%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU678^1 : 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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:27:11 AM UTC 2026
% Result : Theorem 251.81s 33.51s
% Output : CNFRefutation 251.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU678^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n005.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 14:07:31 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.23/0.27 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.Tm82AomJ7g/E---3.1_1722397.p
% 251.81/33.51 % Version: 3.5.1-ho
% 251.81/33.51 % Preprocessing class: HSLMSLSSLLLCHSA.
% 251.81/33.51 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 251.81/33.51 % Starting ho_unfolding_5 with 1200s (4) cores
% 251.81/33.51 % Starting pre_casc_3 with 300s (1) cores
% 251.81/33.51 % Starting new_ho_10_cnf2 with 300s (1) cores
% 251.81/33.51 % Starting full_lambda_10 with 300s (1) cores
% 251.81/33.51 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 251.81/33.51 % pre_casc_3 with pid 1722411 completed with status 0
% 251.81/33.51 % Result found by pre_casc_3
% 251.81/33.51 % Preprocessing class: HSLMSLSSLLLCHSA.
% 251.81/33.51 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 251.81/33.51 % Starting ho_unfolding_5 with 1200s (4) cores
% 251.81/33.51 % Starting pre_casc_3 with 300s (1) cores
% 251.81/33.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 251.81/33.51 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 251.81/33.51 % Search class: HGHSM-FSLM32-MHSMMSBN
% 251.81/33.51 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 251.81/33.51 % Starting SubtermCWHack with 31s (1) cores
% 251.81/33.51 % SubtermCWHack with pid 1722416 completed with status 8
% 251.81/33.51 % Starting full_lambda_5 with 28s (1) cores
% 251.81/33.51 % full_lambda_5 with pid 1722427 completed with status 0
% 251.81/33.51 % Result found by full_lambda_5
% 251.81/33.51 % Preprocessing class: HSLMSLSSLLLCHSA.
% 251.81/33.51 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 251.81/33.51 % Starting ho_unfolding_5 with 1200s (4) cores
% 251.81/33.51 % Starting pre_casc_3 with 300s (1) cores
% 251.81/33.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 251.81/33.51 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 251.81/33.51 % Search class: HGHSM-FSLM32-MHSMMSBN
% 251.81/33.51 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 251.81/33.51 % Starting SubtermCWHack with 31s (1) cores
% 251.81/33.51 % SubtermCWHack with pid 1722416 completed with status 8
% 251.81/33.51 % Starting full_lambda_5 with 28s (1) cores
% 251.81/33.51 % Preprocessing time : 0.005 s
% 251.81/33.51 % Presaturation interreduction done
% 251.81/33.51
% 251.81/33.51 % Proof found!
% 251.81/33.51 % SZS status Theorem
% 251.81/33.51 % SZS output start CNFRefutation
% 251.81/33.51 thf(decl_23, type, in: $i > $i > $o).
% 251.81/33.51 thf(decl_25, type, setextAx: $o).
% 251.81/33.51 thf(decl_26, type, emptyset: $i).
% 251.81/33.51 thf(decl_27, type, emptysetAx: $o).
% 251.81/33.51 thf(decl_28, type, setadjoin: $i > $i > $i).
% 251.81/33.51 thf(decl_29, type, setadjoinAx: $o).
% 251.81/33.51 thf(decl_31, type, powersetAx: $o).
% 251.81/33.51 thf(decl_32, type, setunion: $i > $i).
% 251.81/33.51 thf(decl_33, type, setunionAx: $o).
% 251.81/33.51 thf(decl_35, type, omega0Ax: $o).
% 251.81/33.51 thf(decl_36, type, omegaSAx: $o).
% 251.81/33.51 thf(decl_37, type, omegaIndAx: $o).
% 251.81/33.51 thf(decl_38, type, replAx: $o).
% 251.81/33.51 thf(decl_39, type, foundationAx: $o).
% 251.81/33.51 thf(decl_40, type, wellorderingAx: $o).
% 251.81/33.51 thf(decl_42, type, descrp: $o).
% 251.81/33.51 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 251.81/33.51 thf(decl_44, type, dsetconstrI: $o).
% 251.81/33.51 thf(decl_45, type, dsetconstrEL: $o).
% 251.81/33.51 thf(decl_46, type, dsetconstrER: $o).
% 251.81/33.51 thf(decl_47, type, exuE1: $o).
% 251.81/33.51 thf(decl_49, type, prop2setE: $o).
% 251.81/33.51 thf(decl_50, type, emptysetE: $o).
% 251.81/33.51 thf(decl_51, type, emptysetimpfalse: $o).
% 251.81/33.51 thf(decl_52, type, notinemptyset: $o).
% 251.81/33.51 thf(decl_53, type, exuE3e: $o).
% 251.81/33.51 thf(decl_54, type, setext: $o).
% 251.81/33.51 thf(decl_55, type, emptyI: $o).
% 251.81/33.51 thf(decl_56, type, noeltsimpempty: $o).
% 251.81/33.51 thf(decl_57, type, setbeta: $o).
% 251.81/33.51 thf(decl_59, type, nonemptyE1: $o).
% 251.81/33.51 thf(decl_60, type, nonemptyI: $o).
% 251.81/33.51 thf(decl_61, type, nonemptyI1: $o).
% 251.81/33.51 thf(decl_62, type, setadjoinIL: $o).
% 251.81/33.51 thf(decl_63, type, emptyinunitempty: $o).
% 251.81/33.51 thf(decl_64, type, setadjoinIR: $o).
% 251.81/33.51 thf(decl_65, type, setadjoinE: $o).
% 251.81/33.51 thf(decl_66, type, setadjoinOr: $o).
% 251.81/33.51 thf(decl_67, type, setoftrueEq: $o).
% 251.81/33.51 thf(decl_68, type, powersetI: $o).
% 251.81/33.51 thf(decl_69, type, emptyinPowerset: $o).
% 251.81/33.51 thf(decl_70, type, emptyInPowerset: $o).
% 251.81/33.51 thf(decl_71, type, powersetE: $o).
% 251.81/33.51 thf(decl_72, type, setunionI: $o).
% 251.81/33.51 thf(decl_73, type, setunionE: $o).
% 251.81/33.51 thf(decl_74, type, subPowSU: $o).
% 251.81/33.51 thf(decl_75, type, exuE2: $o).
% 251.81/33.51 thf(decl_76, type, nonemptyImpWitness: $o).
% 251.81/33.51 thf(decl_77, type, uniqinunit: $o).
% 251.81/33.51 thf(decl_78, type, notinsingleton: $o).
% 251.81/33.51 thf(decl_79, type, eqinunit: $o).
% 251.81/33.51 thf(decl_80, type, singletonsswitch: $o).
% 251.81/33.51 thf(decl_81, type, upairsetE: $o).
% 251.81/33.51 thf(decl_82, type, upairsetIL: $o).
% 251.81/33.51 thf(decl_83, type, upairsetIR: $o).
% 251.81/33.51 thf(decl_84, type, emptyE1: $o).
% 251.81/33.51 thf(decl_85, type, vacuousDall: $o).
% 251.81/33.51 thf(decl_86, type, quantDeMorgan1: $o).
% 251.81/33.51 thf(decl_87, type, quantDeMorgan2: $o).
% 251.81/33.51 thf(decl_88, type, quantDeMorgan3: $o).
% 251.81/33.51 thf(decl_89, type, quantDeMorgan4: $o).
% 251.81/33.51 thf(decl_90, type, prop2setI: $o).
% 251.81/33.51 thf(decl_92, type, prop2set2propI: $o).
% 251.81/33.51 thf(decl_93, type, notdexE: $o).
% 251.81/33.51 thf(decl_94, type, notdallE: $o).
% 251.81/33.51 thf(decl_95, type, exuI1: $o).
% 251.81/33.51 thf(decl_96, type, exuI3: $o).
% 251.81/33.51 thf(decl_97, type, exuI2: $o).
% 251.81/33.51 thf(decl_98, type, inCongP: $o).
% 251.81/33.51 thf(decl_99, type, in__Cong: $o).
% 251.81/33.51 thf(decl_100, type, exuE3u: $o).
% 251.81/33.51 thf(decl_101, type, exu__Cong: $o).
% 251.81/33.51 thf(decl_102, type, emptyset__Cong: $o).
% 251.81/33.51 thf(decl_103, type, setadjoin__Cong: $o).
% 251.81/33.51 thf(decl_104, type, powerset__Cong: $o).
% 251.81/33.51 thf(decl_105, type, setunion__Cong: $o).
% 251.81/33.51 thf(decl_106, type, omega__Cong: $o).
% 251.81/33.51 thf(decl_107, type, exuEu: $o).
% 251.81/33.51 thf(decl_108, type, descr__Cong: $o).
% 251.81/33.51 thf(decl_109, type, dsetconstr__Cong: $o).
% 251.81/33.51 thf(decl_110, type, subset: $i > $i > $o).
% 251.81/33.51 thf(decl_113, type, subsetI1: $o).
% 251.81/33.51 thf(decl_114, type, eqimpsubset2: $o).
% 251.81/33.51 thf(decl_115, type, eqimpsubset1: $o).
% 251.81/33.51 thf(decl_116, type, subsetI2: $o).
% 251.81/33.51 thf(decl_117, type, emptysetsubset: $o).
% 251.81/33.51 thf(decl_118, type, subsetE: $o).
% 251.81/33.51 thf(decl_119, type, subsetE2: $o).
% 251.81/33.51 thf(decl_120, type, notsubsetI: $o).
% 251.81/33.51 thf(decl_121, type, notequalI1: $o).
% 251.81/33.51 thf(decl_122, type, notequalI2: $o).
% 251.81/33.51 thf(decl_123, type, subsetRefl: $o).
% 251.81/33.51 thf(decl_124, type, subsetTrans: $o).
% 251.81/33.51 thf(decl_125, type, setadjoinSub: $o).
% 251.81/33.51 thf(decl_126, type, setadjoinSub2: $o).
% 251.81/33.51 thf(decl_127, type, subset2powerset: $o).
% 251.81/33.51 thf(decl_128, type, setextsub: $o).
% 251.81/33.51 thf(decl_129, type, subsetemptysetimpeq: $o).
% 251.81/33.51 thf(decl_130, type, powersetI1: $o).
% 251.81/33.51 thf(decl_131, type, powersetE1: $o).
% 251.81/33.51 thf(decl_132, type, inPowerset: $o).
% 251.81/33.51 thf(decl_133, type, powersetsubset: $o).
% 251.81/33.51 thf(decl_134, type, sepInPowerset: $o).
% 251.81/33.51 thf(decl_135, type, sepSubset: $o).
% 251.81/33.51 thf(decl_137, type, binunionIL: $o).
% 251.81/33.51 thf(decl_138, type, upairset2IR: $o).
% 251.81/33.51 thf(decl_139, type, binunionIR: $o).
% 251.81/33.51 thf(decl_140, type, binunionEcases: $o).
% 251.81/33.51 thf(decl_141, type, binunionE: $o).
% 251.81/33.51 thf(decl_142, type, binunionLsub: $o).
% 251.81/33.51 thf(decl_143, type, binunionRsub: $o).
% 251.81/33.51 thf(decl_145, type, binintersectI: $o).
% 251.81/33.51 thf(decl_146, type, binintersectSubset5: $o).
% 251.81/33.51 thf(decl_147, type, binintersectEL: $o).
% 251.81/33.51 thf(decl_148, type, binintersectLsub: $o).
% 251.81/33.51 thf(decl_149, type, binintersectSubset2: $o).
% 251.81/33.51 thf(decl_150, type, binintersectSubset3: $o).
% 251.81/33.51 thf(decl_151, type, binintersectER: $o).
% 251.81/33.51 thf(decl_152, type, disjointsetsI1: $o).
% 251.81/33.51 thf(decl_153, type, binintersectRsub: $o).
% 251.81/33.51 thf(decl_154, type, binintersectSubset4: $o).
% 251.81/33.51 thf(decl_155, type, binintersectSubset1: $o).
% 251.81/33.51 thf(decl_156, type, bs114d: $o).
% 251.81/33.51 thf(decl_159, type, setminusI: $o).
% 251.81/33.51 thf(decl_160, type, setminusEL: $o).
% 251.81/33.51 thf(decl_161, type, setminusER: $o).
% 251.81/33.51 thf(decl_162, type, setminusSubset2: $o).
% 251.81/33.51 thf(decl_163, type, setminusERneg: $o).
% 251.81/33.51 thf(decl_164, type, setminusELneg: $o).
% 251.81/33.51 thf(decl_165, type, setminusILneg: $o).
% 251.81/33.51 thf(decl_166, type, setminusIRneg: $o).
% 251.81/33.51 thf(decl_167, type, setminusLsub: $o).
% 251.81/33.51 thf(decl_168, type, setminusSubset1: $o).
% 251.81/33.51 thf(decl_170, type, symdiffE: $o).
% 251.81/33.51 thf(decl_171, type, symdiffI1: $o).
% 251.81/33.51 thf(decl_172, type, symdiffI2: $o).
% 251.81/33.51 thf(decl_173, type, symdiffIneg1: $o).
% 251.81/33.51 thf(decl_174, type, symdiffIneg2: $o).
% 251.81/33.51 thf(decl_175, type, iskpair: $i > $o).
% 251.81/33.51 thf(decl_176, type, secondinupair: $o).
% 251.81/33.51 thf(decl_177, type, setukpairIL: $o).
% 251.81/33.51 thf(decl_178, type, setukpairIR: $o).
% 251.81/33.51 thf(decl_179, type, kpairiskpair: $o).
% 251.81/33.51 thf(decl_180, type, kpair: $i > $i > $i).
% 251.81/33.51 thf(decl_181, type, kpairp: $o).
% 251.81/33.51 thf(decl_182, type, cartprod: $i > $i > $i).
% 251.81/33.51 thf(decl_183, type, singletonsubset: $o).
% 251.81/33.51 thf(decl_184, type, singletoninpowerset: $o).
% 251.81/33.51 thf(decl_185, type, singletoninpowunion: $o).
% 251.81/33.51 thf(decl_186, type, upairset2E: $o).
% 251.81/33.51 thf(decl_187, type, upairsubunion: $o).
% 251.81/33.51 thf(decl_188, type, upairinpowunion: $o).
% 251.81/33.51 thf(decl_189, type, ubforcartprodlem1: $o).
% 251.81/33.51 thf(decl_190, type, ubforcartprodlem2: $o).
% 251.81/33.51 thf(decl_191, type, ubforcartprodlem3: $o).
% 251.81/33.51 thf(decl_192, type, cartprodpairin: $o).
% 251.81/33.51 thf(decl_193, type, cartprodmempair1: $o).
% 251.81/33.51 thf(decl_194, type, cartprodmempair: $o).
% 251.81/33.51 thf(decl_195, type, setunionE2: $o).
% 251.81/33.51 thf(decl_196, type, setunionsingleton1: $o).
% 251.81/33.51 thf(decl_197, type, setunionsingleton2: $o).
% 251.81/33.51 thf(decl_198, type, setunionsingleton: $o).
% 251.81/33.51 thf(decl_199, type, singleton: $i > $o).
% 251.81/33.51 thf(decl_200, type, singletonprop: $o).
% 251.81/33.51 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 251.81/33.51 thf(decl_202, type, ex1E1: $o).
% 251.81/33.51 thf(decl_203, type, ex1I: $o).
% 251.81/33.51 thf(decl_204, type, ex1I2: $o).
% 251.81/33.51 thf(decl_205, type, singletonsuniq: $o).
% 251.81/33.51 thf(decl_210, type, setukpairinjL1: $o).
% 251.81/33.51 thf(decl_211, type, kfstsingleton: $o).
% 251.81/33.51 thf(decl_212, type, theprop: $o).
% 251.81/33.51 thf(decl_213, type, kfst: $i > $i).
% 251.81/33.51 thf(decl_214, type, kfstpairEq: $o).
% 251.81/33.51 thf(decl_215, type, cartprodfstin: $o).
% 251.81/33.51 thf(decl_216, type, setukpairinjL2: $o).
% 251.81/33.51 thf(decl_217, type, setukpairinjL: $o).
% 251.81/33.51 thf(decl_218, type, setukpairinjR11: $o).
% 251.81/33.51 thf(decl_219, type, setukpairinjR12: $o).
% 251.81/33.51 thf(decl_220, type, setukpairinjR1: $o).
% 251.81/33.51 thf(decl_221, type, upairequniteq: $o).
% 251.81/33.51 thf(decl_222, type, setukpairinjR2: $o).
% 251.81/33.51 thf(decl_223, type, setukpairinjR: $o).
% 251.81/33.51 thf(decl_224, type, ksndsingleton: $o).
% 251.81/33.51 thf(decl_225, type, ksnd: $i > $i).
% 251.81/33.51 thf(decl_226, type, ksndpairEq: $o).
% 251.81/33.51 thf(decl_227, type, kpairsurjEq: $o).
% 251.81/33.51 thf(decl_228, type, cartprodsndin: $o).
% 251.81/33.51 thf(decl_229, type, cartprodpairmemEL: $o).
% 251.81/33.51 thf(decl_230, type, cartprodpairmemER: $o).
% 251.81/33.51 thf(decl_231, type, cartprodmempaircEq: $o).
% 251.81/33.51 thf(decl_232, type, cartprodfstpairEq: $o).
% 251.81/33.51 thf(decl_233, type, cartprodsndpairEq: $o).
% 251.81/33.51 thf(decl_234, type, cartprodpairsurjEq: $o).
% 251.81/33.51 thf(decl_235, type, breln: $i > $i > $i > $o).
% 251.81/33.51 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 251.81/33.51 thf(decl_237, type, dpsetconstrI: $o).
% 251.81/33.51 thf(decl_238, type, dpsetconstrSub: $o).
% 251.81/33.51 thf(decl_239, type, setOfPairsIsBReln: $o).
% 251.81/33.51 thf(decl_240, type, dpsetconstrERa: $o).
% 251.81/33.51 thf(decl_241, type, dpsetconstrEL1: $o).
% 251.81/33.51 thf(decl_242, type, dpsetconstrEL2: $o).
% 251.81/33.51 thf(decl_243, type, dpsetconstrER: $o).
% 251.81/33.51 thf(decl_244, type, func: $i > $i > $i > $o).
% 251.81/33.51 thf(decl_245, type, funcSet: $i > $i > $i).
% 251.81/33.51 thf(decl_246, type, funcImageSingleton: $o).
% 251.81/33.51 thf(decl_247, type, apProp: $o).
% 251.81/33.51 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 251.81/33.51 thf(decl_249, type, app: $o).
% 251.81/33.51 thf(decl_250, type, infuncsetfunc: $o).
% 251.81/33.51 thf(decl_251, type, ap2p: $o).
% 251.81/33.51 thf(decl_252, type, funcinfuncset: $o).
% 251.81/33.51 thf(decl_253, type, esk1_3: $i > $i > $i > $i).
% 251.81/33.51 thf(decl_254, type, esk2_3: $i > $i > $i > $i).
% 251.81/33.51 thf(decl_255, type, esk3_2: $i > ($i > $o) > $i).
% 251.81/33.51 thf(decl_256, type, esk4_2: $i > ($i > $o) > $i).
% 251.81/33.51 thf(decl_257, type, esk5_2: $i > ($i > $o) > $i).
% 251.81/33.51 thf(decl_258, type, esk6_2: $i > ($i > $o) > $i).
% 251.81/33.51 thf(decl_259, type, esk7_3: $i > ($i > $o) > $i > $i).
% 251.81/33.51 thf(decl_260, type, esk8_3: $i > ($i > $o) > $i > $i).
% 251.81/33.51 thf(decl_261, type, esk9_2: $i > ($i > $o) > $i).
% 251.81/33.51 thf(decl_262, type, esk10_2: $i > ($i > $o) > $i).
% 251.81/33.51 thf(decl_263, type, esk11_2: $i > ($i > $o) > $i).
% 251.81/33.51 thf(decl_264, type, esk12_1: $i > $i).
% 251.81/33.51 thf(decl_265, type, esk13_1: $i > $i).
% 251.81/33.51 thf(decl_266, type, esk14_3: $i > $i > $i > $i).
% 251.81/33.51 thf(decl_267, type, esk15_4: $i > $i > $i > $i > $i).
% 251.81/33.51 thf(decl_268, type, esk16_3: $i > $i > $i > $i).
% 251.81/33.51 thf(decl_269, type, esk17_3: $i > $i > $i > $i).
% 251.81/33.51 thf(decl_270, type, esk18_4: $i > $i > $i > $i > $i).
% 251.81/33.51 thf(decl_271, type, esk19_3: $i > $i > $i > $i).
% 251.81/33.51 thf(decl_272, type, esk20_0: $i).
% 251.81/33.51 thf(decl_273, type, esk21_0: $i).
% 251.81/33.51 thf(decl_274, type, esk22_0: $i > $i).
% 251.81/33.51 thf(decl_275, type, esk23_0: $i).
% 251.81/33.51 thf(decl_276, type, epred1_0: $i > $i > $o).
% 251.81/33.51 thf(decl_277, type, epred2_0: $i > $o).
% 251.81/33.51 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', ex1)).
% 251.81/33.51 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', singleton)).
% 251.81/33.51 thf(func, axiom, ((func)=(^[X4:$i, X5:$i, X29:$i]:((((breln @ X4 @ X5 @ X29))&(![X2:$i]:((((in @ X2 @ X4))=>((ex1 @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', func)).
% 251.81/33.51 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', breln)).
% 251.81/33.51 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.Tm82AomJ7g/E---3.1_1722397.p', ksndsingleton)).
% 251.81/33.51 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.Tm82AomJ7g/E---3.1_1722397.p', kfstsingleton)).
% 251.81/33.51 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', singletonprop)).
% 251.81/33.51 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', ex1I2)).
% 251.81/33.51 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.Tm82AomJ7g/E---3.1_1722397.p', ex1I)).
% 251.81/33.51 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', ex1E1)).
% 251.81/33.51 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', setOfPairsIsBReln)).
% 251.81/33.51 thf(apProp, axiom, ((apProp)<=>![X4:$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.Tm82AomJ7g/E---3.1_1722397.p', apProp)).
% 251.81/33.51 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.Tm82AomJ7g/E---3.1_1722397.p', funcImageSingleton)).
% 251.81/33.51 thf(lamProp, 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)=>![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.Tm82AomJ7g/E---3.1_1722397.p', lamProp)).
% 251.81/33.51 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', theprop)).
% 251.81/33.51 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', dpsetconstrER)).
% 251.81/33.51 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', dpsetconstrEL2)).
% 251.81/33.51 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', dpsetconstrEL1)).
% 251.81/33.51 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', dpsetconstrERa)).
% 251.81/33.51 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', dpsetconstrSub)).
% 251.81/33.51 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', dpsetconstrI)).
% 251.81/33.51 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>(in @ X30 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', funcinfuncset)).
% 251.81/33.51 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', infuncsetfunc)).
% 251.81/33.51 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', app)).
% 251.81/33.51 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', cartprodsndpairEq)).
% 251.81/33.51 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', ksndpairEq)).
% 251.81/33.51 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', cartprodfstpairEq)).
% 251.81/33.51 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', kfstpairEq)).
% 251.81/33.51 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', kpairsurjEq)).
% 251.81/33.51 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', kpairp)).
% 251.81/33.51 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.Tm82AomJ7g/E---3.1_1722397.p', kpairiskpair)).
% 251.81/33.51 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', cartprodpairsurjEq)).
% 251.81/33.51 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', cartprodpairmemER)).
% 251.81/33.51 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', cartprodpairmemEL)).
% 251.81/33.51 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', cartprodsndin)).
% 251.81/33.51 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', cartprodfstin)).
% 251.81/33.51 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', cartprodmempair)).
% 251.81/33.51 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', cartprodmempair1)).
% 251.81/33.51 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', cartprodpairin)).
% 251.81/33.51 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Tm82AomJ7g/E---3.1_1722397.p', ap2p)).
% 251.81/33.51 thf(c_0_40, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X156:$i]:((((in @ X156 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X156 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 251.81/33.51 thf(c_0_41, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 251.81/33.51 thf(c_0_42, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X163:$i]:((((in @ X163 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X163 @ emptyset)))))))))))))), inference(fof_simplification,[status(thm)],[func])).
% 251.81/33.51 thf(c_0_43, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 251.81/33.51 thf(c_0_44, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X156:$i]:((((in @ X156 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X156 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_40, c_0_41])).
% 251.81/33.51 thf(c_0_45, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 251.81/33.51 thf(c_0_46, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 251.81/33.51 thf(c_0_47, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 251.81/33.51 thf(c_0_48, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 251.81/33.51 thf(c_0_49, plain, ((ex1I)<=>![X4:$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])).
% 251.81/33.51 thf(c_0_50, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 251.81/33.51 thf(c_0_51, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 251.81/33.51 thf(c_0_52, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X163:$i]:((((in @ X163 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X163 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_42, c_0_43]), c_0_44])).
% 251.81/33.51 thf(c_0_53, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 251.81/33.51 thf(c_0_54, plain, ((funcImageSingleton)<=>![X4:$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])).
% 251.81/33.51 thf(c_0_55, 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)=>![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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[lamProp])).
% 251.81/33.51 thf(c_0_56, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X162:$i]:((((in @ X162 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X162 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_45, c_0_41])).
% 251.81/33.51 thf(c_0_57, axiom, ((theprop)=(![X21:$i]:((((?[X161:$i]:((((in @ X161 @ X21))&(((X21)=(setadjoin @ X161 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_41])).
% 251.81/33.51 thf(c_0_58, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X160:$i]:((((in @ X160 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X160 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_46, c_0_41])).
% 251.81/33.51 thf(c_0_59, 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)))))=>((?[X155:$i]:((((in @ X155 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X155 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_41])).
% 251.81/33.51 thf(c_0_60, plain, ((ex1I2)=(![X4:$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)))))=>((?[X159:$i]:((((in @ X159 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X159 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_48, c_0_44])).
% 251.81/33.51 thf(c_0_61, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X158:$i]:((((in @ X158 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X158 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_49, c_0_44])).
% 251.81/33.51 thf(c_0_62, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X157:$i]:((((in @ X157 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X157 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_50, c_0_44])).
% 251.81/33.51 thf(c_0_63, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 251.81/33.51 thf(c_0_64, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 251.81/33.51 thf(c_0_65, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 251.81/33.51 thf(c_0_66, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 251.81/33.51 thf(c_0_67, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_51, c_0_43])).
% 251.81/33.51 thf(c_0_68, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 251.81/33.51 thf(c_0_69, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 251.81/33.51 thf(c_0_70, axiom, ((funcinfuncset)=(![X4:$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)))))))))))))=>((in @ X30 @ (funcSet @ X4 @ X5))))))), inference(apply_def,[status(thm)],[funcinfuncset, c_0_52])).
% 251.81/33.51 thf(c_0_71, axiom, ((infuncsetfunc)=(![X4:$i, X5:$i, X30:$i]:((((in @ X30 @ (funcSet @ X4 @ X5)))=>((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X171:$i]:((((in @ X171 @ X4))=>((?[X172:$i]:((((in @ X172 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X171 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X171 @ Z0) @ X30)))))=(setadjoin @ X172 @ emptyset))))))))))))))))), inference(apply_def,[status(thm)],[infuncsetfunc, c_0_52])).
% 251.81/33.51 thf(c_0_72, axiom, ((app)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X169:$i]:((((in @ X169 @ X4))=>((?[X170:$i]:((((in @ X170 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X169 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X169 @ Z0) @ X30)))))=(setadjoin @ X170 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5))))))))), inference(apply_def,[status(thm)],[app, c_0_52])).
% 251.81/33.51 thf(c_0_73, plain, ((apProp)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X167:$i]:((((in @ X167 @ X4))=>((?[X168:$i]:((((in @ X168 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X167 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X167 @ Z0) @ X30)))))=(setadjoin @ X168 @ 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_53, c_0_52])).
% 251.81/33.51 thf(c_0_74, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X164:$i]:((((in @ X164 @ X4))=>((?[X165:$i]:((((in @ X165 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X164 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X164 @ Z0) @ X30)))))=(setadjoin @ X165 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X166:$i]:((((in @ X166 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))=(setadjoin @ X166 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_54, c_0_41]), c_0_52])).
% 251.81/33.51 thf(c_0_75, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>(![X175:$i, X176:$i]:((iskpair @ (setadjoin @ (setadjoin @ X175 @ emptyset) @ (setadjoin @ (setadjoin @ X175 @ (setadjoin @ X176 @ emptyset)) @ emptyset))))=>(![X177:$i, X178:$i]:((iskpair @ (kpair @ X177 @ X178)))=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>(![X179:$i, X180:$i, X181:$i]:(((in @ X181 @ X179)=>![X182:$i]:(((in @ X182 @ X180)=>(in @ (kpair @ X181 @ X182) @ (cartprod @ X179 @ X180))))))=>(![X183:$i, X184:$i, X185:$i]:(((in @ X185 @ (cartprod @ X183 @ X184))=>?[X186:$i]:(((in @ X186 @ X183)&?[X187:$i]:(((in @ X187 @ X184)&((X185)=(kpair @ X186 @ X187))))))))=>(![X188:$i, X189:$i, X190:$i]:(((in @ X190 @ (cartprod @ X188 @ X189))=>(iskpair @ X190)))=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(![X191:$i, X192:$i > $o]:((![X193:$i]:(((in @ X193 @ X191)=>![X194:$i]:(((in @ X194 @ X191)=>((X192 @ X193)=>((X192 @ X194)=>((X193)=(X194))))))))=>(?[X195:$i]:(((in @ X195 @ X191)&(X192 @ X195)))=>?[X196:$i]:(((in @ X196 @ (dsetconstr @ X191 @ X192))&((dsetconstr @ X191 @ X192)=(setadjoin @ X196 @ emptyset)))))))=>(![X197:$i, X198:$i > $o]:((?[X199:$i]:(((in @ X199 @ (dsetconstr @ X197 @ X198))&((dsetconstr @ X197 @ X198)=(setadjoin @ X199 @ emptyset))))=>?[X200:$i]:(((in @ X200 @ X197)&(X198 @ X200)))))=>(![X201:$i, X202:$i > $o, X203:$i]:(((in @ X203 @ X201)=>((X202 @ X203)=>(![X204:$i]:(((in @ X204 @ X201)=>((X202 @ X204)=>((X204)=(X203)))))=>?[X205:$i]:(((in @ X205 @ (dsetconstr @ X201 @ X202))&((dsetconstr @ X201 @ X202)=(setadjoin @ X205 @ emptyset))))))))=>(![X206:$i, X207:$i > $o]:((![X208:$i]:(((in @ X208 @ X206)=>![X209:$i]:(((in @ X209 @ X206)=>((X207 @ X208)=>((X207 @ X209)=>((X208)=(X209))))))))=>(?[X210:$i]:(((in @ X210 @ X206)&(X207 @ X210)))=>?[X211:$i]:(((in @ X211 @ (dsetconstr @ X206 @ X207))&((dsetconstr @ X206 @ X207)=(setadjoin @ X211 @ emptyset)))))))=>((singletonsuniq)=>((setukpairinjL1)=>(![X212:$i]:(((iskpair @ X212)=>?[X213:$i]:(((in @ X213 @ (dsetconstr @ (setunion @ X212) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X212)))))&((dsetconstr @ (setunion @ X212) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X212))))=(setadjoin @ X213 @ emptyset))))))=>(![X214:$i]:((?[X215:$i]:(((in @ X215 @ X214)&((X214)=(setadjoin @ X215 @ emptyset))))=>(in @ (setunion @ X214) @ X214)))=>(![X216:$i, X217:$i]:(((kfst @ (kpair @ X216 @ X217))=(X216)))=>(![X218:$i, X219:$i, X220:$i]:(((in @ X220 @ (cartprod @ X218 @ X219))=>(in @ (kfst @ X220) @ X218)))=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>(![X221:$i]:(((iskpair @ X221)=>?[X222:$i]:(((in @ X222 @ (dsetconstr @ (setunion @ X221) @ (^[Z0:$i]:(((X221)=(kpair @ (kfst @ X221) @ Z0))))))&((dsetconstr @ (setunion @ X221) @ (^[Z0:$i]:(((X221)=(kpair @ (kfst @ X221) @ Z0)))))=(setadjoin @ X222 @ emptyset))))))=>(![X223:$i, X224:$i]:(((ksnd @ (kpair @ X223 @ X224))=(X224)))=>(![X225:$i]:(((iskpair @ X225)=>((kpair @ (kfst @ X225) @ (ksnd @ X225))=(X225))))=>(![X226:$i, X227:$i, X228:$i]:(((in @ X228 @ (cartprod @ X226 @ X227))=>(in @ (ksnd @ X228) @ X227)))=>(![X229:$i, X230:$i, X231:$i, X232:$i]:(((in @ (kpair @ X231 @ X232) @ (cartprod @ X229 @ X230))=>(in @ X231 @ X229)))=>(![X233:$i, X234:$i, X235:$i, X236:$i]:(((in @ (kpair @ X235 @ X236) @ (cartprod @ X233 @ X234))=>(in @ X236 @ X234)))=>((cartprodmempaircEq)=>(![X237:$i, X238:$i, X239:$i]:(((in @ X239 @ X237)=>![X240:$i]:(((in @ X240 @ X238)=>((kfst @ (kpair @ X239 @ X240))=(X239))))))=>(![X241:$i, X242:$i, X243:$i]:(((in @ X243 @ X241)=>![X244:$i]:(((in @ X244 @ X242)=>((ksnd @ (kpair @ X243 @ X244))=(X244))))))=>(![X245:$i, X246:$i, X247:$i]:(((in @ X247 @ (cartprod @ X245 @ X246))=>((kpair @ (kfst @ X247) @ (ksnd @ X247))=(X247))))=>(![X248:$i, X249:$i, X250:$i > $i > $o, X251:$i]:(((in @ X251 @ X248)=>![X252:$i]:(((in @ X252 @ X249)=>((X250 @ X251 @ X252)=>(in @ (kpair @ X251 @ X252) @ (dpsetconstr @ X248 @ X249 @ X250)))))))=>(![X253:$i, X254:$i, X255:$i > $i > $o]:((subset @ (dpsetconstr @ X253 @ X254 @ X255) @ (cartprod @ X253 @ X254)))=>(![X256:$i, X257:$i, X258:$i > $i > $o]:((subset @ (dpsetconstr @ X256 @ X257 @ X258) @ (cartprod @ X256 @ X257)))=>(![X259:$i, X260:$i, X261:$i > $i > $o, X262:$i]:(((in @ X262 @ X259)=>![X263:$i]:(((in @ X263 @ X260)=>((in @ (kpair @ X262 @ X263) @ (dpsetconstr @ X259 @ X260 @ X261))=>(X261 @ X262 @ X263))))))=>(![X264:$i, X265:$i, X266:$i > $i > $o, X267:$i, X268:$i]:(((in @ (kpair @ X267 @ X268) @ (dpsetconstr @ X264 @ X265 @ X266))=>(in @ X267 @ X264)))=>(![X269:$i, X270:$i, X271:$i > $i > $o, X272:$i, X273:$i]:(((in @ (kpair @ X272 @ X273) @ (dpsetconstr @ X269 @ X270 @ X271))=>(in @ X273 @ X270)))=>(![X274:$i, X275:$i, X276:$i > $i > $o, X277:$i, X278:$i]:(((in @ (kpair @ X277 @ X278) @ (dpsetconstr @ X274 @ X275 @ X276))=>(X276 @ X277 @ X278)))=>(![X279:$i, X280:$i, X281:$i]:((((subset @ X281 @ (cartprod @ X279 @ X280))&![X282:$i]:(((in @ X282 @ X279)=>?[X283:$i]:(((in @ X283 @ (dsetconstr @ X280 @ (^[Z0:$i]:((in @ (kpair @ X282 @ Z0) @ X281)))))&((dsetconstr @ X280 @ (^[Z0:$i]:((in @ (kpair @ X282 @ Z0) @ X281))))=(setadjoin @ X283 @ emptyset)))))))=>![X284:$i]:(((in @ X284 @ X279)=>?[X285:$i]:(((in @ X285 @ (dsetconstr @ X280 @ (^[Z0:$i]:((in @ (kpair @ X284 @ Z0) @ X281)))))&((dsetconstr @ X280 @ (^[Z0:$i]:((in @ (kpair @ X284 @ Z0) @ X281))))=(setadjoin @ X285 @ emptyset))))))))=>(![X286:$i, X287:$i, X288:$i]:((((subset @ X288 @ (cartprod @ X286 @ X287))&![X289:$i]:(((in @ X289 @ X286)=>?[X290:$i]:(((in @ X290 @ (dsetconstr @ X287 @ (^[Z0:$i]:((in @ (kpair @ X289 @ Z0) @ X288)))))&((dsetconstr @ X287 @ (^[Z0:$i]:((in @ (kpair @ X289 @ Z0) @ X288))))=(setadjoin @ X290 @ emptyset)))))))=>![X291:$i]:(((in @ X291 @ X286)=>(in @ (setunion @ (dsetconstr @ X287 @ (^[Z0:$i]:((in @ (kpair @ X291 @ Z0) @ X288))))) @ X287)))))=>(![X292:$i, X293:$i, X294:$i]:((((subset @ X294 @ (cartprod @ X292 @ X293))&![X295:$i]:(((in @ X295 @ X292)=>?[X296:$i]:(((in @ X296 @ (dsetconstr @ X293 @ (^[Z0:$i]:((in @ (kpair @ X295 @ Z0) @ X294)))))&((dsetconstr @ X293 @ (^[Z0:$i]:((in @ (kpair @ X295 @ Z0) @ X294))))=(setadjoin @ X296 @ emptyset)))))))=>![X297:$i]:(((in @ X297 @ X292)=>(in @ (ap @ X292 @ X293 @ X294 @ X297) @ X293)))))=>(![X298:$i, X299:$i, X300:$i]:(((in @ X300 @ (funcSet @ X298 @ X299))=>((subset @ X300 @ (cartprod @ X298 @ X299))&![X301:$i]:(((in @ X301 @ X298)=>?[X302:$i]:(((in @ X302 @ (dsetconstr @ X299 @ (^[Z0:$i]:((in @ (kpair @ X301 @ Z0) @ X300)))))&((dsetconstr @ X299 @ (^[Z0:$i]:((in @ (kpair @ X301 @ Z0) @ X300))))=(setadjoin @ X302 @ emptyset)))))))))=>(![X303:$i, X304:$i, X305:$i]:(((in @ X305 @ (funcSet @ X303 @ X304))=>![X306:$i]:(((in @ X306 @ X303)=>(in @ (ap @ X303 @ X304 @ X305 @ X306) @ X304)))))=>(![X307:$i, X308:$i, X309:$i]:((((subset @ X309 @ (cartprod @ X307 @ X308))&![X310:$i]:(((in @ X310 @ X307)=>?[X311:$i]:(((in @ X311 @ (dsetconstr @ X308 @ (^[Z0:$i]:((in @ (kpair @ X310 @ Z0) @ X309)))))&((dsetconstr @ X308 @ (^[Z0:$i]:((in @ (kpair @ X310 @ Z0) @ X309))))=(setadjoin @ X311 @ emptyset)))))))=>(in @ X309 @ (funcSet @ X307 @ X308))))=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i]:($eq @ (X31 @ Z0)))) @ (cartprod @ X4 @ X5))&![X312:$i]:(((in @ X312 @ X4)=>?[X313:$i]:(((in @ X313 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X312 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1:$i]:($eq @ (X31 @ Z1)))))))))&((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X312 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1:$i]:($eq @ (X31 @ Z1))))))))=(setadjoin @ X313 @ 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(fof_simplification,[status(thm)],[c_0_55]), cartprodsndpairEq]), ksndpairEq]), cartprodfstpairEq]), kfstpairEq]), kpairsurjEq]), kpairp]), kpairiskpair]), cartprodpairsurjEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), cartprodfstin]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ap2p]), c_0_56]), c_0_57]), c_0_58]), c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_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_52])])).
% 251.81/33.51 thf(c_0_76, negated_conjecture, ![X318:$i, X319:$i, X320:$i, X321:$i, X322:$i, X323:$i, X324:$i, X325:$i, X326:$i, X327:$i, X328:$i, X331:$i, X332:$i, X333:$i, X334:$i, X335:$i > $o, X338:$i, X340:$i, X341:$i > $o, X342:$i, X344:$i, X345:$i > $o, X346:$i, X349:$i, X350:$i > $o, X353:$i, X355:$i, X357:$i, X358:$i, X359:$i, X360:$i, X361:$i, X362:$i, X363:$i, X364:$i, X366:$i, X367:$i, X368:$i, X369:$i, X370:$i, X371:$i, X372:$i, X373:$i, X374:$i, X375:$i, X376:$i, X377:$i, X378:$i, X379:$i, X380:$i, X381:$i, X382:$i, X383:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i, X389:$i, X390:$i, X391:$i, X392:$i, X393:$i > $i > $o, X394:$i, X395:$i, X396:$i, X397:$i, X398:$i > $i > $o, X399:$i, X400:$i, X401:$i > $i > $o, X402:$i, X403:$i, X404:$i > $i > $o, X405:$i, X406:$i, X407:$i, X408:$i, X409:$i > $i > $o, X410:$i, X411:$i, X412:$i, X413:$i, X414:$i > $i > $o, X415:$i, X416:$i, X417:$i, X418:$i, X419:$i > $i > $o, X420:$i, X421:$i, X422:$i, X423:$i, X424:$i, X426:$i, X427:$i, X429:$i, X430:$i, X431:$i, X433:$i, X434:$i, X435:$i, X436:$i, X437:$i, X439:$i, X440:$i, X441:$i, X442:$i, X443:$i, X444:$i, X446:$i, X447:$i, X448:$i, X449:$i, X450:$i, X451:$i, X452:$i, X454:$i, X458:$i, X460:$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 @ X318 @ emptyset) @ (setadjoin @ (setadjoin @ X318 @ (setadjoin @ X319 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X320 @ X321))&((singletonsubset)&((singletoninpowerset)&((singletoninpowunion)&((upairset2E)&((upairsubunion)&((upairinpowunion)&((ubforcartprodlem1)&((ubforcartprodlem2)&((ubforcartprodlem3)&((~(in @ X324 @ X322)|(~(in @ X325 @ X323)|(in @ (kpair @ X324 @ X325) @ (cartprod @ X322 @ X323))))&((((in @ (esk1_3 @ X326 @ X327 @ X328) @ X326)|~(in @ X328 @ (cartprod @ X326 @ X327)))&(((in @ (esk2_3 @ X326 @ X327 @ X328) @ X327)|~(in @ X328 @ (cartprod @ X326 @ X327)))&(((X328)=(kpair @ (esk1_3 @ X326 @ X327 @ X328) @ (esk2_3 @ X326 @ X327 @ X328)))|~(in @ X328 @ (cartprod @ X326 @ X327)))))&((~(in @ X333 @ (cartprod @ X331 @ X332))|(iskpair @ X333))&((setunionE2)&((setunionsingleton1)&((setunionsingleton2)&((setunionsingleton)&(((((in @ (esk5_2 @ X334 @ X335) @ (dsetconstr @ X334 @ X335))|(~(in @ X338 @ X334)|~(X335 @ X338))|(in @ (esk3_2 @ X334 @ X335) @ X334))&(((dsetconstr @ X334 @ X335)=(setadjoin @ (esk5_2 @ X334 @ X335) @ emptyset))|(~(in @ X338 @ X334)|~(X335 @ X338))|(in @ (esk3_2 @ X334 @ X335) @ X334)))&((((in @ (esk5_2 @ X334 @ X335) @ (dsetconstr @ X334 @ X335))|(~(in @ X338 @ X334)|~(X335 @ X338))|(in @ (esk4_2 @ X334 @ X335) @ X334))&(((dsetconstr @ X334 @ X335)=(setadjoin @ (esk5_2 @ X334 @ X335) @ emptyset))|(~(in @ X338 @ X334)|~(X335 @ X338))|(in @ (esk4_2 @ X334 @ X335) @ X334)))&((((in @ (esk5_2 @ X334 @ X335) @ (dsetconstr @ X334 @ X335))|(~(in @ X338 @ X334)|~(X335 @ X338))|(X335 @ (esk3_2 @ X334 @ X335)))&(((dsetconstr @ X334 @ X335)=(setadjoin @ (esk5_2 @ X334 @ X335) @ emptyset))|(~(in @ X338 @ X334)|~(X335 @ X338))|(X335 @ (esk3_2 @ X334 @ X335))))&((((in @ (esk5_2 @ X334 @ X335) @ (dsetconstr @ X334 @ X335))|(~(in @ X338 @ X334)|~(X335 @ X338))|(X335 @ (esk4_2 @ X334 @ X335)))&(((dsetconstr @ X334 @ X335)=(setadjoin @ (esk5_2 @ X334 @ X335) @ emptyset))|(~(in @ X338 @ X334)|~(X335 @ X338))|(X335 @ (esk4_2 @ X334 @ X335))))&(((in @ (esk5_2 @ X334 @ X335) @ (dsetconstr @ X334 @ X335))|(~(in @ X338 @ X334)|~(X335 @ X338))|((esk3_2 @ X334 @ X335)!=(esk4_2 @ X334 @ X335)))&(((dsetconstr @ X334 @ X335)=(setadjoin @ (esk5_2 @ X334 @ X335) @ emptyset))|(~(in @ X338 @ X334)|~(X335 @ X338))|((esk3_2 @ X334 @ X335)!=(esk4_2 @ X334 @ X335))))))))&((((in @ (esk6_2 @ X340 @ X341) @ X340)|(~(in @ X342 @ (dsetconstr @ X340 @ X341))|((dsetconstr @ X340 @ X341)!=(setadjoin @ X342 @ emptyset))))&((X341 @ (esk6_2 @ X340 @ X341))|(~(in @ X342 @ (dsetconstr @ X340 @ X341))|((dsetconstr @ X340 @ X341)!=(setadjoin @ X342 @ emptyset)))))&(((((in @ (esk8_3 @ X344 @ X345 @ X346) @ (dsetconstr @ X344 @ X345))|(in @ (esk7_3 @ X344 @ X345 @ X346) @ X344)|~(X345 @ X346)|~(in @ X346 @ X344))&(((dsetconstr @ X344 @ X345)=(setadjoin @ (esk8_3 @ X344 @ X345 @ X346) @ emptyset))|(in @ (esk7_3 @ X344 @ X345 @ X346) @ X344)|~(X345 @ X346)|~(in @ X346 @ X344)))&((((in @ (esk8_3 @ X344 @ X345 @ X346) @ (dsetconstr @ X344 @ X345))|(X345 @ (esk7_3 @ X344 @ X345 @ X346))|~(X345 @ X346)|~(in @ X346 @ X344))&(((dsetconstr @ X344 @ X345)=(setadjoin @ (esk8_3 @ X344 @ X345 @ X346) @ emptyset))|(X345 @ (esk7_3 @ X344 @ X345 @ X346))|~(X345 @ X346)|~(in @ X346 @ X344)))&(((in @ (esk8_3 @ X344 @ X345 @ X346) @ (dsetconstr @ X344 @ X345))|((esk7_3 @ X344 @ X345 @ X346)!=(X346))|~(X345 @ X346)|~(in @ X346 @ X344))&(((dsetconstr @ X344 @ X345)=(setadjoin @ (esk8_3 @ X344 @ X345 @ X346) @ emptyset))|((esk7_3 @ X344 @ X345 @ X346)!=(X346))|~(X345 @ X346)|~(in @ X346 @ X344)))))&(((((in @ (esk11_2 @ X349 @ X350) @ (dsetconstr @ X349 @ X350))|(~(in @ X353 @ X349)|~(X350 @ X353))|(in @ (esk9_2 @ X349 @ X350) @ X349))&(((dsetconstr @ X349 @ X350)=(setadjoin @ (esk11_2 @ X349 @ X350) @ emptyset))|(~(in @ X353 @ X349)|~(X350 @ X353))|(in @ (esk9_2 @ X349 @ X350) @ X349)))&((((in @ (esk11_2 @ X349 @ X350) @ (dsetconstr @ X349 @ X350))|(~(in @ X353 @ X349)|~(X350 @ X353))|(in @ (esk10_2 @ X349 @ X350) @ X349))&(((dsetconstr @ X349 @ X350)=(setadjoin @ (esk11_2 @ X349 @ X350) @ emptyset))|(~(in @ X353 @ X349)|~(X350 @ X353))|(in @ (esk10_2 @ X349 @ X350) @ X349)))&((((in @ (esk11_2 @ X349 @ X350) @ (dsetconstr @ X349 @ X350))|(~(in @ X353 @ X349)|~(X350 @ X353))|(X350 @ (esk9_2 @ X349 @ X350)))&(((dsetconstr @ X349 @ X350)=(setadjoin @ (esk11_2 @ X349 @ X350) @ emptyset))|(~(in @ X353 @ X349)|~(X350 @ X353))|(X350 @ (esk9_2 @ X349 @ X350))))&((((in @ (esk11_2 @ X349 @ X350) @ (dsetconstr @ X349 @ X350))|(~(in @ X353 @ X349)|~(X350 @ X353))|(X350 @ (esk10_2 @ X349 @ X350)))&(((dsetconstr @ X349 @ X350)=(setadjoin @ (esk11_2 @ X349 @ X350) @ emptyset))|(~(in @ X353 @ X349)|~(X350 @ X353))|(X350 @ (esk10_2 @ X349 @ X350))))&(((in @ (esk11_2 @ X349 @ X350) @ (dsetconstr @ X349 @ X350))|(~(in @ X353 @ X349)|~(X350 @ X353))|((esk9_2 @ X349 @ X350)!=(esk10_2 @ X349 @ X350)))&(((dsetconstr @ X349 @ X350)=(setadjoin @ (esk11_2 @ X349 @ X350) @ emptyset))|(~(in @ X353 @ X349)|~(X350 @ X353))|((esk9_2 @ X349 @ X350)!=(esk10_2 @ X349 @ X350))))))))&((singletonsuniq)&((setukpairinjL1)&((((in @ (esk12_1 @ X355) @ (dsetconstr @ (setunion @ X355) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X355)))))|~(iskpair @ X355))&(((dsetconstr @ (setunion @ X355) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X355))))=(setadjoin @ (esk12_1 @ X355) @ emptyset))|~(iskpair @ X355)))&((~(in @ X358 @ X357)|((X357)!=(setadjoin @ X358 @ emptyset))|(in @ (setunion @ X357) @ X357))&(((kfst @ (kpair @ X359 @ X360))=(X359))&((~(in @ X363 @ (cartprod @ X361 @ X362))|(in @ (kfst @ X363) @ X361))&((setukpairinjL2)&((setukpairinjL)&((setukpairinjR11)&((setukpairinjR12)&((setukpairinjR1)&((upairequniteq)&((setukpairinjR2)&((setukpairinjR)&((((in @ (esk13_1 @ X364) @ (dsetconstr @ (setunion @ X364) @ (^[Z0:$i]:(((X364)=(kpair @ (kfst @ X364) @ Z0))))))|~(iskpair @ X364))&(((dsetconstr @ (setunion @ X364) @ (^[Z0:$i]:(((X364)=(kpair @ (kfst @ X364) @ Z0)))))=(setadjoin @ (esk13_1 @ X364) @ emptyset))|~(iskpair @ X364)))&(((ksnd @ (kpair @ X366 @ X367))=(X367))&((~(iskpair @ X368)|((kpair @ (kfst @ X368) @ (ksnd @ X368))=(X368)))&((~(in @ X371 @ (cartprod @ X369 @ X370))|(in @ (ksnd @ X371) @ X370))&((~(in @ (kpair @ X374 @ X375) @ (cartprod @ X372 @ X373))|(in @ X374 @ X372))&((~(in @ (kpair @ X378 @ X379) @ (cartprod @ X376 @ X377))|(in @ X379 @ X377))&((cartprodmempaircEq)&((~(in @ X382 @ X380)|(~(in @ X383 @ X381)|((kfst @ (kpair @ X382 @ X383))=(X382))))&((~(in @ X386 @ X384)|(~(in @ X387 @ X385)|((ksnd @ (kpair @ X386 @ X387))=(X387))))&((~(in @ X390 @ (cartprod @ X388 @ X389))|((kpair @ (kfst @ X390) @ (ksnd @ X390))=(X390)))&((~(in @ X394 @ X391)|(~(in @ X395 @ X392)|(~(X393 @ X394 @ X395)|(in @ (kpair @ X394 @ X395) @ (dpsetconstr @ X391 @ X392 @ X393)))))&((subset @ (dpsetconstr @ X396 @ X397 @ X398) @ (cartprod @ X396 @ X397))&((subset @ (dpsetconstr @ X399 @ X400 @ X401) @ (cartprod @ X399 @ X400))&((~(in @ X405 @ X402)|(~(in @ X406 @ X403)|(~(in @ (kpair @ X405 @ X406) @ (dpsetconstr @ X402 @ X403 @ X404))|(X404 @ X405 @ X406))))&((~(in @ (kpair @ X410 @ X411) @ (dpsetconstr @ X407 @ X408 @ X409))|(in @ X410 @ X407))&((~(in @ (kpair @ X415 @ X416) @ (dpsetconstr @ X412 @ X413 @ X414))|(in @ X416 @ X413))&((~(in @ (kpair @ X420 @ X421) @ (dpsetconstr @ X417 @ X418 @ X419))|(X419 @ X420 @ X421))&(((((in @ (esk15_4 @ X422 @ X423 @ X424 @ X427) @ (dsetconstr @ X423 @ (^[Z0:$i]:((in @ (kpair @ X427 @ Z0) @ X424)))))|~(in @ X427 @ X422)|((in @ (esk14_3 @ X422 @ X423 @ X424) @ X422)|~(subset @ X424 @ (cartprod @ X422 @ X423))))&(((dsetconstr @ X423 @ (^[Z0:$i]:((in @ (kpair @ X427 @ Z0) @ X424))))=(setadjoin @ (esk15_4 @ X422 @ X423 @ X424 @ X427) @ emptyset))|~(in @ X427 @ X422)|((in @ (esk14_3 @ X422 @ X423 @ X424) @ X422)|~(subset @ X424 @ (cartprod @ X422 @ X423)))))&(((in @ (esk15_4 @ X422 @ X423 @ X424 @ X427) @ (dsetconstr @ X423 @ (^[Z0:$i]:((in @ (kpair @ X427 @ Z0) @ X424)))))|~(in @ X427 @ X422)|(~(in @ X426 @ (dsetconstr @ X423 @ (^[Z0:$i]:((in @ (kpair @ (esk14_3 @ X422 @ X423 @ X424) @ Z0) @ X424)))))|((dsetconstr @ X423 @ (^[Z0:$i]:((in @ (kpair @ (esk14_3 @ X422 @ X423 @ X424) @ Z0) @ X424))))!=(setadjoin @ X426 @ emptyset))|~(subset @ X424 @ (cartprod @ X422 @ X423))))&(((dsetconstr @ X423 @ (^[Z0:$i]:((in @ (kpair @ X427 @ Z0) @ X424))))=(setadjoin @ (esk15_4 @ X422 @ X423 @ X424 @ X427) @ emptyset))|~(in @ X427 @ X422)|(~(in @ X426 @ (dsetconstr @ X423 @ (^[Z0:$i]:((in @ (kpair @ (esk14_3 @ X422 @ X423 @ X424) @ Z0) @ X424)))))|((dsetconstr @ X423 @ (^[Z0:$i]:((in @ (kpair @ (esk14_3 @ X422 @ X423 @ X424) @ Z0) @ X424))))!=(setadjoin @ X426 @ emptyset))|~(subset @ X424 @ (cartprod @ X422 @ X423))))))&((((in @ (esk16_3 @ X429 @ X430 @ X431) @ X429)|~(subset @ X431 @ (cartprod @ X429 @ X430))|(~(in @ X434 @ X429)|(in @ (setunion @ (dsetconstr @ X430 @ (^[Z0:$i]:((in @ (kpair @ X434 @ Z0) @ X431))))) @ X430)))&(~(in @ X433 @ (dsetconstr @ X430 @ (^[Z0:$i]:((in @ (kpair @ (esk16_3 @ X429 @ X430 @ X431) @ Z0) @ X431)))))|((dsetconstr @ X430 @ (^[Z0:$i]:((in @ (kpair @ (esk16_3 @ X429 @ X430 @ X431) @ Z0) @ X431))))!=(setadjoin @ X433 @ emptyset))|~(subset @ X431 @ (cartprod @ X429 @ X430))|(~(in @ X434 @ X429)|(in @ (setunion @ (dsetconstr @ X430 @ (^[Z0:$i]:((in @ (kpair @ X434 @ Z0) @ X431))))) @ X430))))&((((in @ (esk17_3 @ X435 @ X436 @ X437) @ X435)|~(subset @ X437 @ (cartprod @ X435 @ X436))|(~(in @ X440 @ X435)|(in @ (ap @ X435 @ X436 @ X437 @ X440) @ X436)))&(~(in @ X439 @ (dsetconstr @ X436 @ (^[Z0:$i]:((in @ (kpair @ (esk17_3 @ X435 @ X436 @ X437) @ Z0) @ X437)))))|((dsetconstr @ X436 @ (^[Z0:$i]:((in @ (kpair @ (esk17_3 @ X435 @ X436 @ X437) @ Z0) @ X437))))!=(setadjoin @ X439 @ emptyset))|~(subset @ X437 @ (cartprod @ X435 @ X436))|(~(in @ X440 @ X435)|(in @ (ap @ X435 @ X436 @ X437 @ X440) @ X436))))&((((subset @ X443 @ (cartprod @ X441 @ X442))|~(in @ X443 @ (funcSet @ X441 @ X442)))&(((in @ (esk18_4 @ X441 @ X442 @ X443 @ X444) @ (dsetconstr @ X442 @ (^[Z0:$i]:((in @ (kpair @ X444 @ Z0) @ X443)))))|~(in @ X444 @ X441)|~(in @ X443 @ (funcSet @ X441 @ X442)))&(((dsetconstr @ X442 @ (^[Z0:$i]:((in @ (kpair @ X444 @ Z0) @ X443))))=(setadjoin @ (esk18_4 @ X441 @ X442 @ X443 @ X444) @ emptyset))|~(in @ X444 @ X441)|~(in @ X443 @ (funcSet @ X441 @ X442)))))&((~(in @ X448 @ (funcSet @ X446 @ X447))|(~(in @ X449 @ X446)|(in @ (ap @ X446 @ X447 @ X448 @ X449) @ X447)))&((((in @ (esk19_3 @ X450 @ X451 @ X452) @ X450)|~(subset @ X452 @ (cartprod @ X450 @ X451))|(in @ X452 @ (funcSet @ X450 @ X451)))&(~(in @ X454 @ (dsetconstr @ X451 @ (^[Z0:$i]:((in @ (kpair @ (esk19_3 @ X450 @ X451 @ X452) @ Z0) @ X452)))))|((dsetconstr @ X451 @ (^[Z0:$i]:((in @ (kpair @ (esk19_3 @ X450 @ X451 @ X452) @ Z0) @ X452))))!=(setadjoin @ X454 @ emptyset))|~(subset @ X452 @ (cartprod @ X450 @ X451))|(in @ X452 @ (funcSet @ X450 @ X451))))&((~(in @ X458 @ esk20_0)|(in @ (esk22_0 @ X458) @ esk21_0))&(((in @ esk23_0 @ esk20_0)|~(subset @ (dpsetconstr @ esk20_0 @ esk21_0 @ (^[Z0:$i]:($eq @ (esk22_0 @ Z0)))) @ (cartprod @ esk20_0 @ esk21_0)))&(~(in @ X460 @ (dsetconstr @ esk21_0 @ (^[Z0:$i]:((in @ (kpair @ esk23_0 @ Z0) @ (dpsetconstr @ esk20_0 @ esk21_0 @ (^[Z1:$i]:($eq @ (esk22_0 @ Z1)))))))))|((dsetconstr @ esk21_0 @ (^[Z0:$i]:((in @ (kpair @ esk23_0 @ Z0) @ (dpsetconstr @ esk20_0 @ esk21_0 @ (^[Z1:$i]:($eq @ (esk22_0 @ Z1))))))))!=(setadjoin @ X460 @ emptyset))|~(subset @ (dpsetconstr @ esk20_0 @ esk21_0 @ (^[Z0:$i]:($eq @ (esk22_0 @ Z0)))) @ (cartprod @ esk20_0 @ esk21_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_75])])])])])])).
% 251.81/33.51 thf(c_0_77, plain, ![X465:$i]:(((epred1_0 @ X465)=($eq @ (esk22_0 @ X465)))), introduced(definition)).
% 251.81/33.51 thf(c_0_78, negated_conjecture, ((in @ esk23_0 @ esk20_0)|~((((subset @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0) @ (cartprod @ esk20_0 @ esk21_0)))=(($true))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_76]), c_0_77])).
% 251.81/33.51 thf(c_0_79, plain, ![X506:$i]:(((epred1_0 @ X506)=($eq @ (esk22_0 @ X506)))), inference(variable_rename,[status(thm)],[])).
% 251.81/33.51 thf(c_0_80, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ (esk5_2 @ X2 @ X1) @ (dsetconstr @ X2 @ X1))|(X1 @ (esk3_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_81, negated_conjecture, ![X2:$i]:(((in @ (esk22_0 @ X2) @ esk21_0)|~((in @ X2 @ esk20_0)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_82, negated_conjecture, ((in @ esk23_0 @ esk20_0)|~((subset @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0) @ (cartprod @ esk20_0 @ esk21_0)))), inference(cn,[status(thm)],[c_0_78])).
% 251.81/33.51 thf(c_0_83, 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_76])).
% 251.81/33.51 thf(c_0_84, plain, ![X2:$i]:(((epred1_0 @ X2)=($eq @ (esk22_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_79])).
% 251.81/33.51 thf(c_0_85, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk5_2 @ X2 @ X1) @ emptyset))|(X1 @ (esk3_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_86, negated_conjecture, ![X1:$i > $o, X2:$i]:(((in @ (esk5_2 @ esk21_0 @ X1) @ (dsetconstr @ esk21_0 @ X1))|(X1 @ (esk3_2 @ esk21_0 @ X1))|~((in @ X2 @ esk20_0))|~((X1 @ (esk22_0 @ X2))))), inference(spm,[status(thm)],[c_0_80, c_0_81])).
% 251.81/33.51 thf(c_0_87, negated_conjecture, (in @ esk23_0 @ esk20_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82, c_0_83])])).
% 251.81/33.51 thf(c_0_88, plain, ![X2:$i, X507:$i]:((((esk22_0 @ X2)=(X507))<=>(epred1_0 @ X2 @ X507))), inference(arg_cong,[status(thm)],[c_0_84])).
% 251.81/33.51 thf(c_0_89, negated_conjecture, ![X1:$i > $o, X2:$i]:((((setadjoin @ (esk5_2 @ esk21_0 @ X1) @ emptyset)=(dsetconstr @ esk21_0 @ X1))|(X1 @ (esk3_2 @ esk21_0 @ X1))|~((in @ X2 @ esk20_0))|~((X1 @ (esk22_0 @ X2))))), inference(spm,[status(thm)],[c_0_85, c_0_81])).
% 251.81/33.51 thf(c_0_90, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk21_0 @ X1) @ (dsetconstr @ esk21_0 @ X1))|(X1 @ (esk3_2 @ esk21_0 @ X1))|~((X1 @ (esk22_0 @ esk23_0))))), inference(spm,[status(thm)],[c_0_86, c_0_87])).
% 251.81/33.51 thf(c_0_91, plain, ![X2:$i]:((epred1_0 @ X2 @ (esk22_0 @ X2))), inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_88])])).
% 251.81/33.51 thf(c_0_92, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk21_0 @ X1) @ emptyset)=(dsetconstr @ esk21_0 @ X1))|(X1 @ (esk3_2 @ esk21_0 @ X1))|~((X1 @ (esk22_0 @ esk23_0))))), inference(spm,[status(thm)],[c_0_89, c_0_87])).
% 251.81/33.51 thf(c_0_93, plain, ![X2:$i, X3:$i]:((((esk22_0 @ X2)=(X3))|~((epred1_0 @ X2 @ X3)))), inference(dynamic_cnf,[status(thm)],[c_0_88])).
% 251.81/33.51 thf(c_0_94, plain, ((in @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ (dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))|(epred1_0 @ esk23_0 @ (esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0)))), inference(spm,[status(thm)],[c_0_90, c_0_91])).
% 251.81/33.51 thf(c_0_95, plain, (((setadjoin @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ emptyset)=(dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))|(epred1_0 @ esk23_0 @ (esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0)))), inference(spm,[status(thm)],[c_0_92, c_0_91])).
% 251.81/33.51 thf(c_0_96, plain, (((esk22_0 @ esk23_0)=(esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0)))|(in @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ (dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))), inference(spm,[status(thm)],[c_0_93, c_0_94])).
% 251.81/33.51 thf(c_0_97, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ (esk5_2 @ X2 @ X1) @ (dsetconstr @ X2 @ X1))|(X1 @ (esk4_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_98, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ (esk5_2 @ X2 @ X1) @ (dsetconstr @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3))|((esk3_2 @ X2 @ X1)!=(esk4_2 @ X2 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_99, plain, (((setadjoin @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ emptyset)=(dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))|((esk22_0 @ esk23_0)=(esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0)))), inference(spm,[status(thm)],[c_0_93, c_0_95])).
% 251.81/33.51 thf(c_0_100, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk5_2 @ X2 @ X1) @ emptyset))|(X1 @ (esk4_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_101, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk5_2 @ X2 @ X1) @ emptyset))|~((in @ X3 @ X2))|~((X1 @ X3))|((esk3_2 @ X2 @ X1)!=(esk4_2 @ X2 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_102, plain, ((($eq @ (esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0)))=(epred1_0 @ esk23_0))|(in @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ (dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))), inference(spm,[status(thm)],[c_0_84, c_0_96])).
% 251.81/33.51 thf(c_0_103, negated_conjecture, ![X1:$i > $o, X2:$i]:(((in @ (esk5_2 @ esk21_0 @ X1) @ (dsetconstr @ esk21_0 @ X1))|(X1 @ (esk4_2 @ esk21_0 @ X1))|~((in @ X2 @ esk20_0))|~((X1 @ (esk22_0 @ X2))))), inference(spm,[status(thm)],[c_0_97, c_0_81])).
% 251.81/33.51 thf(c_0_104, negated_conjecture, ![X1:$i > $o, X2:$i]:(((in @ (esk5_2 @ esk21_0 @ X1) @ (dsetconstr @ esk21_0 @ X1))|((esk4_2 @ esk21_0 @ X1)!=(esk3_2 @ esk21_0 @ X1))|~((in @ X2 @ esk20_0))|~((X1 @ (esk22_0 @ X2))))), inference(spm,[status(thm)],[c_0_98, c_0_81])).
% 251.81/33.51 thf(c_0_105, plain, (((setadjoin @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ emptyset)=(dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))|(($eq @ (esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0)))=(epred1_0 @ esk23_0))), inference(spm,[status(thm)],[c_0_84, c_0_99])).
% 251.81/33.51 thf(c_0_106, negated_conjecture, ![X1:$i > $o, X2:$i]:((((setadjoin @ (esk5_2 @ esk21_0 @ X1) @ emptyset)=(dsetconstr @ esk21_0 @ X1))|(X1 @ (esk4_2 @ esk21_0 @ X1))|~((in @ X2 @ esk20_0))|~((X1 @ (esk22_0 @ X2))))), inference(spm,[status(thm)],[c_0_100, c_0_81])).
% 251.81/33.51 thf(c_0_107, negated_conjecture, ![X1:$i > $o, X2:$i]:((((setadjoin @ (esk5_2 @ esk21_0 @ X1) @ emptyset)=(dsetconstr @ esk21_0 @ X1))|((esk4_2 @ esk21_0 @ X1)!=(esk3_2 @ esk21_0 @ X1))|~((in @ X2 @ esk20_0))|~((X1 @ (esk22_0 @ X2))))), inference(spm,[status(thm)],[c_0_101, c_0_81])).
% 251.81/33.51 thf(c_0_108, plain, ![X551:$i]:((((epred1_0 @ esk23_0 @ X551)<=>((esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0))=(X551)))|(in @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ (dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0))))), inference(arg_cong,[status(thm)],[c_0_102])).
% 251.81/33.51 thf(c_0_109, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk21_0 @ X1) @ (dsetconstr @ esk21_0 @ X1))|(X1 @ (esk4_2 @ esk21_0 @ X1))|~((X1 @ (esk22_0 @ esk23_0))))), inference(spm,[status(thm)],[c_0_103, c_0_87])).
% 251.81/33.51 thf(c_0_110, negated_conjecture, ![X1:$i > $o]:(((in @ (esk5_2 @ esk21_0 @ X1) @ (dsetconstr @ esk21_0 @ X1))|((esk4_2 @ esk21_0 @ X1)!=(esk3_2 @ esk21_0 @ X1))|~((X1 @ (esk22_0 @ esk23_0))))), inference(spm,[status(thm)],[c_0_104, c_0_87])).
% 251.81/33.51 thf(c_0_111, plain, ![X523:$i]:((((setadjoin @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ emptyset)=(dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))|((epred1_0 @ esk23_0 @ X523)<=>((esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0))=(X523))))), inference(arg_cong,[status(thm)],[c_0_105])).
% 251.81/33.51 thf(c_0_112, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk21_0 @ X1) @ emptyset)=(dsetconstr @ esk21_0 @ X1))|(X1 @ (esk4_2 @ esk21_0 @ X1))|~((X1 @ (esk22_0 @ esk23_0))))), inference(spm,[status(thm)],[c_0_106, c_0_87])).
% 251.81/33.51 thf(c_0_113, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk5_2 @ esk21_0 @ X1) @ emptyset)=(dsetconstr @ esk21_0 @ X1))|((esk4_2 @ esk21_0 @ X1)!=(esk3_2 @ esk21_0 @ X1))|~((X1 @ (esk22_0 @ esk23_0))))), inference(spm,[status(thm)],[c_0_107, c_0_87])).
% 251.81/33.51 thf(c_0_114, plain, ![X2:$i]:((((esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0))=(X2))|(in @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ (dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))|~((epred1_0 @ esk23_0 @ X2)))), inference(dynamic_cnf,[status(thm)],[c_0_108])).
% 251.81/33.51 thf(c_0_115, plain, ((in @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ (dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))|(epred1_0 @ esk23_0 @ (esk4_2 @ esk21_0 @ (epred1_0 @ esk23_0)))), inference(spm,[status(thm)],[c_0_109, c_0_91])).
% 251.81/33.51 thf(c_0_116, plain, ((in @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ (dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))|((esk4_2 @ esk21_0 @ (epred1_0 @ esk23_0))!=(esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0)))), inference(spm,[status(thm)],[c_0_110, c_0_91])).
% 251.81/33.51 thf(c_0_117, plain, ![X2:$i]:((((setadjoin @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ emptyset)=(dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))|((esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0))=(X2))|~((epred1_0 @ esk23_0 @ X2)))), inference(dynamic_cnf,[status(thm)],[c_0_111])).
% 251.81/33.51 thf(c_0_118, plain, (((setadjoin @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ emptyset)=(dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))|(epred1_0 @ esk23_0 @ (esk4_2 @ esk21_0 @ (epred1_0 @ esk23_0)))), inference(spm,[status(thm)],[c_0_112, c_0_91])).
% 251.81/33.51 thf(c_0_119, plain, (((setadjoin @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ emptyset)=(dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0)))|((esk4_2 @ esk21_0 @ (epred1_0 @ esk23_0))!=(esk3_2 @ esk21_0 @ (epred1_0 @ esk23_0)))), inference(spm,[status(thm)],[c_0_113, c_0_91])).
% 251.81/33.51 thf(c_0_120, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((X1 @ (esk6_2 @ X2 @ X1))|~((in @ X3 @ (dsetconstr @ X2 @ X1)))|((dsetconstr @ X2 @ X1)!=(setadjoin @ X3 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_121, plain, (in @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ (dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_115]), c_0_116])).
% 251.81/33.51 thf(c_0_122, plain, ((setadjoin @ (esk5_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ emptyset)=(dsetconstr @ esk21_0 @ (epred1_0 @ esk23_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_118]), c_0_119])).
% 251.81/33.51 thf(c_0_123, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ (esk6_2 @ X2 @ X1) @ X2)|~((in @ X3 @ (dsetconstr @ X2 @ X1)))|((dsetconstr @ X2 @ X1)!=(setadjoin @ X3 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_124, negated_conjecture, (epred1_0 @ esk23_0 @ (esk6_2 @ esk21_0 @ (epred1_0 @ esk23_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_121]), c_0_122])])).
% 251.81/33.51 thf(c_0_125, plain, ![X505:$i]:(((~(epred2_0 @ X505)|(in @ (kpair @ esk23_0 @ X505) @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0)))&(~(in @ (kpair @ esk23_0 @ X505) @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0))|(epred2_0 @ X505)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])).
% 251.81/33.51 thf(c_0_126, negated_conjecture, ![X3:$i, X2:$i, X6:$i > $i > $o, X5:$i, X4:$i]:(((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X5 @ X6))|~((in @ X2 @ X3))|~((in @ X4 @ X5))|~((X6 @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_127, negated_conjecture, (in @ (esk6_2 @ esk21_0 @ (epred1_0 @ esk23_0)) @ esk21_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_121]), c_0_122])])).
% 251.81/33.51 thf(c_0_128, plain, ((esk6_2 @ esk21_0 @ (epred1_0 @ esk23_0))=(esk22_0 @ esk23_0)), inference(spm,[status(thm)],[c_0_93, c_0_124])).
% 251.81/33.51 thf(c_0_129, plain, ![X2:$i]:(((epred2_0 @ X2)|~((in @ (kpair @ esk23_0 @ X2) @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0))))), inference(split_conjunct,[status(thm)],[c_0_125])).
% 251.81/33.51 thf(c_0_130, plain, ![X2:$i, X4:$i, X3:$i]:(((in @ (kpair @ X2 @ (esk22_0 @ X2)) @ (dpsetconstr @ X3 @ X4 @ epred1_0))|~((in @ (esk22_0 @ X2) @ X4))|~((in @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_126, c_0_91])).
% 251.81/33.51 thf(c_0_131, negated_conjecture, (in @ (esk22_0 @ esk23_0) @ esk21_0), inference(rw,[status(thm)],[c_0_127, c_0_128])).
% 251.81/33.51 thf(c_0_132, plain, (epred2_0 @ (esk22_0 @ esk23_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_130]), c_0_131]), c_0_87])])).
% 251.81/33.51 thf(c_0_133, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i, X6:$i > $i > $o]:(((X6 @ X2 @ X3)|~((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ X6))))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_134, negated_conjecture, ![X2:$i]:((((kpair @ (kfst @ X2) @ (ksnd @ X2))=(X2))|~((iskpair @ X2)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_135, plain, ![X2:$i]:(((in @ (kpair @ esk23_0 @ X2) @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_125])).
% 251.81/33.51 thf(c_0_136, negated_conjecture, ((in @ (esk5_2 @ esk21_0 @ epred2_0) @ (dsetconstr @ esk21_0 @ epred2_0))|(epred2_0 @ (esk3_2 @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_90, c_0_132])).
% 251.81/33.51 thf(c_0_137, negated_conjecture, ((in @ (esk5_2 @ esk21_0 @ epred2_0) @ (dsetconstr @ esk21_0 @ epred2_0))|(epred2_0 @ (esk4_2 @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_109, c_0_132])).
% 251.81/33.51 thf(c_0_138, negated_conjecture, (((setadjoin @ (esk5_2 @ esk21_0 @ epred2_0) @ emptyset)=(dsetconstr @ esk21_0 @ epred2_0))|(epred2_0 @ (esk3_2 @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_92, c_0_132])).
% 251.81/33.51 thf(c_0_139, negated_conjecture, (((setadjoin @ (esk5_2 @ esk21_0 @ epred2_0) @ emptyset)=(dsetconstr @ esk21_0 @ epred2_0))|(epred2_0 @ (esk4_2 @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_112, c_0_132])).
% 251.81/33.51 thf(c_0_140, plain, ![X466:$i]:(((epred2_0 @ X466)<=>(in @ (kpair @ esk23_0 @ X466) @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0)))), introduced(definition)).
% 251.81/33.51 thf(c_0_141, negated_conjecture, ![X3:$i, X6:$i > $i > $o, X4:$i, X2:$i]:(((X6 @ (kfst @ X2) @ (ksnd @ X2))|~((in @ X2 @ (dpsetconstr @ X3 @ X4 @ X6)))|~((iskpair @ X2)))), inference(spm,[status(thm)],[c_0_133, c_0_134])).
% 251.81/33.51 thf(c_0_142, plain, ((in @ (kpair @ esk23_0 @ (esk3_2 @ esk21_0 @ epred2_0)) @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0))|(in @ (esk5_2 @ esk21_0 @ epred2_0) @ (dsetconstr @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_135, c_0_136])).
% 251.81/33.51 thf(c_0_143, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_144, negated_conjecture, ![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_145, negated_conjecture, ![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 251.81/33.51 thf(c_0_146, plain, ((in @ (kpair @ esk23_0 @ (esk4_2 @ esk21_0 @ epred2_0)) @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0))|(in @ (esk5_2 @ esk21_0 @ epred2_0) @ (dsetconstr @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_135, c_0_137])).
% 251.81/33.51 thf(c_0_147, plain, (((setadjoin @ (esk5_2 @ esk21_0 @ epred2_0) @ emptyset)=(dsetconstr @ esk21_0 @ epred2_0))|(in @ (kpair @ esk23_0 @ (esk3_2 @ esk21_0 @ epred2_0)) @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_135, c_0_138])).
% 251.81/33.51 thf(c_0_148, plain, (((setadjoin @ (esk5_2 @ esk21_0 @ epred2_0) @ emptyset)=(dsetconstr @ esk21_0 @ epred2_0))|(in @ (kpair @ esk23_0 @ (esk4_2 @ esk21_0 @ epred2_0)) @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0))), inference(spm,[status(thm)],[c_0_135, c_0_139])).
% 251.81/33.51 thf(c_0_149, negated_conjecture, ![X2:$i]:((~((((in @ X2 @ (dsetconstr @ esk21_0 @ epred2_0)))=(($true))))|((dsetconstr @ esk21_0 @ epred2_0)!=(setadjoin @ X2 @ emptyset))|~((((subset @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0) @ (cartprod @ esk20_0 @ esk21_0)))=(($true)))))), inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_76]), c_0_77]), c_0_140]), c_0_77]), c_0_140]), c_0_77])).
% 251.81/33.51 thf(c_0_150, negated_conjecture, ((in @ (esk5_2 @ esk21_0 @ epred2_0) @ (dsetconstr @ esk21_0 @ epred2_0))|(epred1_0 @ esk23_0 @ (esk3_2 @ esk21_0 @ epred2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_142]), c_0_143]), c_0_144]), c_0_145])])).
% 251.81/33.51 thf(c_0_151, negated_conjecture, ((in @ (esk5_2 @ esk21_0 @ epred2_0) @ (dsetconstr @ esk21_0 @ epred2_0))|(epred1_0 @ esk23_0 @ (esk4_2 @ esk21_0 @ epred2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_146]), c_0_143]), c_0_144]), c_0_145])])).
% 251.81/33.51 thf(c_0_152, negated_conjecture, (((setadjoin @ (esk5_2 @ esk21_0 @ epred2_0) @ emptyset)=(dsetconstr @ esk21_0 @ epred2_0))|(epred1_0 @ esk23_0 @ (esk3_2 @ esk21_0 @ epred2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_147]), c_0_143]), c_0_144]), c_0_145])])).
% 251.81/33.51 thf(c_0_153, negated_conjecture, (((setadjoin @ (esk5_2 @ esk21_0 @ epred2_0) @ emptyset)=(dsetconstr @ esk21_0 @ epred2_0))|(epred1_0 @ esk23_0 @ (esk4_2 @ esk21_0 @ epred2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_148]), c_0_143]), c_0_144]), c_0_145])])).
% 251.81/33.51 thf(c_0_154, negated_conjecture, ![X2:$i]:((((dsetconstr @ esk21_0 @ epred2_0)!=(setadjoin @ X2 @ emptyset))|~((subset @ (dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0) @ (cartprod @ esk20_0 @ esk21_0)))|~((in @ X2 @ (dsetconstr @ esk21_0 @ epred2_0))))), inference(cn,[status(thm)],[c_0_149])).
% 251.81/33.51 thf(c_0_155, plain, (((esk22_0 @ esk23_0)=(esk3_2 @ esk21_0 @ epred2_0))|(in @ (esk5_2 @ esk21_0 @ epred2_0) @ (dsetconstr @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_93, c_0_150])).
% 251.81/33.51 thf(c_0_156, plain, (((esk22_0 @ esk23_0)=(esk4_2 @ esk21_0 @ epred2_0))|(in @ (esk5_2 @ esk21_0 @ epred2_0) @ (dsetconstr @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_93, c_0_151])).
% 251.81/33.51 thf(c_0_157, negated_conjecture, ((in @ (esk5_2 @ esk21_0 @ epred2_0) @ (dsetconstr @ esk21_0 @ epred2_0))|((esk4_2 @ esk21_0 @ epred2_0)!=(esk3_2 @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_110, c_0_132])).
% 251.81/33.51 thf(c_0_158, plain, (((setadjoin @ (esk5_2 @ esk21_0 @ epred2_0) @ emptyset)=(dsetconstr @ esk21_0 @ epred2_0))|((esk22_0 @ esk23_0)=(esk3_2 @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_93, c_0_152])).
% 251.81/33.51 thf(c_0_159, plain, (((setadjoin @ (esk5_2 @ esk21_0 @ epred2_0) @ emptyset)=(dsetconstr @ esk21_0 @ epred2_0))|((esk22_0 @ esk23_0)=(esk4_2 @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_93, c_0_153])).
% 251.81/33.51 thf(c_0_160, negated_conjecture, (((setadjoin @ (esk5_2 @ esk21_0 @ epred2_0) @ emptyset)=(dsetconstr @ esk21_0 @ epred2_0))|((esk4_2 @ esk21_0 @ epred2_0)!=(esk3_2 @ esk21_0 @ epred2_0))), inference(spm,[status(thm)],[c_0_113, c_0_132])).
% 251.81/33.51 thf(c_0_161, negated_conjecture, ![X2:$i]:((((dsetconstr @ esk21_0 @ epred2_0)!=(setadjoin @ X2 @ emptyset))|~((in @ X2 @ (dsetconstr @ esk21_0 @ epred2_0))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_154, c_0_83])])).
% 251.81/33.51 thf(c_0_162, plain, (in @ (esk5_2 @ esk21_0 @ epred2_0) @ (dsetconstr @ esk21_0 @ epred2_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_156]), c_0_157])).
% 251.81/33.51 thf(c_0_163, plain, ((setadjoin @ (esk5_2 @ esk21_0 @ epred2_0) @ emptyset)=(dsetconstr @ esk21_0 @ epred2_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158, c_0_159]), c_0_160])).
% 251.81/33.51 thf(c_0_164, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161, c_0_162]), c_0_163])]), ['proof']).
% 251.81/33.51 % SZS output end CNFRefutation
% 251.81/33.51 % Parsed axioms : 432
% 251.81/33.51 % Removed by relevancy pruning/SinE : 391
% 251.81/33.51 % Initial clauses : 245
% 251.81/33.51 % Removed in clause preprocessing : 0
% 251.81/33.51 % Initial clauses in saturation : 245
% 251.81/33.51 % Processed clauses : 1962
% 251.81/33.51 % ...of these trivial : 19
% 251.81/33.51 % ...subsumed : 502
% 251.81/33.51 % ...remaining for further processing : 1441
% 251.81/33.51 % Other redundant clauses eliminated : 105
% 251.81/33.51 % Clauses deleted for lack of memory : 0
% 251.81/33.51 % Backward-subsumed : 24
% 251.81/33.51 % Backward-rewritten : 125
% 251.81/33.51 % Generated clauses : 14315
% 251.81/33.51 % ...of the previous two non-redundant : 13885
% 251.81/33.51 % ...aggressively subsumed : 0
% 251.81/33.51 % Contextual simplify-reflections : 16
% 251.81/33.51 % Paramodulations : 13866
% 251.81/33.51 % Factorizations : 0
% 251.81/33.51 % NegExts : 110
% 251.81/33.51 % Equation resolutions : 105
% 251.81/33.51 % Disequality decompositions : 0
% 251.81/33.51 % Total rewrite steps : 1217
% 251.81/33.51 % ...of those cached : 1039
% 251.81/33.51 % Propositional unsat checks : 0
% 251.81/33.51 % Propositional check models : 0
% 251.81/33.51 % Propositional check unsatisfiable : 0
% 251.81/33.51 % Propositional clauses : 0
% 251.81/33.51 % Propositional clauses after purity: 0
% 251.81/33.51 % Propositional unsat core size : 0
% 251.81/33.51 % Propositional preprocessing time : 0.000
% 251.81/33.51 % Propositional encoding time : 0.000
% 251.81/33.51 % Propositional solver time : 0.000
% 251.81/33.51 % Success case prop preproc time : 0.000
% 251.81/33.51 % Success case prop encoding time : 0.000
% 251.81/33.51 % Success case prop solver time : 0.000
% 251.81/33.51 % Current number of processed clauses : 984
% 251.81/33.51 % Positive orientable unit clauses : 194
% 251.81/33.51 % Positive unorientable unit clauses: 0
% 251.81/33.51 % Negative unit clauses : 0
% 251.81/33.51 % Non-unit-clauses : 790
% 251.81/33.51 % Current number of unprocessed clauses: 12102
% 251.81/33.51 % ...number of literals in the above : 52830
% 251.81/33.51 % Current number of archived formulas : 0
% 251.81/33.51 % Current number of archived clauses : 456
% 251.81/33.51 % Clause-clause subsumption calls (NU) : 108191
% 251.81/33.51 % Rec. Clause-clause subsumption calls : 61841
% 251.81/33.51 % Non-unit clause-clause subsumptions : 537
% 251.81/33.51 % Unit Clause-clause subsumption calls : 2055
% 251.81/33.51 % Rewrite failures with RHS unbound : 0
% 251.81/33.51 % BW rewrite match attempts : 94
% 251.81/33.51 % BW rewrite match successes : 19
% 251.81/33.51 % Condensation attempts : 0
% 251.81/33.51 % Condensation successes : 0
% 251.81/33.51 % Termbank termtop insertions : 558698
% 251.81/33.51 % Search garbage collected termcells : 8619
% 251.81/33.51
% 251.81/33.51 % -------------------------------------------------
% 251.81/33.51 % User time : 31.115 s
% 251.81/33.51 % System time : 0.653 s
% 251.81/33.51 % Total time : 31.767 s
% 251.81/33.51 % Maximum resident set size: 6640 pages
% 251.81/33.51
% 251.81/33.51 % -------------------------------------------------
% 251.81/33.51 % User time : 31.126 s
% 251.81/33.51 % System time : 0.660 s
% 251.81/33.51 % Total time : 31.787 s
% 251.81/33.51 % Maximum resident set size: 5376 pages
% 251.81/33.51 % E exiting
%------------------------------------------------------------------------------