%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU717^1 : 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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:25:20 AM UTC 2026
% Result : Theorem 6.40s 1.39s
% Output : CNFRefutation 6.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU717^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:14:44 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.21/0.28 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.AgVsZ9S4s0/E---3.1_1349318.p
% 6.40/1.39 % Version: 3.5.1-ho
% 6.40/1.39 % Preprocessing class: HSLMSLSSLLLCHFA.
% 6.40/1.39 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 6.40/1.39 % Starting ehoh_best5 with 300s (1) cores
% 6.40/1.39 % Starting almost_fo_3_lam with 300s (1) cores
% 6.40/1.39 % Starting new_bool_5 with 300s (1) cores
% 6.40/1.39 % Starting pre_casc_3 with 300s (1) cores
% 6.40/1.39 % Starting ho_unfolding_8 with 300s (1) cores
% 6.40/1.39 % Starting new_ho_10_cnf2 with 300s (1) cores
% 6.40/1.39 % Starting new_bool_3 with 300s (1) cores
% 6.40/1.39 % Starting new_ho_5 with 300s (1) cores
% 6.40/1.39 % pre_casc_3 with pid 1349334 completed with status 9
% 6.40/1.39 % new_ho_5 with pid 1349338 completed with status 9
% 6.40/1.39 % new_bool_3 with pid 1349337 completed with status 0
% 6.40/1.39 % Result found by new_bool_3
% 6.40/1.39 % Preprocessing class: HSLMSLSSLLLCHFA.
% 6.40/1.39 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 6.40/1.39 % Starting ehoh_best5 with 300s (1) cores
% 6.40/1.39 % Starting almost_fo_3_lam with 300s (1) cores
% 6.40/1.39 % Starting new_bool_5 with 300s (1) cores
% 6.40/1.39 % Starting pre_casc_3 with 300s (1) cores
% 6.40/1.39 % Starting ho_unfolding_8 with 300s (1) cores
% 6.40/1.39 % Starting new_ho_10_cnf2 with 300s (1) cores
% 6.40/1.39 % Starting new_bool_3 with 300s (1) cores
% 6.40/1.39 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.40/1.39 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.40/1.39 % Search class: HGHSM-FSLM32-MHFMMSBN
% 6.40/1.39 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 6.40/1.39 % Starting SubtermCWHack with 31s (1) cores
% 6.40/1.39 % SubtermCWHack with pid 1349349 completed with status 0
% 6.40/1.39 % Result found by SubtermCWHack
% 6.40/1.39 % Preprocessing class: HSLMSLSSLLLCHFA.
% 6.40/1.39 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 6.40/1.39 % Starting ehoh_best5 with 300s (1) cores
% 6.40/1.39 % Starting almost_fo_3_lam with 300s (1) cores
% 6.40/1.39 % Starting new_bool_5 with 300s (1) cores
% 6.40/1.39 % Starting pre_casc_3 with 300s (1) cores
% 6.40/1.39 % Starting ho_unfolding_8 with 300s (1) cores
% 6.40/1.39 % Starting new_ho_10_cnf2 with 300s (1) cores
% 6.40/1.39 % Starting new_bool_3 with 300s (1) cores
% 6.40/1.39 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.40/1.39 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.40/1.39 % Search class: HGHSM-FSLM32-MHFMMSBN
% 6.40/1.39 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 6.40/1.39 % Starting SubtermCWHack with 31s (1) cores
% 6.40/1.39 % Preprocessing time : 0.004 s
% 6.40/1.39
% 6.40/1.39 % Proof found!
% 6.40/1.39 % SZS status Theorem
% 6.40/1.39 % SZS output start CNFRefutation
% 6.40/1.39 thf(decl_23, type, in: $i > $i > $o).
% 6.40/1.39 thf(decl_24, type, exu: ($i > $o) > $o).
% 6.40/1.39 thf(decl_25, type, setextAx: $o).
% 6.40/1.39 thf(decl_26, type, emptyset: $i).
% 6.40/1.39 thf(decl_27, type, emptysetAx: $o).
% 6.40/1.39 thf(decl_28, type, setadjoin: $i > $i > $i).
% 6.40/1.39 thf(decl_29, type, setadjoinAx: $o).
% 6.40/1.39 thf(decl_30, type, powerset: $i > $i).
% 6.40/1.39 thf(decl_31, type, powersetAx: $o).
% 6.40/1.39 thf(decl_32, type, setunion: $i > $i).
% 6.40/1.39 thf(decl_33, type, setunionAx: $o).
% 6.40/1.39 thf(decl_34, type, omega: $i).
% 6.40/1.39 thf(decl_35, type, omega0Ax: $o).
% 6.40/1.39 thf(decl_36, type, omegaSAx: $o).
% 6.40/1.39 thf(decl_37, type, omegaIndAx: $o).
% 6.40/1.39 thf(decl_38, type, replAx: $o).
% 6.40/1.39 thf(decl_39, type, foundationAx: $o).
% 6.40/1.39 thf(decl_40, type, wellorderingAx: $o).
% 6.40/1.39 thf(decl_41, type, descr: ($i > $o) > $i).
% 6.40/1.39 thf(decl_42, type, descrp: $o).
% 6.40/1.39 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_44, type, dsetconstrI: $o).
% 6.40/1.39 thf(decl_45, type, dsetconstrEL: $o).
% 6.40/1.39 thf(decl_46, type, dsetconstrER: $o).
% 6.40/1.39 thf(decl_47, type, exuE1: $o).
% 6.40/1.39 thf(decl_48, type, prop2set: $o > $i).
% 6.40/1.39 thf(decl_49, type, prop2setE: $o).
% 6.40/1.39 thf(decl_50, type, emptysetE: $o).
% 6.40/1.39 thf(decl_51, type, emptysetimpfalse: $o).
% 6.40/1.39 thf(decl_52, type, notinemptyset: $o).
% 6.40/1.39 thf(decl_53, type, exuE3e: $o).
% 6.40/1.39 thf(decl_54, type, setext: $o).
% 6.40/1.39 thf(decl_55, type, emptyI: $o).
% 6.40/1.39 thf(decl_56, type, noeltsimpempty: $o).
% 6.40/1.39 thf(decl_57, type, setbeta: $o).
% 6.40/1.39 thf(decl_58, type, nonempty: $i > $o).
% 6.40/1.39 thf(decl_59, type, nonemptyE1: $o).
% 6.40/1.39 thf(decl_60, type, nonemptyI: $o).
% 6.40/1.39 thf(decl_61, type, nonemptyI1: $o).
% 6.40/1.39 thf(decl_62, type, setadjoinIL: $o).
% 6.40/1.39 thf(decl_63, type, emptyinunitempty: $o).
% 6.40/1.39 thf(decl_64, type, setadjoinIR: $o).
% 6.40/1.39 thf(decl_65, type, setadjoinE: $o).
% 6.40/1.39 thf(decl_66, type, setadjoinOr: $o).
% 6.40/1.39 thf(decl_67, type, setoftrueEq: $o).
% 6.40/1.39 thf(decl_68, type, powersetI: $o).
% 6.40/1.39 thf(decl_69, type, emptyinPowerset: $o).
% 6.40/1.39 thf(decl_70, type, emptyInPowerset: $o).
% 6.40/1.39 thf(decl_71, type, powersetE: $o).
% 6.40/1.39 thf(decl_72, type, setunionI: $o).
% 6.40/1.39 thf(decl_73, type, setunionE: $o).
% 6.40/1.39 thf(decl_74, type, subPowSU: $o).
% 6.40/1.39 thf(decl_75, type, exuE2: $o).
% 6.40/1.39 thf(decl_76, type, nonemptyImpWitness: $o).
% 6.40/1.39 thf(decl_77, type, uniqinunit: $o).
% 6.40/1.39 thf(decl_78, type, notinsingleton: $o).
% 6.40/1.39 thf(decl_79, type, eqinunit: $o).
% 6.40/1.39 thf(decl_80, type, singletonsswitch: $o).
% 6.40/1.39 thf(decl_81, type, upairsetE: $o).
% 6.40/1.39 thf(decl_82, type, upairsetIL: $o).
% 6.40/1.39 thf(decl_83, type, upairsetIR: $o).
% 6.40/1.39 thf(decl_84, type, emptyE1: $o).
% 6.40/1.39 thf(decl_85, type, vacuousDall: $o).
% 6.40/1.39 thf(decl_86, type, quantDeMorgan1: $o).
% 6.40/1.39 thf(decl_87, type, quantDeMorgan2: $o).
% 6.40/1.39 thf(decl_88, type, quantDeMorgan3: $o).
% 6.40/1.39 thf(decl_89, type, quantDeMorgan4: $o).
% 6.40/1.39 thf(decl_90, type, prop2setI: $o).
% 6.40/1.39 thf(decl_92, type, prop2set2propI: $o).
% 6.40/1.39 thf(decl_93, type, notdexE: $o).
% 6.40/1.39 thf(decl_94, type, notdallE: $o).
% 6.40/1.39 thf(decl_95, type, exuI1: $o).
% 6.40/1.39 thf(decl_96, type, exuI3: $o).
% 6.40/1.39 thf(decl_97, type, exuI2: $o).
% 6.40/1.39 thf(decl_98, type, inCongP: $o).
% 6.40/1.39 thf(decl_99, type, in__Cong: $o).
% 6.40/1.39 thf(decl_100, type, exuE3u: $o).
% 6.40/1.39 thf(decl_101, type, exu__Cong: $o).
% 6.40/1.39 thf(decl_102, type, emptyset__Cong: $o).
% 6.40/1.39 thf(decl_103, type, setadjoin__Cong: $o).
% 6.40/1.39 thf(decl_104, type, powerset__Cong: $o).
% 6.40/1.39 thf(decl_105, type, setunion__Cong: $o).
% 6.40/1.39 thf(decl_106, type, omega__Cong: $o).
% 6.40/1.39 thf(decl_107, type, exuEu: $o).
% 6.40/1.39 thf(decl_108, type, descr__Cong: $o).
% 6.40/1.39 thf(decl_109, type, dsetconstr__Cong: $o).
% 6.40/1.39 thf(decl_110, type, subset: $i > $i > $o).
% 6.40/1.39 thf(decl_113, type, subsetI1: $o).
% 6.40/1.39 thf(decl_114, type, eqimpsubset2: $o).
% 6.40/1.39 thf(decl_115, type, eqimpsubset1: $o).
% 6.40/1.39 thf(decl_116, type, subsetI2: $o).
% 6.40/1.39 thf(decl_117, type, emptysetsubset: $o).
% 6.40/1.39 thf(decl_118, type, subsetE: $o).
% 6.40/1.39 thf(decl_119, type, subsetE2: $o).
% 6.40/1.39 thf(decl_120, type, notsubsetI: $o).
% 6.40/1.39 thf(decl_121, type, notequalI1: $o).
% 6.40/1.39 thf(decl_122, type, notequalI2: $o).
% 6.40/1.39 thf(decl_123, type, subsetRefl: $o).
% 6.40/1.39 thf(decl_124, type, subsetTrans: $o).
% 6.40/1.39 thf(decl_125, type, setadjoinSub: $o).
% 6.40/1.39 thf(decl_126, type, setadjoinSub2: $o).
% 6.40/1.39 thf(decl_127, type, subset2powerset: $o).
% 6.40/1.39 thf(decl_128, type, setextsub: $o).
% 6.40/1.39 thf(decl_129, type, subsetemptysetimpeq: $o).
% 6.40/1.39 thf(decl_130, type, powersetI1: $o).
% 6.40/1.39 thf(decl_131, type, powersetE1: $o).
% 6.40/1.39 thf(decl_132, type, inPowerset: $o).
% 6.40/1.39 thf(decl_133, type, powersetsubset: $o).
% 6.40/1.39 thf(decl_134, type, sepInPowerset: $o).
% 6.40/1.39 thf(decl_135, type, sepSubset: $o).
% 6.40/1.39 thf(decl_136, type, binunion: $i > $i > $i).
% 6.40/1.39 thf(decl_137, type, binunionIL: $o).
% 6.40/1.39 thf(decl_138, type, upairset2IR: $o).
% 6.40/1.39 thf(decl_139, type, binunionIR: $o).
% 6.40/1.39 thf(decl_140, type, binunionEcases: $o).
% 6.40/1.39 thf(decl_141, type, binunionE: $o).
% 6.40/1.39 thf(decl_142, type, binunionLsub: $o).
% 6.40/1.39 thf(decl_143, type, binunionRsub: $o).
% 6.40/1.39 thf(decl_144, type, binintersect: $i > $i > $i).
% 6.40/1.39 thf(decl_145, type, binintersectI: $o).
% 6.40/1.39 thf(decl_146, type, binintersectSubset5: $o).
% 6.40/1.39 thf(decl_147, type, binintersectEL: $o).
% 6.40/1.39 thf(decl_148, type, binintersectLsub: $o).
% 6.40/1.39 thf(decl_149, type, binintersectSubset2: $o).
% 6.40/1.39 thf(decl_150, type, binintersectSubset3: $o).
% 6.40/1.39 thf(decl_151, type, binintersectER: $o).
% 6.40/1.39 thf(decl_152, type, disjointsetsI1: $o).
% 6.40/1.39 thf(decl_153, type, binintersectRsub: $o).
% 6.40/1.39 thf(decl_154, type, binintersectSubset4: $o).
% 6.40/1.39 thf(decl_155, type, binintersectSubset1: $o).
% 6.40/1.39 thf(decl_156, type, bs114d: $o).
% 6.40/1.39 thf(decl_158, type, setminus: $i > $i > $i).
% 6.40/1.39 thf(decl_159, type, setminusI: $o).
% 6.40/1.39 thf(decl_160, type, setminusEL: $o).
% 6.40/1.39 thf(decl_161, type, setminusER: $o).
% 6.40/1.39 thf(decl_162, type, setminusSubset2: $o).
% 6.40/1.39 thf(decl_163, type, setminusERneg: $o).
% 6.40/1.39 thf(decl_164, type, setminusELneg: $o).
% 6.40/1.39 thf(decl_165, type, setminusILneg: $o).
% 6.40/1.39 thf(decl_166, type, setminusIRneg: $o).
% 6.40/1.39 thf(decl_167, type, setminusLsub: $o).
% 6.40/1.39 thf(decl_168, type, setminusSubset1: $o).
% 6.40/1.39 thf(decl_169, type, symdiff: $i > $i > $i).
% 6.40/1.39 thf(decl_170, type, symdiffE: $o).
% 6.40/1.39 thf(decl_171, type, symdiffI1: $o).
% 6.40/1.39 thf(decl_172, type, symdiffI2: $o).
% 6.40/1.39 thf(decl_173, type, symdiffIneg1: $o).
% 6.40/1.39 thf(decl_174, type, symdiffIneg2: $o).
% 6.40/1.39 thf(decl_175, type, iskpair: $i > $o).
% 6.40/1.39 thf(decl_176, type, secondinupair: $o).
% 6.40/1.39 thf(decl_177, type, setukpairIL: $o).
% 6.40/1.39 thf(decl_178, type, setukpairIR: $o).
% 6.40/1.39 thf(decl_179, type, kpairiskpair: $o).
% 6.40/1.39 thf(decl_180, type, kpair: $i > $i > $i).
% 6.40/1.39 thf(decl_181, type, kpairp: $o).
% 6.40/1.39 thf(decl_182, type, cartprod: $i > $i > $i).
% 6.40/1.39 thf(decl_183, type, singletonsubset: $o).
% 6.40/1.39 thf(decl_184, type, singletoninpowerset: $o).
% 6.40/1.39 thf(decl_185, type, singletoninpowunion: $o).
% 6.40/1.39 thf(decl_186, type, upairset2E: $o).
% 6.40/1.39 thf(decl_187, type, upairsubunion: $o).
% 6.40/1.39 thf(decl_188, type, upairinpowunion: $o).
% 6.40/1.39 thf(decl_189, type, ubforcartprodlem1: $o).
% 6.40/1.39 thf(decl_190, type, ubforcartprodlem2: $o).
% 6.40/1.39 thf(decl_191, type, ubforcartprodlem3: $o).
% 6.40/1.39 thf(decl_192, type, cartprodpairin: $o).
% 6.40/1.39 thf(decl_193, type, cartprodmempair1: $o).
% 6.40/1.39 thf(decl_194, type, cartprodmempair: $o).
% 6.40/1.39 thf(decl_195, type, setunionE2: $o).
% 6.40/1.39 thf(decl_196, type, setunionsingleton1: $o).
% 6.40/1.39 thf(decl_197, type, setunionsingleton2: $o).
% 6.40/1.39 thf(decl_198, type, setunionsingleton: $o).
% 6.40/1.39 thf(decl_199, type, singleton: $i > $o).
% 6.40/1.39 thf(decl_200, type, singletonprop: $o).
% 6.40/1.39 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 6.40/1.39 thf(decl_202, type, ex1E1: $o).
% 6.40/1.39 thf(decl_203, type, ex1I: $o).
% 6.40/1.39 thf(decl_204, type, ex1I2: $o).
% 6.40/1.39 thf(decl_205, type, singletonsuniq: $o).
% 6.40/1.39 thf(decl_210, type, setukpairinjL1: $o).
% 6.40/1.39 thf(decl_211, type, kfstsingleton: $o).
% 6.40/1.39 thf(decl_212, type, theprop: $o).
% 6.40/1.39 thf(decl_213, type, kfst: $i > $i).
% 6.40/1.39 thf(decl_214, type, kfstpairEq: $o).
% 6.40/1.39 thf(decl_215, type, cartprodfstin: $o).
% 6.40/1.39 thf(decl_216, type, setukpairinjL2: $o).
% 6.40/1.39 thf(decl_217, type, setukpairinjL: $o).
% 6.40/1.39 thf(decl_218, type, setukpairinjR11: $o).
% 6.40/1.39 thf(decl_219, type, setukpairinjR12: $o).
% 6.40/1.39 thf(decl_220, type, setukpairinjR1: $o).
% 6.40/1.39 thf(decl_221, type, upairequniteq: $o).
% 6.40/1.39 thf(decl_222, type, setukpairinjR2: $o).
% 6.40/1.39 thf(decl_223, type, setukpairinjR: $o).
% 6.40/1.39 thf(decl_224, type, ksndsingleton: $o).
% 6.40/1.39 thf(decl_225, type, ksnd: $i > $i).
% 6.40/1.39 thf(decl_226, type, ksndpairEq: $o).
% 6.40/1.39 thf(decl_227, type, kpairsurjEq: $o).
% 6.40/1.39 thf(decl_228, type, cartprodsndin: $o).
% 6.40/1.39 thf(decl_229, type, cartprodpairmemEL: $o).
% 6.40/1.39 thf(decl_230, type, cartprodpairmemER: $o).
% 6.40/1.39 thf(decl_231, type, cartprodmempaircEq: $o).
% 6.40/1.39 thf(decl_232, type, cartprodfstpairEq: $o).
% 6.40/1.39 thf(decl_233, type, cartprodsndpairEq: $o).
% 6.40/1.39 thf(decl_234, type, cartprodpairsurjEq: $o).
% 6.40/1.39 thf(decl_235, type, breln: $i > $i > $i > $o).
% 6.40/1.39 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 6.40/1.39 thf(decl_237, type, dpsetconstrI: $o).
% 6.40/1.39 thf(decl_238, type, dpsetconstrSub: $o).
% 6.40/1.39 thf(decl_239, type, setOfPairsIsBReln: $o).
% 6.40/1.39 thf(decl_240, type, dpsetconstrERa: $o).
% 6.40/1.39 thf(decl_241, type, dpsetconstrEL1: $o).
% 6.40/1.39 thf(decl_242, type, dpsetconstrEL2: $o).
% 6.40/1.39 thf(decl_243, type, dpsetconstrER: $o).
% 6.40/1.39 thf(decl_244, type, func: $i > $i > $i > $o).
% 6.40/1.39 thf(decl_245, type, funcSet: $i > $i > $i).
% 6.40/1.39 thf(decl_246, type, funcImageSingleton: $o).
% 6.40/1.39 thf(decl_247, type, apProp: $o).
% 6.40/1.39 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 6.40/1.39 thf(decl_249, type, app: $o).
% 6.40/1.39 thf(decl_250, type, infuncsetfunc: $o).
% 6.40/1.39 thf(decl_251, type, ap2p: $o).
% 6.40/1.39 thf(decl_252, type, funcinfuncset: $o).
% 6.40/1.39 thf(decl_253, type, lamProp: $o).
% 6.40/1.39 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 6.40/1.39 thf(decl_255, type, lamp: $o).
% 6.40/1.39 thf(decl_256, type, lam2p: $o).
% 6.40/1.39 thf(decl_257, type, brelnall1: $o).
% 6.40/1.39 thf(decl_258, type, brelnall2: $o).
% 6.40/1.39 thf(decl_259, type, ex1E2: $o).
% 6.40/1.39 thf(decl_260, type, funcGraphProp1: $o).
% 6.40/1.39 thf(decl_261, type, funcGraphProp3: $o).
% 6.40/1.39 thf(decl_262, type, funcGraphProp2: $o).
% 6.40/1.39 thf(decl_263, type, funcextLem: $o).
% 6.40/1.39 thf(decl_264, type, funcGraphProp4: $o).
% 6.40/1.39 thf(decl_265, type, subbreln: $o).
% 6.40/1.39 thf(decl_266, type, eqbreln: $o).
% 6.40/1.39 thf(decl_267, type, funcext: $o).
% 6.40/1.39 thf(decl_268, type, funcext2: $o).
% 6.40/1.39 thf(decl_269, type, ap2apEq1: $o).
% 6.40/1.39 thf(decl_270, type, ap2apEq2: $o).
% 6.40/1.39 thf(decl_271, type, beta1: $o).
% 6.40/1.39 thf(decl_272, type, eta1: $o).
% 6.40/1.39 thf(decl_273, type, lam2lamEq: $o).
% 6.40/1.39 thf(decl_274, type, beta2: $o).
% 6.40/1.39 thf(decl_275, type, eta2: $o).
% 6.40/1.39 thf(decl_276, type, iffalseProp1: $o).
% 6.40/1.39 thf(decl_277, type, iffalseProp2: $o).
% 6.40/1.39 thf(decl_278, type, iftrueProp1: $o).
% 6.40/1.39 thf(decl_279, type, iftrueProp2: $o).
% 6.40/1.39 thf(decl_280, type, ifSingleton: $o).
% 6.40/1.39 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 6.40/1.39 thf(decl_282, type, ifp: $o).
% 6.40/1.39 thf(decl_283, type, theeq: $o).
% 6.40/1.39 thf(decl_284, type, iftrue: $o).
% 6.40/1.39 thf(decl_285, type, iffalse: $o).
% 6.40/1.39 thf(decl_286, type, iftrueorfalse: $o).
% 6.40/1.39 thf(decl_287, type, binintersectT_lem: $o).
% 6.40/1.39 thf(decl_288, type, binunionT_lem: $o).
% 6.40/1.39 thf(decl_289, type, powersetT_lem: $o).
% 6.40/1.39 thf(decl_290, type, setminusT_lem: $o).
% 6.40/1.39 thf(decl_291, type, complementT_lem: $o).
% 6.40/1.39 thf(decl_292, type, setextT: $o).
% 6.40/1.39 thf(decl_293, type, subsetTI: $o).
% 6.40/1.39 thf(decl_294, type, epred1_0: $o).
% 6.40/1.39 thf(decl_295, type, esk1_2: $i > $i > $i).
% 6.40/1.39 thf(decl_296, type, esk2_2: $i > $i > $i).
% 6.40/1.39 thf(decl_297, type, esk3_2: $i > $i > $i).
% 6.40/1.39 thf(decl_298, type, esk4_1: $i > $i).
% 6.40/1.39 thf(decl_299, type, esk5_2: ($i > $i > $o) > $i > $i).
% 6.40/1.39 thf(decl_300, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 6.40/1.39 thf(decl_301, type, esk7_2: ($i > $i > $o) > $i > $i).
% 6.40/1.39 thf(decl_302, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 6.40/1.39 thf(decl_303, type, esk9_1: $i > $i).
% 6.40/1.39 thf(decl_304, type, esk10_2: ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_305, type, esk11_2: ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_306, type, esk12_1: ($i > $o) > $i).
% 6.40/1.39 thf(decl_307, type, esk13_2: ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_308, type, esk14_1: ($i > $o) > $i).
% 6.40/1.39 thf(decl_309, type, esk15_2: $i > $i > $i).
% 6.40/1.39 thf(decl_310, type, esk16_2: $i > $i > $i).
% 6.40/1.39 thf(decl_311, type, esk17_1: $i > $i).
% 6.40/1.39 thf(decl_312, type, esk18_1: $i > $i).
% 6.40/1.39 thf(decl_313, type, esk19_1: $i > $i).
% 6.40/1.39 thf(decl_314, type, esk20_2: $i > $i > $i).
% 6.40/1.39 thf(decl_315, type, esk21_3: $i > $i > $o > $i).
% 6.40/1.39 thf(decl_316, type, esk22_2: ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_317, type, esk23_1: ($i > $o) > $i).
% 6.40/1.39 thf(decl_318, type, esk24_1: $i > $i).
% 6.40/1.39 thf(decl_319, type, esk25_2: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_320, type, esk26_2: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_321, type, esk27_2: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_322, type, esk28_2: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_323, type, esk29_2: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_324, type, esk30_2: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_325, type, esk31_2: ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_326, type, esk32_1: ($i > $o) > $i).
% 6.40/1.39 thf(decl_327, type, esk33_1: ($i > $o) > $i).
% 6.40/1.39 thf(decl_328, type, esk34_1: ($i > $o) > $i).
% 6.40/1.39 thf(decl_329, type, esk35_1: ($i > $o) > $i).
% 6.40/1.39 thf(decl_330, type, esk36_2: ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_331, type, esk37_1: ($i > $o) > $i).
% 6.40/1.39 thf(decl_332, type, esk38_2: ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_333, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 6.40/1.39 thf(decl_334, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 6.40/1.39 thf(decl_335, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_336, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 6.40/1.39 thf(decl_337, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_338, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 6.40/1.39 thf(decl_339, type, esk45_2: ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_340, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 6.40/1.39 thf(decl_341, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 6.40/1.39 thf(decl_342, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_343, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_344, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 6.40/1.39 thf(decl_345, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 6.40/1.39 thf(decl_346, type, esk52_2: $i > $i > $i).
% 6.40/1.39 thf(decl_347, type, esk53_2: $i > $i > $i).
% 6.40/1.39 thf(decl_348, type, esk54_2: $i > $i > $i).
% 6.40/1.39 thf(decl_349, type, esk55_3: $i > $i > $i > $i).
% 6.40/1.39 thf(decl_350, type, esk56_3: $i > $i > $i > $i).
% 6.40/1.39 thf(decl_351, type, esk57_2: $i > $i > $i).
% 6.40/1.39 thf(decl_352, type, esk58_2: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_353, type, esk59_2: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_354, type, esk60_2: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_355, type, esk61_3: $i > ($i > $o) > $i > $i).
% 6.40/1.39 thf(decl_356, type, esk62_2: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_357, type, esk63_2: $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_358, type, esk64_3: $i > $i > ($i > $i) > $i).
% 6.40/1.39 thf(decl_359, type, esk65_3: $i > $i > ($i > $i) > $i).
% 6.40/1.39 thf(decl_360, type, esk66_3: $i > $i > ($i > $i) > $i).
% 6.40/1.39 thf(decl_361, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_362, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_363, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_364, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
% 6.40/1.39 thf(decl_365, type, esk71_4: $i > $i > $i > $i > $i).
% 6.40/1.39 thf(decl_366, type, esk72_4: $i > $i > $i > $i > $i).
% 6.40/1.39 thf(decl_367, type, esk73_4: $i > $i > $i > $i > $i).
% 6.40/1.39 thf(decl_368, type, esk74_4: $i > $i > $i > $i > $i).
% 6.40/1.39 thf(decl_369, type, esk75_4: $i > $i > $i > $i > $i).
% 6.40/1.39 thf(decl_370, type, esk76_4: $i > $i > $i > $i > $i).
% 6.40/1.39 thf(decl_371, type, esk77_4: $i > $i > $i > $i > $i).
% 6.40/1.39 thf(decl_372, type, esk78_4: $i > $i > $i > $i > $i).
% 6.40/1.39 thf(decl_373, type, esk79_4: $i > $i > $i > $i > $i).
% 6.40/1.39 thf(decl_374, type, esk80_3: $i > $i > ($i > $i) > $i).
% 6.40/1.39 thf(decl_375, type, esk81_3: $i > $i > ($i > $i) > $i).
% 6.40/1.39 thf(decl_376, type, esk82_3: $i > $i > ($i > $i) > $i).
% 6.40/1.39 thf(decl_377, type, esk83_3: $i > $i > $i > $i).
% 6.40/1.39 thf(decl_378, type, esk84_3: $i > $i > $i > $i).
% 6.40/1.39 thf(decl_379, type, esk85_3: $i > $i > $i > $i).
% 6.40/1.39 thf(decl_380, type, esk86_0: $i).
% 6.40/1.39 thf(decl_381, type, esk87_0: $i).
% 6.40/1.39 thf(decl_382, type, esk88_0: $i).
% 6.40/1.39 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', breln)).
% 6.40/1.39 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ex1E2)).
% 6.40/1.39 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ex1)).
% 6.40/1.39 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', exuI2)).
% 6.40/1.39 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', exu)).
% 6.40/1.39 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', exuI3)).
% 6.40/1.39 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', exuI1)).
% 6.40/1.39 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', exuE3u)).
% 6.40/1.39 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', exuEu)).
% 6.40/1.39 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', exu__Cong)).
% 6.40/1.39 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', descr__Cong)).
% 6.40/1.39 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ex1I2)).
% 6.40/1.39 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.AgVsZ9S4s0/E---3.1_1349318.p', ex1I)).
% 6.40/1.39 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ex1E1)).
% 6.40/1.39 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setOfPairsIsBReln)).
% 6.40/1.39 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', nonempty)).
% 6.40/1.39 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', exuE2)).
% 6.40/1.39 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', nonemptyI)).
% 6.40/1.39 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', exuE3e)).
% 6.40/1.39 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', exuE1)).
% 6.40/1.39 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', descrp)).
% 6.40/1.39 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', replAx)).
% 6.40/1.39 thf(powersetTI1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', powersetTI1)).
% 6.40/1.39 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', brelnall1)).
% 6.40/1.39 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', brelnall2)).
% 6.40/1.39 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', subbreln)).
% 6.40/1.39 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', emptyE1)).
% 6.40/1.39 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', eqbreln)).
% 6.40/1.39 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', beta1)).
% 6.40/1.39 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', eta1)).
% 6.40/1.39 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', lam2lamEq)).
% 6.40/1.39 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', beta2)).
% 6.40/1.39 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', eta2)).
% 6.40/1.39 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', iffalseProp1)).
% 6.40/1.39 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', iffalseProp2)).
% 6.40/1.39 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', iftrueProp1)).
% 6.40/1.39 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', iftrueProp2)).
% 6.40/1.39 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ifSingleton)).
% 6.40/1.39 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', dsetconstr__Cong)).
% 6.40/1.39 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', sepInPowerset)).
% 6.40/1.39 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', sepSubset)).
% 6.40/1.39 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', singletonprop)).
% 6.40/1.39 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', kfstsingleton)).
% 6.40/1.39 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ksndsingleton)).
% 6.40/1.39 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', dpsetconstrERa)).
% 6.40/1.39 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', dpsetconstrSub)).
% 6.40/1.39 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', dpsetconstrI)).
% 6.40/1.39 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', dpsetconstrEL1)).
% 6.40/1.39 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', apProp)).
% 6.40/1.39 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', funcImageSingleton)).
% 6.40/1.39 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', dpsetconstrER)).
% 6.40/1.39 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', dpsetconstrEL2)).
% 6.40/1.39 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', lamProp)).
% 6.40/1.39 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', lamp)).
% 6.40/1.39 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', lam2p)).
% 6.40/1.39 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', nonemptyImpWitness)).
% 6.40/1.39 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setoftrueEq)).
% 6.40/1.39 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', nonemptyI1)).
% 6.40/1.39 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', nonemptyE1)).
% 6.40/1.39 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setbeta)).
% 6.40/1.39 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', dsetconstrER)).
% 6.40/1.39 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', dsetconstrEL)).
% 6.40/1.39 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', dsetconstrI)).
% 6.40/1.39 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', funcGraphProp1)).
% 6.40/1.39 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', quantDeMorgan4)).
% 6.40/1.39 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', funcGraphProp3)).
% 6.40/1.39 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', quantDeMorgan3)).
% 6.40/1.39 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', funcGraphProp2)).
% 6.40/1.39 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', quantDeMorgan2)).
% 6.40/1.39 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', funcextLem)).
% 6.40/1.39 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', quantDeMorgan1)).
% 6.40/1.39 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', funcGraphProp4)).
% 6.40/1.39 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', vacuousDall)).
% 6.40/1.39 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', upairsetIR)).
% 6.40/1.39 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', funcext)).
% 6.40/1.39 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', prop2setI)).
% 6.40/1.39 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', funcext2)).
% 6.40/1.39 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ap2apEq1)).
% 6.40/1.39 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ap2apEq2)).
% 6.40/1.39 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ifp)).
% 6.40/1.39 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', in__Cong)).
% 6.40/1.39 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', theeq)).
% 6.40/1.39 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', inCongP)).
% 6.40/1.39 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', iftrue)).
% 6.40/1.39 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', iffalse)).
% 6.40/1.39 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', iftrueorfalse)).
% 6.40/1.39 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binintersectT_lem)).
% 6.40/1.39 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', notdallE)).
% 6.40/1.39 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binunionT_lem)).
% 6.40/1.39 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', notdexE)).
% 6.40/1.39 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', powersetT_lem)).
% 6.40/1.39 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setminusT_lem)).
% 6.40/1.39 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', complementT_lem)).
% 6.40/1.39 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setextT)).
% 6.40/1.39 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', subsetTI)).
% 6.40/1.39 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', omega__Cong)).
% 6.40/1.39 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setunion__Cong)).
% 6.40/1.39 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', powerset__Cong)).
% 6.40/1.39 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setadjoin__Cong)).
% 6.40/1.39 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', emptyset__Cong)).
% 6.40/1.39 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', subsetE)).
% 6.40/1.39 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', emptysetsubset)).
% 6.40/1.39 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', subsetI2)).
% 6.40/1.39 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', eqimpsubset1)).
% 6.40/1.39 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', eqimpsubset2)).
% 6.40/1.39 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', subsetI1)).
% 6.40/1.39 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', subsetE2)).
% 6.40/1.39 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setadjoinSub2)).
% 6.40/1.39 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setadjoinSub)).
% 6.40/1.39 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', subsetTrans)).
% 6.40/1.39 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', subsetRefl)).
% 6.40/1.39 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', notequalI2)).
% 6.40/1.39 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', notequalI1)).
% 6.40/1.39 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', notsubsetI)).
% 6.40/1.39 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', subset2powerset)).
% 6.40/1.39 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', powersetsubset)).
% 6.40/1.39 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', inPowerset)).
% 6.40/1.39 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', powersetE1)).
% 6.40/1.39 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', powersetI1)).
% 6.40/1.39 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', subsetemptysetimpeq)).
% 6.40/1.39 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setextsub)).
% 6.40/1.39 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binunionRsub)).
% 6.40/1.39 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binunionLsub)).
% 6.40/1.39 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binunionE)).
% 6.40/1.39 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binunionEcases)).
% 6.40/1.39 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binunionIR)).
% 6.40/1.39 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', upairset2IR)).
% 6.40/1.39 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binunionIL)).
% 6.40/1.39 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binintersectI)).
% 6.40/1.39 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', disjointsetsI1)).
% 6.40/1.39 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binintersectER)).
% 6.40/1.39 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binintersectSubset3)).
% 6.40/1.39 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binintersectSubset2)).
% 6.40/1.39 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binintersectLsub)).
% 6.40/1.39 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binintersectEL)).
% 6.40/1.39 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binintersectSubset5)).
% 6.40/1.39 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binintersectRsub)).
% 6.40/1.39 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setminusSubset2)).
% 6.40/1.39 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setminusER)).
% 6.40/1.39 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setminusEL)).
% 6.40/1.39 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setminusI)).
% 6.40/1.39 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', bs114d)).
% 6.40/1.39 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binintersectSubset1)).
% 6.40/1.39 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', binintersectSubset4)).
% 6.40/1.39 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setminusERneg)).
% 6.40/1.39 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', symdiffI1)).
% 6.40/1.39 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', symdiffE)).
% 6.40/1.39 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setminusSubset1)).
% 6.40/1.39 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setminusLsub)).
% 6.40/1.39 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setminusIRneg)).
% 6.40/1.39 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setminusILneg)).
% 6.40/1.39 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setminusELneg)).
% 6.40/1.39 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', symdiffI2)).
% 6.40/1.39 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', kpairp)).
% 6.40/1.39 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', kpairiskpair)).
% 6.40/1.39 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setukpairIR)).
% 6.40/1.39 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setukpairIL)).
% 6.40/1.39 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', secondinupair)).
% 6.40/1.39 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', symdiffIneg2)).
% 6.40/1.39 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', symdiffIneg1)).
% 6.40/1.39 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', singletonsubset)).
% 6.40/1.39 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ubforcartprodlem2)).
% 6.40/1.39 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ubforcartprodlem1)).
% 6.40/1.39 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', upairinpowunion)).
% 6.40/1.39 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', upairsubunion)).
% 6.40/1.39 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', upairset2E)).
% 6.40/1.39 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', singletoninpowunion)).
% 6.40/1.39 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', singletoninpowerset)).
% 6.40/1.39 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ubforcartprodlem3)).
% 6.40/1.39 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setunionsingleton)).
% 6.40/1.39 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setunionsingleton2)).
% 6.40/1.39 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setunionsingleton1)).
% 6.40/1.39 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setunionE2)).
% 6.40/1.39 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', cartprodmempair)).
% 6.40/1.39 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', cartprodmempair1)).
% 6.40/1.39 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', cartprodpairin)).
% 6.40/1.39 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', theprop)).
% 6.40/1.39 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setukpairinjL1)).
% 6.40/1.39 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', singletonsuniq)).
% 6.40/1.39 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', kfstpairEq)).
% 6.40/1.39 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', upairequniteq)).
% 6.40/1.39 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setukpairinjR1)).
% 6.40/1.39 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setukpairinjR12)).
% 6.40/1.39 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setukpairinjR11)).
% 6.40/1.39 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setukpairinjL)).
% 6.40/1.39 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setukpairinjL2)).
% 6.40/1.39 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', cartprodfstin)).
% 6.40/1.39 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setukpairinjR2)).
% 6.40/1.39 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', cartprodpairmemER)).
% 6.40/1.39 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', cartprodpairmemEL)).
% 6.40/1.39 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', cartprodsndin)).
% 6.40/1.39 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', kpairsurjEq)).
% 6.40/1.39 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ksndpairEq)).
% 6.40/1.39 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setukpairinjR)).
% 6.40/1.39 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', cartprodmempaircEq)).
% 6.40/1.39 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', cartprodpairsurjEq)).
% 6.40/1.39 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.AgVsZ9S4s0/E---3.1_1349318.p', cartprodsndpairEq)).
% 6.40/1.39 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.AgVsZ9S4s0/E---3.1_1349318.p', cartprodfstpairEq)).
% 6.40/1.39 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', ap2p)).
% 6.40/1.39 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', infuncsetfunc)).
% 6.40/1.39 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', app)).
% 6.40/1.39 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', funcinfuncset)).
% 6.40/1.39 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', upairsetIL)).
% 6.40/1.39 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', upairsetE)).
% 6.40/1.39 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', singletonsswitch)).
% 6.40/1.39 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', eqinunit)).
% 6.40/1.39 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', notinsingleton)).
% 6.40/1.39 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', uniqinunit)).
% 6.40/1.39 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', subPowSU)).
% 6.40/1.39 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setunionE)).
% 6.40/1.39 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setunionI)).
% 6.40/1.39 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', powersetE)).
% 6.40/1.39 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', emptyInPowerset)).
% 6.40/1.39 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', emptyinPowerset)).
% 6.40/1.39 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', powersetI)).
% 6.40/1.39 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setadjoinOr)).
% 6.40/1.39 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setadjoinE)).
% 6.40/1.39 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setadjoinIR)).
% 6.40/1.39 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', emptyinunitempty)).
% 6.40/1.39 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setadjoinIL)).
% 6.40/1.39 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', noeltsimpempty)).
% 6.40/1.39 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', emptyI)).
% 6.40/1.39 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setext)).
% 6.40/1.39 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', notinemptyset)).
% 6.40/1.39 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', emptysetimpfalse)).
% 6.40/1.39 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', emptysetE)).
% 6.40/1.39 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', prop2setE)).
% 6.40/1.39 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', wellorderingAx)).
% 6.40/1.39 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', foundationAx)).
% 6.40/1.39 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', omegaIndAx)).
% 6.40/1.39 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', omegaSAx)).
% 6.40/1.39 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', omega0Ax)).
% 6.40/1.39 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setunionAx)).
% 6.40/1.39 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', powersetAx)).
% 6.40/1.39 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setadjoinAx)).
% 6.40/1.39 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', emptysetAx)).
% 6.40/1.39 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.AgVsZ9S4s0/E---3.1_1349318.p', setextAx)).
% 6.40/1.39 thf(c_0_237, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 6.40/1.39 thf(c_0_238, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 6.40/1.39 thf(c_0_239, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 6.40/1.39 thf(c_0_240, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 6.40/1.39 thf(c_0_241, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 6.40/1.39 thf(c_0_242, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 6.40/1.39 thf(c_0_243, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 6.40/1.39 thf(c_0_244, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 6.40/1.39 thf(c_0_245, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 6.40/1.39 thf(c_0_246, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 6.40/1.39 thf(c_0_247, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 6.40/1.39 thf(c_0_248, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 6.40/1.39 thf(c_0_249, plain, ((ex1I)<=>![X4:$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])).
% 6.40/1.39 thf(c_0_250, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 6.40/1.39 thf(c_0_251, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 6.40/1.39 thf(c_0_252, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 6.40/1.39 thf(c_0_253, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 6.40/1.39 thf(c_0_254, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 6.40/1.39 thf(c_0_255, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 6.40/1.39 thf(c_0_256, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 6.40/1.39 thf(c_0_257, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 6.40/1.39 thf(c_0_258, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 6.40/1.39 thf(c_0_259, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[powersetTI1])).
% 6.40/1.39 thf(c_0_260, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_237])).
% 6.40/1.39 thf(c_0_261, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_237])).
% 6.40/1.39 thf(c_0_262, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_239])).
% 6.40/1.39 thf(c_0_263, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_237])).
% 6.40/1.39 thf(c_0_264, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 6.40/1.39 thf(c_0_265, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_237])).
% 6.40/1.39 thf(c_0_266, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
% 6.40/1.39 thf(c_0_267, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
% 6.40/1.39 thf(c_0_268, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
% 6.40/1.39 thf(c_0_269, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
% 6.40/1.39 thf(c_0_270, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
% 6.40/1.39 thf(c_0_271, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 6.40/1.39 thf(c_0_272, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 6.40/1.39 thf(c_0_273, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 6.40/1.39 thf(c_0_274, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 6.40/1.39 thf(c_0_275, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 6.40/1.39 thf(c_0_276, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X784:$i]:(((((X1 @ X784)))&(![X785:$i]:(((((X1 @ X785)))=>(((X784)=(X785)))))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_241])).
% 6.40/1.39 thf(c_0_277, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X782:$i]:(((((X1 @ X782)))&(![X783:$i]:(((((X1 @ X783)))=>(((X782)=(X783)))))))))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_241])).
% 6.40/1.39 thf(c_0_278, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X780:$i]:(((((X1 @ X780)))&(![X781:$i]:(((((X1 @ X781)))=>(((X780)=(X781)))))))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_241])).
% 6.40/1.39 thf(c_0_279, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X786:$i]:(((((X1 @ X786)))&(![X787:$i]:(((((X1 @ X787)))=>(((X786)=(X787))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_241])).
% 6.40/1.39 thf(c_0_280, plain, ((exuEu)=(![X1:$i > $o]:((((?[X792:$i]:(((((X1 @ X792)))&(![X793:$i]:(((((X1 @ X793)))=>(((X792)=(X793))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_241])).
% 6.40/1.39 thf(c_0_281, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X788:$i]:(((((X1 @ X788)))&(![X789:$i]:(((((X1 @ X789)))=>(((X788)=(X789))))))))))<=>((?[X790:$i]:(((((X17 @ X790)))&(![X791:$i]:(((((X17 @ X791)))=>(((X790)=(X791)))))))))))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_241])).
% 6.40/1.39 thf(c_0_282, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X794:$i]:(((((X1 @ X794)))&(![X795:$i]:(((((X1 @ X795)))=>(((X794)=(X795))))))))))=>((((?[X796:$i]:(((((X17 @ X796)))&(![X797:$i]:(((((X17 @ X797)))=>(((X796)=(X797))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_247, c_0_241])).
% 6.40/1.39 thf(c_0_283, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 6.40/1.39 thf(c_0_284, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 6.40/1.39 thf(c_0_285, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 6.40/1.39 thf(c_0_286, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 6.40/1.39 thf(c_0_287, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 6.40/1.39 thf(c_0_288, plain, ((ex1I2)=(![X4:$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)))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_248, c_0_239])).
% 6.40/1.39 thf(c_0_289, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))))), inference(apply_def,[status(thm)],[c_0_249, c_0_239])).
% 6.40/1.39 thf(c_0_290, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_250, c_0_239])).
% 6.40/1.39 thf(c_0_291, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 6.40/1.39 thf(c_0_292, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 6.40/1.39 thf(c_0_293, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_251, c_0_237])).
% 6.40/1.39 thf(c_0_294, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 6.40/1.39 thf(c_0_295, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 6.40/1.39 thf(c_0_296, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 6.40/1.39 thf(c_0_297, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 6.40/1.39 thf(c_0_298, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 6.40/1.39 thf(c_0_299, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 6.40/1.39 thf(c_0_300, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 6.40/1.39 thf(c_0_301, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 6.40/1.39 thf(c_0_302, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 6.40/1.39 thf(c_0_303, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 6.40/1.39 thf(c_0_304, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_252])).
% 6.40/1.39 thf(c_0_305, plain, ((exuE2)=(![X1:$i > $o]:((((?[X778:$i]:(((((X1 @ X778)))&(![X779:$i]:(((((X1 @ X779)))=>(((X778)=(X779))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_253, c_0_241])).
% 6.40/1.39 thf(c_0_306, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 6.40/1.39 thf(c_0_307, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_252])).
% 6.40/1.39 thf(c_0_308, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_254, c_0_252])).
% 6.40/1.39 thf(c_0_309, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_252])).
% 6.40/1.39 thf(c_0_310, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 6.40/1.39 thf(c_0_311, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X776:$i]:(((((X1 @ X776)))&(![X777:$i]:(((((X1 @ X777)))=>(((X776)=(X777))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_255, c_0_241])).
% 6.40/1.39 thf(c_0_312, plain, ((exuE1)=(![X1:$i > $o]:((((?[X774:$i]:(((((X1 @ X774)))&(![X775:$i]:(((((X1 @ X775)))=>(((X774)=(X775))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_256, c_0_241])).
% 6.40/1.39 thf(c_0_313, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 6.40/1.39 thf(c_0_314, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 6.40/1.39 thf(c_0_315, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 6.40/1.39 thf(c_0_316, plain, ((descrp)=(![X1:$i > $o]:((((?[X772:$i]:(((((X1 @ X772)))&(![X773:$i]:(((((X1 @ X773)))=>(((X772)=(X773))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_257, c_0_241])).
% 6.40/1.39 thf(c_0_317, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X770:$i]:(((((X6 @ X2 @ X770)))&(![X771:$i]:(((((X6 @ X2 @ X771)))=>(((X770)=(X771)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_258, c_0_241])).
% 6.40/1.39 thf(c_0_318, plain, ((epred1_0)<=>![X827:$i]:(?[X828:$i]:((((![X829:$i]:(((in @ X829 @ X828)=>![X830:$i]:(((in @ X830 @ X829)=>(in @ X830 @ X827)))))&![X831:$i, X832:$i]:((((in @ X831 @ X827)&(in @ X832 @ X827))=>(![X833:$i]:(((in @ X833 @ X828)=>((in @ X831 @ X833)<=>(in @ X832 @ X833))))=>((X831)=(X832))))))&![X834:$i, X835:$i]:((((in @ X834 @ X828)&(in @ X835 @ X828))=>(![X836:$i]:(((in @ X836 @ X834)=>(in @ X836 @ X835)))|![X837:$i]:(((in @ X837 @ X835)=>(in @ X837 @ X834)))))))&![X838:$i]:(((![X839:$i]:(((in @ X839 @ X838)=>(in @ X839 @ X827)))&?[X840:$i]:((in @ X840 @ X838)))=>?[X841:$i, X842:$i]:(((((in @ X841 @ X828)&(in @ X842 @ X838))&~(?[X843:$i]:(((in @ X843 @ X841)&(in @ X843 @ X838)))))&![X844:$i]:(((in @ X844 @ X828)=>(![X845:$i]:(((in @ X845 @ X844)=>(in @ X845 @ X841)))|(in @ X842 @ X844)))))))))))), introduced(definition)).
% 6.40/1.39 thf(c_0_319, negated_conjecture, ~((![X798:$i, X799:$i]:((![X800:$i]:(((in @ X800 @ X798)<=>(in @ X800 @ X799)))=>((X798)=(X799))))=>(![X801:$i]:(~(in @ X801 @ emptyset))=>(![X802:$i, X803:$i, X804:$i]:(((in @ X804 @ (setadjoin @ X802 @ X803))<=>(((X804)=(X802))|(in @ X804 @ X803))))=>(![X805:$i, X806:$i]:(((in @ X806 @ (powerset @ X805))<=>![X807:$i]:(((in @ X807 @ X806)=>(in @ X807 @ X805)))))=>(![X808:$i, X809:$i]:(((in @ X809 @ (setunion @ X808))<=>?[X810:$i]:(((in @ X809 @ X810)&(in @ X810 @ X808)))))=>((in @ emptyset @ omega)=>(![X811:$i]:(((in @ X811 @ omega)=>(in @ (setadjoin @ X811 @ X811) @ omega)))=>(![X812:$i]:((((in @ emptyset @ X812)&![X813:$i]:((((in @ X813 @ omega)&(in @ X813 @ X812))=>(in @ (setadjoin @ X813 @ X813) @ X812))))=>![X814:$i]:(((in @ X814 @ omega)=>(in @ X814 @ X812)))))=>(![X815:$i > $i > $o, X816:$i]:((![X817:$i]:(((in @ X817 @ X816)=>?[X818:$i]:(((X815 @ X817 @ X818)&![X819:$i]:(((X815 @ X817 @ X819)=>((X818)=(X819))))))))=>?[X820:$i]:(![X821:$i]:(((in @ X821 @ X820)<=>?[X822:$i]:(((in @ X822 @ X816)&(X815 @ X822 @ X821))))))))=>(![X823:$i]:((?[X824:$i]:((in @ X824 @ X823))=>?[X825:$i]:(((in @ X825 @ X823)&~(?[X826:$i]:(((in @ X826 @ X825)&(in @ X826 @ X823))))))))=>((epred1_0)=>(![X846:$i > $o]:((?[X847:$i]:(((X846 @ X847)&![X848:$i]:(((X846 @ X848)=>((X847)=(X848))))))=>(X846 @ (descr @ (^[Z0:$i]:(X846 @ Z0))))))=>(![X849:$i, X850:$i > $o, X851:$i]:(((in @ X851 @ X849)=>((X850 @ X851)=>(in @ X851 @ (dsetconstr @ X849 @ X850)))))=>(![X852:$i, X853:$i > $o, X854:$i]:(((in @ X854 @ (dsetconstr @ X852 @ X853))=>(in @ X854 @ X852)))=>(![X855:$i, X856:$i > $o, X857:$i]:(((in @ X857 @ (dsetconstr @ X855 @ X856))=>(X856 @ X857)))=>(![X858:$i > $o]:((?[X859:$i]:(((X858 @ X859)&![X860:$i]:(((X858 @ X860)=>((X859)=(X860))))))=>?[X861:$i]:(((X858 @ X861)&![X862:$i]:(((X858 @ X862)=>((X861)=(X862))))))))=>(![X863:$o, X864:$i]:(((in @ X864 @ (prop2set @ ((X863))))=>(X863)))=>(![X865:$i]:(((in @ X865 @ emptyset)=>![X866:$o]:((X866))))=>(![X867:$i]:(((in @ X867 @ emptyset)=>~($true)))=>(![X868:$i]:(~(in @ X868 @ emptyset))=>(![X869:$i > $o]:((?[X870:$i]:(((X869 @ X870)&![X871:$i]:(((X869 @ X871)=>((X870)=(X871))))))=>?[X872:$i]:((X869 @ X872))))=>(![X873:$i, X874:$i]:((![X875:$i]:(((in @ X875 @ X873)=>(in @ X875 @ X874)))=>(![X876:$i]:(((in @ X876 @ X874)=>(in @ X876 @ X873)))=>((X873)=(X874)))))=>(![X877:$i]:((![X878:$i]:(~(in @ X878 @ X877))=>((X877)=(emptyset))))=>(![X879:$i]:((![X880:$i]:(~(in @ X880 @ X879))=>((X879)=(emptyset))))=>(![X881:$i, X882:$i > $o, X883:$i]:(((in @ X883 @ X881)=>((in @ X883 @ (dsetconstr @ X881 @ X882))<=>(X882 @ X883))))=>(![X884:$i]:((((X884)!=(emptyset))=>?[X885:$i]:((in @ X885 @ X884))))=>(![X886:$i, X887:$i > $o, X888:$i]:(((in @ X888 @ X886)=>((X887 @ X888)=>((dsetconstr @ X886 @ X887)!=(emptyset)))))=>(![X889:$i]:((?[X890:$i]:((in @ X890 @ X889))=>((X889)!=(emptyset))))=>(![X891:$i, X892:$i]:((in @ X891 @ (setadjoin @ X891 @ X892)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X893:$i, X894:$i, X895:$i]:(((in @ X895 @ X894)=>(in @ X895 @ (setadjoin @ X893 @ X894))))=>(![X896:$i, X897:$i, X898:$i]:(((in @ X898 @ (setadjoin @ X896 @ X897))=>![X899:$o]:(((((X898)=(X896))=>(X899))=>(((in @ X898 @ X897)=>(X899))=>(X899))))))=>(![X900:$i, X901:$i, X902:$i]:(((in @ X902 @ (setadjoin @ X900 @ X901))=>(((X902)=(X900))|(in @ X902 @ X901))))=>(![X903:$i]:(((dsetconstr @ X903 @ (^[Z0:$i]:($true)))=(X903)))=>(![X904:$i, X905:$i]:((![X906:$i]:(((in @ X906 @ X905)=>(in @ X906 @ X904)))=>(in @ X905 @ (powerset @ X904))))=>(![X907:$i]:((in @ emptyset @ (powerset @ X907)))=>(![X908:$i]:((in @ emptyset @ (powerset @ X908)))=>(![X909:$i, X910:$i, X911:$i]:(((in @ X910 @ (powerset @ X909))=>((in @ X911 @ X910)=>(in @ X911 @ X909))))=>(![X912:$i, X913:$i, X914:$i]:(((in @ X913 @ X914)=>((in @ X914 @ X912)=>(in @ X913 @ (setunion @ X912)))))=>(![X915:$i, X916:$i]:(((in @ X916 @ (setunion @ X915))=>![X917:$o]:((![X918:$i]:(((in @ X916 @ X918)=>((in @ X918 @ X915)=>(X917))))=>(X917)))))=>(![X919:$i, X920:$i]:(((in @ X920 @ X919)=>(in @ X920 @ (powerset @ (setunion @ X919)))))=>(![X921:$i > $o]:((?[X922:$i]:(((X921 @ X922)&![X923:$i]:(((X921 @ X923)=>((X922)=(X923))))))=>?[X924:$i]:(![X925:$i]:(((X921 @ X925)<=>((X925)=(X924)))))))=>(![X926:$i]:((((X926)!=(emptyset))=>?[X927:$i]:(((in @ X927 @ X926)&$true))))=>(![X928:$i, X929:$i]:(((in @ X928 @ (setadjoin @ X929 @ emptyset))=>((X928)=(X929))))=>(![X930:$i, X931:$i]:((((X930)!=(X931))=>~(in @ X931 @ (setadjoin @ X930 @ emptyset))))=>(![X932:$i, X933:$i]:((((X932)=(X933))=>(in @ X932 @ (setadjoin @ X933 @ emptyset))))=>(![X934:$i, X935:$i]:(((in @ X934 @ (setadjoin @ X935 @ emptyset))=>(in @ X935 @ (setadjoin @ X934 @ emptyset))))=>(![X936:$i, X937:$i, X938:$i]:(((in @ X938 @ (setadjoin @ X936 @ (setadjoin @ X937 @ emptyset)))=>(((X938)=(X936))|((X938)=(X937)))))=>(![X939:$i, X940:$i]:((in @ X939 @ (setadjoin @ X939 @ (setadjoin @ X940 @ emptyset))))=>(![X941:$i, X942:$i]:((in @ X942 @ (setadjoin @ X941 @ (setadjoin @ X942 @ emptyset))))=>(![X943:$i, X944:$i > $o]:((?[X945:$i]:(((in @ X945 @ X943)&(X944 @ X945)))=>(((dsetconstr @ X943 @ X944)=(emptyset))=>~($true))))=>(![X946:$i > $o, X947:$i]:(((in @ X947 @ emptyset)=>(X946 @ X947)))=>(![X948:$i, X949:$i > $o]:((~(![X950:$i]:(((in @ X950 @ X948)=>(X949 @ X950))))=>?[X951:$i]:(((in @ X951 @ X948)&~((X949 @ X951))))))=>(![X952:$i, X953:$i > $o]:((![X954:$i]:(((in @ X954 @ X952)=>~((X953 @ X954))))=>~(?[X955:$i]:(((in @ X955 @ X952)&(X953 @ X955))))))=>(![X956:$i, X957:$i > $o]:((~(?[X958:$i]:(((in @ X958 @ X956)&(X957 @ X958))))=>![X959:$i]:(((in @ X959 @ X956)=>~((X957 @ X959))))))=>(![X960:$i, X961:$i > $o]:((?[X962:$i]:(((in @ X962 @ X960)&~((X961 @ X962))))=>~(![X963:$i]:(((in @ X963 @ X960)=>(X961 @ X963))))))=>(![X964:$o]:(((X964)=>(in @ emptyset @ (prop2set @ ((X964))))))=>((prop2set2propI)=>(![X965:$i, X966:$i > $o]:((~(?[X967:$i]:(((in @ X967 @ X965)&(X966 @ X967))))=>![X968:$i]:(((in @ X968 @ X965)=>~((X966 @ X968))))))=>(![X969:$i, X970:$i > $o]:((~(![X971:$i]:(((in @ X971 @ X969)=>(X970 @ X971))))=>?[X972:$i]:(((in @ X972 @ X969)&~((X970 @ X972))))))=>(![X973:$i > $o]:((?[X974:$i]:(((X973 @ X974)&![X975:$i]:(((X973 @ X975)=>((X974)=(X975))))))=>?[X976:$i]:(((X973 @ X976)&![X977:$i]:(((X973 @ X977)=>((X976)=(X977))))))))=>(![X978:$i > $o]:((?[X979:$i]:((X978 @ X979))=>(![X980:$i, X981:$i]:(((X978 @ X980)=>((X978 @ X981)=>((X980)=(X981)))))=>?[X982:$i]:(((X978 @ X982)&![X983:$i]:(((X978 @ X983)=>((X982)=(X983)))))))))=>(![X984:$i > $o]:((?[X985:$i]:(![X986:$i]:(((X984 @ X986)<=>((X986)=(X985)))))=>?[X987:$i]:(((X984 @ X987)&![X988:$i]:(((X984 @ X988)=>((X987)=(X988))))))))=>(![X989:$i, X990:$i]:((((X989)=(X990))=>![X991:$i, X992:$i]:((((X991)=(X992))=>((in @ X991 @ X989)=>(in @ X992 @ X990))))))=>(![X993:$i, X994:$i]:((((X993)=(X994))=>![X995:$i, X996:$i]:((((X995)=(X996))=>((in @ X995 @ X993)<=>(in @ X996 @ X994))))))=>(![X997:$i > $o]:((?[X998:$i]:(((X997 @ X998)&![X999:$i]:(((X997 @ X999)=>((X998)=(X999))))))=>![X1000:$i, X1001:$i]:(((X997 @ X1000)=>((X997 @ X1001)=>((X1000)=(X1001)))))))=>(![X1002:$i > $o, X1003:$i > $o]:((![X1004:$i, X1005:$i]:((((X1004)=(X1005))=>((X1002 @ X1004)<=>(X1003 @ X1005))))=>(?[X1006:$i]:(((X1002 @ X1006)&![X1007:$i]:(((X1002 @ X1007)=>((X1006)=(X1007))))))<=>?[X1008:$i]:(((X1003 @ X1008)&![X1009:$i]:(((X1003 @ X1009)=>((X1008)=(X1009)))))))))=>(((emptyset)=(emptyset))=>(![X1010:$i, X1011:$i]:((((X1010)=(X1011))=>![X1012:$i, X1013:$i]:((((X1012)=(X1013))=>((setadjoin @ X1010 @ X1012)=(setadjoin @ X1011 @ X1013))))))=>(![X1014:$i, X1015:$i]:((((X1014)=(X1015))=>((powerset @ X1014)=(powerset @ X1015))))=>(![X1016:$i, X1017:$i]:((((X1016)=(X1017))=>((setunion @ X1016)=(setunion @ X1017))))=>(((omega)=(omega))=>(![X1018:$i > $o]:((?[X1019:$i]:(((X1018 @ X1019)&![X1020:$i]:(((X1018 @ X1020)=>((X1019)=(X1020))))))=>![X1021:$i, X1022:$i]:(((X1018 @ X1021)=>((X1018 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(powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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)],[c_0_259, c_0_260]), c_0_261]), c_0_262]), funcGraphProp1]), quantDeMorgan4]), funcGraphProp3]), quantDeMorgan3]), funcGraphProp2]), quantDeMorgan2]), funcextLem]), quantDeMorgan1]), funcGraphProp4]), vacuousDall]), c_0_263]), c_0_264]), c_0_265]), upairsetIR]), funcext]), prop2setI]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_266]), c_0_267]), c_0_268]), c_0_269]), c_0_270]), c_0_271]), c_0_272]), c_0_273]), c_0_274]), c_0_275]), ifp]), in__Cong]), theeq]), inCongP]), iftrue]), c_0_276]), iffalse]), c_0_277]), iftrueorfalse]), c_0_278]), binintersectT_lem]), notdallE]), binunionT_lem]), notdexE]), powersetT_lem]), c_0_279]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), c_0_280]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_281]), c_0_282]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_283]), subsetE2]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subset2powerset]), c_0_284]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), c_0_285]), binunionRsub]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), binintersectI]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectRsub]), setminusSubset2]), setminusER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), setminusERneg]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), symdiffI2]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffIneg1]), singletonsubset]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), ubforcartprodlem3]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), c_0_286]), theprop]), c_0_287]), setukpairinjL1]), singletonsuniq]), c_0_288]), c_0_289]), c_0_290]), kfstpairEq]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), setukpairinjR2]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), c_0_291]), setukpairinjR]), cartprodmempaircEq]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodfstpairEq]), c_0_296]), ap2p]), infuncsetfunc]), app]), c_0_297]), c_0_298]), c_0_299]), c_0_300]), funcinfuncset]), c_0_301]), c_0_302]), c_0_303]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_304]), c_0_305]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_306]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_307]), c_0_308]), c_0_309]), c_0_310]), noeltsimpempty]), emptyI]), setext]), c_0_311]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), wellorderingAx]), foundationAx]), c_0_317]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_318])).
% 6.40/1.39 thf(c_0_320, negated_conjecture, ![X1543:$i, X1544:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1556:$i, X1557:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1565:$i, X1566:$i > $i > $o, X1567:$i, X1569:$i, X1572:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1579:$i, X1580:$i > $o, X1581:$i, X1583:$i, X1584:$i > $o, X1585:$i, X1586:$i, X1587:$i > $o, X1588:$i, X1589:$i, X1590:$i > $o, X1591:$i, X1592:$i > $o, X1593:$i, X1596:$i, X1597:$o, X1598:$i, X1599:$i, X1600:$o, X1601:$i, X1602:$i, X1603:$i > $o, X1604:$i, X1607:$i, X1608:$i, X1611:$i, X1613:$i, X1615:$i, X1616:$i > $o, X1617:$i, X1618:$i, X1620:$i, X1621:$i > $o, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$o, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$o, X1653:$i, X1654:$i, X1655:$i > $o, X1656:$i, X1659:$i, X1660:$i, X1661:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i > $o, X1680:$i, X1681:$i > $o, X1682:$i, X1683:$i, X1684:$i > $o, X1685:$i, X1687:$i, X1688:$i > $o, X1690:$i, X1691:$i, X1692:$i > $o, X1694:$i, X1695:$i, X1696:$i > $o, X1697:$i, X1699:$o, X1700:$i, X1701:$i > $o, X1703:$i, X1704:$i, X1705:$i > $o, X1706:$i, X1708:$i > $o, X1709:$i, X1712:$i, X1713:$i > $o, X1714:$i, X1718:$i, X1719:$i > $o, X1720:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i > $o, X1733:$i, X1735:$i, X1736:$i, X1737:$i > $o, X1738:$i > $o, X1741:$i, X1744:$i, X1745:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i > $o, X1758:$i, X1760:$i, X1761:$i, X1762:$i > $o, X1763:$i > $o, X1766:$i, X1768:$i, X1770:$i, X1771:$i, X1772:$i > $o, X1773:$i > $o, X1776:$i, X1777:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i > $o, X1824:$i, X1825:$i > $o, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$o, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$o, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i > $o, X1980:$i, X1981:$i, X1982:$i > $o, X1984:$i, X1985:$i > $o, X1986:$i, X1988:$i, X1989:$i > $o, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i > $i > $o, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i > $i > $o, X2070:$i, X2071:$i, X2072:$i > $i > $o, X2073:$i, X2074:$i, X2075:$i > $i > $o, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i > $i > $o, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i > $i > $o, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i > $i > $o, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i > $i, X2119:$i, X2120:$i, X2121:$i > $i, X2123:$i, X2124:$i, X2125:$i > $i, X2127:$i, X2128:$i, X2129:$i, X2130:$i > $o, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i > $o, X2140:$i, X2141:$i, X2142:$i > $o, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2184:$i, X2185:$i, 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X2176 @ X2177)))))))))&((((in @ (esk78_4 @ X2184 @ X2185 @ X2186 @ X2187) @ X2184)|((X2186)=(X2187))|~(func @ X2184 @ X2185 @ X2187)|~(func @ X2184 @ X2185 @ X2186))&(((ap @ X2184 @ X2185 @ X2186 @ (esk78_4 @ X2184 @ X2185 @ X2186 @ X2187))!=(ap @ X2184 @ X2185 @ X2187 @ (esk78_4 @ X2184 @ X2185 @ X2186 @ X2187)))|((X2186)=(X2187))|~(func @ X2184 @ X2185 @ X2187)|~(func @ X2184 @ X2185 @ X2186)))&((((in @ (esk79_4 @ X2189 @ X2190 @ X2191 @ X2192) @ X2189)|((X2191)=(X2192))|~(in @ X2192 @ (funcSet @ X2189 @ X2190))|~(in @ X2191 @ (funcSet @ X2189 @ X2190)))&(((ap @ X2189 @ X2190 @ X2191 @ (esk79_4 @ X2189 @ X2190 @ X2191 @ X2192))!=(ap @ X2189 @ X2190 @ X2192 @ (esk79_4 @ X2189 @ X2190 @ X2191 @ X2192)))|((X2191)=(X2192))|~(in @ X2192 @ (funcSet @ X2189 @ X2190))|~(in @ X2191 @ (funcSet @ X2189 @ X2190))))&((~(in @ X2196 @ (funcSet @ X2194 @ X2195))|(~(in @ X2197 @ X2194)|((ap @ X2194 @ X2195 @ X2196 @ X2197)=(ap @ X2194 @ X2195 @ X2196 @ X2197))))&((~(func @ X2198 @ X2199 @ X2200)|(~(in @ X2201 @ X2198)|((ap @ X2198 @ X2199 @ X2200 @ X2201)=(ap @ X2198 @ X2199 @ X2200 @ X2201))))&((((in @ (esk80_3 @ X2202 @ X2203 @ X2204) @ X2202)|(~(in @ X2206 @ X2202)|((ap @ X2202 @ X2203 @ (lam @ X2202 @ X2203 @ X2204) @ X2206)=(X2204 @ X2206))))&(~(in @ (X2204 @ (esk80_3 @ X2202 @ X2203 @ X2204)) @ X2203)|(~(in @ X2206 @ X2202)|((ap @ X2202 @ X2203 @ (lam @ X2202 @ X2203 @ X2204) @ X2206)=(X2204 @ X2206)))))&((~(func @ X2207 @ X2208 @ X2209)|((lam @ X2207 @ X2208 @ (ap @ X2207 @ X2208 @ X2209))=(X2209)))&((((in @ (esk81_3 @ X2210 @ X2211 @ X2212) @ X2210)|((lam @ X2210 @ X2211 @ X2212)=(lam @ X2210 @ X2211 @ X2212)))&(~(in @ (X2212 @ (esk81_3 @ X2210 @ X2211 @ X2212)) @ X2211)|((lam @ X2210 @ X2211 @ X2212)=(lam @ X2210 @ X2211 @ X2212))))&((((in @ (esk82_3 @ X2214 @ X2215 @ X2216) @ X2214)|(~(in @ X2218 @ X2214)|((ap @ X2214 @ X2215 @ (lam @ X2214 @ X2215 @ X2216) @ X2218)=(X2216 @ X2218))))&(~(in @ (X2216 @ (esk82_3 @ X2214 @ X2215 @ X2216)) @ X2215)|(~(in @ X2218 @ X2214)|((ap @ X2214 @ X2215 @ (lam @ X2214 @ X2215 @ X2216) @ X2218)=(X2216 @ X2218)))))&((~(in @ X2221 @ (funcSet @ X2219 @ X2220))|((lam @ X2219 @ X2220 @ (ap @ X2219 @ X2220 @ X2221))=(X2221)))&((~(in @ X2224 @ X2222)|(~(in @ X2225 @ X2222)|((X2223)|(in @ X2225 @ (dsetconstr @ X2222 @ (^[Z0:$i]:((((((X2223))&(((Z0)=(X2224)))))|(((~((X2223)))&(((Z0)=(X2225)))))))))))))&((~(in @ X2228 @ X2226)|(~(in @ X2229 @ X2226)|((X2227)|((dsetconstr @ X2226 @ (^[Z0:$i]:((((((X2227))&(((Z0)=(X2228)))))|(((~((X2227)))&(((Z0)=(X2229)))))))))=(setadjoin @ X2229 @ emptyset)))))&((~(in @ X2232 @ X2230)|(~(in @ X2233 @ X2230)|(~(X2231)|(in @ X2232 @ (dsetconstr @ X2230 @ (^[Z0:$i]:((((((X2231))&(((Z0)=(X2232)))))|(((~((X2231)))&(((Z0)=(X2233)))))))))))))&((~(in @ X2236 @ X2234)|(~(in @ X2237 @ X2234)|(~(X2235)|((dsetconstr @ X2234 @ (^[Z0:$i]:((((((X2235))&(((Z0)=(X2236)))))|(((~((X2235)))&(((Z0)=(X2237)))))))))=(setadjoin @ X2236 @ emptyset)))))&((~(in @ X2240 @ X2238)|(~(in @ X2241 @ X2238)|(singleton @ (dsetconstr @ X2238 @ (^[Z0:$i]:((((((X2239))&(((Z0)=(X2240)))))|(((~((X2239)))&(((Z0)=(X2241))))))))))))&((~(in @ X2244 @ X2242)|(~(in @ X2245 @ X2242)|(in @ (if @ X2242 @ ((X2243)) @ X2244 @ X2245) @ X2242)))&((~(singleton @ X2246)|(~(in @ X2247 @ X2246)|((setunion @ X2246)=(X2247))))&((~(in @ X2250 @ X2248)|(~(in @ X2251 @ X2248)|(~(X2249)|((if @ X2248 @ ((X2249)) @ X2250 @ X2251)=(X2250)))))&((~(in @ X2254 @ X2252)|(~(in @ X2255 @ X2252)|((X2253)|((if @ X2252 @ ((X2253)) @ X2254 @ X2255)=(X2255)))))&((~(in @ X2258 @ X2256)|(~(in @ X2259 @ X2256)|(in @ (if @ X2256 @ ((X2257)) @ X2258 @ X2259) @ (setadjoin @ X2258 @ (setadjoin @ X2259 @ emptyset)))))&((~(in @ X2261 @ (powerset @ X2260))|(~(in @ X2262 @ (powerset @ X2260))|(in @ (binintersect @ X2261 @ X2262) @ (powerset @ X2260))))&((~(in @ X2264 @ (powerset @ X2263))|(~(in @ X2265 @ (powerset @ X2263))|(in @ (binunion @ X2264 @ X2265) @ (powerset @ X2263))))&((~(in @ X2267 @ (powerset @ X2266))|(in @ (powerset @ X2267) @ (powerset @ (powerset @ X2266))))&((~(in @ X2269 @ (powerset @ X2268))|(~(in @ X2270 @ (powerset @ X2268))|(in @ (setminus @ X2269 @ X2270) @ (powerset @ X2268))))&((~(in @ X2272 @ (powerset @ X2271))|(in @ (setminus @ X2271 @ X2272) @ (powerset @ X2271)))&(((((in @ (esk84_3 @ X2273 @ X2274 @ X2275) @ X2273)|((X2274)=(X2275))|(in @ (esk83_3 @ X2273 @ X2274 @ X2275) @ X2273)|~(in @ X2275 @ (powerset @ X2273))|~(in @ X2274 @ (powerset @ X2273)))&(((in @ (esk84_3 @ X2273 @ X2274 @ X2275) @ X2275)|((X2274)=(X2275))|(in @ (esk83_3 @ X2273 @ X2274 @ X2275) @ X2273)|~(in @ X2275 @ (powerset @ X2273))|~(in @ X2274 @ (powerset @ X2273)))&(~(in @ (esk84_3 @ X2273 @ X2274 @ X2275) @ X2274)|((X2274)=(X2275))|(in @ (esk83_3 @ X2273 @ X2274 @ X2275) @ X2273)|~(in @ X2275 @ (powerset @ X2273))|~(in @ X2274 @ (powerset @ X2273)))))&((((in @ (esk84_3 @ X2273 @ X2274 @ X2275) @ X2273)|((X2274)=(X2275))|(in @ (esk83_3 @ X2273 @ X2274 @ X2275) @ X2274)|~(in @ X2275 @ (powerset @ X2273))|~(in @ X2274 @ (powerset @ X2273)))&(((in @ (esk84_3 @ X2273 @ X2274 @ X2275) @ X2275)|((X2274)=(X2275))|(in @ (esk83_3 @ X2273 @ X2274 @ X2275) @ X2274)|~(in @ X2275 @ (powerset @ X2273))|~(in @ X2274 @ (powerset @ X2273)))&(~(in @ (esk84_3 @ X2273 @ X2274 @ X2275) @ X2274)|((X2274)=(X2275))|(in @ (esk83_3 @ X2273 @ X2274 @ X2275) @ X2274)|~(in @ X2275 @ (powerset @ X2273))|~(in @ X2274 @ (powerset @ X2273)))))&(((in @ (esk84_3 @ X2273 @ X2274 @ X2275) @ X2273)|((X2274)=(X2275))|~(in @ (esk83_3 @ X2273 @ X2274 @ X2275) @ X2275)|~(in @ X2275 @ (powerset @ X2273))|~(in @ X2274 @ (powerset @ X2273)))&(((in @ (esk84_3 @ X2273 @ X2274 @ X2275) @ X2275)|((X2274)=(X2275))|~(in @ (esk83_3 @ X2273 @ X2274 @ X2275) @ X2275)|~(in @ X2275 @ (powerset @ X2273))|~(in @ X2274 @ (powerset @ X2273)))&(~(in @ (esk84_3 @ X2273 @ X2274 @ X2275) @ X2274)|((X2274)=(X2275))|~(in @ (esk83_3 @ X2273 @ X2274 @ X2275) @ X2275)|~(in @ X2275 @ (powerset @ X2273))|~(in @ X2274 @ (powerset @ X2273)))))))&((((in @ (esk85_3 @ X2278 @ X2279 @ X2280) @ X2278)|(subset @ X2279 @ X2280)|~(in @ X2280 @ (powerset @ X2278))|~(in @ X2279 @ (powerset @ X2278)))&(((in @ (esk85_3 @ X2278 @ X2279 @ X2280) @ X2279)|(subset @ X2279 @ X2280)|~(in @ X2280 @ (powerset @ X2278))|~(in @ X2279 @ (powerset @ X2278)))&(~(in @ (esk85_3 @ X2278 @ X2279 @ X2280) @ X2280)|(subset @ X2279 @ X2280)|~(in @ X2280 @ (powerset @ X2278))|~(in @ X2279 @ (powerset @ X2278)))))&((in @ esk87_0 @ (powerset @ esk86_0))&((in @ esk88_0 @ (powerset @ esk86_0))&((~(in @ X2285 @ esk86_0)|(~(in @ X2285 @ esk87_0)|(in @ X2285 @ esk88_0)))&~(in @ esk87_0 @ (powerset @ esk88_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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_319])])])])])])])).
% 6.40/1.39 thf(c_0_321, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 6.40/1.39 thf(c_0_322, negated_conjecture, (in @ esk87_0 @ (powerset @ esk86_0)), inference(split_conjunct,[status(thm)],[c_0_320])).
% 6.40/1.39 thf(c_0_323, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 6.40/1.39 thf(c_0_324, negated_conjecture, (subset @ esk87_0 @ esk86_0), inference(spm,[status(thm)],[c_0_321, c_0_322])).
% 6.40/1.39 thf(c_0_325, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 6.40/1.39 thf(c_0_326, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk88_0)|~((in @ X2 @ esk86_0))|~((in @ X2 @ esk87_0)))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 6.40/1.39 thf(c_0_327, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk86_0)|~((in @ X2 @ esk87_0)))), inference(spm,[status(thm)],[c_0_323, c_0_324])).
% 6.40/1.39 thf(c_0_328, negated_conjecture, ~((in @ esk87_0 @ (powerset @ esk88_0))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 6.40/1.39 thf(c_0_329, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 6.40/1.39 thf(c_0_330, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk88_0)|~((in @ (esk53_2 @ X2 @ esk88_0) @ esk87_0)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_325, c_0_326]), c_0_327])).
% 6.40/1.39 thf(c_0_331, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_320])).
% 6.40/1.39 thf(c_0_332, negated_conjecture, ~((subset @ esk87_0 @ esk88_0)), inference(spm,[status(thm)],[c_0_328, c_0_329])).
% 6.40/1.39 thf(c_0_333, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_330, c_0_331]), c_0_332]), ['proof']).
% 6.40/1.39 % SZS output end CNFRefutation
% 6.40/1.39 % Parsed axioms : 509
% 6.40/1.39 % Removed by relevancy pruning/SinE : 272
% 6.40/1.39 % Initial clauses : 416
% 6.40/1.39 % Removed in clause preprocessing : 29
% 6.40/1.39 % Initial clauses in saturation : 387
% 6.40/1.39 % Processed clauses : 5764
% 6.40/1.39 % ...of these trivial : 185
% 6.40/1.39 % ...subsumed : 3738
% 6.40/1.39 % ...remaining for further processing : 1841
% 6.40/1.39 % Other redundant clauses eliminated : 330
% 6.40/1.39 % Clauses deleted for lack of memory : 0
% 6.40/1.39 % Backward-subsumed : 81
% 6.40/1.39 % Backward-rewritten : 38
% 6.40/1.39 % Generated clauses : 106640
% 6.40/1.39 % ...of the previous two non-redundant : 98328
% 6.40/1.39 % ...aggressively subsumed : 0
% 6.40/1.39 % Contextual simplify-reflections : 2
% 6.40/1.39 % Paramodulations : 106297
% 6.40/1.39 % Factorizations : 6
% 6.40/1.39 % NegExts : 0
% 6.40/1.39 % Equation resolutions : 337
% 6.40/1.39 % Disequality decompositions : 0
% 6.40/1.39 % Total rewrite steps : 18464
% 6.40/1.39 % ...of those cached : 17741
% 6.40/1.39 % Propositional unsat checks : 0
% 6.40/1.39 % Propositional check models : 0
% 6.40/1.39 % Propositional check unsatisfiable : 0
% 6.40/1.39 % Propositional clauses : 0
% 6.40/1.39 % Propositional clauses after purity: 0
% 6.40/1.39 % Propositional unsat core size : 0
% 6.40/1.39 % Propositional preprocessing time : 0.000
% 6.40/1.39 % Propositional encoding time : 0.000
% 6.40/1.39 % Propositional solver time : 0.000
% 6.40/1.39 % Success case prop preproc time : 0.000
% 6.40/1.39 % Success case prop encoding time : 0.000
% 6.40/1.39 % Success case prop solver time : 0.000
% 6.40/1.39 % Current number of processed clauses : 1707
% 6.40/1.39 % Positive orientable unit clauses : 559
% 6.40/1.39 % Positive unorientable unit clauses: 0
% 6.40/1.39 % Negative unit clauses : 15
% 6.40/1.39 % Non-unit-clauses : 1133
% 6.40/1.39 % Current number of unprocessed clauses: 86137
% 6.40/1.39 % ...number of literals in the above : 293240
% 6.40/1.39 % Current number of archived formulas : 0
% 6.40/1.39 % Current number of archived clauses : 119
% 6.40/1.39 % Clause-clause subsumption calls (NU) : 136129
% 6.40/1.39 % Rec. Clause-clause subsumption calls : 87844
% 6.40/1.39 % Non-unit clause-clause subsumptions : 2666
% 6.40/1.39 % Unit Clause-clause subsumption calls : 9965
% 6.40/1.39 % Rewrite failures with RHS unbound : 0
% 6.40/1.39 % BW rewrite match attempts : 5646
% 6.40/1.39 % BW rewrite match successes : 23
% 6.40/1.39 % Condensation attempts : 0
% 6.40/1.39 % Condensation successes : 0
% 6.40/1.39 % Termbank termtop insertions : 1762527
% 6.40/1.39 % Search garbage collected termcells : 23917
% 6.40/1.39
% 6.40/1.39 % -------------------------------------------------
% 6.40/1.39 % User time : 0.996 s
% 6.40/1.39 % System time : 0.051 s
% 6.40/1.39 % Total time : 1.047 s
% 6.40/1.39 % Maximum resident set size: 9560 pages
% 6.40/1.39
% 6.40/1.39 % -------------------------------------------------
% 6.40/1.39 % User time : 1.254 s
% 6.40/1.39 % System time : 0.154 s
% 6.40/1.39 % Total time : 1.409 s
% 6.40/1.39 % Maximum resident set size: 5632 pages
% 6.40/1.39 % E exiting
%------------------------------------------------------------------------------