%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU679^1 : 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 : n001.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 08:25:00 AM UTC 2026
% Result : Theorem 253.30s 33.53s
% Output : CNFRefutation 253.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU679^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n001.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:13:50 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.22/0.30 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p
% 253.30/33.53 % Version: 3.5.1-ho
% 253.30/33.53 % Preprocessing class: HSLMSLSSLLLCHSA.
% 253.30/33.53 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 253.30/33.53 % Starting ho_unfolding_5 with 1200s (4) cores
% 253.30/33.53 % Starting pre_casc_3 with 300s (1) cores
% 253.30/33.53 % Starting new_ho_10_cnf2 with 300s (1) cores
% 253.30/33.53 % Starting full_lambda_10 with 300s (1) cores
% 253.30/33.53 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 253.30/33.53 % pre_casc_3 with pid 1304975 completed with status 0
% 253.30/33.53 % Result found by pre_casc_3
% 253.30/33.53 % Preprocessing class: HSLMSLSSLLLCHSA.
% 253.30/33.53 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 253.30/33.53 % Starting ho_unfolding_5 with 1200s (4) cores
% 253.30/33.53 % Starting pre_casc_3 with 300s (1) cores
% 253.30/33.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 253.30/33.53 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 253.30/33.53 % Search class: HGHSM-FSLM32-MHSMMSBN
% 253.30/33.53 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 253.30/33.53 % Starting SubtermCWHack with 31s (1) cores
% 253.30/33.53 % SubtermCWHack with pid 1304980 completed with status 8
% 253.30/33.53 % Starting full_lambda_5 with 28s (1) cores
% 253.30/33.53 % full_lambda_5 with pid 1305030 completed with status 0
% 253.30/33.53 % Result found by full_lambda_5
% 253.30/33.53 % Preprocessing class: HSLMSLSSLLLCHSA.
% 253.30/33.53 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 253.30/33.53 % Starting ho_unfolding_5 with 1200s (4) cores
% 253.30/33.53 % Starting pre_casc_3 with 300s (1) cores
% 253.30/33.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 253.30/33.53 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 253.30/33.53 % Search class: HGHSM-FSLM32-MHSMMSBN
% 253.30/33.53 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 253.30/33.53 % Starting SubtermCWHack with 31s (1) cores
% 253.30/33.53 % SubtermCWHack with pid 1304980 completed with status 8
% 253.30/33.53 % Starting full_lambda_5 with 28s (1) cores
% 253.30/33.53 % Preprocessing time : 0.004 s
% 253.30/33.53 % Presaturation interreduction done
% 253.30/33.53
% 253.30/33.53 % Proof found!
% 253.30/33.53 % SZS status Theorem
% 253.30/33.53 % SZS output start CNFRefutation
% 253.30/33.53 thf(decl_23, type, in: $i > $i > $o).
% 253.30/33.53 thf(decl_25, type, setextAx: $o).
% 253.30/33.53 thf(decl_26, type, emptyset: $i).
% 253.30/33.53 thf(decl_27, type, emptysetAx: $o).
% 253.30/33.53 thf(decl_28, type, setadjoin: $i > $i > $i).
% 253.30/33.53 thf(decl_29, type, setadjoinAx: $o).
% 253.30/33.53 thf(decl_31, type, powersetAx: $o).
% 253.30/33.53 thf(decl_32, type, setunion: $i > $i).
% 253.30/33.53 thf(decl_33, type, setunionAx: $o).
% 253.30/33.53 thf(decl_35, type, omega0Ax: $o).
% 253.30/33.53 thf(decl_36, type, omegaSAx: $o).
% 253.30/33.53 thf(decl_37, type, omegaIndAx: $o).
% 253.30/33.53 thf(decl_38, type, replAx: $o).
% 253.30/33.53 thf(decl_39, type, foundationAx: $o).
% 253.30/33.53 thf(decl_40, type, wellorderingAx: $o).
% 253.30/33.53 thf(decl_42, type, descrp: $o).
% 253.30/33.53 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 253.30/33.53 thf(decl_44, type, dsetconstrI: $o).
% 253.30/33.53 thf(decl_45, type, dsetconstrEL: $o).
% 253.30/33.53 thf(decl_46, type, dsetconstrER: $o).
% 253.30/33.53 thf(decl_47, type, exuE1: $o).
% 253.30/33.53 thf(decl_49, type, prop2setE: $o).
% 253.30/33.53 thf(decl_50, type, emptysetE: $o).
% 253.30/33.53 thf(decl_51, type, emptysetimpfalse: $o).
% 253.30/33.53 thf(decl_52, type, notinemptyset: $o).
% 253.30/33.53 thf(decl_53, type, exuE3e: $o).
% 253.30/33.53 thf(decl_54, type, setext: $o).
% 253.30/33.53 thf(decl_55, type, emptyI: $o).
% 253.30/33.53 thf(decl_56, type, noeltsimpempty: $o).
% 253.30/33.53 thf(decl_57, type, setbeta: $o).
% 253.30/33.53 thf(decl_59, type, nonemptyE1: $o).
% 253.30/33.53 thf(decl_60, type, nonemptyI: $o).
% 253.30/33.53 thf(decl_61, type, nonemptyI1: $o).
% 253.30/33.53 thf(decl_62, type, setadjoinIL: $o).
% 253.30/33.53 thf(decl_63, type, emptyinunitempty: $o).
% 253.30/33.53 thf(decl_64, type, setadjoinIR: $o).
% 253.30/33.53 thf(decl_65, type, setadjoinE: $o).
% 253.30/33.53 thf(decl_66, type, setadjoinOr: $o).
% 253.30/33.53 thf(decl_67, type, setoftrueEq: $o).
% 253.30/33.53 thf(decl_68, type, powersetI: $o).
% 253.30/33.53 thf(decl_69, type, emptyinPowerset: $o).
% 253.30/33.53 thf(decl_70, type, emptyInPowerset: $o).
% 253.30/33.53 thf(decl_71, type, powersetE: $o).
% 253.30/33.53 thf(decl_72, type, setunionI: $o).
% 253.30/33.53 thf(decl_73, type, setunionE: $o).
% 253.30/33.53 thf(decl_74, type, subPowSU: $o).
% 253.30/33.53 thf(decl_75, type, exuE2: $o).
% 253.30/33.53 thf(decl_76, type, nonemptyImpWitness: $o).
% 253.30/33.53 thf(decl_77, type, uniqinunit: $o).
% 253.30/33.53 thf(decl_78, type, notinsingleton: $o).
% 253.30/33.53 thf(decl_79, type, eqinunit: $o).
% 253.30/33.53 thf(decl_80, type, singletonsswitch: $o).
% 253.30/33.53 thf(decl_81, type, upairsetE: $o).
% 253.30/33.53 thf(decl_82, type, upairsetIL: $o).
% 253.30/33.53 thf(decl_83, type, upairsetIR: $o).
% 253.30/33.53 thf(decl_84, type, emptyE1: $o).
% 253.30/33.53 thf(decl_85, type, vacuousDall: $o).
% 253.30/33.53 thf(decl_86, type, quantDeMorgan1: $o).
% 253.30/33.53 thf(decl_87, type, quantDeMorgan2: $o).
% 253.30/33.53 thf(decl_88, type, quantDeMorgan3: $o).
% 253.30/33.53 thf(decl_89, type, quantDeMorgan4: $o).
% 253.30/33.53 thf(decl_90, type, prop2setI: $o).
% 253.30/33.53 thf(decl_92, type, prop2set2propI: $o).
% 253.30/33.53 thf(decl_93, type, notdexE: $o).
% 253.30/33.53 thf(decl_94, type, notdallE: $o).
% 253.30/33.53 thf(decl_95, type, exuI1: $o).
% 253.30/33.53 thf(decl_96, type, exuI3: $o).
% 253.30/33.53 thf(decl_97, type, exuI2: $o).
% 253.30/33.53 thf(decl_98, type, inCongP: $o).
% 253.30/33.53 thf(decl_99, type, in__Cong: $o).
% 253.30/33.53 thf(decl_100, type, exuE3u: $o).
% 253.30/33.53 thf(decl_101, type, exu__Cong: $o).
% 253.30/33.53 thf(decl_102, type, emptyset__Cong: $o).
% 253.30/33.53 thf(decl_103, type, setadjoin__Cong: $o).
% 253.30/33.53 thf(decl_104, type, powerset__Cong: $o).
% 253.30/33.53 thf(decl_105, type, setunion__Cong: $o).
% 253.30/33.53 thf(decl_106, type, omega__Cong: $o).
% 253.30/33.53 thf(decl_107, type, exuEu: $o).
% 253.30/33.53 thf(decl_108, type, descr__Cong: $o).
% 253.30/33.53 thf(decl_109, type, dsetconstr__Cong: $o).
% 253.30/33.53 thf(decl_110, type, subset: $i > $i > $o).
% 253.30/33.53 thf(decl_113, type, subsetI1: $o).
% 253.30/33.53 thf(decl_114, type, eqimpsubset2: $o).
% 253.30/33.53 thf(decl_115, type, eqimpsubset1: $o).
% 253.30/33.53 thf(decl_116, type, subsetI2: $o).
% 253.30/33.53 thf(decl_117, type, emptysetsubset: $o).
% 253.30/33.53 thf(decl_118, type, subsetE: $o).
% 253.30/33.53 thf(decl_119, type, subsetE2: $o).
% 253.30/33.53 thf(decl_120, type, notsubsetI: $o).
% 253.30/33.53 thf(decl_121, type, notequalI1: $o).
% 253.30/33.53 thf(decl_122, type, notequalI2: $o).
% 253.30/33.53 thf(decl_123, type, subsetRefl: $o).
% 253.30/33.53 thf(decl_124, type, subsetTrans: $o).
% 253.30/33.53 thf(decl_125, type, setadjoinSub: $o).
% 253.30/33.53 thf(decl_126, type, setadjoinSub2: $o).
% 253.30/33.53 thf(decl_127, type, subset2powerset: $o).
% 253.30/33.53 thf(decl_128, type, setextsub: $o).
% 253.30/33.53 thf(decl_129, type, subsetemptysetimpeq: $o).
% 253.30/33.53 thf(decl_130, type, powersetI1: $o).
% 253.30/33.53 thf(decl_131, type, powersetE1: $o).
% 253.30/33.53 thf(decl_132, type, inPowerset: $o).
% 253.30/33.53 thf(decl_133, type, powersetsubset: $o).
% 253.30/33.53 thf(decl_134, type, sepInPowerset: $o).
% 253.30/33.53 thf(decl_135, type, sepSubset: $o).
% 253.30/33.53 thf(decl_137, type, binunionIL: $o).
% 253.30/33.53 thf(decl_138, type, upairset2IR: $o).
% 253.30/33.53 thf(decl_139, type, binunionIR: $o).
% 253.30/33.53 thf(decl_140, type, binunionEcases: $o).
% 253.30/33.53 thf(decl_141, type, binunionE: $o).
% 253.30/33.53 thf(decl_142, type, binunionLsub: $o).
% 253.30/33.53 thf(decl_143, type, binunionRsub: $o).
% 253.30/33.53 thf(decl_145, type, binintersectI: $o).
% 253.30/33.53 thf(decl_146, type, binintersectSubset5: $o).
% 253.30/33.53 thf(decl_147, type, binintersectEL: $o).
% 253.30/33.53 thf(decl_148, type, binintersectLsub: $o).
% 253.30/33.53 thf(decl_149, type, binintersectSubset2: $o).
% 253.30/33.53 thf(decl_150, type, binintersectSubset3: $o).
% 253.30/33.53 thf(decl_151, type, binintersectER: $o).
% 253.30/33.53 thf(decl_152, type, disjointsetsI1: $o).
% 253.30/33.53 thf(decl_153, type, binintersectRsub: $o).
% 253.30/33.53 thf(decl_154, type, binintersectSubset4: $o).
% 253.30/33.53 thf(decl_155, type, binintersectSubset1: $o).
% 253.30/33.53 thf(decl_156, type, bs114d: $o).
% 253.30/33.53 thf(decl_159, type, setminusI: $o).
% 253.30/33.53 thf(decl_160, type, setminusEL: $o).
% 253.30/33.53 thf(decl_161, type, setminusER: $o).
% 253.30/33.53 thf(decl_162, type, setminusSubset2: $o).
% 253.30/33.53 thf(decl_163, type, setminusERneg: $o).
% 253.30/33.53 thf(decl_164, type, setminusELneg: $o).
% 253.30/33.53 thf(decl_165, type, setminusILneg: $o).
% 253.30/33.53 thf(decl_166, type, setminusIRneg: $o).
% 253.30/33.53 thf(decl_167, type, setminusLsub: $o).
% 253.30/33.53 thf(decl_168, type, setminusSubset1: $o).
% 253.30/33.53 thf(decl_170, type, symdiffE: $o).
% 253.30/33.53 thf(decl_171, type, symdiffI1: $o).
% 253.30/33.53 thf(decl_172, type, symdiffI2: $o).
% 253.30/33.53 thf(decl_173, type, symdiffIneg1: $o).
% 253.30/33.53 thf(decl_174, type, symdiffIneg2: $o).
% 253.30/33.53 thf(decl_175, type, iskpair: $i > $o).
% 253.30/33.53 thf(decl_176, type, secondinupair: $o).
% 253.30/33.53 thf(decl_177, type, setukpairIL: $o).
% 253.30/33.53 thf(decl_178, type, setukpairIR: $o).
% 253.30/33.53 thf(decl_179, type, kpairiskpair: $o).
% 253.30/33.53 thf(decl_180, type, kpair: $i > $i > $i).
% 253.30/33.53 thf(decl_181, type, kpairp: $o).
% 253.30/33.53 thf(decl_182, type, cartprod: $i > $i > $i).
% 253.30/33.53 thf(decl_183, type, singletonsubset: $o).
% 253.30/33.53 thf(decl_184, type, singletoninpowerset: $o).
% 253.30/33.53 thf(decl_185, type, singletoninpowunion: $o).
% 253.30/33.53 thf(decl_186, type, upairset2E: $o).
% 253.30/33.53 thf(decl_187, type, upairsubunion: $o).
% 253.30/33.53 thf(decl_188, type, upairinpowunion: $o).
% 253.30/33.53 thf(decl_189, type, ubforcartprodlem1: $o).
% 253.30/33.53 thf(decl_190, type, ubforcartprodlem2: $o).
% 253.30/33.53 thf(decl_191, type, ubforcartprodlem3: $o).
% 253.30/33.53 thf(decl_192, type, cartprodpairin: $o).
% 253.30/33.53 thf(decl_193, type, cartprodmempair1: $o).
% 253.30/33.53 thf(decl_194, type, cartprodmempair: $o).
% 253.30/33.53 thf(decl_195, type, setunionE2: $o).
% 253.30/33.53 thf(decl_196, type, setunionsingleton1: $o).
% 253.30/33.53 thf(decl_197, type, setunionsingleton2: $o).
% 253.30/33.53 thf(decl_198, type, setunionsingleton: $o).
% 253.30/33.53 thf(decl_199, type, singleton: $i > $o).
% 253.30/33.53 thf(decl_200, type, singletonprop: $o).
% 253.30/33.53 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 253.30/33.53 thf(decl_202, type, ex1E1: $o).
% 253.30/33.53 thf(decl_203, type, ex1I: $o).
% 253.30/33.53 thf(decl_204, type, ex1I2: $o).
% 253.30/33.53 thf(decl_205, type, singletonsuniq: $o).
% 253.30/33.53 thf(decl_210, type, setukpairinjL1: $o).
% 253.30/33.53 thf(decl_211, type, kfstsingleton: $o).
% 253.30/33.53 thf(decl_212, type, theprop: $o).
% 253.30/33.53 thf(decl_213, type, kfst: $i > $i).
% 253.30/33.53 thf(decl_214, type, kfstpairEq: $o).
% 253.30/33.53 thf(decl_215, type, cartprodfstin: $o).
% 253.30/33.53 thf(decl_216, type, setukpairinjL2: $o).
% 253.30/33.53 thf(decl_217, type, setukpairinjL: $o).
% 253.30/33.53 thf(decl_218, type, setukpairinjR11: $o).
% 253.30/33.53 thf(decl_219, type, setukpairinjR12: $o).
% 253.30/33.53 thf(decl_220, type, setukpairinjR1: $o).
% 253.30/33.53 thf(decl_221, type, upairequniteq: $o).
% 253.30/33.53 thf(decl_222, type, setukpairinjR2: $o).
% 253.30/33.53 thf(decl_223, type, setukpairinjR: $o).
% 253.30/33.53 thf(decl_224, type, ksndsingleton: $o).
% 253.30/33.53 thf(decl_225, type, ksnd: $i > $i).
% 253.30/33.53 thf(decl_226, type, ksndpairEq: $o).
% 253.30/33.53 thf(decl_227, type, kpairsurjEq: $o).
% 253.30/33.53 thf(decl_228, type, cartprodsndin: $o).
% 253.30/33.53 thf(decl_229, type, cartprodpairmemEL: $o).
% 253.30/33.53 thf(decl_230, type, cartprodpairmemER: $o).
% 253.30/33.53 thf(decl_231, type, cartprodmempaircEq: $o).
% 253.30/33.53 thf(decl_232, type, cartprodfstpairEq: $o).
% 253.30/33.53 thf(decl_233, type, cartprodsndpairEq: $o).
% 253.30/33.53 thf(decl_234, type, cartprodpairsurjEq: $o).
% 253.30/33.53 thf(decl_235, type, breln: $i > $i > $i > $o).
% 253.30/33.53 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 253.30/33.53 thf(decl_237, type, dpsetconstrI: $o).
% 253.30/33.53 thf(decl_238, type, dpsetconstrSub: $o).
% 253.30/33.53 thf(decl_239, type, setOfPairsIsBReln: $o).
% 253.30/33.53 thf(decl_240, type, dpsetconstrERa: $o).
% 253.30/33.53 thf(decl_241, type, dpsetconstrEL1: $o).
% 253.30/33.53 thf(decl_242, type, dpsetconstrEL2: $o).
% 253.30/33.53 thf(decl_243, type, dpsetconstrER: $o).
% 253.30/33.53 thf(decl_244, type, func: $i > $i > $i > $o).
% 253.30/33.53 thf(decl_245, type, funcSet: $i > $i > $i).
% 253.30/33.53 thf(decl_246, type, funcImageSingleton: $o).
% 253.30/33.53 thf(decl_247, type, apProp: $o).
% 253.30/33.53 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 253.30/33.53 thf(decl_249, type, app: $o).
% 253.30/33.53 thf(decl_250, type, infuncsetfunc: $o).
% 253.30/33.53 thf(decl_251, type, ap2p: $o).
% 253.30/33.53 thf(decl_252, type, funcinfuncset: $o).
% 253.30/33.53 thf(decl_253, type, lamProp: $o).
% 253.30/33.53 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 253.30/33.53 thf(decl_255, type, esk1_3: $i > $i > $i > $i).
% 253.30/33.53 thf(decl_256, type, esk2_3: $i > $i > $i > $i).
% 253.30/33.53 thf(decl_257, type, esk3_2: $i > ($i > $o) > $i).
% 253.30/33.53 thf(decl_258, type, esk4_2: $i > ($i > $o) > $i).
% 253.30/33.53 thf(decl_259, type, esk5_2: $i > ($i > $o) > $i).
% 253.30/33.53 thf(decl_260, type, esk6_2: $i > ($i > $o) > $i).
% 253.30/33.53 thf(decl_261, type, esk7_3: $i > ($i > $o) > $i > $i).
% 253.30/33.53 thf(decl_262, type, esk8_3: $i > ($i > $o) > $i > $i).
% 253.30/33.53 thf(decl_263, type, esk9_2: $i > ($i > $o) > $i).
% 253.30/33.53 thf(decl_264, type, esk10_2: $i > ($i > $o) > $i).
% 253.30/33.53 thf(decl_265, type, esk11_2: $i > ($i > $o) > $i).
% 253.30/33.53 thf(decl_266, type, esk12_1: $i > $i).
% 253.30/33.53 thf(decl_267, type, esk13_1: $i > $i).
% 253.30/33.53 thf(decl_268, type, esk14_3: $i > $i > $i > $i).
% 253.30/33.53 thf(decl_269, type, esk15_4: $i > $i > $i > $i > $i).
% 253.30/33.53 thf(decl_270, type, esk16_3: $i > $i > $i > $i).
% 253.30/33.53 thf(decl_271, type, esk17_3: $i > $i > $i > $i).
% 253.30/33.53 thf(decl_272, type, esk18_4: $i > $i > $i > $i > $i).
% 253.30/33.53 thf(decl_273, type, esk19_3: $i > $i > $i > $i).
% 253.30/33.53 thf(decl_274, type, esk20_3: $i > $i > ($i > $i) > $i).
% 253.30/33.53 thf(decl_275, type, esk21_4: $i > $i > ($i > $i) > $i > $i).
% 253.30/33.53 thf(decl_276, type, esk22_0: $i).
% 253.30/33.53 thf(decl_277, type, esk23_0: $i).
% 253.30/33.53 thf(decl_278, type, esk24_0: $i > $i).
% 253.30/33.53 thf(decl_279, type, esk25_0: $i).
% 253.30/33.53 thf(decl_280, type, epred1_0: $i > $o).
% 253.30/33.53 thf(decl_281, type, epred2_1: ($i > $i) > $i > $i > $o).
% 253.30/33.53 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', ex1)).
% 253.30/33.53 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', singleton)).
% 253.30/33.53 thf(func, axiom, ((func)=(^[X4:$i, X5:$i, X29:$i]:((((breln @ X4 @ X5 @ X29))&(![X2:$i]:((((in @ X2 @ X4))=>((ex1 @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', func)).
% 253.30/33.53 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', breln)).
% 253.30/33.53 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.xEcMoPMqzp/E---3.1_1304960.p', ksndsingleton)).
% 253.30/33.53 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.xEcMoPMqzp/E---3.1_1304960.p', kfstsingleton)).
% 253.30/33.53 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', singletonprop)).
% 253.30/33.53 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', setOfPairsIsBReln)).
% 253.30/33.53 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', ex1I2)).
% 253.30/33.53 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.xEcMoPMqzp/E---3.1_1304960.p', ex1I)).
% 253.30/33.53 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', ex1E1)).
% 253.30/33.53 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X31 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', lamProp)).
% 253.30/33.53 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', apProp)).
% 253.30/33.53 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', funcImageSingleton)).
% 253.30/33.53 thf(lamp, 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)=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X33 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', lamp)).
% 253.30/33.53 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', dpsetconstrER)).
% 253.30/33.53 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', dpsetconstrEL2)).
% 253.30/33.53 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', dpsetconstrEL1)).
% 253.30/33.53 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', dpsetconstrERa)).
% 253.30/33.53 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', dpsetconstrSub)).
% 253.30/33.53 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', dpsetconstrI)).
% 253.30/33.53 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', theprop)).
% 253.30/33.53 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>(in @ X30 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', funcinfuncset)).
% 253.30/33.53 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', infuncsetfunc)).
% 253.30/33.53 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', app)).
% 253.30/33.53 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.xEcMoPMqzp/E---3.1_1304960.p', cartprodsndpairEq)).
% 253.30/33.53 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', ksndpairEq)).
% 253.30/33.53 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.xEcMoPMqzp/E---3.1_1304960.p', cartprodfstpairEq)).
% 253.30/33.53 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', kfstpairEq)).
% 253.30/33.53 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', kpairsurjEq)).
% 253.30/33.53 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', kpairp)).
% 253.30/33.53 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', kpairiskpair)).
% 253.30/33.53 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', cartprodpairsurjEq)).
% 253.30/33.53 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.xEcMoPMqzp/E---3.1_1304960.p', cartprodpairmemER)).
% 253.30/33.53 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.xEcMoPMqzp/E---3.1_1304960.p', cartprodpairmemEL)).
% 253.30/33.53 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', cartprodsndin)).
% 253.30/33.53 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', cartprodfstin)).
% 253.30/33.53 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', cartprodmempair)).
% 253.30/33.53 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.xEcMoPMqzp/E---3.1_1304960.p', cartprodmempair1)).
% 253.30/33.53 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.xEcMoPMqzp/E---3.1_1304960.p', cartprodpairin)).
% 253.30/33.53 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', ap2p)).
% 253.30/33.53 thf(lam, axiom, ((lam)=(^[X4:$i, X5:$i, X32:$i > $i]:(dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X32 @ X2)=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.xEcMoPMqzp/E---3.1_1304960.p', lam)).
% 253.30/33.53 thf(c_0_42, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X162:$i]:((((in @ X162 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X162 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 253.30/33.53 thf(c_0_43, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 253.30/33.53 thf(c_0_44, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X169:$i]:((((in @ X169 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X169 @ emptyset)))))))))))))), inference(fof_simplification,[status(thm)],[func])).
% 253.30/33.53 thf(c_0_45, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 253.30/33.53 thf(c_0_46, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X162:$i]:((((in @ X162 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X162 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_42, c_0_43])).
% 253.30/33.53 thf(c_0_47, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 253.30/33.53 thf(c_0_48, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 253.30/33.53 thf(c_0_49, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 253.30/33.53 thf(c_0_50, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 253.30/33.53 thf(c_0_51, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 253.30/33.53 thf(c_0_52, plain, ((ex1I)<=>![X4:$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])).
% 253.30/33.53 thf(c_0_53, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 253.30/33.53 thf(c_0_54, plain, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 253.30/33.53 thf(c_0_55, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X169:$i]:((((in @ X169 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X169 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_44, c_0_45]), c_0_46])).
% 253.30/33.53 thf(c_0_56, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 253.30/33.53 thf(c_0_57, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 253.30/33.53 thf(c_0_58, 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)=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X33 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[lamp])).
% 253.30/33.53 thf(c_0_59, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 253.30/33.53 thf(c_0_60, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 253.30/33.53 thf(c_0_61, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 253.30/33.53 thf(c_0_62, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 253.30/33.53 thf(c_0_63, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 253.30/33.53 thf(c_0_64, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 253.30/33.53 thf(c_0_65, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X168:$i]:((((in @ X168 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X168 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_43])).
% 253.30/33.53 thf(c_0_66, axiom, ((theprop)=(![X21:$i]:((((?[X167:$i]:((((in @ X167 @ X21))&(((X21)=(setadjoin @ X167 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_43])).
% 253.30/33.53 thf(c_0_67, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X166:$i]:((((in @ X166 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X166 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_48, c_0_43])).
% 253.30/33.53 thf(c_0_68, plain, ((singletonprop)=(![X4:$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)))))=>((?[X161:$i]:((((in @ X161 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X161 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_49, c_0_43])).
% 253.30/33.53 thf(c_0_69, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_50, c_0_45])).
% 253.30/33.53 thf(c_0_70, plain, ((ex1I2)=(![X4:$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)))))=>((?[X165:$i]:((((in @ X165 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X165 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_51, c_0_46])).
% 253.30/33.53 thf(c_0_71, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X164:$i]:((((in @ X164 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X164 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_52, c_0_46])).
% 253.30/33.53 thf(c_0_72, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X163:$i]:((((in @ X163 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X163 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_53, c_0_46])).
% 253.30/33.53 thf(c_0_73, plain, ((lamProp)=(![X4:$i, X5:$i, X31:$i > $i]:(((![X2:$i]:((((in @ X2 @ X4))=>((in @ (X31 @ X2) @ X5)))))=>((((((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))) @ (cartprod @ X4 @ X5))))&(![X181:$i]:((((in @ X181 @ X4))=>((?[X182:$i]:((((in @ X182 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X181 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1:$i, Z2:$i]:(((X31 @ Z1)=(Z2))))))))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X181 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1:$i, Z2:$i]:(((X31 @ Z1)=(Z2))))))))))=(setadjoin @ X182 @ emptyset))))))))))))))))), inference(apply_def,[status(thm)],[c_0_54, c_0_55])).
% 253.30/33.53 thf(c_0_74, axiom, ((funcinfuncset)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X179:$i]:((((in @ X179 @ X4))=>((?[X180:$i]:((((in @ X180 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X179 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X179 @ Z0) @ X30)))))=(setadjoin @ X180 @ emptyset)))))))))))))=>((in @ X30 @ (funcSet @ X4 @ X5))))))), inference(apply_def,[status(thm)],[funcinfuncset, c_0_55])).
% 253.30/33.53 thf(c_0_75, axiom, ((infuncsetfunc)=(![X4:$i, X5:$i, X30:$i]:((((in @ X30 @ (funcSet @ X4 @ X5)))=>((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X177:$i]:((((in @ X177 @ X4))=>((?[X178:$i]:((((in @ X178 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X177 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X177 @ Z0) @ X30)))))=(setadjoin @ X178 @ emptyset))))))))))))))))), inference(apply_def,[status(thm)],[infuncsetfunc, c_0_55])).
% 253.30/33.53 thf(c_0_76, axiom, ((app)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X175:$i]:((((in @ X175 @ X4))=>((?[X176:$i]:((((in @ X176 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X175 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X175 @ Z0) @ X30)))))=(setadjoin @ X176 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5))))))))), inference(apply_def,[status(thm)],[app, c_0_55])).
% 253.30/33.53 thf(c_0_77, plain, ((apProp)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X173:$i]:((((in @ X173 @ X4))=>((?[X174:$i]:((((in @ X174 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X173 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X173 @ Z0) @ X30)))))=(setadjoin @ X174 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5))))))))), inference(apply_def,[status(thm)],[c_0_56, c_0_55])).
% 253.30/33.53 thf(c_0_78, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X170:$i]:((((in @ X170 @ X4))=>((?[X171:$i]:((((in @ X171 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X170 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X170 @ Z0) @ X30)))))=(setadjoin @ X171 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X172:$i]:((((in @ X172 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))=(setadjoin @ X172 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_57, c_0_43]), c_0_55])).
% 253.30/33.53 thf(c_0_79, 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)=>(![X183:$i, X184:$i]:((iskpair @ (setadjoin @ (setadjoin @ X183 @ emptyset) @ (setadjoin @ (setadjoin @ X183 @ (setadjoin @ X184 @ emptyset)) @ emptyset))))=>(![X185:$i, X186:$i]:((iskpair @ (kpair @ X185 @ X186)))=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>(![X187:$i, X188:$i, X189:$i]:(((in @ X189 @ X187)=>![X190:$i]:(((in @ X190 @ X188)=>(in @ (kpair @ X189 @ X190) @ (cartprod @ X187 @ X188))))))=>(![X191:$i, X192:$i, X193:$i]:(((in @ X193 @ (cartprod @ X191 @ X192))=>?[X194:$i]:(((in @ X194 @ X191)&?[X195:$i]:(((in @ X195 @ X192)&((X193)=(kpair @ X194 @ X195))))))))=>(![X196:$i, X197:$i, X198:$i]:(((in @ X198 @ (cartprod @ X196 @ X197))=>(iskpair @ X198)))=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(![X199:$i, X200:$i > $o]:((![X201:$i]:(((in @ X201 @ X199)=>![X202:$i]:(((in @ X202 @ X199)=>((X200 @ X201)=>((X200 @ X202)=>((X201)=(X202))))))))=>(?[X203:$i]:(((in @ X203 @ X199)&(X200 @ X203)))=>?[X204:$i]:(((in @ X204 @ (dsetconstr @ X199 @ X200))&((dsetconstr @ X199 @ X200)=(setadjoin @ X204 @ emptyset)))))))=>(![X205:$i, X206:$i > $o]:((?[X207:$i]:(((in @ X207 @ (dsetconstr @ X205 @ X206))&((dsetconstr @ X205 @ X206)=(setadjoin @ X207 @ emptyset))))=>?[X208:$i]:(((in @ X208 @ X205)&(X206 @ X208)))))=>(![X209:$i, X210:$i > $o, X211:$i]:(((in @ X211 @ X209)=>((X210 @ X211)=>(![X212:$i]:(((in @ X212 @ X209)=>((X210 @ X212)=>((X212)=(X211)))))=>?[X213:$i]:(((in @ X213 @ (dsetconstr @ X209 @ X210))&((dsetconstr @ X209 @ X210)=(setadjoin @ X213 @ emptyset))))))))=>(![X214:$i, X215:$i > $o]:((![X216:$i]:(((in @ X216 @ X214)=>![X217:$i]:(((in @ X217 @ X214)=>((X215 @ X216)=>((X215 @ X217)=>((X216)=(X217))))))))=>(?[X218:$i]:(((in @ X218 @ X214)&(X215 @ X218)))=>?[X219:$i]:(((in @ X219 @ (dsetconstr @ X214 @ X215))&((dsetconstr @ X214 @ X215)=(setadjoin @ X219 @ emptyset)))))))=>((singletonsuniq)=>((setukpairinjL1)=>(![X220:$i]:(((iskpair @ X220)=>?[X221:$i]:(((in @ X221 @ (dsetconstr @ (setunion @ X220) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X220)))))&((dsetconstr @ (setunion @ X220) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X220))))=(setadjoin @ X221 @ emptyset))))))=>(![X222:$i]:((?[X223:$i]:(((in @ X223 @ X222)&((X222)=(setadjoin @ X223 @ emptyset))))=>(in @ (setunion @ X222) @ X222)))=>(![X224:$i, X225:$i]:(((kfst @ (kpair @ X224 @ X225))=(X224)))=>(![X226:$i, X227:$i, X228:$i]:(((in @ X228 @ (cartprod @ X226 @ X227))=>(in @ (kfst @ X228) @ X226)))=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>(![X229:$i]:(((iskpair @ X229)=>?[X230:$i]:(((in @ X230 @ (dsetconstr @ (setunion @ X229) @ (^[Z0:$i]:(((X229)=(kpair @ (kfst @ X229) @ Z0))))))&((dsetconstr @ (setunion @ X229) @ (^[Z0:$i]:(((X229)=(kpair @ (kfst @ X229) @ Z0)))))=(setadjoin @ X230 @ emptyset))))))=>(![X231:$i, X232:$i]:(((ksnd @ (kpair @ X231 @ X232))=(X232)))=>(![X233:$i]:(((iskpair @ X233)=>((kpair @ (kfst @ X233) @ (ksnd @ X233))=(X233))))=>(![X234:$i, X235:$i, X236:$i]:(((in @ X236 @ (cartprod @ X234 @ X235))=>(in @ (ksnd @ X236) @ X235)))=>(![X237:$i, X238:$i, X239:$i, X240:$i]:(((in @ (kpair @ X239 @ X240) @ (cartprod @ X237 @ X238))=>(in @ X239 @ X237)))=>(![X241:$i, X242:$i, X243:$i, X244:$i]:(((in @ (kpair @ X243 @ X244) @ (cartprod @ X241 @ X242))=>(in @ X244 @ X242)))=>((cartprodmempaircEq)=>(![X245:$i, X246:$i, X247:$i]:(((in @ X247 @ X245)=>![X248:$i]:(((in @ X248 @ X246)=>((kfst @ (kpair @ X247 @ X248))=(X247))))))=>(![X249:$i, X250:$i, X251:$i]:(((in @ X251 @ X249)=>![X252:$i]:(((in @ X252 @ X250)=>((ksnd @ (kpair @ X251 @ X252))=(X252))))))=>(![X253:$i, X254:$i, X255:$i]:(((in @ X255 @ (cartprod @ X253 @ X254))=>((kpair @ (kfst @ X255) @ (ksnd @ X255))=(X255))))=>(![X256:$i, X257:$i, X258:$i > $i > $o, X259:$i]:(((in @ X259 @ X256)=>![X260:$i]:(((in @ X260 @ X257)=>((X258 @ X259 @ X260)=>(in @ (kpair @ X259 @ X260) @ (dpsetconstr @ X256 @ X257 @ X258)))))))=>(![X261:$i, X262:$i, X263:$i > $i > $o]:((subset @ (dpsetconstr @ X261 @ X262 @ X263) @ (cartprod @ X261 @ X262)))=>(![X264:$i, X265:$i, X266:$i > $i > $o]:((subset @ (dpsetconstr @ X264 @ X265 @ X266) @ (cartprod @ X264 @ X265)))=>(![X267:$i, X268:$i, X269:$i > $i > $o, X270:$i]:(((in @ X270 @ X267)=>![X271:$i]:(((in @ X271 @ X268)=>((in @ (kpair @ X270 @ X271) @ (dpsetconstr @ X267 @ X268 @ X269))=>(X269 @ X270 @ X271))))))=>(![X272:$i, X273:$i, X274:$i > $i > $o, X275:$i, X276:$i]:(((in @ (kpair @ X275 @ X276) @ (dpsetconstr @ X272 @ X273 @ X274))=>(in @ X275 @ X272)))=>(![X277:$i, X278:$i, X279:$i > $i > $o, X280:$i, X281:$i]:(((in @ (kpair @ X280 @ X281) @ (dpsetconstr @ X277 @ X278 @ X279))=>(in @ X281 @ X278)))=>(![X282:$i, X283:$i, X284:$i > $i > $o, X285:$i, X286:$i]:(((in @ (kpair @ X285 @ X286) @ (dpsetconstr @ X282 @ X283 @ X284))=>(X284 @ X285 @ X286)))=>(![X287:$i, X288:$i, X289:$i]:((((subset @ X289 @ (cartprod @ X287 @ X288))&![X290:$i]:(((in @ X290 @ X287)=>?[X291:$i]:(((in @ X291 @ (dsetconstr @ X288 @ (^[Z0:$i]:((in @ (kpair @ X290 @ Z0) @ X289)))))&((dsetconstr @ X288 @ (^[Z0:$i]:((in @ (kpair @ X290 @ Z0) @ X289))))=(setadjoin @ X291 @ emptyset)))))))=>![X292:$i]:(((in @ X292 @ X287)=>?[X293:$i]:(((in @ X293 @ (dsetconstr @ X288 @ (^[Z0:$i]:((in @ (kpair @ X292 @ Z0) @ X289)))))&((dsetconstr @ X288 @ (^[Z0:$i]:((in @ (kpair @ X292 @ Z0) @ X289))))=(setadjoin @ X293 @ emptyset))))))))=>(![X294:$i, X295:$i, X296:$i]:((((subset @ X296 @ (cartprod @ X294 @ X295))&![X297:$i]:(((in @ X297 @ X294)=>?[X298:$i]:(((in @ X298 @ (dsetconstr @ X295 @ (^[Z0:$i]:((in @ (kpair @ X297 @ Z0) @ X296)))))&((dsetconstr @ X295 @ (^[Z0:$i]:((in @ (kpair @ X297 @ Z0) @ X296))))=(setadjoin @ X298 @ emptyset)))))))=>![X299:$i]:(((in @ X299 @ X294)=>(in @ (setunion @ (dsetconstr @ X295 @ (^[Z0:$i]:((in @ (kpair @ X299 @ Z0) @ X296))))) @ X295)))))=>(![X300:$i, X301:$i, X302:$i]:((((subset @ X302 @ (cartprod @ X300 @ X301))&![X303:$i]:(((in @ X303 @ X300)=>?[X304:$i]:(((in @ X304 @ (dsetconstr @ X301 @ (^[Z0:$i]:((in @ (kpair @ X303 @ Z0) @ X302)))))&((dsetconstr @ X301 @ (^[Z0:$i]:((in @ (kpair @ X303 @ Z0) @ X302))))=(setadjoin @ X304 @ emptyset)))))))=>![X305:$i]:(((in @ X305 @ X300)=>(in @ (ap @ X300 @ X301 @ X302 @ X305) @ X301)))))=>(![X306:$i, X307:$i, X308:$i]:(((in @ X308 @ (funcSet @ X306 @ X307))=>((subset @ X308 @ (cartprod @ X306 @ X307))&![X309:$i]:(((in @ X309 @ X306)=>?[X310:$i]:(((in @ X310 @ (dsetconstr @ X307 @ (^[Z0:$i]:((in @ (kpair @ X309 @ Z0) @ X308)))))&((dsetconstr @ X307 @ (^[Z0:$i]:((in @ (kpair @ X309 @ Z0) @ X308))))=(setadjoin @ X310 @ emptyset)))))))))=>(![X311:$i, X312:$i, X313:$i]:(((in @ X313 @ (funcSet @ X311 @ X312))=>![X314:$i]:(((in @ X314 @ X311)=>(in @ (ap @ X311 @ X312 @ X313 @ X314) @ X312)))))=>(![X315:$i, X316:$i, X317:$i]:((((subset @ X317 @ (cartprod @ X315 @ X316))&![X318:$i]:(((in @ X318 @ X315)=>?[X319:$i]:(((in @ X319 @ (dsetconstr @ X316 @ (^[Z0:$i]:((in @ (kpair @ X318 @ Z0) @ X317)))))&((dsetconstr @ X316 @ (^[Z0:$i]:((in @ (kpair @ X318 @ Z0) @ X317))))=(setadjoin @ X319 @ emptyset)))))))=>(in @ X317 @ (funcSet @ X315 @ X316))))=>(![X320:$i, X321:$i, X322:$i > $i]:((![X323:$i]:(((in @ X323 @ X320)=>(in @ (X322 @ X323) @ X321)))=>((subset @ (dpsetconstr @ X320 @ X321 @ (^[Z0:$i]:($eq @ (X322 @ Z0)))) @ (cartprod @ X320 @ X321))&![X324:$i]:(((in @ X324 @ X320)=>?[X325:$i]:(((in @ X325 @ (dsetconstr @ X321 @ (^[Z0:$i]:((in @ (kpair @ X324 @ Z0) @ (dpsetconstr @ X320 @ X321 @ (^[Z1:$i]:($eq @ (X322 @ Z1)))))))))&((dsetconstr @ X321 @ (^[Z0:$i]:((in @ (kpair @ X324 @ Z0) @ (dpsetconstr @ X320 @ X321 @ (^[Z1:$i]:($eq @ (X322 @ Z1))))))))=(setadjoin @ X325 @ emptyset)))))))))=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>((subset @ (lam @ X4 @ X5 @ X33) @ (cartprod @ X4 @ X5))&![X326:$i]:(((in @ X326 @ X4)=>?[X327:$i]:(((in @ X327 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X326 @ Z0) @ (lam @ X4 @ X5 @ X33))))))&((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X326 @ Z0) @ (lam @ X4 @ X5 @ X33)))))=(setadjoin @ X327 @ 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_58]), cartprodsndpairEq]), ksndpairEq]), cartprodfstpairEq]), kfstpairEq]), kpairsurjEq]), kpairp]), kpairiskpair]), cartprodpairsurjEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), cartprodfstin]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), ap2p]), c_0_65]), 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_75]), c_0_76]), c_0_77]), c_0_78]), c_0_55])])).
% 253.30/33.53 thf(c_0_80, plain, ![X328:$i, X329:$i, X330:$i > $i]:(((lam @ X328 @ X329 @ X330)=(dpsetconstr @ X328 @ X329 @ (^[Z0:$i]:($eq @ (X330 @ Z0)))))), inference(fool_unroll,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[lam])])])).
% 253.30/33.53 thf(c_0_81, negated_conjecture, ![X335:$i, X336:$i, X337:$i, X338:$i, X339:$i, X340:$i, X341:$i, X342:$i, X343:$i, X344:$i, X345:$i, X348:$i, X349:$i, X350:$i, X351:$i, X352:$i > $o, X355:$i, X357:$i, X358:$i > $o, X359:$i, X361:$i, X362:$i > $o, X363:$i, X366:$i, X367:$i > $o, X370:$i, X372:$i, X374:$i, X375:$i, X376:$i, X377:$i, X378:$i, X379:$i, X380:$i, X381:$i, X383:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i, X389:$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 > $i > $o, X411:$i, X412:$i, X413:$i, X414:$i, X415:$i > $i > $o, X416:$i, X417:$i, X418:$i > $i > $o, X419:$i, X420:$i, X421:$i > $i > $o, X422:$i, X423:$i, X424:$i, X425:$i, X426:$i > $i > $o, X427:$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, X440:$i, X441:$i, X443:$i, X444:$i, X446:$i, X447:$i, X448:$i, X450:$i, X451:$i, X452:$i, X453:$i, X454:$i, X456:$i, X457:$i, X458:$i, X459:$i, X460:$i, X461:$i, X463:$i, X464:$i, X465:$i, X466:$i, X467:$i, X468:$i, X469:$i, X471:$i, X472:$i, X473:$i, X474:$i > $i, X476:$i, X481:$i, X483:$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 @ X335 @ emptyset) @ (setadjoin @ (setadjoin @ X335 @ (setadjoin @ X336 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X337 @ X338))&((singletonsubset)&((singletoninpowerset)&((singletoninpowunion)&((upairset2E)&((upairsubunion)&((upairinpowunion)&((ubforcartprodlem1)&((ubforcartprodlem2)&((ubforcartprodlem3)&((~(in @ X341 @ X339)|(~(in @ X342 @ X340)|(in @ (kpair @ X341 @ X342) @ (cartprod @ X339 @ X340))))&((((in @ (esk1_3 @ X343 @ X344 @ X345) @ X343)|~(in @ X345 @ (cartprod @ X343 @ X344)))&(((in @ (esk2_3 @ X343 @ X344 @ X345) @ X344)|~(in @ X345 @ (cartprod @ X343 @ X344)))&(((X345)=(kpair @ (esk1_3 @ X343 @ X344 @ X345) @ (esk2_3 @ X343 @ X344 @ X345)))|~(in @ X345 @ (cartprod @ X343 @ X344)))))&((~(in @ X350 @ (cartprod @ X348 @ X349))|(iskpair @ X350))&((setunionE2)&((setunionsingleton1)&((setunionsingleton2)&((setunionsingleton)&(((((in @ (esk5_2 @ X351 @ X352) @ (dsetconstr @ X351 @ X352))|(~(in @ X355 @ X351)|~(X352 @ X355))|(in @ (esk3_2 @ X351 @ X352) @ X351))&(((dsetconstr @ X351 @ X352)=(setadjoin @ (esk5_2 @ X351 @ X352) @ emptyset))|(~(in @ X355 @ X351)|~(X352 @ X355))|(in @ (esk3_2 @ X351 @ X352) @ X351)))&((((in @ (esk5_2 @ X351 @ X352) @ (dsetconstr @ X351 @ X352))|(~(in @ X355 @ X351)|~(X352 @ X355))|(in @ (esk4_2 @ X351 @ X352) @ X351))&(((dsetconstr @ X351 @ X352)=(setadjoin @ (esk5_2 @ X351 @ X352) @ emptyset))|(~(in @ X355 @ X351)|~(X352 @ X355))|(in @ (esk4_2 @ X351 @ X352) @ X351)))&((((in @ (esk5_2 @ X351 @ X352) @ (dsetconstr @ X351 @ X352))|(~(in @ X355 @ X351)|~(X352 @ X355))|(X352 @ (esk3_2 @ X351 @ X352)))&(((dsetconstr @ X351 @ X352)=(setadjoin @ (esk5_2 @ X351 @ X352) @ emptyset))|(~(in @ X355 @ X351)|~(X352 @ X355))|(X352 @ (esk3_2 @ X351 @ X352))))&((((in @ (esk5_2 @ X351 @ X352) @ (dsetconstr @ X351 @ X352))|(~(in @ X355 @ X351)|~(X352 @ X355))|(X352 @ (esk4_2 @ X351 @ X352)))&(((dsetconstr @ X351 @ X352)=(setadjoin @ (esk5_2 @ X351 @ X352) @ emptyset))|(~(in @ X355 @ X351)|~(X352 @ X355))|(X352 @ (esk4_2 @ X351 @ X352))))&(((in @ (esk5_2 @ X351 @ X352) @ (dsetconstr @ X351 @ X352))|(~(in @ X355 @ X351)|~(X352 @ X355))|((esk3_2 @ X351 @ X352)!=(esk4_2 @ X351 @ X352)))&(((dsetconstr @ X351 @ X352)=(setadjoin @ (esk5_2 @ X351 @ X352) @ emptyset))|(~(in @ X355 @ X351)|~(X352 @ X355))|((esk3_2 @ X351 @ X352)!=(esk4_2 @ X351 @ X352))))))))&((((in @ (esk6_2 @ X357 @ X358) @ X357)|(~(in @ X359 @ (dsetconstr @ X357 @ X358))|((dsetconstr @ X357 @ X358)!=(setadjoin @ X359 @ emptyset))))&((X358 @ (esk6_2 @ X357 @ X358))|(~(in @ X359 @ (dsetconstr @ X357 @ X358))|((dsetconstr @ X357 @ X358)!=(setadjoin @ X359 @ emptyset)))))&(((((in @ (esk8_3 @ X361 @ X362 @ X363) @ (dsetconstr @ X361 @ X362))|(in @ (esk7_3 @ X361 @ X362 @ X363) @ X361)|~(X362 @ X363)|~(in @ X363 @ X361))&(((dsetconstr @ X361 @ X362)=(setadjoin @ (esk8_3 @ X361 @ X362 @ X363) @ emptyset))|(in @ (esk7_3 @ X361 @ X362 @ X363) @ X361)|~(X362 @ X363)|~(in @ X363 @ X361)))&((((in @ (esk8_3 @ X361 @ X362 @ X363) @ (dsetconstr @ X361 @ X362))|(X362 @ (esk7_3 @ X361 @ X362 @ X363))|~(X362 @ X363)|~(in @ X363 @ X361))&(((dsetconstr @ X361 @ X362)=(setadjoin @ (esk8_3 @ X361 @ X362 @ X363) @ emptyset))|(X362 @ (esk7_3 @ X361 @ X362 @ X363))|~(X362 @ X363)|~(in @ X363 @ X361)))&(((in @ (esk8_3 @ X361 @ X362 @ X363) @ (dsetconstr @ X361 @ X362))|((esk7_3 @ X361 @ X362 @ X363)!=(X363))|~(X362 @ X363)|~(in @ X363 @ X361))&(((dsetconstr @ X361 @ X362)=(setadjoin @ (esk8_3 @ X361 @ X362 @ X363) @ emptyset))|((esk7_3 @ X361 @ X362 @ X363)!=(X363))|~(X362 @ X363)|~(in @ X363 @ X361)))))&(((((in @ (esk11_2 @ X366 @ X367) @ (dsetconstr @ X366 @ X367))|(~(in @ X370 @ X366)|~(X367 @ X370))|(in @ (esk9_2 @ X366 @ X367) @ X366))&(((dsetconstr @ X366 @ X367)=(setadjoin @ (esk11_2 @ X366 @ X367) @ emptyset))|(~(in @ X370 @ X366)|~(X367 @ X370))|(in @ (esk9_2 @ X366 @ X367) @ X366)))&((((in @ (esk11_2 @ X366 @ X367) @ (dsetconstr @ X366 @ X367))|(~(in @ X370 @ X366)|~(X367 @ X370))|(in @ (esk10_2 @ X366 @ X367) @ X366))&(((dsetconstr @ X366 @ X367)=(setadjoin @ (esk11_2 @ X366 @ X367) @ emptyset))|(~(in @ X370 @ X366)|~(X367 @ X370))|(in @ (esk10_2 @ X366 @ X367) @ X366)))&((((in @ (esk11_2 @ X366 @ X367) @ (dsetconstr @ X366 @ X367))|(~(in @ X370 @ X366)|~(X367 @ X370))|(X367 @ (esk9_2 @ X366 @ X367)))&(((dsetconstr @ X366 @ X367)=(setadjoin @ (esk11_2 @ X366 @ X367) @ emptyset))|(~(in @ X370 @ X366)|~(X367 @ X370))|(X367 @ (esk9_2 @ X366 @ X367))))&((((in @ (esk11_2 @ X366 @ X367) @ (dsetconstr @ X366 @ X367))|(~(in @ X370 @ X366)|~(X367 @ X370))|(X367 @ (esk10_2 @ X366 @ X367)))&(((dsetconstr @ X366 @ X367)=(setadjoin @ (esk11_2 @ X366 @ X367) @ emptyset))|(~(in @ X370 @ X366)|~(X367 @ X370))|(X367 @ (esk10_2 @ X366 @ X367))))&(((in @ (esk11_2 @ X366 @ X367) @ (dsetconstr @ X366 @ X367))|(~(in @ X370 @ X366)|~(X367 @ X370))|((esk9_2 @ X366 @ X367)!=(esk10_2 @ X366 @ X367)))&(((dsetconstr @ X366 @ X367)=(setadjoin @ (esk11_2 @ X366 @ X367) @ emptyset))|(~(in @ X370 @ X366)|~(X367 @ X370))|((esk9_2 @ X366 @ X367)!=(esk10_2 @ X366 @ X367))))))))&((singletonsuniq)&((setukpairinjL1)&((((in @ (esk12_1 @ X372) @ (dsetconstr @ (setunion @ X372) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X372)))))|~(iskpair @ X372))&(((dsetconstr @ (setunion @ X372) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X372))))=(setadjoin @ (esk12_1 @ X372) @ emptyset))|~(iskpair @ X372)))&((~(in @ X375 @ X374)|((X374)!=(setadjoin @ X375 @ emptyset))|(in @ (setunion @ X374) @ X374))&(((kfst @ (kpair @ X376 @ X377))=(X376))&((~(in @ X380 @ (cartprod @ X378 @ X379))|(in @ (kfst @ X380) @ X378))&((setukpairinjL2)&((setukpairinjL)&((setukpairinjR11)&((setukpairinjR12)&((setukpairinjR1)&((upairequniteq)&((setukpairinjR2)&((setukpairinjR)&((((in @ (esk13_1 @ X381) @ (dsetconstr @ (setunion @ X381) @ (^[Z0:$i]:(((X381)=(kpair @ (kfst @ X381) @ Z0))))))|~(iskpair @ X381))&(((dsetconstr @ (setunion @ X381) @ (^[Z0:$i]:(((X381)=(kpair @ (kfst @ X381) @ Z0)))))=(setadjoin @ (esk13_1 @ X381) @ emptyset))|~(iskpair @ X381)))&(((ksnd @ (kpair @ X383 @ X384))=(X384))&((~(iskpair @ X385)|((kpair @ (kfst @ X385) @ (ksnd @ X385))=(X385)))&((~(in @ X388 @ (cartprod @ X386 @ X387))|(in @ (ksnd @ X388) @ X387))&((~(in @ (kpair @ X391 @ X392) @ (cartprod @ X389 @ X390))|(in @ X391 @ X389))&((~(in @ (kpair @ X395 @ X396) @ (cartprod @ X393 @ X394))|(in @ X396 @ X394))&((cartprodmempaircEq)&((~(in @ X399 @ X397)|(~(in @ X400 @ X398)|((kfst @ (kpair @ X399 @ X400))=(X399))))&((~(in @ X403 @ X401)|(~(in @ X404 @ X402)|((ksnd @ (kpair @ X403 @ X404))=(X404))))&((~(in @ X407 @ (cartprod @ X405 @ X406))|((kpair @ (kfst @ X407) @ (ksnd @ X407))=(X407)))&((~(in @ X411 @ X408)|(~(in @ X412 @ X409)|(~(X410 @ X411 @ X412)|(in @ (kpair @ X411 @ X412) @ (dpsetconstr @ X408 @ X409 @ X410)))))&((subset @ (dpsetconstr @ X413 @ X414 @ X415) @ (cartprod @ X413 @ X414))&((subset @ (dpsetconstr @ X416 @ X417 @ X418) @ (cartprod @ X416 @ X417))&((~(in @ X422 @ X419)|(~(in @ X423 @ X420)|(~(in @ (kpair @ X422 @ X423) @ (dpsetconstr @ X419 @ X420 @ X421))|(X421 @ X422 @ X423))))&((~(in @ (kpair @ X427 @ X428) @ (dpsetconstr @ X424 @ X425 @ X426))|(in @ X427 @ X424))&((~(in @ (kpair @ X432 @ X433) @ (dpsetconstr @ X429 @ X430 @ X431))|(in @ X433 @ X430))&((~(in @ (kpair @ X437 @ X438) @ (dpsetconstr @ X434 @ X435 @ X436))|(X436 @ X437 @ X438))&(((((in @ (esk15_4 @ X439 @ X440 @ X441 @ X444) @ (dsetconstr @ X440 @ (^[Z0:$i]:((in @ (kpair @ X444 @ Z0) @ X441)))))|~(in @ X444 @ X439)|((in @ (esk14_3 @ X439 @ X440 @ X441) @ X439)|~(subset @ X441 @ (cartprod @ X439 @ X440))))&(((dsetconstr @ X440 @ (^[Z0:$i]:((in @ (kpair @ X444 @ Z0) @ X441))))=(setadjoin @ (esk15_4 @ X439 @ X440 @ X441 @ X444) @ emptyset))|~(in @ X444 @ X439)|((in @ (esk14_3 @ X439 @ X440 @ X441) @ X439)|~(subset @ X441 @ (cartprod @ X439 @ X440)))))&(((in @ (esk15_4 @ X439 @ X440 @ X441 @ X444) @ (dsetconstr @ X440 @ (^[Z0:$i]:((in @ (kpair @ X444 @ Z0) @ X441)))))|~(in @ X444 @ X439)|(~(in @ X443 @ (dsetconstr @ X440 @ (^[Z0:$i]:((in @ (kpair @ (esk14_3 @ X439 @ X440 @ X441) @ Z0) @ X441)))))|((dsetconstr @ X440 @ (^[Z0:$i]:((in @ (kpair @ (esk14_3 @ X439 @ X440 @ X441) @ Z0) @ X441))))!=(setadjoin @ X443 @ emptyset))|~(subset @ X441 @ (cartprod @ X439 @ X440))))&(((dsetconstr @ X440 @ (^[Z0:$i]:((in @ (kpair @ X444 @ Z0) @ X441))))=(setadjoin @ (esk15_4 @ X439 @ X440 @ X441 @ X444) @ emptyset))|~(in @ X444 @ X439)|(~(in @ X443 @ (dsetconstr @ X440 @ (^[Z0:$i]:((in @ (kpair @ (esk14_3 @ X439 @ X440 @ X441) @ Z0) @ X441)))))|((dsetconstr @ X440 @ (^[Z0:$i]:((in @ (kpair @ (esk14_3 @ X439 @ X440 @ X441) @ Z0) @ X441))))!=(setadjoin @ X443 @ emptyset))|~(subset @ X441 @ (cartprod @ X439 @ X440))))))&((((in @ (esk16_3 @ X446 @ X447 @ X448) @ X446)|~(subset @ X448 @ (cartprod @ X446 @ X447))|(~(in @ X451 @ X446)|(in @ (setunion @ (dsetconstr @ X447 @ (^[Z0:$i]:((in @ (kpair @ X451 @ Z0) @ X448))))) @ X447)))&(~(in @ X450 @ (dsetconstr @ X447 @ (^[Z0:$i]:((in @ (kpair @ (esk16_3 @ X446 @ X447 @ X448) @ Z0) @ X448)))))|((dsetconstr @ X447 @ (^[Z0:$i]:((in @ (kpair @ (esk16_3 @ X446 @ X447 @ X448) @ Z0) @ X448))))!=(setadjoin @ X450 @ emptyset))|~(subset @ X448 @ (cartprod @ X446 @ X447))|(~(in @ X451 @ X446)|(in @ (setunion @ (dsetconstr @ X447 @ (^[Z0:$i]:((in @ (kpair @ X451 @ Z0) @ X448))))) @ X447))))&((((in @ (esk17_3 @ X452 @ X453 @ X454) @ X452)|~(subset @ X454 @ (cartprod @ X452 @ X453))|(~(in @ X457 @ X452)|(in @ (ap @ X452 @ X453 @ X454 @ X457) @ X453)))&(~(in @ X456 @ (dsetconstr @ X453 @ (^[Z0:$i]:((in @ (kpair @ (esk17_3 @ X452 @ X453 @ X454) @ Z0) @ X454)))))|((dsetconstr @ X453 @ (^[Z0:$i]:((in @ (kpair @ (esk17_3 @ X452 @ X453 @ X454) @ Z0) @ X454))))!=(setadjoin @ X456 @ emptyset))|~(subset @ X454 @ (cartprod @ X452 @ X453))|(~(in @ X457 @ X452)|(in @ (ap @ X452 @ X453 @ X454 @ X457) @ X453))))&((((subset @ X460 @ (cartprod @ X458 @ X459))|~(in @ X460 @ (funcSet @ X458 @ X459)))&(((in @ (esk18_4 @ X458 @ X459 @ X460 @ X461) @ (dsetconstr @ X459 @ (^[Z0:$i]:((in @ (kpair @ X461 @ Z0) @ X460)))))|~(in @ X461 @ X458)|~(in @ X460 @ (funcSet @ X458 @ X459)))&(((dsetconstr @ X459 @ (^[Z0:$i]:((in @ (kpair @ X461 @ Z0) @ X460))))=(setadjoin @ (esk18_4 @ X458 @ X459 @ X460 @ X461) @ emptyset))|~(in @ X461 @ X458)|~(in @ X460 @ (funcSet @ X458 @ X459)))))&((~(in @ X465 @ (funcSet @ X463 @ X464))|(~(in @ X466 @ X463)|(in @ (ap @ X463 @ X464 @ X465 @ X466) @ X464)))&((((in @ (esk19_3 @ X467 @ X468 @ X469) @ X467)|~(subset @ X469 @ (cartprod @ X467 @ X468))|(in @ X469 @ (funcSet @ X467 @ X468)))&(~(in @ X471 @ (dsetconstr @ X468 @ (^[Z0:$i]:((in @ (kpair @ (esk19_3 @ X467 @ X468 @ X469) @ Z0) @ X469)))))|((dsetconstr @ X468 @ (^[Z0:$i]:((in @ (kpair @ (esk19_3 @ X467 @ X468 @ X469) @ Z0) @ X469))))!=(setadjoin @ X471 @ emptyset))|~(subset @ X469 @ (cartprod @ X467 @ X468))|(in @ X469 @ (funcSet @ X467 @ X468))))&(((((subset @ (dpsetconstr @ X472 @ X473 @ (^[Z0:$i]:($eq @ (X474 @ Z0)))) @ (cartprod @ X472 @ X473))|(in @ (esk20_3 @ X472 @ X473 @ X474) @ X472))&(((in @ (esk21_4 @ X472 @ X473 @ X474 @ X476) @ (dsetconstr @ X473 @ (^[Z0:$i]:((in @ (kpair @ X476 @ Z0) @ (dpsetconstr @ X472 @ X473 @ (^[Z1:$i]:($eq @ (X474 @ Z1)))))))))|~(in @ X476 @ X472)|(in @ (esk20_3 @ X472 @ X473 @ X474) @ X472))&(((dsetconstr @ X473 @ (^[Z0:$i]:((in @ (kpair @ X476 @ Z0) @ (dpsetconstr @ X472 @ X473 @ (^[Z1:$i]:($eq @ (X474 @ Z1))))))))=(setadjoin @ (esk21_4 @ X472 @ X473 @ X474 @ X476) @ emptyset))|~(in @ X476 @ X472)|(in @ (esk20_3 @ X472 @ X473 @ X474) @ X472))))&(((subset @ (dpsetconstr @ X472 @ X473 @ (^[Z0:$i]:($eq @ (X474 @ Z0)))) @ (cartprod @ X472 @ X473))|~(in @ (X474 @ (esk20_3 @ X472 @ X473 @ X474)) @ X473))&(((in @ (esk21_4 @ X472 @ X473 @ X474 @ X476) @ (dsetconstr @ X473 @ (^[Z0:$i]:((in @ (kpair @ X476 @ Z0) @ (dpsetconstr @ X472 @ X473 @ (^[Z1:$i]:($eq @ (X474 @ Z1)))))))))|~(in @ X476 @ X472)|~(in @ (X474 @ (esk20_3 @ X472 @ X473 @ X474)) @ X473))&(((dsetconstr @ X473 @ (^[Z0:$i]:((in @ (kpair @ X476 @ Z0) @ (dpsetconstr @ X472 @ X473 @ (^[Z1:$i]:($eq @ (X474 @ Z1))))))))=(setadjoin @ (esk21_4 @ X472 @ X473 @ X474 @ X476) @ emptyset))|~(in @ X476 @ X472)|~(in @ (X474 @ (esk20_3 @ X472 @ X473 @ X474)) @ X473)))))&((~(in @ X481 @ esk22_0)|(in @ (esk24_0 @ X481) @ esk23_0))&(((in @ esk25_0 @ esk22_0)|~(subset @ (lam @ esk22_0 @ esk23_0 @ esk24_0) @ (cartprod @ esk22_0 @ esk23_0)))&(~(in @ X483 @ (dsetconstr @ esk23_0 @ (^[Z0:$i]:((in @ (kpair @ esk25_0 @ Z0) @ (lam @ esk22_0 @ esk23_0 @ esk24_0))))))|((dsetconstr @ esk23_0 @ (^[Z0:$i]:((in @ (kpair @ esk25_0 @ Z0) @ (lam @ esk22_0 @ esk23_0 @ esk24_0)))))!=(setadjoin @ X483 @ emptyset))|~(subset @ (lam @ esk22_0 @ esk23_0 @ esk24_0) @ (cartprod @ esk22_0 @ esk23_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_79])])])])])])).
% 253.30/33.53 thf(c_0_82, plain, ![X484:$i, X485:$i, X486:$i > $i]:(((lam @ X484 @ X485 @ X486)=(dpsetconstr @ X484 @ X485 @ (^[Z0:$i]:($eq @ (X486 @ Z0)))))), inference(variable_rename,[status(thm)],[c_0_80])).
% 253.30/33.53 thf(c_0_83, plain, ![X493:$i, X31:$i > $i]:(((epred2_1 @ X31 @ X493)=($eq @ (X31 @ X493)))), introduced(definition)).
% 253.30/33.53 thf(c_0_84, plain, ![X543:$i, X544:$i > $i]:(((epred2_1 @ X544 @ X543)=($eq @ (X544 @ X543)))), inference(variable_rename,[status(thm)],[])).
% 253.30/33.53 thf(c_0_85, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ (esk5_2 @ X2 @ X1) @ (dsetconstr @ X2 @ X1))|(X1 @ (esk3_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_86, negated_conjecture, ![X2:$i]:(((in @ (esk24_0 @ X2) @ esk23_0)|~((in @ X2 @ esk22_0)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_87, negated_conjecture, ((in @ esk25_0 @ esk22_0)|~((subset @ (lam @ esk22_0 @ esk23_0 @ esk24_0) @ (cartprod @ esk22_0 @ esk23_0)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_88, plain, ![X2:$i, X3:$i, X31:$i > $i]:(((lam @ X2 @ X3 @ X31)=(dpsetconstr @ X2 @ X3 @ (epred2_1 @ X31)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_82]), c_0_83])).
% 253.30/33.53 thf(c_0_89, negated_conjecture, ![X2:$i, X6:$i > $i > $o, X3:$i]:((subset @ (dpsetconstr @ X2 @ X3 @ X6) @ (cartprod @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_90, plain, ![X31:$i > $i, X2:$i]:(((epred2_1 @ X31 @ X2)=($eq @ (X31 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_84])).
% 253.30/33.53 thf(c_0_91, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ (esk5_2 @ X2 @ X1) @ (dsetconstr @ X2 @ X1))|(X1 @ (esk4_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_92, negated_conjecture, ![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_93, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk5_2 @ X2 @ X1) @ emptyset))|(X1 @ (esk3_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_94, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk5_2 @ X2 @ X1) @ emptyset))|(X1 @ (esk4_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_95, negated_conjecture, ![X1:$i > $o, X2:$i]:(((in @ (esk5_2 @ esk23_0 @ X1) @ (dsetconstr @ esk23_0 @ X1))|(X1 @ (esk3_2 @ esk23_0 @ X1))|~((in @ X2 @ esk22_0))|~((X1 @ (esk24_0 @ X2))))), inference(spm,[status(thm)],[c_0_85, c_0_86])).
% 253.30/33.53 thf(c_0_96, negated_conjecture, (in @ esk25_0 @ esk22_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87, c_0_88]), c_0_89])])).
% 253.30/33.53 thf(c_0_97, plain, ![X2:$i, X31:$i > $i, X546:$i]:(((epred2_1 @ X31 @ X2 @ X546)<=>((X31 @ X2)=(X546)))), inference(arg_cong,[status(thm)],[c_0_90])).
% 253.30/33.53 thf(c_0_98, negated_conjecture, ![X1:$i > $o, X2:$i]:(((in @ (esk5_2 @ esk23_0 @ X1) @ (dsetconstr @ esk23_0 @ X1))|(X1 @ (esk4_2 @ esk23_0 @ X1))|~((in @ X2 @ esk22_0))|~((X1 @ (esk24_0 @ X2))))), inference(spm,[status(thm)],[c_0_91, c_0_86])).
% 253.30/33.53 thf(c_0_99, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ (esk5_2 @ X2 @ X1) @ (dsetconstr @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3))|((esk3_2 @ X2 @ X1)!=(esk4_2 @ X2 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_100, negated_conjecture, ![X2:$i, X3:$i]:(((epred2_1 @ ksnd @ (kpair @ X2 @ X3))=($eq @ X3))), inference(spm,[status(thm)],[c_0_90, c_0_92])).
% 253.30/33.53 thf(c_0_101, negated_conjecture, ![X1:$i > $o, X2:$i]:((((setadjoin @ (esk5_2 @ esk23_0 @ X1) @ emptyset)=(dsetconstr @ esk23_0 @ X1))|(X1 @ (esk3_2 @ esk23_0 @ X1))|~((in @ X2 @ esk22_0))|~((X1 @ (esk24_0 @ X2))))), inference(spm,[status(thm)],[c_0_93, c_0_86])).
% 253.30/33.53 thf(c_0_102, negated_conjecture, ![X1:$i > $o, X2:$i]:((((setadjoin @ (esk5_2 @ esk23_0 @ X1) @ emptyset)=(dsetconstr @ esk23_0 @ X1))|(X1 @ (esk4_2 @ esk23_0 @ X1))|~((in @ X2 @ esk22_0))|~((X1 @ (esk24_0 @ X2))))), inference(spm,[status(thm)],[c_0_94, c_0_86])).
% 253.30/33.53 thf(c_0_103, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk5_2 @ X2 @ X1) @ emptyset))|~((in @ X3 @ X2))|~((X1 @ X3))|((esk3_2 @ X2 @ X1)!=(esk4_2 @ X2 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_104, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk23_0 @ X1) @ (dsetconstr @ esk23_0 @ X1))|(X1 @ (esk3_2 @ esk23_0 @ X1))|~((X1 @ (esk24_0 @ esk25_0))))), inference(spm,[status(thm)],[c_0_95, c_0_96])).
% 253.30/33.53 thf(c_0_105, plain, ![X31:$i > $i, X2:$i]:((epred2_1 @ X31 @ X2 @ (X31 @ X2))), inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_97])])).
% 253.30/33.53 thf(c_0_106, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk23_0 @ X1) @ (dsetconstr @ esk23_0 @ X1))|(X1 @ (esk4_2 @ esk23_0 @ X1))|~((X1 @ (esk24_0 @ esk25_0))))), inference(spm,[status(thm)],[c_0_98, c_0_96])).
% 253.30/33.53 thf(c_0_107, negated_conjecture, ![X1:$i > $o, X2:$i]:(((in @ (esk5_2 @ esk23_0 @ X1) @ (dsetconstr @ esk23_0 @ X1))|((esk4_2 @ esk23_0 @ X1)!=(esk3_2 @ esk23_0 @ X1))|~((in @ X2 @ esk22_0))|~((X1 @ (esk24_0 @ X2))))), inference(spm,[status(thm)],[c_0_99, c_0_86])).
% 253.30/33.53 thf(c_0_108, negated_conjecture, ![X2:$i, X3:$i, X547:$i]:(((epred2_1 @ ksnd @ (kpair @ X2 @ X3) @ X547)<=>((X3)=(X547)))), inference(arg_cong,[status(thm)],[c_0_100])).
% 253.30/33.53 thf(c_0_109, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk23_0 @ X1) @ emptyset)=(dsetconstr @ esk23_0 @ X1))|(X1 @ (esk3_2 @ esk23_0 @ X1))|~((X1 @ (esk24_0 @ esk25_0))))), inference(spm,[status(thm)],[c_0_101, c_0_96])).
% 253.30/33.53 thf(c_0_110, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk23_0 @ X1) @ emptyset)=(dsetconstr @ esk23_0 @ X1))|(X1 @ (esk4_2 @ esk23_0 @ X1))|~((X1 @ (esk24_0 @ esk25_0))))), inference(spm,[status(thm)],[c_0_102, c_0_96])).
% 253.30/33.53 thf(c_0_111, negated_conjecture, ![X1:$i > $o, X2:$i]:((((setadjoin @ (esk5_2 @ esk23_0 @ X1) @ emptyset)=(dsetconstr @ esk23_0 @ X1))|((esk4_2 @ esk23_0 @ X1)!=(esk3_2 @ esk23_0 @ X1))|~((in @ X2 @ esk22_0))|~((X1 @ (esk24_0 @ X2))))), inference(spm,[status(thm)],[c_0_103, c_0_86])).
% 253.30/33.53 thf(c_0_112, plain, ![X2:$i, X31:$i > $i, X3:$i]:((((X31 @ X2)=(X3))|~((epred2_1 @ X31 @ X2 @ X3)))), inference(dynamic_cnf,[status(thm)],[c_0_97])).
% 253.30/33.53 thf(c_0_113, plain, ((in @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ (dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))|(epred2_1 @ esk24_0 @ esk25_0 @ (esk3_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))), inference(spm,[status(thm)],[c_0_104, c_0_105])).
% 253.30/33.53 thf(c_0_114, plain, ((in @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ (dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))|(epred2_1 @ esk24_0 @ esk25_0 @ (esk4_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))), inference(spm,[status(thm)],[c_0_106, c_0_105])).
% 253.30/33.53 thf(c_0_115, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk23_0 @ X1) @ (dsetconstr @ esk23_0 @ X1))|((esk4_2 @ esk23_0 @ X1)!=(esk3_2 @ esk23_0 @ X1))|~((X1 @ (esk24_0 @ esk25_0))))), inference(spm,[status(thm)],[c_0_107, c_0_96])).
% 253.30/33.53 thf(c_0_116, negated_conjecture, ![X2:$i, X3:$i]:((epred2_1 @ ksnd @ (kpair @ X2 @ X3) @ X3)), inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_108])])).
% 253.30/33.53 thf(c_0_117, plain, (((setadjoin @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ emptyset)=(dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))|(epred2_1 @ esk24_0 @ esk25_0 @ (esk3_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))), inference(spm,[status(thm)],[c_0_109, c_0_105])).
% 253.30/33.53 thf(c_0_118, plain, (((setadjoin @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ emptyset)=(dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))|(epred2_1 @ esk24_0 @ esk25_0 @ (esk4_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))), inference(spm,[status(thm)],[c_0_110, c_0_105])).
% 253.30/33.53 thf(c_0_119, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk23_0 @ X1) @ emptyset)=(dsetconstr @ esk23_0 @ X1))|((esk4_2 @ esk23_0 @ X1)!=(esk3_2 @ esk23_0 @ X1))|~((X1 @ (esk24_0 @ esk25_0))))), inference(spm,[status(thm)],[c_0_111, c_0_96])).
% 253.30/33.53 thf(c_0_120, plain, (((esk24_0 @ esk25_0)=(esk3_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))|(in @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ (dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))), inference(spm,[status(thm)],[c_0_112, c_0_113])).
% 253.30/33.53 thf(c_0_121, plain, (((esk24_0 @ esk25_0)=(esk4_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))|(in @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ (dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))), inference(spm,[status(thm)],[c_0_112, c_0_114])).
% 253.30/33.53 thf(c_0_122, negated_conjecture, ((in @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ (dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))|((esk4_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0))!=(esk3_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116]), c_0_100]), c_0_100]), c_0_100]), c_0_100]), c_0_90]), c_0_90]), c_0_90]), c_0_90])).
% 253.30/33.53 thf(c_0_123, plain, (((setadjoin @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ emptyset)=(dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))|((esk24_0 @ esk25_0)=(esk3_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))), inference(spm,[status(thm)],[c_0_112, c_0_117])).
% 253.30/33.53 thf(c_0_124, plain, (((setadjoin @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ emptyset)=(dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))|((esk24_0 @ esk25_0)=(esk4_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))), inference(spm,[status(thm)],[c_0_112, c_0_118])).
% 253.30/33.53 thf(c_0_125, negated_conjecture, (((setadjoin @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ emptyset)=(dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))|((esk4_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0))!=(esk3_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_116]), c_0_100]), c_0_90]), c_0_100]), c_0_90]), c_0_100]), c_0_90]), c_0_100]), c_0_90])).
% 253.30/33.53 thf(c_0_126, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((X1 @ (esk6_2 @ X2 @ X1))|~((in @ X3 @ (dsetconstr @ X2 @ X1)))|((dsetconstr @ X2 @ X1)!=(setadjoin @ X3 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_127, plain, (in @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ (dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_121]), c_0_122])).
% 253.30/33.53 thf(c_0_128, plain, ((setadjoin @ (esk5_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ emptyset)=(dsetconstr @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_124]), c_0_125])).
% 253.30/33.53 thf(c_0_129, plain, ![X545:$i]:(((~(epred1_0 @ X545)|(in @ (kpair @ esk25_0 @ X545) @ (lam @ esk22_0 @ esk23_0 @ esk24_0)))&(~(in @ (kpair @ esk25_0 @ X545) @ (lam @ esk22_0 @ esk23_0 @ esk24_0))|(epred1_0 @ X545)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])).
% 253.30/33.53 thf(c_0_130, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ (esk6_2 @ X2 @ X1) @ X2)|~((in @ X3 @ (dsetconstr @ X2 @ X1)))|((dsetconstr @ X2 @ X1)!=(setadjoin @ X3 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_131, negated_conjecture, (epred2_1 @ esk24_0 @ esk25_0 @ (esk6_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_127]), c_0_128])])).
% 253.30/33.53 thf(c_0_132, plain, ![X2:$i]:(((epred1_0 @ X2)|~((in @ (kpair @ esk25_0 @ X2) @ (lam @ esk22_0 @ esk23_0 @ esk24_0))))), inference(split_conjunct,[status(thm)],[c_0_129])).
% 253.30/33.53 thf(c_0_133, negated_conjecture, ![X3:$i, X2:$i, X6:$i > $i > $o, X5:$i, X4:$i]:(((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X5 @ X6))|~((in @ X2 @ X3))|~((in @ X4 @ X5))|~((X6 @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_134, negated_conjecture, (in @ (esk6_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0)) @ esk23_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130, c_0_127]), c_0_128])])).
% 253.30/33.53 thf(c_0_135, plain, ((esk6_2 @ esk23_0 @ (epred2_1 @ esk24_0 @ esk25_0))=(esk24_0 @ esk25_0)), inference(spm,[status(thm)],[c_0_112, c_0_131])).
% 253.30/33.53 thf(c_0_136, plain, ![X2:$i]:(((epred1_0 @ X2)|~((in @ (kpair @ esk25_0 @ X2) @ (dpsetconstr @ esk22_0 @ esk23_0 @ (epred2_1 @ esk24_0)))))), inference(rw,[status(thm)],[c_0_132, c_0_88])).
% 253.30/33.53 thf(c_0_137, plain, ![X2:$i, X31:$i > $i, X4:$i, X3:$i]:(((in @ (kpair @ X2 @ (X31 @ X2)) @ (dpsetconstr @ X3 @ X4 @ (epred2_1 @ X31)))|~((in @ (X31 @ X2) @ X4))|~((in @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_133, c_0_105])).
% 253.30/33.53 thf(c_0_138, negated_conjecture, (in @ (esk24_0 @ esk25_0) @ esk23_0), inference(rw,[status(thm)],[c_0_134, c_0_135])).
% 253.30/33.53 thf(c_0_139, plain, ![X2:$i]:(((in @ (kpair @ esk25_0 @ X2) @ (lam @ esk22_0 @ esk23_0 @ esk24_0))|~((epred1_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_129])).
% 253.30/33.53 thf(c_0_140, plain, (epred1_0 @ (esk24_0 @ esk25_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_137]), c_0_138]), c_0_96])])).
% 253.30/33.53 thf(c_0_141, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i, X6:$i > $i > $o]:(((X6 @ X2 @ X3)|~((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ X6))))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_142, negated_conjecture, ![X2:$i]:((((kpair @ (kfst @ X2) @ (ksnd @ X2))=(X2))|~((iskpair @ X2)))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_143, plain, ![X2:$i]:(((in @ (kpair @ esk25_0 @ X2) @ (dpsetconstr @ esk22_0 @ esk23_0 @ (epred2_1 @ esk24_0)))|~((epred1_0 @ X2)))), inference(rw,[status(thm)],[c_0_139, c_0_88])).
% 253.30/33.53 thf(c_0_144, negated_conjecture, ((in @ (esk5_2 @ esk23_0 @ epred1_0) @ (dsetconstr @ esk23_0 @ epred1_0))|(epred1_0 @ (esk3_2 @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_104, c_0_140])).
% 253.30/33.53 thf(c_0_145, negated_conjecture, ((in @ (esk5_2 @ esk23_0 @ epred1_0) @ (dsetconstr @ esk23_0 @ epred1_0))|(epred1_0 @ (esk4_2 @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_106, c_0_140])).
% 253.30/33.53 thf(c_0_146, negated_conjecture, (((setadjoin @ (esk5_2 @ esk23_0 @ epred1_0) @ emptyset)=(dsetconstr @ esk23_0 @ epred1_0))|(epred1_0 @ (esk3_2 @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_109, c_0_140])).
% 253.30/33.53 thf(c_0_147, negated_conjecture, (((setadjoin @ (esk5_2 @ esk23_0 @ epred1_0) @ emptyset)=(dsetconstr @ esk23_0 @ epred1_0))|(epred1_0 @ (esk4_2 @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_110, c_0_140])).
% 253.30/33.53 thf(c_0_148, plain, ![X491:$i]:(((epred1_0 @ X491)<=>(in @ (kpair @ esk25_0 @ X491) @ (lam @ esk22_0 @ esk23_0 @ esk24_0)))), introduced(definition)).
% 253.30/33.53 thf(c_0_149, negated_conjecture, ![X3:$i, X6:$i > $i > $o, X4:$i, X2:$i]:(((X6 @ (kfst @ X2) @ (ksnd @ X2))|~((in @ X2 @ (dpsetconstr @ X3 @ X4 @ X6)))|~((iskpair @ X2)))), inference(spm,[status(thm)],[c_0_141, c_0_142])).
% 253.30/33.53 thf(c_0_150, plain, ((in @ (kpair @ esk25_0 @ (esk3_2 @ esk23_0 @ epred1_0)) @ (dpsetconstr @ esk22_0 @ esk23_0 @ (epred2_1 @ esk24_0)))|(in @ (esk5_2 @ esk23_0 @ epred1_0) @ (dsetconstr @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_143, c_0_144])).
% 253.30/33.53 thf(c_0_151, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_152, negated_conjecture, ![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_81])).
% 253.30/33.53 thf(c_0_153, plain, ((in @ (kpair @ esk25_0 @ (esk4_2 @ esk23_0 @ epred1_0)) @ (dpsetconstr @ esk22_0 @ esk23_0 @ (epred2_1 @ esk24_0)))|(in @ (esk5_2 @ esk23_0 @ epred1_0) @ (dsetconstr @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_143, c_0_145])).
% 253.30/33.53 thf(c_0_154, plain, (((setadjoin @ (esk5_2 @ esk23_0 @ epred1_0) @ emptyset)=(dsetconstr @ esk23_0 @ epred1_0))|(in @ (kpair @ esk25_0 @ (esk3_2 @ esk23_0 @ epred1_0)) @ (dpsetconstr @ esk22_0 @ esk23_0 @ (epred2_1 @ esk24_0)))), inference(spm,[status(thm)],[c_0_143, c_0_146])).
% 253.30/33.53 thf(c_0_155, plain, (((setadjoin @ (esk5_2 @ esk23_0 @ epred1_0) @ emptyset)=(dsetconstr @ esk23_0 @ epred1_0))|(in @ (kpair @ esk25_0 @ (esk4_2 @ esk23_0 @ epred1_0)) @ (dpsetconstr @ esk22_0 @ esk23_0 @ (epred2_1 @ esk24_0)))), inference(spm,[status(thm)],[c_0_143, c_0_147])).
% 253.30/33.53 thf(c_0_156, negated_conjecture, ![X2:$i]:((~((((in @ X2 @ (dsetconstr @ esk23_0 @ epred1_0)))=(($true))))|((dsetconstr @ esk23_0 @ epred1_0)!=(setadjoin @ X2 @ emptyset))|~((subset @ (lam @ esk22_0 @ esk23_0 @ esk24_0) @ (cartprod @ esk22_0 @ esk23_0))))), inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_81]), c_0_148]), c_0_148])).
% 253.30/33.53 thf(c_0_157, negated_conjecture, ((in @ (esk5_2 @ esk23_0 @ epred1_0) @ (dsetconstr @ esk23_0 @ epred1_0))|(epred2_1 @ esk24_0 @ esk25_0 @ (esk3_2 @ esk23_0 @ epred1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_150]), c_0_151]), c_0_92]), c_0_152])])).
% 253.30/33.53 thf(c_0_158, negated_conjecture, ((in @ (esk5_2 @ esk23_0 @ epred1_0) @ (dsetconstr @ esk23_0 @ epred1_0))|(epred2_1 @ esk24_0 @ esk25_0 @ (esk4_2 @ esk23_0 @ epred1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_153]), c_0_151]), c_0_92]), c_0_152])])).
% 253.30/33.53 thf(c_0_159, negated_conjecture, (((setadjoin @ (esk5_2 @ esk23_0 @ epred1_0) @ emptyset)=(dsetconstr @ esk23_0 @ epred1_0))|(epred2_1 @ esk24_0 @ esk25_0 @ (esk3_2 @ esk23_0 @ epred1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_154]), c_0_151]), c_0_92]), c_0_152])])).
% 253.30/33.53 thf(c_0_160, negated_conjecture, (((setadjoin @ (esk5_2 @ esk23_0 @ epred1_0) @ emptyset)=(dsetconstr @ esk23_0 @ epred1_0))|(epred2_1 @ esk24_0 @ esk25_0 @ (esk4_2 @ esk23_0 @ epred1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_155]), c_0_151]), c_0_92]), c_0_152])])).
% 253.30/33.53 thf(c_0_161, negated_conjecture, ![X2:$i]:((((dsetconstr @ esk23_0 @ epred1_0)!=(setadjoin @ X2 @ emptyset))|~((subset @ (lam @ esk22_0 @ esk23_0 @ esk24_0) @ (cartprod @ esk22_0 @ esk23_0)))|~((in @ X2 @ (dsetconstr @ esk23_0 @ epred1_0))))), inference(cn,[status(thm)],[c_0_156])).
% 253.30/33.53 thf(c_0_162, plain, (((esk24_0 @ esk25_0)=(esk3_2 @ esk23_0 @ epred1_0))|(in @ (esk5_2 @ esk23_0 @ epred1_0) @ (dsetconstr @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_112, c_0_157])).
% 253.30/33.53 thf(c_0_163, plain, (((esk24_0 @ esk25_0)=(esk4_2 @ esk23_0 @ epred1_0))|(in @ (esk5_2 @ esk23_0 @ epred1_0) @ (dsetconstr @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_112, c_0_158])).
% 253.30/33.53 thf(c_0_164, negated_conjecture, ((in @ (esk5_2 @ esk23_0 @ epred1_0) @ (dsetconstr @ esk23_0 @ epred1_0))|((esk4_2 @ esk23_0 @ epred1_0)!=(esk3_2 @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_115, c_0_140])).
% 253.30/33.53 thf(c_0_165, plain, (((setadjoin @ (esk5_2 @ esk23_0 @ epred1_0) @ emptyset)=(dsetconstr @ esk23_0 @ epred1_0))|((esk24_0 @ esk25_0)=(esk3_2 @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_112, c_0_159])).
% 253.30/33.53 thf(c_0_166, plain, (((setadjoin @ (esk5_2 @ esk23_0 @ epred1_0) @ emptyset)=(dsetconstr @ esk23_0 @ epred1_0))|((esk24_0 @ esk25_0)=(esk4_2 @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_112, c_0_160])).
% 253.30/33.53 thf(c_0_167, negated_conjecture, (((setadjoin @ (esk5_2 @ esk23_0 @ epred1_0) @ emptyset)=(dsetconstr @ esk23_0 @ epred1_0))|((esk4_2 @ esk23_0 @ epred1_0)!=(esk3_2 @ esk23_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_119, c_0_140])).
% 253.30/33.53 thf(c_0_168, negated_conjecture, ![X2:$i]:((((dsetconstr @ esk23_0 @ epred1_0)!=(setadjoin @ X2 @ emptyset))|~((in @ X2 @ (dsetconstr @ esk23_0 @ epred1_0))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_161, c_0_88]), c_0_89])])).
% 253.30/33.53 thf(c_0_169, plain, (in @ (esk5_2 @ esk23_0 @ epred1_0) @ (dsetconstr @ esk23_0 @ epred1_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_162, c_0_163]), c_0_164])).
% 253.30/33.53 thf(c_0_170, plain, ((setadjoin @ (esk5_2 @ esk23_0 @ epred1_0) @ emptyset)=(dsetconstr @ esk23_0 @ epred1_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_165, c_0_166]), c_0_167])).
% 253.30/33.53 thf(c_0_171, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168, c_0_169]), c_0_170])]), ['proof']).
% 253.30/33.53 % SZS output end CNFRefutation
% 253.30/33.53 % Parsed axioms : 436
% 253.30/33.53 % Removed by relevancy pruning/SinE : 393
% 253.30/33.53 % Initial clauses : 254
% 253.30/33.53 % Removed in clause preprocessing : 0
% 253.30/33.53 % Initial clauses in saturation : 254
% 253.30/33.53 % Processed clauses : 2072
% 253.30/33.53 % ...of these trivial : 36
% 253.30/33.53 % ...subsumed : 596
% 253.30/33.53 % ...remaining for further processing : 1440
% 253.30/33.53 % Other redundant clauses eliminated : 197
% 253.30/33.53 % Clauses deleted for lack of memory : 0
% 253.30/33.53 % Backward-subsumed : 64
% 253.30/33.53 % Backward-rewritten : 160
% 253.30/33.53 % Generated clauses : 13774
% 253.30/33.53 % ...of the previous two non-redundant : 13081
% 253.30/33.53 % ...aggressively subsumed : 0
% 253.30/33.53 % Contextual simplify-reflections : 35
% 253.30/33.53 % Paramodulations : 13177
% 253.30/33.53 % Factorizations : 0
% 253.30/33.53 % NegExts : 98
% 253.30/33.53 % Equation resolutions : 197
% 253.30/33.53 % Disequality decompositions : 0
% 253.30/33.53 % Total rewrite steps : 2316
% 253.30/33.53 % ...of those cached : 2067
% 253.30/33.53 % Propositional unsat checks : 0
% 253.30/33.53 % Propositional check models : 0
% 253.30/33.53 % Propositional check unsatisfiable : 0
% 253.30/33.53 % Propositional clauses : 0
% 253.30/33.53 % Propositional clauses after purity: 0
% 253.30/33.53 % Propositional unsat core size : 0
% 253.30/33.53 % Propositional preprocessing time : 0.000
% 253.30/33.53 % Propositional encoding time : 0.000
% 253.30/33.53 % Propositional solver time : 0.000
% 253.30/33.53 % Success case prop preproc time : 0.000
% 253.30/33.53 % Success case prop encoding time : 0.000
% 253.30/33.53 % Success case prop solver time : 0.000
% 253.30/33.53 % Current number of processed clauses : 908
% 253.30/33.53 % Positive orientable unit clauses : 225
% 253.30/33.53 % Positive unorientable unit clauses: 1
% 253.30/33.53 % Negative unit clauses : 0
% 253.30/33.53 % Non-unit-clauses : 682
% 253.30/33.53 % Current number of unprocessed clauses: 11293
% 253.30/33.53 % ...number of literals in the above : 47549
% 253.30/33.53 % Current number of archived formulas : 0
% 253.30/33.53 % Current number of archived clauses : 531
% 253.30/33.53 % Clause-clause subsumption calls (NU) : 52247
% 253.30/33.53 % Rec. Clause-clause subsumption calls : 31833
% 253.30/33.53 % Non-unit clause-clause subsumptions : 688
% 253.30/33.53 % Unit Clause-clause subsumption calls : 2527
% 253.30/33.53 % Rewrite failures with RHS unbound : 0
% 253.30/33.53 % BW rewrite match attempts : 532
% 253.30/33.53 % BW rewrite match successes : 20
% 253.30/33.53 % Condensation attempts : 0
% 253.30/33.53 % Condensation successes : 0
% 253.30/33.53 % Termbank termtop insertions : 501307
% 253.30/33.53 % Search garbage collected termcells : 8939
% 253.30/33.53
% 253.30/33.53 % -------------------------------------------------
% 253.30/33.53 % User time : 30.892 s
% 253.30/33.53 % System time : 0.648 s
% 253.30/33.53 % Total time : 31.540 s
% 253.30/33.53 % Maximum resident set size: 6392 pages
% 253.30/33.53
% 253.30/33.53 % -------------------------------------------------
% 253.30/33.53 % User time : 30.902 s
% 253.30/33.53 % System time : 0.657 s
% 253.30/33.53 % Total time : 31.560 s
% 253.30/33.53 % Maximum resident set size: 5376 pages
% 253.30/33.53 % E exiting
%------------------------------------------------------------------------------