%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU774^1 : 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 : n009.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 08:25:34 AM UTC 2026
% Result : Theorem 2.91s 0.64s
% Output : CNFRefutation 2.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU774^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n009.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 14:27:52 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.25 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.TuEImBDgKn/E---3.1_4075482.p
% 2.91/0.64 % Version: 3.5.1-ho
% 2.91/0.64 % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.91/0.64 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.91/0.64 % Starting ehoh_best5 with 300s (1) cores
% 2.91/0.64 % Starting almost_fo_3_lam with 300s (1) cores
% 2.91/0.64 % Starting new_bool_5 with 300s (1) cores
% 2.91/0.64 % Starting pre_casc_3 with 300s (1) cores
% 2.91/0.64 % Starting ho_unfolding_8 with 300s (1) cores
% 2.91/0.64 % Starting new_ho_10_cnf2 with 300s (1) cores
% 2.91/0.64 % Starting new_bool_3 with 300s (1) cores
% 2.91/0.64 % Starting new_ho_5 with 300s (1) cores
% 2.91/0.64 % new_bool_3 with pid 4075532 completed with status 0
% 2.91/0.64 % Result found by new_bool_3
% 2.91/0.64 % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.91/0.64 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.91/0.64 % Starting ehoh_best5 with 300s (1) cores
% 2.91/0.64 % Starting almost_fo_3_lam with 300s (1) cores
% 2.91/0.64 % Starting new_bool_5 with 300s (1) cores
% 2.91/0.64 % Starting pre_casc_3 with 300s (1) cores
% 2.91/0.64 % Starting ho_unfolding_8 with 300s (1) cores
% 2.91/0.64 % Starting new_ho_10_cnf2 with 300s (1) cores
% 2.91/0.64 % Starting new_bool_3 with 300s (1) cores
% 2.91/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.91/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.91/0.64 % Search class: HGHSM-FSLM32-MHFMMSBN
% 2.91/0.64 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 2.91/0.64 % Starting SubtermCWHack with 31s (1) cores
% 2.91/0.64 % SubtermCWHack with pid 4075558 completed with status 0
% 2.91/0.64 % Result found by SubtermCWHack
% 2.91/0.64 % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.91/0.64 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.91/0.64 % Starting ehoh_best5 with 300s (1) cores
% 2.91/0.64 % Starting almost_fo_3_lam with 300s (1) cores
% 2.91/0.64 % Starting new_bool_5 with 300s (1) cores
% 2.91/0.64 % Starting pre_casc_3 with 300s (1) cores
% 2.91/0.64 % Starting ho_unfolding_8 with 300s (1) cores
% 2.91/0.64 % Starting new_ho_10_cnf2 with 300s (1) cores
% 2.91/0.64 % Starting new_bool_3 with 300s (1) cores
% 2.91/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.91/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.91/0.64 % Search class: HGHSM-FSLM32-MHFMMSBN
% 2.91/0.64 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 2.91/0.64 % Starting SubtermCWHack with 31s (1) cores
% 2.91/0.64 % Preprocessing time : 0.005 s
% 2.91/0.64
% 2.91/0.64 % Proof found!
% 2.91/0.64 % SZS status Theorem
% 2.91/0.64 % SZS output start CNFRefutation
% 2.91/0.64 thf(decl_23, type, in: $i > $i > $o).
% 2.91/0.64 thf(decl_24, type, exu: ($i > $o) > $o).
% 2.91/0.64 thf(decl_25, type, setextAx: $o).
% 2.91/0.64 thf(decl_26, type, emptyset: $i).
% 2.91/0.64 thf(decl_27, type, emptysetAx: $o).
% 2.91/0.64 thf(decl_28, type, setadjoin: $i > $i > $i).
% 2.91/0.64 thf(decl_29, type, setadjoinAx: $o).
% 2.91/0.64 thf(decl_30, type, powerset: $i > $i).
% 2.91/0.64 thf(decl_31, type, powersetAx: $o).
% 2.91/0.64 thf(decl_32, type, setunion: $i > $i).
% 2.91/0.64 thf(decl_33, type, setunionAx: $o).
% 2.91/0.64 thf(decl_34, type, omega: $i).
% 2.91/0.64 thf(decl_35, type, omega0Ax: $o).
% 2.91/0.64 thf(decl_36, type, omegaSAx: $o).
% 2.91/0.64 thf(decl_37, type, omegaIndAx: $o).
% 2.91/0.64 thf(decl_38, type, replAx: $o).
% 2.91/0.64 thf(decl_39, type, foundationAx: $o).
% 2.91/0.64 thf(decl_40, type, wellorderingAx: $o).
% 2.91/0.64 thf(decl_41, type, descr: ($i > $o) > $i).
% 2.91/0.64 thf(decl_42, type, descrp: $o).
% 2.91/0.64 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 2.91/0.64 thf(decl_44, type, dsetconstrI: $o).
% 2.91/0.64 thf(decl_45, type, dsetconstrEL: $o).
% 2.91/0.65 thf(decl_46, type, dsetconstrER: $o).
% 2.91/0.65 thf(decl_47, type, exuE1: $o).
% 2.91/0.65 thf(decl_48, type, prop2set: $o > $i).
% 2.91/0.65 thf(decl_49, type, prop2setE: $o).
% 2.91/0.65 thf(decl_50, type, emptysetE: $o).
% 2.91/0.65 thf(decl_51, type, emptysetimpfalse: $o).
% 2.91/0.65 thf(decl_52, type, notinemptyset: $o).
% 2.91/0.65 thf(decl_53, type, exuE3e: $o).
% 2.91/0.65 thf(decl_54, type, setext: $o).
% 2.91/0.65 thf(decl_55, type, emptyI: $o).
% 2.91/0.65 thf(decl_56, type, noeltsimpempty: $o).
% 2.91/0.65 thf(decl_57, type, setbeta: $o).
% 2.91/0.65 thf(decl_58, type, nonempty: $i > $o).
% 2.91/0.65 thf(decl_59, type, nonemptyE1: $o).
% 2.91/0.65 thf(decl_60, type, nonemptyI: $o).
% 2.91/0.65 thf(decl_61, type, nonemptyI1: $o).
% 2.91/0.65 thf(decl_62, type, setadjoinIL: $o).
% 2.91/0.65 thf(decl_63, type, emptyinunitempty: $o).
% 2.91/0.65 thf(decl_64, type, setadjoinIR: $o).
% 2.91/0.65 thf(decl_65, type, setadjoinE: $o).
% 2.91/0.65 thf(decl_66, type, setadjoinOr: $o).
% 2.91/0.65 thf(decl_67, type, setoftrueEq: $o).
% 2.91/0.65 thf(decl_68, type, powersetI: $o).
% 2.91/0.65 thf(decl_69, type, emptyinPowerset: $o).
% 2.91/0.65 thf(decl_70, type, emptyInPowerset: $o).
% 2.91/0.65 thf(decl_71, type, powersetE: $o).
% 2.91/0.65 thf(decl_72, type, setunionI: $o).
% 2.91/0.65 thf(decl_73, type, setunionE: $o).
% 2.91/0.65 thf(decl_74, type, subPowSU: $o).
% 2.91/0.65 thf(decl_75, type, exuE2: $o).
% 2.91/0.65 thf(decl_76, type, nonemptyImpWitness: $o).
% 2.91/0.65 thf(decl_77, type, uniqinunit: $o).
% 2.91/0.65 thf(decl_78, type, notinsingleton: $o).
% 2.91/0.65 thf(decl_79, type, eqinunit: $o).
% 2.91/0.65 thf(decl_80, type, singletonsswitch: $o).
% 2.91/0.65 thf(decl_81, type, upairsetE: $o).
% 2.91/0.65 thf(decl_82, type, upairsetIL: $o).
% 2.91/0.65 thf(decl_83, type, upairsetIR: $o).
% 2.91/0.65 thf(decl_84, type, emptyE1: $o).
% 2.91/0.65 thf(decl_85, type, vacuousDall: $o).
% 2.91/0.65 thf(decl_86, type, quantDeMorgan1: $o).
% 2.91/0.65 thf(decl_87, type, quantDeMorgan2: $o).
% 2.91/0.65 thf(decl_88, type, quantDeMorgan3: $o).
% 2.91/0.65 thf(decl_89, type, quantDeMorgan4: $o).
% 2.91/0.65 thf(decl_90, type, prop2setI: $o).
% 2.91/0.65 thf(decl_92, type, prop2set2propI: $o).
% 2.91/0.65 thf(decl_93, type, notdexE: $o).
% 2.91/0.65 thf(decl_94, type, notdallE: $o).
% 2.91/0.65 thf(decl_95, type, exuI1: $o).
% 2.91/0.65 thf(decl_96, type, exuI3: $o).
% 2.91/0.65 thf(decl_97, type, exuI2: $o).
% 2.91/0.65 thf(decl_98, type, inCongP: $o).
% 2.91/0.65 thf(decl_99, type, in__Cong: $o).
% 2.91/0.65 thf(decl_100, type, exuE3u: $o).
% 2.91/0.65 thf(decl_101, type, exu__Cong: $o).
% 2.91/0.65 thf(decl_102, type, emptyset__Cong: $o).
% 2.91/0.65 thf(decl_103, type, setadjoin__Cong: $o).
% 2.91/0.65 thf(decl_104, type, powerset__Cong: $o).
% 2.91/0.65 thf(decl_105, type, setunion__Cong: $o).
% 2.91/0.65 thf(decl_106, type, omega__Cong: $o).
% 2.91/0.65 thf(decl_107, type, exuEu: $o).
% 2.91/0.65 thf(decl_108, type, descr__Cong: $o).
% 2.91/0.65 thf(decl_109, type, dsetconstr__Cong: $o).
% 2.91/0.65 thf(decl_110, type, subset: $i > $i > $o).
% 2.91/0.65 thf(decl_113, type, subsetI1: $o).
% 2.91/0.65 thf(decl_114, type, eqimpsubset2: $o).
% 2.91/0.65 thf(decl_115, type, eqimpsubset1: $o).
% 2.91/0.65 thf(decl_116, type, subsetI2: $o).
% 2.91/0.65 thf(decl_117, type, emptysetsubset: $o).
% 2.91/0.65 thf(decl_118, type, subsetE: $o).
% 2.91/0.65 thf(decl_119, type, subsetE2: $o).
% 2.91/0.65 thf(decl_120, type, notsubsetI: $o).
% 2.91/0.65 thf(decl_121, type, notequalI1: $o).
% 2.91/0.65 thf(decl_122, type, notequalI2: $o).
% 2.91/0.65 thf(decl_123, type, subsetRefl: $o).
% 2.91/0.65 thf(decl_124, type, subsetTrans: $o).
% 2.91/0.65 thf(decl_125, type, setadjoinSub: $o).
% 2.91/0.65 thf(decl_126, type, setadjoinSub2: $o).
% 2.91/0.65 thf(decl_127, type, subset2powerset: $o).
% 2.91/0.65 thf(decl_128, type, setextsub: $o).
% 2.91/0.65 thf(decl_129, type, subsetemptysetimpeq: $o).
% 2.91/0.65 thf(decl_130, type, powersetI1: $o).
% 2.91/0.65 thf(decl_131, type, powersetE1: $o).
% 2.91/0.65 thf(decl_132, type, inPowerset: $o).
% 2.91/0.65 thf(decl_133, type, powersetsubset: $o).
% 2.91/0.65 thf(decl_134, type, sepInPowerset: $o).
% 2.91/0.65 thf(decl_135, type, sepSubset: $o).
% 2.91/0.65 thf(decl_136, type, binunion: $i > $i > $i).
% 2.91/0.65 thf(decl_137, type, binunionIL: $o).
% 2.91/0.65 thf(decl_138, type, upairset2IR: $o).
% 2.91/0.65 thf(decl_139, type, binunionIR: $o).
% 2.91/0.65 thf(decl_140, type, binunionEcases: $o).
% 2.91/0.65 thf(decl_141, type, binunionE: $o).
% 2.91/0.65 thf(decl_142, type, binunionLsub: $o).
% 2.91/0.65 thf(decl_143, type, binunionRsub: $o).
% 2.91/0.65 thf(decl_144, type, binintersect: $i > $i > $i).
% 2.91/0.65 thf(decl_145, type, binintersectI: $o).
% 2.91/0.65 thf(decl_146, type, binintersectSubset5: $o).
% 2.91/0.65 thf(decl_147, type, binintersectEL: $o).
% 2.91/0.65 thf(decl_148, type, binintersectLsub: $o).
% 2.91/0.65 thf(decl_149, type, binintersectSubset2: $o).
% 2.91/0.65 thf(decl_150, type, binintersectSubset3: $o).
% 2.91/0.65 thf(decl_151, type, binintersectER: $o).
% 2.91/0.65 thf(decl_152, type, disjointsetsI1: $o).
% 2.91/0.65 thf(decl_153, type, binintersectRsub: $o).
% 2.91/0.65 thf(decl_154, type, binintersectSubset4: $o).
% 2.91/0.65 thf(decl_155, type, binintersectSubset1: $o).
% 2.91/0.65 thf(decl_156, type, bs114d: $o).
% 2.91/0.65 thf(decl_158, type, setminus: $i > $i > $i).
% 2.91/0.65 thf(decl_159, type, setminusI: $o).
% 2.91/0.65 thf(decl_160, type, setminusEL: $o).
% 2.91/0.65 thf(decl_161, type, setminusER: $o).
% 2.91/0.65 thf(decl_162, type, setminusSubset2: $o).
% 2.91/0.65 thf(decl_163, type, setminusERneg: $o).
% 2.91/0.65 thf(decl_164, type, setminusELneg: $o).
% 2.91/0.65 thf(decl_165, type, setminusILneg: $o).
% 2.91/0.65 thf(decl_166, type, setminusIRneg: $o).
% 2.91/0.65 thf(decl_167, type, setminusLsub: $o).
% 2.91/0.65 thf(decl_168, type, setminusSubset1: $o).
% 2.91/0.65 thf(decl_169, type, symdiff: $i > $i > $i).
% 2.91/0.65 thf(decl_170, type, symdiffE: $o).
% 2.91/0.65 thf(decl_171, type, symdiffI1: $o).
% 2.91/0.65 thf(decl_172, type, symdiffI2: $o).
% 2.91/0.65 thf(decl_173, type, symdiffIneg1: $o).
% 2.91/0.65 thf(decl_174, type, symdiffIneg2: $o).
% 2.91/0.65 thf(decl_175, type, iskpair: $i > $o).
% 2.91/0.65 thf(decl_176, type, secondinupair: $o).
% 2.91/0.65 thf(decl_177, type, setukpairIL: $o).
% 2.91/0.65 thf(decl_178, type, setukpairIR: $o).
% 2.91/0.65 thf(decl_179, type, kpairiskpair: $o).
% 2.91/0.65 thf(decl_180, type, kpair: $i > $i > $i).
% 2.91/0.65 thf(decl_181, type, kpairp: $o).
% 2.91/0.65 thf(decl_182, type, cartprod: $i > $i > $i).
% 2.91/0.65 thf(decl_183, type, singletonsubset: $o).
% 2.91/0.65 thf(decl_184, type, singletoninpowerset: $o).
% 2.91/0.65 thf(decl_185, type, singletoninpowunion: $o).
% 2.91/0.65 thf(decl_186, type, upairset2E: $o).
% 2.91/0.65 thf(decl_187, type, upairsubunion: $o).
% 2.91/0.65 thf(decl_188, type, upairinpowunion: $o).
% 2.91/0.65 thf(decl_189, type, ubforcartprodlem1: $o).
% 2.91/0.65 thf(decl_190, type, ubforcartprodlem2: $o).
% 2.91/0.65 thf(decl_191, type, ubforcartprodlem3: $o).
% 2.91/0.65 thf(decl_192, type, cartprodpairin: $o).
% 2.91/0.65 thf(decl_193, type, cartprodmempair1: $o).
% 2.91/0.65 thf(decl_194, type, cartprodmempair: $o).
% 2.91/0.65 thf(decl_195, type, setunionE2: $o).
% 2.91/0.65 thf(decl_196, type, setunionsingleton1: $o).
% 2.91/0.65 thf(decl_197, type, setunionsingleton2: $o).
% 2.91/0.65 thf(decl_198, type, setunionsingleton: $o).
% 2.91/0.65 thf(decl_199, type, singleton: $i > $o).
% 2.91/0.65 thf(decl_200, type, singletonprop: $o).
% 2.91/0.65 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 2.91/0.65 thf(decl_202, type, ex1E1: $o).
% 2.91/0.65 thf(decl_203, type, ex1I: $o).
% 2.91/0.65 thf(decl_204, type, ex1I2: $o).
% 2.91/0.65 thf(decl_205, type, singletonsuniq: $o).
% 2.91/0.65 thf(decl_210, type, setukpairinjL1: $o).
% 2.91/0.65 thf(decl_211, type, kfstsingleton: $o).
% 2.91/0.65 thf(decl_212, type, theprop: $o).
% 2.91/0.65 thf(decl_213, type, kfst: $i > $i).
% 2.91/0.65 thf(decl_214, type, kfstpairEq: $o).
% 2.91/0.65 thf(decl_215, type, cartprodfstin: $o).
% 2.91/0.65 thf(decl_216, type, setukpairinjL2: $o).
% 2.91/0.65 thf(decl_217, type, setukpairinjL: $o).
% 2.91/0.65 thf(decl_218, type, setukpairinjR11: $o).
% 2.91/0.65 thf(decl_219, type, setukpairinjR12: $o).
% 2.91/0.65 thf(decl_220, type, setukpairinjR1: $o).
% 2.91/0.65 thf(decl_221, type, upairequniteq: $o).
% 2.91/0.65 thf(decl_222, type, setukpairinjR2: $o).
% 2.91/0.65 thf(decl_223, type, setukpairinjR: $o).
% 2.91/0.65 thf(decl_224, type, ksndsingleton: $o).
% 2.91/0.65 thf(decl_225, type, ksnd: $i > $i).
% 2.91/0.65 thf(decl_226, type, ksndpairEq: $o).
% 2.91/0.65 thf(decl_227, type, kpairsurjEq: $o).
% 2.91/0.65 thf(decl_228, type, cartprodsndin: $o).
% 2.91/0.65 thf(decl_229, type, cartprodpairmemEL: $o).
% 2.91/0.65 thf(decl_230, type, cartprodpairmemER: $o).
% 2.91/0.65 thf(decl_231, type, cartprodmempaircEq: $o).
% 2.91/0.65 thf(decl_232, type, cartprodfstpairEq: $o).
% 2.91/0.65 thf(decl_233, type, cartprodsndpairEq: $o).
% 2.91/0.65 thf(decl_234, type, cartprodpairsurjEq: $o).
% 2.91/0.65 thf(decl_235, type, breln: $i > $i > $i > $o).
% 2.91/0.65 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 2.91/0.65 thf(decl_237, type, dpsetconstrI: $o).
% 2.91/0.65 thf(decl_238, type, dpsetconstrSub: $o).
% 2.91/0.65 thf(decl_239, type, setOfPairsIsBReln: $o).
% 2.91/0.65 thf(decl_240, type, dpsetconstrERa: $o).
% 2.91/0.65 thf(decl_241, type, dpsetconstrEL1: $o).
% 2.91/0.65 thf(decl_242, type, dpsetconstrEL2: $o).
% 2.91/0.65 thf(decl_243, type, dpsetconstrER: $o).
% 2.91/0.65 thf(decl_244, type, func: $i > $i > $i > $o).
% 2.91/0.65 thf(decl_245, type, funcSet: $i > $i > $i).
% 2.91/0.65 thf(decl_246, type, funcImageSingleton: $o).
% 2.91/0.65 thf(decl_247, type, apProp: $o).
% 2.91/0.65 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 2.91/0.65 thf(decl_249, type, app: $o).
% 2.91/0.65 thf(decl_250, type, infuncsetfunc: $o).
% 2.91/0.65 thf(decl_251, type, ap2p: $o).
% 2.91/0.65 thf(decl_252, type, funcinfuncset: $o).
% 2.91/0.65 thf(decl_253, type, lamProp: $o).
% 2.91/0.65 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 2.91/0.65 thf(decl_255, type, lamp: $o).
% 2.91/0.65 thf(decl_256, type, lam2p: $o).
% 2.91/0.65 thf(decl_257, type, brelnall1: $o).
% 2.91/0.65 thf(decl_258, type, brelnall2: $o).
% 2.91/0.65 thf(decl_259, type, ex1E2: $o).
% 2.91/0.65 thf(decl_260, type, funcGraphProp1: $o).
% 2.91/0.65 thf(decl_261, type, funcGraphProp3: $o).
% 2.91/0.65 thf(decl_262, type, funcGraphProp2: $o).
% 2.91/0.65 thf(decl_263, type, funcextLem: $o).
% 2.91/0.65 thf(decl_264, type, funcGraphProp4: $o).
% 2.91/0.65 thf(decl_265, type, subbreln: $o).
% 2.91/0.65 thf(decl_266, type, eqbreln: $o).
% 2.91/0.65 thf(decl_267, type, funcext: $o).
% 2.91/0.65 thf(decl_268, type, funcext2: $o).
% 2.91/0.65 thf(decl_269, type, ap2apEq1: $o).
% 2.91/0.65 thf(decl_270, type, ap2apEq2: $o).
% 2.91/0.65 thf(decl_271, type, beta1: $o).
% 2.91/0.65 thf(decl_272, type, eta1: $o).
% 2.91/0.65 thf(decl_273, type, lam2lamEq: $o).
% 2.91/0.65 thf(decl_274, type, beta2: $o).
% 2.91/0.65 thf(decl_275, type, eta2: $o).
% 2.91/0.65 thf(decl_276, type, iffalseProp1: $o).
% 2.91/0.65 thf(decl_277, type, iffalseProp2: $o).
% 2.91/0.65 thf(decl_278, type, iftrueProp1: $o).
% 2.91/0.65 thf(decl_279, type, iftrueProp2: $o).
% 2.91/0.65 thf(decl_280, type, ifSingleton: $o).
% 2.91/0.65 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 2.91/0.65 thf(decl_282, type, ifp: $o).
% 2.91/0.65 thf(decl_283, type, theeq: $o).
% 2.91/0.65 thf(decl_284, type, iftrue: $o).
% 2.91/0.65 thf(decl_285, type, iffalse: $o).
% 2.91/0.65 thf(decl_286, type, iftrueorfalse: $o).
% 2.91/0.65 thf(decl_287, type, binintersectT_lem: $o).
% 2.91/0.65 thf(decl_288, type, binunionT_lem: $o).
% 2.91/0.65 thf(decl_289, type, powersetT_lem: $o).
% 2.91/0.65 thf(decl_290, type, setminusT_lem: $o).
% 2.91/0.65 thf(decl_291, type, complementT_lem: $o).
% 2.91/0.65 thf(decl_292, type, setextT: $o).
% 2.91/0.65 thf(decl_293, type, subsetTI: $o).
% 2.91/0.65 thf(decl_294, type, powersetTI1: $o).
% 2.91/0.65 thf(decl_295, type, powersetTE1: $o).
% 2.91/0.65 thf(decl_296, type, complementTI1: $o).
% 2.91/0.65 thf(decl_297, type, complementTE1: $o).
% 2.91/0.65 thf(decl_298, type, binintersectTELcontra: $o).
% 2.91/0.65 thf(decl_299, type, binintersectTERcontra: $o).
% 2.91/0.65 thf(decl_300, type, contrasubsetT: $o).
% 2.91/0.65 thf(decl_301, type, contrasubsetT1: $o).
% 2.91/0.65 thf(decl_302, type, contrasubsetT2: $o).
% 2.91/0.65 thf(decl_303, type, contrasubsetT3: $o).
% 2.91/0.65 thf(decl_304, type, doubleComplementI1: $o).
% 2.91/0.65 thf(decl_305, type, doubleComplementE1: $o).
% 2.91/0.65 thf(decl_306, type, doubleComplementSub1: $o).
% 2.91/0.65 thf(decl_307, type, doubleComplementSub2: $o).
% 2.91/0.65 thf(decl_308, type, doubleComplementEq: $o).
% 2.91/0.65 thf(decl_309, type, complementTnotintersectT: $o).
% 2.91/0.65 thf(decl_310, type, complementImpComplementIntersect: $o).
% 2.91/0.65 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 2.91/0.65 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 2.91/0.65 thf(decl_313, type, contraSubsetComplement: $o).
% 2.91/0.65 thf(decl_314, type, complementTcontraSubset: $o).
% 2.91/0.65 thf(decl_315, type, binunionTILcontra: $o).
% 2.91/0.65 thf(decl_316, type, binunionTIRcontra: $o).
% 2.91/0.65 thf(decl_317, type, inIntersectImpInUnion: $o).
% 2.91/0.65 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 2.91/0.65 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 2.91/0.65 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 2.91/0.65 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 2.91/0.65 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 2.91/0.65 thf(decl_323, type, binunionTE: $o).
% 2.91/0.65 thf(decl_324, type, binunionTEcontra: $o).
% 2.91/0.65 thf(decl_325, type, demorgan2a1: $o).
% 2.91/0.65 thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 2.91/0.65 thf(decl_327, type, demorgan2a2: $o).
% 2.91/0.65 thf(decl_328, type, demorgan1a: $o).
% 2.91/0.65 thf(decl_329, type, demorgan1b: $o).
% 2.91/0.65 thf(decl_330, type, demorgan1: $o).
% 2.91/0.65 thf(decl_331, type, demorgan2a: $o).
% 2.91/0.65 thf(decl_332, type, demorgan2b2: $o).
% 2.91/0.65 thf(decl_333, type, demorgan2b: $o).
% 2.91/0.65 thf(decl_334, type, demorgan2: $o).
% 2.91/0.65 thf(decl_335, type, woz13rule0: $o).
% 2.91/0.65 thf(decl_336, type, woz13rule1: $o).
% 2.91/0.65 thf(decl_337, type, woz13rule2: $o).
% 2.91/0.65 thf(decl_338, type, woz13rule3: $o).
% 2.91/0.65 thf(decl_339, type, woz13rule4: $o).
% 2.91/0.65 thf(decl_340, type, woz1_1: $o).
% 2.91/0.65 thf(decl_341, type, woz1_2: $o).
% 2.91/0.65 thf(decl_342, type, woz1_3: $o).
% 2.91/0.65 thf(decl_343, type, woz1_4: $o).
% 2.91/0.65 thf(decl_344, type, woz1_5: $o).
% 2.91/0.65 thf(decl_345, type, breln1: $i > $i > $o).
% 2.91/0.65 thf(decl_346, type, breln1all2: $o).
% 2.91/0.65 thf(decl_347, type, breln1Set: $i > $i).
% 2.91/0.65 thf(decl_348, type, breln1SetBreln1: $o).
% 2.91/0.65 thf(decl_355, type, choice2fnsingleton: $o).
% 2.91/0.65 thf(decl_356, type, setOfPairsIsBReln1: $o).
% 2.91/0.65 thf(decl_357, type, breln1all1: $o).
% 2.91/0.65 thf(decl_358, type, subbreln1: $o).
% 2.91/0.65 thf(decl_359, type, epred1_0: $o).
% 2.91/0.65 thf(decl_360, type, esk1_2: $i > $i > $i).
% 2.91/0.65 thf(decl_361, type, esk2_2: $i > $i > $i).
% 2.91/0.65 thf(decl_362, type, esk3_2: $i > $i > $i).
% 2.91/0.65 thf(decl_363, type, esk4_1: $i > $i).
% 2.91/0.65 thf(decl_364, type, esk5_2: ($i > $i > $o) > $i > $i).
% 2.91/0.65 thf(decl_365, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 2.91/0.65 thf(decl_366, type, esk7_2: ($i > $i > $o) > $i > $i).
% 2.91/0.65 thf(decl_367, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 2.91/0.65 thf(decl_368, type, esk9_1: $i > $i).
% 2.91/0.65 thf(decl_369, type, esk10_2: ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_370, type, esk11_2: ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_371, type, esk12_1: ($i > $o) > $i).
% 2.91/0.65 thf(decl_372, type, esk13_2: ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_373, type, esk14_1: ($i > $o) > $i).
% 2.91/0.65 thf(decl_374, type, esk15_2: $i > $i > $i).
% 2.91/0.65 thf(decl_375, type, esk16_2: $i > $i > $i).
% 2.91/0.65 thf(decl_376, type, esk17_1: $i > $i).
% 2.91/0.65 thf(decl_377, type, esk18_1: $i > $i).
% 2.91/0.65 thf(decl_378, type, esk19_1: $i > $i).
% 2.91/0.65 thf(decl_379, type, esk20_2: $i > $i > $i).
% 2.91/0.65 thf(decl_380, type, esk21_3: $i > $i > $o > $i).
% 2.91/0.65 thf(decl_381, type, esk22_2: ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_382, type, esk23_1: ($i > $o) > $i).
% 2.91/0.65 thf(decl_383, type, esk24_1: $i > $i).
% 2.91/0.65 thf(decl_384, type, esk25_2: $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_385, type, esk26_2: $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_386, type, esk27_2: $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_387, type, esk28_2: $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_388, type, esk29_2: $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_389, type, esk30_2: $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_390, type, esk31_2: ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_391, type, esk32_1: ($i > $o) > $i).
% 2.91/0.65 thf(decl_392, type, esk33_1: ($i > $o) > $i).
% 2.91/0.65 thf(decl_393, type, esk34_1: ($i > $o) > $i).
% 2.91/0.65 thf(decl_394, type, esk35_1: ($i > $o) > $i).
% 2.91/0.65 thf(decl_395, type, esk36_2: ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_396, type, esk37_1: ($i > $o) > $i).
% 2.91/0.65 thf(decl_397, type, esk38_2: ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_398, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 2.91/0.65 thf(decl_399, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 2.91/0.65 thf(decl_400, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_401, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 2.91/0.65 thf(decl_402, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_403, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 2.91/0.65 thf(decl_404, type, esk45_2: ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_405, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 2.91/0.65 thf(decl_406, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 2.91/0.65 thf(decl_407, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_408, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_409, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.91/0.65 thf(decl_410, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.91/0.65 thf(decl_411, type, esk52_2: $i > $i > $i).
% 2.91/0.65 thf(decl_412, type, esk53_2: $i > $i > $i).
% 2.91/0.65 thf(decl_413, type, esk54_2: $i > $i > $i).
% 2.91/0.65 thf(decl_414, type, esk55_3: $i > $i > $i > $i).
% 2.91/0.65 thf(decl_415, type, esk56_3: $i > $i > $i > $i).
% 2.91/0.65 thf(decl_416, type, esk57_2: $i > $i > $i).
% 2.91/0.65 thf(decl_417, type, esk58_2: $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_418, type, esk59_2: $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_419, type, esk60_2: $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_420, type, esk61_3: $i > ($i > $o) > $i > $i).
% 2.91/0.65 thf(decl_421, type, esk62_2: $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_422, type, esk63_2: $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_423, type, esk64_3: $i > $i > ($i > $i) > $i).
% 2.91/0.65 thf(decl_424, type, esk65_3: $i > $i > ($i > $i) > $i).
% 2.91/0.65 thf(decl_425, type, esk66_3: $i > $i > ($i > $i) > $i).
% 2.91/0.65 thf(decl_426, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_427, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_428, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_429, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_430, type, esk71_4: $i > $i > $i > $i > $i).
% 2.91/0.65 thf(decl_431, type, esk72_4: $i > $i > $i > $i > $i).
% 2.91/0.65 thf(decl_432, type, esk73_4: $i > $i > $i > $i > $i).
% 2.91/0.65 thf(decl_433, type, esk74_4: $i > $i > $i > $i > $i).
% 2.91/0.65 thf(decl_434, type, esk75_4: $i > $i > $i > $i > $i).
% 2.91/0.65 thf(decl_435, type, esk76_4: $i > $i > $i > $i > $i).
% 2.91/0.65 thf(decl_436, type, esk77_4: $i > $i > $i > $i > $i).
% 2.91/0.65 thf(decl_437, type, esk78_4: $i > $i > $i > $i > $i).
% 2.91/0.65 thf(decl_438, type, esk79_4: $i > $i > $i > $i > $i).
% 2.91/0.65 thf(decl_439, type, esk80_3: $i > $i > ($i > $i) > $i).
% 2.91/0.65 thf(decl_440, type, esk81_3: $i > $i > ($i > $i) > $i).
% 2.91/0.65 thf(decl_441, type, esk82_3: $i > $i > ($i > $i) > $i).
% 2.91/0.65 thf(decl_442, type, esk83_3: $i > $i > $i > $i).
% 2.91/0.65 thf(decl_443, type, esk84_3: $i > $i > $i > $i).
% 2.91/0.65 thf(decl_444, type, esk85_3: $i > $i > $i > $i).
% 2.91/0.65 thf(decl_445, type, esk86_3: $i > $i > $i > $i).
% 2.91/0.65 thf(decl_446, type, esk87_3: $i > $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_447, type, esk88_3: $i > $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_448, type, esk89_3: $i > $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_449, type, esk90_3: $i > $i > ($i > $o) > $i).
% 2.91/0.65 thf(decl_450, type, esk91_3: $i > $i > $i > $i).
% 2.91/0.65 thf(decl_451, type, esk92_3: $i > $i > $i > $i).
% 2.91/0.65 thf(decl_452, type, esk93_0: $i).
% 2.91/0.65 thf(decl_453, type, esk94_0: $i).
% 2.91/0.65 thf(decl_454, type, esk95_0: $i).
% 2.91/0.65 thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', breln1)).
% 2.91/0.65 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', breln)).
% 2.91/0.65 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', exu__Cong)).
% 2.91/0.65 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', exu)).
% 2.91/0.65 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', exuE3u)).
% 2.91/0.65 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', descr__Cong)).
% 2.91/0.65 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', exuEu)).
% 2.91/0.65 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setOfPairsIsBReln1)).
% 2.91/0.65 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setOfPairsIsBReln)).
% 2.91/0.65 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', exuI2)).
% 2.91/0.65 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', exuI3)).
% 2.91/0.65 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', exuI1)).
% 2.91/0.65 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', nonempty)).
% 2.91/0.65 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', exuE2)).
% 2.91/0.65 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', nonemptyI)).
% 2.91/0.65 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', exuE3e)).
% 2.91/0.65 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', exuE1)).
% 2.91/0.65 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', descrp)).
% 2.91/0.65 thf(replAx, axiom, ((replAx)<=>![X6:$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.TuEImBDgKn/E---3.1_4075482.p', replAx)).
% 2.91/0.65 thf(eqbreln1, 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)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', eqbreln1)).
% 2.91/0.65 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', dsetconstr__Cong)).
% 2.91/0.65 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', breln1all2)).
% 2.91/0.65 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', breln1SetBreln1)).
% 2.91/0.65 thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', breln1all1)).
% 2.91/0.65 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', subbreln1)).
% 2.91/0.65 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', sepSubset)).
% 2.91/0.65 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', sepInPowerset)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', subbreln)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', beta2)).
% 2.91/0.65 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', ex1I2)).
% 2.91/0.65 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', ex1I)).
% 2.91/0.65 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', ex1E1)).
% 2.91/0.65 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', singletonprop)).
% 2.91/0.65 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', kfstsingleton)).
% 2.91/0.65 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', ksndsingleton)).
% 2.91/0.65 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', dpsetconstrSub)).
% 2.91/0.65 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', dpsetconstrI)).
% 2.91/0.65 thf(apProp, axiom, ((apProp)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', apProp)).
% 2.91/0.65 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', funcImageSingleton)).
% 2.91/0.65 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', dpsetconstrER)).
% 2.91/0.65 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', dpsetconstrEL2)).
% 2.91/0.65 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', dpsetconstrEL1)).
% 2.91/0.65 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', dpsetconstrERa)).
% 2.91/0.65 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', brelnall2)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', brelnall1)).
% 2.91/0.65 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', lam2p)).
% 2.91/0.65 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', lamp)).
% 2.91/0.65 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', lamProp)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', ex1E2)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', eqbreln)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', lam2lamEq)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', eta1)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', beta1)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', eta2)).
% 2.91/0.65 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', ifSingleton)).
% 2.91/0.65 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', iftrueProp2)).
% 2.91/0.65 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', iftrueProp1)).
% 2.91/0.65 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', iffalseProp2)).
% 2.91/0.65 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', iffalseProp1)).
% 2.91/0.65 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', emptyE1)).
% 2.91/0.65 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', nonemptyImpWitness)).
% 2.91/0.65 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setoftrueEq)).
% 2.91/0.65 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', nonemptyI1)).
% 2.91/0.65 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', nonemptyE1)).
% 2.91/0.65 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setbeta)).
% 2.91/0.65 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', dsetconstrER)).
% 2.91/0.65 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', dsetconstrEL)).
% 2.91/0.65 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', dsetconstrI)).
% 2.91/0.65 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', doubleComplementE1)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', doubleComplementSub1)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', doubleComplementSub2)).
% 2.91/0.65 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', doubleComplementEq)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', complementTnotintersectT)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', complementImpComplementIntersect)).
% 2.91/0.65 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', complementSubsetComplementIntersect)).
% 2.91/0.65 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', complementInPowersetComplementIntersect)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', contraSubsetComplement)).
% 2.91/0.65 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setunion__Cong)).
% 2.91/0.65 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', complementTcontraSubset)).
% 2.91/0.65 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', powerset__Cong)).
% 2.91/0.65 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binunionTILcontra)).
% 2.91/0.65 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setadjoin__Cong)).
% 2.91/0.65 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binunionTIRcontra)).
% 2.91/0.65 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', emptyset__Cong)).
% 2.91/0.65 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', inIntersectImpInUnion)).
% 2.91/0.65 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', inIntersectImpInUnion2)).
% 2.91/0.65 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', inIntersectImpInIntersectUnions)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', intersectInPowersetIntersectUnions)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', in__Cong)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', inComplementUnionImpNotIn1)).
% 2.91/0.65 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', omega__Cong)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', inComplementUnionImpInComplement1)).
% 2.91/0.65 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binunionTE)).
% 2.91/0.65 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binunionTEcontra)).
% 2.91/0.65 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', demorgan2a1)).
% 2.91/0.65 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', complementUnionInPowersetComplement)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', demorgan2a2)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', demorgan1a)).
% 2.91/0.65 thf(demorgan1b, axiom, ((demorgan1b)<=>![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.TuEImBDgKn/E---3.1_4075482.p', demorgan1b)).
% 2.91/0.65 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', demorgan1)).
% 2.91/0.65 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', demorgan2a)).
% 2.91/0.65 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', demorgan2b2)).
% 2.91/0.65 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', demorgan2b)).
% 2.91/0.65 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', demorgan2)).
% 2.91/0.65 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', subsetI2)).
% 2.91/0.65 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', woz13rule0)).
% 2.91/0.65 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', eqimpsubset1)).
% 2.91/0.65 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', woz13rule1)).
% 2.91/0.65 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', eqimpsubset2)).
% 2.91/0.65 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', woz13rule2)).
% 2.91/0.65 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', subsetI1)).
% 2.91/0.65 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', woz13rule3)).
% 2.91/0.65 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', woz13rule4)).
% 2.91/0.65 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', woz1_1)).
% 2.91/0.65 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', woz1_2)).
% 2.91/0.65 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', emptysetsubset)).
% 2.91/0.65 thf(woz1_3, axiom, ((woz1_3)<=>![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.TuEImBDgKn/E---3.1_4075482.p', woz1_3)).
% 2.91/0.65 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', woz1_4)).
% 2.91/0.65 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', woz1_5)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', inCongP)).
% 2.91/0.65 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', subsetTrans)).
% 2.91/0.65 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', subsetRefl)).
% 2.91/0.65 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', notequalI2)).
% 2.91/0.65 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', notequalI1)).
% 2.91/0.65 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', notsubsetI)).
% 2.91/0.65 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', subsetE2)).
% 2.91/0.65 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', subsetE)).
% 2.91/0.65 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setadjoinSub)).
% 2.91/0.65 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setminusER)).
% 2.91/0.65 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', inPowerset)).
% 2.91/0.65 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', powersetE1)).
% 2.91/0.65 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', powersetI1)).
% 2.91/0.65 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', subsetemptysetimpeq)).
% 2.91/0.65 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setextsub)).
% 2.91/0.65 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', subset2powerset)).
% 2.91/0.65 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setadjoinSub2)).
% 2.91/0.65 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', powersetsubset)).
% 2.91/0.65 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binunionE)).
% 2.91/0.65 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binunionEcases)).
% 2.91/0.65 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binunionIR)).
% 2.91/0.65 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', upairset2IR)).
% 2.91/0.65 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binunionIL)).
% 2.91/0.65 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binunionLsub)).
% 2.91/0.65 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectSubset3)).
% 2.91/0.65 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectSubset2)).
% 2.91/0.65 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectLsub)).
% 2.91/0.65 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectEL)).
% 2.91/0.65 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectSubset5)).
% 2.91/0.65 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectI)).
% 2.91/0.65 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binunionRsub)).
% 2.91/0.65 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectER)).
% 2.91/0.65 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setminusEL)).
% 2.91/0.65 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setminusI)).
% 2.91/0.65 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', bs114d)).
% 2.91/0.65 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectSubset1)).
% 2.91/0.65 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectSubset4)).
% 2.91/0.65 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectRsub)).
% 2.91/0.65 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', disjointsetsI1)).
% 2.91/0.65 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', funcGraphProp4)).
% 2.91/0.65 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', funcextLem)).
% 2.91/0.65 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', funcGraphProp2)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', funcGraphProp3)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', funcGraphProp1)).
% 2.91/0.65 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', funcext)).
% 2.91/0.65 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setminusSubset1)).
% 2.91/0.65 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setminusLsub)).
% 2.91/0.65 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setminusIRneg)).
% 2.91/0.65 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setminusILneg)).
% 2.91/0.65 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setminusELneg)).
% 2.91/0.65 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setminusERneg)).
% 2.91/0.65 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setminusSubset2)).
% 2.91/0.65 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', symdiffE)).
% 2.91/0.65 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setukpairIR)).
% 2.91/0.65 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setukpairIL)).
% 2.91/0.65 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', secondinupair)).
% 2.91/0.65 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', symdiffIneg2)).
% 2.91/0.65 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', symdiffIneg1)).
% 2.91/0.65 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', symdiffI2)).
% 2.91/0.65 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', symdiffI1)).
% 2.91/0.65 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', kpairiskpair)).
% 2.91/0.65 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', upairinpowunion)).
% 2.91/0.65 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', upairsubunion)).
% 2.91/0.65 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', upairset2E)).
% 2.91/0.65 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', singletoninpowunion)).
% 2.91/0.65 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', singletoninpowerset)).
% 2.91/0.65 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', singletonsubset)).
% 2.91/0.65 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', kpairp)).
% 2.91/0.65 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', ubforcartprodlem1)).
% 2.91/0.65 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setunionsingleton1)).
% 2.91/0.65 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setunionE2)).
% 2.91/0.65 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', cartprodmempair)).
% 2.91/0.65 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', cartprodmempair1)).
% 2.91/0.65 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', cartprodpairin)).
% 2.91/0.65 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', ubforcartprodlem3)).
% 2.91/0.65 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', ubforcartprodlem2)).
% 2.91/0.65 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setunionsingleton2)).
% 2.91/0.65 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setukpairinjL1)).
% 2.91/0.65 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', singletonsuniq)).
% 2.91/0.65 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setunionsingleton)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', setukpairinjR12)).
% 2.91/0.65 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setukpairinjR11)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', setukpairinjL)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', setukpairinjL2)).
% 2.91/0.65 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', cartprodfstin)).
% 2.91/0.65 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', kfstpairEq)).
% 2.91/0.65 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', theprop)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', setukpairinjR1)).
% 2.91/0.65 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', cartprodsndin)).
% 2.91/0.65 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', kpairsurjEq)).
% 2.91/0.65 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', ksndpairEq)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', setukpairinjR)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', setukpairinjR2)).
% 2.91/0.65 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', upairequniteq)).
% 2.91/0.65 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', cartprodpairmemEL)).
% 2.91/0.65 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', cartprodpairsurjEq)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', cartprodsndpairEq)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', cartprodfstpairEq)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', cartprodmempaircEq)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', cartprodpairmemER)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', app)).
% 2.91/0.65 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', infuncsetfunc)).
% 2.91/0.65 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', funcinfuncset)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', ap2p)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', ap2apEq2)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', ap2apEq1)).
% 2.91/0.65 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', funcext2)).
% 2.91/0.65 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', theeq)).
% 2.91/0.65 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', ifp)).
% 2.91/0.65 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', iftrue)).
% 2.91/0.65 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', complementT_lem)).
% 2.91/0.65 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', setminusT_lem)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', powersetT_lem)).
% 2.91/0.65 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binunionT_lem)).
% 2.91/0.65 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', binintersectT_lem)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', iftrueorfalse)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', iffalse)).
% 2.91/0.65 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setextT)).
% 2.91/0.65 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectTERcontra)).
% 2.91/0.65 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', binintersectTELcontra)).
% 2.91/0.65 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', complementTE1)).
% 2.91/0.65 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', complementTI1)).
% 2.91/0.65 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', powersetTE1)).
% 2.91/0.65 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', powersetTI1)).
% 2.91/0.65 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', subsetTI)).
% 2.91/0.65 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', contrasubsetT)).
% 2.91/0.65 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', contrasubsetT1)).
% 2.91/0.65 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', contrasubsetT2)).
% 2.91/0.65 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', contrasubsetT3)).
% 2.91/0.65 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', doubleComplementI1)).
% 2.91/0.65 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', notdallE)).
% 2.91/0.65 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', notdexE)).
% 2.91/0.65 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', prop2setI)).
% 2.91/0.65 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', quantDeMorgan4)).
% 2.91/0.65 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', quantDeMorgan3)).
% 2.91/0.65 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', quantDeMorgan2)).
% 2.91/0.65 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', quantDeMorgan1)).
% 2.91/0.65 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', vacuousDall)).
% 2.91/0.65 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', upairsetIR)).
% 2.91/0.65 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', upairsetIL)).
% 2.91/0.65 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', upairsetE)).
% 2.91/0.65 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', singletonsswitch)).
% 2.91/0.65 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', eqinunit)).
% 2.91/0.65 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', notinsingleton)).
% 2.91/0.65 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', uniqinunit)).
% 2.91/0.65 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', subPowSU)).
% 2.91/0.65 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setunionE)).
% 2.91/0.65 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setunionI)).
% 2.91/0.65 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', powersetE)).
% 2.91/0.65 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', emptyInPowerset)).
% 2.91/0.65 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', emptyinPowerset)).
% 2.91/0.65 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', powersetI)).
% 2.91/0.65 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setadjoinOr)).
% 2.91/0.65 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setadjoinE)).
% 2.91/0.65 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setadjoinIR)).
% 2.91/0.65 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', emptyinunitempty)).
% 2.91/0.65 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setadjoinIL)).
% 2.91/0.65 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', noeltsimpempty)).
% 2.91/0.65 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', emptyI)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', setext)).
% 2.91/0.65 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', notinemptyset)).
% 2.91/0.65 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', emptysetimpfalse)).
% 2.91/0.65 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', emptysetE)).
% 2.91/0.65 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', prop2setE)).
% 2.91/0.65 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.TuEImBDgKn/E---3.1_4075482.p', wellorderingAx)).
% 2.91/0.65 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.TuEImBDgKn/E---3.1_4075482.p', foundationAx)).
% 2.91/0.65 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', omegaIndAx)).
% 2.91/0.65 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', omegaSAx)).
% 2.91/0.65 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', omega0Ax)).
% 2.91/0.65 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setunionAx)).
% 2.91/0.65 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', powersetAx)).
% 2.91/0.65 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setadjoinAx)).
% 2.91/0.65 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', emptysetAx)).
% 2.91/0.65 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.TuEImBDgKn/E---3.1_4075482.p', setextAx)).
% 2.91/0.65 thf(c_0_293, plain, ((breln1)=(^[Z0:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
% 2.91/0.65 thf(c_0_294, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 2.91/0.65 thf(c_0_295, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 2.91/0.65 thf(c_0_296, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 2.91/0.65 thf(c_0_297, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 2.91/0.65 thf(c_0_298, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 2.91/0.65 thf(c_0_299, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 2.91/0.65 thf(c_0_300, plain, ((breln1)=(^[Z0:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_293, c_0_294])).
% 2.91/0.65 thf(c_0_301, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
% 2.91/0.65 thf(c_0_302, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 2.91/0.65 thf(c_0_303, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 2.91/0.65 thf(c_0_304, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 2.91/0.65 thf(c_0_305, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 2.91/0.65 thf(c_0_306, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 2.91/0.65 thf(c_0_307, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 2.91/0.65 thf(c_0_308, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 2.91/0.65 thf(c_0_309, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 2.91/0.65 thf(c_0_310, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 2.91/0.65 thf(c_0_311, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 2.91/0.65 thf(c_0_312, plain, ((replAx)<=>![X6:$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])).
% 2.91/0.65 thf(c_0_313, 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)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[eqbreln1])).
% 2.91/0.65 thf(c_0_314, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1006:$i]:(((((X1 @ X1006)))&(![X1007:$i]:(((((X1 @ X1007)))=>(((X1006)=(X1007))))))))))<=>((?[X1008:$i]:(((((X17 @ X1008)))&(![X1009:$i]:(((((X17 @ X1009)))=>(((X1008)=(X1009)))))))))))))))), inference(apply_def,[status(thm)],[c_0_295, c_0_296])).
% 2.91/0.65 thf(c_0_315, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X1004:$i]:(((((X1 @ X1004)))&(![X1005:$i]:(((((X1 @ X1005)))=>(((X1004)=(X1005))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_297, c_0_296])).
% 2.91/0.65 thf(c_0_316, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 2.91/0.65 thf(c_0_317, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1012:$i]:(((((X1 @ X1012)))&(![X1013:$i]:(((((X1 @ X1013)))=>(((X1012)=(X1013))))))))))=>((((?[X1014:$i]:(((((X17 @ X1014)))&(![X1015:$i]:(((((X17 @ X1015)))=>(((X1014)=(X1015))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_298, c_0_296])).
% 2.91/0.65 thf(c_0_318, plain, ((exuEu)=(![X1:$i > $o]:((((?[X1010:$i]:(((((X1 @ X1010)))&(![X1011:$i]:(((((X1 @ X1011)))=>(((X1010)=(X1011))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_299, c_0_296])).
% 2.91/0.65 thf(c_0_319, axiom, ((breln1all2)=(![X4:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X4))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[breln1all2, c_0_300])).
% 2.91/0.65 thf(c_0_320, axiom, ((breln1SetBreln1)=(![X4:$i, X33:$i]:((((in @ X33 @ (breln1Set @ X4)))=>(((subset @ X33 @ (cartprod @ X4 @ X4)))))))), inference(apply_def,[status(thm)],[breln1SetBreln1, c_0_300])).
% 2.91/0.65 thf(c_0_321, plain, ((setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X4)))))), inference(apply_def,[status(thm)],[c_0_301, c_0_300])).
% 2.91/0.65 thf(c_0_322, axiom, ((breln1all1)=(![X4:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X4))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[breln1all1, c_0_300])).
% 2.91/0.65 thf(c_0_323, axiom, ((subbreln1)=(![X4:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X4))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X4))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln1, c_0_300])).
% 2.91/0.65 thf(c_0_324, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 2.91/0.65 thf(c_0_325, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 2.91/0.65 thf(c_0_326, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_294])).
% 2.91/0.65 thf(c_0_327, 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])).
% 2.91/0.65 thf(c_0_328, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 2.91/0.65 thf(c_0_329, plain, ((ex1I)<=>![X4:$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])).
% 2.91/0.65 thf(c_0_330, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 2.91/0.65 thf(c_0_331, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 2.91/0.65 thf(c_0_332, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 2.91/0.65 thf(c_0_333, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 2.91/0.65 thf(c_0_334, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 2.91/0.65 thf(c_0_335, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 2.91/0.65 thf(c_0_336, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_302, c_0_294])).
% 2.91/0.65 thf(c_0_337, plain, ((apProp)<=>![X4:$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])).
% 2.91/0.65 thf(c_0_338, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 2.91/0.65 thf(c_0_339, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 2.91/0.65 thf(c_0_340, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 2.91/0.65 thf(c_0_341, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 2.91/0.65 thf(c_0_342, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 2.91/0.65 thf(c_0_343, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_294])).
% 2.91/0.65 thf(c_0_344, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_294])).
% 2.91/0.65 thf(c_0_345, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 2.91/0.65 thf(c_0_346, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 2.91/0.65 thf(c_0_347, plain, ((lamProp)<=>![X4:$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])).
% 2.91/0.65 thf(c_0_348, 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])).
% 2.91/0.65 thf(c_0_349, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_294])).
% 2.91/0.65 thf(c_0_350, 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])).
% 2.91/0.65 thf(c_0_351, 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])).
% 2.91/0.65 thf(c_0_352, 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])).
% 2.91/0.65 thf(c_0_353, 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])).
% 2.91/0.65 thf(c_0_354, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 2.91/0.65 thf(c_0_355, plain, ((iftrueProp2)<=>![X4:$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])).
% 2.91/0.65 thf(c_0_356, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 2.91/0.65 thf(c_0_357, plain, ((iffalseProp2)<=>![X4:$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])).
% 2.91/0.65 thf(c_0_358, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 2.91/0.65 thf(c_0_359, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X1002:$i]:(((((X1 @ X1002)))&(![X1003:$i]:(((((X1 @ X1003)))=>(((X1002)=(X1003)))))))))))))), inference(apply_def,[status(thm)],[c_0_303, c_0_296])).
% 2.91/0.65 thf(c_0_360, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X1000:$i]:(((((X1 @ X1000)))&(![X1001:$i]:(((((X1 @ X1001)))=>(((X1000)=(X1001)))))))))))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_296])).
% 2.91/0.65 thf(c_0_361, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X998:$i]:(((((X1 @ X998)))&(![X999:$i]:(((((X1 @ X999)))=>(((X998)=(X999)))))))))))))), inference(apply_def,[status(thm)],[c_0_305, c_0_296])).
% 2.91/0.65 thf(c_0_362, plain, ((emptyE1)<=>![X4:$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])).
% 2.91/0.65 thf(c_0_363, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_306])).
% 2.91/0.65 thf(c_0_364, plain, ((exuE2)=(![X1:$i > $o]:((((?[X996:$i]:(((((X1 @ X996)))&(![X997:$i]:(((((X1 @ X997)))=>(((X996)=(X997))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_296])).
% 2.91/0.65 thf(c_0_365, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 2.91/0.65 thf(c_0_366, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_306])).
% 2.91/0.65 thf(c_0_367, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_308, c_0_306])).
% 2.91/0.65 thf(c_0_368, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_306])).
% 2.91/0.65 thf(c_0_369, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 2.91/0.65 thf(c_0_370, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X994:$i]:(((((X1 @ X994)))&(![X995:$i]:(((((X1 @ X995)))=>(((X994)=(X995))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_309, c_0_296])).
% 2.91/0.65 thf(c_0_371, plain, ((exuE1)=(![X1:$i > $o]:((((?[X992:$i]:(((((X1 @ X992)))&(![X993:$i]:(((((X1 @ X993)))=>(((X992)=(X993))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_310, c_0_296])).
% 2.91/0.65 thf(c_0_372, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 2.91/0.65 thf(c_0_373, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 2.91/0.65 thf(c_0_374, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 2.91/0.65 thf(c_0_375, plain, ((descrp)=(![X1:$i > $o]:((((?[X990:$i]:(((((X1 @ X990)))&(![X991:$i]:(((((X1 @ X991)))=>(((X990)=(X991))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_311, c_0_296])).
% 2.91/0.65 thf(c_0_376, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X988:$i]:(((((X6 @ X2 @ X988)))&(![X989:$i]:(((((X6 @ X2 @ X989)))=>(((X988)=(X989)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_312, c_0_296])).
% 2.91/0.65 thf(c_0_377, plain, ((epred1_0)<=>![X1045:$i]:(?[X1046:$i]:((((![X1047:$i]:(((in @ X1047 @ X1046)=>![X1048:$i]:(((in @ X1048 @ X1047)=>(in @ X1048 @ X1045)))))&![X1049:$i, X1050:$i]:((((in @ X1049 @ X1045)&(in @ X1050 @ X1045))=>(![X1051:$i]:(((in @ X1051 @ X1046)=>((in @ X1049 @ X1051)<=>(in @ X1050 @ X1051))))=>((X1049)=(X1050))))))&![X1052:$i, X1053:$i]:((((in @ X1052 @ X1046)&(in @ X1053 @ X1046))=>(![X1054:$i]:(((in @ X1054 @ X1052)=>(in @ X1054 @ X1053)))|![X1055:$i]:(((in @ X1055 @ X1053)=>(in @ X1055 @ X1052)))))))&![X1056:$i]:(((![X1057:$i]:(((in @ X1057 @ X1056)=>(in @ X1057 @ X1045)))&?[X1058:$i]:((in @ X1058 @ X1056)))=>?[X1059:$i, X1060:$i]:(((((in @ X1059 @ X1046)&(in @ X1060 @ X1056))&~(?[X1061:$i]:(((in @ X1061 @ X1059)&(in @ X1061 @ X1056)))))&![X1062:$i]:(((in @ X1062 @ X1046)=>(![X1063:$i]:(((in @ X1063 @ X1062)=>(in @ X1063 @ X1059)))|(in @ X1060 @ X1062)))))))))))), introduced(definition)).
% 2.91/0.65 thf(c_0_378, negated_conjecture, ~((![X1016:$i, X1017:$i]:((![X1018:$i]:(((in @ X1018 @ X1016)<=>(in @ X1018 @ X1017)))=>((X1016)=(X1017))))=>(![X1019:$i]:(~(in @ X1019 @ emptyset))=>(![X1020:$i, X1021:$i, X1022:$i]:(((in @ X1022 @ (setadjoin @ X1020 @ X1021))<=>(((X1022)=(X1020))|(in @ X1022 @ X1021))))=>(![X1023:$i, X1024:$i]:(((in @ X1024 @ (powerset @ X1023))<=>![X1025:$i]:(((in @ X1025 @ X1024)=>(in @ X1025 @ X1023)))))=>(![X1026:$i, X1027:$i]:(((in @ X1027 @ (setunion @ X1026))<=>?[X1028:$i]:(((in @ X1027 @ X1028)&(in @ X1028 @ X1026)))))=>((in @ emptyset @ omega)=>(![X1029:$i]:(((in @ X1029 @ omega)=>(in @ (setadjoin @ X1029 @ X1029) @ omega)))=>(![X1030:$i]:((((in @ emptyset @ X1030)&![X1031:$i]:((((in @ X1031 @ omega)&(in @ X1031 @ X1030))=>(in @ (setadjoin @ X1031 @ X1031) @ X1030))))=>![X1032:$i]:(((in @ X1032 @ omega)=>(in @ X1032 @ X1030)))))=>(![X1033:$i > $i > $o, X1034:$i]:((![X1035:$i]:(((in @ X1035 @ X1034)=>?[X1036:$i]:(((X1033 @ X1035 @ X1036)&![X1037:$i]:(((X1033 @ X1035 @ X1037)=>((X1036)=(X1037))))))))=>?[X1038:$i]:(![X1039:$i]:(((in @ X1039 @ X1038)<=>?[X1040:$i]:(((in @ X1040 @ X1034)&(X1033 @ X1040 @ X1039))))))))=>(![X1041:$i]:((?[X1042:$i]:((in @ X1042 @ X1041))=>?[X1043:$i]:(((in @ X1043 @ X1041)&~(?[X1044:$i]:(((in @ X1044 @ X1043)&(in @ X1044 @ X1041))))))))=>((epred1_0)=>(![X1064:$i > $o]:((?[X1065:$i]:(((X1064 @ X1065)&![X1066:$i]:(((X1064 @ X1066)=>((X1065)=(X1066))))))=>(X1064 @ (descr @ (^[Z0:$i]:(X1064 @ Z0))))))=>(![X1067:$i, X1068:$i > $o, X1069:$i]:(((in @ X1069 @ X1067)=>((X1068 @ X1069)=>(in @ X1069 @ (dsetconstr @ X1067 @ X1068)))))=>(![X1070:$i, X1071:$i > $o, X1072:$i]:(((in @ X1072 @ (dsetconstr @ X1070 @ X1071))=>(in @ X1072 @ X1070)))=>(![X1073:$i, X1074:$i > $o, X1075:$i]:(((in @ X1075 @ (dsetconstr @ X1073 @ X1074))=>(X1074 @ X1075)))=>(![X1076:$i > $o]:((?[X1077:$i]:(((X1076 @ X1077)&![X1078:$i]:(((X1076 @ X1078)=>((X1077)=(X1078))))))=>?[X1079:$i]:(((X1076 @ X1079)&![X1080:$i]:(((X1076 @ X1080)=>((X1079)=(X1080))))))))=>(![X1081:$o, X1082:$i]:(((in @ X1082 @ (prop2set @ ((X1081))))=>(X1081)))=>(![X1083:$i]:(((in @ X1083 @ emptyset)=>![X1084:$o]:((X1084))))=>(![X1085:$i]:(((in @ X1085 @ emptyset)=>~($true)))=>(![X1086:$i]:(~(in @ X1086 @ emptyset))=>(![X1087:$i > $o]:((?[X1088:$i]:(((X1087 @ X1088)&![X1089:$i]:(((X1087 @ X1089)=>((X1088)=(X1089))))))=>?[X1090:$i]:((X1087 @ X1090))))=>(![X1091:$i, X1092:$i]:((![X1093:$i]:(((in @ X1093 @ X1091)=>(in @ X1093 @ X1092)))=>(![X1094:$i]:(((in @ X1094 @ X1092)=>(in @ X1094 @ X1091)))=>((X1091)=(X1092)))))=>(![X1095:$i]:((![X1096:$i]:(~(in @ X1096 @ X1095))=>((X1095)=(emptyset))))=>(![X1097:$i]:((![X1098:$i]:(~(in @ X1098 @ X1097))=>((X1097)=(emptyset))))=>(![X1099:$i, X1100:$i > $o, X1101:$i]:(((in @ X1101 @ X1099)=>((in @ X1101 @ (dsetconstr @ X1099 @ X1100))<=>(X1100 @ X1101))))=>(![X1102:$i]:((((X1102)!=(emptyset))=>?[X1103:$i]:((in @ X1103 @ X1102))))=>(![X1104:$i, X1105:$i > $o, X1106:$i]:(((in @ X1106 @ X1104)=>((X1105 @ X1106)=>((dsetconstr @ X1104 @ X1105)!=(emptyset)))))=>(![X1107:$i]:((?[X1108:$i]:((in @ X1108 @ X1107))=>((X1107)!=(emptyset))))=>(![X1109:$i, X1110:$i]:((in @ X1109 @ (setadjoin @ X1109 @ X1110)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1111:$i, X1112:$i, X1113:$i]:(((in @ X1113 @ X1112)=>(in @ X1113 @ (setadjoin @ X1111 @ X1112))))=>(![X1114:$i, X1115:$i, X1116:$i]:(((in @ X1116 @ (setadjoin @ X1114 @ X1115))=>![X1117:$o]:(((((X1116)=(X1114))=>(X1117))=>(((in @ X1116 @ X1115)=>(X1117))=>(X1117))))))=>(![X1118:$i, X1119:$i, X1120:$i]:(((in @ X1120 @ (setadjoin @ X1118 @ X1119))=>(((X1120)=(X1118))|(in @ X1120 @ X1119))))=>(![X1121:$i]:(((dsetconstr @ X1121 @ (^[Z0:$i]:($true)))=(X1121)))=>(![X1122:$i, X1123:$i]:((![X1124:$i]:(((in @ X1124 @ X1123)=>(in @ X1124 @ X1122)))=>(in @ X1123 @ (powerset @ X1122))))=>(![X1125:$i]:((in @ emptyset @ (powerset @ X1125)))=>(![X1126:$i]:((in @ emptyset @ (powerset @ X1126)))=>(![X1127:$i, X1128:$i, X1129:$i]:(((in @ X1128 @ (powerset @ X1127))=>((in @ X1129 @ X1128)=>(in @ X1129 @ X1127))))=>(![X1130:$i, X1131:$i, X1132:$i]:(((in @ X1131 @ X1132)=>((in @ X1132 @ X1130)=>(in @ X1131 @ (setunion @ X1130)))))=>(![X1133:$i, X1134:$i]:(((in @ X1134 @ (setunion @ X1133))=>![X1135:$o]:((![X1136:$i]:(((in @ X1134 @ X1136)=>((in @ X1136 @ X1133)=>(X1135))))=>(X1135)))))=>(![X1137:$i, X1138:$i]:(((in @ X1138 @ X1137)=>(in @ X1138 @ (powerset @ (setunion @ X1137)))))=>(![X1139:$i > $o]:((?[X1140:$i]:(((X1139 @ X1140)&![X1141:$i]:(((X1139 @ X1141)=>((X1140)=(X1141))))))=>?[X1142:$i]:(![X1143:$i]:(((X1139 @ X1143)<=>((X1143)=(X1142)))))))=>(![X1144:$i]:((((X1144)!=(emptyset))=>?[X1145:$i]:(((in @ X1145 @ X1144)&$true))))=>(![X1146:$i, X1147:$i]:(((in @ X1146 @ (setadjoin @ X1147 @ emptyset))=>((X1146)=(X1147))))=>(![X1148:$i, X1149:$i]:((((X1148)!=(X1149))=>~(in @ X1149 @ (setadjoin @ X1148 @ emptyset))))=>(![X1150:$i, X1151:$i]:((((X1150)=(X1151))=>(in @ X1150 @ (setadjoin @ X1151 @ emptyset))))=>(![X1152:$i, X1153:$i]:(((in @ X1152 @ (setadjoin @ X1153 @ emptyset))=>(in @ X1153 @ (setadjoin @ X1152 @ emptyset))))=>(![X1154:$i, X1155:$i, X1156:$i]:(((in @ X1156 @ (setadjoin @ X1154 @ (setadjoin @ X1155 @ emptyset)))=>(((X1156)=(X1154))|((X1156)=(X1155)))))=>(![X1157:$i, X1158:$i]:((in @ X1157 @ (setadjoin @ X1157 @ (setadjoin @ X1158 @ emptyset))))=>(![X1159:$i, X1160:$i]:((in @ X1160 @ (setadjoin @ X1159 @ (setadjoin @ X1160 @ emptyset))))=>(![X1161:$i, X1162:$i > $o]:((?[X1163:$i]:(((in @ X1163 @ X1161)&(X1162 @ X1163)))=>(((dsetconstr @ X1161 @ X1162)=(emptyset))=>~($true))))=>(![X1164:$i > $o, X1165:$i]:(((in @ X1165 @ emptyset)=>(X1164 @ X1165)))=>(![X1166:$i, X1167:$i > $o]:((~(![X1168:$i]:(((in @ X1168 @ X1166)=>(X1167 @ X1168))))=>?[X1169:$i]:(((in @ X1169 @ X1166)&~((X1167 @ X1169))))))=>(![X1170:$i, X1171:$i > $o]:((![X1172:$i]:(((in @ X1172 @ X1170)=>~((X1171 @ X1172))))=>~(?[X1173:$i]:(((in @ X1173 @ X1170)&(X1171 @ X1173))))))=>(![X1174:$i, X1175:$i > $o]:((~(?[X1176:$i]:(((in @ X1176 @ X1174)&(X1175 @ X1176))))=>![X1177:$i]:(((in @ X1177 @ X1174)=>~((X1175 @ X1177))))))=>(![X1178:$i, X1179:$i > $o]:((?[X1180:$i]:(((in @ X1180 @ X1178)&~((X1179 @ X1180))))=>~(![X1181:$i]:(((in @ X1181 @ X1178)=>(X1179 @ X1181))))))=>(![X1182:$o]:(((X1182)=>(in @ emptyset @ (prop2set @ ((X1182))))))=>((prop2set2propI)=>(![X1183:$i, X1184:$i > $o]:((~(?[X1185:$i]:(((in @ X1185 @ X1183)&(X1184 @ X1185))))=>![X1186:$i]:(((in @ X1186 @ X1183)=>~((X1184 @ X1186))))))=>(![X1187:$i, X1188:$i > $o]:((~(![X1189:$i]:(((in @ X1189 @ X1187)=>(X1188 @ X1189))))=>?[X1190:$i]:(((in @ X1190 @ X1187)&~((X1188 @ X1190))))))=>(![X1191:$i > $o]:((?[X1192:$i]:(((X1191 @ X1192)&![X1193:$i]:(((X1191 @ X1193)=>((X1192)=(X1193))))))=>?[X1194:$i]:(((X1191 @ X1194)&![X1195:$i]:(((X1191 @ X1195)=>((X1194)=(X1195))))))))=>(![X1196:$i > $o]:((?[X1197:$i]:((X1196 @ X1197))=>(![X1198:$i, X1199:$i]:(((X1196 @ X1198)=>((X1196 @ X1199)=>((X1198)=(X1199)))))=>?[X1200:$i]:(((X1196 @ X1200)&![X1201:$i]:(((X1196 @ X1201)=>((X1200)=(X1201)))))))))=>(![X1202:$i > $o]:((?[X1203:$i]:(![X1204:$i]:(((X1202 @ X1204)<=>((X1204)=(X1203)))))=>?[X1205:$i]:(((X1202 @ X1205)&![X1206:$i]:(((X1202 @ X1206)=>((X1205)=(X1206))))))))=>(![X1207:$i, X1208:$i]:((((X1207)=(X1208))=>![X1209:$i, X1210:$i]:((((X1209)=(X1210))=>((in @ X1209 @ X1207)=>(in @ X1210 @ X1208))))))=>(![X1211:$i, X1212:$i]:((((X1211)=(X1212))=>![X1213:$i, X1214:$i]:((((X1213)=(X1214))=>((in @ X1213 @ X1211)<=>(in @ X1214 @ X1212))))))=>(![X1215:$i > $o]:((?[X1216:$i]:(((X1215 @ X1216)&![X1217:$i]:(((X1215 @ X1217)=>((X1216)=(X1217))))))=>![X1218:$i, X1219:$i]:(((X1215 @ X1218)=>((X1215 @ X1219)=>((X1218)=(X1219)))))))=>(![X1220:$i > $o, X1221:$i > $o]:((![X1222:$i, X1223:$i]:((((X1222)=(X1223))=>((X1220 @ X1222)<=>(X1221 @ X1223))))=>(?[X1224:$i]:(((X1220 @ X1224)&![X1225:$i]:(((X1220 @ X1225)=>((X1224)=(X1225))))))<=>?[X1226:$i]:(((X1221 @ X1226)&![X1227:$i]:(((X1221 @ X1227)=>((X1226)=(X1227)))))))))=>(((emptyset)=(emptyset))=>(![X1228:$i, X1229:$i]:((((X1228)=(X1229))=>![X1230:$i, X1231:$i]:((((X1230)=(X1231))=>((setadjoin @ X1228 @ X1230)=(setadjoin @ X1229 @ X1231))))))=>(![X1232:$i, X1233:$i]:((((X1232)=(X1233))=>((powerset @ X1232)=(powerset @ X1233))))=>(![X1234:$i, X1235:$i]:((((X1234)=(X1235))=>((setunion @ X1234)=(setunion @ X1235))))=>(((omega)=(omega))=>(![X1236:$i > $o]:((?[X1237:$i]:(((X1236 @ X1237)&![X1238:$i]:(((X1236 @ X1238)=>((X1237)=(X1238))))))=>![X1239:$i, X1240:$i]:(((X1236 @ X1239)=>((X1236 @ X1240)=>((X1239)=(X1240)))))))=>(![X1241:$i > $o, X1242:$i > $o]:((![X1243:$i, X1244:$i]:((((X1243)=(X1244))=>((X1241 @ X1243)<=>(X1242 @ X1244))))=>(?[X1245:$i]:(((X1241 @ X1245)&![X1246:$i]:(((X1241 @ X1246)=>((X1245)=(X1246))))))=>(?[X1247:$i]:(((X1242 @ X1247)&![X1248:$i]:(((X1242 @ X1248)=>((X1247)=(X1248))))))=>((descr @ X1241)=(descr @ X1242))))))=>(![X1249:$i, X1250:$i]:((((X1249)=(X1250))=>![X1251:$i > $o, X1252:$i > $o]:((![X1253:$i]:(((in @ X1253 @ X1249)=>![X1254:$i]:(((in @ X1254 @ X1250)=>(((X1253)=(X1254))=>((X1251 @ X1253)<=>(X1252 @ X1254)))))))=>((dsetconstr @ X1249 @ X1251)=(dsetconstr @ X1250 @ X1252))))))=>(![X1255:$i, X1256:$i]:((![X1257:$i]:(((in @ X1257 @ X1255)=>(in @ X1257 @ X1256)))=>(subset @ X1255 @ X1256)))=>(![X1258:$i, X1259:$i]:((((X1258)=(X1259))=>(subset @ X1259 @ X1258)))=>(![X1260:$i, X1261:$i]:((((X1260)=(X1261))=>(subset @ X1260 @ X1261)))=>(![X1262:$i, X1263:$i]:((![X1264:$i]:(((in @ X1264 @ X1262)=>(in @ X1264 @ X1263)))=>(subset @ X1262 @ X1263)))=>(![X1265:$i]:((subset @ emptyset @ X1265))=>(![X1266:$i, X1267:$i, X1268:$i]:(((subset @ X1266 @ X1267)=>((in @ X1268 @ X1266)=>(in @ X1268 @ X1267))))=>(![X1269:$i, X1270:$i, X1271:$i]:(((subset @ X1269 @ X1270)=>(~(in @ X1271 @ X1270)=>~(in @ X1271 @ X1269))))=>(![X1272:$i, X1273:$i, X1274:$i]:(((in @ X1274 @ X1272)=>(~(in @ X1274 @ X1273)=>~(subset @ X1272 @ X1273))))=>(![X1275:$i, X1276:$i]:((~(subset @ X1275 @ X1276)=>((X1275)!=(X1276))))=>(![X1277:$i, X1278:$i, X1279:$i]:(((in @ X1279 @ X1277)=>(~(in @ X1279 @ X1278)=>((X1277)!=(X1278)))))=>(![X1280:$i]:((subset @ X1280 @ X1280))=>(![X1281:$i, X1282:$i, X1283:$i]:(((subset @ X1281 @ X1282)=>((subset @ X1282 @ X1283)=>(subset @ X1281 @ X1283))))=>(![X1284:$i, X1285:$i]:((subset @ X1285 @ (setadjoin @ X1284 @ X1285)))=>(![X1286:$i, X1287:$i, X1288:$i]:(((subset @ X1286 @ X1288)=>(subset @ X1286 @ (setadjoin @ X1287 @ X1288))))=>(![X1289:$i, X1290:$i]:(((subset @ X1289 @ X1290)=>(in @ X1289 @ (powerset @ X1290))))=>(![X1291:$i, X1292:$i]:(((subset @ X1291 @ X1292)=>((subset @ X1292 @ X1291)=>((X1291)=(X1292)))))=>(![X1293:$i]:(((subset @ X1293 @ emptyset)=>((X1293)=(emptyset))))=>(![X1294:$i, X1295:$i]:(((subset @ X1295 @ X1294)=>(in @ X1295 @ (powerset @ X1294))))=>(![X1296:$i, X1297:$i]:(((in @ X1297 @ (powerset @ X1296))=>(subset @ X1297 @ X1296)))=>(![X1298:$i]:((in @ X1298 @ (powerset @ X1298)))=>(![X1299:$i, X1300:$i]:(((subset @ X1299 @ X1300)=>(subset @ (powerset @ X1299) @ (powerset @ X1300))))=>(![X1301:$i, X1302:$i > $o]:((in @ (dsetconstr @ X1301 @ X1302) @ (powerset @ X1301)))=>(![X1303:$i, X1304:$i > $o]:((subset @ (dsetconstr @ X1303 @ X1304) @ X1303))=>(![X1305:$i, X1306:$i, X1307:$i]:(((in @ X1307 @ X1305)=>(in @ X1307 @ (binunion @ X1305 @ X1306))))=>(![X1308:$i, X1309:$i]:((in @ X1309 @ (setadjoin @ X1308 @ (setadjoin @ X1309 @ emptyset))))=>(![X1310:$i, X1311:$i, X1312:$i]:(((in @ X1312 @ X1311)=>(in @ X1312 @ (binunion @ X1310 @ X1311))))=>(![X1313:$i, X1314:$i, X1315:$i, X1316:$o]:(((in @ X1315 @ (binunion @ X1313 @ X1314))=>(((in @ X1315 @ X1313)=>(X1316))=>(((in @ X1315 @ X1314)=>(X1316))=>(X1316)))))=>(![X1317:$i, X1318:$i, X1319:$i]:(((in @ X1319 @ (binunion @ X1317 @ X1318))=>((in @ X1319 @ X1317)|(in @ X1319 @ X1318))))=>(![X1320:$i, X1321:$i]:((subset @ X1320 @ (binunion @ X1320 @ X1321)))=>(![X1322:$i, X1323:$i]:((subset @ X1323 @ (binunion @ X1322 @ X1323)))=>(![X1324:$i, X1325:$i, X1326:$i]:(((in @ X1326 @ X1324)=>((in @ X1326 @ X1325)=>(in @ X1326 @ (binintersect @ 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X1935 @ X1938) @ (setminus @ X1935 @ X1939))))))))))))=>(![X1940:$i, X1941:$i]:(((in @ X1941 @ (powerset @ X1940))=>![X1942:$i]:(((in @ X1942 @ (powerset @ X1940))=>![X1943:$i]:(((in @ X1943 @ (powerset @ X1940))=>(in @ (binintersect @ X1941 @ X1942) @ (powerset @ (binintersect @ (binunion @ X1941 @ X1943) @ (binunion @ X1942 @ X1943))))))))))=>(![X1944:$i, X1945:$i]:(((in @ X1945 @ (powerset @ X1944))=>![X1946:$i]:(((in @ X1946 @ (powerset @ X1944))=>((subset @ X1945 @ (setminus @ X1944 @ X1946))=>(subset @ X1946 @ (setminus @ X1944 @ X1945)))))))=>(![X1947:$i, X1948:$i]:(((in @ X1948 @ (powerset @ X1947))=>![X1949:$i]:(((in @ X1949 @ (powerset @ X1947))=>(in @ (setminus @ X1947 @ (binunion @ X1948 @ X1949)) @ (powerset @ (setminus @ X1947 @ X1948)))))))=>(![X1950:$i, X1951:$i]:(((subset @ X1951 @ (cartprod @ X1950 @ X1950))=>![X1952:$i > $o]:((![X1953:$i]:(((in @ X1953 @ X1950)=>![X1954:$i]:(((in @ X1954 @ X1950)=>((in @ (kpair @ X1953 @ X1954) @ X1951)=>(X1952 @ (kpair @ X1953 @ X1954)))))))=>![X1955:$i]:(((in @ X1955 @ X1951)=>(X1952 @ X1955)))))))=>(![X1956:$i, X1957:$i]:(((in @ X1957 @ (breln1Set @ X1956))=>(subset @ X1957 @ (cartprod @ X1956 @ X1956))))=>((choice2fnsingleton)=>(![X1958:$i, X1959:$i > $i > $o]:((subset @ (dpsetconstr @ X1958 @ X1958 @ X1959) @ (cartprod @ X1958 @ X1958)))=>(![X1960:$i, X1961:$i]:(((subset @ X1961 @ (cartprod @ X1960 @ X1960))=>![X1962:$i > $o]:((![X1963:$i]:(((in @ X1963 @ X1960)=>![X1964:$i]:(((in @ X1964 @ X1960)=>((in @ (kpair @ X1963 @ X1964) @ X1961)=>(X1962 @ (kpair @ X1963 @ X1964)))))))=>![X1965:$i]:(((in @ X1965 @ X1961)=>(X1962 @ X1965)))))))=>(![X1966:$i, X1967:$i]:(((subset @ X1967 @ (cartprod @ X1966 @ X1966))=>![X1968:$i]:(((subset @ X1968 @ (cartprod @ X1966 @ X1966))=>(![X1969:$i]:(((in @ X1969 @ X1966)=>![X1970:$i]:(((in @ X1970 @ X1966)=>((in @ (kpair @ X1969 @ X1970) @ X1967)=>(in @ (kpair @ X1969 @ X1970) @ X1968))))))=>(subset @ X1967 @ X1968))))))=>![X4:$i, X33:$i]:(((subset @ X33 @ (cartprod @ X4 @ X4))=>![X35:$i]:(((subset @ X35 @ (cartprod @ X4 @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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woz1_1]), c_0_318]), woz1_2]), emptysetsubset]), woz1_3]), woz1_4]), woz1_5]), c_0_319]), c_0_320]), inCongP]), c_0_321]), c_0_322]), c_0_323]), c_0_300]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), setadjoinSub]), setminusER]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), powersetsubset]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_324]), c_0_325]), binunionLsub]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), binintersectER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), c_0_326]), funcGraphProp4]), funcextLem]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), funcext]), c_0_327]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), symdiffE]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), kpairiskpair]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), ubforcartprodlem1]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), setunionsingleton2]), setukpairinjL1]), singletonsuniq]), c_0_328]), c_0_329]), c_0_330]), c_0_331]), setunionsingleton]), c_0_332]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), theprop]), setukpairinjR1]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), c_0_333]), setukpairinjR]), setukpairinjR2]), upairequniteq]), cartprodpairmemEL]), c_0_334]), c_0_335]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemER]), c_0_336]), app]), c_0_337]), c_0_338]), c_0_339]), c_0_340]), c_0_341]), c_0_342]), infuncsetfunc]), c_0_343]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), funcinfuncset]), ap2p]), c_0_348]), c_0_349]), c_0_350]), c_0_351]), c_0_352]), ap2apEq2]), ap2apEq1]), funcext2]), c_0_353]), theeq]), ifp]), c_0_354]), c_0_355]), c_0_356]), c_0_357]), c_0_358]), iftrue]), complementT_lem]), setminusT_lem]), powersetT_lem]), binunionT_lem]), binintersectT_lem]), iftrueorfalse]), iffalse]), setextT]), binintersectTERcontra]), binintersectTELcontra]), complementTE1]), complementTI1]), powersetTE1]), powersetTI1]), subsetTI]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), c_0_359]), c_0_360]), c_0_361]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_362]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_363]), c_0_364]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_365]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_366]), c_0_367]), c_0_368]), c_0_369]), noeltsimpempty]), emptyI]), setext]), c_0_370]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_371]), c_0_372]), c_0_373]), c_0_374]), c_0_375]), wellorderingAx]), foundationAx]), c_0_376]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_377])).
% 2.91/0.65 thf(c_0_379, negated_conjecture, ![X1971:$i, X1972:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1984:$i, X1985:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1993:$i, X1994:$i > $i > $o, X1995:$i, X1997:$i, X2000:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2007:$i, X2008:$i > $o, X2009:$i, X2011:$i, X2012:$i > $o, X2013:$i, X2014:$i, X2015:$i > $o, X2016:$i, X2017:$i, X2018:$i > $o, X2019:$i, X2020:$i > $o, X2021:$i, X2024:$i, X2025:$o, X2026:$i, X2027:$i, X2028:$o, X2029:$i, X2030:$i, X2031:$i > $o, X2032:$i, X2035:$i, X2036:$i, X2039:$i, X2041:$i, X2043:$i, X2044:$i > $o, X2045:$i, X2046:$i, X2048:$i, X2049:$i > $o, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$o, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$o, X2081:$i, X2082:$i, X2083:$i > $o, X2084:$i, X2087:$i, X2088:$i, X2089:$i, X2091:$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 > $o, X2108:$i, X2109:$i > $o, X2110:$i, X2111:$i, X2112:$i > $o, X2113:$i, X2115:$i, X2116:$i > $o, X2118:$i, X2119:$i, X2120:$i > $o, X2122:$i, X2123:$i, X2124:$i > $o, X2125:$i, X2127:$o, X2128:$i, X2129:$i > $o, X2131:$i, X2132:$i, X2133:$i > $o, X2134:$i, X2136:$i > $o, X2137:$i, X2140:$i, X2141:$i > $o, X2142:$i, X2146:$i, X2147:$i > $o, X2148:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i > $o, X2161:$i, X2163:$i, X2164:$i, X2165:$i > $o, X2166:$i > $o, X2169:$i, X2172:$i, X2173:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i > $o, X2186:$i, X2188:$i, X2189:$i, X2190:$i > $o, X2191:$i > $o, X2194:$i, X2196:$i, X2198:$i, X2199:$i, X2200:$i > $o, X2201:$i > $o, X2204:$i, X2205:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2214:$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, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i > $o, X2252:$i, X2253:$i > $o, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$o, X2266:$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:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$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, X2332:$i, X2333:$o, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i > $o, X2408:$i, X2409:$i, X2410:$i > $o, X2412:$i, X2413:$i > $o, X2414:$i, X2416:$i, X2417:$i > $o, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$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:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$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 > $i > $o, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i > $i > $o, X2498:$i, X2499:$i, X2500:$i > $i > $o, X2501:$i, X2502:$i, X2503:$i > $i > $o, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i > $i > $o, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i > $i > $o, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i > $i > $o, X2519:$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 > $i, X2547:$i, X2548:$i, X2549:$i > $i, X2551:$i, X2552:$i, X2553:$i > $i, X2555:$i, X2556:$i, X2557:$i, X2558:$i > $o, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i > $o, X2568:$i, X2569:$i, X2570:$i > $o, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2622:$i, X2623:$i, X2624:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i, X2630:$i, X2631:$i, X2632:$i > $i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i > $i, X2642:$i, X2643:$i, X2644:$i > $i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$o, X2652:$i, X2653:$i, X2654:$i, X2655:$o, X2656:$i, X2657:$i, X2658:$i, X2659:$o, X2660:$i, X2661:$i, X2662:$i, X2663:$o, X2664:$i, X2665:$i, X2666:$i, X2667:$o, X2668:$i, X2669:$i, X2670:$i, X2671:$o, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$o, X2678:$i, X2679:$i, X2680:$i, X2681:$o, X2682:$i, X2683:$i, X2684:$i, X2685:$o, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2706:$i, X2707:$i, X2708:$i, X2710:$i, X2711:$i, X2712:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$i, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$o, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2851:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2856:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i, X2871:$i, X2872:$i, X2873:$i, X2874:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$i, X2885:$i, X2886:$i, X2887:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2901:$i > $o, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i > $i > $o, X2909:$i, X2910:$i, X2911:$i > $o, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i]:((((~(in @ (esk1_2 @ X1971 @ X1972) @ X1971)|~(in @ (esk1_2 @ X1971 @ X1972) @ X1972)|((X1971)=(X1972)))&((in @ (esk1_2 @ X1971 @ X1972) @ X1971)|(in @ (esk1_2 @ X1971 @ X1972) @ X1972)|((X1971)=(X1972))))&(~(in @ X1974 @ emptyset)&(((~(in @ X1977 @ (setadjoin @ X1975 @ X1976))|(((X1977)=(X1975))|(in @ X1977 @ X1976)))&((((X1977)!=(X1975))|(in @ X1977 @ (setadjoin @ X1975 @ X1976)))&(~(in @ X1977 @ X1976)|(in @ X1977 @ (setadjoin @ X1975 @ X1976)))))&(((~(in @ X1979 @ (powerset @ X1978))|(~(in @ X1980 @ X1979)|(in @ X1980 @ X1978)))&(((in @ (esk2_2 @ X1981 @ X1982) @ X1982)|(in @ X1982 @ (powerset @ X1981)))&(~(in @ (esk2_2 @ X1981 @ X1982) @ X1981)|(in @ X1982 @ (powerset @ X1981)))))&(((((in @ X1985 @ (esk3_2 @ X1984 @ X1985))|~(in @ X1985 @ (setunion @ X1984)))&((in @ (esk3_2 @ X1984 @ X1985) @ X1984)|~(in @ X1985 @ (setunion @ X1984))))&(~(in @ X1988 @ X1989)|~(in @ X1989 @ X1987)|(in @ X1988 @ (setunion @ X1987))))&((in @ emptyset @ omega)&((~(in @ X1990 @ omega)|(in @ (setadjoin @ X1990 @ X1990) @ omega))&(((((in @ (esk4_1 @ X1991) @ omega)|~(in @ emptyset @ X1991)|(~(in @ X1993 @ omega)|(in @ X1993 @ X1991)))&((in @ (esk4_1 @ X1991) @ X1991)|~(in @ emptyset @ X1991)|(~(in @ X1993 @ omega)|(in @ X1993 @ X1991))))&(~(in @ (setadjoin @ (esk4_1 @ X1991) @ (esk4_1 @ X1991)) @ X1991)|~(in @ emptyset @ X1991)|(~(in @ X1993 @ omega)|(in @ X1993 @ X1991))))&((((((in @ (esk8_3 @ X1994 @ X1995 @ X2000) @ X1995)|~(in @ X2000 @ (esk7_2 @ X1994 @ X1995))|(in @ (esk5_2 @ X1994 @ X1995) @ X1995))&((X1994 @ (esk8_3 @ X1994 @ X1995 @ X2000) @ X2000)|~(in @ X2000 @ (esk7_2 @ X1994 @ X1995))|(in @ (esk5_2 @ X1994 @ X1995) @ X1995)))&(~(in @ X2003 @ X1995)|~(X1994 @ X2003 @ X2002)|(in @ X2002 @ (esk7_2 @ X1994 @ X1995))|(in @ (esk5_2 @ X1994 @ X1995) @ X1995)))&(((((in @ (esk8_3 @ X1994 @ X1995 @ X2000) @ X1995)|~(in @ X2000 @ (esk7_2 @ X1994 @ X1995))|((X1994 @ (esk5_2 @ X1994 @ X1995) @ (esk6_3 @ X1994 @ X1995 @ X1997))|~(X1994 @ (esk5_2 @ X1994 @ X1995) @ X1997)))&((X1994 @ (esk8_3 @ X1994 @ X1995 @ X2000) @ X2000)|~(in @ X2000 @ (esk7_2 @ X1994 @ X1995))|((X1994 @ (esk5_2 @ X1994 @ X1995) @ (esk6_3 @ X1994 @ X1995 @ X1997))|~(X1994 @ (esk5_2 @ X1994 @ X1995) @ X1997))))&(~(in @ X2003 @ X1995)|~(X1994 @ X2003 @ X2002)|(in @ X2002 @ (esk7_2 @ X1994 @ X1995))|((X1994 @ (esk5_2 @ X1994 @ X1995) @ (esk6_3 @ X1994 @ X1995 @ X1997))|~(X1994 @ (esk5_2 @ X1994 @ X1995) @ X1997))))&((((in @ (esk8_3 @ X1994 @ X1995 @ X2000) @ X1995)|~(in @ X2000 @ (esk7_2 @ X1994 @ X1995))|(((X1997)!=(esk6_3 @ X1994 @ X1995 @ X1997))|~(X1994 @ (esk5_2 @ X1994 @ X1995) @ X1997)))&((X1994 @ (esk8_3 @ X1994 @ X1995 @ X2000) @ X2000)|~(in @ X2000 @ (esk7_2 @ X1994 @ X1995))|(((X1997)!=(esk6_3 @ X1994 @ X1995 @ X1997))|~(X1994 @ (esk5_2 @ X1994 @ X1995) @ X1997))))&(~(in @ X2003 @ X1995)|~(X1994 @ X2003 @ X2002)|(in @ X2002 @ (esk7_2 @ X1994 @ X1995))|(((X1997)!=(esk6_3 @ X1994 @ X1995 @ X1997))|~(X1994 @ (esk5_2 @ X1994 @ X1995) @ X1997))))))&((((in @ (esk9_1 @ X2004) @ X2004)|~(in @ X2005 @ X2004))&(~(in @ X2007 @ (esk9_1 @ X2004))|~(in @ X2007 @ X2004)|~(in @ X2005 @ X2004)))&((epred1_0)&((((X2008 @ (esk10_2 @ X2008 @ X2009))|~(X2008 @ X2009)|(X2008 @ (descr @ X2008)))&(((X2009)!=(esk10_2 @ X2008 @ X2009))|~(X2008 @ X2009)|(X2008 @ (descr @ X2008))))&((~(in @ X2013 @ X2011)|(~(X2012 @ X2013)|(in @ X2013 @ (dsetconstr @ X2011 @ X2012))))&((~(in @ X2016 @ (dsetconstr @ X2014 @ X2015))|(in @ X2016 @ X2014))&((~(in @ X2019 @ (dsetconstr @ X2017 @ X2018))|(X2018 @ X2019))&(((((X2020 @ (esk12_1 @ X2020))|((X2020 @ (esk11_2 @ X2020 @ X2021))|~(X2020 @ X2021)))&(~(X2020 @ X2024)|((esk12_1 @ X2020)=(X2024))|((X2020 @ (esk11_2 @ X2020 @ X2021))|~(X2020 @ X2021))))&(((X2020 @ (esk12_1 @ X2020))|(((X2021)!=(esk11_2 @ X2020 @ X2021))|~(X2020 @ X2021)))&(~(X2020 @ X2024)|((esk12_1 @ X2020)=(X2024))|(((X2021)!=(esk11_2 @ X2020 @ X2021))|~(X2020 @ X2021)))))&((~(in @ X2026 @ (prop2set @ ((X2025))))|(X2025))&((~(in @ X2027 @ emptyset)|(X2028))&((~(in @ X2029 @ emptyset)|~($true))&(~(in @ 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X2719)))))&((~(in @ X2722 @ (powerset @ X2721))|(~(in @ X2723 @ X2721)|((in @ X2723 @ (setminus @ X2721 @ X2722))|(in @ X2723 @ X2722))))&((~(in @ X2725 @ (powerset @ X2724))|(~(in @ X2726 @ (powerset @ X2724))|(~(in @ X2727 @ X2724)|((in @ X2727 @ X2725)|~(in @ X2727 @ (binintersect @ X2725 @ X2726))))))&((~(in @ X2729 @ (powerset @ X2728))|(~(in @ X2730 @ (powerset @ X2728))|(~(in @ X2731 @ X2728)|((in @ X2731 @ X2730)|~(in @ X2731 @ (binintersect @ X2729 @ X2730))))))&((~(in @ X2733 @ (powerset @ X2732))|(~(in @ X2734 @ (powerset @ X2732))|(~(in @ X2735 @ X2732)|(~(subset @ X2733 @ (setminus @ X2732 @ X2734))|(~(in @ X2735 @ X2734)|~(in @ X2735 @ X2733))))))&((~(in @ X2737 @ (powerset @ X2736))|(~(in @ X2738 @ (powerset @ X2736))|(~(in @ X2739 @ X2736)|(~(subset @ X2737 @ X2738)|((in @ X2739 @ X2738)|~(in @ X2739 @ X2737))))))&((~(in @ X2741 @ (powerset @ X2740))|(~(in @ X2742 @ (powerset @ X2740))|(~(subset @ X2741 @ X2742)|(subset @ (setminus @ X2740 @ X2742) @ (setminus @ X2740 @ 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(powerset @ X2762))|(~(in @ X2764 @ (powerset @ X2762))|(~(in @ X2765 @ X2762)|(~(in @ X2765 @ (setminus @ X2762 @ X2763))|(in @ X2765 @ (setminus @ X2762 @ (binintersect @ X2763 @ X2764)))))))&((~(in @ X2767 @ (powerset @ X2766))|(~(in @ X2768 @ (powerset @ X2766))|(subset @ (setminus @ X2766 @ X2767) @ (setminus @ X2766 @ (binintersect @ X2767 @ X2768)))))&((~(in @ X2770 @ (powerset @ X2769))|(~(in @ X2771 @ (powerset @ X2769))|(in @ (setminus @ X2769 @ X2770) @ (powerset @ (setminus @ X2769 @ (binintersect @ X2770 @ X2771))))))&((~(in @ X2773 @ (powerset @ X2772))|(~(in @ X2774 @ (powerset @ X2772))|(~(subset @ X2773 @ (setminus @ X2772 @ X2774))|(~(in @ X2775 @ X2772)|(~(in @ X2775 @ X2774)|(in @ X2775 @ (setminus @ X2772 @ X2773)))))))&((~(in @ X2777 @ (powerset @ X2776))|(~(in @ X2778 @ (powerset @ X2776))|(~(subset @ X2777 @ (setminus @ X2776 @ X2778))|(subset @ X2778 @ (setminus @ X2776 @ X2777)))))&((~(in @ X2780 @ (powerset @ X2779))|(~(in @ X2781 @ (powerset @ X2779))|(~(in @ X2782 @ X2779)|((in @ X2782 @ (binunion @ X2780 @ X2781))|~(in @ X2782 @ X2780)))))&((~(in @ X2784 @ (powerset @ X2783))|(~(in @ X2785 @ (powerset @ X2783))|(~(in @ X2786 @ X2783)|((in @ X2786 @ (binunion @ X2784 @ X2785))|~(in @ X2786 @ X2785)))))&((~(in @ X2788 @ (powerset @ X2787))|(~(in @ X2789 @ (powerset @ X2787))|(~(in @ X2790 @ (powerset @ X2787))|(~(in @ X2791 @ X2787)|(~(in @ X2791 @ (binintersect @ X2788 @ X2789))|(in @ X2791 @ (binunion @ X2788 @ X2790)))))))&((~(in @ X2793 @ (powerset @ X2792))|(~(in @ X2794 @ (powerset @ X2792))|(~(in @ X2795 @ (powerset @ X2792))|(~(in @ X2796 @ X2792)|(~(in @ X2796 @ (binintersect @ X2793 @ X2794))|(in @ X2796 @ (binunion @ X2794 @ X2795)))))))&((~(in @ X2798 @ (powerset @ X2797))|(~(in @ X2799 @ (powerset @ X2797))|(~(in @ X2800 @ (powerset @ X2797))|(~(in @ X2801 @ X2797)|(~(in @ X2801 @ (binintersect @ X2798 @ X2799))|(in @ X2801 @ (binintersect @ (binunion @ X2798 @ X2800) @ (binunion @ X2799 @ X2800))))))))&((~(in @ X2803 @ (powerset @ X2802))|(~(in @ X2804 @ (powerset @ X2802))|(~(in @ X2805 @ (powerset @ X2802))|(in @ (binintersect @ X2803 @ X2804) @ (powerset @ (binintersect @ (binunion @ X2803 @ X2805) @ (binunion @ X2804 @ X2805)))))))&((~(in @ X2807 @ (powerset @ X2806))|(~(in @ X2808 @ (powerset @ X2806))|(~(in @ X2809 @ X2806)|(~(in @ X2809 @ (setminus @ X2806 @ (binunion @ X2807 @ X2808)))|~(in @ X2809 @ X2807)))))&((~(in @ X2811 @ (powerset @ X2810))|(~(in @ X2812 @ (powerset @ X2810))|(~(in @ X2813 @ X2810)|(~(in @ X2813 @ (setminus @ X2810 @ (binunion @ X2811 @ X2812)))|(in @ X2813 @ (setminus @ X2810 @ X2811))))))&(((((in @ X2818 @ X2816)|(X2817)|(in @ X2818 @ X2815)|~(in @ X2818 @ (binunion @ X2815 @ X2816))|~(in @ X2818 @ X2814)|~(in @ X2816 @ (powerset @ X2814))|~(in @ X2815 @ (powerset @ X2814)))&(~(X2817)|(X2817)|(in @ X2818 @ X2815)|~(in @ X2818 @ (binunion @ X2815 @ X2816))|~(in @ X2818 @ X2814)|~(in @ X2816 @ (powerset @ X2814))|~(in @ X2815 @ (powerset @ X2814))))&(((in @ X2818 @ X2816)|(X2817)|~(X2817)|~(in @ X2818 @ (binunion @ X2815 @ X2816))|~(in @ X2818 @ X2814)|~(in @ X2816 @ (powerset @ X2814))|~(in @ X2815 @ (powerset @ X2814)))&(~(X2817)|(X2817)|~(X2817)|~(in @ X2818 @ (binunion @ X2815 @ X2816))|~(in @ X2818 @ X2814)|~(in @ X2816 @ (powerset @ X2814))|~(in @ X2815 @ (powerset @ X2814)))))&((~(in @ X2820 @ (powerset @ X2819))|(~(in @ X2821 @ (powerset @ X2819))|(~(in @ X2822 @ X2819)|((in @ X2822 @ X2820)|((in @ X2822 @ X2821)|~(in @ X2822 @ (binunion @ X2820 @ X2821)))))))&((~(in @ X2824 @ (powerset @ X2823))|(~(in @ X2825 @ (powerset @ X2823))|(~(in @ X2826 @ X2823)|(~(in @ X2826 @ (setminus @ X2823 @ (binunion @ X2824 @ X2825)))|(in @ X2826 @ (setminus @ X2823 @ X2824))))))&((~(in @ X2828 @ (powerset @ X2827))|(~(in @ X2829 @ (powerset @ X2827))|(in @ (setminus @ X2827 @ (binunion @ X2828 @ X2829)) @ (powerset @ (setminus @ X2827 @ X2828)))))&((~(in @ X2831 @ (powerset @ X2830))|(~(in @ X2832 @ (powerset @ X2830))|(~(in @ X2833 @ X2830)|(~(in @ X2833 @ (setminus @ X2830 @ (binunion @ X2831 @ X2832)))|(in @ X2833 @ (setminus @ X2830 @ X2832))))))&((~(in @ X2835 @ (powerset @ X2834))|(~(in @ X2836 @ (powerset @ X2834))|(~(in @ X2837 @ X2834)|(~(in @ X2837 @ (setminus @ X2834 @ (binintersect @ X2835 @ X2836)))|(in @ X2837 @ (binunion @ (setminus @ X2834 @ X2835) @ (setminus @ X2834 @ X2836)))))))&((~(in @ X2839 @ (powerset @ X2838))|(~(in @ X2840 @ (powerset @ X2838))|(~(in @ X2841 @ X2838)|(~(in @ X2841 @ (binunion @ (setminus @ X2838 @ X2839) @ (setminus @ X2838 @ X2840)))|(in @ X2841 @ (setminus @ X2838 @ (binintersect @ X2839 @ X2840)))))))&((~(in @ X2843 @ (powerset @ X2842))|(~(in @ X2844 @ (powerset @ X2842))|((setminus @ X2842 @ (binintersect @ X2843 @ X2844))=(binunion @ (setminus @ X2842 @ X2843) @ (setminus @ X2842 @ X2844)))))&((~(in @ X2846 @ (powerset @ X2845))|(~(in @ X2847 @ (powerset @ X2845))|(~(in @ X2848 @ X2845)|(~(in @ X2848 @ (setminus @ X2845 @ (binunion @ X2846 @ X2847)))|(in @ X2848 @ (binintersect @ (setminus @ X2845 @ X2846) @ (setminus @ X2845 @ X2847)))))))&((~(in @ X2850 @ (powerset @ X2849))|(~(in @ X2851 @ (powerset @ X2849))|(~(in @ X2852 @ X2849)|(~(in @ X2852 @ (setminus @ X2849 @ X2850))|(~(in @ X2852 @ (setminus @ X2849 @ X2851))|(in @ X2852 @ (setminus @ X2849 @ (binunion @ X2850 @ X2851))))))))&((~(in @ X2854 @ (powerset @ X2853))|(~(in @ X2855 @ (powerset @ X2853))|(~(in @ X2856 @ X2853)|(~(in @ X2856 @ (binintersect @ (setminus @ X2853 @ X2854) @ (setminus @ X2853 @ X2855)))|(in @ X2856 @ (setminus @ X2853 @ (binunion @ X2854 @ X2855)))))))&((~(in @ X2858 @ (powerset @ X2857))|(~(in @ X2859 @ (powerset @ X2857))|((setminus @ X2857 @ (binunion @ X2858 @ X2859))=(binintersect @ (setminus @ X2857 @ X2858) @ (setminus @ X2857 @ X2859)))))&((~(in @ X2861 @ (powerset @ X2860))|(~(in @ X2862 @ (powerset @ X2860))|(~(in @ X2863 @ (binintersect @ X2861 @ X2862))|(in @ X2863 @ X2860))))&((~(in @ X2865 @ (powerset @ X2864))|(~(in @ X2866 @ (powerset @ X2864))|(~(in @ X2867 @ (powerset @ X2864))|(~(subset @ X2865 @ X2867)|(subset @ (binintersect @ X2865 @ X2866) @ X2867)))))&((~(in @ X2869 @ (powerset @ X2868))|(~(in @ X2870 @ (powerset @ X2868))|(~(in @ X2871 @ (powerset @ X2868))|(~(subset @ X2870 @ X2871)|(subset @ (binintersect @ X2869 @ X2870) @ X2871)))))&((~(in @ X2873 @ (powerset @ X2872))|(~(in @ X2874 @ (powerset @ X2872))|(~(in @ X2875 @ (powerset @ X2872))|(~(subset @ X2873 @ X2874)|(~(subset @ X2873 @ X2875)|(subset @ X2873 @ (binintersect @ X2874 @ X2875)))))))&((~(in @ X2877 @ (powerset @ X2876))|(~(in @ X2878 @ (powerset @ X2876))|(~(in @ X2879 @ (powerset @ X2876))|(~(in @ X2880 @ (powerset @ X2876))|(~(subset @ X2877 @ X2879)|(~(subset @ X2878 @ X2880)|(subset @ (binintersect @ X2877 @ X2878) @ (binintersect @ X2879 @ X2880))))))))&((~(in @ X2882 @ (powerset @ X2881))|(~(in @ X2883 @ (powerset @ X2881))|(in @ (setminus @ X2881 @ X2882) @ (powerset @ (setminus @ X2881 @ (binintersect @ X2882 @ X2883))))))&((~(in @ X2885 @ (powerset @ X2884))|(~(in @ X2886 @ (powerset @ X2884))|(~(in @ X2887 @ (powerset @ X2884))|(~(in @ X2888 @ (powerset @ X2884))|((setminus @ X2884 @ (binintersect @ (binunion @ X2885 @ X2886) @ (binunion @ X2887 @ X2888)))=(binunion @ (binintersect @ (setminus @ X2884 @ X2885) @ (setminus @ X2884 @ X2886)) @ (binintersect @ (setminus @ X2884 @ X2887) @ (setminus @ X2884 @ X2888))))))))&((~(in @ X2890 @ (powerset @ X2889))|(~(in @ X2891 @ (powerset @ X2889))|(~(in @ X2892 @ (powerset @ X2889))|(in @ (binintersect @ X2890 @ X2891) @ (powerset @ (binintersect @ (binunion @ X2890 @ X2892) @ (binunion @ X2891 @ X2892)))))))&((~(in @ X2894 @ (powerset @ X2893))|(~(in @ X2895 @ (powerset @ X2893))|(~(subset @ X2894 @ (setminus @ X2893 @ X2895))|(subset @ X2895 @ (setminus @ X2893 @ X2894)))))&((~(in @ X2897 @ (powerset @ X2896))|(~(in @ X2898 @ (powerset @ X2896))|(in @ (setminus @ X2896 @ (binunion @ X2897 @ X2898)) @ (powerset @ (setminus @ X2896 @ X2897)))))&((((in @ (esk87_3 @ X2899 @ X2900 @ X2901) @ X2899)|(~(in @ X2904 @ X2900)|(X2901 @ X2904))|~(subset @ X2900 @ (cartprod @ X2899 @ X2899)))&(((in @ (esk88_3 @ X2899 @ X2900 @ X2901) @ X2899)|(~(in @ X2904 @ X2900)|(X2901 @ X2904))|~(subset @ X2900 @ (cartprod @ X2899 @ X2899)))&(((in @ (kpair @ (esk87_3 @ X2899 @ X2900 @ X2901) @ (esk88_3 @ X2899 @ X2900 @ X2901)) @ X2900)|(~(in @ X2904 @ X2900)|(X2901 @ X2904))|~(subset @ X2900 @ (cartprod @ X2899 @ X2899)))&(~(X2901 @ (kpair @ (esk87_3 @ X2899 @ X2900 @ X2901) @ (esk88_3 @ X2899 @ X2900 @ X2901)))|(~(in @ X2904 @ X2900)|(X2901 @ X2904))|~(subset @ X2900 @ (cartprod @ X2899 @ X2899))))))&((~(in @ X2906 @ (breln1Set @ X2905))|(subset @ X2906 @ (cartprod @ X2905 @ X2905)))&((choice2fnsingleton)&((subset @ (dpsetconstr @ X2907 @ X2907 @ X2908) @ (cartprod @ X2907 @ X2907))&((((in @ (esk89_3 @ X2909 @ X2910 @ X2911) @ X2909)|(~(in @ X2914 @ X2910)|(X2911 @ X2914))|~(subset @ X2910 @ (cartprod @ X2909 @ X2909)))&(((in @ (esk90_3 @ X2909 @ X2910 @ X2911) @ X2909)|(~(in @ X2914 @ X2910)|(X2911 @ X2914))|~(subset @ X2910 @ (cartprod @ X2909 @ X2909)))&(((in @ (kpair @ (esk89_3 @ X2909 @ X2910 @ X2911) @ (esk90_3 @ X2909 @ X2910 @ X2911)) @ X2910)|(~(in @ X2914 @ X2910)|(X2911 @ X2914))|~(subset @ X2910 @ (cartprod @ X2909 @ X2909)))&(~(X2911 @ (kpair @ (esk89_3 @ X2909 @ X2910 @ X2911) @ (esk90_3 @ X2909 @ X2910 @ X2911)))|(~(in @ X2914 @ X2910)|(X2911 @ X2914))|~(subset @ X2910 @ (cartprod @ X2909 @ X2909))))))&((((in @ (esk91_3 @ X2915 @ X2916 @ X2917) @ X2915)|(subset @ X2916 @ X2917)|~(subset @ X2917 @ (cartprod @ X2915 @ X2915))|~(subset @ X2916 @ (cartprod @ X2915 @ X2915)))&(((in @ (esk92_3 @ X2915 @ X2916 @ X2917) @ X2915)|(subset @ X2916 @ X2917)|~(subset @ X2917 @ (cartprod @ X2915 @ X2915))|~(subset @ X2916 @ (cartprod @ X2915 @ X2915)))&(((in @ (kpair @ (esk91_3 @ X2915 @ X2916 @ X2917) @ (esk92_3 @ X2915 @ X2916 @ X2917)) @ X2916)|(subset @ X2916 @ X2917)|~(subset @ X2917 @ (cartprod @ X2915 @ X2915))|~(subset @ X2916 @ (cartprod @ X2915 @ X2915)))&(~(in @ (kpair @ (esk91_3 @ X2915 @ X2916 @ X2917) @ (esk92_3 @ X2915 @ X2916 @ X2917)) @ X2917)|(subset @ X2916 @ X2917)|~(subset @ X2917 @ (cartprod @ X2915 @ X2915))|~(subset @ X2916 @ (cartprod @ X2915 @ X2915))))))&((subset @ esk94_0 @ (cartprod @ esk93_0 @ esk93_0))&((subset @ esk95_0 @ (cartprod @ esk93_0 @ esk93_0))&((~(in @ X2923 @ esk93_0)|(~(in @ X2924 @ esk93_0)|(~(in @ (kpair @ X2923 @ X2924) @ esk94_0)|(in @ (kpair @ X2923 @ X2924) @ esk95_0))))&((~(in @ X2925 @ esk93_0)|(~(in @ X2926 @ esk93_0)|(~(in @ (kpair @ X2925 @ X2926) @ esk95_0)|(in @ (kpair @ X2925 @ X2926) @ esk94_0))))&((esk94_0)!=(esk95_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_378])])])])])])])).
% 2.91/0.65 thf(c_0_380, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_381, negated_conjecture, (subset @ esk95_0 @ (cartprod @ esk93_0 @ esk93_0)), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_382, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (kfst @ X2) @ X3)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_383, negated_conjecture, ![X2:$i]:(((in @ X2 @ (cartprod @ esk93_0 @ esk93_0))|~((in @ X2 @ esk95_0)))), inference(spm,[status(thm)],[c_0_380, c_0_381])).
% 2.91/0.65 thf(c_0_384, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (ksnd @ X2) @ X4)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_385, negated_conjecture, (subset @ esk94_0 @ (cartprod @ esk93_0 @ esk93_0)), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_386, negated_conjecture, ![X2:$i]:(((in @ (kfst @ X2) @ esk93_0)|~((in @ X2 @ esk95_0)))), inference(spm,[status(thm)],[c_0_382, c_0_383])).
% 2.91/0.65 thf(c_0_387, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_388, negated_conjecture, ![X2:$i]:(((in @ (ksnd @ X2) @ esk93_0)|~((in @ X2 @ esk95_0)))), inference(spm,[status(thm)],[c_0_384, c_0_383])).
% 2.91/0.65 thf(c_0_389, negated_conjecture, ![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_390, negated_conjecture, ![X2:$i]:(((in @ X2 @ (cartprod @ esk93_0 @ esk93_0))|~((in @ X2 @ esk94_0)))), inference(spm,[status(thm)],[c_0_380, c_0_385])).
% 2.91/0.65 thf(c_0_391, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ esk94_0)|~((in @ X2 @ esk93_0))|~((in @ X3 @ esk93_0))|~((in @ (kpair @ X2 @ X3) @ esk95_0)))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_392, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ esk93_0)|~((in @ (kpair @ X2 @ X3) @ esk95_0)))), inference(spm,[status(thm)],[c_0_386, c_0_387])).
% 2.91/0.65 thf(c_0_393, negated_conjecture, ![X3:$i, X2:$i]:(((in @ X2 @ esk93_0)|~((in @ (kpair @ X3 @ X2) @ esk95_0)))), inference(spm,[status(thm)],[c_0_388, c_0_389])).
% 2.91/0.65 thf(c_0_394, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((iskpair @ X2)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_395, negated_conjecture, ![X2:$i]:(((in @ (kfst @ X2) @ esk93_0)|~((in @ X2 @ esk94_0)))), inference(spm,[status(thm)],[c_0_382, c_0_390])).
% 2.91/0.65 thf(c_0_396, negated_conjecture, ![X2:$i]:(((in @ (ksnd @ X2) @ esk93_0)|~((in @ X2 @ esk94_0)))), inference(spm,[status(thm)],[c_0_384, c_0_390])).
% 2.91/0.65 thf(c_0_397, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ esk94_0)|~((in @ (kpair @ X2 @ X3) @ esk95_0)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_391, c_0_392]), c_0_393])).
% 2.91/0.65 thf(c_0_398, negated_conjecture, ![X2:$i]:((((kpair @ (kfst @ X2) @ (ksnd @ X2))=(X2))|~((iskpair @ X2)))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_399, negated_conjecture, ![X2:$i]:(((iskpair @ X2)|~((in @ X2 @ esk95_0)))), inference(spm,[status(thm)],[c_0_394, c_0_383])).
% 2.91/0.65 thf(c_0_400, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ esk95_0)|~((in @ X2 @ esk93_0))|~((in @ X3 @ esk93_0))|~((in @ (kpair @ X2 @ X3) @ esk94_0)))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_401, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ esk93_0)|~((in @ (kpair @ X2 @ X3) @ esk94_0)))), inference(spm,[status(thm)],[c_0_395, c_0_387])).
% 2.91/0.65 thf(c_0_402, negated_conjecture, ![X3:$i, X2:$i]:(((in @ X2 @ esk93_0)|~((in @ (kpair @ X3 @ X2) @ esk94_0)))), inference(spm,[status(thm)],[c_0_396, c_0_389])).
% 2.91/0.65 thf(c_0_403, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk94_0)|~((in @ X2 @ esk95_0)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_397, c_0_398]), c_0_399])).
% 2.91/0.65 thf(c_0_404, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_405, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ esk95_0)|~((in @ (kpair @ X2 @ X3) @ esk94_0)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_400, c_0_401]), c_0_402])).
% 2.91/0.65 thf(c_0_406, negated_conjecture, ![X2:$i]:(((iskpair @ X2)|~((in @ X2 @ esk94_0)))), inference(spm,[status(thm)],[c_0_394, c_0_390])).
% 2.91/0.65 thf(c_0_407, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_408, negated_conjecture, ![X2:$i]:(((in @ (esk53_2 @ esk95_0 @ X2) @ esk94_0)|(subset @ esk95_0 @ X2))), inference(spm,[status(thm)],[c_0_403, c_0_404])).
% 2.91/0.65 thf(c_0_409, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk95_0)|~((in @ X2 @ esk94_0)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_405, c_0_398]), c_0_406])).
% 2.91/0.65 thf(c_0_410, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((subset @ X2 @ X3))|~((subset @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_411, negated_conjecture, (subset @ esk95_0 @ esk94_0), inference(spm,[status(thm)],[c_0_407, c_0_408])).
% 2.91/0.65 thf(c_0_412, negated_conjecture, ((esk94_0)!=(esk95_0)), inference(split_conjunct,[status(thm)],[c_0_379])).
% 2.91/0.65 thf(c_0_413, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk95_0)|~((in @ (esk53_2 @ X2 @ esk95_0) @ esk94_0)))), inference(spm,[status(thm)],[c_0_407, c_0_409])).
% 2.91/0.65 thf(c_0_414, negated_conjecture, ~((subset @ esk94_0 @ esk95_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_410, c_0_411]), c_0_412])).
% 2.91/0.65 thf(c_0_415, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_413, c_0_404]), c_0_414]), ['proof']).
% 2.91/0.65 % SZS output end CNFRefutation
% 2.91/0.65 % Parsed axioms : 631
% 2.91/0.65 % Removed by relevancy pruning/SinE : 338
% 2.91/0.65 % Initial clauses : 488
% 2.91/0.65 % Removed in clause preprocessing : 32
% 2.91/0.65 % Initial clauses in saturation : 456
% 2.91/0.65 % Processed clauses : 1743
% 2.91/0.65 % ...of these trivial : 44
% 2.91/0.65 % ...subsumed : 1036
% 2.91/0.65 % ...remaining for further processing : 663
% 2.91/0.65 % Other redundant clauses eliminated : 32
% 2.91/0.65 % Clauses deleted for lack of memory : 0
% 2.91/0.65 % Backward-subsumed : 3
% 2.91/0.65 % Backward-rewritten : 6
% 2.91/0.65 % Generated clauses : 21233
% 2.91/0.65 % ...of the previous two non-redundant : 17732
% 2.91/0.65 % ...aggressively subsumed : 0
% 2.91/0.65 % Contextual simplify-reflections : 8
% 2.91/0.65 % Paramodulations : 21196
% 2.91/0.65 % Factorizations : 2
% 2.91/0.65 % NegExts : 0
% 2.91/0.65 % Equation resolutions : 35
% 2.91/0.65 % Disequality decompositions : 0
% 2.91/0.65 % Total rewrite steps : 6867
% 2.91/0.65 % ...of those cached : 6536
% 2.91/0.65 % Propositional unsat checks : 0
% 2.91/0.65 % Propositional check models : 0
% 2.91/0.65 % Propositional check unsatisfiable : 0
% 2.91/0.65 % Propositional clauses : 0
% 2.91/0.65 % Propositional clauses after purity: 0
% 2.91/0.65 % Propositional unsat core size : 0
% 2.91/0.65 % Propositional preprocessing time : 0.000
% 2.91/0.65 % Propositional encoding time : 0.000
% 2.91/0.65 % Propositional solver time : 0.000
% 2.91/0.65 % Success case prop preproc time : 0.000
% 2.91/0.65 % Success case prop encoding time : 0.000
% 2.91/0.65 % Success case prop solver time : 0.000
% 2.91/0.65 % Current number of processed clauses : 645
% 2.91/0.65 % Positive orientable unit clauses : 230
% 2.91/0.65 % Positive unorientable unit clauses: 0
% 2.91/0.65 % Negative unit clauses : 6
% 2.91/0.65 % Non-unit-clauses : 409
% 2.91/0.65 % Current number of unprocessed clauses: 16425
% 2.91/0.65 % ...number of literals in the above : 48805
% 2.91/0.65 % Current number of archived formulas : 0
% 2.91/0.65 % Current number of archived clauses : 9
% 2.91/0.65 % Clause-clause subsumption calls (NU) : 18418
% 2.91/0.65 % Rec. Clause-clause subsumption calls : 14704
% 2.91/0.65 % Non-unit clause-clause subsumptions : 830
% 2.91/0.65 % Unit Clause-clause subsumption calls : 136
% 2.91/0.65 % Rewrite failures with RHS unbound : 0
% 2.91/0.65 % BW rewrite match attempts : 351
% 2.91/0.65 % BW rewrite match successes : 4
% 2.91/0.65 % Condensation attempts : 0
% 2.91/0.65 % Condensation successes : 0
% 2.91/0.65 % Termbank termtop insertions : 357606
% 2.91/0.65 % Search garbage collected termcells : 31343
% 2.91/0.65
% 2.91/0.65 % -------------------------------------------------
% 2.91/0.65 % User time : 0.283 s
% 2.91/0.65 % System time : 0.028 s
% 2.91/0.65 % Total time : 0.311 s
% 2.91/0.65 % Maximum resident set size: 11256 pages
% 2.91/0.65
% 2.91/0.65 % -------------------------------------------------
% 2.91/0.65 % User time : 0.293 s
% 2.91/0.65 % System time : 0.034 s
% 2.91/0.65 % Total time : 0.328 s
% 2.91/0.65 % Maximum resident set size: 5888 pages
% 2.91/0.65 % E exiting
%------------------------------------------------------------------------------