E-SAT---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E-SAT---3.5.1
% Problem  : SEU706^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:27:28 AM UTC 2026

% Result   : Theorem 0.22s 0.37s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU706^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18  % Computer : n009.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 14:13:00 UTC 2026
% 0.07/0.18  % CPUTime  : 
% 0.07/0.18  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23  Running higher-order theorem proving
% 0.07/0.26  Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p
% 0.22/0.37  % Version: 3.5.1-ho
% 0.22/0.37  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.37  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.37  % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.37  % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.37  % Starting new_bool_5 with 300s (1) cores
% 0.22/0.37  % Starting pre_casc_3 with 300s (1) cores
% 0.22/0.37  % Starting ho_unfolding_8 with 300s (1) cores
% 0.22/0.37  % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.22/0.37  % Starting new_bool_3 with 300s (1) cores
% 0.22/0.37  % Starting new_ho_5 with 300s (1) cores
% 0.22/0.37  % new_bool_5 with pid 4065133 completed with status 0
% 0.22/0.37  % Result found by new_bool_5
% 0.22/0.37  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.37  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.37  % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.37  % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.37  % Starting new_bool_5 with 300s (1) cores
% 0.22/0.37  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.22/0.37  % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.22/0.37  % Search class: HGHSM-FSLM32-MHFMMSBN
% 0.22/0.37  % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.37  % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.37  % SubtermCWHack with pid 4065157 completed with status 0
% 0.22/0.37  % Result found by SubtermCWHack
% 0.22/0.37  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.37  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.37  % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.37  % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.37  % Starting new_bool_5 with 300s (1) cores
% 0.22/0.37  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.22/0.37  % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.22/0.37  % Search class: HGHSM-FSLM32-MHFMMSBN
% 0.22/0.37  % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.37  % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.37  % Preprocessing time       : 0.004 s
% 0.22/0.37  
% 0.22/0.37  % Proof found!
% 0.22/0.37  % SZS status Theorem
% 0.22/0.37  % SZS output start CNFRefutation
% 0.22/0.37  thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.37  thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.37  thf(decl_25, type, setextAx: $o).
% 0.22/0.37  thf(decl_26, type, emptyset: $i).
% 0.22/0.37  thf(decl_27, type, emptysetAx: $o).
% 0.22/0.37  thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.37  thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.37  thf(decl_30, type, powerset: $i > $i).
% 0.22/0.37  thf(decl_31, type, powersetAx: $o).
% 0.22/0.37  thf(decl_32, type, setunion: $i > $i).
% 0.22/0.37  thf(decl_33, type, setunionAx: $o).
% 0.22/0.37  thf(decl_34, type, omega: $i).
% 0.22/0.37  thf(decl_35, type, omega0Ax: $o).
% 0.22/0.37  thf(decl_36, type, omegaSAx: $o).
% 0.22/0.37  thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.37  thf(decl_38, type, replAx: $o).
% 0.22/0.37  thf(decl_39, type, foundationAx: $o).
% 0.22/0.37  thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.37  thf(decl_41, type, descr: ($i > $o) > $i).
% 0.22/0.37  thf(decl_42, type, descrp: $o).
% 0.22/0.37  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.37  thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.37  thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.37  thf(decl_47, type, exuE1: $o).
% 0.22/0.37  thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.37  thf(decl_49, type, prop2setE: $o).
% 0.22/0.37  thf(decl_50, type, emptysetE: $o).
% 0.22/0.37  thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.37  thf(decl_52, type, notinemptyset: $o).
% 0.22/0.37  thf(decl_53, type, exuE3e: $o).
% 0.22/0.37  thf(decl_54, type, setext: $o).
% 0.22/0.37  thf(decl_55, type, emptyI: $o).
% 0.22/0.37  thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.37  thf(decl_57, type, setbeta: $o).
% 0.22/0.37  thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.37  thf(decl_59, type, nonemptyE1: $o).
% 0.22/0.37  thf(decl_60, type, nonemptyI: $o).
% 0.22/0.37  thf(decl_61, type, nonemptyI1: $o).
% 0.22/0.37  thf(decl_62, type, setadjoinIL: $o).
% 0.22/0.37  thf(decl_63, type, emptyinunitempty: $o).
% 0.22/0.37  thf(decl_64, type, setadjoinIR: $o).
% 0.22/0.37  thf(decl_65, type, setadjoinE: $o).
% 0.22/0.37  thf(decl_66, type, setadjoinOr: $o).
% 0.22/0.37  thf(decl_67, type, setoftrueEq: $o).
% 0.22/0.37  thf(decl_68, type, powersetI: $o).
% 0.22/0.37  thf(decl_69, type, emptyinPowerset: $o).
% 0.22/0.37  thf(decl_70, type, emptyInPowerset: $o).
% 0.22/0.37  thf(decl_71, type, powersetE: $o).
% 0.22/0.37  thf(decl_72, type, setunionI: $o).
% 0.22/0.37  thf(decl_73, type, setunionE: $o).
% 0.22/0.37  thf(decl_74, type, subPowSU: $o).
% 0.22/0.37  thf(decl_75, type, exuE2: $o).
% 0.22/0.37  thf(decl_76, type, nonemptyImpWitness: $o).
% 0.22/0.37  thf(decl_77, type, uniqinunit: $o).
% 0.22/0.37  thf(decl_78, type, notinsingleton: $o).
% 0.22/0.37  thf(decl_79, type, eqinunit: $o).
% 0.22/0.37  thf(decl_80, type, singletonsswitch: $o).
% 0.22/0.37  thf(decl_81, type, upairsetE: $o).
% 0.22/0.37  thf(decl_82, type, upairsetIL: $o).
% 0.22/0.37  thf(decl_83, type, upairsetIR: $o).
% 0.22/0.37  thf(decl_84, type, emptyE1: $o).
% 0.22/0.37  thf(decl_85, type, vacuousDall: $o).
% 0.22/0.37  thf(decl_86, type, quantDeMorgan1: $o).
% 0.22/0.37  thf(decl_87, type, quantDeMorgan2: $o).
% 0.22/0.37  thf(decl_88, type, quantDeMorgan3: $o).
% 0.22/0.37  thf(decl_89, type, quantDeMorgan4: $o).
% 0.22/0.37  thf(decl_90, type, prop2setI: $o).
% 0.22/0.37  thf(decl_92, type, prop2set2propI: $o).
% 0.22/0.37  thf(decl_93, type, notdexE: $o).
% 0.22/0.37  thf(decl_94, type, notdallE: $o).
% 0.22/0.37  thf(decl_95, type, exuI1: $o).
% 0.22/0.37  thf(decl_96, type, exuI3: $o).
% 0.22/0.37  thf(decl_97, type, exuI2: $o).
% 0.22/0.37  thf(decl_98, type, inCongP: $o).
% 0.22/0.37  thf(decl_99, type, in__Cong: $o).
% 0.22/0.37  thf(decl_100, type, exuE3u: $o).
% 0.22/0.37  thf(decl_101, type, exu__Cong: $o).
% 0.22/0.37  thf(decl_102, type, emptyset__Cong: $o).
% 0.22/0.37  thf(decl_103, type, setadjoin__Cong: $o).
% 0.22/0.37  thf(decl_104, type, powerset__Cong: $o).
% 0.22/0.37  thf(decl_105, type, setunion__Cong: $o).
% 0.22/0.37  thf(decl_106, type, omega__Cong: $o).
% 0.22/0.37  thf(decl_107, type, exuEu: $o).
% 0.22/0.37  thf(decl_108, type, descr__Cong: $o).
% 0.22/0.37  thf(decl_109, type, dsetconstr__Cong: $o).
% 0.22/0.37  thf(decl_110, type, subset: $i > $i > $o).
% 0.22/0.37  thf(decl_113, type, subsetI1: $o).
% 0.22/0.37  thf(decl_114, type, eqimpsubset2: $o).
% 0.22/0.37  thf(decl_115, type, eqimpsubset1: $o).
% 0.22/0.37  thf(decl_116, type, subsetI2: $o).
% 0.22/0.37  thf(decl_117, type, emptysetsubset: $o).
% 0.22/0.37  thf(decl_118, type, subsetE: $o).
% 0.22/0.37  thf(decl_119, type, subsetE2: $o).
% 0.22/0.37  thf(decl_120, type, notsubsetI: $o).
% 0.22/0.37  thf(decl_121, type, notequalI1: $o).
% 0.22/0.37  thf(decl_122, type, notequalI2: $o).
% 0.22/0.37  thf(decl_123, type, subsetRefl: $o).
% 0.22/0.37  thf(decl_124, type, subsetTrans: $o).
% 0.22/0.37  thf(decl_125, type, setadjoinSub: $o).
% 0.22/0.37  thf(decl_126, type, setadjoinSub2: $o).
% 0.22/0.37  thf(decl_127, type, subset2powerset: $o).
% 0.22/0.37  thf(decl_128, type, setextsub: $o).
% 0.22/0.37  thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.22/0.37  thf(decl_130, type, powersetI1: $o).
% 0.22/0.37  thf(decl_131, type, powersetE1: $o).
% 0.22/0.37  thf(decl_132, type, inPowerset: $o).
% 0.22/0.37  thf(decl_133, type, powersetsubset: $o).
% 0.22/0.37  thf(decl_134, type, sepInPowerset: $o).
% 0.22/0.37  thf(decl_135, type, sepSubset: $o).
% 0.22/0.37  thf(decl_136, type, binunion: $i > $i > $i).
% 0.22/0.37  thf(decl_137, type, binunionIL: $o).
% 0.22/0.37  thf(decl_138, type, upairset2IR: $o).
% 0.22/0.37  thf(decl_139, type, binunionIR: $o).
% 0.22/0.37  thf(decl_140, type, binunionEcases: $o).
% 0.22/0.37  thf(decl_141, type, binunionE: $o).
% 0.22/0.37  thf(decl_142, type, binunionLsub: $o).
% 0.22/0.37  thf(decl_143, type, binunionRsub: $o).
% 0.22/0.37  thf(decl_144, type, binintersect: $i > $i > $i).
% 0.22/0.37  thf(decl_145, type, binintersectI: $o).
% 0.22/0.37  thf(decl_146, type, binintersectSubset5: $o).
% 0.22/0.37  thf(decl_147, type, binintersectEL: $o).
% 0.22/0.37  thf(decl_148, type, binintersectLsub: $o).
% 0.22/0.37  thf(decl_149, type, binintersectSubset2: $o).
% 0.22/0.37  thf(decl_150, type, binintersectSubset3: $o).
% 0.22/0.37  thf(decl_151, type, binintersectER: $o).
% 0.22/0.37  thf(decl_152, type, disjointsetsI1: $o).
% 0.22/0.37  thf(decl_153, type, binintersectRsub: $o).
% 0.22/0.37  thf(decl_154, type, binintersectSubset4: $o).
% 0.22/0.37  thf(decl_155, type, binintersectSubset1: $o).
% 0.22/0.37  thf(decl_156, type, bs114d: $o).
% 0.22/0.37  thf(decl_158, type, setminus: $i > $i > $i).
% 0.22/0.37  thf(decl_159, type, setminusI: $o).
% 0.22/0.37  thf(decl_160, type, setminusEL: $o).
% 0.22/0.37  thf(decl_161, type, setminusER: $o).
% 0.22/0.37  thf(decl_162, type, setminusSubset2: $o).
% 0.22/0.37  thf(decl_163, type, setminusERneg: $o).
% 0.22/0.37  thf(decl_164, type, setminusELneg: $o).
% 0.22/0.37  thf(decl_165, type, setminusILneg: $o).
% 0.22/0.37  thf(decl_166, type, setminusIRneg: $o).
% 0.22/0.37  thf(decl_167, type, setminusLsub: $o).
% 0.22/0.37  thf(decl_168, type, setminusSubset1: $o).
% 0.22/0.37  thf(decl_169, type, symdiff: $i > $i > $i).
% 0.22/0.37  thf(decl_170, type, symdiffE: $o).
% 0.22/0.37  thf(decl_171, type, symdiffI1: $o).
% 0.22/0.37  thf(decl_172, type, symdiffI2: $o).
% 0.22/0.37  thf(decl_173, type, symdiffIneg1: $o).
% 0.22/0.37  thf(decl_174, type, symdiffIneg2: $o).
% 0.22/0.37  thf(decl_175, type, iskpair: $i > $o).
% 0.22/0.37  thf(decl_176, type, secondinupair: $o).
% 0.22/0.37  thf(decl_177, type, setukpairIL: $o).
% 0.22/0.37  thf(decl_178, type, setukpairIR: $o).
% 0.22/0.37  thf(decl_179, type, kpairiskpair: $o).
% 0.22/0.37  thf(decl_180, type, kpair: $i > $i > $i).
% 0.22/0.37  thf(decl_181, type, kpairp: $o).
% 0.22/0.37  thf(decl_182, type, cartprod: $i > $i > $i).
% 0.22/0.37  thf(decl_183, type, singletonsubset: $o).
% 0.22/0.37  thf(decl_184, type, singletoninpowerset: $o).
% 0.22/0.37  thf(decl_185, type, singletoninpowunion: $o).
% 0.22/0.37  thf(decl_186, type, upairset2E: $o).
% 0.22/0.37  thf(decl_187, type, upairsubunion: $o).
% 0.22/0.37  thf(decl_188, type, upairinpowunion: $o).
% 0.22/0.37  thf(decl_189, type, ubforcartprodlem1: $o).
% 0.22/0.37  thf(decl_190, type, ubforcartprodlem2: $o).
% 0.22/0.37  thf(decl_191, type, ubforcartprodlem3: $o).
% 0.22/0.37  thf(decl_192, type, cartprodpairin: $o).
% 0.22/0.37  thf(decl_193, type, cartprodmempair1: $o).
% 0.22/0.37  thf(decl_194, type, cartprodmempair: $o).
% 0.22/0.37  thf(decl_195, type, setunionE2: $o).
% 0.22/0.37  thf(decl_196, type, setunionsingleton1: $o).
% 0.22/0.37  thf(decl_197, type, setunionsingleton2: $o).
% 0.22/0.37  thf(decl_198, type, setunionsingleton: $o).
% 0.22/0.37  thf(decl_199, type, singleton: $i > $o).
% 0.22/0.37  thf(decl_200, type, singletonprop: $o).
% 0.22/0.37  thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 0.22/0.37  thf(decl_202, type, ex1E1: $o).
% 0.22/0.37  thf(decl_203, type, ex1I: $o).
% 0.22/0.37  thf(decl_204, type, ex1I2: $o).
% 0.22/0.37  thf(decl_205, type, singletonsuniq: $o).
% 0.22/0.37  thf(decl_210, type, setukpairinjL1: $o).
% 0.22/0.37  thf(decl_211, type, kfstsingleton: $o).
% 0.22/0.37  thf(decl_212, type, theprop: $o).
% 0.22/0.37  thf(decl_213, type, kfst: $i > $i).
% 0.22/0.37  thf(decl_214, type, kfstpairEq: $o).
% 0.22/0.37  thf(decl_215, type, cartprodfstin: $o).
% 0.22/0.37  thf(decl_216, type, setukpairinjL2: $o).
% 0.22/0.37  thf(decl_217, type, setukpairinjL: $o).
% 0.22/0.37  thf(decl_218, type, setukpairinjR11: $o).
% 0.22/0.37  thf(decl_219, type, setukpairinjR12: $o).
% 0.22/0.37  thf(decl_220, type, setukpairinjR1: $o).
% 0.22/0.37  thf(decl_221, type, upairequniteq: $o).
% 0.22/0.37  thf(decl_222, type, setukpairinjR2: $o).
% 0.22/0.37  thf(decl_223, type, setukpairinjR: $o).
% 0.22/0.37  thf(decl_224, type, ksndsingleton: $o).
% 0.22/0.37  thf(decl_225, type, ksnd: $i > $i).
% 0.22/0.37  thf(decl_226, type, ksndpairEq: $o).
% 0.22/0.37  thf(decl_227, type, kpairsurjEq: $o).
% 0.22/0.37  thf(decl_228, type, cartprodsndin: $o).
% 0.22/0.37  thf(decl_229, type, cartprodpairmemEL: $o).
% 0.22/0.37  thf(decl_230, type, cartprodpairmemER: $o).
% 0.22/0.37  thf(decl_231, type, cartprodmempaircEq: $o).
% 0.22/0.37  thf(decl_232, type, cartprodfstpairEq: $o).
% 0.22/0.37  thf(decl_233, type, cartprodsndpairEq: $o).
% 0.22/0.37  thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.22/0.37  thf(decl_235, type, breln: $i > $i > $i > $o).
% 0.22/0.37  thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.22/0.37  thf(decl_237, type, dpsetconstrI: $o).
% 0.22/0.37  thf(decl_238, type, dpsetconstrSub: $o).
% 0.22/0.37  thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.22/0.37  thf(decl_240, type, dpsetconstrERa: $o).
% 0.22/0.37  thf(decl_241, type, dpsetconstrEL1: $o).
% 0.22/0.37  thf(decl_242, type, dpsetconstrEL2: $o).
% 0.22/0.37  thf(decl_243, type, dpsetconstrER: $o).
% 0.22/0.37  thf(decl_244, type, func: $i > $i > $i > $o).
% 0.22/0.37  thf(decl_245, type, funcSet: $i > $i > $i).
% 0.22/0.37  thf(decl_246, type, funcImageSingleton: $o).
% 0.22/0.37  thf(decl_247, type, apProp: $o).
% 0.22/0.37  thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 0.22/0.37  thf(decl_249, type, app: $o).
% 0.22/0.37  thf(decl_250, type, infuncsetfunc: $o).
% 0.22/0.37  thf(decl_251, type, ap2p: $o).
% 0.22/0.37  thf(decl_252, type, funcinfuncset: $o).
% 0.22/0.37  thf(decl_253, type, lamProp: $o).
% 0.22/0.37  thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 0.22/0.37  thf(decl_255, type, lamp: $o).
% 0.22/0.37  thf(decl_256, type, lam2p: $o).
% 0.22/0.37  thf(decl_257, type, brelnall1: $o).
% 0.22/0.37  thf(decl_258, type, brelnall2: $o).
% 0.22/0.37  thf(decl_259, type, ex1E2: $o).
% 0.22/0.37  thf(decl_260, type, funcGraphProp1: $o).
% 0.22/0.37  thf(decl_261, type, funcGraphProp3: $o).
% 0.22/0.37  thf(decl_262, type, funcGraphProp2: $o).
% 0.22/0.37  thf(decl_263, type, funcextLem: $o).
% 0.22/0.37  thf(decl_264, type, funcGraphProp4: $o).
% 0.22/0.37  thf(decl_265, type, subbreln: $o).
% 0.22/0.37  thf(decl_266, type, eqbreln: $o).
% 0.22/0.37  thf(decl_267, type, funcext: $o).
% 0.22/0.37  thf(decl_268, type, funcext2: $o).
% 0.22/0.37  thf(decl_269, type, ap2apEq1: $o).
% 0.22/0.37  thf(decl_270, type, ap2apEq2: $o).
% 0.22/0.37  thf(decl_271, type, beta1: $o).
% 0.22/0.37  thf(decl_272, type, eta1: $o).
% 0.22/0.37  thf(decl_273, type, lam2lamEq: $o).
% 0.22/0.37  thf(decl_274, type, beta2: $o).
% 0.22/0.37  thf(decl_275, type, eta2: $o).
% 0.22/0.37  thf(decl_276, type, iffalseProp1: $o).
% 0.22/0.37  thf(decl_277, type, iffalseProp2: $o).
% 0.22/0.37  thf(decl_278, type, iftrueProp1: $o).
% 0.22/0.37  thf(decl_279, type, iftrueProp2: $o).
% 0.22/0.37  thf(decl_280, type, ifSingleton: $o).
% 0.22/0.37  thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 0.22/0.37  thf(decl_282, type, ifp: $o).
% 0.22/0.37  thf(decl_283, type, epred1_0: $o).
% 0.22/0.37  thf(decl_284, type, esk1_2: $i > $i > $i).
% 0.22/0.37  thf(decl_285, type, esk2_2: $i > $i > $i).
% 0.22/0.37  thf(decl_286, type, esk3_2: $i > $i > $i).
% 0.22/0.37  thf(decl_287, type, esk4_1: $i > $i).
% 0.22/0.37  thf(decl_288, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.22/0.37  thf(decl_289, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.22/0.37  thf(decl_290, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.37  thf(decl_291, type, esk8_1: $i > $i).
% 0.22/0.37  thf(decl_292, type, esk9_1: ($i > $o) > $i).
% 0.22/0.37  thf(decl_293, type, esk10_1: ($i > $o) > $i).
% 0.22/0.37  thf(decl_294, type, esk11_2: $i > $i > $i).
% 0.22/0.37  thf(decl_295, type, esk12_2: $i > $i > $i).
% 0.22/0.37  thf(decl_296, type, esk13_1: $i > $i).
% 0.22/0.37  thf(decl_297, type, esk14_1: $i > $i).
% 0.22/0.37  thf(decl_298, type, esk15_1: $i > $i).
% 0.22/0.37  thf(decl_299, type, esk16_2: $i > $i > $i).
% 0.22/0.37  thf(decl_300, type, esk17_3: $i > $i > $o > $i).
% 0.22/0.37  thf(decl_301, type, esk18_1: ($i > $o) > $i).
% 0.22/0.37  thf(decl_302, type, esk19_1: $i > $i).
% 0.22/0.37  thf(decl_303, type, esk20_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_304, type, esk21_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_305, type, esk22_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_306, type, esk23_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_307, type, esk24_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_308, type, esk25_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_309, type, esk26_2: ($i > $o) > $i > $i).
% 0.22/0.37  thf(decl_310, type, esk27_1: ($i > $o) > $i).
% 0.22/0.37  thf(decl_311, type, esk28_1: ($i > $o) > $i).
% 0.22/0.37  thf(decl_312, type, esk29_2: ($i > $o) > $i > $i).
% 0.22/0.37  thf(decl_313, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.37  thf(decl_314, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.37  thf(decl_315, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.37  thf(decl_316, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.37  thf(decl_317, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.37  thf(decl_318, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.37  thf(decl_319, type, esk36_2: $i > $i > $i).
% 0.22/0.37  thf(decl_320, type, esk37_2: $i > $i > $i).
% 0.22/0.37  thf(decl_321, type, esk38_2: $i > $i > $i).
% 0.22/0.37  thf(decl_322, type, esk39_3: $i > $i > $i > $i).
% 0.22/0.37  thf(decl_323, type, esk40_3: $i > $i > $i > $i).
% 0.22/0.37  thf(decl_324, type, esk41_2: $i > $i > $i).
% 0.22/0.37  thf(decl_325, type, esk42_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_326, type, esk43_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_327, type, esk44_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_328, type, esk45_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_329, type, esk46_3: $i > ($i > $o) > $i > $i).
% 0.22/0.37  thf(decl_330, type, esk47_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_331, type, esk48_2: $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_332, type, esk49_1: $i > $i).
% 0.22/0.37  thf(decl_333, type, esk50_1: $i > $i).
% 0.22/0.37  thf(decl_334, type, esk51_4: $i > $i > $i > $i > $i).
% 0.22/0.37  thf(decl_335, type, esk52_3: $i > $i > ($i > $i) > $i).
% 0.22/0.37  thf(decl_336, type, esk53_3: $i > $i > ($i > $i) > $i).
% 0.22/0.37  thf(decl_337, type, esk54_3: $i > $i > ($i > $i) > $i).
% 0.22/0.37  thf(decl_338, type, esk55_4: $i > $i > $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_339, type, esk56_4: $i > $i > $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_340, type, esk57_4: $i > $i > $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_341, type, esk58_4: $i > $i > $i > ($i > $o) > $i).
% 0.22/0.37  thf(decl_342, type, esk59_4: $i > $i > $i > $i > $i).
% 0.22/0.37  thf(decl_343, type, esk60_4: $i > $i > $i > $i > $i).
% 0.22/0.37  thf(decl_344, type, esk61_4: $i > $i > $i > $i > $i).
% 0.22/0.37  thf(decl_345, type, esk62_4: $i > $i > $i > $i > $i).
% 0.22/0.37  thf(decl_346, type, esk63_4: $i > $i > $i > $i > $i).
% 0.22/0.37  thf(decl_347, type, esk64_4: $i > $i > $i > $i > $i).
% 0.22/0.37  thf(decl_348, type, esk65_4: $i > $i > $i > $i > $i).
% 0.22/0.37  thf(decl_349, type, esk66_4: $i > $i > $i > $i > $i).
% 0.22/0.37  thf(decl_350, type, esk67_4: $i > $i > $i > $i > $i).
% 0.22/0.37  thf(decl_351, type, esk68_3: $i > $i > ($i > $i) > $i).
% 0.22/0.37  thf(decl_352, type, esk69_3: $i > $i > ($i > $i) > $i).
% 0.22/0.37  thf(decl_353, type, esk70_3: $i > $i > ($i > $i) > $i).
% 0.22/0.37  thf(decl_354, type, esk71_4: $i > $o > $i > $i > $i).
% 0.22/0.37  thf(decl_355, type, esk72_0: $i).
% 0.22/0.37  thf(decl_356, type, esk73_0: $i).
% 0.22/0.37  thf(decl_357, type, esk74_0: $i).
% 0.22/0.37  thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', funcImageSingleton)).
% 0.22/0.37  thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', singleton)).
% 0.22/0.37  thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ifSingleton)).
% 0.22/0.37  thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', singletonprop)).
% 0.22/0.37  thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', kfstsingleton)).
% 0.22/0.37  thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ksndsingleton)).
% 0.22/0.37  thf(theeq, 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)=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', theeq)).
% 0.22/0.37  thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', dpsetconstrI)).
% 0.22/0.37  thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', dpsetconstrSub)).
% 0.22/0.37  thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setOfPairsIsBReln)).
% 0.22/0.37  thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', dpsetconstrERa)).
% 0.22/0.37  thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', dpsetconstrEL1)).
% 0.22/0.37  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', exuE2)).
% 0.22/0.37  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:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', dpsetconstrEL2)).
% 0.22/0.37  thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', dpsetconstrER)).
% 0.22/0.37  thf(apProp, axiom, ((apProp)<=>![X4:$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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', apProp)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', lamProp)).
% 0.22/0.37  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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', lamp)).
% 0.22/0.37  thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', lam2p)).
% 0.22/0.37  thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ex1E2)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', emptyE1)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', beta1)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', eta1)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', lam2lamEq)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', beta2)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', eta2)).
% 0.22/0.37  thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', iffalseProp1)).
% 0.22/0.37  thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', iffalseProp2)).
% 0.22/0.37  thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', iftrueProp1)).
% 0.22/0.37  thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', iftrueProp2)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', exuI1)).
% 0.22/0.37  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', exuI3)).
% 0.22/0.37  thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', exu__Cong)).
% 0.22/0.37  thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', exuE3u)).
% 0.22/0.37  thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', exuI2)).
% 0.22/0.37  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', dsetconstr__Cong)).
% 0.22/0.37  thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', descr__Cong)).
% 0.22/0.37  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', exuEu)).
% 0.22/0.37  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', sepSubset)).
% 0.22/0.37  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', sepInPowerset)).
% 0.22/0.37  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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ex1I2)).
% 0.22/0.37  thf(ex1I, axiom, ((ex1I)<=>![X4:$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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ex1I)).
% 0.22/0.37  thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ex1E1)).
% 0.22/0.37  thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', theprop)).
% 0.22/0.37  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setoftrueEq)).
% 0.22/0.37  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', nonemptyI)).
% 0.22/0.37  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setbeta)).
% 0.22/0.37  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', exuE3e)).
% 0.22/0.37  thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', exuE1)).
% 0.22/0.37  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', dsetconstrER)).
% 0.22/0.37  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', dsetconstrEL)).
% 0.22/0.37  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', dsetconstrI)).
% 0.22/0.37  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', descrp)).
% 0.22/0.37  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', replAx)).
% 0.22/0.37  thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', cartprodsndpairEq)).
% 0.22/0.37  thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', cartprodfstpairEq)).
% 0.22/0.37  thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', cartprodpairsurjEq)).
% 0.22/0.37  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', uniqinunit)).
% 0.22/0.37  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', nonemptyImpWitness)).
% 0.22/0.37  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', subPowSU)).
% 0.22/0.37  thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setunionE)).
% 0.22/0.37  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setunionI)).
% 0.22/0.37  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', powersetE)).
% 0.22/0.37  thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', app)).
% 0.22/0.37  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', notinsingleton)).
% 0.22/0.37  thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', infuncsetfunc)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ap2p)).
% 0.22/0.37  thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', funcinfuncset)).
% 0.22/0.37  thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', brelnall1)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', brelnall2)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', funcGraphProp1)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', funcGraphProp3)).
% 0.22/0.37  thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', funcGraphProp2)).
% 0.22/0.37  thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', funcextLem)).
% 0.22/0.37  thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', funcGraphProp4)).
% 0.22/0.37  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', vacuousDall)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', subbreln)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', eqbreln)).
% 0.22/0.37  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', upairsetIR)).
% 0.22/0.37  thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', funcext)).
% 0.22/0.37  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', upairsetIL)).
% 0.22/0.37  thf(funcext2, axiom, ((funcext2)<=>![X4:$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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', funcext2)).
% 0.22/0.37  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', upairsetE)).
% 0.22/0.37  thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ap2apEq1)).
% 0.22/0.37  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', singletonsswitch)).
% 0.22/0.37  thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ap2apEq2)).
% 0.22/0.37  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', eqinunit)).
% 0.22/0.37  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', quantDeMorgan1)).
% 0.22/0.37  thf(ifp, axiom, ((ifp)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X45)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ifp)).
% 0.22/0.37  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', notdallE)).
% 0.22/0.37  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', notdexE)).
% 0.22/0.37  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', prop2setI)).
% 0.22/0.37  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', quantDeMorgan4)).
% 0.22/0.37  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', quantDeMorgan3)).
% 0.22/0.37  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', quantDeMorgan2)).
% 0.22/0.37  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setadjoin__Cong)).
% 0.22/0.37  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', emptyset__Cong)).
% 0.22/0.37  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', in__Cong)).
% 0.22/0.37  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', inCongP)).
% 0.22/0.37  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', powerset__Cong)).
% 0.22/0.37  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', eqimpsubset2)).
% 0.22/0.37  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', subsetI1)).
% 0.22/0.37  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', omega__Cong)).
% 0.22/0.37  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setunion__Cong)).
% 0.22/0.37  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', eqimpsubset1)).
% 0.22/0.37  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', notequalI2)).
% 0.22/0.37  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', notequalI1)).
% 0.22/0.37  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', notsubsetI)).
% 0.22/0.37  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', subsetE2)).
% 0.22/0.37  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', subsetE)).
% 0.22/0.37  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', emptysetsubset)).
% 0.22/0.37  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', subsetI2)).
% 0.22/0.37  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', subsetRefl)).
% 0.22/0.37  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', powersetI1)).
% 0.22/0.37  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', subsetemptysetimpeq)).
% 0.22/0.37  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setextsub)).
% 0.22/0.37  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', subset2powerset)).
% 0.22/0.37  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setadjoinSub2)).
% 0.22/0.37  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setadjoinSub)).
% 0.22/0.37  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', subsetTrans)).
% 0.22/0.37  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', powersetE1)).
% 0.22/0.37  thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binunionIR)).
% 0.22/0.37  thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', upairset2IR)).
% 0.22/0.37  thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binunionIL)).
% 0.22/0.37  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', powersetsubset)).
% 0.22/0.37  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', inPowerset)).
% 0.22/0.37  thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binunionEcases)).
% 0.22/0.37  thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binintersectLsub)).
% 0.22/0.37  thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binintersectEL)).
% 0.22/0.37  thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binintersectSubset5)).
% 0.22/0.37  thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binintersectI)).
% 0.22/0.37  thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binunionRsub)).
% 0.22/0.37  thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binunionLsub)).
% 0.22/0.37  thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binunionE)).
% 0.22/0.37  thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binintersectSubset2)).
% 0.22/0.37  thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', bs114d)).
% 0.22/0.37  thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binintersectSubset1)).
% 0.22/0.37  thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binintersectSubset4)).
% 0.22/0.37  thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binintersectRsub)).
% 0.22/0.37  thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', disjointsetsI1)).
% 0.22/0.37  thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binintersectER)).
% 0.22/0.37  thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', binintersectSubset3)).
% 0.22/0.37  thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setminusI)).
% 0.22/0.37  thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setminusIRneg)).
% 0.22/0.37  thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setminusILneg)).
% 0.22/0.37  thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setminusELneg)).
% 0.22/0.37  thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setminusERneg)).
% 0.22/0.37  thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setminusSubset2)).
% 0.22/0.37  thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setminusER)).
% 0.22/0.37  thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setminusEL)).
% 0.22/0.37  thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setminusLsub)).
% 0.22/0.37  thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', secondinupair)).
% 0.22/0.37  thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', symdiffIneg2)).
% 0.22/0.37  thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', symdiffIneg1)).
% 0.22/0.37  thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', symdiffI2)).
% 0.22/0.37  thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', symdiffI1)).
% 0.22/0.37  thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', symdiffE)).
% 0.22/0.37  thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setminusSubset1)).
% 0.22/0.37  thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setukpairIL)).
% 0.22/0.37  thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', upairset2E)).
% 0.22/0.37  thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', singletoninpowunion)).
% 0.22/0.37  thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', singletoninpowerset)).
% 0.22/0.37  thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', singletonsubset)).
% 0.22/0.37  thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', kpairp)).
% 0.22/0.37  thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', kpairiskpair)).
% 0.22/0.37  thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setukpairIR)).
% 0.22/0.37  thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', upairsubunion)).
% 0.22/0.37  thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', cartprodmempair)).
% 0.22/0.37  thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', cartprodmempair1)).
% 0.22/0.37  thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', cartprodpairin)).
% 0.22/0.37  thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ubforcartprodlem3)).
% 0.22/0.37  thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ubforcartprodlem2)).
% 0.22/0.37  thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ubforcartprodlem1)).
% 0.22/0.37  thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', upairinpowunion)).
% 0.22/0.37  thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setunionE2)).
% 0.22/0.37  thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setunionsingleton)).
% 0.22/0.37  thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setunionsingleton2)).
% 0.22/0.37  thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setunionsingleton1)).
% 0.22/0.37  thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', singletonsuniq)).
% 0.22/0.37  thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setukpairinjL)).
% 0.22/0.37  thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setukpairinjL2)).
% 0.22/0.37  thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', cartprodfstin)).
% 0.22/0.37  thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', kfstpairEq)).
% 0.22/0.37  thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setukpairinjL1)).
% 0.22/0.37  thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setukpairinjR11)).
% 0.22/0.37  thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', ksndpairEq)).
% 0.22/0.37  thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setukpairinjR)).
% 0.22/0.37  thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setukpairinjR2)).
% 0.22/0.37  thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', upairequniteq)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setukpairinjR1)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setukpairinjR12)).
% 0.22/0.37  thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', cartprodsndin)).
% 0.22/0.37  thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', cartprodpairmemEL)).
% 0.22/0.37  thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', cartprodpairmemER)).
% 0.22/0.37  thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', cartprodmempaircEq)).
% 0.22/0.37  thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', kpairsurjEq)).
% 0.22/0.37  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', emptyInPowerset)).
% 0.22/0.37  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', emptyinPowerset)).
% 0.22/0.37  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', powersetI)).
% 0.22/0.37  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setadjoinOr)).
% 0.22/0.37  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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setadjoinE)).
% 0.22/0.37  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setadjoinIR)).
% 0.22/0.37  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', emptyinunitempty)).
% 0.22/0.37  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setadjoinIL)).
% 0.22/0.37  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', nonemptyI1)).
% 0.22/0.37  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', nonemptyE1)).
% 0.22/0.37  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', noeltsimpempty)).
% 0.22/0.37  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', emptyI)).
% 0.22/0.37  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setext)).
% 0.22/0.37  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', notinemptyset)).
% 0.22/0.37  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', emptysetimpfalse)).
% 0.22/0.37  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', emptysetE)).
% 0.22/0.37  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', prop2setE)).
% 0.22/0.37  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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', wellorderingAx)).
% 0.22/0.37  thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', foundationAx)).
% 0.22/0.37  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', omegaIndAx)).
% 0.22/0.37  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', omegaSAx)).
% 0.22/0.37  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', omega0Ax)).
% 0.22/0.37  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setunionAx)).
% 0.22/0.37  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', powersetAx)).
% 0.22/0.37  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setadjoinAx)).
% 0.22/0.37  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', emptysetAx)).
% 0.22/0.37  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.utgEzTcv50/E---3.1_4065097.p', setextAx)).
% 0.22/0.37  thf(c_0_223, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 0.22/0.37  thf(c_0_224, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 0.22/0.37  thf(c_0_225, plain, ((ifSingleton)<=>![X4:$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])).
% 0.22/0.37  thf(c_0_226, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 0.22/0.37  thf(c_0_227, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 0.22/0.37  thf(c_0_228, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 0.22/0.37  thf(c_0_229, 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)=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[theeq])).
% 0.22/0.37  thf(c_0_230, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 0.22/0.37  thf(c_0_231, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 0.22/0.37  thf(c_0_232, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 0.22/0.37  thf(c_0_233, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 0.22/0.37  thf(c_0_234, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 0.22/0.37  thf(c_0_235, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.22/0.37  thf(c_0_236, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 0.22/0.37  thf(c_0_237, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 0.22/0.37  thf(c_0_238, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:((((func @ X4 @ X5 @ X29))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X733:$i]:((((in @ X733 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X733 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[c_0_223, c_0_224])).
% 0.22/0.37  thf(c_0_239, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 0.22/0.37  thf(c_0_240, plain, ((lamProp)<=>![X4:$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])).
% 0.22/0.37  thf(c_0_241, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 0.22/0.37  thf(c_0_242, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 0.22/0.37  thf(c_0_243, plain, ((ex1E2)<=>![X4:$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])).
% 0.22/0.37  thf(c_0_244, 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])).
% 0.22/0.37  thf(c_0_245, 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])).
% 0.22/0.37  thf(c_0_246, 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])).
% 0.22/0.37  thf(c_0_247, 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])).
% 0.22/0.37  thf(c_0_248, 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])).
% 0.22/0.37  thf(c_0_249, 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])).
% 0.22/0.37  thf(c_0_250, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 0.22/0.37  thf(c_0_251, plain, ((iffalseProp2)<=>![X4:$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])).
% 0.22/0.37  thf(c_0_252, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 0.22/0.37  thf(c_0_253, plain, ((iftrueProp2)<=>![X4:$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])).
% 0.22/0.37  thf(c_0_254, plain, ((ifSingleton)=(![X4:$i, X43:$o, X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((?[X734:$i]:((((in @ X734 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3)))))))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3)))))))))=(setadjoin @ X734 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[c_0_225, c_0_224])).
% 0.22/0.37  thf(c_0_255, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.22/0.37  thf(c_0_256, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.22/0.37  thf(c_0_257, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.22/0.37  thf(c_0_258, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.22/0.37  thf(c_0_259, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.22/0.37  thf(c_0_260, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.22/0.37  thf(c_0_261, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.22/0.37  thf(c_0_262, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.22/0.37  thf(c_0_263, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.22/0.37  thf(c_0_264, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.22/0.37  thf(c_0_265, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 0.22/0.37  thf(c_0_266, plain, ((ex1I)<=>![X4:$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])).
% 0.22/0.37  thf(c_0_267, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 0.22/0.37  thf(c_0_268, plain, ((singletonprop)=(![X4:$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)))))=>((?[X729:$i]:((((in @ X729 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X729 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_224])).
% 0.22/0.37  thf(c_0_269, axiom, ((theprop)=(![X21:$i]:((((?[X731:$i]:((((in @ X731 @ X21))&(((X21)=(setadjoin @ X731 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_224])).
% 0.22/0.37  thf(c_0_270, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X730:$i]:((((in @ X730 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X730 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_227, c_0_224])).
% 0.22/0.37  thf(c_0_271, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X732:$i]:((((in @ X732 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X732 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_224])).
% 0.22/0.37  thf(c_0_272, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.22/0.37  thf(c_0_273, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.37  thf(c_0_274, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.37  thf(c_0_275, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.37  thf(c_0_276, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.22/0.37  thf(c_0_277, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.37  thf(c_0_278, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.37  thf(c_0_279, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.37  thf(c_0_280, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.22/0.37  thf(c_0_281, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.37  thf(c_0_282, plain, ((epred1_0)<=>![X762:$i]:(?[X763:$i]:((((![X764:$i]:(((in @ X764 @ X763)=>![X765:$i]:(((in @ X765 @ X764)=>(in @ X765 @ X762)))))&![X766:$i, X767:$i]:((((in @ X766 @ X762)&(in @ X767 @ X762))=>(![X768:$i]:(((in @ X768 @ X763)=>((in @ X766 @ X768)<=>(in @ X767 @ X768))))=>((X766)=(X767))))))&![X769:$i, X770:$i]:((((in @ X769 @ X763)&(in @ X770 @ X763))=>(![X771:$i]:(((in @ X771 @ X769)=>(in @ X771 @ X770)))|![X772:$i]:(((in @ X772 @ X770)=>(in @ X772 @ X769)))))))&![X773:$i]:(((![X774:$i]:(((in @ X774 @ X773)=>(in @ X774 @ X762)))&?[X775:$i]:((in @ X775 @ X773)))=>?[X776:$i, X777:$i]:(((((in @ X776 @ X763)&(in @ X777 @ X773))&~(?[X778:$i]:(((in @ X778 @ X776)&(in @ X778 @ X773)))))&![X779:$i]:(((in @ X779 @ X763)=>(![X780:$i]:(((in @ X780 @ X779)=>(in @ X780 @ X776)))|(in @ X777 @ X779)))))))))))), introduced(definition)).
% 0.22/0.37  thf(c_0_283, negated_conjecture, ~((![X735:$i, X736:$i]:((![X737:$i]:(((in @ X737 @ X735)<=>(in @ X737 @ X736)))=>((X735)=(X736))))=>(![X738:$i]:(~(in @ X738 @ emptyset))=>(![X739:$i, X740:$i, X741:$i]:(((in @ X741 @ (setadjoin @ X739 @ X740))<=>(((X741)=(X739))|(in @ X741 @ X740))))=>(![X742:$i, X743:$i]:(((in @ X743 @ (powerset @ X742))<=>![X744:$i]:(((in @ X744 @ X743)=>(in @ X744 @ X742)))))=>(![X745:$i, X746:$i]:(((in @ X746 @ (setunion @ X745))<=>?[X747:$i]:(((in @ X746 @ X747)&(in @ X747 @ X745)))))=>((in @ emptyset @ omega)=>(![X748:$i]:(((in @ X748 @ omega)=>(in @ (setadjoin @ X748 @ X748) @ omega)))=>(![X749:$i]:((((in @ emptyset @ X749)&![X750:$i]:((((in @ X750 @ omega)&(in @ X750 @ X749))=>(in @ (setadjoin @ X750 @ X750) @ X749))))=>![X751:$i]:(((in @ X751 @ omega)=>(in @ X751 @ X749)))))=>(![X752:$i > $i > $o, X753:$i]:((![X754:$i]:(((in @ X754 @ X753)=>(exu @ (X752 @ X754))))=>?[X755:$i]:(![X756:$i]:(((in @ X756 @ X755)<=>?[X757:$i]:(((in @ X757 @ X753)&(X752 @ X757 @ X756))))))))=>(![X758:$i]:((?[X759:$i]:((in @ X759 @ X758))=>?[X760:$i]:(((in @ X760 @ X758)&~(?[X761:$i]:(((in @ X761 @ X760)&(in @ X761 @ X758))))))))=>((epred1_0)=>(![X781:$i > $o]:(((exu @ X781)=>(X781 @ (descr @ (^[Z0:$i]:(X781 @ Z0))))))=>(![X782:$i, X783:$i > $o, X784:$i]:(((in @ X784 @ X782)=>((X783 @ X784)=>(in @ X784 @ (dsetconstr @ X782 @ X783)))))=>(![X785:$i, X786:$i > $o, X787:$i]:(((in @ X787 @ (dsetconstr @ X785 @ X786))=>(in @ X787 @ X785)))=>(![X788:$i, X789:$i > $o, X790:$i]:(((in @ X790 @ (dsetconstr @ X788 @ X789))=>(X789 @ X790)))=>(![X791:$i > $o]:(((exu @ X791)=>?[X792:$i]:(((X791 @ X792)&![X793:$i]:(((X791 @ X793)=>((X792)=(X793))))))))=>(![X794:$o, X795:$i]:(((in @ X795 @ (prop2set @ ((X794))))=>(X794)))=>(![X796:$i]:(((in @ X796 @ emptyset)=>![X797:$o]:((X797))))=>(![X798:$i]:(((in @ X798 @ emptyset)=>~($true)))=>(![X799:$i]:(~(in @ X799 @ emptyset))=>(![X800:$i > $o]:(((exu @ X800)=>?[X801:$i]:((X800 @ X801))))=>(![X802:$i, X803:$i]:((![X804:$i]:(((in @ X804 @ X802)=>(in @ X804 @ X803)))=>(![X805:$i]:(((in @ X805 @ X803)=>(in @ X805 @ X802)))=>((X802)=(X803)))))=>(![X806:$i]:((![X807:$i]:(~(in @ X807 @ X806))=>((X806)=(emptyset))))=>(![X808:$i]:((![X809:$i]:(~(in @ X809 @ X808))=>((X808)=(emptyset))))=>(![X810:$i, X811:$i > $o, X812:$i]:(((in @ X812 @ X810)=>((in @ X812 @ (dsetconstr @ X810 @ X811))<=>(X811 @ X812))))=>(![X813:$i]:(((nonempty @ X813)=>?[X814:$i]:((in @ X814 @ X813))))=>(![X815:$i, X816:$i > $o, X817:$i]:(((in @ X817 @ X815)=>((X816 @ X817)=>(nonempty @ (dsetconstr @ X815 @ X816)))))=>(![X818:$i]:((?[X819:$i]:((in @ X819 @ X818))=>(nonempty @ X818)))=>(![X820:$i, X821:$i]:((in @ X820 @ (setadjoin @ X820 @ X821)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X822:$i, X823:$i, X824:$i]:(((in @ X824 @ X823)=>(in @ X824 @ (setadjoin @ X822 @ X823))))=>(![X825:$i, X826:$i, X827:$i]:(((in @ X827 @ (setadjoin @ X825 @ X826))=>![X828:$o]:(((((X827)=(X825))=>(X828))=>(((in @ X827 @ X826)=>(X828))=>(X828))))))=>(![X829:$i, X830:$i, X831:$i]:(((in @ X831 @ (setadjoin @ X829 @ X830))=>(((X831)=(X829))|(in @ X831 @ X830))))=>(![X832:$i]:(((dsetconstr @ X832 @ (^[Z0:$i]:($true)))=(X832)))=>(![X833:$i, X834:$i]:((![X835:$i]:(((in @ X835 @ X834)=>(in @ X835 @ X833)))=>(in @ X834 @ (powerset @ X833))))=>(![X836:$i]:((in @ emptyset @ (powerset @ X836)))=>(![X837:$i]:((in @ emptyset @ (powerset @ X837)))=>(![X838:$i, X839:$i, X840:$i]:(((in @ X839 @ (powerset @ X838))=>((in @ X840 @ X839)=>(in @ X840 @ X838))))=>(![X841:$i, X842:$i, X843:$i]:(((in @ X842 @ X843)=>((in @ X843 @ X841)=>(in @ X842 @ (setunion @ X841)))))=>(![X844:$i, X845:$i]:(((in @ X845 @ (setunion @ X844))=>![X846:$o]:((![X847:$i]:(((in @ X845 @ X847)=>((in @ X847 @ X844)=>(X846))))=>(X846)))))=>(![X848:$i, X849:$i]:(((in @ X849 @ X848)=>(in @ X849 @ (powerset @ (setunion @ X848)))))=>(![X850:$i > $o]:(((exu @ X850)=>?[X851:$i]:(![X852:$i]:(((X850 @ X852)<=>((X852)=(X851)))))))=>(![X853:$i]:(((nonempty @ X853)=>?[X854:$i]:(((in @ X854 @ X853)&$true))))=>(![X855:$i, X856:$i]:(((in @ X855 @ (setadjoin @ X856 @ emptyset))=>((X855)=(X856))))=>(![X857:$i, X858:$i]:((((X857)!=(X858))=>~(in @ X858 @ (setadjoin @ X857 @ emptyset))))=>(![X859:$i, X860:$i]:((((X859)=(X860))=>(in @ X859 @ (setadjoin @ X860 @ emptyset))))=>(![X861:$i, X862:$i]:(((in @ X861 @ (setadjoin @ X862 @ emptyset))=>(in @ X862 @ (setadjoin @ X861 @ emptyset))))=>(![X863:$i, X864:$i, X865:$i]:(((in @ X865 @ (setadjoin @ X863 @ (setadjoin @ X864 @ emptyset)))=>(((X865)=(X863))|((X865)=(X864)))))=>(![X866:$i, X867:$i]:((in @ X866 @ (setadjoin @ X866 @ (setadjoin @ X867 @ emptyset))))=>(![X868:$i, X869:$i]:((in @ X869 @ (setadjoin @ X868 @ (setadjoin @ X869 @ emptyset))))=>(![X870:$i, X871:$i > $o]:((?[X872:$i]:(((in @ X872 @ X870)&(X871 @ X872)))=>(((dsetconstr @ X870 @ X871)=(emptyset))=>~($true))))=>(![X873:$i > $o, X874:$i]:(((in @ X874 @ emptyset)=>(X873 @ X874)))=>(![X875:$i, X876:$i > $o]:((~(![X877:$i]:(((in @ X877 @ 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(^[Z0:$i]:((((((X1414))&(((Z0)=(X1415)))))|(((~((X1414)))&(((Z0)=(X1416))))))))))&((dsetconstr @ X1413 @ (^[Z0:$i]:((((((X1414))&(((Z0)=(X1415)))))|(((~((X1414)))&(((Z0)=(X1416)))))))))=(setadjoin @ X1417 @ emptyset))))))))=>(![X1418:$i, X1419:$o, X1420:$i]:(((in @ X1420 @ X1418)=>![X1421:$i]:(((in @ X1421 @ X1418)=>(in @ (if @ X1418 @ ((X1419)) @ X1420 @ X1421) @ X1418)))))=>![X21:$i]:((?[X1422:$i]:(((in @ X1422 @ X21)&((X21)=(setadjoin @ X1422 @ emptyset))))=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_229, cartprodsndpairEq]), cartprodfstpairEq]), cartprodpairsurjEq]), c_0_230]), c_0_231]), c_0_232]), uniqinunit]), c_0_233]), nonemptyImpWitness]), c_0_234]), c_0_235]), c_0_236]), subPowSU]), c_0_237]), setunionE]), c_0_238]), setunionI]), c_0_239]), powersetE]), app]), notinsingleton]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_240]), c_0_241]), c_0_242]), brelnall1]), brelnall2]), c_0_243]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), vacuousDall]), subbreln]), c_0_244]), eqbreln]), upairsetIR]), funcext]), upairsetIL]), funcext2]), upairsetE]), ap2apEq1]), singletonsswitch]), ap2apEq2]), eqinunit]), c_0_245]), quantDeMorgan1]), c_0_246]), c_0_247]), c_0_248]), c_0_249]), c_0_250]), c_0_251]), c_0_252]), c_0_253]), c_0_254]), ifp]), c_0_224]), c_0_255]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), c_0_256]), setadjoin__Cong]), emptyset__Cong]), c_0_257]), c_0_258]), in__Cong]), inCongP]), c_0_259]), powerset__Cong]), eqimpsubset2]), subsetI1]), c_0_260]), c_0_261]), c_0_262]), omega__Cong]), setunion__Cong]), eqimpsubset1]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), emptysetsubset]), subsetI2]), subsetRefl]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), powersetE1]), binunionIR]), upairset2IR]), binunionIL]), c_0_263]), c_0_264]), powersetsubset]), inPowerset]), binunionEcases]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), binintersectSubset2]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectER]), binintersectSubset3]), setminusI]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), setminusEL]), setminusLsub]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setukpairIL]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), upairsubunion]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), setunionE2]), c_0_265]), c_0_266]), c_0_267]), c_0_268]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), singletonsuniq]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), c_0_269]), c_0_270]), setukpairinjL1]), setukpairinjR11]), ksndpairEq]), c_0_271]), setukpairinjR]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), kpairsurjEq]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_272]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_273]), nonemptyE1]), c_0_274]), noeltsimpempty]), emptyI]), setext]), c_0_275]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_276]), c_0_277]), c_0_278]), c_0_279]), c_0_280]), wellorderingAx]), foundationAx]), c_0_281]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_282])).
% 0.22/0.38  thf(c_0_284, negated_conjecture, ![X1423:$i, X1424:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1436:$i, X1437:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1445:$i, X1446:$i > $i > $o, X1447:$i, X1450:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1457:$i, X1458:$i > $o, X1459:$i, X1460:$i > $o, X1461:$i, X1462:$i, X1463:$i > $o, X1464:$i, X1465:$i, X1466:$i > $o, X1467:$i, X1468:$i > $o, X1470:$i, X1471:$o, X1472:$i, X1473:$i, X1474:$o, X1475:$i, X1476:$i, X1477:$i > $o, X1479:$i, X1480:$i, X1483:$i, X1485:$i, X1487:$i, X1488:$i > $o, X1489:$i, X1490:$i, X1492:$i, X1493:$i > $o, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$o, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$o, X1525:$i, X1526:$i, X1527:$i > $o, X1529:$i, X1530:$i, X1531:$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:$i, X1548:$i, X1549:$i > $o, X1550:$i, X1551:$i > $o, X1552:$i, X1553:$i, X1554:$i > $o, X1555:$i, X1557:$i, X1558:$i > $o, X1560:$i, X1561:$i, X1562:$i > $o, X1564:$i, X1565:$i, X1566:$i > $o, X1567:$i, X1569:$o, X1570:$i, X1571:$i > $o, X1573:$i, X1574:$i, X1575:$i > $o, X1576:$i, X1578:$i > $o, X1579:$i, X1581:$i > $o, X1582:$i, X1585:$i > $o, X1586:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i > $o, X1597:$i, X1598:$i, X1599:$i > $o, X1600:$i > $o, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i > $o, X1612:$i, X1613:$i, X1614:$i > $o, X1615:$i > $o, X1618:$i, X1619:$i, X1620:$i > $o, X1621:$i > $o, X1624:$i, X1625:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1634:$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:$i, X1670:$i, X1671:$i > $o, X1672:$i, X1673:$i > $o, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$o, X1686:$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, X1711:$i, X1712:$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:$i, X1751:$i, X1752:$i, X1753:$o, 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:$i, X1811:$i, X1812:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i > $o, X1828:$i, X1830:$i, X1831:$i > $o, X1833:$i, X1834:$i > $o, X1835:$i, X1837:$i, X1838:$i > $o, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$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:$i, X1885:$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:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i > $i > $o, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i > $i > $o, X1922:$i, X1923:$i, X1924:$i > $i > $o, X1925:$i, X1926:$i, X1927:$i > $i > $o, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i > $i > $o, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i > $i > $o, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i > $i > $o, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i > $i, X1972:$i, X1973:$i, X1974:$i > $i, X1976:$i, X1977:$i, X1978:$i > $i, X1980:$i, X1981:$i, X1982:$i, X1983:$i > $o, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i > $o, X1993:$i, X1994:$i, X1995:$i > $o, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, 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(kpair @ (esk55_4 @ X1980 @ X1981 @ X1982 @ X1983) @ (esk56_4 @ X1980 @ X1981 @ X1982 @ X1983)) @ X1982)|(~(in @ X1986 @ X1982)|(X1983 @ X1986))|~(breln @ X1980 @ X1981 @ X1982))&(~(X1983 @ (kpair @ (esk55_4 @ X1980 @ X1981 @ X1982 @ X1983) @ (esk56_4 @ X1980 @ X1981 @ X1982 @ X1983)))|(~(in @ X1986 @ X1982)|(X1983 @ X1986))|~(breln @ X1980 @ X1981 @ X1982)))))&((((in @ (esk57_4 @ X1987 @ X1988 @ X1989 @ X1990) @ X1987)|(~(in @ X1993 @ X1989)|(X1990 @ X1993))|~(breln @ X1987 @ X1988 @ X1989))&(((in @ (esk58_4 @ X1987 @ X1988 @ X1989 @ X1990) @ X1988)|(~(in @ X1993 @ X1989)|(X1990 @ X1993))|~(breln @ X1987 @ X1988 @ X1989))&(((in @ (kpair @ (esk57_4 @ X1987 @ X1988 @ X1989 @ X1990) @ (esk58_4 @ X1987 @ X1988 @ X1989 @ X1990)) @ X1989)|(~(in @ X1993 @ X1989)|(X1990 @ X1993))|~(breln @ X1987 @ X1988 @ X1989))&(~(X1990 @ (kpair @ (esk57_4 @ X1987 @ X1988 @ X1989 @ X1990) @ (esk58_4 @ X1987 @ X1988 @ X1989 @ X1990)))|(~(in @ X1993 @ X1989)|(X1990 @ X1993))|~(breln @ X1987 @ X1988 @ X1989)))))&((~(ex1 @ X1994 @ X1995)|(~(in @ X1996 @ X1994)|(~(in @ X1997 @ X1994)|(~(X1995 @ X1996)|(~(X1995 @ X1997)|((X1996)=(X1997)))))))&((~(func @ X1998 @ X1999 @ X2000)|(~(in @ X2001 @ X1998)|(in @ (kpair @ X2001 @ (ap @ X1998 @ X1999 @ X2000 @ X2001)) @ X2000)))&((~(in @ X2004 @ (funcSet @ X2002 @ X2003))|(~(in @ X2005 @ X2002)|(in @ (kpair @ X2005 @ (ap @ X2002 @ X2003 @ X2004 @ X2005)) @ X2004)))&((~(func @ X2006 @ X2007 @ X2008)|(~(in @ X2009 @ X2006)|(~(in @ X2010 @ X2007)|(~(in @ (kpair @ X2009 @ X2010) @ X2008)|((ap @ X2006 @ X2007 @ X2008 @ X2009)=(X2010))))))&((((in @ (esk59_4 @ X2011 @ X2012 @ X2013 @ X2014) @ X2011)|(~(in @ X2016 @ X2011)|(~(in @ X2017 @ X2012)|(~(in @ (kpair @ X2016 @ X2017) @ X2014)|(in @ (kpair @ X2016 @ X2017) @ X2013))))|~(func @ X2011 @ X2012 @ X2014)|~(func @ X2011 @ X2012 @ X2013))&(((ap @ X2011 @ X2012 @ X2013 @ (esk59_4 @ X2011 @ X2012 @ X2013 @ X2014))!=(ap @ X2011 @ X2012 @ X2014 @ (esk59_4 @ X2011 @ X2012 @ X2013 @ X2014)))|(~(in @ X2016 @ X2011)|(~(in @ X2017 @ X2012)|(~(in @ (kpair @ X2016 @ X2017) @ X2014)|(in @ (kpair @ X2016 @ X2017) @ X2013))))|~(func @ X2011 @ X2012 @ X2014)|~(func @ X2011 @ X2012 @ X2013)))&((~(in @ X2020 @ (funcSet @ X2018 @ X2019))|(~(in @ X2021 @ X2018)|(~(in @ X2022 @ X2019)|(~(in @ (kpair @ X2021 @ X2022) @ X2020)|((ap @ X2018 @ X2019 @ X2020 @ X2021)=(X2022))))))&((((in @ (esk60_4 @ X2023 @ X2024 @ X2025 @ X2026) @ X2023)|(subset @ X2025 @ X2026)|~(breln @ X2023 @ X2024 @ X2026)|~(breln @ X2023 @ X2024 @ X2025))&(((in @ (esk61_4 @ X2023 @ X2024 @ X2025 @ X2026) @ X2024)|(subset @ X2025 @ X2026)|~(breln @ X2023 @ X2024 @ X2026)|~(breln @ X2023 @ X2024 @ X2025))&(((in @ (kpair @ (esk60_4 @ X2023 @ X2024 @ X2025 @ X2026) @ (esk61_4 @ X2023 @ X2024 @ X2025 @ X2026)) @ X2025)|(subset @ X2025 @ X2026)|~(breln @ X2023 @ X2024 @ X2026)|~(breln @ X2023 @ X2024 @ X2025))&(~(in @ (kpair @ (esk60_4 @ X2023 @ X2024 @ X2025 @ X2026) @ (esk61_4 @ X2023 @ X2024 @ X2025 @ X2026)) @ X2026)|(subset @ X2025 @ X2026)|~(breln @ X2023 @ X2024 @ X2026)|~(breln @ X2023 @ X2024 @ X2025)))))&(((((in @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2029)|((X2031)=(X2032))|(in @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2029)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(((in @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2030)|((X2031)=(X2032))|(in @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2029)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(((in @ (kpair @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2032)|((X2031)=(X2032))|(in @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2029)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(~(in @ (kpair @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2031)|((X2031)=(X2032))|(in @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2029)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031)))))&((((in @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2029)|((X2031)=(X2032))|(in @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2030)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(((in @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2030)|((X2031)=(X2032))|(in @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2030)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(((in @ (kpair @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2032)|((X2031)=(X2032))|(in @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2030)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(~(in @ (kpair @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2031)|((X2031)=(X2032))|(in @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2030)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031)))))&((((in @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2029)|((X2031)=(X2032))|(in @ (kpair @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2031)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(((in @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2030)|((X2031)=(X2032))|(in @ (kpair @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2031)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(((in @ (kpair @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2032)|((X2031)=(X2032))|(in @ (kpair @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2031)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(~(in @ (kpair @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2031)|((X2031)=(X2032))|(in @ (kpair @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2031)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031)))))&(((in @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2029)|((X2031)=(X2032))|~(in @ (kpair @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2032)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(((in @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032) @ X2030)|((X2031)=(X2032))|~(in @ (kpair @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2032)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(((in @ (kpair @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2032)|((X2031)=(X2032))|~(in @ (kpair @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2032)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))&(~(in @ (kpair @ (esk64_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk65_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2031)|((X2031)=(X2032))|~(in @ (kpair @ (esk62_4 @ X2029 @ X2030 @ X2031 @ X2032) @ (esk63_4 @ X2029 @ X2030 @ X2031 @ X2032)) @ X2032)|~(breln @ X2029 @ X2030 @ X2032)|~(breln @ X2029 @ X2030 @ X2031))))))))&((((in @ (esk66_4 @ X2037 @ X2038 @ X2039 @ X2040) @ X2037)|((X2039)=(X2040))|~(func @ X2037 @ X2038 @ X2040)|~(func @ X2037 @ X2038 @ X2039))&(((ap @ X2037 @ X2038 @ X2039 @ (esk66_4 @ X2037 @ X2038 @ X2039 @ X2040))!=(ap @ X2037 @ X2038 @ X2040 @ (esk66_4 @ X2037 @ X2038 @ X2039 @ X2040)))|((X2039)=(X2040))|~(func @ X2037 @ X2038 @ X2040)|~(func @ X2037 @ X2038 @ X2039)))&((((in @ (esk67_4 @ X2042 @ X2043 @ X2044 @ X2045) @ X2042)|((X2044)=(X2045))|~(in @ X2045 @ (funcSet @ X2042 @ X2043))|~(in @ X2044 @ (funcSet @ X2042 @ X2043)))&(((ap @ X2042 @ X2043 @ X2044 @ (esk67_4 @ X2042 @ X2043 @ X2044 @ X2045))!=(ap @ X2042 @ X2043 @ X2045 @ (esk67_4 @ X2042 @ X2043 @ X2044 @ X2045)))|((X2044)=(X2045))|~(in @ X2045 @ (funcSet @ X2042 @ X2043))|~(in @ X2044 @ (funcSet @ X2042 @ X2043))))&((~(in @ X2049 @ (funcSet @ X2047 @ X2048))|(~(in @ X2050 @ X2047)|((ap @ X2047 @ X2048 @ X2049 @ X2050)=(ap @ X2047 @ X2048 @ X2049 @ X2050))))&((~(func @ X2051 @ X2052 @ X2053)|(~(in @ X2054 @ X2051)|((ap @ X2051 @ X2052 @ X2053 @ X2054)=(ap @ X2051 @ X2052 @ X2053 @ X2054))))&((((in @ (esk68_3 @ X2055 @ X2056 @ X2057) @ X2055)|(~(in @ X2059 @ X2055)|((ap @ X2055 @ X2056 @ (lam @ X2055 @ X2056 @ X2057) @ X2059)=(X2057 @ X2059))))&(~(in @ (X2057 @ (esk68_3 @ X2055 @ X2056 @ X2057)) @ X2056)|(~(in @ X2059 @ X2055)|((ap @ X2055 @ X2056 @ (lam @ X2055 @ X2056 @ X2057) @ X2059)=(X2057 @ X2059)))))&((~(func @ X2060 @ X2061 @ X2062)|((lam @ X2060 @ X2061 @ (ap @ X2060 @ X2061 @ X2062))=(X2062)))&((((in @ (esk69_3 @ X2063 @ X2064 @ X2065) @ X2063)|((lam @ X2063 @ X2064 @ X2065)=(lam @ X2063 @ X2064 @ X2065)))&(~(in @ (X2065 @ (esk69_3 @ X2063 @ X2064 @ X2065)) @ X2064)|((lam @ X2063 @ X2064 @ X2065)=(lam @ X2063 @ X2064 @ X2065))))&((((in @ (esk70_3 @ X2067 @ X2068 @ X2069) @ X2067)|(~(in @ X2071 @ X2067)|((ap @ X2067 @ X2068 @ (lam @ X2067 @ X2068 @ X2069) @ X2071)=(X2069 @ X2071))))&(~(in @ (X2069 @ (esk70_3 @ X2067 @ X2068 @ X2069)) @ X2068)|(~(in @ X2071 @ X2067)|((ap @ X2067 @ X2068 @ (lam @ X2067 @ X2068 @ X2069) @ X2071)=(X2069 @ X2071)))))&((~(in @ X2074 @ (funcSet @ X2072 @ X2073))|((lam @ X2072 @ X2073 @ (ap @ X2072 @ X2073 @ X2074))=(X2074)))&((~(in @ X2077 @ X2075)|(~(in @ X2078 @ X2075)|((X2076)|(in @ X2078 @ (dsetconstr @ X2075 @ (^[Z0:$i]:((((((X2076))&(((Z0)=(X2077)))))|(((~((X2076)))&(((Z0)=(X2078)))))))))))))&((~(in @ X2081 @ X2079)|(~(in @ X2082 @ X2079)|((X2080)|((dsetconstr @ X2079 @ (^[Z0:$i]:((((((X2080))&(((Z0)=(X2081)))))|(((~((X2080)))&(((Z0)=(X2082)))))))))=(setadjoin @ X2082 @ emptyset)))))&((~(in @ X2085 @ X2083)|(~(in @ X2086 @ X2083)|(~(X2084)|(in @ X2085 @ (dsetconstr @ X2083 @ (^[Z0:$i]:((((((X2084))&(((Z0)=(X2085)))))|(((~((X2084)))&(((Z0)=(X2086)))))))))))))&((~(in @ X2089 @ X2087)|(~(in @ X2090 @ X2087)|(~(X2088)|((dsetconstr @ X2087 @ (^[Z0:$i]:((((((X2088))&(((Z0)=(X2089)))))|(((~((X2088)))&(((Z0)=(X2090)))))))))=(setadjoin @ X2089 @ emptyset)))))&((((in @ (esk71_4 @ X2091 @ X2092 @ X2093 @ X2094) @ (dsetconstr @ X2091 @ (^[Z0:$i]:((((((X2092))&(((Z0)=(X2093)))))|(((~((X2092)))&(((Z0)=(X2094))))))))))|~(in @ X2094 @ X2091)|~(in @ X2093 @ X2091))&(((dsetconstr @ X2091 @ (^[Z0:$i]:((((((X2092))&(((Z0)=(X2093)))))|(((~((X2092)))&(((Z0)=(X2094)))))))))=(setadjoin @ (esk71_4 @ X2091 @ X2092 @ X2093 @ X2094) @ emptyset))|~(in @ X2094 @ X2091)|~(in @ X2093 @ X2091)))&((~(in @ X2098 @ X2096)|(~(in @ X2099 @ X2096)|(in @ (if @ X2096 @ ((X2097)) @ X2098 @ X2099) @ X2096)))&(((in @ esk73_0 @ esk72_0)&((esk72_0)=(setadjoin @ esk73_0 @ emptyset)))&((in @ esk74_0 @ esk72_0)&((setunion @ esk72_0)!=(esk74_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_283])])])])])])])).
% 0.22/0.38  thf(c_0_285, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_284])).
% 0.22/0.38  thf(c_0_286, negated_conjecture, ((esk72_0)=(setadjoin @ esk73_0 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_284])).
% 0.22/0.38  thf(c_0_287, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((in @ X3 @ (setadjoin @ X2 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_284])).
% 0.22/0.38  thf(c_0_288, negated_conjecture, ((setunion @ esk72_0)!=(esk74_0)), inference(split_conjunct,[status(thm)],[c_0_284])).
% 0.22/0.38  thf(c_0_289, negated_conjecture, ((setunion @ esk72_0)=(esk73_0)), inference(spm,[status(thm)],[c_0_285, c_0_286])).
% 0.22/0.38  thf(c_0_290, negated_conjecture, ![X2:$i]:((((esk73_0)=(X2))|~((in @ X2 @ esk72_0)))), inference(spm,[status(thm)],[c_0_287, c_0_286])).
% 0.22/0.38  thf(c_0_291, negated_conjecture, (in @ esk74_0 @ esk72_0), inference(split_conjunct,[status(thm)],[c_0_284])).
% 0.22/0.38  thf(c_0_292, negated_conjecture, ((esk74_0)!=(esk73_0)), inference(rw,[status(thm)],[c_0_288, c_0_289])).
% 0.22/0.38  thf(c_0_293, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_290, c_0_291]), c_0_292]), ['proof']).
% 0.22/0.38  % SZS output end CNFRefutation
% 0.22/0.38  % Parsed axioms                        : 489
% 0.22/0.38  % Removed by relevancy pruning/SinE    : 266
% 0.22/0.38  % Initial clauses                      : 380
% 0.22/0.38  % Removed in clause preprocessing      : 34
% 0.22/0.38  % Initial clauses in saturation        : 346
% 0.22/0.38  % Processed clauses                    : 436
% 0.22/0.38  % ...of these trivial                  : 12
% 0.22/0.38  % ...subsumed                          : 201
% 0.22/0.38  % ...remaining for further processing  : 223
% 0.22/0.38  % Other redundant clauses eliminated   : 24
% 0.22/0.38  % Clauses deleted for lack of memory   : 0
% 0.22/0.38  % Backward-subsumed                    : 3
% 0.22/0.38  % Backward-rewritten                   : 5
% 0.22/0.38  % Generated clauses                    : 1105
% 0.22/0.38  % ...of the previous two non-redundant : 908
% 0.22/0.38  % ...aggressively subsumed             : 0
% 0.22/0.38  % Contextual simplify-reflections      : 0
% 0.22/0.38  % Paramodulations                      : 1077
% 0.22/0.38  % Factorizations                       : 0
% 0.22/0.38  % NegExts                              : 0
% 0.22/0.38  % Equation resolutions                 : 27
% 0.22/0.38  % Disequality decompositions           : 0
% 0.22/0.38  % Total rewrite steps                  : 182
% 0.22/0.38  % ...of those cached                   : 131
% 0.22/0.38  % Propositional unsat checks           : 0
% 0.22/0.38  %    Propositional check models        : 0
% 0.22/0.38  %    Propositional check unsatisfiable : 0
% 0.22/0.38  %    Propositional clauses             : 0
% 0.22/0.38  %    Propositional clauses after purity: 0
% 0.22/0.38  %    Propositional unsat core size     : 0
% 0.22/0.38  %    Propositional preprocessing time  : 0.000
% 0.22/0.38  %    Propositional encoding time       : 0.000
% 0.22/0.38  %    Propositional solver time         : 0.000
% 0.22/0.38  %    Success case prop preproc time    : 0.000
% 0.22/0.38  %    Success case prop encoding time   : 0.000
% 0.22/0.38  %    Success case prop solver time     : 0.000
% 0.22/0.38  % Current number of processed clauses  : 207
% 0.22/0.38  %    Positive orientable unit clauses  : 53
% 0.22/0.38  %    Positive unorientable unit clauses: 0
% 0.22/0.38  %    Negative unit clauses             : 3
% 0.22/0.38  %    Non-unit-clauses                  : 151
% 0.22/0.38  % Current number of unprocessed clauses: 775
% 0.22/0.38  % ...number of literals in the above   : 2145
% 0.22/0.38  % Current number of archived formulas  : 0
% 0.22/0.38  % Current number of archived clauses   : 8
% 0.22/0.38  % Clause-clause subsumption calls (NU) : 5714
% 0.22/0.38  % Rec. Clause-clause subsumption calls : 5504
% 0.22/0.38  % Non-unit clause-clause subsumptions  : 194
% 0.22/0.38  % Unit Clause-clause subsumption calls : 87
% 0.22/0.38  % Rewrite failures with RHS unbound    : 0
% 0.22/0.38  % BW rewrite match attempts            : 8
% 0.22/0.38  % BW rewrite match successes           : 4
% 0.22/0.38  % Condensation attempts                : 0
% 0.22/0.38  % Condensation successes               : 0
% 0.22/0.38  % Termbank termtop insertions          : 65475
% 0.22/0.38  % Search garbage collected termcells   : 21785
% 0.22/0.38  
% 0.22/0.38  % -------------------------------------------------
% 0.22/0.38  % User time                : 0.074 s
% 0.22/0.38  % System time              : 0.009 s
% 0.22/0.38  % Total time               : 0.083 s
% 0.22/0.38  % Maximum resident set size: 9228 pages
% 0.22/0.38  
% 0.22/0.38  % -------------------------------------------------
% 0.22/0.38  % User time                : 0.087 s
% 0.22/0.38  % System time              : 0.016 s
% 0.22/0.38  % Total time               : 0.103 s
% 0.22/0.38  % Maximum resident set size: 5632 pages
% 0.22/0.38  % E exiting
%------------------------------------------------------------------------------