).
% 0.44/0.39 thf(decl_380, type, esk16_3: $i > $i > ($i > $i > $o) > $i).
% 0.44/0.39 thf(decl_381, type, esk17_0: $i).
% 0.44/0.39 thf(decl_382, type, esk18_0: $i).
% 0.44/0.39 thf(decl_383, type, esk19_0: $i).
% 0.44/0.39 thf(decl_390, type, epred7_3: $i > $i > $i > $i > $i > $o).
% 0.44/0.39 thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', breln1)).
% 0.44/0.39 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', breln)).
% 0.44/0.39 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', setOfPairsIsBReln1)).
% 0.44/0.39 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', setOfPairsIsBReln)).
% 0.44/0.39 thf(breln1compprop, 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)=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', breln1compprop)).
% 0.44/0.39 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', ifSingleton)).
% 0.44/0.39 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', funcImageSingleton)).
% 0.44/0.39 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', singletonprop)).
% 0.44/0.39 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', ksndsingleton)).
% 0.44/0.39 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', kfstsingleton)).
% 0.44/0.39 thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((((X52 @ X2 @ X3))&(![X14:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ X3 @ X14) @ X33)))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', choice2fnsingleton)).
% 0.44/0.39 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', lamProp)).
% 0.44/0.39 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', dpsetconstrER)).
% 0.44/0.39 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', dpsetconstrEL2)).
% 0.44/0.39 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', dpsetconstrEL1)).
% 0.44/0.39 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', dpsetconstrERa)).
% 0.44/0.39 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', dpsetconstrSub)).
% 0.44/0.39 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', dpsetconstrI)).
% 0.44/0.39 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', eqbreln)).
% 0.44/0.39 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', subbreln)).
% 0.44/0.39 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', brelnall2)).
% 0.44/0.39 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', brelnall1)).
% 0.44/0.39 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', theeq)).
% 0.44/0.39 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', theprop)).
% 0.44/0.39 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', cartprodsndpairEq)).
% 0.44/0.39 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', ksndpairEq)).
% 0.44/0.39 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', cartprodfstpairEq)).
% 0.44/0.39 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', kfstpairEq)).
% 0.44/0.39 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', kpairsurjEq)).
% 0.44/0.39 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', kpairp)).
% 0.44/0.39 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', kpairiskpair)).
% 0.44/0.39 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', cartprodpairsurjEq)).
% 0.44/0.39 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', cartprodpairmemER)).
% 0.44/0.39 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', cartprodpairmemEL)).
% 0.44/0.39 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', cartprodsndin)).
% 0.44/0.39 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', cartprodfstin)).
% 0.44/0.39 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', cartprodmempair)).
% 0.44/0.39 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', cartprodmempair1)).
% 0.44/0.39 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', cartprodpairin)).
% 0.44/0.39 thf(breln1compset, axiom, ((breln1compset)=(^[X4:$i, X33:$i, X35:$i]:(dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:(?[X14:$i]:((((((in @ X14 @ X4))&((in @ (kpair @ X2 @ X14) @ X33))))&((in @ (kpair @ X14 @ X3) @ X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.L8OJ5wyhpI/E---3.1_156427.p', breln1compset)).
% 0.44/0.39 thf(c_0_40, plain, ((breln1)=(^[Z0:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
% 0.44/0.39 thf(c_0_41, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 0.44/0.39 thf(c_0_42, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
% 0.44/0.39 thf(c_0_43, plain, ((breln1)=(^[Z0:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_40, c_0_41])).
% 0.44/0.39 thf(c_0_44, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 0.44/0.39 thf(c_0_45, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((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)=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[breln1compprop])).
% 0.44/0.39 thf(c_0_46, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 0.44/0.39 thf(c_0_47, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 0.44/0.39 thf(c_0_48, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 0.44/0.39 thf(c_0_49, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 0.44/0.39 thf(c_0_50, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 0.44/0.39 thf(c_0_51, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((((X52 @ X2 @ Z0))&(![X14:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ Z0 @ X14) @ X33)))))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])).
% 0.44/0.39 thf(c_0_52, plain, ((setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X4)))))), inference(apply_def,[status(thm)],[c_0_42, c_0_43])).
% 0.44/0.39 thf(c_0_53, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 0.44/0.39 thf(c_0_54, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 0.44/0.39 thf(c_0_55, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 0.44/0.39 thf(c_0_56, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 0.44/0.39 thf(c_0_57, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 0.44/0.39 thf(c_0_58, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 0.44/0.39 thf(c_0_59, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 0.44/0.39 thf(c_0_60, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_41])).
% 0.44/0.39 thf(c_0_61, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_41])).
% 0.44/0.39 thf(c_0_62, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_41])).
% 0.44/0.39 thf(c_0_63, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_41])).
% 0.44/0.39 thf(c_0_64, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_44, c_0_41])).
% 0.44/0.39 thf(c_0_65, 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)=>(![X193:$i, X194:$i]:((iskpair @ (setadjoin @ (setadjoin @ X193 @ emptyset) @ (setadjoin @ (setadjoin @ X193 @ (setadjoin @ X194 @ emptyset)) @ emptyset))))=>(![X195:$i, X196:$i]:((iskpair @ (kpair @ X195 @ X196)))=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>(![X197:$i, X198:$i, X199:$i]:(((in @ X199 @ X197)=>![X200:$i]:(((in @ X200 @ X198)=>(in @ (kpair @ X199 @ X200) @ (cartprod @ X197 @ X198))))))=>(![X201:$i, X202:$i, X203:$i]:(((in @ X203 @ (cartprod @ X201 @ X202))=>?[X204:$i]:(((in @ X204 @ X201)&?[X205:$i]:(((in @ X205 @ X202)&((X203)=(kpair @ X204 @ X205))))))))=>(![X206:$i, X207:$i, X208:$i]:(((in @ X208 @ (cartprod @ X206 @ X207))=>(iskpair @ X208)))=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(![X209:$i, X210:$i > $o]:((![X211:$i]:(((in @ X211 @ X209)=>![X212:$i]:(((in @ X212 @ X209)=>((X210 @ X211)=>((X210 @ X212)=>((X211)=(X212))))))))=>(?[X213:$i]:(((in @ X213 @ X209)&(X210 @ X213)))=>(singleton @ (dsetconstr @ X209 @ X210)))))=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>(![X214:$i]:(((iskpair @ X214)=>(singleton @ (dsetconstr @ (setunion @ X214) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X214)))))))=>(![X215:$i]:(((singleton @ X215)=>(in @ (setunion @ X215) @ X215)))=>(![X216:$i, X217:$i]:(((kfst @ (kpair @ X216 @ X217))=(X216)))=>(![X218:$i, X219:$i, X220:$i]:(((in @ X220 @ (cartprod @ X218 @ X219))=>(in @ (kfst @ X220) @ X218)))=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>(![X221:$i]:(((iskpair @ X221)=>(singleton @ (dsetconstr @ (setunion @ X221) @ (^[Z0:$i]:(((X221)=(kpair @ (kfst @ X221) @ Z0))))))))=>(![X222:$i, X223:$i]:(((ksnd @ (kpair @ X222 @ X223))=(X223)))=>(![X224:$i]:(((iskpair @ X224)=>((kpair @ (kfst @ X224) @ (ksnd @ X224))=(X224))))=>(![X225:$i, X226:$i, X227:$i]:(((in @ X227 @ (cartprod @ X225 @ X226))=>(in @ (ksnd @ X227) @ X226)))=>(![X228:$i, X229:$i, X230:$i, X231:$i]:(((in @ (kpair @ X230 @ X231) @ (cartprod @ X228 @ X229))=>(in @ X230 @ X228)))=>(![X232:$i, X233:$i, X234:$i, X235:$i]:(((in @ (kpair @ X234 @ X235) @ (cartprod @ X232 @ X233))=>(in @ X235 @ X233)))=>((cartprodmempaircEq)=>(![X236:$i, X237:$i, X238:$i]:(((in @ X238 @ X236)=>![X239:$i]:(((in @ X239 @ X237)=>((kfst @ (kpair @ X238 @ X239))=(X238))))))=>(![X240:$i, X241:$i, X242:$i]:(((in @ X242 @ X240)=>![X243:$i]:(((in @ X243 @ X241)=>((ksnd @ (kpair @ X242 @ X243))=(X243))))))=>(![X244:$i, X245:$i, X246:$i]:(((in @ X246 @ (cartprod @ X244 @ X245))=>((kpair @ (kfst @ X246) @ (ksnd @ X246))=(X246))))=>(![X247:$i, X248:$i, X249:$i > $i > $o, X250:$i]:(((in @ X250 @ X247)=>![X251:$i]:(((in @ X251 @ X248)=>((X249 @ X250 @ X251)=>(in @ (kpair @ X250 @ X251) @ (dpsetconstr @ X247 @ X248 @ X249)))))))=>(![X252:$i, X253:$i, X254:$i > $i > $o]:((subset @ (dpsetconstr @ X252 @ X253 @ X254) @ (cartprod @ X252 @ X253)))=>(![X255:$i, X256:$i, X257:$i > $i > $o]:((subset @ (dpsetconstr @ X255 @ X256 @ X257) @ (cartprod @ X255 @ X256)))=>(![X258:$i, X259:$i, X260:$i > $i > $o, X261:$i]:(((in @ X261 @ X258)=>![X262:$i]:(((in @ X262 @ X259)=>((in @ (kpair @ X261 @ X262) @ (dpsetconstr @ X258 @ X259 @ X260))=>(X260 @ X261 @ X262))))))=>(![X263:$i, X264:$i, X265:$i > $i > $o, X266:$i, X267:$i]:(((in @ (kpair @ X266 @ X267) @ (dpsetconstr @ X263 @ X264 @ X265))=>(in @ X266 @ X263)))=>(![X268:$i, X269:$i, X270:$i > $i > $o, X271:$i, X272:$i]:(((in @ (kpair @ X271 @ X272) @ (dpsetconstr @ X268 @ X269 @ X270))=>(in @ X272 @ X269)))=>(![X273:$i, X274:$i, X275:$i > $i > $o, X276:$i, X277:$i]:(((in @ (kpair @ X276 @ X277) @ (dpsetconstr @ X273 @ X274 @ X275))=>(X275 @ X276 @ X277)))=>(![X278:$i, X279:$i, X280:$i]:(((func @ X278 @ X279 @ X280)=>![X281:$i]:(((in @ X281 @ X278)=>(singleton @ (dsetconstr @ X279 @ (^[Z0:$i]:((in @ (kpair @ X281 @ Z0) @ X280)))))))))=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>(![X282:$i, X283:$i, X284:$i > $i]:((![X285:$i]:(((in @ X285 @ X282)=>(in @ (X284 @ X285) @ X283)))=>(func @ X282 @ X283 @ (dpsetconstr @ X282 @ X283 @ (^[Z0:$i]:($eq @ (X284 @ Z0)))))))=>((lamp)=>((lam2p)=>(![X286:$i, X287:$i, X288:$i]:(((subset @ X288 @ (cartprod @ X286 @ X287))=>![X289:$i > $o]:((![X290:$i]:(((in @ X290 @ X286)=>![X291:$i]:(((in @ X291 @ X287)=>((in @ (kpair @ X290 @ X291) @ X288)=>(X289 @ (kpair @ X290 @ X291)))))))=>![X292:$i]:(((in @ X292 @ X288)=>(X289 @ X292)))))))=>(![X293:$i, X294:$i, X295:$i]:(((subset @ X295 @ (cartprod @ X293 @ X294))=>![X296:$i > $o]:((![X297:$i]:(((in @ X297 @ X293)=>![X298:$i]:(((in @ X298 @ X294)=>((in @ (kpair @ X297 @ X298) @ X295)=>(X296 @ (kpair @ X297 @ X298)))))))=>![X299:$i]:(((in @ X299 @ X295)=>(X296 @ X299)))))))=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(![X300:$i, X301:$i, X302:$i]:(((subset @ X302 @ (cartprod @ X300 @ X301))=>![X303:$i]:(((subset @ X303 @ (cartprod @ X300 @ X301))=>(![X304:$i]:(((in @ X304 @ X300)=>![X305:$i]:(((in @ X305 @ X301)=>((in @ (kpair @ X304 @ X305) @ X302)=>(in @ (kpair @ X304 @ X305) @ X303))))))=>(subset @ X302 @ X303))))))=>(![X306:$i, X307:$i, X308:$i]:(((subset @ X308 @ (cartprod @ X306 @ X307))=>![X309:$i]:(((subset @ X309 @ (cartprod @ X306 @ X307))=>(![X310:$i]:(((in @ X310 @ X306)=>![X311:$i]:(((in @ X311 @ X307)=>((in @ (kpair @ X310 @ X311) @ X308)=>(in @ (kpair @ X310 @ X311) @ X309))))))=>(![X312:$i]:(((in @ X312 @ X306)=>![X313:$i]:(((in @ X313 @ X307)=>((in @ (kpair @ X312 @ X313) @ X309)=>(in @ (kpair @ X312 @ X313) @ X308))))))=>((X308)=(X309))))))))=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>(![X314:$i, X315:$o, X316:$i]:(((in @ X316 @ X314)=>![X317:$i]:(((in @ X317 @ X314)=>(singleton @ (dsetconstr @ X314 @ (^[Z0:$i]:((((((X315))&(((Z0)=(X316)))))|(((~((X315)))&(((Z0)=(X317))))))))))))))=>((ifp)=>(![X318:$i]:(((singleton @ X318)=>![X319:$i]:(((in @ X319 @ X318)=>((setunion @ X318)=(X319))))))=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>(![X320:$i, X321:$i, X322:$i > $i > $o]:((![X323:$i]:(((in @ X323 @ X320)=>?[X324:$i]:(((in @ X324 @ X321)&(X322 @ X323 @ X324)))))=>![X325:$i]:(((in @ X325 @ (breln1Set @ X321))=>((reflwellordering @ X321 @ X325)=>![X326:$i]:(((in @ X326 @ X320)=>(singleton @ (dsetconstr @ X321 @ (^[Z0:$i]:(((X322 @ X326 @ Z0)&(![X327:$i]:((((in @ X327 @ X321))=>(((X322 @ X326 @ X327)=>((in @ (kpair @ Z0 @ X327) @ X325)))))))))))))))))))=>(![X328:$i, X329:$i > $i > $o]:((subset @ (dpsetconstr @ X328 @ X328 @ X329) @ (cartprod @ X328 @ X328)))=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>![X4:$i, X33:$i]:(((subset @ X33 @ (cartprod @ X4 @ X4))=>![X35:$i]:(((subset @ X35 @ (cartprod @ X4 @ X4))=>(subset @ (breln1compset @ X4 @ X33 @ X35) @ (cartprod @ X4 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_45, theeq]), c_0_46]), c_0_47]), theprop]), c_0_48]), cartprodsndpairEq]), ksndpairEq]), cartprodfstpairEq]), kfstpairEq]), kpairsurjEq]), c_0_49]), c_0_50]), kpairp]), kpairiskpair]), cartprodpairsurjEq]), c_0_51]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), cartprodfstin]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56]), c_0_57]), c_0_58]), c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_43])])).
% 0.44/0.39 thf(c_0_66, plain, ![X330:$i, X331:$i, X332:$i]:(((breln1compset @ X330 @ X331 @ X332)=(dpsetconstr @ X330 @ X330 @ (^[Z0:$i, Z1:$i]:(?[X14:$i]:((((((in @ X14 @ X330))&((in @ (kpair @ Z0 @ X14) @ X331))))&((in @ (kpair @ X14 @ Z1) @ X332))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[breln1compset])])).
% 0.44/0.39 thf(c_0_67, negated_conjecture, ![X333:$i, X334:$i, X335:$i, X336:$i, X337:$i, X338:$i, X339:$i, X340:$i, X341:$i, X342:$i, X343:$i, X346:$i, X347:$i, X348:$i, X349:$i, X350:$i > $o, X353:$i, X354:$i, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i, X360:$i, X361:$i, X362:$i, X363:$i, X364:$i, X365:$i, X366:$i, X367:$i, X368:$i, X369:$i, X370:$i, X371:$i, X372:$i, X373:$i, X374:$i, X375:$i, X376:$i, X377:$i, X378:$i, X379:$i, X380:$i, X381:$i, X382:$i, X383:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i, X389:$i > $i > $o, X390:$i, X391:$i, X392:$i, X393:$i, X394:$i > $i > $o, X395:$i, X396:$i, X397:$i > $i > $o, X398:$i, X399:$i, X400:$i > $i > $o, X401:$i, X402:$i, X403:$i, X404:$i, X405:$i > $i > $o, X406:$i, X407:$i, X408:$i, X409:$i, X410:$i > $i > $o, X411:$i, X412:$i, X413:$i, X414:$i, X415:$i > $i > $o, X416:$i, X417:$i, X418:$i, X419:$i, X420:$i, X421:$i, X422:$i, X423:$i, X424:$i > $i, X426:$i, X427:$i, X428:$i, X429:$i > $o, X432:$i, X433:$i, X434:$i, X435:$i, X436:$i > $o, X439:$i, X440:$i, X441:$i, X442:$i, X443:$i, X446:$i, X447:$i, X448:$i, X449:$i, X454:$i, X455:$o, X456:$i, X457:$i, X458:$i, X459:$i, X460:$i, X461:$i, X462:$i > $i > $o, X464:$i, X465:$i, X466:$i, X467:$i, X468:$i > $i > $o]:(((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)&((iskpair @ (setadjoin @ (setadjoin @ X333 @ emptyset) @ (setadjoin @ (setadjoin @ X333 @ (setadjoin @ X334 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X335 @ X336))&((singletonsubset)&((singletoninpowerset)&((singletoninpowunion)&((upairset2E)&((upairsubunion)&((upairinpowunion)&((ubforcartprodlem1)&((ubforcartprodlem2)&((ubforcartprodlem3)&((~(in @ X339 @ X337)|(~(in @ X340 @ X338)|(in @ (kpair @ X339 @ X340) @ (cartprod @ X337 @ X338))))&((((in @ (esk1_3 @ X341 @ X342 @ X343) @ X341)|~(in @ X343 @ (cartprod @ X341 @ X342)))&(((in @ (esk2_3 @ X341 @ X342 @ X343) @ X342)|~(in @ X343 @ (cartprod @ X341 @ X342)))&(((X343)=(kpair @ (esk1_3 @ X341 @ X342 @ X343) @ (esk2_3 @ X341 @ X342 @ X343)))|~(in @ X343 @ (cartprod @ X341 @ X342)))))&((~(in @ X348 @ (cartprod @ X346 @ X347))|(iskpair @ X348))&((setunionE2)&((setunionsingleton1)&((setunionsingleton2)&((setunionsingleton)&((((in @ (esk3_2 @ X349 @ X350) @ X349)|(~(in @ X353 @ X349)|~(X350 @ X353)|(singleton @ (dsetconstr @ X349 @ X350))))&(((in @ (esk4_2 @ X349 @ X350) @ X349)|(~(in @ X353 @ X349)|~(X350 @ X353)|(singleton @ (dsetconstr @ X349 @ X350))))&(((X350 @ (esk3_2 @ X349 @ X350))|(~(in @ X353 @ X349)|~(X350 @ X353)|(singleton @ (dsetconstr @ X349 @ X350))))&(((X350 @ (esk4_2 @ X349 @ X350))|(~(in @ X353 @ X349)|~(X350 @ X353)|(singleton @ (dsetconstr @ X349 @ X350))))&(((esk3_2 @ X349 @ X350)!=(esk4_2 @ X349 @ X350))|(~(in @ X353 @ X349)|~(X350 @ X353)|(singleton @ (dsetconstr @ X349 @ X350))))))))&((ex1E1)&((ex1I)&((ex1I2)&((singletonsuniq)&((setukpairinjL1)&((~(iskpair @ X354)|(singleton @ (dsetconstr @ (setunion @ X354) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X354))))))&((~(singleton @ X355)|(in @ (setunion @ X355) @ X355))&(((kfst @ (kpair @ X356 @ X357))=(X356))&((~(in @ X360 @ (cartprod @ X358 @ X359))|(in @ (kfst @ X360) @ X358))&((setukpairinjL2)&((setukpairinjL)&((setukpairinjR11)&((setukpairinjR12)&((setukpairinjR1)&((upairequniteq)&((setukpairinjR2)&((setukpairinjR)&((~(iskpair @ X361)|(singleton @ (dsetconstr @ (setunion @ X361) @ (^[Z0:$i]:(((X361)=(kpair @ (kfst @ X361) @ Z0)))))))&(((ksnd @ (kpair @ X362 @ X363))=(X363))&((~(iskpair @ X364)|((kpair @ (kfst @ X364) @ (ksnd @ X364))=(X364)))&((~(in @ X367 @ (cartprod @ X365 @ X366))|(in @ (ksnd @ X367) @ X366))&((~(in @ (kpair @ X370 @ X371) @ (cartprod @ X368 @ X369))|(in @ X370 @ X368))&((~(in @ (kpair @ X374 @ X375) @ (cartprod @ X372 @ X373))|(in @ X375 @ X373))&((cartprodmempaircEq)&((~(in @ X378 @ X376)|(~(in @ X379 @ X377)|((kfst @ (kpair @ X378 @ X379))=(X378))))&((~(in @ X382 @ X380)|(~(in @ X383 @ X381)|((ksnd @ (kpair @ X382 @ X383))=(X383))))&((~(in @ X386 @ (cartprod @ X384 @ X385))|((kpair @ (kfst @ X386) @ (ksnd @ X386))=(X386)))&((~(in @ X390 @ X387)|(~(in @ X391 @ X388)|(~(X389 @ X390 @ X391)|(in @ (kpair @ X390 @ X391) @ (dpsetconstr @ X387 @ X388 @ X389)))))&((subset @ (dpsetconstr @ X392 @ X393 @ X394) @ (cartprod @ X392 @ X393))&((subset @ (dpsetconstr @ X395 @ X396 @ X397) @ (cartprod @ X395 @ X396))&((~(in @ X401 @ X398)|(~(in @ X402 @ X399)|(~(in @ (kpair @ X401 @ X402) @ (dpsetconstr @ X398 @ X399 @ X400))|(X400 @ X401 @ X402))))&((~(in @ (kpair @ X406 @ X407) @ (dpsetconstr @ X403 @ X404 @ X405))|(in @ X406 @ X403))&((~(in @ (kpair @ X411 @ X412) @ (dpsetconstr @ X408 @ X409 @ X410))|(in @ X412 @ X409))&((~(in @ (kpair @ X416 @ X417) @ (dpsetconstr @ X413 @ X414 @ X415))|(X415 @ X416 @ X417))&((~(func @ X418 @ X419 @ X420)|(~(in @ X421 @ X418)|(singleton @ (dsetconstr @ X419 @ (^[Z0:$i]:((in @ (kpair @ X421 @ Z0) @ X420)))))))&((apProp)&((app)&((infuncsetfunc)&((ap2p)&((funcinfuncset)&((((in @ (esk5_3 @ X422 @ X423 @ X424) @ X422)|(func @ X422 @ X423 @ (dpsetconstr @ X422 @ X423 @ (^[Z0:$i]:($eq @ (X424 @ Z0))))))&(~(in @ (X424 @ (esk5_3 @ X422 @ X423 @ X424)) @ X423)|(func @ X422 @ X423 @ (dpsetconstr @ X422 @ X423 @ (^[Z0:$i]:($eq @ (X424 @ Z0)))))))&((lamp)&((lam2p)&((((in @ (esk6_4 @ X426 @ X427 @ X428 @ X429) @ X426)|(~(in @ X432 @ X428)|(X429 @ X432))|~(subset @ X428 @ (cartprod @ X426 @ X427)))&(((in @ (esk7_4 @ X426 @ X427 @ X428 @ X429) @ X427)|(~(in @ X432 @ X428)|(X429 @ X432))|~(subset @ X428 @ (cartprod @ X426 @ X427)))&(((in @ (kpair @ (esk6_4 @ X426 @ X427 @ X428 @ X429) @ (esk7_4 @ X426 @ X427 @ X428 @ X429)) @ X428)|(~(in @ X432 @ X428)|(X429 @ X432))|~(subset @ X428 @ (cartprod @ X426 @ X427)))&(~(X429 @ (kpair @ (esk6_4 @ X426 @ X427 @ X428 @ X429) @ (esk7_4 @ X426 @ X427 @ X428 @ X429)))|(~(in @ X432 @ X428)|(X429 @ X432))|~(subset @ X428 @ (cartprod @ X426 @ X427))))))&((((in @ (esk8_4 @ X433 @ X434 @ X435 @ X436) @ X433)|(~(in @ X439 @ X435)|(X436 @ X439))|~(subset @ X435 @ (cartprod @ X433 @ X434)))&(((in @ (esk9_4 @ X433 @ X434 @ X435 @ X436) @ X434)|(~(in @ X439 @ X435)|(X436 @ X439))|~(subset @ X435 @ (cartprod @ X433 @ X434)))&(((in @ (kpair @ (esk8_4 @ X433 @ X434 @ X435 @ X436) @ (esk9_4 @ X433 @ X434 @ X435 @ X436)) @ X435)|(~(in @ X439 @ X435)|(X436 @ X439))|~(subset @ X435 @ (cartprod @ X433 @ X434)))&(~(X436 @ (kpair @ (esk8_4 @ X433 @ X434 @ X435 @ X436) @ (esk9_4 @ X433 @ X434 @ X435 @ X436)))|(~(in @ X439 @ X435)|(X436 @ X439))|~(subset @ X435 @ (cartprod @ X433 @ X434))))))&((ex1E2)&((funcGraphProp1)&((funcGraphProp3)&((funcGraphProp2)&((funcextLem)&((funcGraphProp4)&((((in @ (esk10_4 @ X440 @ X441 @ X442 @ X443) @ X440)|(subset @ X442 @ X443)|~(subset @ X443 @ (cartprod @ X440 @ X441))|~(subset @ X442 @ (cartprod @ X440 @ X441)))&(((in @ (esk11_4 @ X440 @ X441 @ X442 @ X443) @ X441)|(subset @ X442 @ X443)|~(subset @ X443 @ (cartprod @ X440 @ X441))|~(subset @ X442 @ (cartprod @ X440 @ X441)))&(((in @ (kpair @ (esk10_4 @ X440 @ X441 @ X442 @ X443) @ (esk11_4 @ X440 @ X441 @ X442 @ X443)) @ X442)|(subset @ X442 @ X443)|~(subset @ X443 @ (cartprod @ X440 @ X441))|~(subset @ X442 @ (cartprod @ X440 @ X441)))&(~(in @ (kpair @ (esk10_4 @ X440 @ X441 @ X442 @ X443) @ (esk11_4 @ X440 @ X441 @ X442 @ X443)) @ X443)|(subset @ X442 @ X443)|~(subset @ X443 @ (cartprod @ X440 @ X441))|~(subset @ X442 @ (cartprod @ X440 @ X441))))))&(((((in @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ X446)|((X448)=(X449))|(in @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ X446)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(((in @ (esk15_4 @ X446 @ X447 @ X448 @ X449) @ X447)|((X448)=(X449))|(in @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ X446)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(((in @ (kpair @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ (esk15_4 @ X446 @ X447 @ X448 @ X449)) @ X449)|((X448)=(X449))|(in @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ X446)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(~(in @ (kpair @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ (esk15_4 @ X446 @ X447 @ X448 @ X449)) @ X448)|((X448)=(X449))|(in @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ X446)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447))))))&((((in @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ X446)|((X448)=(X449))|(in @ (esk13_4 @ X446 @ X447 @ X448 @ X449) @ X447)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(((in @ (esk15_4 @ X446 @ X447 @ X448 @ X449) @ X447)|((X448)=(X449))|(in @ (esk13_4 @ X446 @ X447 @ X448 @ X449) @ X447)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(((in @ (kpair @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ (esk15_4 @ X446 @ X447 @ X448 @ X449)) @ X449)|((X448)=(X449))|(in @ (esk13_4 @ X446 @ X447 @ X448 @ X449) @ X447)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(~(in @ (kpair @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ (esk15_4 @ X446 @ X447 @ X448 @ X449)) @ X448)|((X448)=(X449))|(in @ (esk13_4 @ X446 @ X447 @ X448 @ X449) @ X447)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447))))))&((((in @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ X446)|((X448)=(X449))|(in @ (kpair @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ (esk13_4 @ X446 @ X447 @ X448 @ X449)) @ X448)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(((in @ (esk15_4 @ X446 @ X447 @ X448 @ X449) @ X447)|((X448)=(X449))|(in @ (kpair @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ (esk13_4 @ X446 @ X447 @ X448 @ X449)) @ X448)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(((in @ (kpair @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ (esk15_4 @ X446 @ X447 @ X448 @ X449)) @ X449)|((X448)=(X449))|(in @ (kpair @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ (esk13_4 @ X446 @ X447 @ X448 @ X449)) @ X448)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(~(in @ (kpair @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ (esk15_4 @ X446 @ X447 @ X448 @ X449)) @ X448)|((X448)=(X449))|(in @ (kpair @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ (esk13_4 @ X446 @ X447 @ X448 @ X449)) @ X448)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447))))))&(((in @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ X446)|((X448)=(X449))|~(in @ (kpair @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ (esk13_4 @ X446 @ X447 @ X448 @ X449)) @ X449)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(((in @ (esk15_4 @ X446 @ X447 @ X448 @ X449) @ X447)|((X448)=(X449))|~(in @ (kpair @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ (esk13_4 @ X446 @ X447 @ X448 @ X449)) @ X449)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(((in @ (kpair @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ (esk15_4 @ X446 @ X447 @ X448 @ X449)) @ X449)|((X448)=(X449))|~(in @ (kpair @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ (esk13_4 @ X446 @ X447 @ X448 @ X449)) @ X449)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))&(~(in @ (kpair @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ (esk15_4 @ X446 @ X447 @ X448 @ X449)) @ X448)|((X448)=(X449))|~(in @ (kpair @ (esk12_4 @ X446 @ X447 @ X448 @ X449) @ (esk13_4 @ X446 @ X447 @ X448 @ X449)) @ X449)|~(subset @ X449 @ (cartprod @ X446 @ X447))|~(subset @ X448 @ (cartprod @ X446 @ X447)))))))))&((funcext)&((funcext2)&((ap2apEq1)&((ap2apEq2)&((beta1)&((eta1)&((lam2lamEq)&((beta2)&((eta2)&((iffalseProp1)&((iffalseProp2)&((iftrueProp1)&((iftrueProp2)&((~(in @ X456 @ X454)|(~(in @ X457 @ X454)|(singleton @ (dsetconstr @ X454 @ (^[Z0:$i]:((((((X455))&(((Z0)=(X456)))))|(((~((X455)))&(((Z0)=(X457))))))))))))&((ifp)&((~(singleton @ X458)|(~(in @ X459 @ X458)|((setunion @ X458)=(X459))))&((iftrue)&((iffalse)&((iftrueorfalse)&((binintersectT_lem)&((binunionT_lem)&((powersetT_lem)&((setminusT_lem)&((complementT_lem)&((setextT)&((subsetTI)&((powersetTI1)&((powersetTE1)&((complementTI1)&((complementTE1)&((binintersectTELcontra)&((binintersectTERcontra)&((contrasubsetT)&((contrasubsetT1)&((contrasubsetT2)&((contrasubsetT3)&((doubleComplementI1)&((doubleComplementE1)&((doubleComplementSub1)&((doubleComplementSub2)&((doubleComplementEq)&((complementTnotintersectT)&((complementImpComplementIntersect)&((complementSubsetComplementIntersect)&((complementInPowersetComplementIntersect)&((contraSubsetComplement)&((complementTcontraSubset)&((binunionTILcontra)&((binunionTIRcontra)&((inIntersectImpInUnion)&((inIntersectImpInUnion2)&((inIntersectImpInIntersectUnions)&((intersectInPowersetIntersectUnions)&((inComplementUnionImpNotIn1)&((inComplementUnionImpInComplement1)&((binunionTE)&((binunionTEcontra)&((demorgan2a1)&((complementUnionInPowersetComplement)&((demorgan2a2)&((demorgan1a)&((demorgan1b)&((demorgan1)&((demorgan2a)&((demorgan2b2)&((demorgan2b)&((demorgan2)&((woz13rule0)&((woz13rule1)&((woz13rule2)&((woz13rule3)&((woz13rule4)&((woz1_1)&((woz1_2)&((woz1_3)&((woz1_4)&((woz1_5)&((breln1all2)&((breln1SetBreln1)&((((in @ (esk16_3 @ X460 @ X461 @ X462) @ X460)|(~(in @ X465 @ (breln1Set @ X461))|(~(reflwellordering @ X461 @ X465)|(~(in @ X466 @ X460)|(singleton @ (dsetconstr @ X461 @ (^[Z0:$i]:(((X462 @ X466 @ Z0)&(![X327:$i]:((((in @ X327 @ X461))=>(((X462 @ X466 @ X327)=>((in @ (kpair @ Z0 @ X327) @ X465))))))))))))))))&(~(in @ X464 @ X461)|~(X462 @ (esk16_3 @ X460 @ X461 @ X462) @ X464)|(~(in @ X465 @ (breln1Set @ X461))|(~(reflwellordering @ X461 @ X465)|(~(in @ X466 @ X460)|(singleton @ (dsetconstr @ X461 @ (^[Z0:$i]:(((X462 @ X466 @ Z0)&(![X327:$i]:((((in @ X327 @ X461))=>(((X462 @ X466 @ X327)=>((in @ (kpair @ Z0 @ X327) @ X465)))))))))))))))))&((subset @ (dpsetconstr @ X467 @ X467 @ X468) @ (cartprod @ X467 @ X467))&((breln1all1)&((subbreln1)&((eqbreln1)&((breln1invprop)&((breln1invI)&((breln1invE)&((subset @ esk18_0 @ (cartprod @ esk17_0 @ esk17_0))&((subset @ esk19_0 @ (cartprod @ esk17_0 @ esk17_0))&~(subset @ (breln1compset @ esk17_0 @ esk18_0 @ esk19_0) @ (cartprod @ esk17_0 @ esk17_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])])])])).
% 0.44/0.39 thf(c_0_68, plain, ![X472:$i, X473:$i, X474:$i]:(((breln1compset @ X472 @ X473 @ X474)=(dpsetconstr @ X472 @ X472 @ (^[Z0:$i, Z1:$i]:(?[X14:$i]:((((((in @ X14 @ X472))&((in @ (kpair @ Z0 @ X14) @ X473))))&((in @ (kpair @ X14 @ Z1) @ X474))))))))), inference(variable_rename,[status(thm)],[c_0_66])).
% 0.44/0.39 thf(c_0_69, plain, ![X487:$i, X486:$i, X2:$i, X3:$i, X4:$i]:(((epred7_3 @ X4 @ X3 @ X2 @ X486 @ X487)<=>?[X485:$i]:((((in @ X485 @ X2)&(in @ (kpair @ X486 @ X485) @ X3))&(in @ (kpair @ X485 @ X487) @ X4))))), introduced(definition)).
% 0.44/0.39 thf(c_0_70, negated_conjecture, ![X2:$i, X6:$i > $i > $o, X3:$i]:((subset @ (dpsetconstr @ X2 @ X3 @ X6) @ (cartprod @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_67])).
% 0.44/0.39 thf(c_0_71, plain, ![X4:$i, X3:$i, X2:$i]:(((breln1compset @ X2 @ X3 @ X4)=(dpsetconstr @ X2 @ X2 @ (epred7_3 @ X4 @ X3 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_68]), c_0_69])).
% 0.44/0.39 thf(c_0_72, negated_conjecture, ~((subset @ (breln1compset @ esk17_0 @ esk18_0 @ esk19_0) @ (cartprod @ esk17_0 @ esk17_0))), inference(split_conjunct,[status(thm)],[c_0_67])).
% 0.44/0.39 thf(c_0_73, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:((subset @ (breln1compset @ X2 @ X3 @ X4) @ (cartprod @ X2 @ X2))), inference(spm,[status(thm)],[c_0_70, c_0_71])).
% 0.44/0.39 thf(c_0_74, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72, c_0_73])]), ['proof']).
% 0.44/0.39 % SZS output end CNFRefutation
% 0.44/0.39 % Parsed axioms : 642
% 0.44/0.39 % Removed by relevancy pruning/SinE : 602
% 0.44/0.39 % Initial clauses : 352
% 0.44/0.39 % Removed in clause preprocessing : 1
% 0.44/0.39 % Initial clauses in saturation : 351
% 0.44/0.39 % Processed clauses : 314
% 0.44/0.39 % ...of these trivial : 4
% 0.44/0.39 % ...subsumed : 3
% 0.44/0.39 % ...remaining for further processing : 307
% 0.44/0.39 % Other redundant clauses eliminated : 3
% 0.44/0.39 % Clauses deleted for lack of memory : 0
% 0.44/0.39 % Backward-subsumed : 0
% 0.44/0.39 % Backward-rewritten : 1
% 0.44/0.39 % Generated clauses : 55
% 0.44/0.39 % ...of the previous two non-redundant : 42
% 0.44/0.39 % ...aggressively subsumed : 0
% 0.44/0.39 % Contextual simplify-reflections : 0
% 0.44/0.39 % Paramodulations : 49
% 0.44/0.39 % Factorizations : 0
% 0.44/0.39 % NegExts : 0
% 0.44/0.39 % Equation resolutions : 3
% 0.44/0.39 % Disequality decompositions : 0
% 0.44/0.39 % Total rewrite steps : 19
% 0.44/0.39 % ...of those cached : 8
% 0.44/0.39 % Propositional unsat checks : 0
% 0.44/0.39 % Propositional check models : 0
% 0.44/0.39 % Propositional check unsatisfiable : 0
% 0.44/0.39 % Propositional clauses : 0
% 0.44/0.39 % Propositional clauses after purity: 0
% 0.44/0.39 % Propositional unsat core size : 0
% 0.44/0.39 % Propositional preprocessing time : 0.000
% 0.44/0.39 % Propositional encoding time : 0.000
% 0.44/0.39 % Propositional solver time : 0.000
% 0.44/0.39 % Success case prop preproc time : 0.000
% 0.44/0.39 % Success case prop encoding time : 0.000
% 0.44/0.39 % Success case prop solver time : 0.000
% 0.44/0.39 % Current number of processed clauses : 303
% 0.44/0.39 % Positive orientable unit clauses : 272
% 0.44/0.39 % Positive unorientable unit clauses: 0
% 0.44/0.39 % Negative unit clauses : 0
% 0.44/0.39 % Non-unit-clauses : 31
% 0.44/0.39 % Current number of unprocessed clauses: 79
% 0.44/0.39 % ...number of literals in the above : 267
% 0.44/0.39 % Current number of archived formulas : 0
% 0.44/0.39 % Current number of archived clauses : 2
% 0.44/0.39 % Clause-clause subsumption calls (NU) : 121
% 0.44/0.39 % Rec. Clause-clause subsumption calls : 112
% 0.44/0.39 % Non-unit clause-clause subsumptions : 3
% 0.44/0.39 % Unit Clause-clause subsumption calls : 1
% 0.44/0.39 % Rewrite failures with RHS unbound : 0
% 0.44/0.39 % BW rewrite match attempts : 6
% 0.44/0.39 % BW rewrite match successes : 1
% 0.44/0.39 % Condensation attempts : 0
% 0.44/0.39 % Condensation successes : 0
% 0.44/0.39 % Termbank termtop insertions : 28729
% 0.44/0.39 % Search garbage collected termcells : 10865
% 0.44/0.39
% 0.44/0.39 % -------------------------------------------------
% 0.44/0.39 % User time : 0.039 s
% 0.44/0.39 % System time : 0.011 s
% 0.44/0.39 % Total time : 0.050 s
% 0.44/0.39 % Maximum resident set size: 6608 pages
% 0.44/0.39
% 0.44/0.39 % -------------------------------------------------
% 0.44/0.39 % User time : 0.056 s
% 0.44/0.39 % System time : 0.018 s
% 0.44/0.39 % Total time : 0.074 s
% 0.44/0.39 % Maximum resident set size: 5376 pages
% 0.44/0.39 % E exiting
%------------------------------------------------------------------------------