%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU695^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:27:25 AM UTC 2026
% Result : Theorem 82.87s 12.47s
% Output : CNFRefutation 82.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU695^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n002.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:14:22 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.22/0.28 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p
% 82.87/12.47 % Version: 3.5.1-ho
% 82.87/12.47 % Preprocessing class: HSLMSLSSLLLCHSA.
% 82.87/12.47 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 82.87/12.47 % Starting ho_unfolding_5 with 1200s (4) cores
% 82.87/12.47 % Starting pre_casc_3 with 300s (1) cores
% 82.87/12.47 % Starting new_ho_10_cnf2 with 300s (1) cores
% 82.87/12.47 % Starting full_lambda_10 with 300s (1) cores
% 82.87/12.47 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 82.87/12.47 % pre_casc_3 with pid 1349187 completed with status 0
% 82.87/12.47 % Result found by pre_casc_3
% 82.87/12.47 % Preprocessing class: HSLMSLSSLLLCHSA.
% 82.87/12.47 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 82.87/12.47 % Starting ho_unfolding_5 with 1200s (4) cores
% 82.87/12.47 % Starting pre_casc_3 with 300s (1) cores
% 82.87/12.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 82.87/12.47 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 82.87/12.47 % Search class: HGUSM-FSLM32-MHSMMFBN
% 82.87/12.47 % partial match(2): HGHSM-FSLM32-MHSMMSBN
% 82.87/12.47 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 82.87/12.47 % Starting SubtermCWHack with 31s (1) cores
% 82.87/12.47 % SubtermCWHack with pid 1349193 completed with status 0
% 82.87/12.47 % Result found by SubtermCWHack
% 82.87/12.47 % Preprocessing class: HSLMSLSSLLLCHSA.
% 82.87/12.47 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 82.87/12.47 % Starting ho_unfolding_5 with 1200s (4) cores
% 82.87/12.47 % Starting pre_casc_3 with 300s (1) cores
% 82.87/12.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 82.87/12.47 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 82.87/12.47 % Search class: HGUSM-FSLM32-MHSMMFBN
% 82.87/12.47 % partial match(2): HGHSM-FSLM32-MHSMMSBN
% 82.87/12.47 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 82.87/12.47 % Starting SubtermCWHack with 31s (1) cores
% 82.87/12.47 % Preprocessing time : 0.004 s
% 82.87/12.47
% 82.87/12.47 % Proof found!
% 82.87/12.47 % SZS status Theorem
% 82.87/12.47 % SZS output start CNFRefutation
% 82.87/12.47 thf(decl_23, type, in: $i > $i > $o).
% 82.87/12.47 thf(decl_25, type, setextAx: $o).
% 82.87/12.47 thf(decl_26, type, emptyset: $i).
% 82.87/12.47 thf(decl_27, type, emptysetAx: $o).
% 82.87/12.47 thf(decl_28, type, setadjoin: $i > $i > $i).
% 82.87/12.47 thf(decl_29, type, setadjoinAx: $o).
% 82.87/12.47 thf(decl_31, type, powersetAx: $o).
% 82.87/12.47 thf(decl_32, type, setunion: $i > $i).
% 82.87/12.47 thf(decl_33, type, setunionAx: $o).
% 82.87/12.47 thf(decl_35, type, omega0Ax: $o).
% 82.87/12.47 thf(decl_36, type, omegaSAx: $o).
% 82.87/12.47 thf(decl_37, type, omegaIndAx: $o).
% 82.87/12.47 thf(decl_38, type, replAx: $o).
% 82.87/12.47 thf(decl_39, type, foundationAx: $o).
% 82.87/12.47 thf(decl_40, type, wellorderingAx: $o).
% 82.87/12.47 thf(decl_42, type, descrp: $o).
% 82.87/12.47 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 82.87/12.47 thf(decl_44, type, dsetconstrI: $o).
% 82.87/12.47 thf(decl_45, type, dsetconstrEL: $o).
% 82.87/12.47 thf(decl_46, type, dsetconstrER: $o).
% 82.87/12.47 thf(decl_47, type, exuE1: $o).
% 82.87/12.47 thf(decl_49, type, prop2setE: $o).
% 82.87/12.47 thf(decl_50, type, emptysetE: $o).
% 82.87/12.47 thf(decl_51, type, emptysetimpfalse: $o).
% 82.87/12.47 thf(decl_52, type, notinemptyset: $o).
% 82.87/12.47 thf(decl_53, type, exuE3e: $o).
% 82.87/12.47 thf(decl_54, type, setext: $o).
% 82.87/12.47 thf(decl_55, type, emptyI: $o).
% 82.87/12.47 thf(decl_56, type, noeltsimpempty: $o).
% 82.87/12.47 thf(decl_57, type, setbeta: $o).
% 82.87/12.47 thf(decl_59, type, nonemptyE1: $o).
% 82.87/12.47 thf(decl_60, type, nonemptyI: $o).
% 82.87/12.47 thf(decl_61, type, nonemptyI1: $o).
% 82.87/12.47 thf(decl_62, type, setadjoinIL: $o).
% 82.87/12.47 thf(decl_63, type, emptyinunitempty: $o).
% 82.87/12.47 thf(decl_64, type, setadjoinIR: $o).
% 82.87/12.47 thf(decl_65, type, setadjoinE: $o).
% 82.87/12.47 thf(decl_66, type, setadjoinOr: $o).
% 82.87/12.47 thf(decl_67, type, setoftrueEq: $o).
% 82.87/12.47 thf(decl_68, type, powersetI: $o).
% 82.87/12.47 thf(decl_69, type, emptyinPowerset: $o).
% 82.87/12.47 thf(decl_70, type, emptyInPowerset: $o).
% 82.87/12.47 thf(decl_71, type, powersetE: $o).
% 82.87/12.47 thf(decl_72, type, setunionI: $o).
% 82.87/12.47 thf(decl_73, type, setunionE: $o).
% 82.87/12.47 thf(decl_74, type, subPowSU: $o).
% 82.87/12.47 thf(decl_75, type, exuE2: $o).
% 82.87/12.47 thf(decl_76, type, nonemptyImpWitness: $o).
% 82.87/12.47 thf(decl_77, type, uniqinunit: $o).
% 82.87/12.47 thf(decl_78, type, notinsingleton: $o).
% 82.87/12.47 thf(decl_79, type, eqinunit: $o).
% 82.87/12.47 thf(decl_80, type, singletonsswitch: $o).
% 82.87/12.47 thf(decl_81, type, upairsetE: $o).
% 82.87/12.47 thf(decl_82, type, upairsetIL: $o).
% 82.87/12.47 thf(decl_83, type, upairsetIR: $o).
% 82.87/12.47 thf(decl_84, type, emptyE1: $o).
% 82.87/12.47 thf(decl_85, type, vacuousDall: $o).
% 82.87/12.47 thf(decl_86, type, quantDeMorgan1: $o).
% 82.87/12.47 thf(decl_87, type, quantDeMorgan2: $o).
% 82.87/12.47 thf(decl_88, type, quantDeMorgan3: $o).
% 82.87/12.47 thf(decl_89, type, quantDeMorgan4: $o).
% 82.87/12.47 thf(decl_90, type, prop2setI: $o).
% 82.87/12.47 thf(decl_92, type, prop2set2propI: $o).
% 82.87/12.47 thf(decl_93, type, notdexE: $o).
% 82.87/12.47 thf(decl_94, type, notdallE: $o).
% 82.87/12.47 thf(decl_95, type, exuI1: $o).
% 82.87/12.47 thf(decl_96, type, exuI3: $o).
% 82.87/12.47 thf(decl_97, type, exuI2: $o).
% 82.87/12.47 thf(decl_98, type, inCongP: $o).
% 82.87/12.47 thf(decl_99, type, in__Cong: $o).
% 82.87/12.47 thf(decl_100, type, exuE3u: $o).
% 82.87/12.47 thf(decl_101, type, exu__Cong: $o).
% 82.87/12.47 thf(decl_102, type, emptyset__Cong: $o).
% 82.87/12.47 thf(decl_103, type, setadjoin__Cong: $o).
% 82.87/12.47 thf(decl_104, type, powerset__Cong: $o).
% 82.87/12.47 thf(decl_105, type, setunion__Cong: $o).
% 82.87/12.47 thf(decl_106, type, omega__Cong: $o).
% 82.87/12.47 thf(decl_107, type, exuEu: $o).
% 82.87/12.47 thf(decl_108, type, descr__Cong: $o).
% 82.87/12.47 thf(decl_109, type, dsetconstr__Cong: $o).
% 82.87/12.47 thf(decl_110, type, subset: $i > $i > $o).
% 82.87/12.47 thf(decl_113, type, subsetI1: $o).
% 82.87/12.47 thf(decl_114, type, eqimpsubset2: $o).
% 82.87/12.47 thf(decl_115, type, eqimpsubset1: $o).
% 82.87/12.47 thf(decl_116, type, subsetI2: $o).
% 82.87/12.47 thf(decl_117, type, emptysetsubset: $o).
% 82.87/12.47 thf(decl_118, type, subsetE: $o).
% 82.87/12.47 thf(decl_119, type, subsetE2: $o).
% 82.87/12.47 thf(decl_120, type, notsubsetI: $o).
% 82.87/12.47 thf(decl_121, type, notequalI1: $o).
% 82.87/12.47 thf(decl_122, type, notequalI2: $o).
% 82.87/12.47 thf(decl_123, type, subsetRefl: $o).
% 82.87/12.47 thf(decl_124, type, subsetTrans: $o).
% 82.87/12.47 thf(decl_125, type, setadjoinSub: $o).
% 82.87/12.47 thf(decl_126, type, setadjoinSub2: $o).
% 82.87/12.47 thf(decl_127, type, subset2powerset: $o).
% 82.87/12.47 thf(decl_128, type, setextsub: $o).
% 82.87/12.47 thf(decl_129, type, subsetemptysetimpeq: $o).
% 82.87/12.47 thf(decl_130, type, powersetI1: $o).
% 82.87/12.47 thf(decl_131, type, powersetE1: $o).
% 82.87/12.47 thf(decl_132, type, inPowerset: $o).
% 82.87/12.47 thf(decl_133, type, powersetsubset: $o).
% 82.87/12.47 thf(decl_134, type, sepInPowerset: $o).
% 82.87/12.47 thf(decl_135, type, sepSubset: $o).
% 82.87/12.47 thf(decl_137, type, binunionIL: $o).
% 82.87/12.47 thf(decl_138, type, upairset2IR: $o).
% 82.87/12.47 thf(decl_139, type, binunionIR: $o).
% 82.87/12.47 thf(decl_140, type, binunionEcases: $o).
% 82.87/12.47 thf(decl_141, type, binunionE: $o).
% 82.87/12.47 thf(decl_142, type, binunionLsub: $o).
% 82.87/12.47 thf(decl_143, type, binunionRsub: $o).
% 82.87/12.47 thf(decl_145, type, binintersectI: $o).
% 82.87/12.47 thf(decl_146, type, binintersectSubset5: $o).
% 82.87/12.47 thf(decl_147, type, binintersectEL: $o).
% 82.87/12.47 thf(decl_148, type, binintersectLsub: $o).
% 82.87/12.47 thf(decl_149, type, binintersectSubset2: $o).
% 82.87/12.47 thf(decl_150, type, binintersectSubset3: $o).
% 82.87/12.47 thf(decl_151, type, binintersectER: $o).
% 82.87/12.47 thf(decl_152, type, disjointsetsI1: $o).
% 82.87/12.47 thf(decl_153, type, binintersectRsub: $o).
% 82.87/12.47 thf(decl_154, type, binintersectSubset4: $o).
% 82.87/12.47 thf(decl_155, type, binintersectSubset1: $o).
% 82.87/12.47 thf(decl_156, type, bs114d: $o).
% 82.87/12.47 thf(decl_159, type, setminusI: $o).
% 82.87/12.47 thf(decl_160, type, setminusEL: $o).
% 82.87/12.47 thf(decl_161, type, setminusER: $o).
% 82.87/12.47 thf(decl_162, type, setminusSubset2: $o).
% 82.87/12.47 thf(decl_163, type, setminusERneg: $o).
% 82.87/12.47 thf(decl_164, type, setminusELneg: $o).
% 82.87/12.47 thf(decl_165, type, setminusILneg: $o).
% 82.87/12.47 thf(decl_166, type, setminusIRneg: $o).
% 82.87/12.47 thf(decl_167, type, setminusLsub: $o).
% 82.87/12.47 thf(decl_168, type, setminusSubset1: $o).
% 82.87/12.47 thf(decl_170, type, symdiffE: $o).
% 82.87/12.47 thf(decl_171, type, symdiffI1: $o).
% 82.87/12.47 thf(decl_172, type, symdiffI2: $o).
% 82.87/12.47 thf(decl_173, type, symdiffIneg1: $o).
% 82.87/12.47 thf(decl_174, type, symdiffIneg2: $o).
% 82.87/12.47 thf(decl_175, type, iskpair: $i > $o).
% 82.87/12.47 thf(decl_176, type, secondinupair: $o).
% 82.87/12.47 thf(decl_177, type, setukpairIL: $o).
% 82.87/12.47 thf(decl_178, type, setukpairIR: $o).
% 82.87/12.47 thf(decl_179, type, kpairiskpair: $o).
% 82.87/12.47 thf(decl_180, type, kpair: $i > $i > $i).
% 82.87/12.47 thf(decl_181, type, kpairp: $o).
% 82.87/12.47 thf(decl_182, type, cartprod: $i > $i > $i).
% 82.87/12.47 thf(decl_183, type, singletonsubset: $o).
% 82.87/12.47 thf(decl_184, type, singletoninpowerset: $o).
% 82.87/12.47 thf(decl_185, type, singletoninpowunion: $o).
% 82.87/12.47 thf(decl_186, type, upairset2E: $o).
% 82.87/12.47 thf(decl_187, type, upairsubunion: $o).
% 82.87/12.47 thf(decl_188, type, upairinpowunion: $o).
% 82.87/12.47 thf(decl_189, type, ubforcartprodlem1: $o).
% 82.87/12.47 thf(decl_190, type, ubforcartprodlem2: $o).
% 82.87/12.47 thf(decl_191, type, ubforcartprodlem3: $o).
% 82.87/12.47 thf(decl_192, type, cartprodpairin: $o).
% 82.87/12.47 thf(decl_193, type, cartprodmempair1: $o).
% 82.87/12.47 thf(decl_194, type, cartprodmempair: $o).
% 82.87/12.47 thf(decl_195, type, setunionE2: $o).
% 82.87/12.47 thf(decl_196, type, setunionsingleton1: $o).
% 82.87/12.47 thf(decl_197, type, setunionsingleton2: $o).
% 82.87/12.47 thf(decl_198, type, setunionsingleton: $o).
% 82.87/12.47 thf(decl_199, type, singleton: $i > $o).
% 82.87/12.47 thf(decl_200, type, singletonprop: $o).
% 82.87/12.47 thf(decl_202, type, ex1E1: $o).
% 82.87/12.47 thf(decl_203, type, ex1I: $o).
% 82.87/12.47 thf(decl_204, type, ex1I2: $o).
% 82.87/12.47 thf(decl_205, type, singletonsuniq: $o).
% 82.87/12.47 thf(decl_210, type, setukpairinjL1: $o).
% 82.87/12.47 thf(decl_211, type, kfstsingleton: $o).
% 82.87/12.47 thf(decl_212, type, theprop: $o).
% 82.87/12.47 thf(decl_213, type, kfst: $i > $i).
% 82.87/12.47 thf(decl_214, type, kfstpairEq: $o).
% 82.87/12.47 thf(decl_215, type, cartprodfstin: $o).
% 82.87/12.47 thf(decl_216, type, setukpairinjL2: $o).
% 82.87/12.47 thf(decl_217, type, setukpairinjL: $o).
% 82.87/12.47 thf(decl_218, type, setukpairinjR11: $o).
% 82.87/12.47 thf(decl_219, type, setukpairinjR12: $o).
% 82.87/12.47 thf(decl_220, type, setukpairinjR1: $o).
% 82.87/12.47 thf(decl_221, type, upairequniteq: $o).
% 82.87/12.47 thf(decl_222, type, setukpairinjR2: $o).
% 82.87/12.47 thf(decl_223, type, setukpairinjR: $o).
% 82.87/12.47 thf(decl_224, type, ksndsingleton: $o).
% 82.87/12.47 thf(decl_225, type, ksnd: $i > $i).
% 82.87/12.47 thf(decl_226, type, ksndpairEq: $o).
% 82.87/12.47 thf(decl_227, type, kpairsurjEq: $o).
% 82.87/12.47 thf(decl_228, type, cartprodsndin: $o).
% 82.87/12.47 thf(decl_229, type, cartprodpairmemEL: $o).
% 82.87/12.47 thf(decl_230, type, cartprodpairmemER: $o).
% 82.87/12.47 thf(decl_231, type, cartprodmempaircEq: $o).
% 82.87/12.47 thf(decl_232, type, cartprodfstpairEq: $o).
% 82.87/12.47 thf(decl_233, type, cartprodsndpairEq: $o).
% 82.87/12.47 thf(decl_234, type, cartprodpairsurjEq: $o).
% 82.87/12.47 thf(decl_235, type, breln: $i > $i > $i > $o).
% 82.87/12.47 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 82.87/12.47 thf(decl_237, type, dpsetconstrI: $o).
% 82.87/12.47 thf(decl_238, type, dpsetconstrSub: $o).
% 82.87/12.47 thf(decl_239, type, setOfPairsIsBReln: $o).
% 82.87/12.47 thf(decl_240, type, dpsetconstrERa: $o).
% 82.87/12.47 thf(decl_241, type, dpsetconstrEL1: $o).
% 82.87/12.47 thf(decl_242, type, dpsetconstrEL2: $o).
% 82.87/12.47 thf(decl_243, type, dpsetconstrER: $o).
% 82.87/12.47 thf(decl_244, type, func: $i > $i > $i > $o).
% 82.87/12.47 thf(decl_245, type, funcSet: $i > $i > $i).
% 82.87/12.47 thf(decl_246, type, funcImageSingleton: $o).
% 82.87/12.47 thf(decl_247, type, apProp: $o).
% 82.87/12.47 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 82.87/12.47 thf(decl_249, type, app: $o).
% 82.87/12.47 thf(decl_250, type, infuncsetfunc: $o).
% 82.87/12.47 thf(decl_251, type, ap2p: $o).
% 82.87/12.47 thf(decl_252, type, funcinfuncset: $o).
% 82.87/12.47 thf(decl_253, type, lamProp: $o).
% 82.87/12.47 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 82.87/12.47 thf(decl_255, type, lamp: $o).
% 82.87/12.47 thf(decl_256, type, lam2p: $o).
% 82.87/12.47 thf(decl_257, type, brelnall1: $o).
% 82.87/12.47 thf(decl_258, type, brelnall2: $o).
% 82.87/12.47 thf(decl_259, type, ex1E2: $o).
% 82.87/12.47 thf(decl_260, type, funcGraphProp1: $o).
% 82.87/12.47 thf(decl_261, type, funcGraphProp3: $o).
% 82.87/12.47 thf(decl_262, type, funcGraphProp2: $o).
% 82.87/12.47 thf(decl_263, type, funcextLem: $o).
% 82.87/12.47 thf(decl_264, type, funcGraphProp4: $o).
% 82.87/12.47 thf(decl_265, type, subbreln: $o).
% 82.87/12.47 thf(decl_266, type, eqbreln: $o).
% 82.87/12.47 thf(decl_267, type, funcext: $o).
% 82.87/12.47 thf(decl_268, type, funcext2: $o).
% 82.87/12.47 thf(decl_269, type, ap2apEq1: $o).
% 82.87/12.47 thf(decl_270, type, ap2apEq2: $o).
% 82.87/12.47 thf(decl_271, type, esk1_3: $i > $i > $i > $i).
% 82.87/12.47 thf(decl_272, type, esk2_3: $i > $i > $i > $i).
% 82.87/12.47 thf(decl_273, type, esk3_2: $i > ($i > $o) > $i).
% 82.87/12.47 thf(decl_274, type, esk4_2: $i > ($i > $o) > $i).
% 82.87/12.47 thf(decl_275, type, esk5_2: $i > ($i > $o) > $i).
% 82.87/12.47 thf(decl_276, type, esk6_1: $i > $i).
% 82.87/12.47 thf(decl_277, type, esk7_1: $i > $i).
% 82.87/12.47 thf(decl_278, type, esk8_4: $i > $i > $i > $i > $i).
% 82.87/12.47 thf(decl_279, type, esk9_3: $i > $i > ($i > $i) > $i).
% 82.87/12.47 thf(decl_280, type, esk10_3: $i > $i > ($i > $i) > $i).
% 82.87/12.47 thf(decl_281, type, esk11_3: $i > $i > ($i > $i) > $i).
% 82.87/12.47 thf(decl_282, type, esk12_4: $i > $i > $i > ($i > $o) > $i).
% 82.87/12.47 thf(decl_283, type, esk13_4: $i > $i > $i > ($i > $o) > $i).
% 82.87/12.47 thf(decl_284, type, esk14_4: $i > $i > $i > ($i > $o) > $i).
% 82.87/12.47 thf(decl_285, type, esk15_4: $i > $i > $i > ($i > $o) > $i).
% 82.87/12.47 thf(decl_286, type, esk16_4: $i > $i > $i > $i > $i).
% 82.87/12.47 thf(decl_287, type, esk17_4: $i > $i > $i > $i > $i).
% 82.87/12.47 thf(decl_288, type, esk18_4: $i > $i > $i > $i > $i).
% 82.87/12.47 thf(decl_289, type, esk19_4: $i > $i > $i > $i > $i).
% 82.87/12.47 thf(decl_290, type, esk20_4: $i > $i > $i > $i > $i).
% 82.87/12.47 thf(decl_291, type, esk21_4: $i > $i > $i > $i > $i).
% 82.87/12.47 thf(decl_292, type, esk22_4: $i > $i > $i > $i > $i).
% 82.87/12.47 thf(decl_293, type, esk23_0: $i).
% 82.87/12.47 thf(decl_294, type, esk24_0: $i).
% 82.87/12.47 thf(decl_295, type, esk25_0: $i > $i).
% 82.87/12.47 thf(decl_296, type, esk26_0: $i).
% 82.87/12.47 thf(decl_297, type, epred1_1: ($i > $i) > $i > $i > $o).
% 82.87/12.47 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', funcImageSingleton)).
% 82.87/12.47 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', singleton)).
% 82.87/12.47 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', singletonprop)).
% 82.87/12.47 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', ksndsingleton)).
% 82.87/12.47 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', kfstsingleton)).
% 82.87/12.47 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', breln)).
% 82.87/12.47 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/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', setOfPairsIsBReln)).
% 82.87/12.47 thf(beta1, 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)=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X37 @ X3))) @ X2)=(X37 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', beta1)).
% 82.87/12.47 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', theprop)).
% 82.87/12.47 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X36:$i]:(((breln @ X4 @ X5 @ X36)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X36))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X36)=>(in @ (kpair @ X2 @ X3) @ X34))))))=>((X34)=(X36))))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', eqbreln)).
% 82.87/12.47 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X36:$i]:(((breln @ X4 @ X5 @ X36)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X36))))))=>(subset @ X34 @ X36))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', subbreln)).
% 82.87/12.47 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X34)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', brelnall2)).
% 82.87/12.47 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X34)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', brelnall1)).
% 82.87/12.47 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/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', lamProp)).
% 82.87/12.47 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:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', dpsetconstrER)).
% 82.87/12.47 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', dpsetconstrEL2)).
% 82.87/12.47 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', dpsetconstrEL1)).
% 82.87/12.47 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', dpsetconstrERa)).
% 82.87/12.47 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', dpsetconstrSub)).
% 82.87/12.47 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', dpsetconstrI)).
% 82.87/12.47 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X33 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', lam2p)).
% 82.87/12.47 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', lamp)).
% 82.87/12.47 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', cartprodsndpairEq)).
% 82.87/12.47 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', ksndpairEq)).
% 82.87/12.47 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', cartprodfstpairEq)).
% 82.87/12.47 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', kfstpairEq)).
% 82.87/12.47 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', kpairsurjEq)).
% 82.87/12.47 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', kpairp)).
% 82.87/12.47 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', kpairiskpair)).
% 82.87/12.47 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', cartprodpairsurjEq)).
% 82.87/12.47 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', cartprodpairmemER)).
% 82.87/12.47 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', cartprodpairmemEL)).
% 82.87/12.47 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', cartprodsndin)).
% 82.87/12.47 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', cartprodfstin)).
% 82.87/12.47 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', cartprodmempair)).
% 82.87/12.47 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', cartprodmempair1)).
% 82.87/12.47 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', cartprodpairin)).
% 82.87/12.47 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', ap2apEq1)).
% 82.87/12.47 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X35:$i]:(((in @ X35 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>((X29)=(X35)))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', funcext2)).
% 82.87/12.47 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', funcGraphProp4)).
% 82.87/12.47 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', funcGraphProp3)).
% 82.87/12.47 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', funcinfuncset)).
% 82.87/12.47 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', ap2p)).
% 82.87/12.47 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', infuncsetfunc)).
% 82.87/12.47 thf(lam, axiom, ((lam)=(^[X4:$i, X5:$i, X31:$i > $i]:(dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X31 @ X2)=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.vGYDWPW5m2/E---3.1_1349173.p', lam)).
% 82.87/12.47 thf(c_0_45, plain, ((funcImageSingleton)<=>![X4:$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])).
% 82.87/12.47 thf(c_0_46, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 82.87/12.47 thf(c_0_47, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 82.87/12.47 thf(c_0_48, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 82.87/12.47 thf(c_0_49, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 82.87/12.47 thf(c_0_50, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 82.87/12.47 thf(c_0_51, 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])).
% 82.87/12.47 thf(c_0_52, 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)=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X37 @ X3))) @ X2)=(X37 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[beta1])).
% 82.87/12.47 thf(c_0_53, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:((((func @ X4 @ X5 @ X29))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X205:$i]:((((in @ X205 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X205 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[c_0_45, c_0_46])).
% 82.87/12.47 thf(c_0_54, axiom, ((theprop)=(![X21:$i]:((((?[X203:$i]:((((in @ X203 @ X21))&(((X21)=(setadjoin @ X203 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_46])).
% 82.87/12.47 thf(c_0_55, plain, ((singletonprop)=(![X4:$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)))))=>((?[X200:$i]:((((in @ X200 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X200 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_46])).
% 82.87/12.47 thf(c_0_56, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X204:$i]:((((in @ X204 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X204 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_48, c_0_46])).
% 82.87/12.47 thf(c_0_57, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X202:$i]:((((in @ X202 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X202 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_49, c_0_46])).
% 82.87/12.47 thf(c_0_58, axiom, ((eqbreln)=(![X4:$i, X5:$i, X34:$i]:(((((subset @ X34 @ (cartprod @ X4 @ X5))))=>(![X36:$i]:(((((subset @ X36 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X34))=>((in @ (kpair @ X2 @ X3) @ X36))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X36))=>((in @ (kpair @ X2 @ X3) @ X34))))))))))=>(((X34)=(X36)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_50])).
% 82.87/12.47 thf(c_0_59, axiom, ((subbreln)=(![X4:$i, X5:$i, X34:$i]:(((((subset @ X34 @ (cartprod @ X4 @ X5))))=>(![X36:$i]:(((((subset @ X36 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X34))=>((in @ (kpair @ X2 @ X3) @ X36))))))))))=>((subset @ X34 @ X36))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_50])).
% 82.87/12.47 thf(c_0_60, axiom, ((brelnall2)=(![X4:$i, X5:$i, X34:$i]:(((((subset @ X34 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X34))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X34))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_50])).
% 82.87/12.47 thf(c_0_61, axiom, ((brelnall1)=(![X4:$i, X5:$i, X34:$i]:(((((subset @ X34 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X34))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X34))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_50])).
% 82.87/12.47 thf(c_0_62, 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])).
% 82.87/12.47 thf(c_0_63, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 82.87/12.47 thf(c_0_64, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 82.87/12.47 thf(c_0_65, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 82.87/12.47 thf(c_0_66, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 82.87/12.47 thf(c_0_67, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_51, c_0_50])).
% 82.87/12.47 thf(c_0_68, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 82.87/12.47 thf(c_0_69, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 82.87/12.47 thf(c_0_70, plain, ((lam2p)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X33 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 82.87/12.47 thf(c_0_71, plain, ((lamp)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 82.87/12.47 thf(c_0_72, plain, ![X557:$i, X558:$i > $i]:(((epred1_1 @ X558 @ X557)=($eq @ (X558 @ X557)))), inference(variable_rename,[status(thm)],[])).
% 82.87/12.47 thf(c_0_73, 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)=>(![X206:$i, X207:$i]:((iskpair @ (setadjoin @ (setadjoin @ X206 @ emptyset) @ (setadjoin @ (setadjoin @ X206 @ (setadjoin @ X207 @ emptyset)) @ emptyset))))=>(![X208:$i, X209:$i]:((iskpair @ (kpair @ X208 @ X209)))=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>(![X210:$i, X211:$i, X212:$i]:(((in @ X212 @ X210)=>![X213:$i]:(((in @ X213 @ X211)=>(in @ (kpair @ X212 @ X213) @ (cartprod @ X210 @ X211))))))=>(![X214:$i, X215:$i, X216:$i]:(((in @ X216 @ (cartprod @ X214 @ X215))=>?[X217:$i]:(((in @ X217 @ X214)&?[X218:$i]:(((in @ X218 @ X215)&((X216)=(kpair @ X217 @ X218))))))))=>(![X219:$i, X220:$i, X221:$i]:(((in @ X221 @ (cartprod @ X219 @ X220))=>(iskpair @ X221)))=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(![X222:$i, X223:$i > $o]:((![X224:$i]:(((in @ X224 @ X222)=>![X225:$i]:(((in @ X225 @ X222)=>((X223 @ X224)=>((X223 @ X225)=>((X224)=(X225))))))))=>(?[X226:$i]:(((in @ X226 @ X222)&(X223 @ X226)))=>?[X227:$i]:(((in @ X227 @ (dsetconstr @ X222 @ X223))&((dsetconstr @ X222 @ X223)=(setadjoin @ X227 @ emptyset)))))))=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>(![X228:$i]:(((iskpair @ X228)=>?[X229:$i]:(((in @ X229 @ (dsetconstr @ (setunion @ X228) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X228)))))&((dsetconstr @ (setunion @ X228) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X228))))=(setadjoin @ X229 @ emptyset))))))=>(![X230:$i]:((?[X231:$i]:(((in @ X231 @ X230)&((X230)=(setadjoin @ X231 @ emptyset))))=>(in @ (setunion @ X230) @ X230)))=>(![X232:$i, X233:$i]:(((kfst @ (kpair @ X232 @ X233))=(X232)))=>(![X234:$i, X235:$i, X236:$i]:(((in @ X236 @ (cartprod @ X234 @ X235))=>(in @ (kfst @ X236) @ X234)))=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>(![X237:$i]:(((iskpair @ X237)=>?[X238:$i]:(((in @ X238 @ (dsetconstr @ (setunion @ X237) @ (^[Z0:$i]:(((X237)=(kpair @ (kfst @ X237) @ Z0))))))&((dsetconstr @ (setunion @ X237) @ (^[Z0:$i]:(((X237)=(kpair @ (kfst @ X237) @ Z0)))))=(setadjoin @ X238 @ emptyset))))))=>(![X239:$i, X240:$i]:(((ksnd @ (kpair @ X239 @ X240))=(X240)))=>(![X241:$i]:(((iskpair @ X241)=>((kpair @ (kfst @ X241) @ (ksnd @ X241))=(X241))))=>(![X242:$i, X243:$i, X244:$i]:(((in @ X244 @ (cartprod @ X242 @ X243))=>(in @ (ksnd @ X244) @ X243)))=>(![X245:$i, X246:$i, X247:$i, X248:$i]:(((in @ (kpair @ X247 @ X248) @ (cartprod @ X245 @ X246))=>(in @ X247 @ X245)))=>(![X249:$i, X250:$i, X251:$i, X252:$i]:(((in @ (kpair @ X251 @ X252) @ (cartprod @ X249 @ X250))=>(in @ X252 @ X250)))=>((cartprodmempaircEq)=>(![X253:$i, X254:$i, X255:$i]:(((in @ X255 @ X253)=>![X256:$i]:(((in @ X256 @ X254)=>((kfst @ (kpair @ X255 @ X256))=(X255))))))=>(![X257:$i, X258:$i, X259:$i]:(((in @ X259 @ X257)=>![X260:$i]:(((in @ X260 @ X258)=>((ksnd @ (kpair @ X259 @ X260))=(X260))))))=>(![X261:$i, X262:$i, X263:$i]:(((in @ X263 @ (cartprod @ X261 @ X262))=>((kpair @ (kfst @ X263) @ (ksnd @ X263))=(X263))))=>(![X264:$i, X265:$i, X266:$i > $i > $o, X267:$i]:(((in @ X267 @ X264)=>![X268:$i]:(((in @ X268 @ X265)=>((X266 @ X267 @ X268)=>(in @ (kpair @ X267 @ X268) @ (dpsetconstr @ X264 @ X265 @ X266)))))))=>(![X269:$i, X270:$i, X271:$i > $i > $o]:((subset @ (dpsetconstr @ X269 @ X270 @ X271) @ (cartprod @ X269 @ X270)))=>(![X272:$i, X273:$i, X274:$i > $i > $o]:((subset @ (dpsetconstr @ X272 @ X273 @ X274) @ (cartprod @ X272 @ X273)))=>(![X275:$i, X276:$i, X277:$i > $i > $o, X278:$i]:(((in @ X278 @ X275)=>![X279:$i]:(((in @ X279 @ X276)=>((in @ (kpair @ X278 @ X279) @ (dpsetconstr @ X275 @ X276 @ X277))=>(X277 @ X278 @ X279))))))=>(![X280:$i, X281:$i, X282:$i > $i > $o, X283:$i, X284:$i]:(((in @ (kpair @ X283 @ X284) @ (dpsetconstr @ X280 @ X281 @ X282))=>(in @ X283 @ X280)))=>(![X285:$i, X286:$i, X287:$i > $i > $o, X288:$i, X289:$i]:(((in @ (kpair @ X288 @ X289) @ (dpsetconstr @ X285 @ X286 @ X287))=>(in @ X289 @ X286)))=>(![X290:$i, X291:$i, X292:$i > $i > $o, X293:$i, X294:$i]:(((in @ (kpair @ X293 @ X294) @ (dpsetconstr @ X290 @ X291 @ X292))=>(X292 @ X293 @ X294)))=>(![X295:$i, X296:$i, X297:$i]:(((func @ X295 @ X296 @ X297)=>![X298:$i]:(((in @ X298 @ X295)=>?[X299:$i]:(((in @ X299 @ (dsetconstr @ X296 @ (^[Z0:$i]:((in @ (kpair @ X298 @ Z0) @ X297)))))&((dsetconstr @ X296 @ (^[Z0:$i]:((in @ (kpair @ X298 @ Z0) @ X297))))=(setadjoin @ X299 @ emptyset))))))))=>((apProp)=>((app)=>(![X300:$i, X301:$i, X302:$i]:(((in @ X302 @ (funcSet @ X300 @ X301))=>(func @ X300 @ X301 @ X302)))=>(![X303:$i, X304:$i, X305:$i]:(((in @ X305 @ (funcSet @ X303 @ X304))=>![X306:$i]:(((in @ X306 @ X303)=>(in @ (ap @ X303 @ X304 @ X305 @ X306) @ X304)))))=>(![X307:$i, X308:$i, X309:$i]:(((func @ X307 @ X308 @ X309)=>(in @ X309 @ (funcSet @ X307 @ X308))))=>(![X310:$i, X311:$i, X312:$i > $i]:((![X313:$i]:(((in @ X313 @ X310)=>(in @ (X312 @ X313) @ X311)))=>(func @ X310 @ X311 @ (dpsetconstr @ X310 @ X311 @ (^[Z0:$i]:($eq @ (X312 @ Z0)))))))=>(![X314:$i, X315:$i, X316:$i > $i]:((![X317:$i]:(((in @ X317 @ X314)=>(in @ (X316 @ X317) @ X315)))=>(func @ X314 @ X315 @ (lam @ X314 @ X315 @ X316))))=>(![X318:$i, X319:$i, X320:$i > $i]:((![X321:$i]:(((in @ X321 @ X318)=>(in @ (X320 @ X321) @ X319)))=>(in @ (lam @ X318 @ X319 @ X320) @ (funcSet @ X318 @ X319))))=>(![X322:$i, X323:$i, X324:$i]:(((subset @ X324 @ (cartprod @ X322 @ X323))=>![X325:$i > $o]:((![X326:$i]:(((in @ X326 @ X322)=>![X327:$i]:(((in @ X327 @ X323)=>((in @ (kpair @ X326 @ X327) @ X324)=>(X325 @ (kpair @ X326 @ X327)))))))=>![X328:$i]:(((in @ X328 @ X324)=>(X325 @ X328)))))))=>(![X329:$i, X330:$i, X331:$i]:(((subset @ X331 @ (cartprod @ X329 @ X330))=>![X332:$i > $o]:((![X333:$i]:(((in @ X333 @ X329)=>![X334:$i]:(((in @ X334 @ X330)=>((in @ (kpair @ X333 @ X334) @ X331)=>(X332 @ (kpair @ X333 @ X334)))))))=>![X335:$i]:(((in @ X335 @ X331)=>(X332 @ X335)))))))=>((ex1E2)=>((funcGraphProp1)=>(![X336:$i, X337:$i, X338:$i]:(((in @ X338 @ (funcSet @ X336 @ X337))=>![X339:$i]:(((in @ X339 @ X336)=>(in @ (kpair @ X339 @ (ap @ X336 @ X337 @ X338 @ X339)) @ X338)))))=>((funcGraphProp2)=>((funcextLem)=>(![X340:$i, X341:$i, X342:$i]:(((in @ X342 @ (funcSet @ X340 @ X341))=>![X343:$i]:(((in @ X343 @ X340)=>![X344:$i]:(((in @ X344 @ X341)=>((in @ (kpair @ X343 @ X344) @ X342)=>((ap @ X340 @ X341 @ X342 @ X343)=(X344)))))))))=>(![X345:$i, X346:$i, X347:$i]:(((subset @ X347 @ (cartprod @ X345 @ X346))=>![X348:$i]:(((subset @ X348 @ (cartprod @ X345 @ X346))=>(![X349:$i]:(((in @ X349 @ X345)=>![X350:$i]:(((in @ X350 @ X346)=>((in @ (kpair @ X349 @ X350) @ X347)=>(in @ (kpair @ X349 @ X350) @ X348))))))=>(subset @ X347 @ X348))))))=>(![X351:$i, X352:$i, X353:$i]:(((subset @ X353 @ (cartprod @ X351 @ X352))=>![X354:$i]:(((subset @ X354 @ (cartprod @ X351 @ X352))=>(![X355:$i]:(((in @ X355 @ X351)=>![X356:$i]:(((in @ X356 @ X352)=>((in @ (kpair @ X355 @ X356) @ X353)=>(in @ (kpair @ X355 @ X356) @ X354))))))=>(![X357:$i]:(((in @ X357 @ X351)=>![X358:$i]:(((in @ X358 @ X352)=>((in @ (kpair @ X357 @ X358) @ X354)=>(in @ (kpair @ X357 @ X358) @ X353))))))=>((X353)=(X354))))))))=>((funcext)=>(![X359:$i, X360:$i, X361:$i]:(((in @ X361 @ (funcSet @ X359 @ X360))=>![X362:$i]:(((in @ X362 @ (funcSet @ X359 @ X360))=>(![X363:$i]:(((in @ X363 @ X359)=>((ap @ X359 @ X360 @ X361 @ X363)=(ap @ X359 @ X360 @ X362 @ X363))))=>((X361)=(X362)))))))=>(![X364:$i, X365:$i, X366:$i]:(((in @ X366 @ (funcSet @ X364 @ X365))=>![X367:$i]:(((in @ X367 @ X364)=>((ap @ X364 @ X365 @ X366 @ X367)=(ap @ X364 @ X365 @ X366 @ X367))))))=>((ap2apEq2)=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ X37) @ X2)=(X37 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_52]), c_0_53]), c_0_54]), c_0_55]), cartprodsndpairEq]), ksndpairEq]), cartprodfstpairEq]), kfstpairEq]), kpairsurjEq]), c_0_56]), c_0_57]), kpairp]), kpairiskpair]), c_0_58]), c_0_59]), c_0_60]), c_0_61]), cartprodpairsurjEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), cartprodfstin]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ap2apEq1]), funcext2]), funcGraphProp4]), funcGraphProp3]), funcinfuncset]), ap2p]), infuncsetfunc]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), c_0_69]), c_0_70]), c_0_71])])).
% 82.87/12.47 thf(c_0_74, plain, ![X30:$i > $i, X2:$i]:(((epred1_1 @ X30 @ X2)=($eq @ (X30 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_72])).
% 82.87/12.47 thf(c_0_75, negated_conjecture, ![X371:$i, X372:$i, X373:$i, X374:$i, X375:$i, X376:$i, X377:$i, X378:$i, X379:$i, X380:$i, X381:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i > $o, X391:$i, X393:$i, X395:$i, X396:$i, X397:$i, X398:$i, X399:$i, X400:$i, X401:$i, X402:$i, X404:$i, X405:$i, X406:$i, X407:$i, X408:$i, X409:$i, X410:$i, X411:$i, X412:$i, X413:$i, X414:$i, X415:$i, X416:$i, X417:$i, X418:$i, X419:$i, X420:$i, X421:$i, X422:$i, X423:$i, X424:$i, X425:$i, X426:$i, X427:$i, X428:$i, X429:$i, X430:$i, X431:$i > $i > $o, X432:$i, X433:$i, X434:$i, X435:$i, X436:$i > $i > $o, X437:$i, X438:$i, X439:$i > $i > $o, X440:$i, X441:$i, X442:$i > $i > $o, X443:$i, X444:$i, X445:$i, X446:$i, X447:$i > $i > $o, X448:$i, X449:$i, X450:$i, X451:$i, X452:$i > $i > $o, X453:$i, X454:$i, X455:$i, X456:$i, X457:$i > $i > $o, X458:$i, X459:$i, X460:$i, X461:$i, X462:$i, X463:$i, X465:$i, X466:$i, X467:$i, X468:$i, X469:$i, X470:$i, X471:$i, X472:$i, X473:$i, X474:$i, X475:$i, X476:$i, X477:$i > $i, X479:$i, X480:$i, X481:$i > $i, X483:$i, X484:$i, X485:$i > $i, X487:$i, X488:$i, X489:$i, X490:$i > $o, X493:$i, X494:$i, X495:$i, X496:$i, X497:$i > $o, X500:$i, X501:$i, X502:$i, X503:$i, X504:$i, X505:$i, X506:$i, X507:$i, X508:$i, X509:$i, X510:$i, X511:$i, X512:$i, X513:$i, X516:$i, X517:$i, X518:$i, X519:$i, X524:$i, X525:$i, X526:$i, X527:$i, X529:$i, X530:$i, X531:$i, X532:$i, X536:$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)&((iskpair @ (setadjoin @ (setadjoin @ X371 @ emptyset) @ (setadjoin @ (setadjoin @ X371 @ (setadjoin @ X372 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X373 @ X374))&((singletonsubset)&((singletoninpowerset)&((singletoninpowunion)&((upairset2E)&((upairsubunion)&((upairinpowunion)&((ubforcartprodlem1)&((ubforcartprodlem2)&((ubforcartprodlem3)&((~(in @ X377 @ X375)|(~(in @ X378 @ X376)|(in @ (kpair @ X377 @ X378) @ (cartprod @ X375 @ X376))))&((((in @ (esk1_3 @ X379 @ X380 @ X381) @ X379)|~(in @ X381 @ (cartprod @ X379 @ X380)))&(((in @ (esk2_3 @ X379 @ X380 @ X381) @ X380)|~(in @ X381 @ (cartprod @ X379 @ X380)))&(((X381)=(kpair @ (esk1_3 @ X379 @ X380 @ X381) @ (esk2_3 @ X379 @ X380 @ X381)))|~(in @ X381 @ (cartprod @ X379 @ X380)))))&((~(in @ X386 @ (cartprod @ X384 @ X385))|(iskpair @ X386))&((setunionE2)&((setunionsingleton1)&((setunionsingleton2)&((setunionsingleton)&(((((in @ (esk5_2 @ X387 @ X388) @ (dsetconstr @ X387 @ X388))|(~(in @ X391 @ X387)|~(X388 @ X391))|(in @ (esk3_2 @ X387 @ X388) @ X387))&(((dsetconstr @ X387 @ X388)=(setadjoin @ (esk5_2 @ X387 @ X388) @ emptyset))|(~(in @ X391 @ X387)|~(X388 @ X391))|(in @ (esk3_2 @ X387 @ X388) @ X387)))&((((in @ (esk5_2 @ X387 @ X388) @ (dsetconstr @ X387 @ X388))|(~(in @ X391 @ X387)|~(X388 @ X391))|(in @ (esk4_2 @ X387 @ X388) @ X387))&(((dsetconstr @ X387 @ X388)=(setadjoin @ (esk5_2 @ X387 @ X388) @ emptyset))|(~(in @ X391 @ X387)|~(X388 @ X391))|(in @ (esk4_2 @ X387 @ X388) @ X387)))&((((in @ (esk5_2 @ X387 @ X388) @ (dsetconstr @ X387 @ X388))|(~(in @ X391 @ X387)|~(X388 @ X391))|(X388 @ (esk3_2 @ X387 @ X388)))&(((dsetconstr @ X387 @ X388)=(setadjoin @ (esk5_2 @ X387 @ X388) @ emptyset))|(~(in @ X391 @ X387)|~(X388 @ X391))|(X388 @ (esk3_2 @ X387 @ X388))))&((((in @ (esk5_2 @ X387 @ X388) @ (dsetconstr @ X387 @ X388))|(~(in @ X391 @ X387)|~(X388 @ X391))|(X388 @ (esk4_2 @ X387 @ X388)))&(((dsetconstr @ X387 @ X388)=(setadjoin @ (esk5_2 @ X387 @ X388) @ emptyset))|(~(in @ X391 @ X387)|~(X388 @ X391))|(X388 @ (esk4_2 @ X387 @ X388))))&(((in @ (esk5_2 @ X387 @ X388) @ (dsetconstr @ X387 @ X388))|(~(in @ X391 @ X387)|~(X388 @ X391))|((esk3_2 @ X387 @ X388)!=(esk4_2 @ X387 @ X388)))&(((dsetconstr @ X387 @ X388)=(setadjoin @ (esk5_2 @ X387 @ X388) @ emptyset))|(~(in @ X391 @ X387)|~(X388 @ X391))|((esk3_2 @ X387 @ X388)!=(esk4_2 @ X387 @ X388))))))))&((ex1E1)&((ex1I)&((ex1I2)&((singletonsuniq)&((setukpairinjL1)&((((in @ (esk6_1 @ X393) @ (dsetconstr @ (setunion @ X393) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X393)))))|~(iskpair @ X393))&(((dsetconstr @ (setunion @ X393) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X393))))=(setadjoin @ (esk6_1 @ X393) @ emptyset))|~(iskpair @ X393)))&((~(in @ X396 @ X395)|((X395)!=(setadjoin @ X396 @ emptyset))|(in @ (setunion @ X395) @ X395))&(((kfst @ (kpair @ X397 @ X398))=(X397))&((~(in @ X401 @ (cartprod @ X399 @ X400))|(in @ (kfst @ X401) @ X399))&((setukpairinjL2)&((setukpairinjL)&((setukpairinjR11)&((setukpairinjR12)&((setukpairinjR1)&((upairequniteq)&((setukpairinjR2)&((setukpairinjR)&((((in @ (esk7_1 @ X402) @ (dsetconstr @ (setunion @ X402) @ (^[Z0:$i]:(((X402)=(kpair @ (kfst @ X402) @ Z0))))))|~(iskpair @ X402))&(((dsetconstr @ (setunion @ X402) @ (^[Z0:$i]:(((X402)=(kpair @ (kfst @ X402) @ Z0)))))=(setadjoin @ (esk7_1 @ X402) @ emptyset))|~(iskpair @ X402)))&(((ksnd @ (kpair @ X404 @ X405))=(X405))&((~(iskpair @ X406)|((kpair @ (kfst @ X406) @ (ksnd @ X406))=(X406)))&((~(in @ X409 @ (cartprod @ X407 @ X408))|(in @ (ksnd @ X409) @ X408))&((~(in @ (kpair @ X412 @ X413) @ (cartprod @ X410 @ X411))|(in @ X412 @ X410))&((~(in @ (kpair @ X416 @ X417) @ (cartprod @ X414 @ X415))|(in @ X417 @ X415))&((cartprodmempaircEq)&((~(in @ X420 @ X418)|(~(in @ X421 @ X419)|((kfst @ (kpair @ X420 @ X421))=(X420))))&((~(in @ X424 @ X422)|(~(in @ X425 @ X423)|((ksnd @ (kpair @ X424 @ X425))=(X425))))&((~(in @ X428 @ (cartprod @ X426 @ X427))|((kpair @ (kfst @ X428) @ (ksnd @ X428))=(X428)))&((~(in @ X432 @ X429)|(~(in @ X433 @ X430)|(~(X431 @ X432 @ X433)|(in @ (kpair @ X432 @ X433) @ (dpsetconstr @ X429 @ X430 @ X431)))))&((subset @ (dpsetconstr @ X434 @ X435 @ X436) @ (cartprod @ X434 @ X435))&((subset @ (dpsetconstr @ X437 @ X438 @ X439) @ (cartprod @ X437 @ X438))&((~(in @ X443 @ X440)|(~(in @ X444 @ X441)|(~(in @ (kpair @ X443 @ X444) @ (dpsetconstr @ X440 @ X441 @ X442))|(X442 @ X443 @ X444))))&((~(in @ (kpair @ X448 @ X449) @ (dpsetconstr @ X445 @ X446 @ X447))|(in @ X448 @ X445))&((~(in @ (kpair @ X453 @ X454) @ (dpsetconstr @ X450 @ X451 @ X452))|(in @ X454 @ X451))&((~(in @ (kpair @ X458 @ X459) @ (dpsetconstr @ X455 @ X456 @ X457))|(X457 @ X458 @ X459))&((((in @ (esk8_4 @ X460 @ X461 @ X462 @ X463) @ (dsetconstr @ X461 @ (^[Z0:$i]:((in @ (kpair @ X463 @ Z0) @ X462)))))|~(in @ X463 @ X460)|~(func @ X460 @ X461 @ X462))&(((dsetconstr @ X461 @ (^[Z0:$i]:((in @ (kpair @ X463 @ Z0) @ X462))))=(setadjoin @ (esk8_4 @ X460 @ X461 @ X462 @ X463) @ emptyset))|~(in @ X463 @ X460)|~(func @ X460 @ X461 @ X462)))&((apProp)&((app)&((~(in @ X467 @ (funcSet @ X465 @ X466))|(func @ X465 @ X466 @ X467))&((~(in @ X470 @ (funcSet @ X468 @ X469))|(~(in @ X471 @ X468)|(in @ (ap @ X468 @ X469 @ X470 @ X471) @ X469)))&((~(func @ X472 @ X473 @ X474)|(in @ X474 @ (funcSet @ X472 @ X473)))&((((in @ (esk9_3 @ X475 @ X476 @ X477) @ X475)|(func @ X475 @ X476 @ (dpsetconstr @ X475 @ X476 @ (^[Z0:$i]:($eq @ (X477 @ Z0))))))&(~(in @ (X477 @ (esk9_3 @ X475 @ X476 @ X477)) @ X476)|(func @ X475 @ X476 @ (dpsetconstr @ X475 @ X476 @ (^[Z0:$i]:($eq @ (X477 @ Z0)))))))&((((in @ (esk10_3 @ X479 @ X480 @ X481) @ X479)|(func @ X479 @ X480 @ (lam @ X479 @ X480 @ X481)))&(~(in @ (X481 @ (esk10_3 @ X479 @ X480 @ X481)) @ X480)|(func @ X479 @ X480 @ (lam @ X479 @ X480 @ X481))))&((((in @ (esk11_3 @ X483 @ X484 @ X485) @ X483)|(in @ (lam @ X483 @ X484 @ X485) @ (funcSet @ X483 @ X484)))&(~(in @ (X485 @ (esk11_3 @ X483 @ X484 @ X485)) @ X484)|(in @ (lam @ X483 @ X484 @ X485) @ (funcSet @ X483 @ X484))))&((((in @ (esk12_4 @ X487 @ X488 @ X489 @ X490) @ X487)|(~(in @ X493 @ X489)|(X490 @ X493))|~(subset @ X489 @ (cartprod @ X487 @ X488)))&(((in @ (esk13_4 @ X487 @ X488 @ X489 @ X490) @ X488)|(~(in @ X493 @ X489)|(X490 @ X493))|~(subset @ X489 @ (cartprod @ X487 @ X488)))&(((in @ (kpair @ (esk12_4 @ X487 @ X488 @ X489 @ X490) @ (esk13_4 @ X487 @ X488 @ X489 @ X490)) @ X489)|(~(in @ X493 @ X489)|(X490 @ X493))|~(subset @ X489 @ (cartprod @ X487 @ X488)))&(~(X490 @ (kpair @ (esk12_4 @ X487 @ X488 @ X489 @ X490) @ (esk13_4 @ X487 @ X488 @ X489 @ X490)))|(~(in @ X493 @ X489)|(X490 @ X493))|~(subset @ X489 @ (cartprod @ X487 @ X488))))))&((((in @ (esk14_4 @ X494 @ X495 @ X496 @ X497) @ X494)|(~(in @ X500 @ X496)|(X497 @ X500))|~(subset @ X496 @ (cartprod @ X494 @ X495)))&(((in @ (esk15_4 @ X494 @ X495 @ X496 @ X497) @ X495)|(~(in @ X500 @ X496)|(X497 @ X500))|~(subset @ X496 @ (cartprod @ X494 @ X495)))&(((in @ (kpair @ (esk14_4 @ X494 @ X495 @ X496 @ X497) @ (esk15_4 @ X494 @ X495 @ X496 @ X497)) @ X496)|(~(in @ X500 @ X496)|(X497 @ X500))|~(subset @ X496 @ (cartprod @ X494 @ X495)))&(~(X497 @ (kpair @ (esk14_4 @ X494 @ X495 @ X496 @ X497) @ (esk15_4 @ X494 @ X495 @ X496 @ X497)))|(~(in @ X500 @ X496)|(X497 @ X500))|~(subset @ X496 @ (cartprod @ X494 @ X495))))))&((ex1E2)&((funcGraphProp1)&((~(in @ X503 @ (funcSet @ X501 @ X502))|(~(in @ X504 @ X501)|(in @ (kpair @ X504 @ (ap @ X501 @ X502 @ X503 @ X504)) @ X503)))&((funcGraphProp2)&((funcextLem)&((~(in @ X507 @ (funcSet @ X505 @ X506))|(~(in @ X508 @ X505)|(~(in @ X509 @ X506)|(~(in @ (kpair @ X508 @ X509) @ X507)|((ap @ X505 @ X506 @ X507 @ X508)=(X509))))))&((((in @ (esk16_4 @ X510 @ X511 @ X512 @ X513) @ X510)|(subset @ X512 @ X513)|~(subset @ X513 @ (cartprod @ X510 @ X511))|~(subset @ X512 @ (cartprod @ X510 @ X511)))&(((in @ (esk17_4 @ X510 @ X511 @ X512 @ X513) @ X511)|(subset @ X512 @ X513)|~(subset @ X513 @ (cartprod @ X510 @ X511))|~(subset @ X512 @ (cartprod @ X510 @ X511)))&(((in @ (kpair @ (esk16_4 @ X510 @ X511 @ X512 @ X513) @ (esk17_4 @ X510 @ X511 @ X512 @ X513)) @ X512)|(subset @ X512 @ X513)|~(subset @ X513 @ (cartprod @ X510 @ X511))|~(subset @ X512 @ (cartprod @ X510 @ X511)))&(~(in @ (kpair @ (esk16_4 @ X510 @ X511 @ X512 @ X513) @ (esk17_4 @ X510 @ X511 @ X512 @ X513)) @ X513)|(subset @ X512 @ X513)|~(subset @ X513 @ (cartprod @ X510 @ X511))|~(subset @ X512 @ (cartprod @ X510 @ X511))))))&(((((in @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ X516)|((X518)=(X519))|(in @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ X516)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(((in @ (esk21_4 @ X516 @ X517 @ X518 @ X519) @ X517)|((X518)=(X519))|(in @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ X516)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(((in @ (kpair @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ (esk21_4 @ X516 @ X517 @ X518 @ X519)) @ X519)|((X518)=(X519))|(in @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ X516)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(~(in @ (kpair @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ (esk21_4 @ X516 @ X517 @ X518 @ X519)) @ X518)|((X518)=(X519))|(in @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ X516)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517))))))&((((in @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ X516)|((X518)=(X519))|(in @ (esk19_4 @ X516 @ X517 @ X518 @ X519) @ X517)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(((in @ (esk21_4 @ X516 @ X517 @ X518 @ X519) @ X517)|((X518)=(X519))|(in @ (esk19_4 @ X516 @ X517 @ X518 @ X519) @ X517)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(((in @ (kpair @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ (esk21_4 @ X516 @ X517 @ X518 @ X519)) @ X519)|((X518)=(X519))|(in @ (esk19_4 @ X516 @ X517 @ X518 @ X519) @ X517)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(~(in @ (kpair @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ (esk21_4 @ X516 @ X517 @ X518 @ X519)) @ X518)|((X518)=(X519))|(in @ (esk19_4 @ X516 @ X517 @ X518 @ X519) @ X517)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517))))))&((((in @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ X516)|((X518)=(X519))|(in @ (kpair @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ (esk19_4 @ X516 @ X517 @ X518 @ X519)) @ X518)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(((in @ (esk21_4 @ X516 @ X517 @ X518 @ X519) @ X517)|((X518)=(X519))|(in @ (kpair @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ (esk19_4 @ X516 @ X517 @ X518 @ X519)) @ X518)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(((in @ (kpair @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ (esk21_4 @ X516 @ X517 @ X518 @ X519)) @ X519)|((X518)=(X519))|(in @ (kpair @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ (esk19_4 @ X516 @ X517 @ X518 @ X519)) @ X518)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(~(in @ (kpair @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ (esk21_4 @ X516 @ X517 @ X518 @ X519)) @ X518)|((X518)=(X519))|(in @ (kpair @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ (esk19_4 @ X516 @ X517 @ X518 @ X519)) @ X518)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517))))))&(((in @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ X516)|((X518)=(X519))|~(in @ (kpair @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ (esk19_4 @ X516 @ X517 @ X518 @ X519)) @ X519)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(((in @ (esk21_4 @ X516 @ X517 @ X518 @ X519) @ X517)|((X518)=(X519))|~(in @ (kpair @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ (esk19_4 @ X516 @ X517 @ X518 @ X519)) @ X519)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(((in @ (kpair @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ (esk21_4 @ X516 @ X517 @ X518 @ X519)) @ X519)|((X518)=(X519))|~(in @ (kpair @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ (esk19_4 @ X516 @ X517 @ X518 @ X519)) @ X519)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))&(~(in @ (kpair @ (esk20_4 @ X516 @ X517 @ X518 @ X519) @ (esk21_4 @ X516 @ X517 @ X518 @ X519)) @ X518)|((X518)=(X519))|~(in @ (kpair @ (esk18_4 @ X516 @ X517 @ X518 @ X519) @ (esk19_4 @ X516 @ X517 @ X518 @ X519)) @ X519)|~(subset @ X519 @ (cartprod @ X516 @ X517))|~(subset @ X518 @ (cartprod @ X516 @ X517)))))))))&((funcext)&((((in @ (esk22_4 @ X524 @ X525 @ X526 @ X527) @ X524)|((X526)=(X527))|~(in @ X527 @ (funcSet @ X524 @ X525))|~(in @ X526 @ (funcSet @ X524 @ X525)))&(((ap @ X524 @ X525 @ X526 @ (esk22_4 @ X524 @ X525 @ X526 @ X527))!=(ap @ X524 @ X525 @ X527 @ (esk22_4 @ X524 @ X525 @ X526 @ X527)))|((X526)=(X527))|~(in @ X527 @ (funcSet @ X524 @ X525))|~(in @ X526 @ (funcSet @ X524 @ X525))))&((~(in @ X531 @ (funcSet @ X529 @ X530))|(~(in @ X532 @ X529)|((ap @ X529 @ X530 @ X531 @ X532)=(ap @ X529 @ X530 @ X531 @ X532))))&((ap2apEq2)&((~(in @ X536 @ esk23_0)|(in @ (esk25_0 @ X536) @ esk24_0))&((in @ esk26_0 @ esk23_0)&((ap @ esk23_0 @ esk24_0 @ (lam @ esk23_0 @ esk24_0 @ esk25_0) @ esk26_0)!=(esk25_0 @ esk26_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_73])])])])])])).
% 82.87/12.47 thf(c_0_76, plain, ![X368:$i, X369:$i, X370:$i > $i]:(((lam @ X368 @ X369 @ X370)=(dpsetconstr @ X368 @ X369 @ (^[Z0:$i]:($eq @ (X370 @ Z0)))))), inference(fool_unroll,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[lam])])])).
% 82.87/12.47 thf(c_0_77, plain, ![X2:$i, X30:$i > $i, X559:$i]:(((epred1_1 @ X30 @ X2 @ X559)<=>((X30 @ X2)=(X559)))), inference(arg_cong,[status(thm)],[c_0_74])).
% 82.87/12.47 thf(c_0_78, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i, X6:$i > $i > $o]:(((X6 @ X2 @ X3)|~((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ X6))))), inference(split_conjunct,[status(thm)],[c_0_75])).
% 82.87/12.47 thf(c_0_79, negated_conjecture, ![X2:$i, X5:$i, X4:$i, X3:$i]:(((in @ (kpair @ X5 @ (ap @ X3 @ X4 @ X2 @ X5)) @ X2)|~((in @ X2 @ (funcSet @ X3 @ X4)))|~((in @ X5 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_75])).
% 82.87/12.47 thf(c_0_80, plain, ![X538:$i, X539:$i, X540:$i > $i]:(((lam @ X538 @ X539 @ X540)=(dpsetconstr @ X538 @ X539 @ (^[Z0:$i]:($eq @ (X540 @ Z0)))))), inference(variable_rename,[status(thm)],[c_0_76])).
% 82.87/12.47 thf(c_0_81, plain, ![X541:$i, X30:$i > $i]:(((epred1_1 @ X30 @ X541)=($eq @ (X30 @ X541)))), introduced(definition)).
% 82.87/12.47 thf(c_0_82, plain, ![X2:$i, X30:$i > $i, X3:$i]:((((X30 @ X2)=(X3))|~((epred1_1 @ X30 @ X2 @ X3)))), inference(dynamic_cnf,[status(thm)],[c_0_77])).
% 82.87/12.47 thf(c_0_83, negated_conjecture, ![X7:$i, X2:$i, X5:$i, X6:$i > $i > $o, X4:$i, X3:$i]:(((X6 @ X2 @ (ap @ X3 @ X4 @ (dpsetconstr @ X5 @ X7 @ X6) @ X2))|~((in @ (dpsetconstr @ X5 @ X7 @ X6) @ (funcSet @ X3 @ X4)))|~((in @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_78, c_0_79])).
% 82.87/12.47 thf(c_0_84, plain, ![X2:$i, X3:$i, X30:$i > $i]:(((lam @ X2 @ X3 @ X30)=(dpsetconstr @ X2 @ X3 @ (epred1_1 @ X30)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_80]), c_0_81])).
% 82.87/12.47 thf(c_0_85, negated_conjecture, ((ap @ esk23_0 @ esk24_0 @ (lam @ esk23_0 @ esk24_0 @ esk25_0) @ esk26_0)!=(esk25_0 @ esk26_0)), inference(split_conjunct,[status(thm)],[c_0_75])).
% 82.87/12.47 thf(c_0_86, plain, ![X7:$i, X30:$i > $i, X5:$i, X4:$i, X3:$i, X2:$i]:((((ap @ X2 @ X3 @ (lam @ X4 @ X5 @ X30) @ X7)=(X30 @ X7))|~((in @ (lam @ X4 @ X5 @ X30) @ (funcSet @ X2 @ X3)))|~((in @ X7 @ X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83]), c_0_84]), c_0_84])).
% 82.87/12.47 thf(c_0_87, negated_conjecture, (in @ esk26_0 @ esk23_0), inference(split_conjunct,[status(thm)],[c_0_75])).
% 82.87/12.47 thf(c_0_88, negated_conjecture, ![X2:$i, X30:$i > $i, X3:$i]:(((in @ (lam @ X2 @ X3 @ X30) @ (funcSet @ X2 @ X3))|~((in @ (X30 @ (esk11_3 @ X2 @ X3 @ X30)) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_75])).
% 82.87/12.47 thf(c_0_89, negated_conjecture, ![X2:$i]:(((in @ (esk25_0 @ X2) @ esk24_0)|~((in @ X2 @ esk23_0)))), inference(split_conjunct,[status(thm)],[c_0_75])).
% 82.87/12.47 thf(c_0_90, negated_conjecture, ~((in @ (lam @ esk23_0 @ esk24_0 @ esk25_0) @ (funcSet @ esk23_0 @ esk24_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_86]), c_0_87])])).
% 82.87/12.47 thf(c_0_91, negated_conjecture, ![X2:$i, X30:$i > $i, X3:$i]:(((in @ (esk11_3 @ X2 @ X3 @ X30) @ X2)|(in @ (lam @ X2 @ X3 @ X30) @ (funcSet @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_75])).
% 82.87/12.47 thf(c_0_92, negated_conjecture, ![X2:$i]:(((in @ (lam @ X2 @ esk24_0 @ esk25_0) @ (funcSet @ X2 @ esk24_0))|~((in @ (esk11_3 @ X2 @ esk24_0 @ esk25_0) @ esk23_0)))), inference(spm,[status(thm)],[c_0_88, c_0_89])).
% 82.87/12.47 thf(c_0_93, negated_conjecture, (in @ (esk11_3 @ esk23_0 @ esk24_0 @ esk25_0) @ esk23_0), inference(spm,[status(thm)],[c_0_90, c_0_91])).
% 82.87/12.47 thf(c_0_94, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_92]), c_0_93])]), ['proof']).
% 82.87/12.47 % SZS output end CNFRefutation
% 82.87/12.47 % Parsed axioms : 466
% 82.87/12.47 % Removed by relevancy pruning/SinE : 420
% 82.87/12.47 % Initial clauses : 264
% 82.87/12.47 % Removed in clause preprocessing : 1
% 82.87/12.47 % Initial clauses in saturation : 263
% 82.87/12.47 % Processed clauses : 12781
% 82.87/12.47 % ...of these trivial : 32
% 82.87/12.47 % ...subsumed : 8570
% 82.87/12.47 % ...remaining for further processing : 4178
% 82.87/12.47 % Other redundant clauses eliminated : 2
% 82.87/12.47 % Clauses deleted for lack of memory : 0
% 82.87/12.47 % Backward-subsumed : 118
% 82.87/12.47 % Backward-rewritten : 0
% 82.87/12.47 % Generated clauses : 322592
% 82.87/12.47 % ...of the previous two non-redundant : 321833
% 82.87/12.47 % ...aggressively subsumed : 0
% 82.87/12.47 % Contextual simplify-reflections : 63
% 82.87/12.47 % Paramodulations : 322473
% 82.87/12.47 % Factorizations : 0
% 82.87/12.47 % NegExts : 0
% 82.87/12.47 % Equation resolutions : 116
% 82.87/12.47 % Disequality decompositions : 0
% 82.87/12.47 % Total rewrite steps : 52036
% 82.87/12.47 % ...of those cached : 50587
% 82.87/12.47 % Propositional unsat checks : 0
% 82.87/12.47 % Propositional check models : 0
% 82.87/12.47 % Propositional check unsatisfiable : 0
% 82.87/12.47 % Propositional clauses : 0
% 82.87/12.47 % Propositional clauses after purity: 0
% 82.87/12.47 % Propositional unsat core size : 0
% 82.87/12.47 % Propositional preprocessing time : 0.000
% 82.87/12.47 % Propositional encoding time : 0.000
% 82.87/12.47 % Propositional solver time : 0.000
% 82.87/12.47 % Success case prop preproc time : 0.000
% 82.87/12.47 % Success case prop encoding time : 0.000
% 82.87/12.47 % Success case prop solver time : 0.000
% 82.87/12.47 % Current number of processed clauses : 4058
% 82.87/12.47 % Positive orientable unit clauses : 188
% 82.87/12.47 % Positive unorientable unit clauses: 0
% 82.87/12.47 % Negative unit clauses : 2
% 82.87/12.47 % Non-unit-clauses : 3868
% 82.87/12.47 % Current number of unprocessed clauses: 309086
% 82.87/12.47 % ...number of literals in the above : 1643722
% 82.87/12.47 % Current number of archived formulas : 0
% 82.87/12.47 % Current number of archived clauses : 119
% 82.87/12.47 % Clause-clause subsumption calls (NU) : 1739385
% 82.87/12.47 % Rec. Clause-clause subsumption calls : 835647
% 82.87/12.47 % Non-unit clause-clause subsumptions : 8751
% 82.87/12.47 % Unit Clause-clause subsumption calls : 1371
% 82.87/12.47 % Rewrite failures with RHS unbound : 0
% 82.87/12.47 % BW rewrite match attempts : 2
% 82.87/12.47 % BW rewrite match successes : 0
% 82.87/12.47 % Condensation attempts : 0
% 82.87/12.47 % Condensation successes : 0
% 82.87/12.47 % Termbank termtop insertions : 10873843
% 82.87/12.47 % Search garbage collected termcells : 9055
% 82.87/12.47
% 82.87/12.47 % -------------------------------------------------
% 82.87/12.47 % User time : 10.961 s
% 82.87/12.47 % System time : 0.327 s
% 82.87/12.47 % Total time : 11.289 s
% 82.87/12.47 % Maximum resident set size: 6428 pages
% 82.87/12.47
% 82.87/12.47 % -------------------------------------------------
% 82.87/12.47 % User time : 10.973 s
% 82.87/12.47 % System time : 0.335 s
% 82.87/12.47 % Total time : 11.308 s
% 82.87/12.47 % Maximum resident set size: 5376 pages
% 82.87/12.47 % E exiting
%------------------------------------------------------------------------------