%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU704^1 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:25:16 AM UTC 2026
% Result : Theorem 3.93s 0.95s
% Output : CNFRefutation 3.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU704^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n026.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 14:15:12 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running higher-order theorem proving
% 0.25/0.31 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.dwAaJNS78v/E---3.1_661821.p
% 3.93/0.95 % Version: 3.5.1-ho
% 3.93/0.95 % Preprocessing class: HSLMSLSSLLLCHSA.
% 3.93/0.95 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 3.93/0.95 % Starting ho_unfolding_5 with 1200s (4) cores
% 3.93/0.95 % Starting pre_casc_3 with 300s (1) cores
% 3.93/0.95 % Starting new_ho_10_cnf2 with 300s (1) cores
% 3.93/0.95 % Starting full_lambda_10 with 300s (1) cores
% 3.93/0.95 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 3.93/0.95 % pre_casc_3 with pid 661841 completed with status 0
% 3.93/0.95 % Result found by pre_casc_3
% 3.93/0.95 % Preprocessing class: HSLMSLSSLLLCHSA.
% 3.93/0.95 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 3.93/0.95 % Starting ho_unfolding_5 with 1200s (4) cores
% 3.93/0.95 % Starting pre_casc_3 with 300s (1) cores
% 3.93/0.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 3.93/0.95 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 3.93/0.95 % Search class: HGHSM-FSLM32-MHSMMSBN
% 3.93/0.95 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 3.93/0.95 % Starting SubtermCWHack with 31s (1) cores
% 3.93/0.95 % SubtermCWHack with pid 661846 completed with status 0
% 3.93/0.95 % Result found by SubtermCWHack
% 3.93/0.95 % Preprocessing class: HSLMSLSSLLLCHSA.
% 3.93/0.95 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 3.93/0.95 % Starting ho_unfolding_5 with 1200s (4) cores
% 3.93/0.95 % Starting pre_casc_3 with 300s (1) cores
% 3.93/0.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 3.93/0.95 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 3.93/0.95 % Search class: HGHSM-FSLM32-MHSMMSBN
% 3.93/0.95 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 3.93/0.95 % Starting SubtermCWHack with 31s (1) cores
% 3.93/0.95 % Preprocessing time : 0.004 s
% 3.93/0.95
% 3.93/0.95 % Proof found!
% 3.93/0.95 % SZS status Theorem
% 3.93/0.95 % SZS output start CNFRefutation
% 3.93/0.95 thf(decl_23, type, in: $i > $i > $o).
% 3.93/0.95 thf(decl_25, type, setextAx: $o).
% 3.93/0.95 thf(decl_26, type, emptyset: $i).
% 3.93/0.95 thf(decl_27, type, emptysetAx: $o).
% 3.93/0.95 thf(decl_28, type, setadjoin: $i > $i > $i).
% 3.93/0.95 thf(decl_29, type, setadjoinAx: $o).
% 3.93/0.95 thf(decl_31, type, powersetAx: $o).
% 3.93/0.95 thf(decl_32, type, setunion: $i > $i).
% 3.93/0.95 thf(decl_33, type, setunionAx: $o).
% 3.93/0.95 thf(decl_35, type, omega0Ax: $o).
% 3.93/0.95 thf(decl_36, type, omegaSAx: $o).
% 3.93/0.95 thf(decl_37, type, omegaIndAx: $o).
% 3.93/0.95 thf(decl_38, type, replAx: $o).
% 3.93/0.95 thf(decl_39, type, foundationAx: $o).
% 3.93/0.95 thf(decl_40, type, wellorderingAx: $o).
% 3.93/0.95 thf(decl_42, type, descrp: $o).
% 3.93/0.95 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_44, type, dsetconstrI: $o).
% 3.93/0.95 thf(decl_45, type, dsetconstrEL: $o).
% 3.93/0.95 thf(decl_46, type, dsetconstrER: $o).
% 3.93/0.95 thf(decl_47, type, exuE1: $o).
% 3.93/0.95 thf(decl_49, type, prop2setE: $o).
% 3.93/0.95 thf(decl_50, type, emptysetE: $o).
% 3.93/0.95 thf(decl_51, type, emptysetimpfalse: $o).
% 3.93/0.95 thf(decl_52, type, notinemptyset: $o).
% 3.93/0.95 thf(decl_53, type, exuE3e: $o).
% 3.93/0.95 thf(decl_54, type, setext: $o).
% 3.93/0.95 thf(decl_55, type, emptyI: $o).
% 3.93/0.95 thf(decl_56, type, noeltsimpempty: $o).
% 3.93/0.95 thf(decl_57, type, setbeta: $o).
% 3.93/0.95 thf(decl_59, type, nonemptyE1: $o).
% 3.93/0.95 thf(decl_60, type, nonemptyI: $o).
% 3.93/0.95 thf(decl_61, type, nonemptyI1: $o).
% 3.93/0.95 thf(decl_62, type, setadjoinIL: $o).
% 3.93/0.95 thf(decl_63, type, emptyinunitempty: $o).
% 3.93/0.95 thf(decl_64, type, setadjoinIR: $o).
% 3.93/0.95 thf(decl_65, type, setadjoinE: $o).
% 3.93/0.95 thf(decl_66, type, setadjoinOr: $o).
% 3.93/0.95 thf(decl_67, type, setoftrueEq: $o).
% 3.93/0.95 thf(decl_68, type, powersetI: $o).
% 3.93/0.95 thf(decl_69, type, emptyinPowerset: $o).
% 3.93/0.95 thf(decl_70, type, emptyInPowerset: $o).
% 3.93/0.95 thf(decl_71, type, powersetE: $o).
% 3.93/0.95 thf(decl_72, type, setunionI: $o).
% 3.93/0.95 thf(decl_73, type, setunionE: $o).
% 3.93/0.95 thf(decl_74, type, subPowSU: $o).
% 3.93/0.95 thf(decl_75, type, exuE2: $o).
% 3.93/0.95 thf(decl_76, type, nonemptyImpWitness: $o).
% 3.93/0.95 thf(decl_77, type, uniqinunit: $o).
% 3.93/0.95 thf(decl_78, type, notinsingleton: $o).
% 3.93/0.95 thf(decl_79, type, eqinunit: $o).
% 3.93/0.95 thf(decl_80, type, singletonsswitch: $o).
% 3.93/0.95 thf(decl_81, type, upairsetE: $o).
% 3.93/0.95 thf(decl_82, type, upairsetIL: $o).
% 3.93/0.95 thf(decl_83, type, upairsetIR: $o).
% 3.93/0.95 thf(decl_84, type, emptyE1: $o).
% 3.93/0.95 thf(decl_85, type, vacuousDall: $o).
% 3.93/0.95 thf(decl_86, type, quantDeMorgan1: $o).
% 3.93/0.95 thf(decl_87, type, quantDeMorgan2: $o).
% 3.93/0.95 thf(decl_88, type, quantDeMorgan3: $o).
% 3.93/0.95 thf(decl_89, type, quantDeMorgan4: $o).
% 3.93/0.95 thf(decl_90, type, prop2setI: $o).
% 3.93/0.95 thf(decl_92, type, prop2set2propI: $o).
% 3.93/0.95 thf(decl_93, type, notdexE: $o).
% 3.93/0.95 thf(decl_94, type, notdallE: $o).
% 3.93/0.95 thf(decl_95, type, exuI1: $o).
% 3.93/0.95 thf(decl_96, type, exuI3: $o).
% 3.93/0.95 thf(decl_97, type, exuI2: $o).
% 3.93/0.95 thf(decl_98, type, inCongP: $o).
% 3.93/0.95 thf(decl_99, type, in__Cong: $o).
% 3.93/0.95 thf(decl_100, type, exuE3u: $o).
% 3.93/0.95 thf(decl_101, type, exu__Cong: $o).
% 3.93/0.95 thf(decl_102, type, emptyset__Cong: $o).
% 3.93/0.95 thf(decl_103, type, setadjoin__Cong: $o).
% 3.93/0.95 thf(decl_104, type, powerset__Cong: $o).
% 3.93/0.95 thf(decl_105, type, setunion__Cong: $o).
% 3.93/0.95 thf(decl_106, type, omega__Cong: $o).
% 3.93/0.95 thf(decl_107, type, exuEu: $o).
% 3.93/0.95 thf(decl_108, type, descr__Cong: $o).
% 3.93/0.95 thf(decl_109, type, dsetconstr__Cong: $o).
% 3.93/0.95 thf(decl_110, type, subset: $i > $i > $o).
% 3.93/0.95 thf(decl_113, type, subsetI1: $o).
% 3.93/0.95 thf(decl_114, type, eqimpsubset2: $o).
% 3.93/0.95 thf(decl_115, type, eqimpsubset1: $o).
% 3.93/0.95 thf(decl_116, type, subsetI2: $o).
% 3.93/0.95 thf(decl_117, type, emptysetsubset: $o).
% 3.93/0.95 thf(decl_118, type, subsetE: $o).
% 3.93/0.95 thf(decl_119, type, subsetE2: $o).
% 3.93/0.95 thf(decl_120, type, notsubsetI: $o).
% 3.93/0.95 thf(decl_121, type, notequalI1: $o).
% 3.93/0.95 thf(decl_122, type, notequalI2: $o).
% 3.93/0.95 thf(decl_123, type, subsetRefl: $o).
% 3.93/0.95 thf(decl_124, type, subsetTrans: $o).
% 3.93/0.95 thf(decl_125, type, setadjoinSub: $o).
% 3.93/0.95 thf(decl_126, type, setadjoinSub2: $o).
% 3.93/0.95 thf(decl_127, type, subset2powerset: $o).
% 3.93/0.95 thf(decl_128, type, setextsub: $o).
% 3.93/0.95 thf(decl_129, type, subsetemptysetimpeq: $o).
% 3.93/0.95 thf(decl_130, type, powersetI1: $o).
% 3.93/0.95 thf(decl_131, type, powersetE1: $o).
% 3.93/0.95 thf(decl_132, type, inPowerset: $o).
% 3.93/0.95 thf(decl_133, type, powersetsubset: $o).
% 3.93/0.95 thf(decl_134, type, sepInPowerset: $o).
% 3.93/0.95 thf(decl_135, type, sepSubset: $o).
% 3.93/0.95 thf(decl_137, type, binunionIL: $o).
% 3.93/0.95 thf(decl_138, type, upairset2IR: $o).
% 3.93/0.95 thf(decl_139, type, binunionIR: $o).
% 3.93/0.95 thf(decl_140, type, binunionEcases: $o).
% 3.93/0.95 thf(decl_141, type, binunionE: $o).
% 3.93/0.95 thf(decl_142, type, binunionLsub: $o).
% 3.93/0.95 thf(decl_143, type, binunionRsub: $o).
% 3.93/0.95 thf(decl_145, type, binintersectI: $o).
% 3.93/0.95 thf(decl_146, type, binintersectSubset5: $o).
% 3.93/0.95 thf(decl_147, type, binintersectEL: $o).
% 3.93/0.95 thf(decl_148, type, binintersectLsub: $o).
% 3.93/0.95 thf(decl_149, type, binintersectSubset2: $o).
% 3.93/0.95 thf(decl_150, type, binintersectSubset3: $o).
% 3.93/0.95 thf(decl_151, type, binintersectER: $o).
% 3.93/0.95 thf(decl_152, type, disjointsetsI1: $o).
% 3.93/0.95 thf(decl_153, type, binintersectRsub: $o).
% 3.93/0.95 thf(decl_154, type, binintersectSubset4: $o).
% 3.93/0.95 thf(decl_155, type, binintersectSubset1: $o).
% 3.93/0.95 thf(decl_156, type, bs114d: $o).
% 3.93/0.95 thf(decl_159, type, setminusI: $o).
% 3.93/0.95 thf(decl_160, type, setminusEL: $o).
% 3.93/0.95 thf(decl_161, type, setminusER: $o).
% 3.93/0.95 thf(decl_162, type, setminusSubset2: $o).
% 3.93/0.95 thf(decl_163, type, setminusERneg: $o).
% 3.93/0.95 thf(decl_164, type, setminusELneg: $o).
% 3.93/0.95 thf(decl_165, type, setminusILneg: $o).
% 3.93/0.95 thf(decl_166, type, setminusIRneg: $o).
% 3.93/0.95 thf(decl_167, type, setminusLsub: $o).
% 3.93/0.95 thf(decl_168, type, setminusSubset1: $o).
% 3.93/0.95 thf(decl_170, type, symdiffE: $o).
% 3.93/0.95 thf(decl_171, type, symdiffI1: $o).
% 3.93/0.95 thf(decl_172, type, symdiffI2: $o).
% 3.93/0.95 thf(decl_173, type, symdiffIneg1: $o).
% 3.93/0.95 thf(decl_174, type, symdiffIneg2: $o).
% 3.93/0.95 thf(decl_175, type, iskpair: $i > $o).
% 3.93/0.95 thf(decl_176, type, secondinupair: $o).
% 3.93/0.95 thf(decl_177, type, setukpairIL: $o).
% 3.93/0.95 thf(decl_178, type, setukpairIR: $o).
% 3.93/0.95 thf(decl_179, type, kpairiskpair: $o).
% 3.93/0.95 thf(decl_180, type, kpair: $i > $i > $i).
% 3.93/0.95 thf(decl_181, type, kpairp: $o).
% 3.93/0.95 thf(decl_182, type, cartprod: $i > $i > $i).
% 3.93/0.95 thf(decl_183, type, singletonsubset: $o).
% 3.93/0.95 thf(decl_184, type, singletoninpowerset: $o).
% 3.93/0.95 thf(decl_185, type, singletoninpowunion: $o).
% 3.93/0.95 thf(decl_186, type, upairset2E: $o).
% 3.93/0.95 thf(decl_187, type, upairsubunion: $o).
% 3.93/0.95 thf(decl_188, type, upairinpowunion: $o).
% 3.93/0.95 thf(decl_189, type, ubforcartprodlem1: $o).
% 3.93/0.95 thf(decl_190, type, ubforcartprodlem2: $o).
% 3.93/0.95 thf(decl_191, type, ubforcartprodlem3: $o).
% 3.93/0.95 thf(decl_192, type, cartprodpairin: $o).
% 3.93/0.95 thf(decl_193, type, cartprodmempair1: $o).
% 3.93/0.95 thf(decl_194, type, cartprodmempair: $o).
% 3.93/0.95 thf(decl_195, type, setunionE2: $o).
% 3.93/0.95 thf(decl_196, type, setunionsingleton1: $o).
% 3.93/0.95 thf(decl_197, type, setunionsingleton2: $o).
% 3.93/0.95 thf(decl_198, type, setunionsingleton: $o).
% 3.93/0.95 thf(decl_199, type, singleton: $i > $o).
% 3.93/0.95 thf(decl_200, type, singletonprop: $o).
% 3.93/0.95 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 3.93/0.95 thf(decl_202, type, ex1E1: $o).
% 3.93/0.95 thf(decl_203, type, ex1I: $o).
% 3.93/0.95 thf(decl_204, type, ex1I2: $o).
% 3.93/0.95 thf(decl_205, type, singletonsuniq: $o).
% 3.93/0.95 thf(decl_210, type, setukpairinjL1: $o).
% 3.93/0.95 thf(decl_211, type, kfstsingleton: $o).
% 3.93/0.95 thf(decl_212, type, theprop: $o).
% 3.93/0.95 thf(decl_213, type, kfst: $i > $i).
% 3.93/0.95 thf(decl_214, type, kfstpairEq: $o).
% 3.93/0.95 thf(decl_215, type, cartprodfstin: $o).
% 3.93/0.95 thf(decl_216, type, setukpairinjL2: $o).
% 3.93/0.95 thf(decl_217, type, setukpairinjL: $o).
% 3.93/0.95 thf(decl_218, type, setukpairinjR11: $o).
% 3.93/0.95 thf(decl_219, type, setukpairinjR12: $o).
% 3.93/0.95 thf(decl_220, type, setukpairinjR1: $o).
% 3.93/0.95 thf(decl_221, type, upairequniteq: $o).
% 3.93/0.95 thf(decl_222, type, setukpairinjR2: $o).
% 3.93/0.95 thf(decl_223, type, setukpairinjR: $o).
% 3.93/0.95 thf(decl_224, type, ksndsingleton: $o).
% 3.93/0.95 thf(decl_225, type, ksnd: $i > $i).
% 3.93/0.95 thf(decl_226, type, ksndpairEq: $o).
% 3.93/0.95 thf(decl_227, type, kpairsurjEq: $o).
% 3.93/0.95 thf(decl_228, type, cartprodsndin: $o).
% 3.93/0.95 thf(decl_229, type, cartprodpairmemEL: $o).
% 3.93/0.95 thf(decl_230, type, cartprodpairmemER: $o).
% 3.93/0.95 thf(decl_231, type, cartprodmempaircEq: $o).
% 3.93/0.95 thf(decl_232, type, cartprodfstpairEq: $o).
% 3.93/0.95 thf(decl_233, type, cartprodsndpairEq: $o).
% 3.93/0.95 thf(decl_234, type, cartprodpairsurjEq: $o).
% 3.93/0.95 thf(decl_235, type, breln: $i > $i > $i > $o).
% 3.93/0.95 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 3.93/0.95 thf(decl_237, type, dpsetconstrI: $o).
% 3.93/0.95 thf(decl_238, type, dpsetconstrSub: $o).
% 3.93/0.95 thf(decl_239, type, setOfPairsIsBReln: $o).
% 3.93/0.95 thf(decl_240, type, dpsetconstrERa: $o).
% 3.93/0.95 thf(decl_241, type, dpsetconstrEL1: $o).
% 3.93/0.95 thf(decl_242, type, dpsetconstrEL2: $o).
% 3.93/0.95 thf(decl_243, type, dpsetconstrER: $o).
% 3.93/0.95 thf(decl_244, type, func: $i > $i > $i > $o).
% 3.93/0.95 thf(decl_246, type, funcImageSingleton: $o).
% 3.93/0.95 thf(decl_247, type, apProp: $o).
% 3.93/0.95 thf(decl_249, type, app: $o).
% 3.93/0.95 thf(decl_250, type, infuncsetfunc: $o).
% 3.93/0.95 thf(decl_251, type, ap2p: $o).
% 3.93/0.95 thf(decl_252, type, funcinfuncset: $o).
% 3.93/0.95 thf(decl_253, type, lamProp: $o).
% 3.93/0.95 thf(decl_255, type, lamp: $o).
% 3.93/0.95 thf(decl_256, type, lam2p: $o).
% 3.93/0.95 thf(decl_257, type, brelnall1: $o).
% 3.93/0.95 thf(decl_258, type, brelnall2: $o).
% 3.93/0.95 thf(decl_259, type, ex1E2: $o).
% 3.93/0.95 thf(decl_260, type, funcGraphProp1: $o).
% 3.93/0.95 thf(decl_261, type, funcGraphProp3: $o).
% 3.93/0.95 thf(decl_262, type, funcGraphProp2: $o).
% 3.93/0.95 thf(decl_263, type, funcextLem: $o).
% 3.93/0.95 thf(decl_264, type, funcGraphProp4: $o).
% 3.93/0.95 thf(decl_265, type, subbreln: $o).
% 3.93/0.95 thf(decl_266, type, eqbreln: $o).
% 3.93/0.95 thf(decl_267, type, funcext: $o).
% 3.93/0.95 thf(decl_268, type, funcext2: $o).
% 3.93/0.95 thf(decl_269, type, ap2apEq1: $o).
% 3.93/0.95 thf(decl_270, type, ap2apEq2: $o).
% 3.93/0.95 thf(decl_271, type, beta1: $o).
% 3.93/0.95 thf(decl_272, type, eta1: $o).
% 3.93/0.95 thf(decl_273, type, lam2lamEq: $o).
% 3.93/0.95 thf(decl_274, type, beta2: $o).
% 3.93/0.95 thf(decl_275, type, eta2: $o).
% 3.93/0.95 thf(decl_276, type, iffalseProp1: $o).
% 3.93/0.95 thf(decl_277, type, iffalseProp2: $o).
% 3.93/0.95 thf(decl_278, type, iftrueProp1: $o).
% 3.93/0.95 thf(decl_279, type, iftrueProp2: $o).
% 3.93/0.95 thf(decl_280, type, esk1_3: $i > $i > $i > $i).
% 3.93/0.95 thf(decl_281, type, esk2_3: $i > $i > $i > $i).
% 3.93/0.95 thf(decl_282, type, esk3_2: $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_283, type, esk4_2: $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_284, type, esk5_2: $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_285, type, esk6_2: $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_286, type, esk7_3: $i > ($i > $o) > $i > $i).
% 3.93/0.95 thf(decl_287, type, esk8_3: $i > ($i > $o) > $i > $i).
% 3.93/0.95 thf(decl_288, type, esk9_2: $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_289, type, esk10_2: $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_290, type, esk11_2: $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_291, type, esk12_1: $i > $i).
% 3.93/0.95 thf(decl_292, type, esk13_1: $i > $i).
% 3.93/0.95 thf(decl_293, type, esk14_4: $i > $i > $i > $i > $i).
% 3.93/0.95 thf(decl_294, type, esk15_3: $i > $i > ($i > $i) > $i).
% 3.93/0.95 thf(decl_295, type, esk16_4: $i > $i > $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_296, type, esk17_4: $i > $i > $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_297, type, esk18_4: $i > $i > $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_298, type, esk19_4: $i > $i > $i > ($i > $o) > $i).
% 3.93/0.95 thf(decl_299, type, esk20_4: $i > $i > $i > $i > $i).
% 3.93/0.95 thf(decl_300, type, esk21_4: $i > $i > $i > $i > $i).
% 3.93/0.95 thf(decl_301, type, esk22_4: $i > $i > $i > $i > $i).
% 3.93/0.95 thf(decl_302, type, esk23_4: $i > $i > $i > $i > $i).
% 3.93/0.95 thf(decl_303, type, esk24_4: $i > $i > $i > $i > $i).
% 3.93/0.95 thf(decl_304, type, esk25_4: $i > $i > $i > $i > $i).
% 3.93/0.95 thf(decl_305, type, esk26_0: $i).
% 3.93/0.95 thf(decl_306, type, epred1_0: $o).
% 3.93/0.95 thf(decl_307, type, esk27_0: $i).
% 3.93/0.95 thf(decl_308, type, esk28_0: $i).
% 3.93/0.95 thf(decl_309, type, epred2_0: $i > $o).
% 3.93/0.95 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', ex1)).
% 3.93/0.95 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', singleton)).
% 3.93/0.95 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', breln)).
% 3.93/0.95 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', setOfPairsIsBReln)).
% 3.93/0.95 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', ex1E2)).
% 3.93/0.95 thf(ex1I2, axiom, ((ex1I2)<=>![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)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', ex1I2)).
% 3.93/0.95 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', ex1I)).
% 3.93/0.95 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', ex1E1)).
% 3.93/0.95 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', funcImageSingleton)).
% 3.93/0.95 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', ksndsingleton)).
% 3.93/0.95 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', kfstsingleton)).
% 3.93/0.95 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', singletonprop)).
% 3.93/0.95 thf(ifSingleton, 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)=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', ifSingleton)).
% 3.93/0.95 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', lamProp)).
% 3.93/0.95 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', dpsetconstrER)).
% 3.93/0.95 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', dpsetconstrEL2)).
% 3.93/0.95 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', dpsetconstrEL1)).
% 3.93/0.95 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', dpsetconstrERa)).
% 3.93/0.95 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', dpsetconstrI)).
% 3.93/0.95 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', eqbreln)).
% 3.93/0.95 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', subbreln)).
% 3.93/0.95 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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.dwAaJNS78v/E---3.1_661821.p', brelnall2)).
% 3.93/0.95 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.dwAaJNS78v/E---3.1_661821.p', brelnall1)).
% 3.93/0.95 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', dpsetconstrSub)).
% 3.93/0.95 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', theprop)).
% 3.93/0.95 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', cartprodsndpairEq)).
% 3.93/0.95 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', ksndpairEq)).
% 3.93/0.95 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', cartprodpairmemER)).
% 3.93/0.95 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', cartprodpairmemEL)).
% 3.93/0.95 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', cartprodsndin)).
% 3.93/0.95 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', cartprodmempair1)).
% 3.93/0.95 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', cartprodpairin)).
% 3.93/0.95 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', cartprodpairsurjEq)).
% 3.93/0.95 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', cartprodfstpairEq)).
% 3.93/0.95 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', cartprodfstin)).
% 3.93/0.95 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', kfstpairEq)).
% 3.93/0.95 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', kpairsurjEq)).
% 3.93/0.95 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', cartprodmempair)).
% 3.93/0.95 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', kpairp)).
% 3.93/0.95 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dwAaJNS78v/E---3.1_661821.p', kpairiskpair)).
% 3.93/0.95 thf(c_0_40, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X186:$i]:((((in @ X186 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X186 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 3.93/0.95 thf(c_0_41, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 3.93/0.95 thf(c_0_42, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 3.93/0.95 thf(c_0_43, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 3.93/0.95 thf(c_0_44, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 3.93/0.95 thf(c_0_45, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X186:$i]:((((in @ X186 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X186 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_40, c_0_41])).
% 3.93/0.95 thf(c_0_46, plain, ((ex1I2)<=>![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)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 3.93/0.95 thf(c_0_47, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 3.93/0.95 thf(c_0_48, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 3.93/0.95 thf(c_0_49, plain, ((funcImageSingleton)<=>![X4:$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])).
% 3.93/0.95 thf(c_0_50, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 3.93/0.95 thf(c_0_51, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 3.93/0.95 thf(c_0_52, 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])).
% 3.93/0.95 thf(c_0_53, 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)=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[ifSingleton])).
% 3.93/0.95 thf(c_0_54, 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])).
% 3.93/0.95 thf(c_0_55, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 3.93/0.95 thf(c_0_56, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 3.93/0.95 thf(c_0_57, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 3.93/0.95 thf(c_0_58, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 3.93/0.95 thf(c_0_59, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 3.93/0.95 thf(c_0_60, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_42])).
% 3.93/0.95 thf(c_0_61, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_42])).
% 3.93/0.95 thf(c_0_62, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_42])).
% 3.93/0.95 thf(c_0_63, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_42])).
% 3.93/0.95 thf(c_0_64, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_43, c_0_42])).
% 3.93/0.95 thf(c_0_65, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 3.93/0.95 thf(c_0_66, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((?[X194:$i]:((((in @ X194 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X194 @ emptyset)))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_44, c_0_45])).
% 3.93/0.95 thf(c_0_67, plain, ((ex1I2)=(![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)))))=>((?[X189:$i]:((((in @ X189 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X189 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_46, c_0_45])).
% 3.93/0.95 thf(c_0_68, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X188:$i]:((((in @ X188 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X188 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_45])).
% 3.93/0.95 thf(c_0_69, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X187:$i]:((((in @ X187 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X187 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_48, c_0_45])).
% 3.93/0.95 thf(c_0_70, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:((((func @ X4 @ X5 @ X29))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X193:$i]:((((in @ X193 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X193 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[c_0_49, c_0_41])).
% 3.93/0.95 thf(c_0_71, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X192:$i]:((((in @ X192 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X192 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_50, c_0_41])).
% 3.93/0.95 thf(c_0_72, axiom, ((theprop)=(![X21:$i]:((((?[X191:$i]:((((in @ X191 @ X21))&(((X21)=(setadjoin @ X191 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_41])).
% 3.93/0.95 thf(c_0_73, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X190:$i]:((((in @ X190 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X190 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_51, c_0_41])).
% 3.93/0.95 thf(c_0_74, 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)))))=>((?[X185:$i]:((((in @ X185 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X185 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_52, c_0_41])).
% 3.93/0.95 thf(c_0_75, 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)=>(![X195:$i, X196:$i]:((iskpair @ (setadjoin @ (setadjoin @ X195 @ emptyset) @ (setadjoin @ (setadjoin @ X195 @ (setadjoin @ X196 @ emptyset)) @ emptyset))))=>(![X197:$i, X198:$i]:((iskpair @ (kpair @ X197 @ X198)))=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>(![X199:$i, X200:$i, X201:$i]:(((in @ X201 @ X199)=>![X202:$i]:(((in @ X202 @ X200)=>(in @ (kpair @ X201 @ X202) @ (cartprod @ X199 @ X200))))))=>(![X203:$i, X204:$i, X205:$i]:(((in @ X205 @ (cartprod @ X203 @ X204))=>?[X206:$i]:(((in @ X206 @ X203)&?[X207:$i]:(((in @ X207 @ X204)&((X205)=(kpair @ X206 @ X207))))))))=>(![X208:$i, X209:$i, X210:$i]:(((in @ X210 @ (cartprod @ X208 @ X209))=>(iskpair @ X210)))=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(![X211:$i, X212:$i > $o]:((![X213:$i]:(((in @ X213 @ X211)=>![X214:$i]:(((in @ X214 @ X211)=>((X212 @ X213)=>((X212 @ X214)=>((X213)=(X214))))))))=>(?[X215:$i]:(((in @ X215 @ X211)&(X212 @ X215)))=>?[X216:$i]:(((in @ X216 @ (dsetconstr @ X211 @ X212))&((dsetconstr @ X211 @ X212)=(setadjoin @ X216 @ emptyset)))))))=>(![X217:$i, X218:$i > $o]:((?[X219:$i]:(((in @ X219 @ (dsetconstr @ X217 @ X218))&((dsetconstr @ X217 @ X218)=(setadjoin @ X219 @ emptyset))))=>?[X220:$i]:(((in @ X220 @ X217)&(X218 @ X220)))))=>(![X221:$i, X222:$i > $o, X223:$i]:(((in @ X223 @ X221)=>((X222 @ X223)=>(![X224:$i]:(((in @ X224 @ X221)=>((X222 @ X224)=>((X224)=(X223)))))=>?[X225:$i]:(((in @ X225 @ (dsetconstr @ X221 @ X222))&((dsetconstr @ X221 @ X222)=(setadjoin @ X225 @ emptyset))))))))=>(![X226:$i, X227:$i > $o]:((![X228:$i]:(((in @ X228 @ X226)=>![X229:$i]:(((in @ X229 @ X226)=>((X227 @ X228)=>((X227 @ X229)=>((X228)=(X229))))))))=>(?[X230:$i]:(((in @ X230 @ X226)&(X227 @ X230)))=>?[X231:$i]:(((in @ X231 @ (dsetconstr @ X226 @ X227))&((dsetconstr @ X226 @ X227)=(setadjoin @ X231 @ emptyset)))))))=>((singletonsuniq)=>((setukpairinjL1)=>(![X232:$i]:(((iskpair @ X232)=>?[X233:$i]:(((in @ X233 @ (dsetconstr @ (setunion @ X232) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X232)))))&((dsetconstr @ (setunion @ X232) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X232))))=(setadjoin @ X233 @ emptyset))))))=>(![X234:$i]:((?[X235:$i]:(((in @ X235 @ X234)&((X234)=(setadjoin @ X235 @ emptyset))))=>(in @ (setunion @ X234) @ X234)))=>(![X236:$i, X237:$i]:(((kfst @ (kpair @ X236 @ X237))=(X236)))=>(![X238:$i, X239:$i, X240:$i]:(((in @ X240 @ (cartprod @ X238 @ X239))=>(in @ (kfst @ X240) @ X238)))=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>(![X241:$i]:(((iskpair @ X241)=>?[X242:$i]:(((in @ X242 @ (dsetconstr @ (setunion @ X241) @ (^[Z0:$i]:(((X241)=(kpair @ (kfst @ X241) @ Z0))))))&((dsetconstr @ (setunion @ X241) @ (^[Z0:$i]:(((X241)=(kpair @ (kfst @ X241) @ Z0)))))=(setadjoin @ X242 @ emptyset))))))=>(![X243:$i, X244:$i]:(((ksnd @ (kpair @ X243 @ X244))=(X244)))=>(![X245:$i]:(((iskpair @ X245)=>((kpair @ (kfst @ X245) @ (ksnd @ X245))=(X245))))=>(![X246:$i, X247:$i, X248:$i]:(((in @ X248 @ (cartprod @ X246 @ X247))=>(in @ (ksnd @ X248) @ X247)))=>(![X249:$i, X250:$i, X251:$i, X252:$i]:(((in @ (kpair @ X251 @ X252) @ (cartprod @ X249 @ X250))=>(in @ X251 @ X249)))=>(![X253:$i, X254:$i, X255:$i, X256:$i]:(((in @ (kpair @ X255 @ X256) @ (cartprod @ X253 @ X254))=>(in @ X256 @ X254)))=>((cartprodmempaircEq)=>(![X257:$i, X258:$i, X259:$i]:(((in @ X259 @ X257)=>![X260:$i]:(((in @ X260 @ X258)=>((kfst @ (kpair @ X259 @ X260))=(X259))))))=>(![X261:$i, X262:$i, X263:$i]:(((in @ X263 @ X261)=>![X264:$i]:(((in @ X264 @ X262)=>((ksnd @ (kpair @ X263 @ X264))=(X264))))))=>(![X265:$i, X266:$i, X267:$i]:(((in @ X267 @ (cartprod @ X265 @ X266))=>((kpair @ (kfst @ X267) @ (ksnd @ X267))=(X267))))=>(![X268:$i, X269:$i, X270:$i > $i > $o, X271:$i]:(((in @ X271 @ X268)=>![X272:$i]:(((in @ X272 @ X269)=>((X270 @ X271 @ X272)=>(in @ (kpair @ X271 @ X272) @ (dpsetconstr @ X268 @ X269 @ X270)))))))=>(![X273:$i, X274:$i, X275:$i > $i > $o]:((subset @ (dpsetconstr @ X273 @ X274 @ X275) @ (cartprod @ X273 @ X274)))=>(![X276:$i, X277:$i, X278:$i > $i > $o]:((subset @ (dpsetconstr @ X276 @ X277 @ X278) @ (cartprod @ X276 @ X277)))=>(![X279:$i, X280:$i, X281:$i > $i > $o, X282:$i]:(((in @ X282 @ X279)=>![X283:$i]:(((in @ X283 @ X280)=>((in @ (kpair @ X282 @ X283) @ (dpsetconstr @ X279 @ X280 @ X281))=>(X281 @ X282 @ X283))))))=>(![X284:$i, X285:$i, X286:$i > $i > $o, X287:$i, X288:$i]:(((in @ (kpair @ X287 @ X288) @ (dpsetconstr @ X284 @ X285 @ X286))=>(in @ X287 @ X284)))=>(![X289:$i, X290:$i, X291:$i > $i > $o, X292:$i, X293:$i]:(((in @ (kpair @ X292 @ X293) @ (dpsetconstr @ X289 @ X290 @ X291))=>(in @ X293 @ X290)))=>(![X294:$i, X295:$i, X296:$i > $i > $o, X297:$i, X298:$i]:(((in @ (kpair @ X297 @ X298) @ (dpsetconstr @ X294 @ X295 @ X296))=>(X296 @ X297 @ X298)))=>(![X299:$i, X300:$i, X301:$i]:(((func @ X299 @ X300 @ X301)=>![X302:$i]:(((in @ X302 @ X299)=>?[X303:$i]:(((in @ X303 @ (dsetconstr @ X300 @ (^[Z0:$i]:((in @ (kpair @ X302 @ Z0) @ X301)))))&((dsetconstr @ X300 @ (^[Z0:$i]:((in @ (kpair @ X302 @ Z0) @ X301))))=(setadjoin @ X303 @ emptyset))))))))=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>(![X304:$i, X305:$i, X306:$i > $i]:((![X307:$i]:(((in @ X307 @ X304)=>(in @ (X306 @ X307) @ X305)))=>(func @ X304 @ X305 @ (dpsetconstr @ X304 @ X305 @ (^[Z0:$i]:($eq @ (X306 @ Z0)))))))=>((lamp)=>((lam2p)=>(![X308:$i, X309:$i, X310:$i]:(((subset @ X310 @ (cartprod @ X308 @ X309))=>![X311:$i > $o]:((![X312:$i]:(((in @ X312 @ X308)=>![X313:$i]:(((in @ X313 @ X309)=>((in @ (kpair @ X312 @ X313) @ X310)=>(X311 @ (kpair @ X312 @ X313)))))))=>![X314:$i]:(((in @ X314 @ X310)=>(X311 @ X314)))))))=>(![X315:$i, X316:$i, X317:$i]:(((subset @ X317 @ (cartprod @ X315 @ X316))=>![X318:$i > $o]:((![X319:$i]:(((in @ X319 @ X315)=>![X320:$i]:(((in @ X320 @ X316)=>((in @ (kpair @ X319 @ X320) @ X317)=>(X318 @ (kpair @ X319 @ X320)))))))=>![X321:$i]:(((in @ X321 @ X317)=>(X318 @ X321)))))))=>(![X322:$i, X323:$i > $o]:((?[X324:$i]:(((in @ X324 @ (dsetconstr @ X322 @ X323))&((dsetconstr @ X322 @ X323)=(setadjoin @ X324 @ emptyset))))=>![X325:$i]:(((in @ X325 @ X322)=>![X326:$i]:(((in @ X326 @ X322)=>((X323 @ X325)=>((X323 @ X326)=>((X325)=(X326))))))))))=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(![X327:$i, X328:$i, X329:$i]:(((subset @ X329 @ (cartprod @ X327 @ X328))=>![X330:$i]:(((subset @ X330 @ (cartprod @ X327 @ X328))=>(![X331:$i]:(((in @ X331 @ X327)=>![X332:$i]:(((in @ X332 @ X328)=>((in @ (kpair @ X331 @ X332) @ X329)=>(in @ (kpair @ X331 @ X332) @ X330))))))=>(subset @ X329 @ X330))))))=>(![X333:$i, X334:$i, X335:$i]:(((subset @ X335 @ (cartprod @ X333 @ X334))=>![X336:$i]:(((subset @ X336 @ (cartprod @ X333 @ X334))=>(![X337:$i]:(((in @ X337 @ X333)=>![X338:$i]:(((in @ X338 @ X334)=>((in @ (kpair @ X337 @ X338) @ X335)=>(in @ (kpair @ X337 @ X338) @ X336))))))=>(![X339:$i]:(((in @ X339 @ X333)=>![X340:$i]:(((in @ X340 @ X334)=>((in @ (kpair @ X339 @ X340) @ X336)=>(in @ (kpair @ X339 @ X340) @ X335))))))=>((X335)=(X336))))))))=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>?[X341:$i]:(((in @ X341 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))&((dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3)))))))))=(setadjoin @ X341 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(fof_simplification,[status(thm)],[c_0_53]), c_0_54]), c_0_55]), c_0_56]), c_0_57]), c_0_58]), c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), cartprodsndpairEq]), ksndpairEq]), c_0_65]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), cartprodmempair1]), cartprodpairin]), cartprodpairsurjEq]), cartprodfstpairEq]), cartprodfstin]), kfstpairEq]), kpairsurjEq]), cartprodmempair]), kpairp]), kpairiskpair]), c_0_66]), c_0_67]), c_0_68]), c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), c_0_74]), c_0_41])])).
% 3.93/0.95 thf(c_0_76, negated_conjecture, ![X342:$i, X343:$i, X344:$i, X345:$i, X346:$i, X347:$i, X348:$i, X349:$i, X350:$i, X351:$i, X352:$i, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i > $o, X362:$i, X364:$i, X365:$i > $o, X366:$i, X368:$i, X369:$i > $o, X370:$i, X373:$i, X374:$i > $o, X377:$i, X379:$i, X381:$i, X382:$i, X383:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i, X390:$i, X391:$i, X392:$i, X393:$i, X394:$i, X395:$i, X396:$i, X397:$i, X398:$i, X399:$i, X400:$i, X401:$i, X402:$i, X403:$i, X404:$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 > $i > $o, X418:$i, X419:$i, X420:$i, X421:$i, X422:$i > $i > $o, X423:$i, X424:$i, X425:$i > $i > $o, X426:$i, X427:$i, X428:$i > $i > $o, X429:$i, X430:$i, X431:$i, X432:$i, X433:$i > $i > $o, X434:$i, X435:$i, X436:$i, X437:$i, X438:$i > $i > $o, X439:$i, X440:$i, X441:$i, X442:$i, X443:$i > $i > $o, X444:$i, X445:$i, X446:$i, X447:$i, X448:$i, X449:$i, X451:$i, X452:$i, X453:$i > $i, X455:$i, X456:$i, X457:$i, X458:$i > $o, X461:$i, X462:$i, X463:$i, X464:$i, X465:$i > $o, X468:$i, X469:$i, X470:$i > $o, X471:$i, X472:$i, X473:$i, X474:$i, X475:$i, X476:$i, X477:$i, X480:$i, X481:$i, X482:$i, X483:$i, X492:$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 @ X342 @ emptyset) @ (setadjoin @ (setadjoin @ X342 @ (setadjoin @ X343 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X344 @ X345))&((singletonsubset)&((singletoninpowerset)&((singletoninpowunion)&((upairset2E)&((upairsubunion)&((upairinpowunion)&((ubforcartprodlem1)&((ubforcartprodlem2)&((ubforcartprodlem3)&((~(in @ X348 @ X346)|(~(in @ X349 @ X347)|(in @ (kpair @ X348 @ X349) @ (cartprod @ X346 @ X347))))&((((in @ (esk1_3 @ X350 @ X351 @ X352) @ X350)|~(in @ X352 @ (cartprod @ X350 @ X351)))&(((in @ (esk2_3 @ X350 @ X351 @ X352) @ X351)|~(in @ X352 @ (cartprod @ X350 @ X351)))&(((X352)=(kpair @ (esk1_3 @ X350 @ X351 @ X352) @ (esk2_3 @ X350 @ X351 @ X352)))|~(in @ X352 @ (cartprod @ X350 @ X351)))))&((~(in @ X357 @ (cartprod @ X355 @ X356))|(iskpair @ X357))&((setunionE2)&((setunionsingleton1)&((setunionsingleton2)&((setunionsingleton)&(((((in @ (esk5_2 @ X358 @ X359) @ (dsetconstr @ X358 @ X359))|(~(in @ X362 @ X358)|~(X359 @ X362))|(in @ (esk3_2 @ X358 @ X359) @ X358))&(((dsetconstr @ X358 @ X359)=(setadjoin @ (esk5_2 @ X358 @ X359) @ emptyset))|(~(in @ X362 @ X358)|~(X359 @ X362))|(in @ (esk3_2 @ X358 @ X359) @ X358)))&((((in @ (esk5_2 @ X358 @ X359) @ (dsetconstr @ X358 @ X359))|(~(in @ X362 @ X358)|~(X359 @ X362))|(in @ (esk4_2 @ X358 @ X359) @ X358))&(((dsetconstr @ X358 @ X359)=(setadjoin @ (esk5_2 @ X358 @ X359) @ emptyset))|(~(in @ X362 @ X358)|~(X359 @ X362))|(in @ (esk4_2 @ X358 @ X359) @ X358)))&((((in @ (esk5_2 @ X358 @ X359) @ (dsetconstr @ X358 @ X359))|(~(in @ X362 @ X358)|~(X359 @ X362))|(X359 @ (esk3_2 @ X358 @ X359)))&(((dsetconstr @ X358 @ X359)=(setadjoin @ (esk5_2 @ X358 @ X359) @ emptyset))|(~(in @ X362 @ X358)|~(X359 @ X362))|(X359 @ (esk3_2 @ X358 @ X359))))&((((in @ (esk5_2 @ X358 @ X359) @ (dsetconstr @ X358 @ X359))|(~(in @ X362 @ X358)|~(X359 @ X362))|(X359 @ (esk4_2 @ X358 @ X359)))&(((dsetconstr @ X358 @ X359)=(setadjoin @ (esk5_2 @ X358 @ X359) @ emptyset))|(~(in @ X362 @ X358)|~(X359 @ X362))|(X359 @ (esk4_2 @ X358 @ X359))))&(((in @ (esk5_2 @ X358 @ X359) @ (dsetconstr @ X358 @ X359))|(~(in @ X362 @ X358)|~(X359 @ X362))|((esk3_2 @ X358 @ X359)!=(esk4_2 @ X358 @ X359)))&(((dsetconstr @ X358 @ X359)=(setadjoin @ (esk5_2 @ X358 @ X359) @ emptyset))|(~(in @ X362 @ X358)|~(X359 @ X362))|((esk3_2 @ X358 @ X359)!=(esk4_2 @ X358 @ X359))))))))&((((in @ (esk6_2 @ X364 @ X365) @ X364)|(~(in @ X366 @ (dsetconstr @ X364 @ X365))|((dsetconstr @ X364 @ X365)!=(setadjoin @ X366 @ emptyset))))&((X365 @ (esk6_2 @ X364 @ X365))|(~(in @ X366 @ (dsetconstr @ X364 @ X365))|((dsetconstr @ X364 @ X365)!=(setadjoin @ X366 @ emptyset)))))&(((((in @ (esk8_3 @ X368 @ X369 @ X370) @ (dsetconstr @ X368 @ X369))|(in @ (esk7_3 @ X368 @ X369 @ X370) @ X368)|~(X369 @ X370)|~(in @ X370 @ X368))&(((dsetconstr @ X368 @ X369)=(setadjoin @ (esk8_3 @ X368 @ X369 @ X370) @ emptyset))|(in @ (esk7_3 @ X368 @ X369 @ X370) @ X368)|~(X369 @ X370)|~(in @ X370 @ X368)))&((((in @ (esk8_3 @ X368 @ X369 @ X370) @ (dsetconstr @ X368 @ X369))|(X369 @ (esk7_3 @ X368 @ X369 @ X370))|~(X369 @ X370)|~(in @ X370 @ X368))&(((dsetconstr @ X368 @ X369)=(setadjoin @ (esk8_3 @ X368 @ X369 @ X370) @ emptyset))|(X369 @ (esk7_3 @ X368 @ X369 @ X370))|~(X369 @ X370)|~(in @ X370 @ X368)))&(((in @ (esk8_3 @ X368 @ X369 @ X370) @ (dsetconstr @ X368 @ X369))|((esk7_3 @ X368 @ X369 @ X370)!=(X370))|~(X369 @ X370)|~(in @ X370 @ X368))&(((dsetconstr @ X368 @ X369)=(setadjoin @ (esk8_3 @ X368 @ X369 @ X370) @ emptyset))|((esk7_3 @ X368 @ X369 @ X370)!=(X370))|~(X369 @ X370)|~(in @ X370 @ X368)))))&(((((in @ (esk11_2 @ X373 @ X374) @ (dsetconstr @ X373 @ X374))|(~(in @ X377 @ X373)|~(X374 @ X377))|(in @ (esk9_2 @ X373 @ X374) @ X373))&(((dsetconstr @ X373 @ X374)=(setadjoin @ (esk11_2 @ X373 @ X374) @ emptyset))|(~(in @ X377 @ X373)|~(X374 @ X377))|(in @ (esk9_2 @ X373 @ X374) @ X373)))&((((in @ (esk11_2 @ X373 @ X374) @ (dsetconstr @ X373 @ X374))|(~(in @ X377 @ X373)|~(X374 @ X377))|(in @ (esk10_2 @ X373 @ X374) @ X373))&(((dsetconstr @ X373 @ X374)=(setadjoin @ (esk11_2 @ X373 @ X374) @ emptyset))|(~(in @ X377 @ X373)|~(X374 @ X377))|(in @ (esk10_2 @ X373 @ X374) @ X373)))&((((in @ (esk11_2 @ X373 @ X374) @ (dsetconstr @ X373 @ X374))|(~(in @ X377 @ X373)|~(X374 @ X377))|(X374 @ (esk9_2 @ X373 @ X374)))&(((dsetconstr @ X373 @ X374)=(setadjoin @ (esk11_2 @ X373 @ X374) @ emptyset))|(~(in @ X377 @ X373)|~(X374 @ X377))|(X374 @ (esk9_2 @ X373 @ X374))))&((((in @ (esk11_2 @ X373 @ X374) @ (dsetconstr @ X373 @ X374))|(~(in @ X377 @ X373)|~(X374 @ X377))|(X374 @ (esk10_2 @ X373 @ X374)))&(((dsetconstr @ X373 @ X374)=(setadjoin @ (esk11_2 @ X373 @ X374) @ emptyset))|(~(in @ X377 @ X373)|~(X374 @ X377))|(X374 @ (esk10_2 @ X373 @ X374))))&(((in @ (esk11_2 @ X373 @ X374) @ (dsetconstr @ X373 @ X374))|(~(in @ X377 @ X373)|~(X374 @ X377))|((esk9_2 @ X373 @ X374)!=(esk10_2 @ X373 @ X374)))&(((dsetconstr @ X373 @ X374)=(setadjoin @ (esk11_2 @ X373 @ X374) @ emptyset))|(~(in @ X377 @ X373)|~(X374 @ X377))|((esk9_2 @ X373 @ X374)!=(esk10_2 @ X373 @ X374))))))))&((singletonsuniq)&((setukpairinjL1)&((((in @ (esk12_1 @ X379) @ (dsetconstr @ (setunion @ X379) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X379)))))|~(iskpair @ X379))&(((dsetconstr @ (setunion @ X379) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X379))))=(setadjoin @ (esk12_1 @ X379) @ emptyset))|~(iskpair @ X379)))&((~(in @ X382 @ X381)|((X381)!=(setadjoin @ X382 @ emptyset))|(in @ (setunion @ X381) @ X381))&(((kfst @ (kpair @ X383 @ X384))=(X383))&((~(in @ X387 @ (cartprod @ X385 @ X386))|(in @ (kfst @ X387) @ X385))&((setukpairinjL2)&((setukpairinjL)&((setukpairinjR11)&((setukpairinjR12)&((setukpairinjR1)&((upairequniteq)&((setukpairinjR2)&((setukpairinjR)&((((in @ (esk13_1 @ X388) @ (dsetconstr @ (setunion @ X388) @ (^[Z0:$i]:(((X388)=(kpair @ (kfst @ X388) @ Z0))))))|~(iskpair @ X388))&(((dsetconstr @ (setunion @ X388) @ (^[Z0:$i]:(((X388)=(kpair @ (kfst @ X388) @ Z0)))))=(setadjoin @ (esk13_1 @ X388) @ emptyset))|~(iskpair @ X388)))&(((ksnd @ (kpair @ X390 @ X391))=(X391))&((~(iskpair @ X392)|((kpair @ (kfst @ X392) @ (ksnd @ X392))=(X392)))&((~(in @ X395 @ (cartprod @ X393 @ X394))|(in @ (ksnd @ X395) @ X394))&((~(in @ (kpair @ X398 @ X399) @ (cartprod @ X396 @ X397))|(in @ X398 @ X396))&((~(in @ (kpair @ X402 @ X403) @ (cartprod @ X400 @ X401))|(in @ X403 @ X401))&((cartprodmempaircEq)&((~(in @ X406 @ X404)|(~(in @ X407 @ X405)|((kfst @ (kpair @ X406 @ X407))=(X406))))&((~(in @ X410 @ X408)|(~(in @ X411 @ X409)|((ksnd @ (kpair @ X410 @ X411))=(X411))))&((~(in @ X414 @ (cartprod @ X412 @ X413))|((kpair @ (kfst @ X414) @ (ksnd @ X414))=(X414)))&((~(in @ X418 @ X415)|(~(in @ X419 @ X416)|(~(X417 @ X418 @ X419)|(in @ (kpair @ X418 @ X419) @ (dpsetconstr @ X415 @ X416 @ X417)))))&((subset @ (dpsetconstr @ X420 @ X421 @ X422) @ (cartprod @ X420 @ X421))&((subset @ (dpsetconstr @ X423 @ X424 @ X425) @ (cartprod @ X423 @ X424))&((~(in @ X429 @ X426)|(~(in @ X430 @ X427)|(~(in @ (kpair @ X429 @ X430) @ (dpsetconstr @ X426 @ X427 @ X428))|(X428 @ X429 @ X430))))&((~(in @ (kpair @ X434 @ X435) @ (dpsetconstr @ X431 @ X432 @ X433))|(in @ X434 @ X431))&((~(in @ (kpair @ X439 @ X440) @ (dpsetconstr @ X436 @ X437 @ X438))|(in @ X440 @ X437))&((~(in @ (kpair @ X444 @ X445) @ (dpsetconstr @ X441 @ X442 @ X443))|(X443 @ X444 @ X445))&((((in @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ (dsetconstr @ X447 @ (^[Z0:$i]:((in @ (kpair @ X449 @ Z0) @ X448)))))|~(in @ X449 @ X446)|~(func @ X446 @ X447 @ X448))&(((dsetconstr @ X447 @ (^[Z0:$i]:((in @ (kpair @ X449 @ Z0) @ X448))))=(setadjoin @ (esk14_4 @ X446 @ X447 @ X448 @ X449) @ emptyset))|~(in @ X449 @ X446)|~(func @ X446 @ X447 @ X448)))&((apProp)&((app)&((infuncsetfunc)&((ap2p)&((funcinfuncset)&((((in @ (esk15_3 @ X451 @ X452 @ X453) @ X451)|(func @ X451 @ X452 @ (dpsetconstr @ X451 @ X452 @ (^[Z0:$i]:($eq @ (X453 @ Z0))))))&(~(in @ (X453 @ (esk15_3 @ X451 @ X452 @ X453)) @ X452)|(func @ X451 @ X452 @ (dpsetconstr @ X451 @ X452 @ (^[Z0:$i]:($eq @ (X453 @ Z0)))))))&((lamp)&((lam2p)&((((in @ (esk16_4 @ X455 @ X456 @ X457 @ X458) @ X455)|(~(in @ X461 @ X457)|(X458 @ X461))|~(subset @ X457 @ (cartprod @ X455 @ X456)))&(((in @ (esk17_4 @ X455 @ X456 @ X457 @ X458) @ X456)|(~(in @ X461 @ X457)|(X458 @ X461))|~(subset @ X457 @ (cartprod @ X455 @ X456)))&(((in @ (kpair @ (esk16_4 @ X455 @ X456 @ X457 @ X458) @ (esk17_4 @ X455 @ X456 @ X457 @ X458)) @ X457)|(~(in @ X461 @ X457)|(X458 @ X461))|~(subset @ X457 @ (cartprod @ X455 @ X456)))&(~(X458 @ (kpair @ (esk16_4 @ X455 @ X456 @ X457 @ X458) @ (esk17_4 @ X455 @ X456 @ X457 @ X458)))|(~(in @ X461 @ X457)|(X458 @ X461))|~(subset @ X457 @ (cartprod @ X455 @ X456))))))&((((in @ (esk18_4 @ X462 @ X463 @ X464 @ X465) @ X462)|(~(in @ X468 @ X464)|(X465 @ X468))|~(subset @ X464 @ (cartprod @ X462 @ X463)))&(((in @ (esk19_4 @ X462 @ X463 @ X464 @ X465) @ X463)|(~(in @ X468 @ X464)|(X465 @ X468))|~(subset @ X464 @ (cartprod @ X462 @ X463)))&(((in @ (kpair @ (esk18_4 @ X462 @ X463 @ X464 @ X465) @ (esk19_4 @ X462 @ X463 @ X464 @ X465)) @ X464)|(~(in @ X468 @ X464)|(X465 @ X468))|~(subset @ X464 @ (cartprod @ X462 @ X463)))&(~(X465 @ (kpair @ (esk18_4 @ X462 @ X463 @ X464 @ X465) @ (esk19_4 @ X462 @ X463 @ X464 @ X465)))|(~(in @ X468 @ X464)|(X465 @ X468))|~(subset @ X464 @ (cartprod @ X462 @ X463))))))&((~(in @ X471 @ (dsetconstr @ X469 @ X470))|((dsetconstr @ X469 @ X470)!=(setadjoin @ X471 @ emptyset))|(~(in @ X472 @ X469)|(~(in @ X473 @ X469)|(~(X470 @ X472)|(~(X470 @ X473)|((X472)=(X473)))))))&((funcGraphProp1)&((funcGraphProp3)&((funcGraphProp2)&((funcextLem)&((funcGraphProp4)&((((in @ (esk20_4 @ X474 @ X475 @ X476 @ X477) @ X474)|(subset @ X476 @ X477)|~(subset @ X477 @ (cartprod @ X474 @ X475))|~(subset @ X476 @ (cartprod @ X474 @ X475)))&(((in @ (esk21_4 @ X474 @ X475 @ X476 @ X477) @ X475)|(subset @ X476 @ X477)|~(subset @ X477 @ (cartprod @ X474 @ X475))|~(subset @ X476 @ (cartprod @ X474 @ X475)))&(((in @ (kpair @ (esk20_4 @ X474 @ X475 @ X476 @ X477) @ (esk21_4 @ X474 @ X475 @ X476 @ X477)) @ X476)|(subset @ X476 @ X477)|~(subset @ X477 @ (cartprod @ X474 @ X475))|~(subset @ X476 @ (cartprod @ X474 @ X475)))&(~(in @ (kpair @ (esk20_4 @ X474 @ X475 @ X476 @ X477) @ (esk21_4 @ X474 @ X475 @ X476 @ X477)) @ X477)|(subset @ X476 @ X477)|~(subset @ X477 @ (cartprod @ X474 @ X475))|~(subset @ X476 @ (cartprod @ X474 @ X475))))))&(((((in @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ X480)|((X482)=(X483))|(in @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ X480)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(((in @ (esk25_4 @ X480 @ X481 @ X482 @ X483) @ X481)|((X482)=(X483))|(in @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ X480)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(((in @ (kpair @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ (esk25_4 @ X480 @ X481 @ X482 @ X483)) @ X483)|((X482)=(X483))|(in @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ X480)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(~(in @ (kpair @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ (esk25_4 @ X480 @ X481 @ X482 @ X483)) @ X482)|((X482)=(X483))|(in @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ X480)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481))))))&((((in @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ X480)|((X482)=(X483))|(in @ (esk23_4 @ X480 @ X481 @ X482 @ X483) @ X481)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(((in @ (esk25_4 @ X480 @ X481 @ X482 @ X483) @ X481)|((X482)=(X483))|(in @ (esk23_4 @ X480 @ X481 @ X482 @ X483) @ X481)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(((in @ (kpair @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ (esk25_4 @ X480 @ X481 @ X482 @ X483)) @ X483)|((X482)=(X483))|(in @ (esk23_4 @ X480 @ X481 @ X482 @ X483) @ X481)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(~(in @ (kpair @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ (esk25_4 @ X480 @ X481 @ X482 @ X483)) @ X482)|((X482)=(X483))|(in @ (esk23_4 @ X480 @ X481 @ X482 @ X483) @ X481)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481))))))&((((in @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ X480)|((X482)=(X483))|(in @ (kpair @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ (esk23_4 @ X480 @ X481 @ X482 @ X483)) @ X482)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(((in @ (esk25_4 @ X480 @ X481 @ X482 @ X483) @ X481)|((X482)=(X483))|(in @ (kpair @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ (esk23_4 @ X480 @ X481 @ X482 @ X483)) @ X482)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(((in @ (kpair @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ (esk25_4 @ X480 @ X481 @ X482 @ X483)) @ X483)|((X482)=(X483))|(in @ (kpair @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ (esk23_4 @ X480 @ X481 @ X482 @ X483)) @ X482)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(~(in @ (kpair @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ (esk25_4 @ X480 @ X481 @ X482 @ X483)) @ X482)|((X482)=(X483))|(in @ (kpair @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ (esk23_4 @ X480 @ X481 @ X482 @ X483)) @ X482)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481))))))&(((in @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ X480)|((X482)=(X483))|~(in @ (kpair @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ (esk23_4 @ X480 @ X481 @ X482 @ X483)) @ X483)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(((in @ (esk25_4 @ X480 @ X481 @ X482 @ X483) @ X481)|((X482)=(X483))|~(in @ (kpair @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ (esk23_4 @ X480 @ X481 @ X482 @ X483)) @ X483)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(((in @ (kpair @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ (esk25_4 @ X480 @ X481 @ X482 @ X483)) @ X483)|((X482)=(X483))|~(in @ (kpair @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ (esk23_4 @ X480 @ X481 @ X482 @ X483)) @ X483)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))&(~(in @ (kpair @ (esk24_4 @ X480 @ X481 @ X482 @ X483) @ (esk25_4 @ X480 @ X481 @ X482 @ X483)) @ X482)|((X482)=(X483))|~(in @ (kpair @ (esk22_4 @ X480 @ X481 @ X482 @ X483) @ (esk23_4 @ X480 @ X481 @ X482 @ X483)) @ X483)|~(subset @ X483 @ (cartprod @ X480 @ X481))|~(subset @ X482 @ (cartprod @ X480 @ X481)))))))))&((funcext)&((funcext2)&((ap2apEq1)&((ap2apEq2)&((beta1)&((eta1)&((lam2lamEq)&((beta2)&((eta2)&((iffalseProp1)&((iffalseProp2)&((iftrueProp1)&((iftrueProp2)&((in @ esk27_0 @ esk26_0)&((in @ esk28_0 @ esk26_0)&(~(in @ X492 @ (dsetconstr @ esk26_0 @ (^[Z0:$i]:((((((epred1_0))&(((Z0)=(esk27_0)))))|(((~((epred1_0)))&(((Z0)=(esk28_0))))))))))|((dsetconstr @ esk26_0 @ (^[Z0:$i]:((((((epred1_0))&(((Z0)=(esk27_0)))))|(((~((epred1_0)))&(((Z0)=(esk28_0)))))))))!=(setadjoin @ X492 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])])])])).
% 3.93/0.95 thf(c_0_77, plain, ![X493:$i]:(((epred2_0 @ X493)<=>(((epred1_0)&((X493)=(esk27_0)))|(~((epred1_0))&((X493)=(esk28_0)))))), introduced(definition)).
% 3.93/0.95 thf(c_0_78, negated_conjecture, ![X2:$i]:((~((((in @ X2 @ (dsetconstr @ esk26_0 @ epred2_0)))=(($true))))|((dsetconstr @ esk26_0 @ epred2_0)!=(setadjoin @ X2 @ emptyset)))), inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_76]), c_0_77]), c_0_77])).
% 3.93/0.95 thf(c_0_79, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ (esk5_2 @ X2 @ X1) @ (dsetconstr @ X2 @ X1))|(X1 @ (esk4_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 3.93/0.95 thf(c_0_80, negated_conjecture, (in @ esk28_0 @ esk26_0), inference(split_conjunct,[status(thm)],[c_0_76])).
% 3.93/0.95 thf(c_0_81, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk5_2 @ X2 @ X1) @ emptyset))|(X1 @ (esk4_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 3.93/0.95 thf(c_0_82, plain, ![X512:$i]:(((((~(epred1_0)|(epred1_0)|~(epred2_0 @ X512))&(((X512)=(esk28_0))|(epred1_0)|~(epred2_0 @ X512)))&((~(epred1_0)|((X512)=(esk27_0))|~(epred2_0 @ X512))&(((X512)=(esk28_0))|((X512)=(esk27_0))|~(epred2_0 @ X512))))&((~(epred1_0)|((X512)!=(esk27_0))|(epred2_0 @ X512))&((epred1_0)|((X512)!=(esk28_0))|(epred2_0 @ X512))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])])).
% 3.93/0.95 thf(c_0_83, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ (esk5_2 @ X2 @ X1) @ (dsetconstr @ X2 @ X1))|(X1 @ (esk3_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 3.93/0.95 thf(c_0_84, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk5_2 @ X2 @ X1) @ emptyset))|(X1 @ (esk3_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 3.93/0.95 thf(c_0_85, negated_conjecture, (in @ esk27_0 @ esk26_0), inference(split_conjunct,[status(thm)],[c_0_76])).
% 3.93/0.95 thf(c_0_86, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ (esk5_2 @ X2 @ X1) @ (dsetconstr @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3))|((esk3_2 @ X2 @ X1)!=(esk4_2 @ X2 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 3.93/0.95 thf(c_0_87, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk5_2 @ X2 @ X1) @ emptyset))|~((in @ X3 @ X2))|~((X1 @ X3))|((esk3_2 @ X2 @ X1)!=(esk4_2 @ X2 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 3.93/0.95 thf(c_0_88, negated_conjecture, ![X2:$i]:((((setadjoin @ X2 @ emptyset)!=(dsetconstr @ esk26_0 @ epred2_0))|~((in @ X2 @ (dsetconstr @ esk26_0 @ epred2_0))))), inference(cn,[status(thm)],[c_0_78])).
% 3.93/0.95 thf(c_0_89, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk26_0 @ X1) @ (dsetconstr @ esk26_0 @ X1))|(X1 @ (esk4_2 @ esk26_0 @ X1))|~((X1 @ esk28_0)))), inference(spm,[status(thm)],[c_0_79, c_0_80])).
% 3.93/0.95 thf(c_0_90, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk26_0 @ X1) @ emptyset)=(dsetconstr @ esk26_0 @ X1))|(X1 @ (esk4_2 @ esk26_0 @ X1))|~((X1 @ esk28_0)))), inference(spm,[status(thm)],[c_0_81, c_0_80])).
% 3.93/0.95 thf(c_0_91, plain, ![X2:$i]:(((epred1_0)|(epred2_0 @ X2)|((X2)!=(esk28_0)))), inference(split_conjunct,[status(thm)],[c_0_82])).
% 3.93/0.95 thf(c_0_92, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk26_0 @ X1) @ (dsetconstr @ esk26_0 @ X1))|(X1 @ (esk3_2 @ esk26_0 @ X1))|~((X1 @ esk28_0)))), inference(spm,[status(thm)],[c_0_83, c_0_80])).
% 3.93/0.95 thf(c_0_93, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk26_0 @ X1) @ emptyset)=(dsetconstr @ esk26_0 @ X1))|(X1 @ (esk3_2 @ esk26_0 @ X1))|~((X1 @ esk28_0)))), inference(spm,[status(thm)],[c_0_84, c_0_80])).
% 3.93/0.95 thf(c_0_94, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk26_0 @ X1) @ (dsetconstr @ esk26_0 @ X1))|(X1 @ (esk4_2 @ esk26_0 @ X1))|~((X1 @ esk27_0)))), inference(spm,[status(thm)],[c_0_79, c_0_85])).
% 3.93/0.95 thf(c_0_95, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk26_0 @ X1) @ emptyset)=(dsetconstr @ esk26_0 @ X1))|(X1 @ (esk4_2 @ esk26_0 @ X1))|~((X1 @ esk27_0)))), inference(spm,[status(thm)],[c_0_81, c_0_85])).
% 3.93/0.95 thf(c_0_96, plain, ![X2:$i]:(((epred2_0 @ X2)|~((epred1_0))|((X2)!=(esk27_0)))), inference(split_conjunct,[status(thm)],[c_0_82])).
% 3.93/0.95 thf(c_0_97, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk26_0 @ X1) @ (dsetconstr @ esk26_0 @ X1))|((esk4_2 @ esk26_0 @ X1)!=(esk3_2 @ esk26_0 @ X1))|~((X1 @ esk28_0)))), inference(spm,[status(thm)],[c_0_86, c_0_80])).
% 3.93/0.95 thf(c_0_98, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk26_0 @ X1) @ emptyset)=(dsetconstr @ esk26_0 @ X1))|((esk4_2 @ esk26_0 @ X1)!=(esk3_2 @ esk26_0 @ X1))|~((X1 @ esk28_0)))), inference(spm,[status(thm)],[c_0_87, c_0_80])).
% 3.93/0.95 thf(c_0_99, plain, ![X2:$i]:((((X2)=(esk28_0))|(epred1_0)|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_82])).
% 3.93/0.95 thf(c_0_100, negated_conjecture, ((epred2_0 @ (esk4_2 @ esk26_0 @ epred2_0))|~((epred2_0 @ esk28_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_90])).
% 3.93/0.95 thf(c_0_101, plain, ((epred2_0 @ esk28_0)|(epred1_0)), inference(er,[status(thm)],[c_0_91])).
% 3.93/0.95 thf(c_0_102, negated_conjecture, ((epred2_0 @ (esk3_2 @ esk26_0 @ epred2_0))|~((epred2_0 @ esk28_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_92]), c_0_93])).
% 3.93/0.95 thf(c_0_103, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk26_0 @ X1) @ (dsetconstr @ esk26_0 @ X1))|(X1 @ (esk3_2 @ esk26_0 @ X1))|~((X1 @ esk27_0)))), inference(spm,[status(thm)],[c_0_83, c_0_85])).
% 3.93/0.95 thf(c_0_104, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk26_0 @ X1) @ emptyset)=(dsetconstr @ esk26_0 @ X1))|(X1 @ (esk3_2 @ esk26_0 @ X1))|~((X1 @ esk27_0)))), inference(spm,[status(thm)],[c_0_84, c_0_85])).
% 3.93/0.95 thf(c_0_105, plain, ![X2:$i]:((((X2)=(esk27_0))|~((epred1_0))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_82])).
% 3.93/0.95 thf(c_0_106, negated_conjecture, ((epred2_0 @ (esk4_2 @ esk26_0 @ epred2_0))|~((epred2_0 @ esk27_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_94]), c_0_95])).
% 3.93/0.95 thf(c_0_107, plain, ((epred2_0 @ esk27_0)|~((epred1_0))), inference(er,[status(thm)],[c_0_96])).
% 3.93/0.95 thf(c_0_108, negated_conjecture, (((esk4_2 @ esk26_0 @ epred2_0)!=(esk3_2 @ esk26_0 @ epred2_0))|~((epred2_0 @ esk28_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_97]), c_0_98])).
% 3.93/0.95 thf(c_0_109, plain, (((esk4_2 @ esk26_0 @ epred2_0)=(esk28_0))|(epred1_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_100]), c_0_101])).
% 3.93/0.95 thf(c_0_110, plain, (((esk3_2 @ esk26_0 @ epred2_0)=(esk28_0))|(epred1_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_102]), c_0_101])).
% 3.93/0.95 thf(c_0_111, negated_conjecture, ((epred2_0 @ (esk3_2 @ esk26_0 @ epred2_0))|~((epred2_0 @ esk27_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_103]), c_0_104])).
% 3.93/0.95 thf(c_0_112, plain, (((esk4_2 @ esk26_0 @ epred2_0)=(esk27_0))|~((epred1_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_106]), c_0_107])).
% 3.93/0.95 thf(c_0_113, plain, (epred1_0), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109]), c_0_101]), c_0_110])).
% 3.93/0.95 thf(c_0_114, plain, (((esk3_2 @ esk26_0 @ epred2_0)=(esk27_0))|~((epred1_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_111]), c_0_107])).
% 3.93/0.95 thf(c_0_115, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk26_0 @ X1) @ (dsetconstr @ esk26_0 @ X1))|((esk4_2 @ esk26_0 @ X1)!=(esk3_2 @ esk26_0 @ X1))|~((X1 @ esk27_0)))), inference(spm,[status(thm)],[c_0_86, c_0_85])).
% 3.93/0.95 thf(c_0_116, plain, ((esk4_2 @ esk26_0 @ epred2_0)=(esk27_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112, c_0_113])])).
% 3.93/0.95 thf(c_0_117, plain, ((esk3_2 @ esk26_0 @ epred2_0)=(esk27_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114, c_0_113])])).
% 3.93/0.95 thf(c_0_118, plain, (epred2_0 @ esk27_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107, c_0_113])])).
% 3.93/0.95 thf(c_0_119, negated_conjecture, ((setadjoin @ (esk5_2 @ esk26_0 @ epred2_0) @ emptyset)!=(dsetconstr @ esk26_0 @ epred2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_115]), c_0_116]), c_0_117]), c_0_118])])).
% 3.93/0.95 thf(c_0_120, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk26_0 @ X1) @ emptyset)=(dsetconstr @ esk26_0 @ X1))|((esk4_2 @ esk26_0 @ X1)!=(esk3_2 @ esk26_0 @ X1))|~((X1 @ esk27_0)))), inference(spm,[status(thm)],[c_0_87, c_0_85])).
% 3.93/0.95 thf(c_0_121, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_120]), c_0_116]), c_0_117]), c_0_118])]), ['proof']).
% 3.93/0.95 % SZS output end CNFRefutation
% 3.93/0.95 % Parsed axioms : 483
% 3.93/0.95 % Removed by relevancy pruning/SinE : 443
% 3.93/0.95 % Initial clauses : 290
% 3.93/0.95 % Removed in clause preprocessing : 1
% 3.93/0.95 % Initial clauses in saturation : 289
% 3.93/0.95 % Processed clauses : 1372
% 3.93/0.95 % ...of these trivial : 27
% 3.93/0.95 % ...subsumed : 554
% 3.93/0.95 % ...remaining for further processing : 791
% 3.93/0.95 % Other redundant clauses eliminated : 4
% 3.93/0.95 % Clauses deleted for lack of memory : 0
% 3.93/0.95 % Backward-subsumed : 92
% 3.93/0.95 % Backward-rewritten : 121
% 3.93/0.95 % Generated clauses : 13990
% 3.93/0.95 % ...of the previous two non-redundant : 13801
% 3.93/0.95 % ...aggressively subsumed : 0
% 3.93/0.95 % Contextual simplify-reflections : 40
% 3.93/0.95 % Paramodulations : 13941
% 3.93/0.95 % Factorizations : 8
% 3.93/0.95 % NegExts : 0
% 3.93/0.95 % Equation resolutions : 38
% 3.93/0.95 % Disequality decompositions : 0
% 3.93/0.95 % Total rewrite steps : 2344
% 3.93/0.95 % ...of those cached : 2146
% 3.93/0.95 % Propositional unsat checks : 0
% 3.93/0.95 % Propositional check models : 0
% 3.93/0.95 % Propositional check unsatisfiable : 0
% 3.93/0.95 % Propositional clauses : 0
% 3.93/0.95 % Propositional clauses after purity: 0
% 3.93/0.95 % Propositional unsat core size : 0
% 3.93/0.95 % Propositional preprocessing time : 0.000
% 3.93/0.95 % Propositional encoding time : 0.000
% 3.93/0.95 % Propositional solver time : 0.000
% 3.93/0.95 % Success case prop preproc time : 0.000
% 3.93/0.95 % Success case prop encoding time : 0.000
% 3.93/0.95 % Success case prop solver time : 0.000
% 3.93/0.95 % Current number of processed clauses : 574
% 3.93/0.95 % Positive orientable unit clauses : 203
% 3.93/0.95 % Positive unorientable unit clauses: 0
% 3.93/0.95 % Negative unit clauses : 2
% 3.93/0.95 % Non-unit-clauses : 369
% 3.93/0.95 % Current number of unprocessed clauses: 12701
% 3.93/0.95 % ...number of literals in the above : 63226
% 3.93/0.95 % Current number of archived formulas : 0
% 3.93/0.95 % Current number of archived clauses : 214
% 3.93/0.95 % Clause-clause subsumption calls (NU) : 30582
% 3.93/0.95 % Rec. Clause-clause subsumption calls : 17352
% 3.93/0.95 % Non-unit clause-clause subsumptions : 609
% 3.93/0.95 % Unit Clause-clause subsumption calls : 731
% 3.93/0.95 % Rewrite failures with RHS unbound : 0
% 3.93/0.95 % BW rewrite match attempts : 11
% 3.93/0.95 % BW rewrite match successes : 10
% 3.93/0.95 % Condensation attempts : 0
% 3.93/0.95 % Condensation successes : 0
% 3.93/0.95 % Termbank termtop insertions : 338904
% 3.93/0.95 % Search garbage collected termcells : 9522
% 3.93/0.95
% 3.93/0.95 % -------------------------------------------------
% 3.93/0.95 % User time : 0.526 s
% 3.93/0.95 % System time : 0.021 s
% 3.93/0.95 % Total time : 0.547 s
% 3.93/0.95 % Maximum resident set size: 6712 pages
% 3.93/0.95
% 3.93/0.95 % -------------------------------------------------
% 3.93/0.95 % User time : 0.547 s
% 3.93/0.95 % System time : 0.030 s
% 3.93/0.95 % Total time : 0.577 s
% 3.93/0.95 % Maximum resident set size: 5376 pages
% 3.93/0.95 % E exiting
%------------------------------------------------------------------------------