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

%------------------------------------------------------------------------------
% File     : E-SAT---3.5.1
% Problem  : SEU676^1 : 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 : n016.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 08:27:11 AM UTC 2026

% Result   : Theorem 2.93s 0.71s
% Output   : CNFRefutation 2.93s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU676^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17  % Computer : n016.cluster.edu
% 0.10/0.17  % Model    : x86_64 x86_64
% 0.10/0.17  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17  % Memory   : 8046.5625MB
% 0.10/0.17  % OS       : Linux 6.8.0-71-generic
% 0.10/0.17  % CPULimit : 300
% 0.10/0.17  % WCLimit  : 300
% 0.10/0.17  % DateTime : Tue Sep 29 14:12:19 UTC 2026
% 0.10/0.17  % CPUTime  : 
% 0.10/0.17  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22  Running higher-order theorem proving
% 0.21/0.26  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.2B9lyCKtMD/E---3.1_412344.p
% 2.93/0.71  % Version: 3.5.1-ho
% 2.93/0.71  % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.93/0.71  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.93/0.71  % Starting ehoh_best5 with 300s (1) cores
% 2.93/0.71  % Starting almost_fo_3_lam with 300s (1) cores
% 2.93/0.71  % Starting new_bool_5 with 300s (1) cores
% 2.93/0.71  % Starting pre_casc_3 with 300s (1) cores
% 2.93/0.71  % Starting ho_unfolding_8 with 300s (1) cores
% 2.93/0.71  % Starting new_ho_10_cnf2 with 300s (1) cores
% 2.93/0.71  % Starting new_bool_3 with 300s (1) cores
% 2.93/0.71  % Starting new_ho_5 with 300s (1) cores
% 2.93/0.71  % new_bool_5 with pid 412359 completed with status 0
% 2.93/0.71  % Result found by new_bool_5
% 2.93/0.71  % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.93/0.71  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.93/0.71  % Starting ehoh_best5 with 300s (1) cores
% 2.93/0.71  % Starting almost_fo_3_lam with 300s (1) cores
% 2.93/0.71  % Starting new_bool_5 with 300s (1) cores
% 2.93/0.71  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 2.93/0.71  % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.93/0.71  % Search class: HGHSM-FSLM31-MHFMMSBN
% 2.93/0.71  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 2.93/0.71  % Starting SubtermCWHack with 28s (1) cores
% 2.93/0.71  % SubtermCWHack with pid 412368 completed with status 0
% 2.93/0.71  % Result found by SubtermCWHack
% 2.93/0.71  % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.93/0.71  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.93/0.71  % Starting ehoh_best5 with 300s (1) cores
% 2.93/0.71  % Starting almost_fo_3_lam with 300s (1) cores
% 2.93/0.71  % Starting new_bool_5 with 300s (1) cores
% 2.93/0.71  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 2.93/0.71  % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.93/0.71  % Search class: HGHSM-FSLM31-MHFMMSBN
% 2.93/0.71  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 2.93/0.71  % Starting SubtermCWHack with 28s (1) cores
% 2.93/0.71  % Preprocessing time       : 0.005 s
% 2.93/0.71  
% 2.93/0.71  % Proof found!
% 2.93/0.71  % SZS status Theorem
% 2.93/0.71  % SZS output start CNFRefutation
% 2.93/0.71  thf(decl_23, type, in: $i > $i > $o).
% 2.93/0.71  thf(decl_24, type, exu: ($i > $o) > $o).
% 2.93/0.71  thf(decl_25, type, setextAx: $o).
% 2.93/0.71  thf(decl_26, type, emptyset: $i).
% 2.93/0.71  thf(decl_27, type, emptysetAx: $o).
% 2.93/0.71  thf(decl_28, type, setadjoin: $i > $i > $i).
% 2.93/0.71  thf(decl_29, type, setadjoinAx: $o).
% 2.93/0.71  thf(decl_30, type, powerset: $i > $i).
% 2.93/0.71  thf(decl_31, type, powersetAx: $o).
% 2.93/0.71  thf(decl_32, type, setunion: $i > $i).
% 2.93/0.71  thf(decl_33, type, setunionAx: $o).
% 2.93/0.71  thf(decl_34, type, omega: $i).
% 2.93/0.71  thf(decl_35, type, omega0Ax: $o).
% 2.93/0.71  thf(decl_36, type, omegaSAx: $o).
% 2.93/0.71  thf(decl_37, type, omegaIndAx: $o).
% 2.93/0.71  thf(decl_38, type, replAx: $o).
% 2.93/0.71  thf(decl_39, type, foundationAx: $o).
% 2.93/0.71  thf(decl_40, type, wellorderingAx: $o).
% 2.93/0.71  thf(decl_41, type, descr: ($i > $o) > $i).
% 2.93/0.71  thf(decl_42, type, descrp: $o).
% 2.93/0.71  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_44, type, dsetconstrI: $o).
% 2.93/0.71  thf(decl_45, type, dsetconstrEL: $o).
% 2.93/0.71  thf(decl_46, type, dsetconstrER: $o).
% 2.93/0.71  thf(decl_47, type, exuE1: $o).
% 2.93/0.71  thf(decl_48, type, prop2set: $o > $i).
% 2.93/0.71  thf(decl_49, type, prop2setE: $o).
% 2.93/0.71  thf(decl_50, type, emptysetE: $o).
% 2.93/0.71  thf(decl_51, type, emptysetimpfalse: $o).
% 2.93/0.71  thf(decl_52, type, notinemptyset: $o).
% 2.93/0.71  thf(decl_53, type, exuE3e: $o).
% 2.93/0.71  thf(decl_54, type, setext: $o).
% 2.93/0.71  thf(decl_55, type, emptyI: $o).
% 2.93/0.71  thf(decl_56, type, noeltsimpempty: $o).
% 2.93/0.71  thf(decl_57, type, setbeta: $o).
% 2.93/0.71  thf(decl_58, type, nonempty: $i > $o).
% 2.93/0.71  thf(decl_59, type, nonemptyE1: $o).
% 2.93/0.71  thf(decl_60, type, nonemptyI: $o).
% 2.93/0.71  thf(decl_61, type, nonemptyI1: $o).
% 2.93/0.71  thf(decl_62, type, setadjoinIL: $o).
% 2.93/0.71  thf(decl_63, type, emptyinunitempty: $o).
% 2.93/0.71  thf(decl_64, type, setadjoinIR: $o).
% 2.93/0.71  thf(decl_65, type, setadjoinE: $o).
% 2.93/0.71  thf(decl_66, type, setadjoinOr: $o).
% 2.93/0.71  thf(decl_67, type, setoftrueEq: $o).
% 2.93/0.71  thf(decl_68, type, powersetI: $o).
% 2.93/0.71  thf(decl_69, type, emptyinPowerset: $o).
% 2.93/0.71  thf(decl_70, type, emptyInPowerset: $o).
% 2.93/0.71  thf(decl_71, type, powersetE: $o).
% 2.93/0.71  thf(decl_72, type, setunionI: $o).
% 2.93/0.71  thf(decl_73, type, setunionE: $o).
% 2.93/0.71  thf(decl_74, type, subPowSU: $o).
% 2.93/0.71  thf(decl_75, type, exuE2: $o).
% 2.93/0.71  thf(decl_76, type, nonemptyImpWitness: $o).
% 2.93/0.71  thf(decl_77, type, uniqinunit: $o).
% 2.93/0.71  thf(decl_78, type, notinsingleton: $o).
% 2.93/0.71  thf(decl_79, type, eqinunit: $o).
% 2.93/0.71  thf(decl_80, type, singletonsswitch: $o).
% 2.93/0.71  thf(decl_81, type, upairsetE: $o).
% 2.93/0.71  thf(decl_82, type, upairsetIL: $o).
% 2.93/0.71  thf(decl_83, type, upairsetIR: $o).
% 2.93/0.71  thf(decl_84, type, emptyE1: $o).
% 2.93/0.71  thf(decl_85, type, vacuousDall: $o).
% 2.93/0.71  thf(decl_86, type, quantDeMorgan1: $o).
% 2.93/0.71  thf(decl_87, type, quantDeMorgan2: $o).
% 2.93/0.71  thf(decl_88, type, quantDeMorgan3: $o).
% 2.93/0.71  thf(decl_89, type, quantDeMorgan4: $o).
% 2.93/0.71  thf(decl_90, type, prop2setI: $o).
% 2.93/0.71  thf(decl_92, type, prop2set2propI: $o).
% 2.93/0.71  thf(decl_93, type, notdexE: $o).
% 2.93/0.71  thf(decl_94, type, notdallE: $o).
% 2.93/0.71  thf(decl_95, type, exuI1: $o).
% 2.93/0.71  thf(decl_96, type, exuI3: $o).
% 2.93/0.71  thf(decl_97, type, exuI2: $o).
% 2.93/0.71  thf(decl_98, type, inCongP: $o).
% 2.93/0.71  thf(decl_99, type, in__Cong: $o).
% 2.93/0.71  thf(decl_100, type, exuE3u: $o).
% 2.93/0.71  thf(decl_101, type, exu__Cong: $o).
% 2.93/0.71  thf(decl_102, type, emptyset__Cong: $o).
% 2.93/0.71  thf(decl_103, type, setadjoin__Cong: $o).
% 2.93/0.71  thf(decl_104, type, powerset__Cong: $o).
% 2.93/0.71  thf(decl_105, type, setunion__Cong: $o).
% 2.93/0.71  thf(decl_106, type, omega__Cong: $o).
% 2.93/0.71  thf(decl_107, type, exuEu: $o).
% 2.93/0.71  thf(decl_108, type, descr__Cong: $o).
% 2.93/0.71  thf(decl_109, type, dsetconstr__Cong: $o).
% 2.93/0.71  thf(decl_110, type, subset: $i > $i > $o).
% 2.93/0.71  thf(decl_113, type, subsetI1: $o).
% 2.93/0.71  thf(decl_114, type, eqimpsubset2: $o).
% 2.93/0.71  thf(decl_115, type, eqimpsubset1: $o).
% 2.93/0.71  thf(decl_116, type, subsetI2: $o).
% 2.93/0.71  thf(decl_117, type, emptysetsubset: $o).
% 2.93/0.71  thf(decl_118, type, subsetE: $o).
% 2.93/0.71  thf(decl_119, type, subsetE2: $o).
% 2.93/0.71  thf(decl_120, type, notsubsetI: $o).
% 2.93/0.71  thf(decl_121, type, notequalI1: $o).
% 2.93/0.71  thf(decl_122, type, notequalI2: $o).
% 2.93/0.71  thf(decl_123, type, subsetRefl: $o).
% 2.93/0.71  thf(decl_124, type, subsetTrans: $o).
% 2.93/0.71  thf(decl_125, type, setadjoinSub: $o).
% 2.93/0.71  thf(decl_126, type, setadjoinSub2: $o).
% 2.93/0.71  thf(decl_127, type, subset2powerset: $o).
% 2.93/0.71  thf(decl_128, type, setextsub: $o).
% 2.93/0.71  thf(decl_129, type, subsetemptysetimpeq: $o).
% 2.93/0.71  thf(decl_130, type, powersetI1: $o).
% 2.93/0.71  thf(decl_131, type, powersetE1: $o).
% 2.93/0.71  thf(decl_132, type, inPowerset: $o).
% 2.93/0.71  thf(decl_133, type, powersetsubset: $o).
% 2.93/0.71  thf(decl_134, type, sepInPowerset: $o).
% 2.93/0.71  thf(decl_135, type, sepSubset: $o).
% 2.93/0.71  thf(decl_136, type, binunion: $i > $i > $i).
% 2.93/0.71  thf(decl_137, type, binunionIL: $o).
% 2.93/0.71  thf(decl_138, type, upairset2IR: $o).
% 2.93/0.71  thf(decl_139, type, binunionIR: $o).
% 2.93/0.71  thf(decl_140, type, binunionEcases: $o).
% 2.93/0.71  thf(decl_141, type, binunionE: $o).
% 2.93/0.71  thf(decl_142, type, binunionLsub: $o).
% 2.93/0.71  thf(decl_143, type, binunionRsub: $o).
% 2.93/0.71  thf(decl_144, type, binintersect: $i > $i > $i).
% 2.93/0.71  thf(decl_145, type, binintersectI: $o).
% 2.93/0.71  thf(decl_146, type, binintersectSubset5: $o).
% 2.93/0.71  thf(decl_147, type, binintersectEL: $o).
% 2.93/0.71  thf(decl_148, type, binintersectLsub: $o).
% 2.93/0.71  thf(decl_149, type, binintersectSubset2: $o).
% 2.93/0.71  thf(decl_150, type, binintersectSubset3: $o).
% 2.93/0.71  thf(decl_151, type, binintersectER: $o).
% 2.93/0.71  thf(decl_152, type, disjointsetsI1: $o).
% 2.93/0.71  thf(decl_153, type, binintersectRsub: $o).
% 2.93/0.71  thf(decl_154, type, binintersectSubset4: $o).
% 2.93/0.71  thf(decl_155, type, binintersectSubset1: $o).
% 2.93/0.71  thf(decl_156, type, bs114d: $o).
% 2.93/0.71  thf(decl_158, type, setminus: $i > $i > $i).
% 2.93/0.71  thf(decl_159, type, setminusI: $o).
% 2.93/0.71  thf(decl_160, type, setminusEL: $o).
% 2.93/0.71  thf(decl_161, type, setminusER: $o).
% 2.93/0.71  thf(decl_162, type, setminusSubset2: $o).
% 2.93/0.71  thf(decl_163, type, setminusERneg: $o).
% 2.93/0.71  thf(decl_164, type, setminusELneg: $o).
% 2.93/0.71  thf(decl_165, type, setminusILneg: $o).
% 2.93/0.71  thf(decl_166, type, setminusIRneg: $o).
% 2.93/0.71  thf(decl_167, type, setminusLsub: $o).
% 2.93/0.71  thf(decl_168, type, setminusSubset1: $o).
% 2.93/0.71  thf(decl_169, type, symdiff: $i > $i > $i).
% 2.93/0.71  thf(decl_170, type, symdiffE: $o).
% 2.93/0.71  thf(decl_171, type, symdiffI1: $o).
% 2.93/0.71  thf(decl_172, type, symdiffI2: $o).
% 2.93/0.71  thf(decl_173, type, symdiffIneg1: $o).
% 2.93/0.71  thf(decl_174, type, symdiffIneg2: $o).
% 2.93/0.71  thf(decl_175, type, iskpair: $i > $o).
% 2.93/0.71  thf(decl_176, type, secondinupair: $o).
% 2.93/0.71  thf(decl_177, type, setukpairIL: $o).
% 2.93/0.71  thf(decl_178, type, setukpairIR: $o).
% 2.93/0.71  thf(decl_179, type, kpairiskpair: $o).
% 2.93/0.71  thf(decl_180, type, kpair: $i > $i > $i).
% 2.93/0.71  thf(decl_181, type, kpairp: $o).
% 2.93/0.71  thf(decl_182, type, cartprod: $i > $i > $i).
% 2.93/0.71  thf(decl_183, type, singletonsubset: $o).
% 2.93/0.71  thf(decl_184, type, singletoninpowerset: $o).
% 2.93/0.71  thf(decl_185, type, singletoninpowunion: $o).
% 2.93/0.71  thf(decl_186, type, upairset2E: $o).
% 2.93/0.71  thf(decl_187, type, upairsubunion: $o).
% 2.93/0.71  thf(decl_188, type, upairinpowunion: $o).
% 2.93/0.71  thf(decl_189, type, ubforcartprodlem1: $o).
% 2.93/0.71  thf(decl_190, type, ubforcartprodlem2: $o).
% 2.93/0.71  thf(decl_191, type, ubforcartprodlem3: $o).
% 2.93/0.71  thf(decl_192, type, cartprodpairin: $o).
% 2.93/0.71  thf(decl_193, type, cartprodmempair1: $o).
% 2.93/0.71  thf(decl_194, type, cartprodmempair: $o).
% 2.93/0.71  thf(decl_195, type, setunionE2: $o).
% 2.93/0.71  thf(decl_196, type, setunionsingleton1: $o).
% 2.93/0.71  thf(decl_197, type, setunionsingleton2: $o).
% 2.93/0.71  thf(decl_198, type, setunionsingleton: $o).
% 2.93/0.71  thf(decl_199, type, singleton: $i > $o).
% 2.93/0.71  thf(decl_200, type, singletonprop: $o).
% 2.93/0.71  thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 2.93/0.71  thf(decl_202, type, ex1E1: $o).
% 2.93/0.71  thf(decl_203, type, ex1I: $o).
% 2.93/0.71  thf(decl_204, type, ex1I2: $o).
% 2.93/0.71  thf(decl_205, type, singletonsuniq: $o).
% 2.93/0.71  thf(decl_210, type, setukpairinjL1: $o).
% 2.93/0.71  thf(decl_211, type, kfstsingleton: $o).
% 2.93/0.71  thf(decl_212, type, theprop: $o).
% 2.93/0.71  thf(decl_213, type, kfst: $i > $i).
% 2.93/0.71  thf(decl_214, type, kfstpairEq: $o).
% 2.93/0.71  thf(decl_215, type, cartprodfstin: $o).
% 2.93/0.71  thf(decl_216, type, setukpairinjL2: $o).
% 2.93/0.71  thf(decl_217, type, setukpairinjL: $o).
% 2.93/0.71  thf(decl_218, type, setukpairinjR11: $o).
% 2.93/0.71  thf(decl_219, type, setukpairinjR12: $o).
% 2.93/0.71  thf(decl_220, type, setukpairinjR1: $o).
% 2.93/0.71  thf(decl_221, type, upairequniteq: $o).
% 2.93/0.71  thf(decl_222, type, setukpairinjR2: $o).
% 2.93/0.71  thf(decl_223, type, setukpairinjR: $o).
% 2.93/0.71  thf(decl_224, type, ksndsingleton: $o).
% 2.93/0.71  thf(decl_225, type, ksnd: $i > $i).
% 2.93/0.71  thf(decl_226, type, ksndpairEq: $o).
% 2.93/0.71  thf(decl_227, type, kpairsurjEq: $o).
% 2.93/0.71  thf(decl_228, type, cartprodsndin: $o).
% 2.93/0.71  thf(decl_229, type, cartprodpairmemEL: $o).
% 2.93/0.71  thf(decl_230, type, cartprodpairmemER: $o).
% 2.93/0.71  thf(decl_231, type, cartprodmempaircEq: $o).
% 2.93/0.71  thf(decl_232, type, cartprodfstpairEq: $o).
% 2.93/0.71  thf(decl_233, type, cartprodsndpairEq: $o).
% 2.93/0.71  thf(decl_234, type, cartprodpairsurjEq: $o).
% 2.93/0.71  thf(decl_235, type, breln: $i > $i > $i > $o).
% 2.93/0.71  thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 2.93/0.71  thf(decl_237, type, dpsetconstrI: $o).
% 2.93/0.71  thf(decl_238, type, dpsetconstrSub: $o).
% 2.93/0.71  thf(decl_239, type, setOfPairsIsBReln: $o).
% 2.93/0.71  thf(decl_240, type, dpsetconstrERa: $o).
% 2.93/0.71  thf(decl_241, type, dpsetconstrEL1: $o).
% 2.93/0.71  thf(decl_242, type, dpsetconstrEL2: $o).
% 2.93/0.71  thf(decl_243, type, dpsetconstrER: $o).
% 2.93/0.71  thf(decl_244, type, func: $i > $i > $i > $o).
% 2.93/0.71  thf(decl_245, type, funcSet: $i > $i > $i).
% 2.93/0.71  thf(decl_246, type, funcImageSingleton: $o).
% 2.93/0.71  thf(decl_247, type, apProp: $o).
% 2.93/0.71  thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 2.93/0.71  thf(decl_249, type, app: $o).
% 2.93/0.71  thf(decl_250, type, infuncsetfunc: $o).
% 2.93/0.71  thf(decl_251, type, epred1_0: $o).
% 2.93/0.71  thf(decl_252, type, esk1_2: $i > $i > $i).
% 2.93/0.71  thf(decl_253, type, esk2_2: $i > $i > $i).
% 2.93/0.71  thf(decl_254, type, esk3_2: $i > $i > $i).
% 2.93/0.71  thf(decl_255, type, esk4_1: $i > $i).
% 2.93/0.71  thf(decl_256, type, esk5_2: ($i > $i > $o) > $i > $i).
% 2.93/0.71  thf(decl_257, type, esk6_2: ($i > $i > $o) > $i > $i).
% 2.93/0.71  thf(decl_258, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 2.93/0.71  thf(decl_259, type, esk8_1: $i > $i).
% 2.93/0.71  thf(decl_260, type, esk9_1: ($i > $o) > $i).
% 2.93/0.71  thf(decl_261, type, esk10_1: ($i > $o) > $i).
% 2.93/0.71  thf(decl_262, type, esk11_2: $i > $i > $i).
% 2.93/0.71  thf(decl_263, type, esk12_2: $i > $i > $i).
% 2.93/0.71  thf(decl_264, type, esk13_1: $i > $i).
% 2.93/0.71  thf(decl_265, type, esk14_1: $i > $i).
% 2.93/0.71  thf(decl_266, type, esk15_1: $i > $i).
% 2.93/0.71  thf(decl_267, type, esk16_2: $i > $i > $i).
% 2.93/0.71  thf(decl_268, type, esk17_3: $i > $i > $o > $i).
% 2.93/0.71  thf(decl_269, type, esk18_1: ($i > $o) > $i).
% 2.93/0.71  thf(decl_270, type, esk19_1: $i > $i).
% 2.93/0.71  thf(decl_271, type, esk20_2: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_272, type, esk21_2: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_273, type, esk22_2: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_274, type, esk23_2: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_275, type, esk24_2: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_276, type, esk25_2: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_277, type, esk26_2: ($i > $o) > $i > $i).
% 2.93/0.71  thf(decl_278, type, esk27_1: ($i > $o) > $i).
% 2.93/0.71  thf(decl_279, type, esk28_1: ($i > $o) > $i).
% 2.93/0.71  thf(decl_280, type, esk29_2: ($i > $o) > $i > $i).
% 2.93/0.71  thf(decl_281, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 2.93/0.71  thf(decl_282, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 2.93/0.71  thf(decl_283, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 2.93/0.71  thf(decl_284, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 2.93/0.71  thf(decl_285, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.93/0.71  thf(decl_286, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.93/0.71  thf(decl_287, type, esk36_2: $i > $i > $i).
% 2.93/0.71  thf(decl_288, type, esk37_2: $i > $i > $i).
% 2.93/0.71  thf(decl_289, type, esk38_2: $i > $i > $i).
% 2.93/0.71  thf(decl_290, type, esk39_3: $i > $i > $i > $i).
% 2.93/0.71  thf(decl_291, type, esk40_3: $i > $i > $i > $i).
% 2.93/0.71  thf(decl_292, type, esk41_2: $i > $i > $i).
% 2.93/0.71  thf(decl_293, type, esk42_2: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_294, type, esk43_2: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_295, type, esk44_2: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_296, type, esk45_3: $i > ($i > $o) > $i > $i).
% 2.93/0.71  thf(decl_297, type, esk46_2: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_298, type, esk47_2: $i > ($i > $o) > $i).
% 2.93/0.71  thf(decl_299, type, esk48_0: $i).
% 2.93/0.71  thf(decl_300, type, esk49_0: $i).
% 2.93/0.71  thf(decl_301, type, esk50_0: $i).
% 2.93/0.71  thf(decl_302, type, esk51_0: $i).
% 2.93/0.71  thf(ap2p, 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)=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', ap2p)).
% 2.93/0.71  thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', singletonprop)).
% 2.93/0.71  thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', ex1E1)).
% 2.93/0.71  thf(ex1I, axiom, ((ex1I)<=>![X4:$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.2B9lyCKtMD/E---3.1_412344.p', ex1I)).
% 2.93/0.71  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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', ex1I2)).
% 2.93/0.71  thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', kfstsingleton)).
% 2.93/0.71  thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', ksndsingleton)).
% 2.93/0.71  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setoftrueEq)).
% 2.93/0.71  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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', dpsetconstrI)).
% 2.93/0.71  thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', dpsetconstrSub)).
% 2.93/0.71  thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setOfPairsIsBReln)).
% 2.93/0.71  thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', dpsetconstrERa)).
% 2.93/0.71  thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', dpsetconstrEL1)).
% 2.93/0.71  thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', dpsetconstrEL2)).
% 2.93/0.71  thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', dpsetconstrER)).
% 2.93/0.71  thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', funcImageSingleton)).
% 2.93/0.71  thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', apProp)).
% 2.93/0.71  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', exuE2)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', emptyE1)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', exuI2)).
% 2.93/0.71  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', exuI3)).
% 2.93/0.71  thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', exuI1)).
% 2.93/0.71  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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', exu__Cong)).
% 2.93/0.71  thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', exuE3u)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', exuEu)).
% 2.93/0.71  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', dsetconstr__Cong)).
% 2.93/0.71  thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', descr__Cong)).
% 2.93/0.71  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', sepInPowerset)).
% 2.93/0.71  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', sepSubset)).
% 2.93/0.71  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', nonemptyI)).
% 2.93/0.71  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setbeta)).
% 2.93/0.71  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', exuE3e)).
% 2.93/0.71  thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', exuE1)).
% 2.93/0.71  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', dsetconstrER)).
% 2.93/0.71  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', dsetconstrEL)).
% 2.93/0.71  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', dsetconstrI)).
% 2.93/0.71  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', descrp)).
% 2.93/0.71  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', replAx)).
% 2.93/0.71  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', emptyInPowerset)).
% 2.93/0.71  thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setunionsingleton1)).
% 2.93/0.71  thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setunionE2)).
% 2.93/0.71  thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setunionsingleton2)).
% 2.93/0.71  thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setunionsingleton)).
% 2.93/0.71  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setadjoinIR)).
% 2.93/0.71  thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setadjoinE)).
% 2.93/0.71  thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', singletonsuniq)).
% 2.93/0.71  thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.2B9lyCKtMD/E---3.1_412344.p', setukpairinjL1)).
% 2.93/0.71  thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', theprop)).
% 2.93/0.71  thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', kfstpairEq)).
% 2.93/0.71  thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', cartprodfstin)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', setukpairinjL2)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', setukpairinjL)).
% 2.93/0.71  thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setukpairinjR11)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', setukpairinjR12)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', setukpairinjR1)).
% 2.93/0.71  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setunionI)).
% 2.93/0.71  thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', upairequniteq)).
% 2.93/0.71  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', powersetE)).
% 2.93/0.71  thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setukpairinjR2)).
% 2.93/0.71  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', quantDeMorgan1)).
% 2.93/0.71  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', vacuousDall)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', setukpairinjR)).
% 2.93/0.71  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', emptyinPowerset)).
% 2.93/0.71  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', powersetI)).
% 2.93/0.71  thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', ksndpairEq)).
% 2.93/0.71  thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', kpairsurjEq)).
% 2.93/0.71  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setadjoinOr)).
% 2.93/0.71  thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', cartprodsndin)).
% 2.93/0.71  thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setunionE)).
% 2.93/0.71  thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', cartprodpairmemEL)).
% 2.93/0.71  thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', cartprodpairmemER)).
% 2.93/0.71  thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', cartprodmempaircEq)).
% 2.93/0.71  thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', cartprodfstpairEq)).
% 2.93/0.71  thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', cartprodsndpairEq)).
% 2.93/0.71  thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', cartprodpairsurjEq)).
% 2.93/0.71  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', singletonsswitch)).
% 2.93/0.71  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', eqinunit)).
% 2.93/0.71  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', notinsingleton)).
% 2.93/0.71  thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', app)).
% 2.93/0.71  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', uniqinunit)).
% 2.93/0.71  thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', infuncsetfunc)).
% 2.93/0.71  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', nonemptyImpWitness)).
% 2.93/0.71  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', emptyinunitempty)).
% 2.93/0.71  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', subPowSU)).
% 2.93/0.71  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', upairsetE)).
% 2.93/0.71  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', quantDeMorgan3)).
% 2.93/0.71  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', quantDeMorgan2)).
% 2.93/0.71  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', subsetTrans)).
% 2.93/0.71  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', subsetRefl)).
% 2.93/0.71  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', notequalI2)).
% 2.93/0.71  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', notequalI1)).
% 2.93/0.71  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', notsubsetI)).
% 2.93/0.71  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', subsetE2)).
% 2.93/0.71  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', upairsetIR)).
% 2.93/0.71  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', upairsetIL)).
% 2.93/0.71  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', quantDeMorgan4)).
% 2.93/0.71  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', inCongP)).
% 2.93/0.71  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', notdallE)).
% 2.93/0.71  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', notdexE)).
% 2.93/0.71  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', prop2setI)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', in__Cong)).
% 2.93/0.71  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', omega__Cong)).
% 2.93/0.71  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setunion__Cong)).
% 2.93/0.71  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', powerset__Cong)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', setadjoin__Cong)).
% 2.93/0.71  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', emptyset__Cong)).
% 2.93/0.71  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', emptysetsubset)).
% 2.93/0.71  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', subsetI2)).
% 2.93/0.71  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', eqimpsubset1)).
% 2.93/0.71  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', eqimpsubset2)).
% 2.93/0.71  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', subsetI1)).
% 2.93/0.71  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', subsetE)).
% 2.93/0.71  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setadjoinSub)).
% 2.93/0.71  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setadjoinSub2)).
% 2.93/0.71  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', powersetsubset)).
% 2.93/0.71  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', inPowerset)).
% 2.93/0.71  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', powersetE1)).
% 2.93/0.71  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', powersetI1)).
% 2.93/0.71  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', subsetemptysetimpeq)).
% 2.93/0.71  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setextsub)).
% 2.93/0.71  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', subset2powerset)).
% 2.93/0.71  thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binunionLsub)).
% 2.93/0.71  thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binunionE)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', binunionEcases)).
% 2.93/0.71  thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binunionIR)).
% 2.93/0.71  thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', upairset2IR)).
% 2.93/0.71  thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binunionIL)).
% 2.93/0.71  thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binunionRsub)).
% 2.93/0.71  thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binintersectER)).
% 2.93/0.71  thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binintersectSubset3)).
% 2.93/0.71  thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binintersectSubset2)).
% 2.93/0.71  thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binintersectLsub)).
% 2.93/0.71  thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binintersectEL)).
% 2.93/0.71  thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binintersectSubset5)).
% 2.93/0.71  thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binintersectI)).
% 2.93/0.71  thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', disjointsetsI1)).
% 2.93/0.71  thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setminusER)).
% 2.93/0.71  thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setminusEL)).
% 2.93/0.71  thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setminusI)).
% 2.93/0.71  thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', bs114d)).
% 2.93/0.71  thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binintersectSubset1)).
% 2.93/0.71  thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binintersectSubset4)).
% 2.93/0.71  thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', binintersectRsub)).
% 2.93/0.71  thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setminusSubset2)).
% 2.93/0.71  thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', symdiffE)).
% 2.93/0.71  thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setminusSubset1)).
% 2.93/0.71  thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setminusLsub)).
% 2.93/0.71  thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setminusIRneg)).
% 2.93/0.71  thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setminusILneg)).
% 2.93/0.71  thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setminusELneg)).
% 2.93/0.71  thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setminusERneg)).
% 2.93/0.71  thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', symdiffI1)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', kpairiskpair)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', setukpairIR)).
% 2.93/0.71  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.2B9lyCKtMD/E---3.1_412344.p', setukpairIL)).
% 2.93/0.71  thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', secondinupair)).
% 2.93/0.71  thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', symdiffIneg2)).
% 2.93/0.71  thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', symdiffIneg1)).
% 2.93/0.71  thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', symdiffI2)).
% 2.93/0.71  thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', kpairp)).
% 2.93/0.71  thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', ubforcartprodlem1)).
% 2.93/0.71  thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', upairinpowunion)).
% 2.93/0.71  thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', upairsubunion)).
% 2.93/0.71  thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', upairset2E)).
% 2.93/0.71  thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', singletoninpowunion)).
% 2.93/0.71  thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', singletoninpowerset)).
% 2.93/0.71  thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', singletonsubset)).
% 2.93/0.71  thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', ubforcartprodlem3)).
% 2.93/0.71  thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', cartprodpairin)).
% 2.93/0.71  thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.2B9lyCKtMD/E---3.1_412344.p', cartprodmempair1)).
% 2.93/0.71  thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', cartprodmempair)).
% 2.93/0.71  thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', ubforcartprodlem2)).
% 2.93/0.71  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setadjoinIL)).
% 2.93/0.71  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', nonemptyI1)).
% 2.93/0.71  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', nonemptyE1)).
% 2.93/0.71  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', noeltsimpempty)).
% 2.93/0.71  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', emptyI)).
% 2.93/0.71  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setext)).
% 2.93/0.71  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', notinemptyset)).
% 2.93/0.71  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', emptysetimpfalse)).
% 2.93/0.71  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', emptysetE)).
% 2.93/0.71  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', prop2setE)).
% 2.93/0.71  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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', wellorderingAx)).
% 2.93/0.71  thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', foundationAx)).
% 2.93/0.71  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.2B9lyCKtMD/E---3.1_412344.p', omegaIndAx)).
% 2.93/0.71  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', omegaSAx)).
% 2.93/0.71  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', omega0Ax)).
% 2.93/0.71  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setunionAx)).
% 2.93/0.71  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', powersetAx)).
% 2.93/0.71  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setadjoinAx)).
% 2.93/0.71  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', emptysetAx)).
% 2.93/0.71  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.2B9lyCKtMD/E---3.1_412344.p', setextAx)).
% 2.93/0.71  thf(c_0_192, 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)=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[ap2p])).
% 2.93/0.71  thf(c_0_193, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 2.93/0.71  thf(c_0_194, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 2.93/0.71  thf(c_0_195, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 2.93/0.71  thf(c_0_196, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 2.93/0.71  thf(c_0_197, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 2.93/0.71  thf(c_0_198, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 2.93/0.71  thf(c_0_199, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 2.93/0.71  thf(c_0_200, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 2.93/0.71  thf(c_0_201, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 2.93/0.71  thf(c_0_202, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 2.93/0.71  thf(c_0_203, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 2.93/0.71  thf(c_0_204, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 2.93/0.71  thf(c_0_205, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 2.93/0.71  thf(c_0_206, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 2.93/0.71  thf(c_0_207, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 2.93/0.71  thf(c_0_208, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 2.93/0.71  thf(c_0_209, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 2.93/0.71  thf(c_0_210, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 2.93/0.71  thf(c_0_211, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 2.93/0.71  thf(c_0_212, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 2.93/0.71  thf(c_0_213, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 2.93/0.71  thf(c_0_214, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 2.93/0.71  thf(c_0_215, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 2.93/0.71  thf(c_0_216, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 2.93/0.71  thf(c_0_217, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 2.93/0.71  thf(c_0_218, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 2.93/0.71  thf(c_0_219, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 2.93/0.71  thf(c_0_220, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 2.93/0.71  thf(c_0_221, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 2.93/0.71  thf(c_0_222, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 2.93/0.71  thf(c_0_223, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 2.93/0.71  thf(c_0_224, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 2.93/0.71  thf(c_0_225, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 2.93/0.71  thf(c_0_226, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 2.93/0.71  thf(c_0_227, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 2.93/0.71  thf(c_0_228, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 2.93/0.71  thf(c_0_229, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 2.93/0.71  thf(c_0_230, plain, ((epred1_0)<=>![X605:$i]:(?[X606:$i]:((((![X607:$i]:(((in @ X607 @ X606)=>![X608:$i]:(((in @ X608 @ X607)=>(in @ X608 @ X605)))))&![X609:$i, X610:$i]:((((in @ X609 @ X605)&(in @ X610 @ X605))=>(![X611:$i]:(((in @ X611 @ X606)=>((in @ X609 @ X611)<=>(in @ X610 @ X611))))=>((X609)=(X610))))))&![X612:$i, X613:$i]:((((in @ X612 @ X606)&(in @ X613 @ X606))=>(![X614:$i]:(((in @ X614 @ X612)=>(in @ X614 @ X613)))|![X615:$i]:(((in @ X615 @ X613)=>(in @ X615 @ X612)))))))&![X616:$i]:(((![X617:$i]:(((in @ X617 @ X616)=>(in @ X617 @ X605)))&?[X618:$i]:((in @ X618 @ X616)))=>?[X619:$i, X620:$i]:(((((in @ X619 @ X606)&(in @ X620 @ X616))&~(?[X621:$i]:(((in @ X621 @ X619)&(in @ X621 @ X616)))))&![X622:$i]:(((in @ X622 @ X606)=>(![X623:$i]:(((in @ X623 @ X622)=>(in @ X623 @ X619)))|(in @ X620 @ X622)))))))))))), introduced(definition)).
% 2.93/0.71  thf(c_0_231, negated_conjecture, ~((![X578:$i, X579:$i]:((![X580:$i]:(((in @ X580 @ X578)<=>(in @ X580 @ X579)))=>((X578)=(X579))))=>(![X581:$i]:(~(in @ X581 @ emptyset))=>(![X582:$i, X583:$i, X584:$i]:(((in @ X584 @ (setadjoin @ X582 @ X583))<=>(((X584)=(X582))|(in @ X584 @ X583))))=>(![X585:$i, X586:$i]:(((in @ X586 @ (powerset @ X585))<=>![X587:$i]:(((in @ X587 @ X586)=>(in @ X587 @ X585)))))=>(![X588:$i, X589:$i]:(((in @ X589 @ (setunion @ X588))<=>?[X590:$i]:(((in @ X589 @ X590)&(in @ X590 @ X588)))))=>((in @ emptyset @ omega)=>(![X591:$i]:(((in @ X591 @ omega)=>(in @ (setadjoin @ X591 @ X591) @ omega)))=>(![X592:$i]:((((in @ emptyset @ X592)&![X593:$i]:((((in @ X593 @ omega)&(in @ X593 @ X592))=>(in @ (setadjoin @ X593 @ X593) @ X592))))=>![X594:$i]:(((in @ X594 @ omega)=>(in @ X594 @ X592)))))=>(![X595:$i > $i > $o, X596:$i]:((![X597:$i]:(((in @ X597 @ X596)=>(exu @ (X595 @ X597))))=>?[X598:$i]:(![X599:$i]:(((in @ X599 @ X598)<=>?[X600:$i]:(((in @ X600 @ X596)&(X595 @ X600 @ X599))))))))=>(![X601:$i]:((?[X602:$i]:((in @ X602 @ X601))=>?[X603:$i]:(((in @ X603 @ X601)&~(?[X604:$i]:(((in @ X604 @ X603)&(in @ X604 @ X601))))))))=>((epred1_0)=>(![X624:$i > $o]:(((exu @ X624)=>(X624 @ (descr @ (^[Z0:$i]:(X624 @ Z0))))))=>(![X625:$i, X626:$i > $o, X627:$i]:(((in @ X627 @ X625)=>((X626 @ X627)=>(in @ X627 @ (dsetconstr @ X625 @ X626)))))=>(![X628:$i, X629:$i > $o, X630:$i]:(((in @ X630 @ (dsetconstr @ X628 @ X629))=>(in @ X630 @ X628)))=>(![X631:$i, X632:$i > $o, X633:$i]:(((in @ X633 @ (dsetconstr @ X631 @ X632))=>(X632 @ X633)))=>(![X634:$i > $o]:(((exu @ X634)=>?[X635:$i]:(((X634 @ X635)&![X636:$i]:(((X634 @ X636)=>((X635)=(X636))))))))=>(![X637:$o, X638:$i]:(((in @ X638 @ (prop2set @ ((X637))))=>(X637)))=>(![X639:$i]:(((in @ X639 @ emptyset)=>![X640:$o]:((X640))))=>(![X641:$i]:(((in @ X641 @ emptyset)=>~($true)))=>(![X642:$i]:(~(in @ X642 @ emptyset))=>(![X643:$i > $o]:(((exu @ X643)=>?[X644:$i]:((X643 @ X644))))=>(![X645:$i, X646:$i]:((![X647:$i]:(((in @ X647 @ X645)=>(in @ X647 @ X646)))=>(![X648:$i]:(((in @ X648 @ X646)=>(in @ X648 @ X645)))=>((X645)=(X646)))))=>(![X649:$i]:((![X650:$i]:(~(in @ X650 @ X649))=>((X649)=(emptyset))))=>(![X651:$i]:((![X652:$i]:(~(in @ X652 @ X651))=>((X651)=(emptyset))))=>(![X653:$i, X654:$i > $o, X655:$i]:(((in @ X655 @ X653)=>((in @ X655 @ (dsetconstr @ X653 @ X654))<=>(X654 @ X655))))=>(![X656:$i]:(((nonempty @ X656)=>?[X657:$i]:((in @ X657 @ X656))))=>(![X658:$i, X659:$i > $o, X660:$i]:(((in @ X660 @ X658)=>((X659 @ X660)=>(nonempty @ (dsetconstr @ X658 @ X659)))))=>(![X661:$i]:((?[X662:$i]:((in @ X662 @ X661))=>(nonempty @ X661)))=>(![X663:$i, X664:$i]:((in @ X663 @ (setadjoin @ X663 @ X664)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X665:$i, X666:$i, X667:$i]:(((in @ X667 @ X666)=>(in @ X667 @ (setadjoin @ X665 @ X666))))=>(![X668:$i, X669:$i, X670:$i]:(((in @ X670 @ (setadjoin @ X668 @ X669))=>![X671:$o]:(((((X670)=(X668))=>(X671))=>(((in @ X670 @ X669)=>(X671))=>(X671))))))=>(![X672:$i, X673:$i, X674:$i]:(((in @ X674 @ (setadjoin @ X672 @ X673))=>(((X674)=(X672))|(in @ X674 @ X673))))=>(![X675:$i]:(((dsetconstr @ X675 @ (^[Z0:$i]:($true)))=(X675)))=>(![X676:$i, X677:$i]:((![X678:$i]:(((in @ X678 @ X677)=>(in @ X678 @ X676)))=>(in @ X677 @ (powerset @ X676))))=>(![X679:$i]:((in @ emptyset @ (powerset @ X679)))=>(![X680:$i]:((in @ emptyset @ (powerset @ X680)))=>(![X681:$i, X682:$i, X683:$i]:(((in @ X682 @ (powerset @ X681))=>((in @ X683 @ X682)=>(in @ X683 @ X681))))=>(![X684:$i, X685:$i, X686:$i]:(((in @ X685 @ X686)=>((in @ X686 @ X684)=>(in @ X685 @ (setunion @ X684)))))=>(![X687:$i, X688:$i]:(((in @ X688 @ (setunion @ X687))=>![X689:$o]:((![X690:$i]:(((in @ X688 @ X690)=>((in @ X690 @ X687)=>(X689))))=>(X689)))))=>(![X691:$i, X692:$i]:(((in @ X692 @ X691)=>(in @ X692 @ (powerset @ (setunion @ X691)))))=>(![X693:$i > $o]:(((exu @ X693)=>?[X694:$i]:(![X695:$i]:(((X693 @ X695)<=>((X695)=(X694)))))))=>(![X696:$i]:(((nonempty @ X696)=>?[X697:$i]:(((in @ X697 @ X696)&$true))))=>(![X698:$i, X699:$i]:(((in @ X698 @ (setadjoin @ X699 @ emptyset))=>((X698)=(X699))))=>(![X700:$i, X701:$i]:((((X700)!=(X701))=>~(in @ X701 @ (setadjoin @ X700 @ emptyset))))=>(![X702:$i, X703:$i]:((((X702)=(X703))=>(in @ X702 @ (setadjoin @ X703 @ emptyset))))=>(![X704:$i, X705:$i]:(((in @ X704 @ (setadjoin @ X705 @ emptyset))=>(in @ X705 @ (setadjoin @ X704 @ emptyset))))=>(![X706:$i, X707:$i, X708:$i]:(((in @ X708 @ (setadjoin @ X706 @ (setadjoin @ X707 @ emptyset)))=>(((X708)=(X706))|((X708)=(X707)))))=>(![X709:$i, X710:$i]:((in @ X709 @ (setadjoin @ X709 @ (setadjoin @ X710 @ emptyset))))=>(![X711:$i, X712:$i]:((in @ X712 @ (setadjoin @ X711 @ (setadjoin @ X712 @ emptyset))))=>(![X713:$i, X714:$i > $o]:((?[X715:$i]:(((in @ X715 @ X713)&(X714 @ X715)))=>(((dsetconstr @ X713 @ X714)=(emptyset))=>~($true))))=>(![X716:$i > $o, X717:$i]:(((in @ X717 @ emptyset)=>(X716 @ X717)))=>(![X718:$i, X719:$i > $o]:((~(![X720:$i]:(((in @ X720 @ X718)=>(X719 @ X720))))=>?[X721:$i]:(((in @ X721 @ X718)&~((X719 @ X721))))))=>(![X722:$i, X723:$i > $o]:((![X724:$i]:(((in @ X724 @ X722)=>~((X723 @ X724))))=>~(?[X725:$i]:(((in @ X725 @ X722)&(X723 @ X725))))))=>(![X726:$i, X727:$i > $o]:((~(?[X728:$i]:(((in @ X728 @ X726)&(X727 @ X728))))=>![X729:$i]:(((in @ X729 @ X726)=>~((X727 @ X729))))))=>(![X730:$i, X731:$i > $o]:((?[X732:$i]:(((in @ X732 @ X730)&~((X731 @ X732))))=>~(![X733:$i]:(((in @ X733 @ X730)=>(X731 @ X733))))))=>(![X734:$o]:(((X734)=>(in @ emptyset @ (prop2set @ ((X734))))))=>((prop2set2propI)=>(![X735:$i, X736:$i > $o]:((~(?[X737:$i]:(((in @ X737 @ X735)&(X736 @ X737))))=>![X738:$i]:(((in @ X738 @ X735)=>~((X736 @ X738))))))=>(![X739:$i, X740:$i > $o]:((~(![X741:$i]:(((in @ X741 @ X739)=>(X740 @ X741))))=>?[X742:$i]:(((in @ X742 @ X739)&~((X740 @ X742))))))=>(![X743:$i > $o]:((?[X744:$i]:(((X743 @ X744)&![X745:$i]:(((X743 @ X745)=>((X744)=(X745))))))=>(exu @ X743)))=>(![X746:$i > $o]:((?[X747:$i]:((X746 @ X747))=>(![X748:$i, X749:$i]:(((X746 @ X748)=>((X746 @ X749)=>((X748)=(X749)))))=>(exu @ X746))))=>(![X750:$i > $o]:((?[X751:$i]:(![X752:$i]:(((X750 @ X752)<=>((X752)=(X751)))))=>(exu @ X750)))=>(![X753:$i, X754:$i]:((((X753)=(X754))=>![X755:$i, X756:$i]:((((X755)=(X756))=>((in @ X755 @ X753)=>(in @ X756 @ X754))))))=>(![X757:$i, X758:$i]:((((X757)=(X758))=>![X759:$i, X760:$i]:((((X759)=(X760))=>((in @ X759 @ X757)<=>(in @ X760 @ X758))))))=>(![X761:$i > $o]:(((exu @ X761)=>![X762:$i, X763:$i]:(((X761 @ X762)=>((X761 @ X763)=>((X762)=(X763)))))))=>(![X764:$i > $o, X765:$i > $o]:((![X766:$i, X767:$i]:((((X766)=(X767))=>((X764 @ X766)<=>(X765 @ X767))))=>((exu @ X764)<=>(exu @ X765))))=>(((emptyset)=(emptyset))=>(![X768:$i, X769:$i]:((((X768)=(X769))=>![X770:$i, X771:$i]:((((X770)=(X771))=>((setadjoin @ X768 @ X770)=(setadjoin @ X769 @ X771))))))=>(![X772:$i, X773:$i]:((((X772)=(X773))=>((powerset @ X772)=(powerset @ X773))))=>(![X774:$i, X775:$i]:((((X774)=(X775))=>((setunion @ X774)=(setunion @ X775))))=>(((omega)=(omega))=>(![X776:$i > $o]:(((exu @ X776)=>![X777:$i, X778:$i]:(((X776 @ X777)=>((X776 @ X778)=>((X777)=(X778)))))))=>(![X779:$i > $o, X780:$i > $o]:((![X781:$i, X782:$i]:((((X781)=(X782))=>((X779 @ X781)<=>(X780 @ X782))))=>((exu @ X779)=>((exu @ X780)=>((descr @ X779)=(descr @ X780))))))=>(![X783:$i, X784:$i]:((((X783)=(X784))=>![X785:$i > $o, X786:$i > $o]:((![X787:$i]:(((in @ X787 @ X783)=>![X788:$i]:(((in @ X788 @ X784)=>(((X787)=(X788))=>((X785 @ X787)<=>(X786 @ X788)))))))=>((dsetconstr @ X783 @ X785)=(dsetconstr @ X784 @ X786))))))=>(![X789:$i, X790:$i]:((![X791:$i]:(((in @ X791 @ X789)=>(in @ X791 @ X790)))=>(subset @ X789 @ X790)))=>(![X792:$i, X793:$i]:((((X792)=(X793))=>(subset @ X793 @ X792)))=>(![X794:$i, X795:$i]:((((X794)=(X795))=>(subset @ X794 @ X795)))=>(![X796:$i, X797:$i]:((![X798:$i]:(((in @ X798 @ X796)=>(in @ X798 @ X797)))=>(subset @ X796 @ X797)))=>(![X799:$i]:((subset @ emptyset @ X799))=>(![X800:$i, X801:$i, X802:$i]:(((subset @ X800 @ X801)=>((in @ X802 @ X800)=>(in @ X802 @ X801))))=>(![X803:$i, X804:$i, X805:$i]:(((subset @ X803 @ X804)=>(~(in @ X805 @ X804)=>~(in @ X805 @ X803))))=>(![X806:$i, X807:$i, X808:$i]:(((in @ X808 @ X806)=>(~(in @ X808 @ X807)=>~(subset @ X806 @ X807))))=>(![X809:$i, X810:$i]:((~(subset @ X809 @ X810)=>((X809)!=(X810))))=>(![X811:$i, X812:$i, X813:$i]:(((in @ X813 @ X811)=>(~(in @ X813 @ X812)=>((X811)!=(X812)))))=>(![X814:$i]:((subset @ X814 @ X814))=>(![X815:$i, X816:$i, X817:$i]:(((subset @ X815 @ X816)=>((subset @ X816 @ X817)=>(subset @ X815 @ X817))))=>(![X818:$i, X819:$i]:((subset @ X819 @ (setadjoin @ X818 @ X819)))=>(![X820:$i, X821:$i, X822:$i]:(((subset @ X820 @ X822)=>(subset @ X820 @ (setadjoin @ X821 @ X822))))=>(![X823:$i, X824:$i]:(((subset @ X823 @ X824)=>(in @ X823 @ (powerset @ X824))))=>(![X825:$i, X826:$i]:(((subset @ X825 @ X826)=>((subset @ X826 @ X825)=>((X825)=(X826)))))=>(![X827:$i]:(((subset @ X827 @ emptyset)=>((X827)=(emptyset))))=>(![X828:$i, X829:$i]:(((subset @ X829 @ X828)=>(in @ X829 @ (powerset @ X828))))=>(![X830:$i, X831:$i]:(((in @ X831 @ (powerset @ X830))=>(subset @ X831 @ X830)))=>(![X832:$i]:((in @ X832 @ (powerset @ X832)))=>(![X833:$i, X834:$i]:(((subset @ X833 @ X834)=>(subset @ (powerset @ X833) @ (powerset @ X834))))=>(![X835:$i, X836:$i > $o]:((in @ (dsetconstr @ X835 @ X836) @ (powerset @ X835)))=>(![X837:$i, X838:$i > $o]:((subset @ (dsetconstr @ X837 @ X838) @ X837))=>(![X839:$i, X840:$i, X841:$i]:(((in @ X841 @ X839)=>(in @ X841 @ (binunion @ X839 @ X840))))=>(![X842:$i, X843:$i]:((in @ X843 @ (setadjoin @ X842 @ (setadjoin @ X843 @ emptyset))))=>(![X844:$i, X845:$i, X846:$i]:(((in @ X846 @ X845)=>(in @ X846 @ (binunion @ X844 @ X845))))=>(![X847:$i, X848:$i, X849:$i, X850:$o]:(((in @ X849 @ (binunion @ X847 @ X848))=>(((in @ X849 @ X847)=>(X850))=>(((in @ X849 @ X848)=>(X850))=>(X850)))))=>(![X851:$i, X852:$i, X853:$i]:(((in @ X853 @ (binunion @ X851 @ X852))=>((in @ X853 @ X851)|(in @ X853 @ X852))))=>(![X854:$i, X855:$i]:((subset @ X854 @ (binunion @ X854 @ X855)))=>(![X856:$i, X857:$i]:((subset @ X857 @ (binunion @ X856 @ X857)))=>(![X858:$i, X859:$i, X860:$i]:(((in @ X860 @ X858)=>((in @ X860 @ X859)=>(in @ X860 @ (binintersect @ X858 @ X859)))))=>(![X861:$i, X862:$i, X863:$i]:(((subset @ X863 @ X861)=>((subset @ X863 @ X862)=>(subset @ X863 @ (binintersect @ X861 @ X862)))))=>(![X864:$i, X865:$i, X866:$i]:(((in @ X866 @ (binintersect @ X864 @ X865))=>(in @ X866 @ X864)))=>(![X867:$i, X868:$i]:((subset @ (binintersect @ X867 @ X868) @ X867))=>(![X869:$i, X870:$i]:(((subset @ X869 @ X870)=>((binintersect @ X869 @ X870)=(X869))))=>(![X871:$i, X872:$i]:((((binintersect @ X871 @ X872)=(X872))=>(subset @ X872 @ X871)))=>(![X873:$i, X874:$i, X875:$i]:(((in @ X875 @ (binintersect @ X873 @ X874))=>(in @ X875 @ X874)))=>(![X876:$i, X877:$i]:((~(?[X878:$i]:(((in @ X878 @ X876)&(in @ X878 @ X877))))=>((binintersect @ X876 @ X877)=(emptyset))))=>(![X879:$i, X880:$i]:((subset @ (binintersect @ X879 @ X880) @ X880))=>(![X881:$i, X882:$i]:(((subset @ X882 @ X881)=>((binintersect @ X881 @ X882)=(X882))))=>(![X883:$i, X884:$i]:((((binintersect @ X883 @ X884)=(X883))=>(subset @ X883 @ X884)))=>(![X885:$i, X886:$i, X887:$i]:(((binintersect @ X885 @ (binunion @ X886 @ X887))=(binunion @ (binintersect @ X885 @ X886) @ (binintersect @ X885 @ X887))))=>(![X888:$i, X889:$i, X890:$i]:(((in @ X890 @ X888)=>(~(in @ X890 @ X889)=>(in @ X890 @ (setminus @ X888 @ X889)))))=>(![X891:$i, X892:$i, X893:$i]:(((in @ X893 @ (setminus @ X891 @ X892))=>(in @ X893 @ X891)))=>(![X894:$i, X895:$i, X896:$i]:(((in @ X896 @ (setminus @ X894 @ X895))=>~(in @ X896 @ X895)))=>(![X897:$i, X898:$i]:(((subset @ X897 @ X898)=>((setminus @ X897 @ X898)=(emptyset))))=>(![X899:$i, X900:$i, X901:$i]:((~(in @ X901 @ (setminus @ X899 @ X900))=>((in @ X901 @ X899)=>(in @ X901 @ X900))))=>(![X902:$i, X903:$i, X904:$i]:((~(in @ X904 @ (setminus @ X902 @ 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@ (^[Z0:$i]:((in @ (kpair @ X1113 @ Z0) @ X1112))))) @ X1111)))))=>(![X1114:$i, X1115:$i, X1116:$i]:(((func @ X1114 @ X1115 @ X1116)=>![X1117:$i]:(((in @ X1117 @ X1114)=>(in @ (ap @ X1114 @ X1115 @ X1116 @ X1117) @ X1115)))))=>(![X1118:$i, X1119:$i, X1120:$i]:(((in @ X1120 @ (funcSet @ X1118 @ X1119))=>(func @ X1118 @ X1119 @ X1120)))=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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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)],[c_0_192, emptyInPowerset]), setunionsingleton1]), setunionE2]), setunionsingleton2]), setunionsingleton]), setadjoinIR]), c_0_193]), setadjoinE]), c_0_194]), c_0_195]), c_0_196]), singletonsuniq]), setukpairinjL1]), c_0_197]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), setunionI]), upairequniteq]), powersetE]), setukpairinjR2]), quantDeMorgan1]), vacuousDall]), setukpairinjR]), emptyinPowerset]), c_0_198]), powersetI]), ksndpairEq]), c_0_199]), kpairsurjEq]), setadjoinOr]), cartprodsndin]), setunionE]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_200]), c_0_201]), c_0_202]), c_0_203]), c_0_204]), c_0_205]), c_0_206]), singletonsswitch]), c_0_207]), eqinunit]), c_0_208]), notinsingleton]), app]), uniqinunit]), infuncsetfunc]), nonemptyImpWitness]), c_0_209]), emptyinunitempty]), subPowSU]), upairsetE]), quantDeMorgan3]), quantDeMorgan2]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), c_0_210]), upairsetIR]), upairsetIL]), quantDeMorgan4]), inCongP]), c_0_211]), c_0_212]), c_0_213]), notdallE]), notdexE]), prop2setI]), in__Cong]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_214]), c_0_215]), c_0_216]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_217]), c_0_218]), subsetE]), setadjoinSub]), setadjoinSub2]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), c_0_219]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_220]), binunionRsub]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), disjointsetsI1]), setminusER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), setminusSubset2]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), symdiffI1]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), kpairp]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), ubforcartprodlem2]), setadjoinIL]), nonemptyI1]), c_0_221]), nonemptyE1]), c_0_222]), noeltsimpempty]), emptyI]), setext]), c_0_223]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_224]), c_0_225]), c_0_226]), c_0_227]), c_0_228]), wellorderingAx]), foundationAx]), c_0_229]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_230])).
% 2.93/0.71  thf(c_0_232, negated_conjecture, ![X1127:$i, X1128:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1140:$i, X1141:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1149:$i, X1150:$i > $i > $o, X1151:$i, X1154:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1161:$i, X1162:$i > $o, X1163:$i, X1164:$i > $o, X1165:$i, X1166:$i, X1167:$i > $o, X1168:$i, X1169:$i, X1170:$i > $o, X1171:$i, X1172:$i > $o, X1174:$i, X1175:$o, X1176:$i, X1177:$i, X1178:$o, X1179:$i, X1180:$i, X1181:$i > $o, X1183:$i, X1184:$i, X1187:$i, X1189:$i, X1191:$i, X1192:$i > $o, X1193:$i, X1194:$i, X1196:$i, X1197:$i > $o, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$o, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$o, X1229:$i, X1230:$i, X1231:$i > $o, X1233:$i, X1234:$i, X1235:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i > $o, X1254:$i, X1255:$i > $o, X1256:$i, X1257:$i, X1258:$i > $o, X1259:$i, X1261:$i, X1262:$i > $o, X1264:$i, X1265:$i, X1266:$i > $o, X1268:$i, X1269:$i, X1270:$i > $o, X1271:$i, X1273:$o, X1274:$i, X1275:$i > $o, X1277:$i, X1278:$i, X1279:$i > $o, X1280:$i, X1282:$i > $o, X1283:$i, X1285:$i > $o, X1286:$i, X1289:$i > $o, X1290:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i > $o, X1301:$i, X1302:$i, X1303:$i > $o, X1304:$i > $o, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i > $o, X1316:$i, X1317:$i, X1318:$i > $o, X1319:$i > $o, X1322:$i, X1323:$i, X1324:$i > $o, X1325:$i > $o, X1328:$i, X1329:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i > $o, X1376:$i, X1377:$i > $o, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$o, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$o, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i > $o, X1532:$i, X1533:$i, X1534:$i > $o, X1536:$i, X1537:$i > $o, X1538:$i, X1540:$i, X1541:$i > $o, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i > $i > $o, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i > $i > $o, X1622:$i, X1623:$i, X1624:$i > $i > $o, X1625:$i, X1626:$i, X1627:$i > $i > $o, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i > $i > $o, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i > $i > $o, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i > $i > $o, X1643:$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]:((((~(in @ (esk1_2 @ X1127 @ X1128) @ X1127)|~(in @ (esk1_2 @ X1127 @ X1128) @ X1128)|((X1127)=(X1128)))&((in @ (esk1_2 @ X1127 @ X1128) @ X1127)|(in @ (esk1_2 @ X1127 @ X1128) @ X1128)|((X1127)=(X1128))))&(~(in @ X1130 @ emptyset)&(((~(in @ X1133 @ (setadjoin @ X1131 @ X1132))|(((X1133)=(X1131))|(in @ X1133 @ X1132)))&((((X1133)!=(X1131))|(in @ X1133 @ (setadjoin @ X1131 @ X1132)))&(~(in @ X1133 @ X1132)|(in @ X1133 @ (setadjoin @ X1131 @ X1132)))))&(((~(in @ X1135 @ (powerset @ X1134))|(~(in @ X1136 @ X1135)|(in @ X1136 @ X1134)))&(((in @ (esk2_2 @ X1137 @ X1138) @ X1138)|(in @ X1138 @ (powerset @ X1137)))&(~(in @ (esk2_2 @ X1137 @ X1138) @ X1137)|(in @ X1138 @ (powerset @ X1137)))))&(((((in @ X1141 @ (esk3_2 @ X1140 @ X1141))|~(in @ X1141 @ (setunion @ X1140)))&((in @ (esk3_2 @ X1140 @ X1141) @ X1140)|~(in @ X1141 @ (setunion @ X1140))))&(~(in @ X1144 @ X1145)|~(in @ X1145 @ X1143)|(in @ X1144 @ (setunion @ X1143))))&((in @ emptyset @ omega)&((~(in @ X1146 @ omega)|(in @ (setadjoin @ X1146 @ X1146) @ omega))&(((((in @ (esk4_1 @ X1147) @ omega)|~(in @ emptyset @ X1147)|(~(in @ X1149 @ omega)|(in @ X1149 @ X1147)))&((in @ (esk4_1 @ X1147) @ X1147)|~(in @ emptyset @ X1147)|(~(in @ X1149 @ omega)|(in @ X1149 @ X1147))))&(~(in @ (setadjoin @ (esk4_1 @ X1147) @ (esk4_1 @ X1147)) @ X1147)|~(in @ emptyset @ X1147)|(~(in @ X1149 @ omega)|(in @ X1149 @ X1147))))&((((((in @ (esk7_3 @ X1150 @ X1151 @ X1154) @ X1151)|~(in @ X1154 @ (esk6_2 @ X1150 @ X1151))|(in @ (esk5_2 @ X1150 @ X1151) @ X1151))&((X1150 @ (esk7_3 @ X1150 @ X1151 @ X1154) @ X1154)|~(in @ X1154 @ (esk6_2 @ X1150 @ X1151))|(in @ (esk5_2 @ X1150 @ X1151) @ X1151)))&(~(in @ X1157 @ X1151)|~(X1150 @ X1157 @ X1156)|(in @ X1156 @ (esk6_2 @ X1150 @ X1151))|(in @ (esk5_2 @ X1150 @ X1151) @ X1151)))&((((in @ (esk7_3 @ X1150 @ X1151 @ X1154) @ 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X1476 @ emptyset) @ (setadjoin @ (setadjoin @ X1476 @ (setadjoin @ X1477 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1478 @ X1479))&((~(in @ X1481 @ X1480)|(subset @ (setadjoin @ X1481 @ emptyset) @ X1480))&((~(in @ X1483 @ X1482)|(in @ (setadjoin @ X1483 @ emptyset) @ (powerset @ X1482)))&((~(in @ X1486 @ X1484)|(in @ (setadjoin @ X1486 @ emptyset) @ (powerset @ (binunion @ X1484 @ X1485))))&((~(in @ X1489 @ (setadjoin @ X1487 @ (setadjoin @ X1488 @ emptyset)))|(((X1489)=(X1487))|((X1489)=(X1488))))&((~(in @ X1492 @ X1490)|(~(in @ X1493 @ X1491)|(subset @ (setadjoin @ X1492 @ (setadjoin @ X1493 @ emptyset)) @ (binunion @ X1490 @ X1491))))&((~(in @ X1496 @ X1494)|(~(in @ X1497 @ X1495)|(in @ (setadjoin @ X1496 @ (setadjoin @ X1497 @ emptyset)) @ (powerset @ (binunion @ X1494 @ X1495)))))&((~(in @ X1500 @ X1498)|(~(in @ X1501 @ X1499)|(subset @ (setadjoin @ (setadjoin @ X1500 @ emptyset) @ (setadjoin @ (setadjoin @ X1500 @ (setadjoin @ X1501 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1498 @ X1499)))))&((~(in @ X1504 @ X1502)|(~(in @ X1505 @ X1503)|(in @ (setadjoin @ (setadjoin @ X1504 @ emptyset) @ (setadjoin @ (setadjoin @ X1504 @ (setadjoin @ X1505 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1502 @ X1503))))))&((~(in @ X1508 @ X1506)|(~(in @ X1509 @ X1507)|(in @ (kpair @ X1508 @ X1509) @ (powerset @ (powerset @ (binunion @ X1506 @ X1507))))))&((~(in @ X1512 @ X1510)|(~(in @ X1513 @ X1511)|(in @ (kpair @ X1512 @ X1513) @ (cartprod @ X1510 @ X1511))))&((((in @ (esk39_3 @ X1514 @ X1515 @ X1516) @ X1514)|~(in @ X1516 @ (cartprod @ X1514 @ X1515)))&(((in @ (esk40_3 @ X1514 @ X1515 @ X1516) @ X1515)|~(in @ X1516 @ (cartprod @ X1514 @ X1515)))&(((X1516)=(kpair @ (esk39_3 @ X1514 @ X1515 @ X1516) @ (esk40_3 @ X1514 @ X1515 @ X1516)))|~(in @ X1516 @ (cartprod @ X1514 @ X1515)))))&((~(in @ X1521 @ (cartprod @ X1519 @ X1520))|(iskpair @ X1521))&((((in @ (esk41_2 @ X1522 @ X1523) @ X1522)|~(in @ X1523 @ (setunion @ X1522)))&((in @ X1523 @ (esk41_2 @ X1522 @ X1523))|~(in @ X1523 @ (setunion @ X1522))))&((subset @ (setunion @ (setadjoin @ X1525 @ emptyset)) @ X1525)&((subset @ X1526 @ (setunion @ (setadjoin @ X1526 @ emptyset)))&(((setunion @ (setadjoin @ X1527 @ emptyset))=(X1527))&((((in @ (esk42_2 @ X1528 @ X1529) @ X1528)|(~(in @ X1532 @ X1528)|~(X1529 @ X1532)|(singleton @ (dsetconstr @ X1528 @ X1529))))&(((in @ (esk43_2 @ X1528 @ X1529) @ X1528)|(~(in @ X1532 @ X1528)|~(X1529 @ X1532)|(singleton @ (dsetconstr @ X1528 @ X1529))))&(((X1529 @ (esk42_2 @ X1528 @ X1529))|(~(in @ X1532 @ X1528)|~(X1529 @ X1532)|(singleton @ (dsetconstr @ X1528 @ X1529))))&(((X1529 @ (esk43_2 @ X1528 @ X1529))|(~(in @ X1532 @ X1528)|~(X1529 @ X1532)|(singleton @ (dsetconstr @ X1528 @ X1529))))&(((esk42_2 @ X1528 @ X1529)!=(esk43_2 @ X1528 @ X1529))|(~(in @ X1532 @ X1528)|~(X1529 @ X1532)|(singleton @ (dsetconstr @ X1528 @ X1529))))))))&((((in @ (esk44_2 @ X1533 @ X1534) @ X1533)|~(ex1 @ X1533 @ X1534))&((X1534 @ (esk44_2 @ X1533 @ X1534))|~(ex1 @ X1533 @ X1534)))&((((in @ (esk45_3 @ X1536 @ X1537 @ X1538) @ X1536)|(ex1 @ X1536 @ X1537)|~(X1537 @ X1538)|~(in @ X1538 @ X1536))&(((X1537 @ (esk45_3 @ X1536 @ X1537 @ X1538))|(ex1 @ X1536 @ X1537)|~(X1537 @ X1538)|~(in @ X1538 @ X1536))&(((esk45_3 @ X1536 @ X1537 @ X1538)!=(X1538))|(ex1 @ X1536 @ X1537)|~(X1537 @ X1538)|~(in @ X1538 @ X1536))))&((((in @ (esk46_2 @ X1540 @ X1541) @ X1540)|(~(in @ X1544 @ X1540)|~(X1541 @ X1544)|(ex1 @ X1540 @ X1541)))&(((in @ (esk47_2 @ X1540 @ X1541) @ X1540)|(~(in @ X1544 @ X1540)|~(X1541 @ X1544)|(ex1 @ X1540 @ X1541)))&(((X1541 @ (esk46_2 @ X1540 @ X1541))|(~(in @ X1544 @ X1540)|~(X1541 @ X1544)|(ex1 @ X1540 @ X1541)))&(((X1541 @ (esk47_2 @ X1540 @ X1541))|(~(in @ X1544 @ X1540)|~(X1541 @ X1544)|(ex1 @ X1540 @ X1541)))&(((esk46_2 @ X1540 @ X1541)!=(esk47_2 @ X1540 @ X1541))|(~(in @ X1544 @ X1540)|~(X1541 @ X1544)|(ex1 @ X1540 @ X1541)))))))&((((setadjoin @ X1545 @ emptyset)!=(setadjoin @ X1546 @ emptyset))|((X1545)=(X1546)))&((~(in @ (setadjoin @ X1549 @ emptyset) @ (setadjoin @ (setadjoin @ X1547 @ emptyset) @ (setadjoin @ (setadjoin @ X1547 @ (setadjoin @ X1548 @ emptyset)) @ emptyset)))|((X1547)=(X1549)))&((~(iskpair @ X1550)|(singleton @ (dsetconstr @ (setunion @ X1550) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1550))))))&((~(singleton @ X1551)|(in @ (setunion @ X1551) @ X1551))&(((kfst @ (kpair @ X1552 @ X1553))=(X1552))&((~(in @ X1556 @ (cartprod @ X1554 @ X1555))|(in @ (kfst @ X1556) @ X1554))&((((setadjoin @ (setadjoin @ X1557 @ emptyset) @ (setadjoin @ (setadjoin @ X1557 @ (setadjoin @ X1558 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1559 @ emptyset) @ (setadjoin @ (setadjoin @ X1559 @ (setadjoin @ X1560 @ emptyset)) @ emptyset)))|((X1557)=(X1559)))&((((kpair @ X1561 @ X1562)!=(kpair @ X1563 @ X1564))|((X1561)=(X1563)))&((((X1565)!=(X1566))|((setadjoin @ X1565 @ (setadjoin @ X1566 @ emptyset))=(setadjoin @ X1565 @ emptyset)))&((((X1567)!=(X1568))|((setadjoin @ (setadjoin @ X1567 @ emptyset) @ (setadjoin @ (setadjoin @ X1567 @ (setadjoin @ X1568 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1567 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1569 @ emptyset) @ (setadjoin @ (setadjoin @ X1569 @ (setadjoin @ X1570 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1571 @ emptyset) @ (setadjoin @ (setadjoin @ X1571 @ (setadjoin @ X1572 @ emptyset)) @ emptyset)))|(((X1571)!=(X1572))|((X1570)=(X1572))))&((((setadjoin @ X1573 @ (setadjoin @ X1574 @ emptyset))!=(setadjoin @ X1575 @ emptyset))|((X1573)=(X1574)))&((((setadjoin @ (setadjoin @ X1576 @ emptyset) @ (setadjoin @ (setadjoin @ X1576 @ (setadjoin @ X1577 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1578 @ emptyset) @ (setadjoin @ (setadjoin @ X1578 @ (setadjoin @ X1579 @ emptyset)) @ emptyset)))|((X1577)=(X1579)))&((((kpair @ X1580 @ X1581)!=(kpair @ X1582 @ X1583))|((X1581)=(X1583)))&((~(iskpair @ X1584)|(singleton @ (dsetconstr @ (setunion @ X1584) @ (^[Z0:$i]:(((X1584)=(kpair @ (kfst @ X1584) @ Z0)))))))&(((ksnd @ (kpair @ X1585 @ X1586))=(X1586))&((~(iskpair @ X1587)|((kpair @ (kfst @ X1587) @ (ksnd @ X1587))=(X1587)))&((~(in @ X1590 @ (cartprod @ X1588 @ X1589))|(in @ (ksnd @ X1590) @ X1589))&((~(in @ (kpair @ X1593 @ X1594) @ (cartprod @ X1591 @ X1592))|(in @ X1593 @ X1591))&((~(in @ (kpair @ X1597 @ X1598) @ (cartprod @ X1595 @ X1596))|(in @ X1598 @ X1596))&((~(in @ X1601 @ X1599)|(~(in @ X1602 @ X1600)|((kpair @ X1601 @ X1602)=(kpair @ X1601 @ X1602))))&((~(in @ X1605 @ X1603)|(~(in @ X1606 @ X1604)|((kfst @ (kpair @ X1605 @ X1606))=(X1605))))&((~(in @ X1609 @ X1607)|(~(in @ X1610 @ X1608)|((ksnd @ (kpair @ X1609 @ X1610))=(X1610))))&((~(in @ X1613 @ (cartprod @ X1611 @ X1612))|((kpair @ (kfst @ X1613) @ (ksnd @ X1613))=(X1613)))&((~(in @ X1617 @ X1614)|(~(in @ X1618 @ X1615)|(~(X1616 @ X1617 @ X1618)|(in @ (kpair @ X1617 @ X1618) @ (dpsetconstr @ X1614 @ X1615 @ X1616)))))&((subset @ (dpsetconstr @ X1619 @ X1620 @ X1621) @ (cartprod @ X1619 @ X1620))&((breln @ X1622 @ X1623 @ (dpsetconstr @ X1622 @ X1623 @ X1624))&((~(in @ X1628 @ X1625)|(~(in @ X1629 @ X1626)|(~(in @ (kpair @ X1628 @ X1629) @ (dpsetconstr @ X1625 @ X1626 @ X1627))|(X1627 @ X1628 @ X1629))))&((~(in @ (kpair @ X1633 @ X1634) @ (dpsetconstr @ X1630 @ X1631 @ X1632))|(in @ X1633 @ X1630))&((~(in @ (kpair @ X1638 @ X1639) @ (dpsetconstr @ X1635 @ X1636 @ X1637))|(in @ X1639 @ X1636))&((~(in @ (kpair @ X1643 @ X1644) @ (dpsetconstr @ X1640 @ X1641 @ X1642))|(X1642 @ X1643 @ X1644))&((~(func @ X1645 @ X1646 @ X1647)|(~(in @ X1648 @ X1645)|(singleton @ (dsetconstr @ X1646 @ (^[Z0:$i]:((in @ (kpair @ X1648 @ Z0) @ X1647)))))))&((~(func @ X1649 @ X1650 @ X1651)|(~(in @ X1652 @ X1649)|(in @ (setunion @ (dsetconstr @ X1650 @ (^[Z0:$i]:((in @ (kpair @ X1652 @ Z0) @ X1651))))) @ X1650)))&((~(func @ X1653 @ X1654 @ X1655)|(~(in @ X1656 @ X1653)|(in @ (ap @ X1653 @ X1654 @ X1655 @ X1656) @ X1654)))&((~(in @ X1659 @ (funcSet @ X1657 @ X1658))|(func @ X1657 @ X1658 @ X1659))&((in @ esk50_0 @ (funcSet @ esk48_0 @ esk49_0))&((in @ esk51_0 @ esk48_0)&~(in @ (ap @ esk48_0 @ esk49_0 @ esk50_0 @ esk51_0) @ esk49_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_231])])])])])])])).
% 2.93/0.71  thf(c_0_233, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((func @ X3 @ X4 @ X2)|~((in @ X2 @ (funcSet @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_232])).
% 2.93/0.71  thf(c_0_234, negated_conjecture, (in @ esk50_0 @ (funcSet @ esk48_0 @ esk49_0)), inference(split_conjunct,[status(thm)],[c_0_232])).
% 2.93/0.71  thf(c_0_235, negated_conjecture, ~((in @ (ap @ esk48_0 @ esk49_0 @ esk50_0 @ esk51_0) @ esk49_0)), inference(split_conjunct,[status(thm)],[c_0_232])).
% 2.93/0.71  thf(c_0_236, negated_conjecture, ![X3:$i, X5:$i, X4:$i, X2:$i]:(((in @ (ap @ X2 @ X3 @ X4 @ X5) @ X3)|~((func @ X2 @ X3 @ X4))|~((in @ X5 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_232])).
% 2.93/0.71  thf(c_0_237, negated_conjecture, (func @ esk48_0 @ esk49_0 @ esk50_0), inference(spm,[status(thm)],[c_0_233, c_0_234])).
% 2.93/0.71  thf(c_0_238, negated_conjecture, (in @ esk51_0 @ esk48_0), inference(split_conjunct,[status(thm)],[c_0_232])).
% 2.93/0.71  thf(c_0_239, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235, c_0_236]), c_0_237]), c_0_238])]), ['proof']).
% 2.93/0.71  % SZS output end CNFRefutation
% 2.93/0.71  % Parsed axioms                        : 429
% 2.93/0.71  % Removed by relevancy pruning/SinE    : 235
% 2.93/0.71  % Initial clauses                      : 296
% 2.93/0.71  % Removed in clause preprocessing      : 26
% 2.93/0.71  % Initial clauses in saturation        : 270
% 2.93/0.71  % Processed clauses                    : 2046
% 2.93/0.71  % ...of these trivial                  : 59
% 2.93/0.71  % ...subsumed                          : 1258
% 2.93/0.71  % ...remaining for further processing  : 729
% 2.93/0.71  % Other redundant clauses eliminated   : 86
% 2.93/0.71  % Clauses deleted for lack of memory   : 0
% 2.93/0.71  % Backward-subsumed                    : 64
% 2.93/0.71  % Backward-rewritten                   : 26
% 2.93/0.71  % Generated clauses                    : 15363
% 2.93/0.71  % ...of the previous two non-redundant : 13445
% 2.93/0.71  % ...aggressively subsumed             : 0
% 2.93/0.71  % Contextual simplify-reflections      : 0
% 2.93/0.71  % Paramodulations                      : 15270
% 2.93/0.71  % Factorizations                       : 4
% 2.93/0.71  % NegExts                              : 0
% 2.93/0.71  % Equation resolutions                 : 89
% 2.93/0.71  % Disequality decompositions           : 0
% 2.93/0.71  % Total rewrite steps                  : 2274
% 2.93/0.71  % ...of those cached                   : 2051
% 2.93/0.71  % Propositional unsat checks           : 0
% 2.93/0.71  %    Propositional check models        : 0
% 2.93/0.71  %    Propositional check unsatisfiable : 0
% 2.93/0.71  %    Propositional clauses             : 0
% 2.93/0.71  %    Propositional clauses after purity: 0
% 2.93/0.71  %    Propositional unsat core size     : 0
% 2.93/0.71  %    Propositional preprocessing time  : 0.000
% 2.93/0.71  %    Propositional encoding time       : 0.000
% 2.93/0.71  %    Propositional solver time         : 0.000
% 2.93/0.71  %    Success case prop preproc time    : 0.000
% 2.93/0.71  %    Success case prop encoding time   : 0.000
% 2.93/0.71  %    Success case prop solver time     : 0.000
% 2.93/0.71  % Current number of processed clauses  : 628
% 2.93/0.71  %    Positive orientable unit clauses  : 137
% 2.93/0.71  %    Positive unorientable unit clauses: 1
% 2.93/0.71  %    Negative unit clauses             : 4
% 2.93/0.71  %    Non-unit-clauses                  : 486
% 2.93/0.71  % Current number of unprocessed clauses: 11007
% 2.93/0.71  % ...number of literals in the above   : 34533
% 2.93/0.71  % Current number of archived formulas  : 0
% 2.93/0.71  % Current number of archived clauses   : 90
% 2.93/0.71  % Clause-clause subsumption calls (NU) : 46830
% 2.93/0.71  % Rec. Clause-clause subsumption calls : 38854
% 2.93/0.71  % Non-unit clause-clause subsumptions  : 1206
% 2.93/0.71  % Unit Clause-clause subsumption calls : 818
% 2.93/0.71  % Rewrite failures with RHS unbound    : 2
% 2.93/0.71  % BW rewrite match attempts            : 149
% 2.93/0.71  % BW rewrite match successes           : 14
% 2.93/0.71  % Condensation attempts                : 0
% 2.93/0.71  % Condensation successes               : 0
% 2.93/0.71  % Termbank termtop insertions          : 213510
% 2.93/0.71  % Search garbage collected termcells   : 17017
% 2.93/0.71  
% 2.93/0.71  % -------------------------------------------------
% 2.93/0.71  % User time                : 0.327 s
% 2.93/0.71  % System time              : 0.022 s
% 2.93/0.71  % Total time               : 0.349 s
% 2.93/0.71  % Maximum resident set size: 7608 pages
% 2.93/0.71  
% 2.93/0.71  % -------------------------------------------------
% 2.93/0.71  % User time                : 0.338 s
% 2.93/0.71  % System time              : 0.030 s
% 2.93/0.71  % Total time               : 0.369 s
% 2.93/0.71  % Maximum resident set size: 5376 pages
% 2.93/0.71  % E exiting
%------------------------------------------------------------------------------