%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU752^1 : 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 : n014.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 08:25:29 AM UTC 2026
% Result : Theorem 144.20s 29.31s
% Output : CNFRefutation 144.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU752^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:21:15 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.23/0.29 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.1iUZnAgXVJ/E---3.1_2736655.p
% 144.20/29.31 % Version: 3.5.1-ho
% 144.20/29.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 144.20/29.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 144.20/29.31 % Starting ehoh_best5 with 300s (1) cores
% 144.20/29.31 % Starting almost_fo_3_lam with 300s (1) cores
% 144.20/29.31 % Starting new_bool_5 with 300s (1) cores
% 144.20/29.31 % Starting pre_casc_3 with 300s (1) cores
% 144.20/29.31 % Starting ho_unfolding_8 with 300s (1) cores
% 144.20/29.31 % Starting new_ho_10_cnf2 with 300s (1) cores
% 144.20/29.31 % Starting new_bool_3 with 300s (1) cores
% 144.20/29.31 % Starting new_ho_5 with 300s (1) cores
% 144.20/29.31 % new_ho_5 with pid 2736714 completed with status 9
% 144.20/29.31 % pre_casc_3 with pid 2736710 completed with status 9
% 144.20/29.31 % new_bool_5 with pid 2736709 completed with status 0
% 144.20/29.31 % Result found by new_bool_5
% 144.20/29.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 144.20/29.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 144.20/29.31 % Starting ehoh_best5 with 300s (1) cores
% 144.20/29.31 % Starting almost_fo_3_lam with 300s (1) cores
% 144.20/29.31 % Starting new_bool_5 with 300s (1) cores
% 144.20/29.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 144.20/29.31 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 144.20/29.31 % Search class: HGHSM-FSLM32-MHFMMSBN
% 144.20/29.31 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 144.20/29.31 % Starting SubtermCWHack with 28s (1) cores
% 144.20/29.31 % SubtermCWHack with pid 2736757 completed with status 8
% 144.20/29.31 % Starting new_bool_5 with 31s (1) cores
% 144.20/29.31 % new_bool_5 with pid 2737355 completed with status 0
% 144.20/29.31 % Result found by new_bool_5
% 144.20/29.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 144.20/29.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 144.20/29.31 % Starting ehoh_best5 with 300s (1) cores
% 144.20/29.31 % Starting almost_fo_3_lam with 300s (1) cores
% 144.20/29.31 % Starting new_bool_5 with 300s (1) cores
% 144.20/29.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 144.20/29.31 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 144.20/29.31 % Search class: HGHSM-FSLM32-MHFMMSBN
% 144.20/29.31 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 144.20/29.31 % Starting SubtermCWHack with 28s (1) cores
% 144.20/29.31 % SubtermCWHack with pid 2736757 completed with status 8
% 144.20/29.31 % Starting new_bool_5 with 31s (1) cores
% 144.20/29.31 % Preprocessing time : 0.010 s
% 144.20/29.31 % Presaturation interreduction done
% 144.20/29.31
% 144.20/29.31 % Proof found!
% 144.20/29.31 % SZS status Theorem
% 144.20/29.31 % SZS output start CNFRefutation
% 144.20/29.31 thf(decl_23, type, in: $i > $i > $o).
% 144.20/29.31 thf(decl_24, type, exu: ($i > $o) > $o).
% 144.20/29.31 thf(decl_25, type, setextAx: $o).
% 144.20/29.31 thf(decl_26, type, emptyset: $i).
% 144.20/29.31 thf(decl_27, type, emptysetAx: $o).
% 144.20/29.31 thf(decl_28, type, setadjoin: $i > $i > $i).
% 144.20/29.31 thf(decl_29, type, setadjoinAx: $o).
% 144.20/29.31 thf(decl_30, type, powerset: $i > $i).
% 144.20/29.31 thf(decl_31, type, powersetAx: $o).
% 144.20/29.31 thf(decl_32, type, setunion: $i > $i).
% 144.20/29.31 thf(decl_33, type, setunionAx: $o).
% 144.20/29.31 thf(decl_34, type, omega: $i).
% 144.20/29.31 thf(decl_35, type, omega0Ax: $o).
% 144.20/29.31 thf(decl_36, type, omegaSAx: $o).
% 144.20/29.31 thf(decl_37, type, omegaIndAx: $o).
% 144.20/29.31 thf(decl_38, type, replAx: $o).
% 144.20/29.31 thf(decl_39, type, foundationAx: $o).
% 144.20/29.31 thf(decl_40, type, wellorderingAx: $o).
% 144.20/29.31 thf(decl_41, type, descr: ($i > $o) > $i).
% 144.20/29.31 thf(decl_42, type, descrp: $o).
% 144.20/29.31 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_44, type, dsetconstrI: $o).
% 144.20/29.31 thf(decl_45, type, dsetconstrEL: $o).
% 144.20/29.31 thf(decl_46, type, dsetconstrER: $o).
% 144.20/29.31 thf(decl_47, type, exuE1: $o).
% 144.20/29.31 thf(decl_48, type, prop2set: $o > $i).
% 144.20/29.31 thf(decl_49, type, prop2setE: $o).
% 144.20/29.31 thf(decl_50, type, emptysetE: $o).
% 144.20/29.31 thf(decl_51, type, emptysetimpfalse: $o).
% 144.20/29.31 thf(decl_52, type, notinemptyset: $o).
% 144.20/29.31 thf(decl_53, type, exuE3e: $o).
% 144.20/29.31 thf(decl_54, type, setext: $o).
% 144.20/29.31 thf(decl_55, type, emptyI: $o).
% 144.20/29.31 thf(decl_56, type, noeltsimpempty: $o).
% 144.20/29.31 thf(decl_57, type, setbeta: $o).
% 144.20/29.31 thf(decl_58, type, nonempty: $i > $o).
% 144.20/29.31 thf(decl_59, type, nonemptyE1: $o).
% 144.20/29.31 thf(decl_60, type, nonemptyI: $o).
% 144.20/29.31 thf(decl_61, type, nonemptyI1: $o).
% 144.20/29.31 thf(decl_62, type, setadjoinIL: $o).
% 144.20/29.31 thf(decl_63, type, emptyinunitempty: $o).
% 144.20/29.31 thf(decl_64, type, setadjoinIR: $o).
% 144.20/29.31 thf(decl_65, type, setadjoinE: $o).
% 144.20/29.31 thf(decl_66, type, setadjoinOr: $o).
% 144.20/29.31 thf(decl_67, type, setoftrueEq: $o).
% 144.20/29.31 thf(decl_68, type, powersetI: $o).
% 144.20/29.31 thf(decl_69, type, emptyinPowerset: $o).
% 144.20/29.31 thf(decl_70, type, emptyInPowerset: $o).
% 144.20/29.31 thf(decl_71, type, powersetE: $o).
% 144.20/29.31 thf(decl_72, type, setunionI: $o).
% 144.20/29.31 thf(decl_73, type, setunionE: $o).
% 144.20/29.31 thf(decl_74, type, subPowSU: $o).
% 144.20/29.31 thf(decl_75, type, exuE2: $o).
% 144.20/29.31 thf(decl_76, type, nonemptyImpWitness: $o).
% 144.20/29.31 thf(decl_77, type, uniqinunit: $o).
% 144.20/29.31 thf(decl_78, type, notinsingleton: $o).
% 144.20/29.31 thf(decl_79, type, eqinunit: $o).
% 144.20/29.31 thf(decl_80, type, singletonsswitch: $o).
% 144.20/29.31 thf(decl_81, type, upairsetE: $o).
% 144.20/29.31 thf(decl_82, type, upairsetIL: $o).
% 144.20/29.31 thf(decl_83, type, upairsetIR: $o).
% 144.20/29.31 thf(decl_84, type, emptyE1: $o).
% 144.20/29.31 thf(decl_85, type, vacuousDall: $o).
% 144.20/29.31 thf(decl_86, type, quantDeMorgan1: $o).
% 144.20/29.31 thf(decl_87, type, quantDeMorgan2: $o).
% 144.20/29.31 thf(decl_88, type, quantDeMorgan3: $o).
% 144.20/29.31 thf(decl_89, type, quantDeMorgan4: $o).
% 144.20/29.31 thf(decl_90, type, prop2setI: $o).
% 144.20/29.31 thf(decl_92, type, prop2set2propI: $o).
% 144.20/29.31 thf(decl_93, type, notdexE: $o).
% 144.20/29.31 thf(decl_94, type, notdallE: $o).
% 144.20/29.31 thf(decl_95, type, exuI1: $o).
% 144.20/29.31 thf(decl_96, type, exuI3: $o).
% 144.20/29.31 thf(decl_97, type, exuI2: $o).
% 144.20/29.31 thf(decl_98, type, inCongP: $o).
% 144.20/29.31 thf(decl_99, type, in__Cong: $o).
% 144.20/29.31 thf(decl_100, type, exuE3u: $o).
% 144.20/29.31 thf(decl_101, type, exu__Cong: $o).
% 144.20/29.31 thf(decl_102, type, emptyset__Cong: $o).
% 144.20/29.31 thf(decl_103, type, setadjoin__Cong: $o).
% 144.20/29.31 thf(decl_104, type, powerset__Cong: $o).
% 144.20/29.31 thf(decl_105, type, setunion__Cong: $o).
% 144.20/29.31 thf(decl_106, type, omega__Cong: $o).
% 144.20/29.31 thf(decl_107, type, exuEu: $o).
% 144.20/29.31 thf(decl_108, type, descr__Cong: $o).
% 144.20/29.31 thf(decl_109, type, dsetconstr__Cong: $o).
% 144.20/29.31 thf(decl_110, type, subset: $i > $i > $o).
% 144.20/29.31 thf(decl_113, type, subsetI1: $o).
% 144.20/29.31 thf(decl_114, type, eqimpsubset2: $o).
% 144.20/29.31 thf(decl_115, type, eqimpsubset1: $o).
% 144.20/29.31 thf(decl_116, type, subsetI2: $o).
% 144.20/29.31 thf(decl_117, type, emptysetsubset: $o).
% 144.20/29.31 thf(decl_118, type, subsetE: $o).
% 144.20/29.31 thf(decl_119, type, subsetE2: $o).
% 144.20/29.31 thf(decl_120, type, notsubsetI: $o).
% 144.20/29.31 thf(decl_121, type, notequalI1: $o).
% 144.20/29.31 thf(decl_122, type, notequalI2: $o).
% 144.20/29.31 thf(decl_123, type, subsetRefl: $o).
% 144.20/29.31 thf(decl_124, type, subsetTrans: $o).
% 144.20/29.31 thf(decl_125, type, setadjoinSub: $o).
% 144.20/29.31 thf(decl_126, type, setadjoinSub2: $o).
% 144.20/29.31 thf(decl_127, type, subset2powerset: $o).
% 144.20/29.31 thf(decl_128, type, setextsub: $o).
% 144.20/29.31 thf(decl_129, type, subsetemptysetimpeq: $o).
% 144.20/29.31 thf(decl_130, type, powersetI1: $o).
% 144.20/29.31 thf(decl_131, type, powersetE1: $o).
% 144.20/29.31 thf(decl_132, type, inPowerset: $o).
% 144.20/29.31 thf(decl_133, type, powersetsubset: $o).
% 144.20/29.31 thf(decl_134, type, sepInPowerset: $o).
% 144.20/29.31 thf(decl_135, type, sepSubset: $o).
% 144.20/29.31 thf(decl_136, type, binunion: $i > $i > $i).
% 144.20/29.31 thf(decl_137, type, binunionIL: $o).
% 144.20/29.31 thf(decl_138, type, upairset2IR: $o).
% 144.20/29.31 thf(decl_139, type, binunionIR: $o).
% 144.20/29.31 thf(decl_140, type, binunionEcases: $o).
% 144.20/29.31 thf(decl_141, type, binunionE: $o).
% 144.20/29.31 thf(decl_142, type, binunionLsub: $o).
% 144.20/29.31 thf(decl_143, type, binunionRsub: $o).
% 144.20/29.31 thf(decl_144, type, binintersect: $i > $i > $i).
% 144.20/29.31 thf(decl_145, type, binintersectI: $o).
% 144.20/29.31 thf(decl_146, type, binintersectSubset5: $o).
% 144.20/29.31 thf(decl_147, type, binintersectEL: $o).
% 144.20/29.31 thf(decl_148, type, binintersectLsub: $o).
% 144.20/29.31 thf(decl_149, type, binintersectSubset2: $o).
% 144.20/29.31 thf(decl_150, type, binintersectSubset3: $o).
% 144.20/29.31 thf(decl_151, type, binintersectER: $o).
% 144.20/29.31 thf(decl_152, type, disjointsetsI1: $o).
% 144.20/29.31 thf(decl_153, type, binintersectRsub: $o).
% 144.20/29.31 thf(decl_154, type, binintersectSubset4: $o).
% 144.20/29.31 thf(decl_155, type, binintersectSubset1: $o).
% 144.20/29.31 thf(decl_156, type, bs114d: $o).
% 144.20/29.31 thf(decl_158, type, setminus: $i > $i > $i).
% 144.20/29.31 thf(decl_159, type, setminusI: $o).
% 144.20/29.31 thf(decl_160, type, setminusEL: $o).
% 144.20/29.31 thf(decl_161, type, setminusER: $o).
% 144.20/29.31 thf(decl_162, type, setminusSubset2: $o).
% 144.20/29.31 thf(decl_163, type, setminusERneg: $o).
% 144.20/29.31 thf(decl_164, type, setminusELneg: $o).
% 144.20/29.31 thf(decl_165, type, setminusILneg: $o).
% 144.20/29.31 thf(decl_166, type, setminusIRneg: $o).
% 144.20/29.31 thf(decl_167, type, setminusLsub: $o).
% 144.20/29.31 thf(decl_168, type, setminusSubset1: $o).
% 144.20/29.31 thf(decl_169, type, symdiff: $i > $i > $i).
% 144.20/29.31 thf(decl_170, type, symdiffE: $o).
% 144.20/29.31 thf(decl_171, type, symdiffI1: $o).
% 144.20/29.31 thf(decl_172, type, symdiffI2: $o).
% 144.20/29.31 thf(decl_173, type, symdiffIneg1: $o).
% 144.20/29.31 thf(decl_174, type, symdiffIneg2: $o).
% 144.20/29.31 thf(decl_175, type, iskpair: $i > $o).
% 144.20/29.31 thf(decl_176, type, secondinupair: $o).
% 144.20/29.31 thf(decl_177, type, setukpairIL: $o).
% 144.20/29.31 thf(decl_178, type, setukpairIR: $o).
% 144.20/29.31 thf(decl_179, type, kpairiskpair: $o).
% 144.20/29.31 thf(decl_180, type, kpair: $i > $i > $i).
% 144.20/29.31 thf(decl_181, type, kpairp: $o).
% 144.20/29.31 thf(decl_182, type, cartprod: $i > $i > $i).
% 144.20/29.31 thf(decl_183, type, singletonsubset: $o).
% 144.20/29.31 thf(decl_184, type, singletoninpowerset: $o).
% 144.20/29.31 thf(decl_185, type, singletoninpowunion: $o).
% 144.20/29.31 thf(decl_186, type, upairset2E: $o).
% 144.20/29.31 thf(decl_187, type, upairsubunion: $o).
% 144.20/29.31 thf(decl_188, type, upairinpowunion: $o).
% 144.20/29.31 thf(decl_189, type, ubforcartprodlem1: $o).
% 144.20/29.31 thf(decl_190, type, ubforcartprodlem2: $o).
% 144.20/29.31 thf(decl_191, type, ubforcartprodlem3: $o).
% 144.20/29.31 thf(decl_192, type, cartprodpairin: $o).
% 144.20/29.31 thf(decl_193, type, cartprodmempair1: $o).
% 144.20/29.31 thf(decl_194, type, cartprodmempair: $o).
% 144.20/29.31 thf(decl_195, type, setunionE2: $o).
% 144.20/29.31 thf(decl_196, type, setunionsingleton1: $o).
% 144.20/29.31 thf(decl_197, type, setunionsingleton2: $o).
% 144.20/29.31 thf(decl_198, type, setunionsingleton: $o).
% 144.20/29.31 thf(decl_199, type, singleton: $i > $o).
% 144.20/29.31 thf(decl_200, type, singletonprop: $o).
% 144.20/29.31 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 144.20/29.31 thf(decl_202, type, ex1E1: $o).
% 144.20/29.31 thf(decl_203, type, ex1I: $o).
% 144.20/29.31 thf(decl_204, type, ex1I2: $o).
% 144.20/29.31 thf(decl_205, type, singletonsuniq: $o).
% 144.20/29.31 thf(decl_210, type, setukpairinjL1: $o).
% 144.20/29.31 thf(decl_211, type, kfstsingleton: $o).
% 144.20/29.31 thf(decl_212, type, theprop: $o).
% 144.20/29.31 thf(decl_213, type, kfst: $i > $i).
% 144.20/29.31 thf(decl_214, type, kfstpairEq: $o).
% 144.20/29.31 thf(decl_215, type, cartprodfstin: $o).
% 144.20/29.31 thf(decl_216, type, setukpairinjL2: $o).
% 144.20/29.31 thf(decl_217, type, setukpairinjL: $o).
% 144.20/29.31 thf(decl_218, type, setukpairinjR11: $o).
% 144.20/29.31 thf(decl_219, type, setukpairinjR12: $o).
% 144.20/29.31 thf(decl_220, type, setukpairinjR1: $o).
% 144.20/29.31 thf(decl_221, type, upairequniteq: $o).
% 144.20/29.31 thf(decl_222, type, setukpairinjR2: $o).
% 144.20/29.31 thf(decl_223, type, setukpairinjR: $o).
% 144.20/29.31 thf(decl_224, type, ksndsingleton: $o).
% 144.20/29.31 thf(decl_225, type, ksnd: $i > $i).
% 144.20/29.31 thf(decl_226, type, ksndpairEq: $o).
% 144.20/29.31 thf(decl_227, type, kpairsurjEq: $o).
% 144.20/29.31 thf(decl_228, type, cartprodsndin: $o).
% 144.20/29.31 thf(decl_229, type, cartprodpairmemEL: $o).
% 144.20/29.31 thf(decl_230, type, cartprodpairmemER: $o).
% 144.20/29.31 thf(decl_231, type, cartprodmempaircEq: $o).
% 144.20/29.31 thf(decl_232, type, cartprodfstpairEq: $o).
% 144.20/29.31 thf(decl_233, type, cartprodsndpairEq: $o).
% 144.20/29.31 thf(decl_234, type, cartprodpairsurjEq: $o).
% 144.20/29.31 thf(decl_235, type, breln: $i > $i > $i > $o).
% 144.20/29.31 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 144.20/29.31 thf(decl_237, type, dpsetconstrI: $o).
% 144.20/29.31 thf(decl_238, type, dpsetconstrSub: $o).
% 144.20/29.31 thf(decl_239, type, setOfPairsIsBReln: $o).
% 144.20/29.31 thf(decl_240, type, dpsetconstrERa: $o).
% 144.20/29.31 thf(decl_241, type, dpsetconstrEL1: $o).
% 144.20/29.31 thf(decl_242, type, dpsetconstrEL2: $o).
% 144.20/29.31 thf(decl_243, type, dpsetconstrER: $o).
% 144.20/29.31 thf(decl_244, type, func: $i > $i > $i > $o).
% 144.20/29.31 thf(decl_245, type, funcSet: $i > $i > $i).
% 144.20/29.31 thf(decl_246, type, funcImageSingleton: $o).
% 144.20/29.31 thf(decl_247, type, apProp: $o).
% 144.20/29.31 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 144.20/29.31 thf(decl_249, type, app: $o).
% 144.20/29.31 thf(decl_250, type, infuncsetfunc: $o).
% 144.20/29.31 thf(decl_251, type, ap2p: $o).
% 144.20/29.31 thf(decl_252, type, funcinfuncset: $o).
% 144.20/29.31 thf(decl_253, type, lamProp: $o).
% 144.20/29.31 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 144.20/29.31 thf(decl_255, type, lamp: $o).
% 144.20/29.31 thf(decl_256, type, lam2p: $o).
% 144.20/29.31 thf(decl_257, type, brelnall1: $o).
% 144.20/29.31 thf(decl_258, type, brelnall2: $o).
% 144.20/29.31 thf(decl_259, type, ex1E2: $o).
% 144.20/29.31 thf(decl_260, type, funcGraphProp1: $o).
% 144.20/29.31 thf(decl_261, type, funcGraphProp3: $o).
% 144.20/29.31 thf(decl_262, type, funcGraphProp2: $o).
% 144.20/29.31 thf(decl_263, type, funcextLem: $o).
% 144.20/29.31 thf(decl_264, type, funcGraphProp4: $o).
% 144.20/29.31 thf(decl_265, type, subbreln: $o).
% 144.20/29.31 thf(decl_266, type, eqbreln: $o).
% 144.20/29.31 thf(decl_267, type, funcext: $o).
% 144.20/29.31 thf(decl_268, type, funcext2: $o).
% 144.20/29.31 thf(decl_269, type, ap2apEq1: $o).
% 144.20/29.31 thf(decl_270, type, ap2apEq2: $o).
% 144.20/29.31 thf(decl_271, type, beta1: $o).
% 144.20/29.31 thf(decl_272, type, eta1: $o).
% 144.20/29.31 thf(decl_273, type, lam2lamEq: $o).
% 144.20/29.31 thf(decl_274, type, beta2: $o).
% 144.20/29.31 thf(decl_275, type, eta2: $o).
% 144.20/29.31 thf(decl_276, type, iffalseProp1: $o).
% 144.20/29.31 thf(decl_277, type, iffalseProp2: $o).
% 144.20/29.31 thf(decl_278, type, iftrueProp1: $o).
% 144.20/29.31 thf(decl_279, type, iftrueProp2: $o).
% 144.20/29.31 thf(decl_280, type, ifSingleton: $o).
% 144.20/29.31 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 144.20/29.31 thf(decl_282, type, ifp: $o).
% 144.20/29.31 thf(decl_283, type, theeq: $o).
% 144.20/29.31 thf(decl_284, type, iftrue: $o).
% 144.20/29.31 thf(decl_285, type, iffalse: $o).
% 144.20/29.31 thf(decl_286, type, iftrueorfalse: $o).
% 144.20/29.31 thf(decl_287, type, binintersectT_lem: $o).
% 144.20/29.31 thf(decl_288, type, binunionT_lem: $o).
% 144.20/29.31 thf(decl_289, type, powersetT_lem: $o).
% 144.20/29.31 thf(decl_290, type, setminusT_lem: $o).
% 144.20/29.31 thf(decl_291, type, complementT_lem: $o).
% 144.20/29.31 thf(decl_292, type, setextT: $o).
% 144.20/29.31 thf(decl_293, type, subsetTI: $o).
% 144.20/29.31 thf(decl_294, type, powersetTI1: $o).
% 144.20/29.31 thf(decl_295, type, powersetTE1: $o).
% 144.20/29.31 thf(decl_296, type, complementTI1: $o).
% 144.20/29.31 thf(decl_297, type, complementTE1: $o).
% 144.20/29.31 thf(decl_298, type, binintersectTELcontra: $o).
% 144.20/29.31 thf(decl_299, type, binintersectTERcontra: $o).
% 144.20/29.31 thf(decl_300, type, contrasubsetT: $o).
% 144.20/29.31 thf(decl_301, type, contrasubsetT1: $o).
% 144.20/29.31 thf(decl_302, type, contrasubsetT2: $o).
% 144.20/29.31 thf(decl_303, type, contrasubsetT3: $o).
% 144.20/29.31 thf(decl_304, type, doubleComplementI1: $o).
% 144.20/29.31 thf(decl_305, type, doubleComplementE1: $o).
% 144.20/29.31 thf(decl_306, type, doubleComplementSub1: $o).
% 144.20/29.31 thf(decl_307, type, doubleComplementSub2: $o).
% 144.20/29.31 thf(decl_308, type, doubleComplementEq: $o).
% 144.20/29.31 thf(decl_309, type, complementTnotintersectT: $o).
% 144.20/29.31 thf(decl_310, type, complementImpComplementIntersect: $o).
% 144.20/29.31 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 144.20/29.31 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 144.20/29.31 thf(decl_313, type, contraSubsetComplement: $o).
% 144.20/29.31 thf(decl_314, type, complementTcontraSubset: $o).
% 144.20/29.31 thf(decl_315, type, binunionTILcontra: $o).
% 144.20/29.31 thf(decl_316, type, binunionTIRcontra: $o).
% 144.20/29.31 thf(decl_317, type, inIntersectImpInUnion: $o).
% 144.20/29.31 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 144.20/29.31 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 144.20/29.31 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 144.20/29.31 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 144.20/29.31 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 144.20/29.31 thf(decl_323, type, binunionTE: $o).
% 144.20/29.31 thf(decl_324, type, binunionTEcontra: $o).
% 144.20/29.31 thf(decl_325, type, demorgan2a1: $o).
% 144.20/29.31 thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 144.20/29.31 thf(decl_327, type, demorgan2a2: $o).
% 144.20/29.31 thf(decl_328, type, demorgan1a: $o).
% 144.20/29.31 thf(decl_329, type, epred1_0: $o).
% 144.20/29.31 thf(decl_330, type, esk1_2: $i > $i > $i).
% 144.20/29.31 thf(decl_331, type, esk2_2: $i > $i > $i).
% 144.20/29.31 thf(decl_332, type, esk3_2: $i > $i > $i).
% 144.20/29.31 thf(decl_333, type, esk4_1: $i > $i).
% 144.20/29.31 thf(decl_334, type, esk5_2: ($i > $i > $o) > $i > $i).
% 144.20/29.31 thf(decl_335, type, esk6_2: ($i > $i > $o) > $i > $i).
% 144.20/29.31 thf(decl_336, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 144.20/29.31 thf(decl_337, type, esk8_1: $i > $i).
% 144.20/29.31 thf(decl_338, type, esk9_1: ($i > $o) > $i).
% 144.20/29.31 thf(decl_339, type, esk10_1: ($i > $o) > $i).
% 144.20/29.31 thf(decl_340, type, esk11_2: $i > $i > $i).
% 144.20/29.31 thf(decl_341, type, esk12_2: $i > $i > $i).
% 144.20/29.31 thf(decl_342, type, esk13_1: $i > $i).
% 144.20/29.31 thf(decl_343, type, esk14_1: $i > $i).
% 144.20/29.31 thf(decl_344, type, esk15_1: $i > $i).
% 144.20/29.31 thf(decl_345, type, esk16_2: $i > $i > $i).
% 144.20/29.31 thf(decl_346, type, esk17_3: $i > $i > $o > $i).
% 144.20/29.31 thf(decl_347, type, esk18_1: ($i > $o) > $i).
% 144.20/29.31 thf(decl_348, type, esk19_1: $i > $i).
% 144.20/29.31 thf(decl_349, type, esk20_2: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_350, type, esk21_2: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_351, type, esk22_2: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_352, type, esk23_2: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_353, type, esk24_2: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_354, type, esk25_2: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_355, type, esk26_2: ($i > $o) > $i > $i).
% 144.20/29.31 thf(decl_356, type, esk27_1: ($i > $o) > $i).
% 144.20/29.31 thf(decl_357, type, esk28_1: ($i > $o) > $i).
% 144.20/29.31 thf(decl_358, type, esk29_2: ($i > $o) > $i > $i).
% 144.20/29.31 thf(decl_359, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 144.20/29.31 thf(decl_360, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 144.20/29.31 thf(decl_361, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 144.20/29.31 thf(decl_362, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 144.20/29.31 thf(decl_363, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 144.20/29.31 thf(decl_364, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 144.20/29.31 thf(decl_365, type, esk36_2: $i > $i > $i).
% 144.20/29.31 thf(decl_366, type, esk37_2: $i > $i > $i).
% 144.20/29.31 thf(decl_367, type, esk38_2: $i > $i > $i).
% 144.20/29.31 thf(decl_368, type, esk39_3: $i > $i > $i > $i).
% 144.20/29.31 thf(decl_369, type, esk40_3: $i > $i > $i > $i).
% 144.20/29.31 thf(decl_370, type, esk41_2: $i > $i > $i).
% 144.20/29.31 thf(decl_371, type, esk42_2: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_372, type, esk43_2: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_373, type, esk44_2: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_374, type, esk45_3: $i > ($i > $o) > $i > $i).
% 144.20/29.31 thf(decl_375, type, esk46_2: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_376, type, esk47_2: $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_377, type, esk48_3: $i > $i > ($i > $i) > $i).
% 144.20/29.31 thf(decl_378, type, esk49_3: $i > $i > ($i > $i) > $i).
% 144.20/29.31 thf(decl_379, type, esk50_3: $i > $i > ($i > $i) > $i).
% 144.20/29.31 thf(decl_380, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_381, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_382, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_383, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 144.20/29.31 thf(decl_384, type, esk55_4: $i > $i > $i > $i > $i).
% 144.20/29.31 thf(decl_385, type, esk56_4: $i > $i > $i > $i > $i).
% 144.20/29.31 thf(decl_386, type, esk57_4: $i > $i > $i > $i > $i).
% 144.20/29.31 thf(decl_387, type, esk58_4: $i > $i > $i > $i > $i).
% 144.20/29.31 thf(decl_388, type, esk59_4: $i > $i > $i > $i > $i).
% 144.20/29.31 thf(decl_389, type, esk60_4: $i > $i > $i > $i > $i).
% 144.20/29.31 thf(decl_390, type, esk61_4: $i > $i > $i > $i > $i).
% 144.20/29.31 thf(decl_391, type, esk62_4: $i > $i > $i > $i > $i).
% 144.20/29.31 thf(decl_392, type, esk63_4: $i > $i > $i > $i > $i).
% 144.20/29.31 thf(decl_393, type, esk64_3: $i > $i > ($i > $i) > $i).
% 144.20/29.31 thf(decl_394, type, esk65_3: $i > $i > ($i > $i) > $i).
% 144.20/29.31 thf(decl_395, type, esk66_3: $i > $i > ($i > $i) > $i).
% 144.20/29.31 thf(decl_396, type, esk67_3: $i > $i > $i > $i).
% 144.20/29.31 thf(decl_397, type, esk68_3: $i > $i > $i > $i).
% 144.20/29.31 thf(decl_398, type, esk69_3: $i > $i > $i > $i).
% 144.20/29.31 thf(decl_399, type, esk70_3: $i > $i > $i > $i).
% 144.20/29.31 thf(decl_400, type, esk71_0: $i).
% 144.20/29.31 thf(decl_401, type, esk72_0: $i).
% 144.20/29.31 thf(decl_402, type, esk73_0: $i).
% 144.20/29.31 thf(decl_403, type, esk74_0: $i).
% 144.20/29.31 thf(demorgan1b, 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)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', demorgan1b)).
% 144.20/29.31 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', exuE3u)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', exuI2)).
% 144.20/29.31 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', exuI3)).
% 144.20/29.31 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', exuI1)).
% 144.20/29.31 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', exu__Cong)).
% 144.20/29.31 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', descr__Cong)).
% 144.20/29.31 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', exuEu)).
% 144.20/29.31 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', dsetconstr__Cong)).
% 144.20/29.31 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', sepSubset)).
% 144.20/29.31 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', sepInPowerset)).
% 144.20/29.31 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', iffalseProp2)).
% 144.20/29.31 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$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.1iUZnAgXVJ/E---3.1_2736655.p', iffalseProp1)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', eta2)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', beta2)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', lam2lamEq)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', eta1)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', beta1)).
% 144.20/29.31 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', singletonprop)).
% 144.20/29.31 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', ex1E1)).
% 144.20/29.31 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', kfstsingleton)).
% 144.20/29.31 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', ex1I2)).
% 144.20/29.31 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.1iUZnAgXVJ/E---3.1_2736655.p', ex1I)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', ksndsingleton)).
% 144.20/29.31 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:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', dpsetconstrEL1)).
% 144.20/29.31 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', dpsetconstrERa)).
% 144.20/29.31 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setOfPairsIsBReln)).
% 144.20/29.31 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', dpsetconstrSub)).
% 144.20/29.31 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', dpsetconstrI)).
% 144.20/29.31 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', dpsetconstrEL2)).
% 144.20/29.31 thf(apProp, axiom, ((apProp)<=>![X4:$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.1iUZnAgXVJ/E---3.1_2736655.p', apProp)).
% 144.20/29.31 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', funcImageSingleton)).
% 144.20/29.31 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', dpsetconstrER)).
% 144.20/29.31 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.1iUZnAgXVJ/E---3.1_2736655.p', lamProp)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', ex1E2)).
% 144.20/29.31 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', lam2p)).
% 144.20/29.31 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', lamp)).
% 144.20/29.31 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.1iUZnAgXVJ/E---3.1_2736655.p', iftrueProp2)).
% 144.20/29.31 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', ifSingleton)).
% 144.20/29.31 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.1iUZnAgXVJ/E---3.1_2736655.p', iftrueProp1)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', emptyE1)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', exuE2)).
% 144.20/29.31 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setoftrueEq)).
% 144.20/29.31 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', nonemptyI)).
% 144.20/29.31 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setbeta)).
% 144.20/29.31 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', exuE3e)).
% 144.20/29.31 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', exuE1)).
% 144.20/29.31 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', dsetconstrER)).
% 144.20/29.31 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', dsetconstrEL)).
% 144.20/29.31 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', dsetconstrI)).
% 144.20/29.31 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', descrp)).
% 144.20/29.31 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', replAx)).
% 144.20/29.31 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', iffalse)).
% 144.20/29.31 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', iftrue)).
% 144.20/29.31 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', iftrueorfalse)).
% 144.20/29.31 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.1iUZnAgXVJ/E---3.1_2736655.p', binintersectT_lem)).
% 144.20/29.31 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binunionT_lem)).
% 144.20/29.31 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', powersetT_lem)).
% 144.20/29.31 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.1iUZnAgXVJ/E---3.1_2736655.p', setminusT_lem)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', complementT_lem)).
% 144.20/29.31 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setextT)).
% 144.20/29.31 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', subsetTI)).
% 144.20/29.31 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', powersetTI1)).
% 144.20/29.31 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', in__Cong)).
% 144.20/29.31 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', powersetTE1)).
% 144.20/29.31 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', inCongP)).
% 144.20/29.31 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', complementTI1)).
% 144.20/29.31 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', complementTE1)).
% 144.20/29.31 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectTELcontra)).
% 144.20/29.31 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectTERcontra)).
% 144.20/29.31 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', contrasubsetT)).
% 144.20/29.31 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', notdallE)).
% 144.20/29.31 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', contrasubsetT1)).
% 144.20/29.31 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', contrasubsetT2)).
% 144.20/29.31 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', contrasubsetT3)).
% 144.20/29.31 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', doubleComplementI1)).
% 144.20/29.31 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', doubleComplementE1)).
% 144.20/29.31 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', doubleComplementSub1)).
% 144.20/29.31 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', doubleComplementSub2)).
% 144.20/29.31 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', doubleComplementEq)).
% 144.20/29.31 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', complementTnotintersectT)).
% 144.20/29.31 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', complementImpComplementIntersect)).
% 144.20/29.31 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', complementSubsetComplementIntersect)).
% 144.20/29.31 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', complementInPowersetComplementIntersect)).
% 144.20/29.31 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', contraSubsetComplement)).
% 144.20/29.31 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', complementTcontraSubset)).
% 144.20/29.31 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binunionTILcontra)).
% 144.20/29.31 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binunionTIRcontra)).
% 144.20/29.31 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', omega__Cong)).
% 144.20/29.31 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', inIntersectImpInUnion)).
% 144.20/29.31 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setunion__Cong)).
% 144.20/29.31 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', inIntersectImpInUnion2)).
% 144.20/29.31 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', powerset__Cong)).
% 144.20/29.31 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', inIntersectImpInIntersectUnions)).
% 144.20/29.31 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setadjoin__Cong)).
% 144.20/29.31 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', intersectInPowersetIntersectUnions)).
% 144.20/29.31 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', emptyset__Cong)).
% 144.20/29.31 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', inComplementUnionImpNotIn1)).
% 144.20/29.31 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', inComplementUnionImpInComplement1)).
% 144.20/29.31 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binunionTE)).
% 144.20/29.31 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![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 @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binunionTEcontra)).
% 144.20/29.31 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', demorgan2a1)).
% 144.20/29.31 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', complementUnionInPowersetComplement)).
% 144.20/29.31 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', demorgan2a2)).
% 144.20/29.31 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', demorgan1a)).
% 144.20/29.31 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', subsetE2)).
% 144.20/29.31 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', subsetE)).
% 144.20/29.31 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', emptysetsubset)).
% 144.20/29.31 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', subsetI2)).
% 144.20/29.31 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', eqimpsubset1)).
% 144.20/29.31 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', eqimpsubset2)).
% 144.20/29.31 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', subsetI1)).
% 144.20/29.31 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', notsubsetI)).
% 144.20/29.31 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', subset2powerset)).
% 144.20/29.31 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setadjoinSub2)).
% 144.20/29.31 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setadjoinSub)).
% 144.20/29.31 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', subsetTrans)).
% 144.20/29.31 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', subsetRefl)).
% 144.20/29.31 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', notequalI2)).
% 144.20/29.31 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', notequalI1)).
% 144.20/29.31 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setextsub)).
% 144.20/29.31 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', powersetsubset)).
% 144.20/29.31 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', inPowerset)).
% 144.20/29.31 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', powersetE1)).
% 144.20/29.31 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', powersetI1)).
% 144.20/29.31 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', subsetemptysetimpeq)).
% 144.20/29.31 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binunionIL)).
% 144.20/29.31 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectI)).
% 144.20/29.31 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binunionRsub)).
% 144.20/29.31 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binunionLsub)).
% 144.20/29.31 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binunionE)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', binunionEcases)).
% 144.20/29.31 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binunionIR)).
% 144.20/29.31 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', upairset2IR)).
% 144.20/29.31 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectSubset5)).
% 144.20/29.31 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectRsub)).
% 144.20/29.31 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', disjointsetsI1)).
% 144.20/29.31 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectER)).
% 144.20/29.31 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectSubset3)).
% 144.20/29.31 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectSubset2)).
% 144.20/29.31 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectLsub)).
% 144.20/29.31 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectEL)).
% 144.20/29.31 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectSubset4)).
% 144.20/29.31 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', ap2apEq2)).
% 144.20/29.31 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setminusERneg)).
% 144.20/29.31 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setminusSubset2)).
% 144.20/29.31 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setminusER)).
% 144.20/29.31 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setminusEL)).
% 144.20/29.31 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setminusI)).
% 144.20/29.31 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', bs114d)).
% 144.20/29.31 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', binintersectSubset1)).
% 144.20/29.31 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setminusELneg)).
% 144.20/29.31 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', symdiffI2)).
% 144.20/29.31 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', symdiffI1)).
% 144.20/29.31 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', symdiffE)).
% 144.20/29.31 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setminusSubset1)).
% 144.20/29.31 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setminusLsub)).
% 144.20/29.31 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setminusIRneg)).
% 144.20/29.31 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setminusILneg)).
% 144.20/29.31 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', symdiffIneg1)).
% 144.20/29.31 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', singletonsubset)).
% 144.20/29.31 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', kpairp)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', kpairiskpair)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', setukpairIR)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', setukpairIL)).
% 144.20/29.31 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', secondinupair)).
% 144.20/29.31 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', symdiffIneg2)).
% 144.20/29.31 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', singletoninpowerset)).
% 144.20/29.31 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', ubforcartprodlem3)).
% 144.20/29.31 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', ubforcartprodlem2)).
% 144.20/29.31 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', ubforcartprodlem1)).
% 144.20/29.31 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', upairinpowunion)).
% 144.20/29.31 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', upairsubunion)).
% 144.20/29.31 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', upairset2E)).
% 144.20/29.31 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', singletoninpowunion)).
% 144.20/29.31 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', cartprodpairin)).
% 144.20/29.31 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setunionsingleton)).
% 144.20/29.31 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setunionsingleton2)).
% 144.20/29.31 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setunionsingleton1)).
% 144.20/29.31 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setunionE2)).
% 144.20/29.31 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', cartprodmempair)).
% 144.20/29.31 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', cartprodmempair1)).
% 144.20/29.31 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', kfstpairEq)).
% 144.20/29.31 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', theprop)).
% 144.20/29.31 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setukpairinjL1)).
% 144.20/29.31 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', singletonsuniq)).
% 144.20/29.31 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', cartprodfstin)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', setukpairinjR2)).
% 144.20/29.31 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', upairequniteq)).
% 144.20/29.31 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setukpairinjR1)).
% 144.20/29.31 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setukpairinjR12)).
% 144.20/29.31 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setukpairinjR11)).
% 144.20/29.31 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setukpairinjL)).
% 144.20/29.31 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setukpairinjL2)).
% 144.20/29.31 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setukpairinjR)).
% 144.20/29.31 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', cartprodmempaircEq)).
% 144.20/29.31 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', cartprodpairmemER)).
% 144.20/29.31 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', cartprodpairmemEL)).
% 144.20/29.31 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', cartprodsndin)).
% 144.20/29.31 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', kpairsurjEq)).
% 144.20/29.31 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', ksndpairEq)).
% 144.20/29.31 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', cartprodfstpairEq)).
% 144.20/29.31 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', cartprodpairsurjEq)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', cartprodsndpairEq)).
% 144.20/29.31 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', funcinfuncset)).
% 144.20/29.31 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', ap2p)).
% 144.20/29.31 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', infuncsetfunc)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', app)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', funcGraphProp3)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', funcGraphProp1)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', brelnall2)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', brelnall1)).
% 144.20/29.31 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', funcGraphProp2)).
% 144.20/29.31 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', ap2apEq1)).
% 144.20/29.31 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.1iUZnAgXVJ/E---3.1_2736655.p', funcext2)).
% 144.20/29.31 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', funcext)).
% 144.20/29.31 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', eqbreln)).
% 144.20/29.31 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', subbreln)).
% 144.20/29.31 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.1iUZnAgXVJ/E---3.1_2736655.p', funcGraphProp4)).
% 144.20/29.31 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', funcextLem)).
% 144.20/29.31 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', ifp)).
% 144.20/29.31 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', theeq)).
% 144.20/29.31 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', notdexE)).
% 144.20/29.31 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', prop2setI)).
% 144.20/29.31 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', quantDeMorgan4)).
% 144.20/29.31 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', quantDeMorgan3)).
% 144.20/29.31 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', quantDeMorgan2)).
% 144.20/29.31 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', quantDeMorgan1)).
% 144.20/29.31 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', vacuousDall)).
% 144.20/29.31 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', upairsetIR)).
% 144.20/29.31 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', upairsetIL)).
% 144.20/29.31 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', upairsetE)).
% 144.20/29.31 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', singletonsswitch)).
% 144.20/29.31 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', eqinunit)).
% 144.20/29.31 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', notinsingleton)).
% 144.20/29.31 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', uniqinunit)).
% 144.20/29.31 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', nonemptyImpWitness)).
% 144.20/29.31 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', subPowSU)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', setunionE)).
% 144.20/29.31 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setunionI)).
% 144.20/29.31 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', powersetE)).
% 144.20/29.31 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', emptyInPowerset)).
% 144.20/29.31 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', emptyinPowerset)).
% 144.20/29.31 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', powersetI)).
% 144.20/29.31 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setadjoinOr)).
% 144.20/29.31 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.1iUZnAgXVJ/E---3.1_2736655.p', setadjoinE)).
% 144.20/29.31 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setadjoinIR)).
% 144.20/29.31 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', emptyinunitempty)).
% 144.20/29.31 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setadjoinIL)).
% 144.20/29.31 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', nonemptyI1)).
% 144.20/29.31 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', nonemptyE1)).
% 144.20/29.31 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', noeltsimpempty)).
% 144.20/29.31 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', emptyI)).
% 144.20/29.31 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setext)).
% 144.20/29.31 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', notinemptyset)).
% 144.20/29.31 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', emptysetimpfalse)).
% 144.20/29.31 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', emptysetE)).
% 144.20/29.31 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', prop2setE)).
% 144.20/29.31 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', wellorderingAx)).
% 144.20/29.31 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', foundationAx)).
% 144.20/29.31 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.1iUZnAgXVJ/E---3.1_2736655.p', omegaIndAx)).
% 144.20/29.31 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', omegaSAx)).
% 144.20/29.31 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', omega0Ax)).
% 144.20/29.31 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setunionAx)).
% 144.20/29.31 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', powersetAx)).
% 144.20/29.31 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setadjoinAx)).
% 144.20/29.31 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', emptysetAx)).
% 144.20/29.31 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.1iUZnAgXVJ/E---3.1_2736655.p', setextAx)).
% 144.20/29.31 thf(c_0_268, 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)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[demorgan1b])).
% 144.20/29.31 thf(c_0_269, 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])).
% 144.20/29.31 thf(c_0_270, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 144.20/29.31 thf(c_0_271, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 144.20/29.31 thf(c_0_272, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 144.20/29.31 thf(c_0_273, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 144.20/29.31 thf(c_0_274, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 144.20/29.31 thf(c_0_275, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 144.20/29.31 thf(c_0_276, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 144.20/29.31 thf(c_0_277, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 144.20/29.31 thf(c_0_278, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 144.20/29.31 thf(c_0_279, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 144.20/29.31 thf(c_0_280, plain, ((iffalseProp1)<=>![X4:$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])).
% 144.20/29.31 thf(c_0_281, 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])).
% 144.20/29.31 thf(c_0_282, 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])).
% 144.20/29.31 thf(c_0_283, 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])).
% 144.20/29.31 thf(c_0_284, 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])).
% 144.20/29.31 thf(c_0_285, 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])).
% 144.20/29.31 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 144.20/29.31 thf(c_0_287, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 144.20/29.31 thf(c_0_288, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 144.20/29.31 thf(c_0_289, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 144.20/29.31 thf(c_0_290, plain, ((ex1I)<=>![X4:$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])).
% 144.20/29.31 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])).
% 144.20/29.31 thf(c_0_292, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 144.20/29.31 thf(c_0_293, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 144.20/29.31 thf(c_0_294, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 144.20/29.31 thf(c_0_295, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 144.20/29.31 thf(c_0_296, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 144.20/29.31 thf(c_0_297, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 144.20/29.31 thf(c_0_298, plain, ((apProp)<=>![X4:$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])).
% 144.20/29.31 thf(c_0_299, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 144.20/29.31 thf(c_0_300, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 144.20/29.31 thf(c_0_301, plain, ((lamProp)<=>![X4:$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])).
% 144.20/29.31 thf(c_0_302, 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])).
% 144.20/29.31 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:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 144.20/29.31 thf(c_0_304, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 144.20/29.31 thf(c_0_305, plain, ((iftrueProp2)<=>![X4:$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])).
% 144.20/29.31 thf(c_0_306, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 144.20/29.31 thf(c_0_307, plain, ((iftrueProp1)<=>![X4:$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])).
% 144.20/29.31 thf(c_0_308, 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])).
% 144.20/29.31 thf(c_0_309, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 144.20/29.31 thf(c_0_310, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 144.20/29.31 thf(c_0_311, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 144.20/29.31 thf(c_0_312, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 144.20/29.31 thf(c_0_313, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 144.20/29.31 thf(c_0_314, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 144.20/29.31 thf(c_0_315, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 144.20/29.31 thf(c_0_316, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 144.20/29.31 thf(c_0_317, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 144.20/29.31 thf(c_0_318, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 144.20/29.31 thf(c_0_319, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 144.20/29.31 thf(c_0_320, plain, ((epred1_0)<=>![X927:$i]:(?[X928:$i]:((((![X929:$i]:(((in @ X929 @ X928)=>![X930:$i]:(((in @ X930 @ X929)=>(in @ X930 @ X927)))))&![X931:$i, X932:$i]:((((in @ X931 @ X927)&(in @ X932 @ X927))=>(![X933:$i]:(((in @ X933 @ X928)=>((in @ X931 @ X933)<=>(in @ X932 @ X933))))=>((X931)=(X932))))))&![X934:$i, X935:$i]:((((in @ X934 @ X928)&(in @ X935 @ X928))=>(![X936:$i]:(((in @ X936 @ X934)=>(in @ X936 @ X935)))|![X937:$i]:(((in @ X937 @ X935)=>(in @ X937 @ X934)))))))&![X938:$i]:(((![X939:$i]:(((in @ X939 @ X938)=>(in @ X939 @ X927)))&?[X940:$i]:((in @ X940 @ X938)))=>?[X941:$i, X942:$i]:(((((in @ X941 @ X928)&(in @ X942 @ X938))&~(?[X943:$i]:(((in @ X943 @ X941)&(in @ X943 @ X938)))))&![X944:$i]:(((in @ X944 @ X928)=>(![X945:$i]:(((in @ X945 @ X944)=>(in @ X945 @ X941)))|(in @ X942 @ X944)))))))))))), introduced(definition)).
% 144.20/29.31 thf(c_0_321, negated_conjecture, ~((![X900:$i, X901:$i]:((![X902:$i]:(((in @ X902 @ X900)<=>(in @ X902 @ X901)))=>((X900)=(X901))))=>(![X903:$i]:(~(in @ X903 @ emptyset))=>(![X904:$i, X905:$i, X906:$i]:(((in @ X906 @ (setadjoin @ X904 @ X905))<=>(((X906)=(X904))|(in @ X906 @ X905))))=>(![X907:$i, X908:$i]:(((in @ X908 @ (powerset @ X907))<=>![X909:$i]:(((in @ X909 @ X908)=>(in @ X909 @ X907)))))=>(![X910:$i, X911:$i]:(((in @ X911 @ (setunion @ X910))<=>?[X912:$i]:(((in @ X911 @ X912)&(in @ X912 @ X910)))))=>((in @ emptyset @ omega)=>(![X913:$i]:(((in @ X913 @ omega)=>(in @ (setadjoin @ X913 @ X913) @ omega)))=>(![X914:$i]:((((in @ emptyset @ X914)&![X915:$i]:((((in @ X915 @ omega)&(in @ X915 @ X914))=>(in @ (setadjoin @ X915 @ X915) @ X914))))=>![X916:$i]:(((in @ X916 @ omega)=>(in @ X916 @ X914)))))=>(![X917:$i > $i > $o, X918:$i]:((![X919:$i]:(((in @ X919 @ X918)=>(exu @ (X917 @ X919))))=>?[X920:$i]:(![X921:$i]:(((in @ X921 @ X920)<=>?[X922:$i]:(((in @ X922 @ X918)&(X917 @ X922 @ X921))))))))=>(![X923:$i]:((?[X924:$i]:((in @ X924 @ X923))=>?[X925:$i]:(((in @ X925 @ X923)&~(?[X926:$i]:(((in @ X926 @ X925)&(in @ X926 @ X923))))))))=>((epred1_0)=>(![X946:$i > $o]:(((exu @ X946)=>(X946 @ (descr @ (^[Z0:$i]:(X946 @ Z0))))))=>(![X947:$i, X948:$i > $o, X949:$i]:(((in @ X949 @ X947)=>((X948 @ X949)=>(in @ X949 @ (dsetconstr @ X947 @ X948)))))=>(![X950:$i, X951:$i > $o, X952:$i]:(((in @ X952 @ (dsetconstr @ X950 @ X951))=>(in @ X952 @ X950)))=>(![X953:$i, X954:$i > $o, X955:$i]:(((in @ X955 @ (dsetconstr @ X953 @ X954))=>(X954 @ X955)))=>(![X956:$i > $o]:(((exu @ X956)=>?[X957:$i]:(((X956 @ X957)&![X958:$i]:(((X956 @ X958)=>((X957)=(X958))))))))=>(![X959:$o, X960:$i]:(((in @ X960 @ (prop2set @ ((X959))))=>(X959)))=>(![X961:$i]:(((in @ X961 @ emptyset)=>![X962:$o]:((X962))))=>(![X963:$i]:(((in @ X963 @ emptyset)=>~($true)))=>(![X964:$i]:(~(in @ X964 @ emptyset))=>(![X965:$i > $o]:(((exu @ X965)=>?[X966:$i]:((X965 @ X966))))=>(![X967:$i, X968:$i]:((![X969:$i]:(((in @ X969 @ X967)=>(in @ X969 @ X968)))=>(![X970:$i]:(((in @ X970 @ X968)=>(in @ X970 @ X967)))=>((X967)=(X968)))))=>(![X971:$i]:((![X972:$i]:(~(in @ X972 @ X971))=>((X971)=(emptyset))))=>(![X973:$i]:((![X974:$i]:(~(in @ X974 @ X973))=>((X973)=(emptyset))))=>(![X975:$i, X976:$i > $o, X977:$i]:(((in @ X977 @ X975)=>((in @ X977 @ (dsetconstr @ X975 @ X976))<=>(X976 @ X977))))=>(![X978:$i]:(((nonempty @ X978)=>?[X979:$i]:((in @ X979 @ X978))))=>(![X980:$i, X981:$i > $o, X982:$i]:(((in @ X982 @ X980)=>((X981 @ X982)=>(nonempty @ (dsetconstr @ X980 @ X981)))))=>(![X983:$i]:((?[X984:$i]:((in @ X984 @ X983))=>(nonempty @ X983)))=>(![X985:$i, X986:$i]:((in @ X985 @ (setadjoin @ X985 @ X986)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X987:$i, X988:$i, X989:$i]:(((in @ X989 @ X988)=>(in @ X989 @ (setadjoin @ X987 @ X988))))=>(![X990:$i, X991:$i, X992:$i]:(((in @ X992 @ (setadjoin @ X990 @ X991))=>![X993:$o]:(((((X992)=(X990))=>(X993))=>(((in @ X992 @ X991)=>(X993))=>(X993))))))=>(![X994:$i, X995:$i, X996:$i]:(((in @ X996 @ (setadjoin @ X994 @ X995))=>(((X996)=(X994))|(in @ X996 @ X995))))=>(![X997:$i]:(((dsetconstr @ X997 @ (^[Z0:$i]:($true)))=(X997)))=>(![X998:$i, X999:$i]:((![X1000:$i]:(((in @ X1000 @ X999)=>(in @ X1000 @ X998)))=>(in @ X999 @ (powerset @ X998))))=>(![X1001:$i]:((in @ emptyset @ (powerset @ X1001)))=>(![X1002:$i]:((in @ emptyset @ (powerset @ X1002)))=>(![X1003:$i, X1004:$i, X1005:$i]:(((in @ X1004 @ (powerset @ X1003))=>((in @ X1005 @ X1004)=>(in @ X1005 @ X1003))))=>(![X1006:$i, X1007:$i, X1008:$i]:(((in @ X1007 @ X1008)=>((in @ X1008 @ X1006)=>(in @ X1007 @ (setunion @ X1006)))))=>(![X1009:$i, X1010:$i]:(((in @ X1010 @ (setunion @ X1009))=>![X1011:$o]:((![X1012:$i]:(((in @ X1010 @ X1012)=>((in @ X1012 @ X1009)=>(X1011))))=>(X1011)))))=>(![X1013:$i, X1014:$i]:(((in @ X1014 @ X1013)=>(in @ X1014 @ (powerset @ (setunion @ X1013)))))=>(![X1015:$i > $o]:(((exu @ X1015)=>?[X1016:$i]:(![X1017:$i]:(((X1015 @ X1017)<=>((X1017)=(X1016)))))))=>(![X1018:$i]:(((nonempty @ X1018)=>?[X1019:$i]:(((in @ X1019 @ X1018)&$true))))=>(![X1020:$i, X1021:$i]:(((in @ X1020 @ (setadjoin @ X1021 @ emptyset))=>((X1020)=(X1021))))=>(![X1022:$i, X1023:$i]:((((X1022)!=(X1023))=>~(in @ X1023 @ (setadjoin @ X1022 @ emptyset))))=>(![X1024:$i, X1025:$i]:((((X1024)=(X1025))=>(in @ X1024 @ (setadjoin @ X1025 @ emptyset))))=>(![X1026:$i, X1027:$i]:(((in @ X1026 @ (setadjoin @ X1027 @ emptyset))=>(in @ X1027 @ (setadjoin @ X1026 @ emptyset))))=>(![X1028:$i, X1029:$i, X1030:$i]:(((in @ X1030 @ (setadjoin @ X1028 @ (setadjoin @ X1029 @ emptyset)))=>(((X1030)=(X1028))|((X1030)=(X1029)))))=>(![X1031:$i, X1032:$i]:((in @ X1031 @ (setadjoin @ X1031 @ (setadjoin @ X1032 @ emptyset))))=>(![X1033:$i, X1034:$i]:((in @ X1034 @ (setadjoin @ X1033 @ (setadjoin @ X1034 @ emptyset))))=>(![X1035:$i, X1036:$i > $o]:((?[X1037:$i]:(((in @ X1037 @ X1035)&(X1036 @ X1037)))=>(((dsetconstr @ X1035 @ 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iffalse]), iftrue]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), c_0_269]), powersetTI1]), in__Cong]), powersetTE1]), inCongP]), complementTI1]), c_0_270]), complementTE1]), c_0_271]), binintersectTELcontra]), c_0_272]), binintersectTERcontra]), contrasubsetT]), notdallE]), contrasubsetT1]), c_0_273]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), c_0_274]), binunionTILcontra]), c_0_275]), binunionTIRcontra]), omega__Cong]), inIntersectImpInUnion]), setunion__Cong]), inIntersectImpInUnion2]), powerset__Cong]), inIntersectImpInIntersectUnions]), setadjoin__Cong]), intersectInPowersetIntersectUnions]), emptyset__Cong]), inComplementUnionImpNotIn1]), c_0_276]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), subsetE2]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), notsubsetI]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), setextsub]), c_0_277]), c_0_278]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), binunionIL]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binintersectSubset5]), binintersectRsub]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset4]), ap2apEq2]), c_0_279]), c_0_280]), c_0_281]), c_0_282]), c_0_283]), c_0_284]), c_0_285]), setminusERneg]), setminusSubset2]), setminusER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), setminusELneg]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), symdiffIneg1]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), singletoninpowerset]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), cartprodpairin]), c_0_286]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), c_0_287]), kfstpairEq]), theprop]), c_0_288]), setukpairinjL1]), singletonsuniq]), c_0_289]), c_0_290]), cartprodfstin]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), setukpairinjR]), cartprodmempaircEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), c_0_291]), cartprodfstpairEq]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), cartprodpairsurjEq]), cartprodsndpairEq]), c_0_297]), funcinfuncset]), ap2p]), infuncsetfunc]), app]), c_0_298]), c_0_299]), c_0_300]), c_0_301]), funcGraphProp3]), funcGraphProp1]), c_0_302]), brelnall2]), brelnall1]), c_0_303]), c_0_304]), funcGraphProp2]), ap2apEq1]), funcext2]), funcext]), eqbreln]), subbreln]), funcGraphProp4]), funcextLem]), c_0_305]), c_0_306]), ifp]), theeq]), c_0_307]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_308]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), nonemptyImpWitness]), c_0_309]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_310]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_311]), nonemptyE1]), c_0_312]), noeltsimpempty]), emptyI]), setext]), c_0_313]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), c_0_318]), wellorderingAx]), foundationAx]), c_0_319]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_320])).
% 144.20/29.31 thf(c_0_322, negated_conjecture, ![X1745:$i, X1746:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1758:$i, X1759:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1767:$i, X1768:$i > $i > $o, X1769:$i, X1772:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1779:$i, X1780:$i > $o, X1781:$i, X1782:$i > $o, X1783:$i, X1784:$i, X1785:$i > $o, X1786:$i, X1787:$i, X1788:$i > $o, X1789:$i, X1790:$i > $o, X1792:$i, X1793:$o, X1794:$i, X1795:$i, X1796:$o, X1797:$i, X1798:$i, X1799:$i > $o, X1801:$i, X1802:$i, X1805:$i, X1807:$i, X1809:$i, X1810:$i > $o, X1811:$i, X1812:$i, X1814:$i, X1815:$i > $o, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$o, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$o, X1847:$i, X1848:$i, X1849:$i > $o, X1851:$i, X1852:$i, X1853:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i > $o, X1872:$i, X1873:$i > $o, X1874:$i, X1875:$i, X1876:$i > $o, X1877:$i, X1879:$i, X1880:$i > $o, X1882:$i, X1883:$i, X1884:$i > $o, X1886:$i, X1887:$i, X1888:$i > $o, X1889:$i, X1891:$o, X1892:$i, X1893:$i > $o, X1895:$i, X1896:$i, X1897:$i > $o, X1898:$i, X1900:$i > $o, X1901:$i, X1903:$i > $o, X1904:$i, X1907:$i > $o, X1908:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i > $o, X1919:$i, X1920:$i, X1921:$i > $o, X1922:$i > $o, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i > $o, X1934:$i, X1935:$i, X1936:$i > $o, X1937:$i > $o, X1940:$i, X1941:$i, X1942:$i > $o, X1943:$i > $o, X1946:$i, X1947:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i > $o, X1994:$i, X1995:$i > $o, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$o, X2008:$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, 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:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$o, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$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, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i > $o, X2150:$i, X2151:$i, X2152:$i > $o, X2154:$i, X2155:$i > $o, X2156:$i, X2158:$i, X2159:$i > $o, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i > $i > $o, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i > $i > $o, X2240:$i, X2241:$i, X2242:$i > $i > $o, X2243:$i, X2244:$i, X2245:$i > $i > $o, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i > $i > $o, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i > $i > $o, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i > $i > $o, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i > $i, X2289:$i, X2290:$i, X2291:$i > $i, X2293:$i, X2294:$i, X2295:$i > $i, X2297:$i, X2298:$i, X2299:$i, X2300:$i > $o, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i > $o, X2310:$i, X2311:$i, X2312:$i > $o, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i > $i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i > $i, X2384:$i, X2385:$i, X2386:$i > $i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$o, X2394:$i, X2395:$i, X2396:$i, X2397:$o, X2398:$i, X2399:$i, X2400:$i, X2401:$o, X2402:$i, X2403:$i, X2404:$i, X2405:$o, X2406:$i, X2407:$i, X2408:$i, X2409:$o, X2410:$i, X2411:$i, X2412:$i, X2413:$o, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$o, X2420:$i, X2421:$i, X2422:$i, X2423:$o, X2424:$i, X2425:$i, X2426:$i, X2427:$o, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2448:$i, X2449:$i, X2450:$i, X2452:$i, X2453:$i, X2454:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$o, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i]:((((~(in @ (esk1_2 @ X1745 @ X1746) @ X1745)|~(in @ (esk1_2 @ X1745 @ X1746) @ X1746)|((X1745)=(X1746)))&((in @ (esk1_2 @ X1745 @ X1746) @ X1745)|(in @ (esk1_2 @ X1745 @ X1746) @ X1746)|((X1745)=(X1746))))&(~(in @ X1748 @ emptyset)&(((~(in @ X1751 @ (setadjoin @ X1749 @ X1750))|(((X1751)=(X1749))|(in @ X1751 @ X1750)))&((((X1751)!=(X1749))|(in @ X1751 @ (setadjoin @ X1749 @ X1750)))&(~(in @ X1751 @ X1750)|(in @ X1751 @ (setadjoin @ X1749 @ X1750)))))&(((~(in @ X1753 @ (powerset @ X1752))|(~(in @ X1754 @ X1753)|(in @ X1754 @ X1752)))&(((in @ (esk2_2 @ X1755 @ X1756) @ X1756)|(in @ X1756 @ (powerset @ X1755)))&(~(in @ (esk2_2 @ X1755 @ X1756) @ X1755)|(in @ X1756 @ (powerset @ X1755)))))&(((((in @ X1759 @ (esk3_2 @ X1758 @ X1759))|~(in @ X1759 @ (setunion @ X1758)))&((in @ (esk3_2 @ X1758 @ X1759) @ X1758)|~(in @ X1759 @ (setunion @ X1758))))&(~(in @ X1762 @ X1763)|~(in @ X1763 @ X1761)|(in @ X1762 @ (setunion @ X1761))))&((in @ emptyset @ omega)&((~(in @ X1764 @ omega)|(in @ (setadjoin @ X1764 @ X1764) @ omega))&(((((in @ (esk4_1 @ X1765) @ omega)|~(in @ emptyset @ X1765)|(~(in @ X1767 @ omega)|(in @ X1767 @ X1765)))&((in @ (esk4_1 @ X1765) @ X1765)|~(in @ emptyset @ X1765)|(~(in @ X1767 @ omega)|(in @ X1767 @ X1765))))&(~(in @ (setadjoin @ (esk4_1 @ X1765) @ (esk4_1 @ X1765)) @ X1765)|~(in @ emptyset @ X1765)|(~(in @ X1767 @ omega)|(in @ X1767 @ X1765))))&((((((in @ (esk7_3 @ X1768 @ X1769 @ X1772) @ X1769)|~(in @ X1772 @ (esk6_2 @ X1768 @ X1769))|(in @ (esk5_2 @ X1768 @ X1769) @ X1769))&((X1768 @ (esk7_3 @ X1768 @ X1769 @ X1772) @ X1772)|~(in @ X1772 @ (esk6_2 @ X1768 @ X1769))|(in @ (esk5_2 @ X1768 @ X1769) @ X1769)))&(~(in @ X1775 @ X1769)|~(X1768 @ X1775 @ X1774)|(in @ X1774 @ (esk6_2 @ X1768 @ X1769))|(in @ (esk5_2 @ X1768 @ X1769) @ X1769)))&((((in @ (esk7_3 @ X1768 @ X1769 @ X1772) @ X1769)|~(in @ X1772 @ (esk6_2 @ X1768 @ X1769))|~(exu @ (X1768 @ (esk5_2 @ X1768 @ X1769))))&((X1768 @ (esk7_3 @ X1768 @ X1769 @ X1772) @ X1772)|~(in @ X1772 @ (esk6_2 @ X1768 @ X1769))|~(exu @ (X1768 @ (esk5_2 @ X1768 @ X1769)))))&(~(in @ X1775 @ X1769)|~(X1768 @ X1775 @ X1774)|(in @ X1774 @ (esk6_2 @ X1768 @ X1769))|~(exu @ (X1768 @ (esk5_2 @ X1768 @ X1769))))))&((((in @ (esk8_1 @ X1776) @ X1776)|~(in @ X1777 @ X1776))&(~(in @ X1779 @ (esk8_1 @ X1776))|~(in @ X1779 @ X1776)|~(in @ X1777 @ X1776)))&((epred1_0)&((~(exu @ X1780)|(X1780 @ (descr @ X1780)))&((~(in @ X1783 @ X1781)|(~(X1782 @ X1783)|(in @ X1783 @ (dsetconstr @ X1781 @ X1782))))&((~(in @ X1786 @ (dsetconstr @ X1784 @ X1785))|(in @ X1786 @ X1784))&((~(in @ X1789 @ (dsetconstr @ X1787 @ X1788))|(X1788 @ X1789))&((((X1790 @ (esk9_1 @ X1790))|~(exu @ X1790))&(~(X1790 @ X1792)|((esk9_1 @ X1790)=(X1792))|~(exu @ X1790)))&((~(in @ X1794 @ (prop2set @ ((X1793))))|(X1793))&((~(in @ X1795 @ emptyset)|(X1796))&((~(in @ X1797 @ emptyset)|~($true))&(~(in @ X1798 @ emptyset)&((~(exu @ X1799)|(X1799 @ (esk10_1 @ X1799)))&(((((in @ (esk12_2 @ X1801 @ X1802) @ X1802)|((X1801)=(X1802))|(in @ (esk11_2 @ 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@ X2362 @ (funcSet @ X2359 @ X2360))|~(in @ X2361 @ (funcSet @ X2359 @ X2360))))&((~(in @ X2366 @ (funcSet @ X2364 @ X2365))|(~(in @ X2367 @ X2364)|((ap @ X2364 @ X2365 @ X2366 @ X2367)=(ap @ X2364 @ X2365 @ X2366 @ X2367))))&((~(func @ X2368 @ X2369 @ X2370)|(~(in @ X2371 @ X2368)|((ap @ X2368 @ X2369 @ X2370 @ X2371)=(ap @ X2368 @ X2369 @ X2370 @ X2371))))&((((in @ (esk64_3 @ X2372 @ X2373 @ X2374) @ X2372)|(~(in @ X2376 @ X2372)|((ap @ X2372 @ X2373 @ (lam @ X2372 @ X2373 @ X2374) @ X2376)=(X2374 @ X2376))))&(~(in @ (X2374 @ (esk64_3 @ X2372 @ X2373 @ X2374)) @ X2373)|(~(in @ X2376 @ X2372)|((ap @ X2372 @ X2373 @ (lam @ X2372 @ X2373 @ X2374) @ X2376)=(X2374 @ X2376)))))&((~(func @ X2377 @ X2378 @ X2379)|((lam @ X2377 @ X2378 @ (ap @ X2377 @ X2378 @ X2379))=(X2379)))&((((in @ (esk65_3 @ X2380 @ X2381 @ X2382) @ X2380)|((lam @ X2380 @ X2381 @ X2382)=(lam @ X2380 @ X2381 @ X2382)))&(~(in @ (X2382 @ (esk65_3 @ X2380 @ X2381 @ X2382)) @ X2381)|((lam @ X2380 @ X2381 @ X2382)=(lam @ X2380 @ X2381 @ X2382))))&((((in @ (esk66_3 @ X2384 @ X2385 @ X2386) @ X2384)|(~(in @ X2388 @ X2384)|((ap @ X2384 @ X2385 @ (lam @ X2384 @ X2385 @ X2386) @ X2388)=(X2386 @ X2388))))&(~(in @ (X2386 @ (esk66_3 @ X2384 @ X2385 @ X2386)) @ X2385)|(~(in @ X2388 @ X2384)|((ap @ X2384 @ X2385 @ (lam @ X2384 @ X2385 @ X2386) @ X2388)=(X2386 @ X2388)))))&((~(in @ X2391 @ (funcSet @ X2389 @ X2390))|((lam @ X2389 @ X2390 @ (ap @ X2389 @ X2390 @ X2391))=(X2391)))&((~(in @ X2394 @ X2392)|(~(in @ X2395 @ X2392)|((X2393)|(in @ X2395 @ (dsetconstr @ X2392 @ (^[Z0:$i]:((((((X2393))&(((Z0)=(X2394)))))|(((~((X2393)))&(((Z0)=(X2395)))))))))))))&((~(in @ X2398 @ X2396)|(~(in @ X2399 @ X2396)|((X2397)|((dsetconstr @ X2396 @ (^[Z0:$i]:((((((X2397))&(((Z0)=(X2398)))))|(((~((X2397)))&(((Z0)=(X2399)))))))))=(setadjoin @ X2399 @ emptyset)))))&((~(in @ X2402 @ X2400)|(~(in @ X2403 @ X2400)|(~(X2401)|(in @ X2402 @ (dsetconstr @ X2400 @ (^[Z0:$i]:((((((X2401))&(((Z0)=(X2402)))))|(((~((X2401)))&(((Z0)=(X2403)))))))))))))&((~(in @ X2406 @ X2404)|(~(in @ X2407 @ X2404)|(~(X2405)|((dsetconstr @ X2404 @ (^[Z0:$i]:((((((X2405))&(((Z0)=(X2406)))))|(((~((X2405)))&(((Z0)=(X2407)))))))))=(setadjoin @ X2406 @ emptyset)))))&((~(in @ X2410 @ X2408)|(~(in @ X2411 @ X2408)|(singleton @ (dsetconstr @ X2408 @ (^[Z0:$i]:((((((X2409))&(((Z0)=(X2410)))))|(((~((X2409)))&(((Z0)=(X2411))))))))))))&((~(in @ X2414 @ X2412)|(~(in @ X2415 @ X2412)|(in @ (if @ X2412 @ ((X2413)) @ X2414 @ X2415) @ X2412)))&((~(singleton @ X2416)|(~(in @ X2417 @ X2416)|((setunion @ X2416)=(X2417))))&((~(in @ X2420 @ X2418)|(~(in @ X2421 @ X2418)|(~(X2419)|((if @ X2418 @ ((X2419)) @ X2420 @ X2421)=(X2420)))))&((~(in @ X2424 @ X2422)|(~(in @ X2425 @ X2422)|((X2423)|((if @ X2422 @ ((X2423)) @ X2424 @ X2425)=(X2425)))))&((~(in @ X2428 @ X2426)|(~(in @ X2429 @ X2426)|(in @ (if @ X2426 @ ((X2427)) @ X2428 @ X2429) @ (setadjoin @ X2428 @ (setadjoin @ X2429 @ emptyset)))))&((~(in @ X2431 @ (powerset @ X2430))|(~(in @ X2432 @ (powerset @ X2430))|(in @ (binintersect @ X2431 @ X2432) @ (powerset @ X2430))))&((~(in @ X2434 @ (powerset @ X2433))|(~(in @ X2435 @ (powerset @ X2433))|(in @ (binunion @ X2434 @ X2435) @ (powerset @ X2433))))&((~(in @ X2437 @ (powerset @ X2436))|(in @ (powerset @ X2437) @ (powerset @ (powerset @ X2436))))&((~(in @ X2439 @ (powerset @ X2438))|(~(in @ X2440 @ (powerset @ X2438))|(in @ (setminus @ X2439 @ X2440) @ (powerset @ X2438))))&((~(in @ X2442 @ (powerset @ X2441))|(in @ (setminus @ X2441 @ X2442) @ (powerset @ X2441)))&(((((in @ (esk68_3 @ X2443 @ X2444 @ X2445) @ X2443)|((X2444)=(X2445))|(in @ (esk67_3 @ X2443 @ X2444 @ X2445) @ X2443)|~(in @ X2445 @ (powerset @ X2443))|~(in @ X2444 @ (powerset @ X2443)))&(((in @ (esk68_3 @ X2443 @ X2444 @ X2445) @ X2445)|((X2444)=(X2445))|(in @ (esk67_3 @ X2443 @ X2444 @ X2445) @ X2443)|~(in @ X2445 @ (powerset @ X2443))|~(in @ X2444 @ (powerset @ X2443)))&(~(in @ (esk68_3 @ X2443 @ X2444 @ X2445) @ X2444)|((X2444)=(X2445))|(in @ (esk67_3 @ X2443 @ X2444 @ X2445) @ X2443)|~(in @ X2445 @ (powerset @ X2443))|~(in @ X2444 @ (powerset @ X2443)))))&((((in @ (esk68_3 @ X2443 @ X2444 @ X2445) @ X2443)|((X2444)=(X2445))|(in @ (esk67_3 @ X2443 @ X2444 @ X2445) @ X2444)|~(in @ X2445 @ (powerset @ X2443))|~(in @ X2444 @ (powerset @ X2443)))&(((in @ (esk68_3 @ X2443 @ X2444 @ X2445) @ X2445)|((X2444)=(X2445))|(in @ (esk67_3 @ X2443 @ X2444 @ X2445) @ X2444)|~(in @ X2445 @ (powerset @ X2443))|~(in @ X2444 @ (powerset @ X2443)))&(~(in @ (esk68_3 @ X2443 @ X2444 @ X2445) @ X2444)|((X2444)=(X2445))|(in @ (esk67_3 @ X2443 @ X2444 @ X2445) @ X2444)|~(in @ X2445 @ (powerset @ X2443))|~(in @ X2444 @ (powerset @ X2443)))))&(((in @ (esk68_3 @ X2443 @ X2444 @ X2445) @ X2443)|((X2444)=(X2445))|~(in @ (esk67_3 @ X2443 @ X2444 @ X2445) @ X2445)|~(in @ X2445 @ (powerset @ X2443))|~(in @ X2444 @ (powerset @ X2443)))&(((in @ (esk68_3 @ X2443 @ X2444 @ X2445) @ X2445)|((X2444)=(X2445))|~(in @ (esk67_3 @ X2443 @ X2444 @ X2445) @ X2445)|~(in @ X2445 @ (powerset @ X2443))|~(in @ X2444 @ (powerset @ X2443)))&(~(in @ (esk68_3 @ X2443 @ X2444 @ X2445) @ X2444)|((X2444)=(X2445))|~(in @ (esk67_3 @ X2443 @ X2444 @ X2445) @ X2445)|~(in @ X2445 @ (powerset @ X2443))|~(in @ X2444 @ (powerset @ X2443)))))))&((((in @ (esk69_3 @ X2448 @ X2449 @ X2450) @ X2448)|(subset @ X2449 @ X2450)|~(in @ X2450 @ (powerset @ X2448))|~(in @ X2449 @ (powerset @ X2448)))&(((in @ (esk69_3 @ X2448 @ X2449 @ X2450) @ X2449)|(subset @ X2449 @ X2450)|~(in @ X2450 @ (powerset @ X2448))|~(in @ X2449 @ (powerset @ X2448)))&(~(in @ (esk69_3 @ X2448 @ X2449 @ X2450) @ X2450)|(subset @ X2449 @ X2450)|~(in @ X2450 @ (powerset @ X2448))|~(in @ X2449 @ (powerset @ X2448)))))&((((in @ (esk70_3 @ X2452 @ X2453 @ X2454) @ X2452)|(in @ X2453 @ (powerset @ X2454))|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))&(((in @ (esk70_3 @ X2452 @ X2453 @ X2454) @ X2453)|(in @ X2453 @ (powerset @ X2454))|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))&(~(in @ (esk70_3 @ X2452 @ X2453 @ X2454) @ X2454)|(in @ X2453 @ (powerset @ X2454))|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))))&((~(in @ X2457 @ (powerset @ X2456))|(~(in @ X2458 @ (powerset @ X2456))|(~(in @ X2459 @ X2456)|(~(in @ X2457 @ (powerset @ X2458))|(~(in @ X2459 @ X2457)|(in @ X2459 @ X2458))))))&((~(in @ X2461 @ (powerset @ X2460))|(~(in @ X2462 @ X2460)|(~(in @ X2462 @ X2461)|~(in @ X2462 @ (setminus @ X2460 @ X2461)))))&((~(in @ X2464 @ (powerset @ X2463))|(~(in @ X2465 @ X2463)|((in @ X2465 @ (setminus @ X2463 @ X2464))|(in @ X2465 @ X2464))))&((~(in @ X2467 @ (powerset @ X2466))|(~(in @ X2468 @ (powerset @ X2466))|(~(in @ X2469 @ X2466)|((in @ X2469 @ X2467)|~(in @ X2469 @ (binintersect @ X2467 @ X2468))))))&((~(in @ X2471 @ (powerset @ X2470))|(~(in @ X2472 @ (powerset @ X2470))|(~(in @ X2473 @ X2470)|((in @ X2473 @ X2472)|~(in @ X2473 @ (binintersect @ X2471 @ X2472))))))&((~(in @ X2475 @ (powerset @ X2474))|(~(in @ X2476 @ (powerset @ X2474))|(~(in @ X2477 @ X2474)|(~(subset @ X2475 @ (setminus @ X2474 @ X2476))|(~(in @ X2477 @ X2476)|~(in @ X2477 @ X2475))))))&((~(in @ X2479 @ (powerset @ X2478))|(~(in @ X2480 @ (powerset @ X2478))|(~(in @ X2481 @ X2478)|(~(subset @ X2479 @ X2480)|((in @ X2481 @ X2480)|~(in @ X2481 @ X2479))))))&((~(in @ X2483 @ (powerset @ X2482))|(~(in @ X2484 @ (powerset @ X2482))|(~(subset @ X2483 @ X2484)|(subset @ (setminus @ X2482 @ X2484) @ (setminus @ X2482 @ X2483)))))&((~(in @ X2486 @ (powerset @ X2485))|(~(in @ X2487 @ (powerset @ X2485))|(~(subset @ (setminus @ X2485 @ X2487) @ (setminus @ X2485 @ X2486))|(subset @ X2486 @ X2487))))&((~(in @ X2489 @ (powerset @ X2488))|(~(in @ X2490 @ X2488)|(~(in @ X2490 @ X2489)|(in @ X2490 @ (setminus @ X2488 @ (setminus @ X2488 @ X2489))))))&((~(in @ X2492 @ (powerset @ X2491))|(~(in @ X2493 @ X2491)|(~(in @ X2493 @ (setminus @ X2491 @ (setminus @ X2491 @ X2492)))|(in @ X2493 @ X2492))))&((~(in @ X2495 @ (powerset @ X2494))|(subset @ X2495 @ (setminus @ X2494 @ (setminus @ X2494 @ X2495))))&((~(in @ X2497 @ (powerset @ X2496))|(subset @ (setminus @ X2496 @ (setminus @ X2496 @ X2497)) @ X2497))&((~(in @ X2499 @ (powerset @ X2498))|((X2499)=(setminus @ X2498 @ (setminus @ X2498 @ X2499))))&((~(in @ X2501 @ (powerset @ X2500))|(~(in @ X2502 @ (powerset @ X2500))|(~(in @ X2503 @ X2500)|(~(in @ X2503 @ (setminus @ X2500 @ X2501))|~(in @ X2503 @ (binintersect @ X2501 @ X2502))))))&((~(in @ X2505 @ (powerset @ X2504))|(~(in @ X2506 @ (powerset @ X2504))|(~(in @ X2507 @ X2504)|(~(in @ X2507 @ (setminus @ X2504 @ X2505))|(in @ X2507 @ (setminus @ X2504 @ (binintersect @ X2505 @ X2506)))))))&((~(in @ X2509 @ (powerset @ X2508))|(~(in @ X2510 @ (powerset @ X2508))|(subset @ (setminus @ X2508 @ X2509) @ (setminus @ X2508 @ (binintersect @ X2509 @ X2510)))))&((~(in @ X2512 @ (powerset @ X2511))|(~(in @ X2513 @ (powerset @ X2511))|(in @ (setminus @ X2511 @ X2512) @ (powerset @ (setminus @ X2511 @ (binintersect @ X2512 @ X2513))))))&((~(in @ X2515 @ (powerset @ X2514))|(~(in @ X2516 @ (powerset @ X2514))|(~(subset @ X2515 @ (setminus @ X2514 @ X2516))|(~(in @ X2517 @ X2514)|(~(in @ X2517 @ X2516)|(in @ X2517 @ (setminus @ X2514 @ X2515)))))))&((~(in @ X2519 @ (powerset @ X2518))|(~(in @ X2520 @ (powerset @ X2518))|(~(subset @ X2519 @ (setminus @ X2518 @ X2520))|(subset @ X2520 @ (setminus @ X2518 @ X2519)))))&((~(in @ X2522 @ (powerset @ X2521))|(~(in @ X2523 @ (powerset @ X2521))|(~(in @ X2524 @ X2521)|((in @ X2524 @ (binunion @ X2522 @ X2523))|~(in @ X2524 @ X2522)))))&((~(in @ X2526 @ (powerset @ X2525))|(~(in @ X2527 @ (powerset @ X2525))|(~(in @ X2528 @ X2525)|((in @ X2528 @ (binunion @ X2526 @ X2527))|~(in @ X2528 @ X2527)))))&((~(in @ X2530 @ (powerset @ X2529))|(~(in @ X2531 @ (powerset @ X2529))|(~(in @ X2532 @ (powerset @ X2529))|(~(in @ X2533 @ X2529)|(~(in @ X2533 @ (binintersect @ X2530 @ X2531))|(in @ X2533 @ (binunion @ X2530 @ X2532)))))))&((~(in @ X2535 @ (powerset @ X2534))|(~(in @ X2536 @ (powerset @ X2534))|(~(in @ X2537 @ (powerset @ X2534))|(~(in @ X2538 @ X2534)|(~(in @ X2538 @ (binintersect @ X2535 @ X2536))|(in @ X2538 @ (binunion @ X2536 @ X2537)))))))&((~(in @ X2540 @ (powerset @ X2539))|(~(in @ X2541 @ (powerset @ X2539))|(~(in @ X2542 @ (powerset @ X2539))|(~(in @ X2543 @ X2539)|(~(in @ X2543 @ (binintersect @ X2540 @ X2541))|(in @ X2543 @ (binintersect @ (binunion @ X2540 @ X2542) @ (binunion @ X2541 @ X2542))))))))&((~(in @ X2545 @ (powerset @ X2544))|(~(in @ X2546 @ (powerset @ X2544))|(~(in @ X2547 @ (powerset @ X2544))|(in @ (binintersect @ X2545 @ X2546) @ (powerset @ (binintersect @ (binunion @ X2545 @ X2547) @ (binunion @ X2546 @ X2547)))))))&((~(in @ X2549 @ (powerset @ X2548))|(~(in @ X2550 @ (powerset @ X2548))|(~(in @ X2551 @ X2548)|(~(in @ X2551 @ (setminus @ X2548 @ (binunion @ X2549 @ X2550)))|~(in @ X2551 @ X2549)))))&((~(in @ X2553 @ (powerset @ X2552))|(~(in @ X2554 @ (powerset @ X2552))|(~(in @ X2555 @ X2552)|(~(in @ X2555 @ (setminus @ X2552 @ (binunion @ X2553 @ X2554)))|(in @ X2555 @ (setminus @ X2552 @ X2553))))))&(((((in @ X2560 @ X2558)|(X2559)|(in @ X2560 @ X2557)|~(in @ X2560 @ (binunion @ X2557 @ X2558))|~(in @ X2560 @ X2556)|~(in @ X2558 @ (powerset @ X2556))|~(in @ X2557 @ (powerset @ X2556)))&(~(X2559)|(X2559)|(in @ X2560 @ X2557)|~(in @ X2560 @ (binunion @ X2557 @ X2558))|~(in @ X2560 @ X2556)|~(in @ X2558 @ (powerset @ X2556))|~(in @ X2557 @ (powerset @ X2556))))&(((in @ X2560 @ X2558)|(X2559)|~(X2559)|~(in @ X2560 @ (binunion @ X2557 @ X2558))|~(in @ X2560 @ X2556)|~(in @ X2558 @ (powerset @ X2556))|~(in @ X2557 @ (powerset @ X2556)))&(~(X2559)|(X2559)|~(X2559)|~(in @ X2560 @ (binunion @ X2557 @ X2558))|~(in @ X2560 @ X2556)|~(in @ X2558 @ (powerset @ X2556))|~(in @ X2557 @ (powerset @ X2556)))))&((~(in @ X2562 @ (powerset @ X2561))|(~(in @ X2563 @ (powerset @ X2561))|(~(in @ X2564 @ X2561)|((in @ X2564 @ X2562)|((in @ X2564 @ X2563)|~(in @ X2564 @ (binunion @ X2562 @ X2563)))))))&((~(in @ X2566 @ (powerset @ X2565))|(~(in @ X2567 @ (powerset @ X2565))|(~(in @ X2568 @ X2565)|(~(in @ X2568 @ (setminus @ X2565 @ (binunion @ X2566 @ X2567)))|(in @ X2568 @ (setminus @ X2565 @ X2566))))))&((~(in @ X2570 @ (powerset @ X2569))|(~(in @ X2571 @ (powerset @ X2569))|(in @ (setminus @ X2569 @ (binunion @ X2570 @ X2571)) @ (powerset @ (setminus @ X2569 @ X2570)))))&((~(in @ X2573 @ (powerset @ X2572))|(~(in @ X2574 @ (powerset @ X2572))|(~(in @ X2575 @ X2572)|(~(in @ X2575 @ (setminus @ X2572 @ (binunion @ X2573 @ X2574)))|(in @ X2575 @ (setminus @ X2572 @ X2574))))))&((~(in @ X2577 @ (powerset @ X2576))|(~(in @ X2578 @ (powerset @ X2576))|(~(in @ X2579 @ X2576)|(~(in @ X2579 @ (setminus @ X2576 @ (binintersect @ X2577 @ X2578)))|(in @ X2579 @ (binunion @ (setminus @ X2576 @ X2577) @ (setminus @ X2576 @ X2578)))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ esk71_0)&((in @ esk74_0 @ (binunion @ (setminus @ esk71_0 @ esk72_0) @ (setminus @ esk71_0 @ esk73_0)))&~(in @ esk74_0 @ (setminus @ esk71_0 @ (binintersect @ esk72_0 @ esk73_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_321])])])])])])])).
% 144.20/29.32 thf(c_0_323, negated_conjecture, ![X5:$i, X4:$i, X3:$i, X2:$i]:(((in @ X5 @ (setminus @ X3 @ (binintersect @ X2 @ X4)))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((in @ X5 @ X3))|~((in @ X5 @ (setminus @ X3 @ X2))))), inference(split_conjunct,[status(thm)],[c_0_322])).
% 144.20/29.32 thf(c_0_324, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_322])).
% 144.20/29.32 thf(c_0_325, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ (binintersect @ esk72_0 @ esk73_0)))), inference(split_conjunct,[status(thm)],[c_0_322])).
% 144.20/29.32 thf(c_0_326, negated_conjecture, ![X2:$i, X5:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ (binintersect @ X4 @ X5)))|~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X5 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3))))), inference(csr,[status(thm)],[c_0_323, c_0_324])).
% 144.20/29.32 thf(c_0_327, negated_conjecture, (in @ esk73_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_322])).
% 144.20/29.32 thf(c_0_328, negated_conjecture, (in @ esk72_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_322])).
% 144.20/29.32 thf(c_0_329, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_322])).
% 144.20/29.32 thf(c_0_330, negated_conjecture, (in @ esk74_0 @ esk71_0), inference(split_conjunct,[status(thm)],[c_0_322])).
% 144.20/29.32 thf(c_0_331, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|(in @ X2 @ X4)|~((in @ X2 @ (binunion @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_322])])])).
% 144.20/29.32 thf(c_0_332, negated_conjecture, (in @ esk74_0 @ (binunion @ (setminus @ esk71_0 @ esk72_0) @ (setminus @ esk71_0 @ esk73_0))), inference(split_conjunct,[status(thm)],[c_0_322])).
% 144.20/29.32 thf(c_0_333, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ esk72_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325, c_0_326]), c_0_327]), c_0_328])])).
% 144.20/29.32 thf(c_0_334, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X4)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_322])).
% 144.20/29.32 thf(c_0_335, negated_conjecture, (in @ esk74_0 @ (binintersect @ esk72_0 @ esk73_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325, c_0_329]), c_0_330])])).
% 144.20/29.32 thf(c_0_336, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_322])).
% 144.20/29.32 thf(c_0_337, negated_conjecture, (in @ esk74_0 @ (setminus @ esk71_0 @ esk73_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_331, c_0_332]), c_0_333])).
% 144.20/29.32 thf(c_0_338, negated_conjecture, (in @ esk74_0 @ esk73_0), inference(spm,[status(thm)],[c_0_334, c_0_335])).
% 144.20/29.32 thf(c_0_339, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_336, c_0_337]), c_0_338])]), ['proof']).
% 144.20/29.32 % SZS output end CNFRefutation
% 144.20/29.32 % Parsed axioms : 579
% 144.20/29.32 % Removed by relevancy pruning/SinE : 311
% 144.20/29.32 % Initial clauses : 433
% 144.20/29.32 % Removed in clause preprocessing : 37
% 144.20/29.32 % Initial clauses in saturation : 396
% 144.20/29.32 % Processed clauses : 1037
% 144.20/29.32 % ...of these trivial : 13
% 144.20/29.32 % ...subsumed : 162
% 144.20/29.32 % ...remaining for further processing : 862
% 144.20/29.32 % Other redundant clauses eliminated : 52
% 144.20/29.32 % Clauses deleted for lack of memory : 0
% 144.20/29.32 % Backward-subsumed : 1
% 144.20/29.32 % Backward-rewritten : 18
% 144.20/29.32 % Generated clauses : 11034
% 144.20/29.32 % ...of the previous two non-redundant : 10643
% 144.20/29.32 % ...aggressively subsumed : 0
% 144.20/29.32 % Contextual simplify-reflections : 10
% 144.20/29.32 % Paramodulations : 10947
% 144.20/29.32 % Factorizations : 2
% 144.20/29.32 % NegExts : 0
% 144.20/29.32 % Equation resolutions : 59
% 144.20/29.32 % Disequality decompositions : 0
% 144.20/29.32 % Total rewrite steps : 461
% 144.20/29.32 % ...of those cached : 328
% 144.20/29.32 % Propositional unsat checks : 0
% 144.20/29.32 % Propositional check models : 0
% 144.20/29.32 % Propositional check unsatisfiable : 0
% 144.20/29.32 % Propositional clauses : 0
% 144.20/29.32 % Propositional clauses after purity: 0
% 144.20/29.32 % Propositional unsat core size : 0
% 144.20/29.32 % Propositional preprocessing time : 0.000
% 144.20/29.32 % Propositional encoding time : 0.000
% 144.20/29.32 % Propositional solver time : 0.000
% 144.20/29.32 % Success case prop preproc time : 0.000
% 144.20/29.32 % Success case prop encoding time : 0.000
% 144.20/29.32 % Success case prop solver time : 0.000
% 144.20/29.32 % Current number of processed clauses : 483
% 144.20/29.32 % Positive orientable unit clauses : 72
% 144.20/29.32 % Positive unorientable unit clauses: 0
% 144.20/29.32 % Negative unit clauses : 10
% 144.20/29.32 % Non-unit-clauses : 401
% 144.20/29.32 % Current number of unprocessed clauses: 10247
% 144.20/29.32 % ...number of literals in the above : 41631
% 144.20/29.32 % Current number of archived formulas : 0
% 144.20/29.32 % Current number of archived clauses : 363
% 144.20/29.32 % Clause-clause subsumption calls (NU) : 86070
% 144.20/29.32 % Rec. Clause-clause subsumption calls : 38760
% 144.20/29.32 % Non-unit clause-clause subsumptions : 111
% 144.20/29.32 % Unit Clause-clause subsumption calls : 959
% 144.20/29.32 % Rewrite failures with RHS unbound : 0
% 144.20/29.32 % BW rewrite match attempts : 38
% 144.20/29.32 % BW rewrite match successes : 11
% 144.20/29.32 % Condensation attempts : 1037
% 144.20/29.32 % Condensation successes : 10
% 144.20/29.32 % Termbank termtop insertions : 262086
% 144.20/29.32 % Search garbage collected termcells : 27189
% 144.20/29.32
% 144.20/29.32 % -------------------------------------------------
% 144.20/29.32 % User time : 27.723 s
% 144.20/29.32 % System time : 0.926 s
% 144.20/29.32 % Total time : 28.650 s
% 144.20/29.32 % Maximum resident set size: 10428 pages
% 144.20/29.32
% 144.20/29.32 % -------------------------------------------------
% 144.20/29.32 % User time : 27.954 s
% 144.20/29.32 % System time : 1.034 s
% 144.20/29.32 % Total time : 28.988 s
% 144.20/29.32 % Maximum resident set size: 5888 pages
% 144.20/29.32 % E exiting
%------------------------------------------------------------------------------