%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU707^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:25:17 AM UTC 2026
% Result : Theorem 251.76s 33.45s
% Output : CNFRefutation 251.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU707^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n001.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:18:50 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.22/0.30 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p
% 251.76/33.45 % Version: 3.5.1-ho
% 251.76/33.45 % Preprocessing class: HSLMSLSSLLLCHFA.
% 251.76/33.45 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 251.76/33.45 % Starting ehoh_best5 with 300s (1) cores
% 251.76/33.45 % Starting almost_fo_3_lam with 300s (1) cores
% 251.76/33.45 % Starting new_bool_5 with 300s (1) cores
% 251.76/33.45 % Starting pre_casc_3 with 300s (1) cores
% 251.76/33.45 % Starting ho_unfolding_8 with 300s (1) cores
% 251.76/33.45 % Starting new_ho_10_cnf2 with 300s (1) cores
% 251.76/33.45 % Starting new_bool_3 with 300s (1) cores
% 251.76/33.45 % Starting new_ho_5 with 300s (1) cores
% 251.76/33.45 % new_bool_5 with pid 1310538 completed with status 0
% 251.76/33.45 % Result found by new_bool_5
% 251.76/33.45 % Preprocessing class: HSLMSLSSLLLCHFA.
% 251.76/33.45 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 251.76/33.45 % Starting ehoh_best5 with 300s (1) cores
% 251.76/33.45 % Starting almost_fo_3_lam with 300s (1) cores
% 251.76/33.45 % Starting new_bool_5 with 300s (1) cores
% 251.76/33.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 251.76/33.45 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 251.76/33.45 % Search class: HGHSM-FSLM32-MHFMMSBN
% 251.76/33.45 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 251.76/33.45 % Starting SubtermCWHack with 28s (1) cores
% 251.76/33.45 % SubtermCWHack with pid 1310547 completed with status 8
% 251.76/33.45 % Starting new_bool_5 with 31s (1) cores
% 251.76/33.45 % new_bool_5 with pid 1310553 completed with status 0
% 251.76/33.45 % Result found by new_bool_5
% 251.76/33.45 % Preprocessing class: HSLMSLSSLLLCHFA.
% 251.76/33.45 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 251.76/33.45 % Starting ehoh_best5 with 300s (1) cores
% 251.76/33.45 % Starting almost_fo_3_lam with 300s (1) cores
% 251.76/33.45 % Starting new_bool_5 with 300s (1) cores
% 251.76/33.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 251.76/33.45 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 251.76/33.45 % Search class: HGHSM-FSLM32-MHFMMSBN
% 251.76/33.45 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 251.76/33.45 % Starting SubtermCWHack with 28s (1) cores
% 251.76/33.45 % SubtermCWHack with pid 1310547 completed with status 8
% 251.76/33.45 % Starting new_bool_5 with 31s (1) cores
% 251.76/33.45 % Preprocessing time : 0.008 s
% 251.76/33.45 % Presaturation interreduction done
% 251.76/33.45
% 251.76/33.45 % Proof found!
% 251.76/33.45 % SZS status Theorem
% 251.76/33.45 % SZS output start CNFRefutation
% 251.76/33.45 thf(decl_23, type, in: $i > $i > $o).
% 251.76/33.45 thf(decl_24, type, exu: ($i > $o) > $o).
% 251.76/33.45 thf(decl_25, type, setextAx: $o).
% 251.76/33.45 thf(decl_26, type, emptyset: $i).
% 251.76/33.45 thf(decl_27, type, emptysetAx: $o).
% 251.76/33.45 thf(decl_28, type, setadjoin: $i > $i > $i).
% 251.76/33.45 thf(decl_29, type, setadjoinAx: $o).
% 251.76/33.45 thf(decl_30, type, powerset: $i > $i).
% 251.76/33.45 thf(decl_31, type, powersetAx: $o).
% 251.76/33.45 thf(decl_32, type, setunion: $i > $i).
% 251.76/33.45 thf(decl_33, type, setunionAx: $o).
% 251.76/33.45 thf(decl_34, type, omega: $i).
% 251.76/33.45 thf(decl_35, type, omega0Ax: $o).
% 251.76/33.45 thf(decl_36, type, omegaSAx: $o).
% 251.76/33.45 thf(decl_37, type, omegaIndAx: $o).
% 251.76/33.45 thf(decl_38, type, replAx: $o).
% 251.76/33.45 thf(decl_39, type, foundationAx: $o).
% 251.76/33.45 thf(decl_40, type, wellorderingAx: $o).
% 251.76/33.45 thf(decl_41, type, descr: ($i > $o) > $i).
% 251.76/33.45 thf(decl_42, type, descrp: $o).
% 251.76/33.45 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 251.76/33.45 thf(decl_44, type, dsetconstrI: $o).
% 251.76/33.45 thf(decl_45, type, dsetconstrEL: $o).
% 251.76/33.45 thf(decl_46, type, dsetconstrER: $o).
% 251.76/33.45 thf(decl_47, type, exuE1: $o).
% 251.76/33.45 thf(decl_48, type, prop2set: $o > $i).
% 251.76/33.45 thf(decl_49, type, prop2setE: $o).
% 251.76/33.45 thf(decl_50, type, emptysetE: $o).
% 251.76/33.45 thf(decl_51, type, emptysetimpfalse: $o).
% 251.76/33.45 thf(decl_52, type, notinemptyset: $o).
% 251.76/33.45 thf(decl_53, type, exuE3e: $o).
% 251.76/33.45 thf(decl_54, type, setext: $o).
% 251.76/33.45 thf(decl_55, type, emptyI: $o).
% 251.76/33.45 thf(decl_56, type, noeltsimpempty: $o).
% 251.76/33.45 thf(decl_57, type, setbeta: $o).
% 251.76/33.45 thf(decl_58, type, nonempty: $i > $o).
% 251.76/33.45 thf(decl_59, type, nonemptyE1: $o).
% 251.76/33.45 thf(decl_60, type, nonemptyI: $o).
% 251.76/33.45 thf(decl_61, type, nonemptyI1: $o).
% 251.76/33.45 thf(decl_62, type, setadjoinIL: $o).
% 251.76/33.45 thf(decl_63, type, emptyinunitempty: $o).
% 251.76/33.45 thf(decl_64, type, setadjoinIR: $o).
% 251.76/33.45 thf(decl_65, type, setadjoinE: $o).
% 251.76/33.45 thf(decl_66, type, setadjoinOr: $o).
% 251.76/33.45 thf(decl_67, type, setoftrueEq: $o).
% 251.76/33.45 thf(decl_68, type, powersetI: $o).
% 251.76/33.45 thf(decl_69, type, emptyinPowerset: $o).
% 251.76/33.45 thf(decl_70, type, emptyInPowerset: $o).
% 251.76/33.45 thf(decl_71, type, powersetE: $o).
% 251.76/33.45 thf(decl_72, type, setunionI: $o).
% 251.76/33.45 thf(decl_73, type, setunionE: $o).
% 251.76/33.45 thf(decl_74, type, subPowSU: $o).
% 251.76/33.45 thf(decl_75, type, exuE2: $o).
% 251.76/33.45 thf(decl_76, type, nonemptyImpWitness: $o).
% 251.76/33.45 thf(decl_77, type, uniqinunit: $o).
% 251.76/33.45 thf(decl_78, type, notinsingleton: $o).
% 251.76/33.45 thf(decl_79, type, eqinunit: $o).
% 251.76/33.45 thf(decl_80, type, singletonsswitch: $o).
% 251.76/33.45 thf(decl_81, type, upairsetE: $o).
% 251.76/33.45 thf(decl_82, type, upairsetIL: $o).
% 251.76/33.45 thf(decl_83, type, upairsetIR: $o).
% 251.76/33.45 thf(decl_84, type, emptyE1: $o).
% 251.76/33.45 thf(decl_85, type, vacuousDall: $o).
% 251.76/33.45 thf(decl_86, type, quantDeMorgan1: $o).
% 251.76/33.45 thf(decl_87, type, quantDeMorgan2: $o).
% 251.76/33.45 thf(decl_88, type, quantDeMorgan3: $o).
% 251.76/33.45 thf(decl_89, type, quantDeMorgan4: $o).
% 251.76/33.45 thf(decl_90, type, prop2setI: $o).
% 251.76/33.45 thf(decl_92, type, prop2set2propI: $o).
% 251.76/33.45 thf(decl_93, type, notdexE: $o).
% 251.76/33.45 thf(decl_94, type, notdallE: $o).
% 251.76/33.45 thf(decl_95, type, exuI1: $o).
% 251.76/33.45 thf(decl_96, type, exuI3: $o).
% 251.76/33.45 thf(decl_97, type, exuI2: $o).
% 251.76/33.45 thf(decl_98, type, inCongP: $o).
% 251.76/33.45 thf(decl_99, type, in__Cong: $o).
% 251.76/33.45 thf(decl_100, type, exuE3u: $o).
% 251.76/33.45 thf(decl_101, type, exu__Cong: $o).
% 251.76/33.45 thf(decl_102, type, emptyset__Cong: $o).
% 251.76/33.45 thf(decl_103, type, setadjoin__Cong: $o).
% 251.76/33.45 thf(decl_104, type, powerset__Cong: $o).
% 251.76/33.45 thf(decl_105, type, setunion__Cong: $o).
% 251.76/33.45 thf(decl_106, type, omega__Cong: $o).
% 251.76/33.45 thf(decl_107, type, exuEu: $o).
% 251.76/33.45 thf(decl_108, type, descr__Cong: $o).
% 251.76/33.45 thf(decl_109, type, dsetconstr__Cong: $o).
% 251.76/33.45 thf(decl_110, type, subset: $i > $i > $o).
% 251.76/33.45 thf(decl_113, type, subsetI1: $o).
% 251.76/33.45 thf(decl_114, type, eqimpsubset2: $o).
% 251.76/33.45 thf(decl_115, type, eqimpsubset1: $o).
% 251.76/33.45 thf(decl_116, type, subsetI2: $o).
% 251.76/33.45 thf(decl_117, type, emptysetsubset: $o).
% 251.76/33.45 thf(decl_118, type, subsetE: $o).
% 251.76/33.45 thf(decl_119, type, subsetE2: $o).
% 251.76/33.45 thf(decl_120, type, notsubsetI: $o).
% 251.76/33.45 thf(decl_121, type, notequalI1: $o).
% 251.76/33.45 thf(decl_122, type, notequalI2: $o).
% 251.76/33.45 thf(decl_123, type, subsetRefl: $o).
% 251.76/33.45 thf(decl_124, type, subsetTrans: $o).
% 251.76/33.45 thf(decl_125, type, setadjoinSub: $o).
% 251.76/33.45 thf(decl_126, type, setadjoinSub2: $o).
% 251.76/33.45 thf(decl_127, type, subset2powerset: $o).
% 251.76/33.45 thf(decl_128, type, setextsub: $o).
% 251.76/33.45 thf(decl_129, type, subsetemptysetimpeq: $o).
% 251.76/33.45 thf(decl_130, type, powersetI1: $o).
% 251.76/33.45 thf(decl_131, type, powersetE1: $o).
% 251.76/33.45 thf(decl_132, type, inPowerset: $o).
% 251.76/33.45 thf(decl_133, type, powersetsubset: $o).
% 251.76/33.45 thf(decl_134, type, sepInPowerset: $o).
% 251.76/33.45 thf(decl_135, type, sepSubset: $o).
% 251.76/33.45 thf(decl_136, type, binunion: $i > $i > $i).
% 251.76/33.45 thf(decl_137, type, binunionIL: $o).
% 251.76/33.45 thf(decl_138, type, upairset2IR: $o).
% 251.76/33.45 thf(decl_139, type, binunionIR: $o).
% 251.76/33.45 thf(decl_140, type, binunionEcases: $o).
% 251.76/33.45 thf(decl_141, type, binunionE: $o).
% 251.76/33.45 thf(decl_142, type, binunionLsub: $o).
% 251.76/33.45 thf(decl_143, type, binunionRsub: $o).
% 251.76/33.45 thf(decl_144, type, binintersect: $i > $i > $i).
% 251.76/33.45 thf(decl_145, type, binintersectI: $o).
% 251.76/33.45 thf(decl_146, type, binintersectSubset5: $o).
% 251.76/33.45 thf(decl_147, type, binintersectEL: $o).
% 251.76/33.45 thf(decl_148, type, binintersectLsub: $o).
% 251.76/33.45 thf(decl_149, type, binintersectSubset2: $o).
% 251.76/33.45 thf(decl_150, type, binintersectSubset3: $o).
% 251.76/33.45 thf(decl_151, type, binintersectER: $o).
% 251.76/33.45 thf(decl_152, type, disjointsetsI1: $o).
% 251.76/33.45 thf(decl_153, type, binintersectRsub: $o).
% 251.76/33.45 thf(decl_154, type, binintersectSubset4: $o).
% 251.76/33.45 thf(decl_155, type, binintersectSubset1: $o).
% 251.76/33.45 thf(decl_156, type, bs114d: $o).
% 251.76/33.45 thf(decl_158, type, setminus: $i > $i > $i).
% 251.76/33.45 thf(decl_159, type, setminusI: $o).
% 251.76/33.45 thf(decl_160, type, setminusEL: $o).
% 251.76/33.45 thf(decl_161, type, setminusER: $o).
% 251.76/33.45 thf(decl_162, type, setminusSubset2: $o).
% 251.76/33.45 thf(decl_163, type, setminusERneg: $o).
% 251.76/33.45 thf(decl_164, type, setminusELneg: $o).
% 251.76/33.45 thf(decl_165, type, setminusILneg: $o).
% 251.76/33.45 thf(decl_166, type, setminusIRneg: $o).
% 251.76/33.45 thf(decl_167, type, setminusLsub: $o).
% 251.76/33.45 thf(decl_168, type, setminusSubset1: $o).
% 251.76/33.45 thf(decl_169, type, symdiff: $i > $i > $i).
% 251.76/33.45 thf(decl_170, type, symdiffE: $o).
% 251.76/33.45 thf(decl_171, type, symdiffI1: $o).
% 251.76/33.45 thf(decl_172, type, symdiffI2: $o).
% 251.76/33.45 thf(decl_173, type, symdiffIneg1: $o).
% 251.76/33.45 thf(decl_174, type, symdiffIneg2: $o).
% 251.76/33.45 thf(decl_175, type, iskpair: $i > $o).
% 251.76/33.45 thf(decl_176, type, secondinupair: $o).
% 251.76/33.45 thf(decl_177, type, setukpairIL: $o).
% 251.76/33.45 thf(decl_178, type, setukpairIR: $o).
% 251.76/33.45 thf(decl_179, type, kpairiskpair: $o).
% 251.76/33.45 thf(decl_180, type, kpair: $i > $i > $i).
% 251.76/33.45 thf(decl_181, type, kpairp: $o).
% 251.76/33.45 thf(decl_182, type, cartprod: $i > $i > $i).
% 251.76/33.45 thf(decl_183, type, singletonsubset: $o).
% 251.76/33.45 thf(decl_184, type, singletoninpowerset: $o).
% 251.76/33.45 thf(decl_185, type, singletoninpowunion: $o).
% 251.76/33.45 thf(decl_186, type, upairset2E: $o).
% 251.76/33.45 thf(decl_187, type, upairsubunion: $o).
% 251.76/33.45 thf(decl_188, type, upairinpowunion: $o).
% 251.76/33.45 thf(decl_189, type, ubforcartprodlem1: $o).
% 251.76/33.45 thf(decl_190, type, ubforcartprodlem2: $o).
% 251.76/33.45 thf(decl_191, type, ubforcartprodlem3: $o).
% 251.76/33.45 thf(decl_192, type, cartprodpairin: $o).
% 251.76/33.45 thf(decl_193, type, cartprodmempair1: $o).
% 251.76/33.45 thf(decl_194, type, cartprodmempair: $o).
% 251.76/33.45 thf(decl_195, type, setunionE2: $o).
% 251.76/33.45 thf(decl_196, type, setunionsingleton1: $o).
% 251.76/33.45 thf(decl_197, type, setunionsingleton2: $o).
% 251.76/33.45 thf(decl_198, type, setunionsingleton: $o).
% 251.76/33.45 thf(decl_199, type, singleton: $i > $o).
% 251.76/33.45 thf(decl_200, type, singletonprop: $o).
% 251.76/33.45 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 251.76/33.45 thf(decl_202, type, ex1E1: $o).
% 251.76/33.45 thf(decl_203, type, ex1I: $o).
% 251.76/33.45 thf(decl_204, type, ex1I2: $o).
% 251.76/33.45 thf(decl_205, type, singletonsuniq: $o).
% 251.76/33.45 thf(decl_210, type, setukpairinjL1: $o).
% 251.76/33.45 thf(decl_211, type, kfstsingleton: $o).
% 251.76/33.45 thf(decl_212, type, theprop: $o).
% 251.76/33.45 thf(decl_213, type, kfst: $i > $i).
% 251.76/33.45 thf(decl_214, type, kfstpairEq: $o).
% 251.76/33.45 thf(decl_215, type, cartprodfstin: $o).
% 251.76/33.45 thf(decl_216, type, setukpairinjL2: $o).
% 251.76/33.45 thf(decl_217, type, setukpairinjL: $o).
% 251.76/33.45 thf(decl_218, type, setukpairinjR11: $o).
% 251.76/33.45 thf(decl_219, type, setukpairinjR12: $o).
% 251.76/33.45 thf(decl_220, type, setukpairinjR1: $o).
% 251.76/33.45 thf(decl_221, type, upairequniteq: $o).
% 251.76/33.45 thf(decl_222, type, setukpairinjR2: $o).
% 251.76/33.45 thf(decl_223, type, setukpairinjR: $o).
% 251.76/33.45 thf(decl_224, type, ksndsingleton: $o).
% 251.76/33.45 thf(decl_225, type, ksnd: $i > $i).
% 251.76/33.45 thf(decl_226, type, ksndpairEq: $o).
% 251.76/33.45 thf(decl_227, type, kpairsurjEq: $o).
% 251.76/33.45 thf(decl_228, type, cartprodsndin: $o).
% 251.76/33.45 thf(decl_229, type, cartprodpairmemEL: $o).
% 251.76/33.45 thf(decl_230, type, cartprodpairmemER: $o).
% 251.76/33.45 thf(decl_231, type, cartprodmempaircEq: $o).
% 251.76/33.45 thf(decl_232, type, cartprodfstpairEq: $o).
% 251.76/33.45 thf(decl_233, type, cartprodsndpairEq: $o).
% 251.76/33.45 thf(decl_234, type, cartprodpairsurjEq: $o).
% 251.76/33.45 thf(decl_235, type, breln: $i > $i > $i > $o).
% 251.76/33.45 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 251.76/33.45 thf(decl_237, type, dpsetconstrI: $o).
% 251.76/33.45 thf(decl_238, type, dpsetconstrSub: $o).
% 251.76/33.45 thf(decl_239, type, setOfPairsIsBReln: $o).
% 251.76/33.45 thf(decl_240, type, dpsetconstrERa: $o).
% 251.76/33.45 thf(decl_241, type, dpsetconstrEL1: $o).
% 251.76/33.45 thf(decl_242, type, dpsetconstrEL2: $o).
% 251.76/33.45 thf(decl_243, type, dpsetconstrER: $o).
% 251.76/33.45 thf(decl_244, type, func: $i > $i > $i > $o).
% 251.76/33.45 thf(decl_245, type, funcSet: $i > $i > $i).
% 251.76/33.45 thf(decl_246, type, funcImageSingleton: $o).
% 251.76/33.45 thf(decl_247, type, apProp: $o).
% 251.76/33.45 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 251.76/33.45 thf(decl_249, type, app: $o).
% 251.76/33.45 thf(decl_250, type, infuncsetfunc: $o).
% 251.76/33.45 thf(decl_251, type, ap2p: $o).
% 251.76/33.45 thf(decl_252, type, funcinfuncset: $o).
% 251.76/33.45 thf(decl_253, type, lamProp: $o).
% 251.76/33.45 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 251.76/33.45 thf(decl_255, type, lamp: $o).
% 251.76/33.45 thf(decl_256, type, lam2p: $o).
% 251.76/33.45 thf(decl_257, type, brelnall1: $o).
% 251.76/33.45 thf(decl_258, type, brelnall2: $o).
% 251.76/33.45 thf(decl_259, type, ex1E2: $o).
% 251.76/33.45 thf(decl_260, type, funcGraphProp1: $o).
% 251.76/33.45 thf(decl_261, type, funcGraphProp3: $o).
% 251.76/33.45 thf(decl_262, type, funcGraphProp2: $o).
% 251.76/33.45 thf(decl_263, type, funcextLem: $o).
% 251.76/33.45 thf(decl_264, type, funcGraphProp4: $o).
% 251.76/33.45 thf(decl_265, type, subbreln: $o).
% 251.76/33.45 thf(decl_266, type, eqbreln: $o).
% 251.76/33.46 thf(decl_267, type, funcext: $o).
% 251.76/33.46 thf(decl_268, type, funcext2: $o).
% 251.76/33.46 thf(decl_269, type, ap2apEq1: $o).
% 251.76/33.46 thf(decl_270, type, ap2apEq2: $o).
% 251.76/33.46 thf(decl_271, type, beta1: $o).
% 251.76/33.46 thf(decl_272, type, eta1: $o).
% 251.76/33.46 thf(decl_273, type, lam2lamEq: $o).
% 251.76/33.46 thf(decl_274, type, beta2: $o).
% 251.76/33.46 thf(decl_275, type, eta2: $o).
% 251.76/33.46 thf(decl_276, type, iffalseProp1: $o).
% 251.76/33.46 thf(decl_277, type, iffalseProp2: $o).
% 251.76/33.46 thf(decl_278, type, iftrueProp1: $o).
% 251.76/33.46 thf(decl_279, type, iftrueProp2: $o).
% 251.76/33.46 thf(decl_280, type, ifSingleton: $o).
% 251.76/33.46 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 251.76/33.46 thf(decl_282, type, ifp: $o).
% 251.76/33.46 thf(decl_283, type, theeq: $o).
% 251.76/33.46 thf(decl_284, type, epred1_0: $o).
% 251.76/33.46 thf(decl_285, type, esk1_2: $i > $i > $i).
% 251.76/33.46 thf(decl_286, type, esk2_2: $i > $i > $i).
% 251.76/33.46 thf(decl_287, type, esk3_2: $i > $i > $i).
% 251.76/33.46 thf(decl_288, type, esk4_1: $i > $i).
% 251.76/33.46 thf(decl_289, type, esk5_2: ($i > $i > $o) > $i > $i).
% 251.76/33.46 thf(decl_290, type, esk6_2: ($i > $i > $o) > $i > $i).
% 251.76/33.46 thf(decl_291, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 251.76/33.46 thf(decl_292, type, esk8_1: $i > $i).
% 251.76/33.46 thf(decl_293, type, esk9_1: ($i > $o) > $i).
% 251.76/33.46 thf(decl_294, type, esk10_1: ($i > $o) > $i).
% 251.76/33.46 thf(decl_295, type, esk11_2: $i > $i > $i).
% 251.76/33.46 thf(decl_296, type, esk12_2: $i > $i > $i).
% 251.76/33.46 thf(decl_297, type, esk13_1: $i > $i).
% 251.76/33.46 thf(decl_298, type, esk14_1: $i > $i).
% 251.76/33.46 thf(decl_299, type, esk15_1: $i > $i).
% 251.76/33.46 thf(decl_300, type, esk16_2: $i > $i > $i).
% 251.76/33.46 thf(decl_301, type, esk17_3: $i > $i > $o > $i).
% 251.76/33.46 thf(decl_302, type, esk18_1: ($i > $o) > $i).
% 251.76/33.46 thf(decl_303, type, esk19_1: $i > $i).
% 251.76/33.46 thf(decl_304, type, esk20_2: $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_305, type, esk21_2: $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_306, type, esk22_2: $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_307, type, esk23_2: $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_308, type, esk24_2: $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_309, type, esk25_2: $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_310, type, esk26_2: ($i > $o) > $i > $i).
% 251.76/33.46 thf(decl_311, type, esk27_1: ($i > $o) > $i).
% 251.76/33.46 thf(decl_312, type, esk28_1: ($i > $o) > $i).
% 251.76/33.46 thf(decl_313, type, esk29_2: ($i > $o) > $i > $i).
% 251.76/33.46 thf(decl_314, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 251.76/33.46 thf(decl_315, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 251.76/33.46 thf(decl_316, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 251.76/33.46 thf(decl_317, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 251.76/33.46 thf(decl_318, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 251.76/33.46 thf(decl_319, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 251.76/33.46 thf(decl_320, type, esk36_2: $i > $i > $i).
% 251.76/33.46 thf(decl_321, type, esk37_2: $i > $i > $i).
% 251.76/33.46 thf(decl_322, type, esk38_2: $i > $i > $i).
% 251.76/33.46 thf(decl_323, type, esk39_3: $i > $i > $i > $i).
% 251.76/33.46 thf(decl_324, type, esk40_3: $i > $i > $i > $i).
% 251.76/33.46 thf(decl_325, type, esk41_2: $i > $i > $i).
% 251.76/33.46 thf(decl_326, type, esk42_2: $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_327, type, esk43_2: $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_328, type, esk44_2: $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_329, type, esk45_3: $i > ($i > $o) > $i > $i).
% 251.76/33.46 thf(decl_330, type, esk46_2: $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_331, type, esk47_2: $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_332, type, esk48_3: $i > $i > ($i > $i) > $i).
% 251.76/33.46 thf(decl_333, type, esk49_3: $i > $i > ($i > $i) > $i).
% 251.76/33.46 thf(decl_334, type, esk50_3: $i > $i > ($i > $i) > $i).
% 251.76/33.46 thf(decl_335, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_336, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_337, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_338, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 251.76/33.46 thf(decl_339, type, esk55_4: $i > $i > $i > $i > $i).
% 251.76/33.46 thf(decl_340, type, esk56_4: $i > $i > $i > $i > $i).
% 251.76/33.46 thf(decl_341, type, esk57_4: $i > $i > $i > $i > $i).
% 251.76/33.46 thf(decl_342, type, esk58_4: $i > $i > $i > $i > $i).
% 251.76/33.46 thf(decl_343, type, esk59_4: $i > $i > $i > $i > $i).
% 251.76/33.46 thf(decl_344, type, esk60_4: $i > $i > $i > $i > $i).
% 251.76/33.46 thf(decl_345, type, esk61_4: $i > $i > $i > $i > $i).
% 251.76/33.46 thf(decl_346, type, esk62_4: $i > $i > $i > $i > $i).
% 251.76/33.46 thf(decl_347, type, esk63_4: $i > $i > $i > $i > $i).
% 251.76/33.46 thf(decl_348, type, esk64_3: $i > $i > ($i > $i) > $i).
% 251.76/33.46 thf(decl_349, type, esk65_3: $i > $i > ($i > $i) > $i).
% 251.76/33.46 thf(decl_350, type, esk66_3: $i > $i > ($i > $i) > $i).
% 251.76/33.46 thf(decl_351, type, esk67_0: $i).
% 251.76/33.46 thf(decl_352, type, epred2_0: $o).
% 251.76/33.46 thf(decl_353, type, esk68_0: $i).
% 251.76/33.46 thf(decl_354, type, esk69_0: $i).
% 251.76/33.46 thf(decl_360, type, epred3_3: $i > $o > $i > $i > $o).
% 251.76/33.46 thf(iftrue, 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)=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X46)=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', iftrue)).
% 251.76/33.46 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', dpsetconstrI)).
% 251.76/33.46 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', dpsetconstrSub)).
% 251.76/33.46 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setOfPairsIsBReln)).
% 251.76/33.46 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', dpsetconstrERa)).
% 251.76/33.46 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', dpsetconstrEL1)).
% 251.76/33.46 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', dpsetconstrEL2)).
% 251.76/33.46 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', dpsetconstrER)).
% 251.76/33.46 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.5lubHWifRY/E---3.1_1310523.p', funcImageSingleton)).
% 251.76/33.46 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', apProp)).
% 251.76/33.46 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', exuE2)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', lamProp)).
% 251.76/33.46 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', lamp)).
% 251.76/33.46 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', lam2p)).
% 251.76/33.46 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.5lubHWifRY/E---3.1_1310523.p', ex1E2)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', beta1)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', emptyE1)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', eta1)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', lam2lamEq)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', beta2)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', eta2)).
% 251.76/33.46 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', iffalseProp1)).
% 251.76/33.46 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.5lubHWifRY/E---3.1_1310523.p', iffalseProp2)).
% 251.76/33.46 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', iftrueProp1)).
% 251.76/33.46 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.5lubHWifRY/E---3.1_1310523.p', iftrueProp2)).
% 251.76/33.46 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ifSingleton)).
% 251.76/33.46 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', exuI2)).
% 251.76/33.46 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', exuI3)).
% 251.76/33.46 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', exuI1)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', exuE3u)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', exuEu)).
% 251.76/33.46 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', exu__Cong)).
% 251.76/33.46 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', descr__Cong)).
% 251.76/33.46 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', dsetconstr__Cong)).
% 251.76/33.46 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', sepInPowerset)).
% 251.76/33.46 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', sepSubset)).
% 251.76/33.46 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', singletonprop)).
% 251.76/33.46 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', kfstsingleton)).
% 251.76/33.46 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ex1I2)).
% 251.76/33.46 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.5lubHWifRY/E---3.1_1310523.p', ex1I)).
% 251.76/33.46 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ex1E1)).
% 251.76/33.46 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ksndsingleton)).
% 251.76/33.46 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setoftrueEq)).
% 251.76/33.46 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', nonemptyI)).
% 251.76/33.46 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setbeta)).
% 251.76/33.46 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', exuE3e)).
% 251.76/33.46 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', exuE1)).
% 251.76/33.46 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', dsetconstrER)).
% 251.76/33.46 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', dsetconstrEL)).
% 251.76/33.46 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', dsetconstrI)).
% 251.76/33.46 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', descrp)).
% 251.76/33.46 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', replAx)).
% 251.76/33.46 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', cartprodpairsurjEq)).
% 251.76/33.46 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', upairsetE)).
% 251.76/33.46 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', singletonsswitch)).
% 251.76/33.46 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', eqinunit)).
% 251.76/33.46 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', notinsingleton)).
% 251.76/33.46 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', uniqinunit)).
% 251.76/33.46 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', app)).
% 251.76/33.46 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', nonemptyImpWitness)).
% 251.76/33.46 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', infuncsetfunc)).
% 251.76/33.46 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ap2p)).
% 251.76/33.46 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', upairsetIL)).
% 251.76/33.46 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', funcinfuncset)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', brelnall1)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', brelnall2)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', funcGraphProp1)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', funcGraphProp3)).
% 251.76/33.46 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', funcGraphProp2)).
% 251.76/33.46 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.5lubHWifRY/E---3.1_1310523.p', funcextLem)).
% 251.76/33.46 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', funcGraphProp4)).
% 251.76/33.46 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', subbreln)).
% 251.76/33.46 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', eqbreln)).
% 251.76/33.46 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', quantDeMorgan4)).
% 251.76/33.46 thf(funcext, axiom, ((funcext)<=>![X4:$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.5lubHWifRY/E---3.1_1310523.p', funcext)).
% 251.76/33.46 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', quantDeMorgan3)).
% 251.76/33.46 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.5lubHWifRY/E---3.1_1310523.p', funcext2)).
% 251.76/33.46 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', quantDeMorgan2)).
% 251.76/33.46 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ap2apEq1)).
% 251.76/33.46 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', quantDeMorgan1)).
% 251.76/33.46 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ap2apEq2)).
% 251.76/33.46 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', vacuousDall)).
% 251.76/33.46 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', upairsetIR)).
% 251.76/33.46 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', prop2setI)).
% 251.76/33.46 thf(ifp, axiom, ((ifp)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X45)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ifp)).
% 251.76/33.46 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', theeq)).
% 251.76/33.46 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', in__Cong)).
% 251.76/33.46 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', inCongP)).
% 251.76/33.46 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', notdallE)).
% 251.76/33.46 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', notdexE)).
% 251.76/33.46 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', omega__Cong)).
% 251.76/33.46 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setunion__Cong)).
% 251.76/33.46 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', powerset__Cong)).
% 251.76/33.46 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setadjoin__Cong)).
% 251.76/33.46 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', emptyset__Cong)).
% 251.76/33.46 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', subsetE)).
% 251.76/33.46 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', emptysetsubset)).
% 251.76/33.46 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', subsetI2)).
% 251.76/33.46 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', eqimpsubset1)).
% 251.76/33.46 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', eqimpsubset2)).
% 251.76/33.46 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', subsetI1)).
% 251.76/33.46 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', subsetE2)).
% 251.76/33.46 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setadjoinSub2)).
% 251.76/33.46 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setadjoinSub)).
% 251.76/33.46 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', subsetTrans)).
% 251.76/33.46 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', subsetRefl)).
% 251.76/33.46 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', notequalI2)).
% 251.76/33.46 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', notequalI1)).
% 251.76/33.46 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', notsubsetI)).
% 251.76/33.46 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', subset2powerset)).
% 251.76/33.46 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', powersetsubset)).
% 251.76/33.46 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', inPowerset)).
% 251.76/33.46 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', powersetE1)).
% 251.76/33.46 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', powersetI1)).
% 251.76/33.46 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', subsetemptysetimpeq)).
% 251.76/33.46 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setextsub)).
% 251.76/33.46 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binunionRsub)).
% 251.76/33.46 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binunionLsub)).
% 251.76/33.46 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binunionE)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', binunionEcases)).
% 251.76/33.46 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binunionIR)).
% 251.76/33.46 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', upairset2IR)).
% 251.76/33.46 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binunionIL)).
% 251.76/33.46 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binintersectI)).
% 251.76/33.46 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', disjointsetsI1)).
% 251.76/33.46 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binintersectER)).
% 251.76/33.46 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binintersectSubset3)).
% 251.76/33.46 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binintersectSubset2)).
% 251.76/33.46 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binintersectLsub)).
% 251.76/33.46 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binintersectEL)).
% 251.76/33.46 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binintersectSubset5)).
% 251.76/33.46 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binintersectRsub)).
% 251.76/33.46 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setminusSubset2)).
% 251.76/33.46 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setminusER)).
% 251.76/33.46 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setminusEL)).
% 251.76/33.46 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setminusI)).
% 251.76/33.46 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', bs114d)).
% 251.76/33.46 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binintersectSubset1)).
% 251.76/33.46 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', binintersectSubset4)).
% 251.76/33.46 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setminusERneg)).
% 251.76/33.46 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', symdiffI1)).
% 251.76/33.46 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', symdiffE)).
% 251.76/33.46 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setminusSubset1)).
% 251.76/33.46 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setminusLsub)).
% 251.76/33.46 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setminusIRneg)).
% 251.76/33.46 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setminusILneg)).
% 251.76/33.46 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setminusELneg)).
% 251.76/33.46 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', symdiffI2)).
% 251.76/33.46 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', kpairp)).
% 251.76/33.46 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', kpairiskpair)).
% 251.76/33.46 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setukpairIR)).
% 251.76/33.46 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setukpairIL)).
% 251.76/33.46 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', secondinupair)).
% 251.76/33.46 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', symdiffIneg2)).
% 251.76/33.46 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', symdiffIneg1)).
% 251.76/33.46 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', singletonsubset)).
% 251.76/33.46 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ubforcartprodlem2)).
% 251.76/33.46 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ubforcartprodlem1)).
% 251.76/33.46 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', upairinpowunion)).
% 251.76/33.46 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', upairsubunion)).
% 251.76/33.46 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', upairset2E)).
% 251.76/33.46 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', singletoninpowunion)).
% 251.76/33.46 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', singletoninpowerset)).
% 251.76/33.46 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ubforcartprodlem3)).
% 251.76/33.46 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setunionsingleton)).
% 251.76/33.46 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setunionsingleton2)).
% 251.76/33.46 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setunionsingleton1)).
% 251.76/33.46 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setunionE2)).
% 251.76/33.46 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', cartprodmempair)).
% 251.76/33.46 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', cartprodmempair1)).
% 251.76/33.46 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', cartprodpairin)).
% 251.76/33.46 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', theprop)).
% 251.76/33.46 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setukpairinjL1)).
% 251.76/33.46 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', singletonsuniq)).
% 251.76/33.46 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', kfstpairEq)).
% 251.76/33.46 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', upairequniteq)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', setukpairinjR1)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', setukpairinjR12)).
% 251.76/33.46 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setukpairinjR11)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', setukpairinjL)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', setukpairinjL2)).
% 251.76/33.46 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', cartprodfstin)).
% 251.76/33.46 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setukpairinjR2)).
% 251.76/33.46 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', cartprodpairmemER)).
% 251.76/33.46 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', cartprodpairmemEL)).
% 251.76/33.46 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', cartprodsndin)).
% 251.76/33.46 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', kpairsurjEq)).
% 251.76/33.46 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', ksndpairEq)).
% 251.76/33.46 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setukpairinjR)).
% 251.76/33.46 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', cartprodmempaircEq)).
% 251.76/33.46 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', cartprodfstpairEq)).
% 251.76/33.46 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', cartprodsndpairEq)).
% 251.76/33.46 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', subPowSU)).
% 251.76/33.46 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setunionE)).
% 251.76/33.46 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setunionI)).
% 251.76/33.46 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', powersetE)).
% 251.76/33.46 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', emptyInPowerset)).
% 251.76/33.46 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', emptyinPowerset)).
% 251.76/33.46 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', powersetI)).
% 251.76/33.46 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setadjoinOr)).
% 251.76/33.46 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setadjoinE)).
% 251.76/33.46 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setadjoinIR)).
% 251.76/33.46 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', emptyinunitempty)).
% 251.76/33.46 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setadjoinIL)).
% 251.76/33.46 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', nonemptyI1)).
% 251.76/33.46 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', nonemptyE1)).
% 251.76/33.46 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', noeltsimpempty)).
% 251.76/33.46 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', emptyI)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', setext)).
% 251.76/33.46 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', notinemptyset)).
% 251.76/33.46 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', emptysetimpfalse)).
% 251.76/33.46 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', emptysetE)).
% 251.76/33.46 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', prop2setE)).
% 251.76/33.46 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.5lubHWifRY/E---3.1_1310523.p', wellorderingAx)).
% 251.76/33.46 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.5lubHWifRY/E---3.1_1310523.p', foundationAx)).
% 251.76/33.46 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', omegaIndAx)).
% 251.76/33.46 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', omegaSAx)).
% 251.76/33.46 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', omega0Ax)).
% 251.76/33.46 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setunionAx)).
% 251.76/33.46 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', powersetAx)).
% 251.76/33.46 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setadjoinAx)).
% 251.76/33.46 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', emptysetAx)).
% 251.76/33.46 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', setextAx)).
% 251.76/33.46 thf(if, axiom, ((if)=(^[X4:$i, X44:$o, X2:$i, X3:$i]:(setunion @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X44))&(((X14)=(X2)))))|(((~((X44)))&(((X14)=(X3)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.5lubHWifRY/E---3.1_1310523.p', if)).
% 251.76/33.46 thf(c_0_224, 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)=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X46)=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[iftrue])).
% 251.76/33.46 thf(c_0_225, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 251.76/33.46 thf(c_0_226, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 251.76/33.46 thf(c_0_227, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 251.76/33.46 thf(c_0_228, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 251.76/33.46 thf(c_0_229, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 251.76/33.46 thf(c_0_230, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 251.76/33.46 thf(c_0_231, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 251.76/33.46 thf(c_0_232, plain, ((funcImageSingleton)<=>![X4:$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])).
% 251.76/33.46 thf(c_0_233, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 251.76/33.46 thf(c_0_234, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 251.76/33.46 thf(c_0_235, 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])).
% 251.76/33.46 thf(c_0_236, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 251.76/33.46 thf(c_0_237, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 251.76/33.46 thf(c_0_238, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 251.76/33.46 thf(c_0_239, 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])).
% 251.76/33.46 thf(c_0_240, 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])).
% 251.76/33.46 thf(c_0_241, 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])).
% 251.76/33.46 thf(c_0_242, 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])).
% 251.76/33.46 thf(c_0_243, 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])).
% 251.76/33.46 thf(c_0_244, 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])).
% 251.76/33.46 thf(c_0_245, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 251.76/33.46 thf(c_0_246, plain, ((iffalseProp2)<=>![X4:$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])).
% 251.76/33.46 thf(c_0_247, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 251.76/33.46 thf(c_0_248, plain, ((iftrueProp2)<=>![X4:$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])).
% 251.76/33.46 thf(c_0_249, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 251.76/33.46 thf(c_0_250, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 251.76/33.46 thf(c_0_251, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 251.76/33.46 thf(c_0_252, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 251.76/33.46 thf(c_0_253, 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])).
% 251.76/33.46 thf(c_0_254, 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])).
% 251.76/33.46 thf(c_0_255, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 251.76/33.46 thf(c_0_256, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 251.76/33.46 thf(c_0_257, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 251.76/33.46 thf(c_0_258, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 251.76/33.46 thf(c_0_259, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 251.76/33.46 thf(c_0_260, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 251.76/33.46 thf(c_0_261, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 251.76/33.46 thf(c_0_262, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 251.76/33.46 thf(c_0_263, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 251.76/33.46 thf(c_0_264, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 251.76/33.46 thf(c_0_265, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 251.76/33.46 thf(c_0_266, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 251.76/33.46 thf(c_0_267, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 251.76/33.46 thf(c_0_268, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 251.76/33.46 thf(c_0_269, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 251.76/33.46 thf(c_0_270, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 251.76/33.46 thf(c_0_271, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 251.76/33.46 thf(c_0_272, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 251.76/33.46 thf(c_0_273, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 251.76/33.46 thf(c_0_274, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 251.76/33.46 thf(c_0_275, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 251.76/33.46 thf(c_0_276, plain, ((epred1_0)<=>![X761:$i]:(?[X762:$i]:((((![X763:$i]:(((in @ X763 @ X762)=>![X764:$i]:(((in @ X764 @ X763)=>(in @ X764 @ X761)))))&![X765:$i, X766:$i]:((((in @ X765 @ X761)&(in @ X766 @ X761))=>(![X767:$i]:(((in @ X767 @ X762)=>((in @ X765 @ X767)<=>(in @ X766 @ X767))))=>((X765)=(X766))))))&![X768:$i, X769:$i]:((((in @ X768 @ X762)&(in @ X769 @ X762))=>(![X770:$i]:(((in @ X770 @ X768)=>(in @ X770 @ X769)))|![X771:$i]:(((in @ X771 @ X769)=>(in @ X771 @ X768)))))))&![X772:$i]:(((![X773:$i]:(((in @ X773 @ X772)=>(in @ X773 @ X761)))&?[X774:$i]:((in @ X774 @ X772)))=>?[X775:$i, X776:$i]:(((((in @ X775 @ X762)&(in @ X776 @ X772))&~(?[X777:$i]:(((in @ X777 @ X775)&(in @ X777 @ X772)))))&![X778:$i]:(((in @ X778 @ X762)=>(![X779:$i]:(((in @ X779 @ X778)=>(in @ X779 @ X775)))|(in @ X776 @ X778)))))))))))), introduced(definition)).
% 251.76/33.46 thf(c_0_277, negated_conjecture, ~((![X734:$i, X735:$i]:((![X736:$i]:(((in @ X736 @ X734)<=>(in @ X736 @ X735)))=>((X734)=(X735))))=>(![X737:$i]:(~(in @ X737 @ emptyset))=>(![X738:$i, X739:$i, X740:$i]:(((in @ X740 @ (setadjoin @ X738 @ X739))<=>(((X740)=(X738))|(in @ X740 @ X739))))=>(![X741:$i, X742:$i]:(((in @ X742 @ (powerset @ X741))<=>![X743:$i]:(((in @ X743 @ X742)=>(in @ X743 @ X741)))))=>(![X744:$i, X745:$i]:(((in @ X745 @ (setunion @ X744))<=>?[X746:$i]:(((in @ X745 @ X746)&(in @ X746 @ X744)))))=>((in @ emptyset @ omega)=>(![X747:$i]:(((in @ X747 @ omega)=>(in @ (setadjoin @ X747 @ X747) @ omega)))=>(![X748:$i]:((((in @ emptyset @ X748)&![X749:$i]:((((in @ X749 @ omega)&(in @ X749 @ X748))=>(in @ (setadjoin @ X749 @ X749) @ X748))))=>![X750:$i]:(((in @ X750 @ omega)=>(in @ X750 @ X748)))))=>(![X751:$i > $i > $o, X752:$i]:((![X753:$i]:(((in @ X753 @ X752)=>(exu @ (X751 @ X753))))=>?[X754:$i]:(![X755:$i]:(((in @ X755 @ X754)<=>?[X756:$i]:(((in @ X756 @ X752)&(X751 @ X756 @ X755))))))))=>(![X757:$i]:((?[X758:$i]:((in @ X758 @ X757))=>?[X759:$i]:(((in @ X759 @ X757)&~(?[X760:$i]:(((in @ X760 @ X759)&(in @ X760 @ X757))))))))=>((epred1_0)=>(![X780:$i > $o]:(((exu @ X780)=>(X780 @ (descr @ (^[Z0:$i]:(X780 @ Z0))))))=>(![X781:$i, X782:$i > $o, X783:$i]:(((in @ X783 @ X781)=>((X782 @ X783)=>(in @ X783 @ (dsetconstr @ X781 @ X782)))))=>(![X784:$i, X785:$i > $o, X786:$i]:(((in @ X786 @ (dsetconstr @ X784 @ X785))=>(in @ X786 @ X784)))=>(![X787:$i, X788:$i > $o, X789:$i]:(((in @ X789 @ (dsetconstr @ X787 @ X788))=>(X788 @ X789)))=>(![X790:$i > $o]:(((exu @ X790)=>?[X791:$i]:(((X790 @ X791)&![X792:$i]:(((X790 @ X792)=>((X791)=(X792))))))))=>(![X793:$o, X794:$i]:(((in @ X794 @ (prop2set @ ((X793))))=>(X793)))=>(![X795:$i]:(((in @ X795 @ emptyset)=>![X796:$o]:((X796))))=>(![X797:$i]:(((in @ X797 @ emptyset)=>~($true)))=>(![X798:$i]:(~(in @ X798 @ emptyset))=>(![X799:$i > $o]:(((exu @ X799)=>?[X800:$i]:((X799 @ X800))))=>(![X801:$i, X802:$i]:((![X803:$i]:(((in @ X803 @ X801)=>(in @ X803 @ X802)))=>(![X804:$i]:(((in @ X804 @ X802)=>(in @ X804 @ X801)))=>((X801)=(X802)))))=>(![X805:$i]:((![X806:$i]:(~(in @ X806 @ X805))=>((X805)=(emptyset))))=>(![X807:$i]:((![X808:$i]:(~(in @ X808 @ X807))=>((X807)=(emptyset))))=>(![X809:$i, X810:$i > $o, X811:$i]:(((in @ X811 @ X809)=>((in @ X811 @ (dsetconstr @ X809 @ X810))<=>(X810 @ X811))))=>(![X812:$i]:(((nonempty @ X812)=>?[X813:$i]:((in @ X813 @ X812))))=>(![X814:$i, X815:$i > $o, X816:$i]:(((in @ X816 @ X814)=>((X815 @ X816)=>(nonempty @ (dsetconstr @ X814 @ X815)))))=>(![X817:$i]:((?[X818:$i]:((in @ X818 @ X817))=>(nonempty @ X817)))=>(![X819:$i, X820:$i]:((in @ X819 @ (setadjoin @ X819 @ X820)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X821:$i, X822:$i, X823:$i]:(((in @ X823 @ X822)=>(in @ X823 @ (setadjoin @ X821 @ X822))))=>(![X824:$i, X825:$i, X826:$i]:(((in @ X826 @ (setadjoin @ X824 @ X825))=>![X827:$o]:(((((X826)=(X824))=>(X827))=>(((in @ X826 @ X825)=>(X827))=>(X827))))))=>(![X828:$i, X829:$i, X830:$i]:(((in @ X830 @ (setadjoin @ X828 @ X829))=>(((X830)=(X828))|(in @ X830 @ X829))))=>(![X831:$i]:(((dsetconstr @ X831 @ (^[Z0:$i]:($true)))=(X831)))=>(![X832:$i, X833:$i]:((![X834:$i]:(((in @ X834 @ X833)=>(in @ X834 @ X832)))=>(in @ X833 @ (powerset @ X832))))=>(![X835:$i]:((in @ emptyset @ (powerset @ X835)))=>(![X836:$i]:((in @ emptyset @ (powerset @ X836)))=>(![X837:$i, X838:$i, X839:$i]:(((in @ X838 @ (powerset @ X837))=>((in @ X839 @ X838)=>(in @ X839 @ X837))))=>(![X840:$i, X841:$i, X842:$i]:(((in @ X841 @ X842)=>((in @ X842 @ X840)=>(in @ X841 @ (setunion @ X840)))))=>(![X843:$i, X844:$i]:(((in @ X844 @ (setunion @ X843))=>![X845:$o]:((![X846:$i]:(((in @ X844 @ X846)=>((in @ X846 @ X843)=>(X845))))=>(X845)))))=>(![X847:$i, X848:$i]:(((in @ X848 @ X847)=>(in @ X848 @ (powerset @ (setunion @ X847)))))=>(![X849:$i > $o]:(((exu @ X849)=>?[X850:$i]:(![X851:$i]:(((X849 @ X851)<=>((X851)=(X850)))))))=>(![X852:$i]:(((nonempty @ X852)=>?[X853:$i]:(((in @ X853 @ X852)&$true))))=>(![X854:$i, X855:$i]:(((in @ X854 @ (setadjoin @ X855 @ emptyset))=>((X854)=(X855))))=>(![X856:$i, X857:$i]:((((X856)!=(X857))=>~(in @ X857 @ (setadjoin @ X856 @ emptyset))))=>(![X858:$i, X859:$i]:((((X858)=(X859))=>(in @ X858 @ (setadjoin @ X859 @ emptyset))))=>(![X860:$i, X861:$i]:(((in @ X860 @ (setadjoin @ X861 @ emptyset))=>(in @ X861 @ (setadjoin @ X860 @ emptyset))))=>(![X862:$i, X863:$i, X864:$i]:(((in @ X864 @ (setadjoin @ X862 @ (setadjoin @ X863 @ emptyset)))=>(((X864)=(X862))|((X864)=(X863)))))=>(![X865:$i, X866:$i]:((in @ X865 @ (setadjoin @ X865 @ (setadjoin @ X866 @ emptyset))))=>(![X867:$i, X868:$i]:((in @ X868 @ (setadjoin @ X867 @ (setadjoin @ X868 @ emptyset))))=>(![X869:$i, X870:$i > $o]:((?[X871:$i]:(((in @ X871 @ X869)&(X870 @ X871)))=>(((dsetconstr @ X869 @ X870)=(emptyset))=>~($true))))=>(![X872:$i > $o, X873:$i]:(((in @ X873 @ emptyset)=>(X872 @ X873)))=>(![X874:$i, X875:$i > $o]:((~(![X876:$i]:(((in @ X876 @ X874)=>(X875 @ X876))))=>?[X877:$i]:(((in @ X877 @ X874)&~((X875 @ X877))))))=>(![X878:$i, X879:$i > $o]:((![X880:$i]:(((in @ X880 @ X878)=>~((X879 @ X880))))=>~(?[X881:$i]:(((in @ X881 @ X878)&(X879 @ X881))))))=>(![X882:$i, X883:$i > $o]:((~(?[X884:$i]:(((in @ X884 @ X882)&(X883 @ X884))))=>![X885:$i]:(((in @ X885 @ X882)=>~((X883 @ X885))))))=>(![X886:$i, X887:$i > $o]:((?[X888:$i]:(((in @ X888 @ X886)&~((X887 @ X888))))=>~(![X889:$i]:(((in @ X889 @ X886)=>(X887 @ X889))))))=>(![X890:$o]:(((X890)=>(in @ emptyset @ (prop2set @ ((X890))))))=>((prop2set2propI)=>(![X891:$i, X892:$i > $o]:((~(?[X893:$i]:(((in @ X893 @ X891)&(X892 @ X893))))=>![X894:$i]:(((in @ X894 @ X891)=>~((X892 @ X894))))))=>(![X895:$i, X896:$i > $o]:((~(![X897:$i]:(((in @ X897 @ X895)=>(X896 @ X897))))=>?[X898:$i]:(((in @ X898 @ X895)&~((X896 @ X898))))))=>(![X899:$i > $o]:((?[X900:$i]:(((X899 @ X900)&![X901:$i]:(((X899 @ X901)=>((X900)=(X901))))))=>(exu @ X899)))=>(![X902:$i > $o]:((?[X903:$i]:((X902 @ X903))=>(![X904:$i, X905:$i]:(((X902 @ X904)=>((X902 @ X905)=>((X904)=(X905)))))=>(exu @ X902))))=>(![X906:$i > $o]:((?[X907:$i]:(![X908:$i]:(((X906 @ X908)<=>((X908)=(X907)))))=>(exu @ X906)))=>(![X909:$i, X910:$i]:((((X909)=(X910))=>![X911:$i, X912:$i]:((((X911)=(X912))=>((in @ X911 @ X909)=>(in @ X912 @ X910))))))=>(![X913:$i, X914:$i]:((((X913)=(X914))=>![X915:$i, X916:$i]:((((X915)=(X916))=>((in @ X915 @ X913)<=>(in @ X916 @ X914))))))=>(![X917:$i > $o]:(((exu @ X917)=>![X918:$i, X919:$i]:(((X917 @ X918)=>((X917 @ X919)=>((X918)=(X919)))))))=>(![X920:$i > $o, X921:$i > $o]:((![X922:$i, X923:$i]:((((X922)=(X923))=>((X920 @ X922)<=>(X921 @ X923))))=>((exu @ X920)<=>(exu @ X921))))=>(((emptyset)=(emptyset))=>(![X924:$i, X925:$i]:((((X924)=(X925))=>![X926:$i, X927:$i]:((((X926)=(X927))=>((setadjoin @ X924 @ X926)=(setadjoin @ X925 @ X927))))))=>(![X928:$i, X929:$i]:((((X928)=(X929))=>((powerset @ X928)=(powerset @ X929))))=>(![X930:$i, X931:$i]:((((X930)=(X931))=>((setunion @ X930)=(setunion @ X931))))=>(((omega)=(omega))=>(![X932:$i > $o]:(((exu @ X932)=>![X933:$i, X934:$i]:(((X932 @ X933)=>((X932 @ X934)=>((X933)=(X934)))))))=>(![X935:$i > $o, X936:$i > $o]:((![X937:$i, X938:$i]:((((X937)=(X938))=>((X935 @ X937)<=>(X936 @ X938))))=>((exu @ X935)=>((exu @ X936)=>((descr @ X935)=(descr @ X936))))))=>(![X939:$i, X940:$i]:((((X939)=(X940))=>![X941:$i > $o, X942:$i > $o]:((![X943:$i]:(((in @ X943 @ X939)=>![X944:$i]:(((in @ X944 @ X940)=>(((X943)=(X944))=>((X941 @ X943)<=>(X942 @ X944)))))))=>((dsetconstr @ X939 @ X941)=(dsetconstr @ X940 @ X942))))))=>(![X945:$i, X946:$i]:((![X947:$i]:(((in @ X947 @ X945)=>(in @ X947 @ X946)))=>(subset @ X945 @ X946)))=>(![X948:$i, X949:$i]:((((X948)=(X949))=>(subset @ X949 @ X948)))=>(![X950:$i, X951:$i]:((((X950)=(X951))=>(subset @ X950 @ X951)))=>(![X952:$i, X953:$i]:((![X954:$i]:(((in @ X954 @ X952)=>(in @ X954 @ X953)))=>(subset @ X952 @ X953)))=>(![X955:$i]:((subset @ emptyset @ X955))=>(![X956:$i, X957:$i, 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cartprodpairsurjEq]), c_0_225]), c_0_226]), c_0_227]), c_0_228]), c_0_229]), upairsetE]), c_0_230]), singletonsswitch]), c_0_231]), eqinunit]), c_0_232]), notinsingleton]), c_0_233]), uniqinunit]), app]), nonemptyImpWitness]), infuncsetfunc]), c_0_234]), ap2p]), upairsetIL]), funcinfuncset]), c_0_235]), c_0_236]), c_0_237]), brelnall1]), brelnall2]), c_0_238]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), subbreln]), eqbreln]), quantDeMorgan4]), funcext]), quantDeMorgan3]), funcext2]), quantDeMorgan2]), ap2apEq1]), quantDeMorgan1]), ap2apEq2]), vacuousDall]), c_0_239]), c_0_240]), c_0_241]), upairsetIR]), c_0_242]), prop2setI]), c_0_243]), c_0_244]), c_0_245]), c_0_246]), c_0_247]), c_0_248]), c_0_249]), ifp]), theeq]), in__Cong]), inCongP]), c_0_250]), c_0_251]), c_0_252]), notdallE]), notdexE]), c_0_253]), c_0_254]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_255]), c_0_256]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_257]), subsetE2]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subset2powerset]), c_0_258]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), c_0_259]), binunionRsub]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), binintersectI]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectRsub]), setminusSubset2]), setminusER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), setminusERneg]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), symdiffI2]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffIneg1]), singletonsubset]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), ubforcartprodlem3]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), c_0_260]), theprop]), c_0_261]), setukpairinjL1]), singletonsuniq]), c_0_262]), c_0_263]), c_0_264]), kfstpairEq]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), setukpairinjR2]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), c_0_265]), setukpairinjR]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_266]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_267]), nonemptyE1]), c_0_268]), noeltsimpempty]), emptyI]), setext]), c_0_269]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_270]), c_0_271]), c_0_272]), c_0_273]), c_0_274]), wellorderingAx]), foundationAx]), c_0_275]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_276])).
% 251.76/33.46 thf(c_0_278, plain, ![X1417:$i, X1418:$o, X1419:$i, X1420:$i]:(((if @ X1417 @ ((X1418)) @ X1419 @ X1420)=(setunion @ (dsetconstr @ X1417 @ (^[Z0:$i]:((((((X1418))&(((Z0)=(X1419)))))|(((~((X1418)))&(((Z0)=(X1420)))))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[if])])).
% 251.76/33.46 thf(c_0_279, negated_conjecture, ![X1421:$i, X1422:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1434:$i, X1435:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1443:$i, X1444:$i > $i > $o, X1445:$i, X1448:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1455:$i, X1456:$i > $o, X1457:$i, X1458:$i > $o, X1459:$i, X1460:$i, X1461:$i > $o, X1462:$i, X1463:$i, X1464:$i > $o, X1465:$i, X1466:$i > $o, X1468:$i, X1469:$o, X1470:$i, X1471:$i, X1472:$o, X1473:$i, X1474:$i, X1475:$i > $o, X1477:$i, X1478:$i, X1481:$i, X1483:$i, X1485:$i, X1486:$i > $o, X1487:$i, X1488:$i, X1490:$i, X1491:$i > $o, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$o, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$o, X1523:$i, X1524:$i, X1525:$i > $o, X1527:$i, X1528:$i, X1529:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i > $o, X1548:$i, X1549:$i > $o, X1550:$i, X1551:$i, X1552:$i > $o, X1553:$i, X1555:$i, X1556:$i > $o, X1558:$i, X1559:$i, X1560:$i > $o, X1562:$i, X1563:$i, X1564:$i > $o, X1565:$i, X1567:$o, X1568:$i, X1569:$i > $o, X1571:$i, X1572:$i, X1573:$i > $o, X1574:$i, X1576:$i > $o, X1577:$i, X1579:$i > $o, X1580:$i, X1583:$i > $o, X1584:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i > $o, X1595:$i, X1596:$i, X1597:$i > $o, X1598:$i > $o, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i > $o, X1610:$i, X1611:$i, X1612:$i > $o, X1613:$i > $o, X1616:$i, X1617:$i, X1618:$i > $o, X1619:$i > $o, X1622:$i, X1623:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i > $o, X1670:$i, X1671:$i > $o, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$o, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$o, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i > $o, X1826:$i, X1827:$i, X1828:$i > $o, X1830:$i, X1831:$i > $o, X1832:$i, X1834:$i, X1835:$i > $o, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i > $i > $o, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i > $i > $o, X1916:$i, X1917:$i, X1918:$i > $i > $o, X1919:$i, X1920:$i, X1921:$i > $i > $o, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i > $i > $o, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i > $i > $o, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i > $i > $o, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i > $i, X1965:$i, X1966:$i, X1967:$i > $i, X1969:$i, X1970:$i, X1971:$i > $i, X1973:$i, X1974:$i, X1975:$i, X1976:$i > $o, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i > $o, X1986:$i, X1987:$i, X1988:$i > $o, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i > $i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i > $i, X2060:$i, X2061:$i, X2062:$i > $i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$o, X2070:$i, X2071:$i, X2072:$i, X2073:$o, X2074:$i, X2075:$i, X2076:$i, X2077:$o, X2078:$i, X2079:$i, X2080:$i, X2081:$o, X2082:$i, X2083:$i, X2084:$i, X2085:$o, X2086:$i, X2087:$i, X2088:$i, X2089:$o, X2090:$i, X2091:$i, X2092:$i, X2093:$i]:((((~(in @ (esk1_2 @ X1421 @ X1422) @ X1421)|~(in @ (esk1_2 @ X1421 @ X1422) @ X1422)|((X1421)=(X1422)))&((in @ (esk1_2 @ X1421 @ X1422) @ X1421)|(in @ (esk1_2 @ X1421 @ X1422) @ X1422)|((X1421)=(X1422))))&(~(in @ X1424 @ emptyset)&(((~(in @ X1427 @ (setadjoin @ X1425 @ X1426))|(((X1427)=(X1425))|(in @ X1427 @ X1426)))&((((X1427)!=(X1425))|(in @ X1427 @ (setadjoin @ X1425 @ X1426)))&(~(in @ X1427 @ X1426)|(in @ X1427 @ (setadjoin @ X1425 @ X1426)))))&(((~(in @ X1429 @ (powerset @ X1428))|(~(in @ X1430 @ X1429)|(in @ X1430 @ X1428)))&(((in @ (esk2_2 @ X1431 @ X1432) @ X1432)|(in @ X1432 @ (powerset @ X1431)))&(~(in @ (esk2_2 @ X1431 @ X1432) @ X1431)|(in @ X1432 @ (powerset @ X1431)))))&(((((in @ X1435 @ (esk3_2 @ X1434 @ X1435))|~(in @ X1435 @ (setunion @ X1434)))&((in @ (esk3_2 @ X1434 @ X1435) @ X1434)|~(in @ X1435 @ (setunion @ X1434))))&(~(in @ X1438 @ X1439)|~(in @ X1439 @ X1437)|(in @ X1438 @ (setunion @ X1437))))&((in @ emptyset @ omega)&((~(in @ X1440 @ omega)|(in @ (setadjoin @ X1440 @ X1440) @ omega))&(((((in @ (esk4_1 @ X1441) @ omega)|~(in @ emptyset @ X1441)|(~(in @ X1443 @ omega)|(in @ X1443 @ X1441)))&((in @ (esk4_1 @ X1441) @ X1441)|~(in @ emptyset @ X1441)|(~(in @ X1443 @ omega)|(in @ X1443 @ X1441))))&(~(in @ (setadjoin @ (esk4_1 @ X1441) @ (esk4_1 @ X1441)) @ X1441)|~(in @ emptyset @ X1441)|(~(in @ X1443 @ omega)|(in @ X1443 @ X1441))))&((((((in @ (esk7_3 @ X1444 @ X1445 @ X1448) @ X1445)|~(in @ X1448 @ (esk6_2 @ X1444 @ X1445))|(in @ (esk5_2 @ X1444 @ X1445) @ X1445))&((X1444 @ (esk7_3 @ X1444 @ X1445 @ X1448) @ X1448)|~(in @ X1448 @ (esk6_2 @ X1444 @ X1445))|(in @ (esk5_2 @ X1444 @ X1445) @ X1445)))&(~(in @ X1451 @ X1445)|~(X1444 @ X1451 @ X1450)|(in @ X1450 @ (esk6_2 @ X1444 @ X1445))|(in @ (esk5_2 @ X1444 @ X1445) @ X1445)))&((((in @ (esk7_3 @ X1444 @ X1445 @ X1448) @ X1445)|~(in @ X1448 @ (esk6_2 @ X1444 @ X1445))|~(exu @ (X1444 @ (esk5_2 @ X1444 @ X1445))))&((X1444 @ (esk7_3 @ X1444 @ X1445 @ X1448) @ X1448)|~(in @ X1448 @ (esk6_2 @ X1444 @ X1445))|~(exu @ (X1444 @ (esk5_2 @ X1444 @ X1445)))))&(~(in @ X1451 @ X1445)|~(X1444 @ X1451 @ X1450)|(in @ X1450 @ (esk6_2 @ X1444 @ X1445))|~(exu @ (X1444 @ (esk5_2 @ X1444 @ X1445))))))&((((in @ (esk8_1 @ X1452) @ X1452)|~(in @ X1453 @ X1452))&(~(in @ X1455 @ (esk8_1 @ X1452))|~(in @ X1455 @ X1452)|~(in @ X1453 @ X1452)))&((epred1_0)&((~(exu @ X1456)|(X1456 @ (descr @ X1456)))&((~(in @ X1459 @ X1457)|(~(X1458 @ X1459)|(in @ X1459 @ (dsetconstr @ X1457 @ X1458))))&((~(in @ X1462 @ (dsetconstr @ X1460 @ X1461))|(in @ X1462 @ X1460))&((~(in @ X1465 @ (dsetconstr @ X1463 @ X1464))|(X1464 @ X1465))&((((X1466 @ (esk9_1 @ X1466))|~(exu @ X1466))&(~(X1466 @ X1468)|((esk9_1 @ X1466)=(X1468))|~(exu @ X1466)))&((~(in @ X1470 @ (prop2set @ ((X1469))))|(X1469))&((~(in @ X1471 @ emptyset)|(X1472))&((~(in @ X1473 @ emptyset)|~($true))&(~(in @ X1474 @ emptyset)&((~(exu @ X1475)|(X1475 @ (esk10_1 @ X1475)))&(((((in @ (esk12_2 @ X1477 @ X1478) @ X1478)|((X1477)=(X1478))|(in @ (esk11_2 @ X1477 @ X1478) @ X1477))&(~(in @ (esk12_2 @ X1477 @ X1478) @ X1477)|((X1477)=(X1478))|(in @ (esk11_2 @ X1477 @ X1478) @ X1477)))&(((in @ (esk12_2 @ X1477 @ X1478) @ X1478)|((X1477)=(X1478))|~(in @ (esk11_2 @ X1477 @ X1478) @ X1478))&(~(in @ (esk12_2 @ X1477 @ X1478) @ X1477)|((X1477)=(X1478))|~(in @ (esk11_2 @ X1477 @ X1478) @ X1478))))&(((in @ (esk13_1 @ X1481) @ X1481)|((X1481)=(emptyset)))&(((in @ (esk14_1 @ X1483) @ X1483)|((X1483)=(emptyset)))&(((~(in @ X1487 @ (dsetconstr @ X1485 @ X1486))|(X1486 @ X1487)|~(in @ X1487 @ X1485))&(~(X1486 @ X1487)|(in @ X1487 @ (dsetconstr 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X1509 @ (powerset @ X1508))))&((in @ emptyset @ (powerset @ X1511))&((in @ emptyset @ (powerset @ X1512))&((~(in @ X1514 @ (powerset @ X1513))|(~(in @ X1515 @ X1514)|(in @ X1515 @ X1513)))&((~(in @ X1517 @ X1518)|(~(in @ X1518 @ X1516)|(in @ X1517 @ (setunion @ X1516))))&((((in @ X1520 @ (esk17_3 @ X1519 @ X1520 @ X1521))|(X1521)|~(in @ X1520 @ (setunion @ X1519)))&(((in @ (esk17_3 @ X1519 @ X1520 @ X1521) @ X1519)|(X1521)|~(in @ X1520 @ (setunion @ X1519)))&(~(X1521)|(X1521)|~(in @ X1520 @ (setunion @ X1519)))))&((~(in @ X1524 @ X1523)|(in @ X1524 @ (powerset @ (setunion @ X1523))))&(((~(X1525 @ X1527)|((X1527)=(esk18_1 @ X1525))|~(exu @ X1525))&(((X1528)!=(esk18_1 @ X1525))|(X1525 @ X1528)|~(exu @ X1525)))&((((in @ (esk19_1 @ X1529) @ X1529)|~(nonempty @ X1529))&(($true)|~(nonempty @ X1529)))&((~(in @ X1531 @ (setadjoin @ X1532 @ emptyset))|((X1531)=(X1532)))&((((X1533)=(X1534))|~(in @ X1534 @ (setadjoin @ X1533 @ emptyset)))&((((X1535)!=(X1536))|(in @ X1535 @ (setadjoin @ X1536 @ 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(lam @ X2048 @ X2049 @ X2050) @ X2052)=(X2050 @ X2052)))))&((~(func @ X2053 @ X2054 @ X2055)|((lam @ X2053 @ X2054 @ (ap @ X2053 @ X2054 @ X2055))=(X2055)))&((((in @ (esk65_3 @ X2056 @ X2057 @ X2058) @ X2056)|((lam @ X2056 @ X2057 @ X2058)=(lam @ X2056 @ X2057 @ X2058)))&(~(in @ (X2058 @ (esk65_3 @ X2056 @ X2057 @ X2058)) @ X2057)|((lam @ X2056 @ X2057 @ X2058)=(lam @ X2056 @ X2057 @ X2058))))&((((in @ (esk66_3 @ X2060 @ X2061 @ X2062) @ X2060)|(~(in @ X2064 @ X2060)|((ap @ X2060 @ X2061 @ (lam @ X2060 @ X2061 @ X2062) @ X2064)=(X2062 @ X2064))))&(~(in @ (X2062 @ (esk66_3 @ X2060 @ X2061 @ X2062)) @ X2061)|(~(in @ X2064 @ X2060)|((ap @ X2060 @ X2061 @ (lam @ X2060 @ X2061 @ X2062) @ X2064)=(X2062 @ X2064)))))&((~(in @ X2067 @ (funcSet @ X2065 @ X2066))|((lam @ X2065 @ X2066 @ (ap @ X2065 @ X2066 @ X2067))=(X2067)))&((~(in @ X2070 @ X2068)|(~(in @ X2071 @ X2068)|((X2069)|(in @ X2071 @ (dsetconstr @ X2068 @ (^[Z0:$i]:((((((X2069))&(((Z0)=(X2070)))))|(((~((X2069)))&(((Z0)=(X2071)))))))))))))&((~(in @ X2074 @ X2072)|(~(in @ X2075 @ X2072)|((X2073)|((dsetconstr @ X2072 @ (^[Z0:$i]:((((((X2073))&(((Z0)=(X2074)))))|(((~((X2073)))&(((Z0)=(X2075)))))))))=(setadjoin @ X2075 @ emptyset)))))&((~(in @ X2078 @ X2076)|(~(in @ X2079 @ X2076)|(~(X2077)|(in @ X2078 @ (dsetconstr @ X2076 @ (^[Z0:$i]:((((((X2077))&(((Z0)=(X2078)))))|(((~((X2077)))&(((Z0)=(X2079)))))))))))))&((~(in @ X2082 @ X2080)|(~(in @ X2083 @ X2080)|(~(X2081)|((dsetconstr @ X2080 @ (^[Z0:$i]:((((((X2081))&(((Z0)=(X2082)))))|(((~((X2081)))&(((Z0)=(X2083)))))))))=(setadjoin @ X2082 @ emptyset)))))&((~(in @ X2086 @ X2084)|(~(in @ X2087 @ X2084)|(singleton @ (dsetconstr @ X2084 @ (^[Z0:$i]:((((((X2085))&(((Z0)=(X2086)))))|(((~((X2085)))&(((Z0)=(X2087))))))))))))&((~(in @ X2090 @ X2088)|(~(in @ X2091 @ X2088)|(in @ (if @ X2088 @ ((X2089)) @ X2090 @ X2091) @ X2088)))&((~(singleton @ X2092)|(~(in @ X2093 @ X2092)|((setunion @ X2092)=(X2093))))&((in @ esk68_0 @ esk67_0)&((in @ esk69_0 @ esk67_0)&((epred2_0)&(((~(epred2_0)|(epred2_0))&(((if @ esk67_0 @ $false @ esk68_0 @ esk69_0)!=(esk68_0))|(epred2_0)))&((~(epred2_0)|((if @ esk67_0 @ $true @ esk68_0 @ esk69_0)!=(esk68_0)))&(((if @ esk67_0 @ $false @ esk68_0 @ esk69_0)!=(esk68_0))|((if @ esk67_0 @ $true @ esk68_0 @ esk69_0)!=(esk68_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_277])])])])])])])])).
% 251.76/33.46 thf(c_0_280, plain, ![X2098:$i, X2099:$o, X2100:$i, X2101:$i]:(((if @ X2098 @ ((X2099)) @ X2100 @ X2101)=(setunion @ (dsetconstr @ X2098 @ (^[Z0:$i]:((((((X2099))&(((Z0)=(X2100)))))|(((~((X2099)))&(((Z0)=(X2101)))))))))))), inference(variable_rename,[status(thm)],[c_0_278])).
% 251.76/33.46 thf(c_0_281, plain, ![X2121:$i, X2:$i, X10:$o, X4:$i]:(((epred3_3 @ X4 @ X10 @ X2 @ X2121)<=>(((X10)&((X2121)=(X2)))|(~((X10))&((X2121)=(X4)))))), introduced(definition)).
% 251.76/33.46 thf(c_0_282, negated_conjecture, (~((epred2_0))|((if @ esk67_0 @ (($true)) @ esk68_0 @ esk69_0)!=(esk68_0))), inference(split_conjunct,[status(thm)],[c_0_279])).
% 251.76/33.46 thf(c_0_283, negated_conjecture, (epred2_0), inference(split_conjunct,[status(thm)],[c_0_279])).
% 251.76/33.46 thf(c_0_284, plain, ![X2:$i, X10:$o, X4:$i, X3:$i]:(((if @ X2 @ ((X10)) @ X3 @ X4)=(setunion @ (dsetconstr @ X2 @ (epred3_3 @ X4 @ ((X10)) @ X3))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_280]), c_0_281])).
% 251.76/33.46 thf(c_0_285, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((dsetconstr @ X3 @ (epred3_3 @ X4 @ (($true)) @ X2))=(setadjoin @ X2 @ emptyset))|~((in @ X2 @ X3))|~((in @ X4 @ X3)))), inference(lift_lambdas,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_279])])]), c_0_281])).
% 251.76/33.46 thf(c_0_286, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_279])).
% 251.76/33.46 thf(c_0_287, negated_conjecture, ((if @ esk67_0 @ (($true)) @ esk68_0 @ esk69_0)!=(esk68_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_282, c_0_283])])).
% 251.76/33.46 thf(c_0_288, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:((((if @ X2 @ (($true)) @ X3 @ X4)=(X3))|~((in @ X4 @ X2))|~((in @ X3 @ X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_284, c_0_285]), c_0_286])).
% 251.76/33.46 thf(c_0_289, negated_conjecture, (in @ esk69_0 @ esk67_0), inference(split_conjunct,[status(thm)],[c_0_279])).
% 251.76/33.46 thf(c_0_290, negated_conjecture, (in @ esk68_0 @ esk67_0), inference(split_conjunct,[status(thm)],[c_0_279])).
% 251.76/33.46 thf(c_0_291, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287, c_0_288]), c_0_289]), c_0_290])]), ['proof']).
% 251.76/33.46 % SZS output end CNFRefutation
% 251.76/33.46 % Parsed axioms : 490
% 251.76/33.46 % Removed by relevancy pruning/SinE : 266
% 251.76/33.46 % Initial clauses : 376
% 251.76/33.46 % Removed in clause preprocessing : 35
% 251.76/33.46 % Initial clauses in saturation : 341
% 251.76/33.46 % Processed clauses : 3474
% 251.76/33.46 % ...of these trivial : 49
% 251.76/33.46 % ...subsumed : 1082
% 251.76/33.46 % ...remaining for further processing : 2343
% 251.76/33.46 % Other redundant clauses eliminated : 147
% 251.76/33.46 % Clauses deleted for lack of memory : 0
% 251.76/33.46 % Backward-subsumed : 113
% 251.76/33.46 % Backward-rewritten : 26
% 251.76/33.46 % Generated clauses : 154695
% 251.76/33.46 % ...of the previous two non-redundant : 152725
% 251.76/33.46 % ...aggressively subsumed : 0
% 251.76/33.46 % Contextual simplify-reflections : 6
% 251.76/33.46 % Paramodulations : 154503
% 251.76/33.46 % Factorizations : 6
% 251.76/33.46 % NegExts : 2
% 251.76/33.46 % Equation resolutions : 154
% 251.76/33.46 % Disequality decompositions : 0
% 251.76/33.46 % Total rewrite steps : 4915
% 251.76/33.46 % ...of those cached : 4451
% 251.76/33.46 % Propositional unsat checks : 0
% 251.76/33.46 % Propositional check models : 0
% 251.76/33.46 % Propositional check unsatisfiable : 0
% 251.76/33.46 % Propositional clauses : 0
% 251.76/33.46 % Propositional clauses after purity: 0
% 251.76/33.46 % Propositional unsat core size : 0
% 251.76/33.46 % Propositional preprocessing time : 0.000
% 251.76/33.46 % Propositional encoding time : 0.000
% 251.76/33.46 % Propositional solver time : 0.000
% 251.76/33.46 % Success case prop preproc time : 0.000
% 251.76/33.46 % Success case prop encoding time : 0.000
% 251.76/33.46 % Success case prop solver time : 0.000
% 251.76/33.46 % Current number of processed clauses : 1888
% 251.76/33.46 % Positive orientable unit clauses : 119
% 251.76/33.46 % Positive unorientable unit clauses: 0
% 251.76/33.46 % Negative unit clauses : 46
% 251.76/33.46 % Non-unit-clauses : 1723
% 251.76/33.46 % Current number of unprocessed clauses: 149637
% 251.76/33.46 % ...number of literals in the above : 546132
% 251.76/33.46 % Current number of archived formulas : 0
% 251.76/33.46 % Current number of archived clauses : 439
% 251.76/33.46 % Clause-clause subsumption calls (NU) : 372179
% 251.76/33.46 % Rec. Clause-clause subsumption calls : 267549
% 251.76/33.46 % Non-unit clause-clause subsumptions : 646
% 251.76/33.46 % Unit Clause-clause subsumption calls : 16451
% 251.76/33.46 % Rewrite failures with RHS unbound : 0
% 251.76/33.46 % BW rewrite match attempts : 58
% 251.76/33.46 % BW rewrite match successes : 21
% 251.76/33.46 % Condensation attempts : 3474
% 251.76/33.46 % Condensation successes : 47
% 251.76/33.46 % Termbank termtop insertions : 2669719
% 251.76/33.46 % Search garbage collected termcells : 23328
% 251.76/33.46
% 251.76/33.46 % -------------------------------------------------
% 251.76/33.46 % User time : 31.040 s
% 251.76/33.46 % System time : 1.017 s
% 251.76/33.46 % Total time : 32.057 s
% 251.76/33.46 % Maximum resident set size: 9028 pages
% 251.76/33.46
% 251.76/33.46 % -------------------------------------------------
% 251.76/33.46 % User time : 31.054 s
% 251.76/33.46 % System time : 1.027 s
% 251.76/33.46 % Total time : 32.081 s
% 251.76/33.46 % Maximum resident set size: 5632 pages
% 251.76/33.46 % E exiting
%------------------------------------------------------------------------------