%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU775^1 : 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 : n012.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 08:27:45 AM UTC 2026
% Result : Theorem 0.09s 0.21s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU775^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:27:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.14 Running higher-order theorem proving
% 0.09/0.17 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.3Fra8IWslQ/E---3.1_178880.p
% 0.09/0.21 % Version: 3.5.1-ho
% 0.09/0.21 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.09/0.21 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.21 % Starting ehoh_best5 with 300s (1) cores
% 0.09/0.21 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.21 % Starting new_bool_5 with 300s (1) cores
% 0.09/0.21 % Starting pre_casc_3 with 300s (1) cores
% 0.09/0.21 % Starting ho_unfolding_8 with 300s (1) cores
% 0.09/0.21 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.09/0.21 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.21 % Starting new_ho_5 with 300s (1) cores
% 0.09/0.21 % new_ho_5 with pid 178913 completed with status 0
% 0.09/0.21 % Result found by new_ho_5
% 0.09/0.21 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.09/0.21 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.21 % Starting ehoh_best5 with 300s (1) cores
% 0.09/0.21 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.21 % Starting new_bool_5 with 300s (1) cores
% 0.09/0.21 % Starting pre_casc_3 with 300s (1) cores
% 0.09/0.21 % Starting ho_unfolding_8 with 300s (1) cores
% 0.09/0.21 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.09/0.21 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.21 % Starting new_ho_5 with 300s (1) cores
% 0.09/0.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
% 0.09/0.21 % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.09/0.21 % Search class: HGUSS-FSMM33-SHFMMFBN
% 0.09/0.21 % partial match(5): HGHSM-FSLM31-SHFMMSBN
% 0.09/0.21 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.21 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.21 % SubtermCWHack with pid 178918 completed with status 0
% 0.09/0.21 % Result found by SubtermCWHack
% 0.09/0.21 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.09/0.21 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.21 % Starting ehoh_best5 with 300s (1) cores
% 0.09/0.21 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.21 % Starting new_bool_5 with 300s (1) cores
% 0.09/0.21 % Starting pre_casc_3 with 300s (1) cores
% 0.09/0.21 % Starting ho_unfolding_8 with 300s (1) cores
% 0.09/0.21 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.09/0.21 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.21 % Starting new_ho_5 with 300s (1) cores
% 0.09/0.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
% 0.09/0.21 % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.09/0.21 % Search class: HGUSS-FSMM33-SHFMMFBN
% 0.09/0.21 % partial match(5): HGHSM-FSLM31-SHFMMSBN
% 0.09/0.21 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.21 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.21 % Preprocessing time : 0.002 s
% 0.09/0.21
% 0.09/0.21 % Proof found!
% 0.09/0.21 % SZS status Theorem
% 0.09/0.21 % SZS output start CNFRefutation
% 0.09/0.21 thf(decl_23, type, in: $i > $i > $o).
% 0.09/0.21 thf(decl_25, type, setextAx: $o).
% 0.09/0.21 thf(decl_27, type, emptysetAx: $o).
% 0.09/0.21 thf(decl_29, type, setadjoinAx: $o).
% 0.09/0.21 thf(decl_31, type, powersetAx: $o).
% 0.09/0.21 thf(decl_33, type, setunionAx: $o).
% 0.09/0.21 thf(decl_35, type, omega0Ax: $o).
% 0.09/0.21 thf(decl_36, type, omegaSAx: $o).
% 0.09/0.21 thf(decl_37, type, omegaIndAx: $o).
% 0.09/0.21 thf(decl_38, type, replAx: $o).
% 0.09/0.21 thf(decl_39, type, foundationAx: $o).
% 0.09/0.21 thf(decl_40, type, wellorderingAx: $o).
% 0.09/0.21 thf(decl_42, type, descrp: $o).
% 0.09/0.21 thf(decl_44, type, dsetconstrI: $o).
% 0.09/0.21 thf(decl_45, type, dsetconstrEL: $o).
% 0.09/0.21 thf(decl_46, type, dsetconstrER: $o).
% 0.09/0.21 thf(decl_47, type, exuE1: $o).
% 0.09/0.21 thf(decl_49, type, prop2setE: $o).
% 0.09/0.21 thf(decl_50, type, emptysetE: $o).
% 0.09/0.21 thf(decl_51, type, emptysetimpfalse: $o).
% 0.09/0.21 thf(decl_52, type, notinemptyset: $o).
% 0.09/0.21 thf(decl_53, type, exuE3e: $o).
% 0.09/0.21 thf(decl_54, type, setext: $o).
% 0.09/0.21 thf(decl_55, type, emptyI: $o).
% 0.09/0.21 thf(decl_56, type, noeltsimpempty: $o).
% 0.09/0.21 thf(decl_57, type, setbeta: $o).
% 0.09/0.21 thf(decl_59, type, nonemptyE1: $o).
% 0.09/0.21 thf(decl_60, type, nonemptyI: $o).
% 0.09/0.21 thf(decl_61, type, nonemptyI1: $o).
% 0.09/0.21 thf(decl_62, type, setadjoinIL: $o).
% 0.09/0.21 thf(decl_63, type, emptyinunitempty: $o).
% 0.09/0.21 thf(decl_64, type, setadjoinIR: $o).
% 0.09/0.21 thf(decl_65, type, setadjoinE: $o).
% 0.09/0.21 thf(decl_66, type, setadjoinOr: $o).
% 0.09/0.21 thf(decl_67, type, setoftrueEq: $o).
% 0.09/0.21 thf(decl_68, type, powersetI: $o).
% 0.09/0.21 thf(decl_69, type, emptyinPowerset: $o).
% 0.09/0.21 thf(decl_70, type, emptyInPowerset: $o).
% 0.09/0.21 thf(decl_71, type, powersetE: $o).
% 0.09/0.21 thf(decl_72, type, setunionI: $o).
% 0.09/0.21 thf(decl_73, type, setunionE: $o).
% 0.09/0.21 thf(decl_74, type, subPowSU: $o).
% 0.09/0.21 thf(decl_75, type, exuE2: $o).
% 0.09/0.21 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.09/0.21 thf(decl_77, type, uniqinunit: $o).
% 0.09/0.21 thf(decl_78, type, notinsingleton: $o).
% 0.09/0.21 thf(decl_79, type, eqinunit: $o).
% 0.09/0.21 thf(decl_80, type, singletonsswitch: $o).
% 0.09/0.21 thf(decl_81, type, upairsetE: $o).
% 0.09/0.21 thf(decl_82, type, upairsetIL: $o).
% 0.09/0.21 thf(decl_83, type, upairsetIR: $o).
% 0.09/0.21 thf(decl_84, type, emptyE1: $o).
% 0.09/0.21 thf(decl_85, type, vacuousDall: $o).
% 0.09/0.21 thf(decl_86, type, quantDeMorgan1: $o).
% 0.09/0.21 thf(decl_87, type, quantDeMorgan2: $o).
% 0.09/0.21 thf(decl_88, type, quantDeMorgan3: $o).
% 0.09/0.21 thf(decl_89, type, quantDeMorgan4: $o).
% 0.09/0.21 thf(decl_90, type, prop2setI: $o).
% 0.09/0.21 thf(decl_92, type, prop2set2propI: $o).
% 0.09/0.21 thf(decl_93, type, notdexE: $o).
% 0.09/0.21 thf(decl_94, type, notdallE: $o).
% 0.09/0.21 thf(decl_95, type, exuI1: $o).
% 0.09/0.21 thf(decl_96, type, exuI3: $o).
% 0.09/0.21 thf(decl_97, type, exuI2: $o).
% 0.09/0.21 thf(decl_98, type, inCongP: $o).
% 0.09/0.21 thf(decl_99, type, in__Cong: $o).
% 0.09/0.21 thf(decl_100, type, exuE3u: $o).
% 0.09/0.21 thf(decl_101, type, exu__Cong: $o).
% 0.09/0.21 thf(decl_102, type, emptyset__Cong: $o).
% 0.09/0.21 thf(decl_103, type, setadjoin__Cong: $o).
% 0.09/0.21 thf(decl_104, type, powerset__Cong: $o).
% 0.09/0.21 thf(decl_105, type, setunion__Cong: $o).
% 0.09/0.21 thf(decl_106, type, omega__Cong: $o).
% 0.09/0.21 thf(decl_107, type, exuEu: $o).
% 0.09/0.21 thf(decl_108, type, descr__Cong: $o).
% 0.09/0.21 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.09/0.21 thf(decl_110, type, subset: $i > $i > $o).
% 0.09/0.21 thf(decl_113, type, subsetI1: $o).
% 0.09/0.21 thf(decl_114, type, eqimpsubset2: $o).
% 0.09/0.21 thf(decl_115, type, eqimpsubset1: $o).
% 0.09/0.21 thf(decl_116, type, subsetI2: $o).
% 0.09/0.21 thf(decl_117, type, emptysetsubset: $o).
% 0.09/0.21 thf(decl_118, type, subsetE: $o).
% 0.09/0.21 thf(decl_119, type, subsetE2: $o).
% 0.09/0.21 thf(decl_120, type, notsubsetI: $o).
% 0.09/0.21 thf(decl_121, type, notequalI1: $o).
% 0.09/0.21 thf(decl_122, type, notequalI2: $o).
% 0.09/0.21 thf(decl_123, type, subsetRefl: $o).
% 0.09/0.21 thf(decl_124, type, subsetTrans: $o).
% 0.09/0.21 thf(decl_125, type, setadjoinSub: $o).
% 0.09/0.21 thf(decl_126, type, setadjoinSub2: $o).
% 0.09/0.21 thf(decl_127, type, subset2powerset: $o).
% 0.09/0.21 thf(decl_128, type, setextsub: $o).
% 0.09/0.21 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.09/0.21 thf(decl_130, type, powersetI1: $o).
% 0.09/0.21 thf(decl_131, type, powersetE1: $o).
% 0.09/0.21 thf(decl_132, type, inPowerset: $o).
% 0.09/0.21 thf(decl_133, type, powersetsubset: $o).
% 0.09/0.21 thf(decl_134, type, sepInPowerset: $o).
% 0.09/0.21 thf(decl_135, type, sepSubset: $o).
% 0.09/0.21 thf(decl_137, type, binunionIL: $o).
% 0.09/0.21 thf(decl_138, type, upairset2IR: $o).
% 0.09/0.21 thf(decl_139, type, binunionIR: $o).
% 0.09/0.21 thf(decl_140, type, binunionEcases: $o).
% 0.09/0.21 thf(decl_141, type, binunionE: $o).
% 0.09/0.21 thf(decl_142, type, binunionLsub: $o).
% 0.09/0.21 thf(decl_143, type, binunionRsub: $o).
% 0.09/0.21 thf(decl_145, type, binintersectI: $o).
% 0.09/0.21 thf(decl_146, type, binintersectSubset5: $o).
% 0.09/0.21 thf(decl_147, type, binintersectEL: $o).
% 0.09/0.21 thf(decl_148, type, binintersectLsub: $o).
% 0.09/0.21 thf(decl_149, type, binintersectSubset2: $o).
% 0.09/0.21 thf(decl_150, type, binintersectSubset3: $o).
% 0.09/0.21 thf(decl_151, type, binintersectER: $o).
% 0.09/0.21 thf(decl_152, type, disjointsetsI1: $o).
% 0.09/0.21 thf(decl_153, type, binintersectRsub: $o).
% 0.09/0.21 thf(decl_154, type, binintersectSubset4: $o).
% 0.09/0.21 thf(decl_155, type, binintersectSubset1: $o).
% 0.09/0.21 thf(decl_156, type, bs114d: $o).
% 0.09/0.21 thf(decl_159, type, setminusI: $o).
% 0.09/0.21 thf(decl_160, type, setminusEL: $o).
% 0.09/0.21 thf(decl_161, type, setminusER: $o).
% 0.09/0.21 thf(decl_162, type, setminusSubset2: $o).
% 0.09/0.21 thf(decl_163, type, setminusERneg: $o).
% 0.09/0.21 thf(decl_164, type, setminusELneg: $o).
% 0.09/0.21 thf(decl_165, type, setminusILneg: $o).
% 0.09/0.21 thf(decl_166, type, setminusIRneg: $o).
% 0.09/0.21 thf(decl_167, type, setminusLsub: $o).
% 0.09/0.21 thf(decl_168, type, setminusSubset1: $o).
% 0.09/0.21 thf(decl_170, type, symdiffE: $o).
% 0.09/0.21 thf(decl_171, type, symdiffI1: $o).
% 0.09/0.21 thf(decl_172, type, symdiffI2: $o).
% 0.09/0.21 thf(decl_173, type, symdiffIneg1: $o).
% 0.09/0.21 thf(decl_174, type, symdiffIneg2: $o).
% 0.09/0.21 thf(decl_176, type, secondinupair: $o).
% 0.09/0.21 thf(decl_177, type, setukpairIL: $o).
% 0.09/0.21 thf(decl_178, type, setukpairIR: $o).
% 0.09/0.21 thf(decl_179, type, kpairiskpair: $o).
% 0.09/0.21 thf(decl_180, type, kpair: $i > $i > $i).
% 0.09/0.21 thf(decl_181, type, kpairp: $o).
% 0.09/0.21 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.09/0.21 thf(decl_183, type, singletonsubset: $o).
% 0.09/0.21 thf(decl_184, type, singletoninpowerset: $o).
% 0.09/0.21 thf(decl_185, type, singletoninpowunion: $o).
% 0.09/0.21 thf(decl_186, type, upairset2E: $o).
% 0.09/0.21 thf(decl_187, type, upairsubunion: $o).
% 0.09/0.21 thf(decl_188, type, upairinpowunion: $o).
% 0.09/0.21 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.09/0.21 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.09/0.21 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.09/0.21 thf(decl_192, type, cartprodpairin: $o).
% 0.09/0.21 thf(decl_193, type, cartprodmempair1: $o).
% 0.09/0.21 thf(decl_194, type, cartprodmempair: $o).
% 0.09/0.21 thf(decl_195, type, setunionE2: $o).
% 0.09/0.21 thf(decl_196, type, setunionsingleton1: $o).
% 0.09/0.21 thf(decl_197, type, setunionsingleton2: $o).
% 0.09/0.21 thf(decl_198, type, setunionsingleton: $o).
% 0.09/0.21 thf(decl_200, type, singletonprop: $o).
% 0.09/0.21 thf(decl_202, type, ex1E1: $o).
% 0.09/0.21 thf(decl_203, type, ex1I: $o).
% 0.09/0.21 thf(decl_204, type, ex1I2: $o).
% 0.09/0.21 thf(decl_205, type, singletonsuniq: $o).
% 0.09/0.21 thf(decl_210, type, setukpairinjL1: $o).
% 0.09/0.21 thf(decl_211, type, kfstsingleton: $o).
% 0.09/0.21 thf(decl_212, type, theprop: $o).
% 0.09/0.21 thf(decl_214, type, kfstpairEq: $o).
% 0.09/0.21 thf(decl_215, type, cartprodfstin: $o).
% 0.09/0.21 thf(decl_216, type, setukpairinjL2: $o).
% 0.09/0.21 thf(decl_217, type, setukpairinjL: $o).
% 0.09/0.21 thf(decl_218, type, setukpairinjR11: $o).
% 0.09/0.21 thf(decl_219, type, setukpairinjR12: $o).
% 0.09/0.21 thf(decl_220, type, setukpairinjR1: $o).
% 0.09/0.21 thf(decl_221, type, upairequniteq: $o).
% 0.09/0.21 thf(decl_222, type, setukpairinjR2: $o).
% 0.09/0.21 thf(decl_223, type, setukpairinjR: $o).
% 0.09/0.21 thf(decl_224, type, ksndsingleton: $o).
% 0.09/0.21 thf(decl_226, type, ksndpairEq: $o).
% 0.09/0.21 thf(decl_227, type, kpairsurjEq: $o).
% 0.09/0.21 thf(decl_228, type, cartprodsndin: $o).
% 0.09/0.21 thf(decl_229, type, cartprodpairmemEL: $o).
% 0.09/0.21 thf(decl_230, type, cartprodpairmemER: $o).
% 0.09/0.21 thf(decl_231, type, cartprodmempaircEq: $o).
% 0.09/0.21 thf(decl_232, type, cartprodfstpairEq: $o).
% 0.09/0.21 thf(decl_233, type, cartprodsndpairEq: $o).
% 0.09/0.21 thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.09/0.21 thf(decl_235, type, breln: $i > $i > $i > $o).
% 0.09/0.21 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.09/0.21 thf(decl_237, type, dpsetconstrI: $o).
% 0.09/0.21 thf(decl_238, type, dpsetconstrSub: $o).
% 0.09/0.21 thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.09/0.21 thf(decl_240, type, dpsetconstrERa: $o).
% 0.09/0.21 thf(decl_241, type, dpsetconstrEL1: $o).
% 0.09/0.21 thf(decl_242, type, dpsetconstrEL2: $o).
% 0.09/0.21 thf(decl_243, type, dpsetconstrER: $o).
% 0.09/0.21 thf(decl_246, type, funcImageSingleton: $o).
% 0.09/0.21 thf(decl_247, type, apProp: $o).
% 0.09/0.21 thf(decl_249, type, app: $o).
% 0.09/0.21 thf(decl_250, type, infuncsetfunc: $o).
% 0.09/0.21 thf(decl_251, type, ap2p: $o).
% 0.09/0.21 thf(decl_252, type, funcinfuncset: $o).
% 0.09/0.21 thf(decl_253, type, lamProp: $o).
% 0.09/0.21 thf(decl_255, type, lamp: $o).
% 0.09/0.21 thf(decl_256, type, lam2p: $o).
% 0.09/0.21 thf(decl_257, type, brelnall1: $o).
% 0.09/0.21 thf(decl_258, type, brelnall2: $o).
% 0.09/0.21 thf(decl_259, type, ex1E2: $o).
% 0.09/0.21 thf(decl_260, type, funcGraphProp1: $o).
% 0.09/0.21 thf(decl_261, type, funcGraphProp3: $o).
% 0.09/0.21 thf(decl_262, type, funcGraphProp2: $o).
% 0.09/0.21 thf(decl_263, type, funcextLem: $o).
% 0.09/0.21 thf(decl_264, type, funcGraphProp4: $o).
% 0.09/0.21 thf(decl_265, type, subbreln: $o).
% 0.09/0.21 thf(decl_266, type, eqbreln: $o).
% 0.09/0.21 thf(decl_267, type, funcext: $o).
% 0.09/0.21 thf(decl_268, type, funcext2: $o).
% 0.09/0.21 thf(decl_269, type, ap2apEq1: $o).
% 0.09/0.21 thf(decl_270, type, ap2apEq2: $o).
% 0.09/0.21 thf(decl_271, type, beta1: $o).
% 0.09/0.21 thf(decl_272, type, eta1: $o).
% 0.09/0.21 thf(decl_273, type, lam2lamEq: $o).
% 0.09/0.21 thf(decl_274, type, beta2: $o).
% 0.09/0.21 thf(decl_275, type, eta2: $o).
% 0.09/0.21 thf(decl_276, type, iffalseProp1: $o).
% 0.09/0.21 thf(decl_277, type, iffalseProp2: $o).
% 0.09/0.21 thf(decl_278, type, iftrueProp1: $o).
% 0.09/0.21 thf(decl_279, type, iftrueProp2: $o).
% 0.09/0.21 thf(decl_280, type, ifSingleton: $o).
% 0.09/0.21 thf(decl_282, type, ifp: $o).
% 0.09/0.21 thf(decl_283, type, theeq: $o).
% 0.09/0.21 thf(decl_284, type, iftrue: $o).
% 0.09/0.21 thf(decl_285, type, iffalse: $o).
% 0.09/0.21 thf(decl_286, type, iftrueorfalse: $o).
% 0.09/0.21 thf(decl_287, type, binintersectT_lem: $o).
% 0.09/0.21 thf(decl_288, type, binunionT_lem: $o).
% 0.09/0.21 thf(decl_289, type, powersetT_lem: $o).
% 0.09/0.21 thf(decl_290, type, setminusT_lem: $o).
% 0.09/0.21 thf(decl_291, type, complementT_lem: $o).
% 0.09/0.21 thf(decl_292, type, setextT: $o).
% 0.09/0.21 thf(decl_293, type, subsetTI: $o).
% 0.09/0.21 thf(decl_294, type, powersetTI1: $o).
% 0.09/0.21 thf(decl_295, type, powersetTE1: $o).
% 0.09/0.21 thf(decl_296, type, complementTI1: $o).
% 0.09/0.21 thf(decl_297, type, complementTE1: $o).
% 0.09/0.21 thf(decl_298, type, binintersectTELcontra: $o).
% 0.09/0.21 thf(decl_299, type, binintersectTERcontra: $o).
% 0.09/0.21 thf(decl_300, type, contrasubsetT: $o).
% 0.09/0.21 thf(decl_301, type, contrasubsetT1: $o).
% 0.09/0.21 thf(decl_302, type, contrasubsetT2: $o).
% 0.09/0.21 thf(decl_303, type, contrasubsetT3: $o).
% 0.09/0.21 thf(decl_304, type, doubleComplementI1: $o).
% 0.09/0.21 thf(decl_305, type, doubleComplementE1: $o).
% 0.09/0.21 thf(decl_306, type, doubleComplementSub1: $o).
% 0.09/0.21 thf(decl_307, type, doubleComplementSub2: $o).
% 0.09/0.21 thf(decl_308, type, doubleComplementEq: $o).
% 0.09/0.21 thf(decl_309, type, complementTnotintersectT: $o).
% 0.09/0.21 thf(decl_310, type, complementImpComplementIntersect: $o).
% 0.09/0.21 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 0.09/0.21 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 0.09/0.21 thf(decl_313, type, contraSubsetComplement: $o).
% 0.09/0.21 thf(decl_314, type, complementTcontraSubset: $o).
% 0.09/0.21 thf(decl_315, type, binunionTILcontra: $o).
% 0.09/0.21 thf(decl_316, type, binunionTIRcontra: $o).
% 0.09/0.21 thf(decl_317, type, inIntersectImpInUnion: $o).
% 0.09/0.21 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 0.09/0.21 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 0.09/0.21 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 0.09/0.21 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 0.09/0.21 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 0.09/0.21 thf(decl_323, type, binunionTE: $o).
% 0.09/0.21 thf(decl_324, type, binunionTEcontra: $o).
% 0.09/0.21 thf(decl_325, type, demorgan2a1: $o).
% 0.09/0.21 thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 0.09/0.21 thf(decl_327, type, demorgan2a2: $o).
% 0.09/0.21 thf(decl_328, type, demorgan1a: $o).
% 0.09/0.21 thf(decl_329, type, demorgan1b: $o).
% 0.09/0.21 thf(decl_330, type, demorgan1: $o).
% 0.09/0.21 thf(decl_331, type, demorgan2a: $o).
% 0.09/0.21 thf(decl_332, type, demorgan2b2: $o).
% 0.09/0.21 thf(decl_333, type, demorgan2b: $o).
% 0.09/0.21 thf(decl_334, type, demorgan2: $o).
% 0.09/0.21 thf(decl_335, type, woz13rule0: $o).
% 0.09/0.21 thf(decl_336, type, woz13rule1: $o).
% 0.09/0.21 thf(decl_337, type, woz13rule2: $o).
% 0.09/0.21 thf(decl_338, type, woz13rule3: $o).
% 0.09/0.21 thf(decl_339, type, woz13rule4: $o).
% 0.09/0.21 thf(decl_340, type, woz1_1: $o).
% 0.09/0.21 thf(decl_341, type, woz1_2: $o).
% 0.09/0.21 thf(decl_342, type, woz1_3: $o).
% 0.09/0.21 thf(decl_343, type, woz1_4: $o).
% 0.09/0.21 thf(decl_344, type, woz1_5: $o).
% 0.09/0.21 thf(decl_345, type, breln1: $i > $i > $o).
% 0.09/0.21 thf(decl_346, type, breln1all2: $o).
% 0.09/0.21 thf(decl_348, type, breln1SetBreln1: $o).
% 0.09/0.21 thf(decl_355, type, choice2fnsingleton: $o).
% 0.09/0.21 thf(decl_356, type, setOfPairsIsBReln1: $o).
% 0.09/0.21 thf(decl_357, type, breln1all1: $o).
% 0.09/0.21 thf(decl_358, type, subbreln1: $o).
% 0.09/0.21 thf(decl_359, type, eqbreln1: $o).
% 0.09/0.21 thf(decl_360, type, breln1invset: $i > $i > $i).
% 0.09/0.21 thf(decl_361, type, esk1_4: $i > $i > $i > ($i > $o) > $i).
% 0.09/0.21 thf(decl_362, type, esk2_4: $i > $i > $i > ($i > $o) > $i).
% 0.09/0.21 thf(decl_363, type, esk3_4: $i > $i > $i > ($i > $o) > $i).
% 0.09/0.21 thf(decl_364, type, esk4_4: $i > $i > $i > ($i > $o) > $i).
% 0.09/0.21 thf(decl_365, type, esk5_4: $i > $i > $i > $i > $i).
% 0.09/0.21 thf(decl_366, type, esk6_4: $i > $i > $i > $i > $i).
% 0.09/0.21 thf(decl_367, type, esk7_4: $i > $i > $i > $i > $i).
% 0.09/0.21 thf(decl_368, type, esk8_4: $i > $i > $i > $i > $i).
% 0.09/0.21 thf(decl_369, type, esk9_4: $i > $i > $i > $i > $i).
% 0.09/0.21 thf(decl_370, type, esk10_4: $i > $i > $i > $i > $i).
% 0.09/0.21 thf(decl_371, type, esk11_0: $i).
% 0.09/0.21 thf(decl_372, type, esk12_0: $i).
% 0.09/0.21 thf(decl_373, type, epred1_1: $i > $i > $i > $o).
% 0.09/0.21 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3Fra8IWslQ/E---3.1_178880.p', breln)).
% 0.09/0.21 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.3Fra8IWslQ/E---3.1_178880.p', setOfPairsIsBReln)).
% 0.09/0.21 thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.3Fra8IWslQ/E---3.1_178880.p', breln1)).
% 0.09/0.21 thf(breln1invprop, 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)=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3Fra8IWslQ/E---3.1_178880.p', breln1invprop)).
% 0.09/0.21 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.3Fra8IWslQ/E---3.1_178880.p', eqbreln)).
% 0.09/0.21 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.3Fra8IWslQ/E---3.1_178880.p', subbreln)).
% 0.09/0.21 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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.3Fra8IWslQ/E---3.1_178880.p', brelnall2)).
% 0.09/0.21 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.3Fra8IWslQ/E---3.1_178880.p', brelnall1)).
% 0.09/0.21 thf(breln1invset, axiom, ((breln1invset)=(^[X4:$i, X33:$i]:(dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((in @ (kpair @ X3 @ X2) @ X33)))))), file('/export/starexec/sandbox2/tmp/tmp.3Fra8IWslQ/E---3.1_178880.p', breln1invset)).
% 0.09/0.21 thf(c_0_9, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 0.09/0.21 thf(c_0_10, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 0.09/0.21 thf(c_0_11, plain, ((breln1)=(^[Z0:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
% 0.09/0.21 thf(c_0_12, 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)=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[breln1invprop])).
% 0.09/0.22 thf(c_0_13, axiom, ((eqbreln)=(![X4:$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:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_9])).
% 0.09/0.22 thf(c_0_14, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_9])).
% 0.09/0.22 thf(c_0_15, axiom, ((brelnall2)=(![X4:$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_9])).
% 0.09/0.22 thf(c_0_16, 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_9])).
% 0.09/0.22 thf(c_0_17, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_10, c_0_9])).
% 0.09/0.22 thf(c_0_18, plain, ((breln1)=(^[Z0:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_11, c_0_9])).
% 0.09/0.22 thf(c_0_19, 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)=>(![X87:$i, X88:$i, X89:$i > $i > $o]:((subset @ (dpsetconstr @ X87 @ X88 @ X89) @ (cartprod @ X87 @ X88)))=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>(![X90:$i, X91:$i, X92:$i]:(((subset @ X92 @ (cartprod @ X90 @ X91))=>![X93:$i > $o]:((![X94:$i]:(((in @ X94 @ X90)=>![X95:$i]:(((in @ X95 @ X91)=>((in @ (kpair @ X94 @ X95) @ X92)=>(X93 @ (kpair @ X94 @ X95)))))))=>![X96:$i]:(((in @ X96 @ X92)=>(X93 @ X96)))))))=>(![X97:$i, X98:$i, X99:$i]:(((subset @ X99 @ (cartprod @ X97 @ X98))=>![X100:$i > $o]:((![X101:$i]:(((in @ X101 @ X97)=>![X102:$i]:(((in @ X102 @ X98)=>((in @ (kpair @ X101 @ X102) @ X99)=>(X100 @ (kpair @ X101 @ X102)))))))=>![X103:$i]:(((in @ X103 @ X99)=>(X100 @ X103)))))))=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(![X104:$i, X105:$i, X106:$i]:(((subset @ X106 @ (cartprod @ X104 @ X105))=>![X107:$i]:(((subset @ X107 @ (cartprod @ X104 @ X105))=>(![X108:$i]:(((in @ X108 @ X104)=>![X109:$i]:(((in @ X109 @ X105)=>((in @ (kpair @ X108 @ X109) @ X106)=>(in @ (kpair @ X108 @ X109) @ X107))))))=>(subset @ X106 @ X107))))))=>(![X110:$i, X111:$i, X112:$i]:(((subset @ X112 @ (cartprod @ X110 @ X111))=>![X113:$i]:(((subset @ X113 @ (cartprod @ X110 @ X111))=>(![X114:$i]:(((in @ X114 @ X110)=>![X115:$i]:(((in @ X115 @ X111)=>((in @ (kpair @ X114 @ X115) @ X112)=>(in @ (kpair @ X114 @ X115) @ X113))))))=>(![X116:$i]:(((in @ X116 @ X110)=>![X117:$i]:(((in @ X117 @ X111)=>((in @ (kpair @ X116 @ X117) @ X113)=>(in @ (kpair @ X116 @ X117) @ X112))))))=>((X112)=(X113))))))))=>((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)=>![X4:$i, X33:$i]:(((subset @ X33 @ (cartprod @ X4 @ X4))=>(subset @ (breln1invset @ X4 @ X33) @ (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)],[c_0_12, c_0_13]), c_0_14]), c_0_15]), c_0_16]), c_0_17]), c_0_18])])).
% 0.09/0.22 thf(c_0_20, plain, ![X118:$i, X119:$i]:(((breln1invset @ X118 @ X119)=(dpsetconstr @ X118 @ X118 @ (^[Z0:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X119)))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[breln1invset])])).
% 0.09/0.22 thf(c_0_21, negated_conjecture, ![X120:$i, X121:$i, X122:$i > $i > $o, X123:$i, X124:$i, X125:$i, X126:$i > $o, X129:$i, X130:$i, X131:$i, X132:$i, X133:$i > $o, X136:$i, X137:$i, X138:$i, X139:$i, X140:$i, X143:$i, X144:$i, X145:$i, X146:$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)&((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)&((subset @ (dpsetconstr @ X120 @ X121 @ X122) @ (cartprod @ X120 @ X121))&((dpsetconstrERa)&((dpsetconstrEL1)&((dpsetconstrEL2)&((dpsetconstrER)&((funcImageSingleton)&((apProp)&((app)&((infuncsetfunc)&((ap2p)&((funcinfuncset)&((lamProp)&((lamp)&((lam2p)&((((in @ (esk1_4 @ X123 @ X124 @ X125 @ X126) @ X123)|(~(in @ X129 @ X125)|(X126 @ X129))|~(subset @ X125 @ (cartprod @ X123 @ X124)))&(((in @ (esk2_4 @ X123 @ X124 @ X125 @ X126) @ X124)|(~(in @ X129 @ X125)|(X126 @ X129))|~(subset @ X125 @ (cartprod @ X123 @ X124)))&(((in @ (kpair @ (esk1_4 @ X123 @ X124 @ X125 @ X126) @ (esk2_4 @ X123 @ X124 @ X125 @ X126)) @ X125)|(~(in @ X129 @ X125)|(X126 @ X129))|~(subset @ X125 @ (cartprod @ X123 @ X124)))&(~(X126 @ (kpair @ (esk1_4 @ X123 @ X124 @ X125 @ X126) @ (esk2_4 @ X123 @ X124 @ X125 @ X126)))|(~(in @ X129 @ X125)|(X126 @ X129))|~(subset @ X125 @ (cartprod @ X123 @ X124))))))&((((in @ (esk3_4 @ X130 @ X131 @ X132 @ X133) @ X130)|(~(in @ X136 @ X132)|(X133 @ X136))|~(subset @ X132 @ (cartprod @ X130 @ X131)))&(((in @ (esk4_4 @ X130 @ X131 @ X132 @ X133) @ X131)|(~(in @ X136 @ X132)|(X133 @ X136))|~(subset @ X132 @ (cartprod @ X130 @ X131)))&(((in @ (kpair @ (esk3_4 @ X130 @ X131 @ X132 @ X133) @ (esk4_4 @ X130 @ X131 @ X132 @ X133)) @ X132)|(~(in @ X136 @ X132)|(X133 @ X136))|~(subset @ X132 @ (cartprod @ X130 @ X131)))&(~(X133 @ (kpair @ (esk3_4 @ X130 @ X131 @ X132 @ X133) @ (esk4_4 @ X130 @ X131 @ X132 @ X133)))|(~(in @ X136 @ X132)|(X133 @ X136))|~(subset @ X132 @ (cartprod @ X130 @ X131))))))&((ex1E2)&((funcGraphProp1)&((funcGraphProp3)&((funcGraphProp2)&((funcextLem)&((funcGraphProp4)&((((in @ (esk5_4 @ X137 @ X138 @ X139 @ X140) @ X137)|(subset @ X139 @ X140)|~(subset @ X140 @ (cartprod @ X137 @ X138))|~(subset @ X139 @ (cartprod @ X137 @ X138)))&(((in @ (esk6_4 @ X137 @ X138 @ X139 @ X140) @ X138)|(subset @ X139 @ X140)|~(subset @ X140 @ (cartprod @ X137 @ X138))|~(subset @ X139 @ (cartprod @ X137 @ X138)))&(((in @ (kpair @ (esk5_4 @ X137 @ X138 @ X139 @ X140) @ (esk6_4 @ X137 @ X138 @ X139 @ X140)) @ X139)|(subset @ X139 @ X140)|~(subset @ X140 @ (cartprod @ X137 @ X138))|~(subset @ X139 @ (cartprod @ X137 @ X138)))&(~(in @ (kpair @ (esk5_4 @ X137 @ X138 @ X139 @ X140) @ (esk6_4 @ X137 @ X138 @ X139 @ X140)) @ X140)|(subset @ X139 @ X140)|~(subset @ X140 @ (cartprod @ X137 @ X138))|~(subset @ X139 @ (cartprod @ X137 @ X138))))))&(((((in @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ X143)|((X145)=(X146))|(in @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ X143)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(((in @ (esk10_4 @ X143 @ X144 @ X145 @ X146) @ X144)|((X145)=(X146))|(in @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ X143)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(((in @ (kpair @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ (esk10_4 @ X143 @ X144 @ X145 @ X146)) @ X146)|((X145)=(X146))|(in @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ X143)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(~(in @ (kpair @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ (esk10_4 @ X143 @ X144 @ X145 @ X146)) @ X145)|((X145)=(X146))|(in @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ X143)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144))))))&((((in @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ X143)|((X145)=(X146))|(in @ (esk8_4 @ X143 @ X144 @ X145 @ X146) @ X144)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(((in @ (esk10_4 @ X143 @ X144 @ X145 @ X146) @ X144)|((X145)=(X146))|(in @ (esk8_4 @ X143 @ X144 @ X145 @ X146) @ X144)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(((in @ (kpair @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ (esk10_4 @ X143 @ X144 @ X145 @ X146)) @ X146)|((X145)=(X146))|(in @ (esk8_4 @ X143 @ X144 @ X145 @ X146) @ X144)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(~(in @ (kpair @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ (esk10_4 @ X143 @ X144 @ X145 @ X146)) @ X145)|((X145)=(X146))|(in @ (esk8_4 @ X143 @ X144 @ X145 @ X146) @ X144)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144))))))&((((in @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ X143)|((X145)=(X146))|(in @ (kpair @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ (esk8_4 @ X143 @ X144 @ X145 @ X146)) @ X145)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(((in @ (esk10_4 @ X143 @ X144 @ X145 @ X146) @ X144)|((X145)=(X146))|(in @ (kpair @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ (esk8_4 @ X143 @ X144 @ X145 @ X146)) @ X145)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(((in @ (kpair @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ (esk10_4 @ X143 @ X144 @ X145 @ X146)) @ X146)|((X145)=(X146))|(in @ (kpair @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ (esk8_4 @ X143 @ X144 @ X145 @ X146)) @ X145)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(~(in @ (kpair @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ (esk10_4 @ X143 @ X144 @ X145 @ X146)) @ X145)|((X145)=(X146))|(in @ (kpair @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ (esk8_4 @ X143 @ X144 @ X145 @ X146)) @ X145)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144))))))&(((in @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ X143)|((X145)=(X146))|~(in @ (kpair @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ (esk8_4 @ X143 @ X144 @ X145 @ X146)) @ X146)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(((in @ (esk10_4 @ X143 @ X144 @ X145 @ X146) @ X144)|((X145)=(X146))|~(in @ (kpair @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ (esk8_4 @ X143 @ X144 @ X145 @ X146)) @ X146)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(((in @ (kpair @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ (esk10_4 @ X143 @ X144 @ X145 @ X146)) @ X146)|((X145)=(X146))|~(in @ (kpair @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ (esk8_4 @ X143 @ X144 @ X145 @ X146)) @ X146)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))&(~(in @ (kpair @ (esk9_4 @ X143 @ X144 @ X145 @ X146) @ (esk10_4 @ X143 @ X144 @ X145 @ X146)) @ X145)|((X145)=(X146))|~(in @ (kpair @ (esk7_4 @ X143 @ X144 @ X145 @ X146) @ (esk8_4 @ X143 @ X144 @ X145 @ X146)) @ X146)|~(subset @ X146 @ (cartprod @ X143 @ X144))|~(subset @ X145 @ (cartprod @ X143 @ X144)))))))))&((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)&((subset @ esk12_0 @ (cartprod @ esk11_0 @ esk11_0))&~(subset @ (breln1invset @ esk11_0 @ esk12_0) @ (cartprod @ esk11_0 @ esk11_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_19])])])])])])).
% 0.09/0.22 thf(c_0_22, plain, ![X153:$i, X154:$i]:(((breln1invset @ X153 @ X154)=(dpsetconstr @ X153 @ X153 @ (^[Z0:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X154)))))), inference(variable_rename,[status(thm)],[c_0_20])).
% 0.09/0.22 thf(c_0_23, plain, ![X156:$i, X155:$i, X3:$i]:(((epred1_1 @ X3 @ X155 @ X156)<=>(in @ (kpair @ X156 @ X155) @ X3))), introduced(definition)).
% 0.09/0.22 thf(c_0_24, negated_conjecture, ![X2:$i, X6:$i > $i > $o, X3:$i]:((subset @ (dpsetconstr @ X2 @ X3 @ X6) @ (cartprod @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_21])).
% 0.09/0.22 thf(c_0_25, plain, ![X2:$i, X3:$i]:(((breln1invset @ X2 @ X3)=(dpsetconstr @ X2 @ X2 @ (epred1_1 @ X3)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_22]), c_0_23])).
% 0.09/0.22 thf(c_0_26, negated_conjecture, ~((subset @ (breln1invset @ esk11_0 @ esk12_0) @ (cartprod @ esk11_0 @ esk11_0))), inference(split_conjunct,[status(thm)],[c_0_21])).
% 0.09/0.22 thf(c_0_27, negated_conjecture, ![X3:$i, X2:$i]:((subset @ (breln1invset @ X2 @ X3) @ (cartprod @ X2 @ X2))), inference(spm,[status(thm)],[c_0_24, c_0_25])).
% 0.09/0.22 thf(c_0_28, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27])]), ['proof']).
% 0.09/0.22 % SZS output end CNFRefutation
% 0.09/0.22 % Parsed axioms : 635
% 0.09/0.22 % Removed by relevancy pruning/SinE : 626
% 0.09/0.22 % Initial clauses : 320
% 0.09/0.22 % Removed in clause preprocessing : 0
% 0.09/0.22 % Initial clauses in saturation : 320
% 0.09/0.22 % Processed clauses : 291
% 0.09/0.22 % ...of these trivial : 0
% 0.09/0.22 % ...subsumed : 0
% 0.09/0.22 % ...remaining for further processing : 291
% 0.09/0.22 % Other redundant clauses eliminated : 0
% 0.09/0.22 % Clauses deleted for lack of memory : 0
% 0.09/0.22 % Backward-subsumed : 0
% 0.09/0.22 % Backward-rewritten : 1
% 0.09/0.22 % Generated clauses : 1
% 0.09/0.22 % ...of the previous two non-redundant : 1
% 0.09/0.22 % ...aggressively subsumed : 0
% 0.09/0.22 % Contextual simplify-reflections : 0
% 0.09/0.22 % Paramodulations : 1
% 0.09/0.22 % Factorizations : 0
% 0.09/0.22 % NegExts : 0
% 0.09/0.22 % Equation resolutions : 0
% 0.09/0.22 % Disequality decompositions : 0
% 0.09/0.22 % Total rewrite steps : 1
% 0.09/0.22 % ...of those cached : 0
% 0.09/0.22 % Propositional unsat checks : 0
% 0.09/0.22 % Propositional check models : 0
% 0.09/0.22 % Propositional check unsatisfiable : 0
% 0.09/0.22 % Propositional clauses : 0
% 0.09/0.22 % Propositional clauses after purity: 0
% 0.09/0.22 % Propositional unsat core size : 0
% 0.09/0.22 % Propositional preprocessing time : 0.000
% 0.09/0.22 % Propositional encoding time : 0.000
% 0.09/0.22 % Propositional solver time : 0.000
% 0.09/0.22 % Success case prop preproc time : 0.000
% 0.09/0.22 % Success case prop encoding time : 0.000
% 0.09/0.22 % Success case prop solver time : 0.000
% 0.09/0.22 % Current number of processed clauses : 290
% 0.09/0.22 % Positive orientable unit clauses : 290
% 0.09/0.22 % Positive unorientable unit clauses: 0
% 0.09/0.22 % Negative unit clauses : 0
% 0.09/0.22 % Non-unit-clauses : 0
% 0.09/0.22 % Current number of unprocessed clauses: 30
% 0.09/0.22 % ...number of literals in the above : 132
% 0.09/0.22 % Current number of archived formulas : 0
% 0.09/0.22 % Current number of archived clauses : 1
% 0.09/0.22 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.22 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.22 % Non-unit clause-clause subsumptions : 0
% 0.09/0.22 % Unit Clause-clause subsumption calls : 0
% 0.09/0.22 % Rewrite failures with RHS unbound : 0
% 0.09/0.22 % BW rewrite match attempts : 2
% 0.09/0.22 % BW rewrite match successes : 1
% 0.09/0.22 % Condensation attempts : 0
% 0.09/0.22 % Condensation successes : 0
% 0.09/0.22 % Termbank termtop insertions : 20461
% 0.09/0.22 % Search garbage collected termcells : 7862
% 0.09/0.22
% 0.09/0.22 % -------------------------------------------------
% 0.09/0.22 % User time : 0.012 s
% 0.09/0.22 % System time : 0.006 s
% 0.09/0.22 % Total time : 0.018 s
% 0.09/0.22 % Maximum resident set size: 6088 pages
% 0.09/0.22
% 0.09/0.22 % -------------------------------------------------
% 0.09/0.22 % User time : 0.021 s
% 0.09/0.22 % System time : 0.009 s
% 0.09/0.22 % Total time : 0.030 s
% 0.09/0.22 % Maximum resident set size: 5632 pages
% 0.09/0.22 % E exiting
%------------------------------------------------------------------------------