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

%------------------------------------------------------------------------------
% File     : E-SAT---3.5.1
% Problem  : SEU766^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n006.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 08:27:43 AM UTC 2026

% Result   : Theorem 2.29s 0.63s
% Output   : CNFRefutation 2.29s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU766^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17  % Computer : n006.cluster.edu
% 0.07/0.17  % Model    : x86_64 x86_64
% 0.07/0.17  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17  % Memory   : 8046.5625MB
% 0.07/0.17  % OS       : Linux 6.8.0-71-generic
% 0.07/0.17  % CPULimit : 300
% 0.07/0.17  % WCLimit  : 300
% 0.07/0.17  % DateTime : Tue Sep 29 14:23:09 UTC 2026
% 0.07/0.18  % CPUTime  : 
% 0.07/0.18  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21  Running higher-order theorem proving
% 0.23/0.28  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p
% 2.29/0.63  % Version: 3.5.1-ho
% 2.29/0.63  % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.29/0.63  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.63  % Starting ehoh_best5 with 300s (1) cores
% 2.29/0.63  % Starting almost_fo_3_lam with 300s (1) cores
% 2.29/0.63  % Starting new_bool_5 with 300s (1) cores
% 2.29/0.63  % Starting pre_casc_3 with 300s (1) cores
% 2.29/0.63  % Starting ho_unfolding_8 with 300s (1) cores
% 2.29/0.63  % Starting new_ho_10_cnf2 with 300s (1) cores
% 2.29/0.63  % Starting new_bool_3 with 300s (1) cores
% 2.29/0.63  % Starting new_ho_5 with 300s (1) cores
% 2.29/0.63  % new_ho_5 with pid 797899 completed with status 9
% 2.29/0.63  % ho_unfolding_8 with pid 797896 completed with status 0
% 2.29/0.63  % Result found by ho_unfolding_8
% 2.29/0.63  % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.29/0.63  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.63  % Starting ehoh_best5 with 300s (1) cores
% 2.29/0.63  % Starting almost_fo_3_lam with 300s (1) cores
% 2.29/0.63  % Starting new_bool_5 with 300s (1) cores
% 2.29/0.63  % Starting pre_casc_3 with 300s (1) cores
% 2.29/0.63  % Starting ho_unfolding_8 with 300s (1) cores
% 2.29/0.63  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.29/0.63  % No SInE strategy applied
% 2.29/0.63  % Search class: HGHSM-FSLM32-MHFMMSBN
% 2.29/0.63  % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 2.29/0.63  % Starting SubtermCWHack with 31s (1) cores
% 2.29/0.63  % SubtermCWHack with pid 797904 completed with status 0
% 2.29/0.63  % Result found by SubtermCWHack
% 2.29/0.63  % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.29/0.63  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.63  % Starting ehoh_best5 with 300s (1) cores
% 2.29/0.63  % Starting almost_fo_3_lam with 300s (1) cores
% 2.29/0.63  % Starting new_bool_5 with 300s (1) cores
% 2.29/0.63  % Starting pre_casc_3 with 300s (1) cores
% 2.29/0.63  % Starting ho_unfolding_8 with 300s (1) cores
% 2.29/0.63  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.29/0.63  % No SInE strategy applied
% 2.29/0.63  % Search class: HGHSM-FSLM32-MHFMMSBN
% 2.29/0.63  % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 2.29/0.63  % Starting SubtermCWHack with 31s (1) cores
% 2.29/0.63  % Preprocessing time       : 0.004 s
% 2.29/0.63  
% 2.29/0.63  % Proof found!
% 2.29/0.63  % SZS status Theorem
% 2.29/0.63  % SZS output start CNFRefutation
% 2.29/0.63  thf(decl_23, type, in: $i > $i > $o).
% 2.29/0.63  thf(decl_24, type, exu: ($i > $o) > $o).
% 2.29/0.63  thf(decl_25, type, setextAx: $o).
% 2.29/0.63  thf(decl_26, type, emptyset: $i).
% 2.29/0.63  thf(decl_27, type, emptysetAx: $o).
% 2.29/0.63  thf(decl_28, type, setadjoin: $i > $i > $i).
% 2.29/0.63  thf(decl_29, type, setadjoinAx: $o).
% 2.29/0.63  thf(decl_30, type, powerset: $i > $i).
% 2.29/0.63  thf(decl_31, type, powersetAx: $o).
% 2.29/0.63  thf(decl_32, type, setunion: $i > $i).
% 2.29/0.63  thf(decl_33, type, setunionAx: $o).
% 2.29/0.63  thf(decl_34, type, omega: $i).
% 2.29/0.63  thf(decl_35, type, omega0Ax: $o).
% 2.29/0.63  thf(decl_36, type, omegaSAx: $o).
% 2.29/0.63  thf(decl_37, type, omegaIndAx: $o).
% 2.29/0.63  thf(decl_38, type, replAx: $o).
% 2.29/0.63  thf(decl_39, type, foundationAx: $o).
% 2.29/0.63  thf(decl_40, type, wellorderingAx: $o).
% 2.29/0.63  thf(decl_41, type, descr: ($i > $o) > $i).
% 2.29/0.63  thf(decl_42, type, descrp: $o).
% 2.29/0.63  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 2.29/0.63  thf(decl_44, type, dsetconstrI: $o).
% 2.29/0.63  thf(decl_45, type, dsetconstrEL: $o).
% 2.29/0.63  thf(decl_46, type, dsetconstrER: $o).
% 2.29/0.63  thf(decl_47, type, exuE1: $o).
% 2.29/0.63  thf(decl_48, type, prop2set: $o > $i).
% 2.29/0.63  thf(decl_49, type, prop2setE: $o).
% 2.29/0.63  thf(decl_50, type, emptysetE: $o).
% 2.29/0.63  thf(decl_51, type, emptysetimpfalse: $o).
% 2.29/0.63  thf(decl_52, type, notinemptyset: $o).
% 2.29/0.63  thf(decl_53, type, exuE3e: $o).
% 2.29/0.63  thf(decl_54, type, setext: $o).
% 2.29/0.63  thf(decl_55, type, emptyI: $o).
% 2.29/0.63  thf(decl_56, type, noeltsimpempty: $o).
% 2.29/0.63  thf(decl_57, type, setbeta: $o).
% 2.29/0.63  thf(decl_58, type, nonempty: $i > $o).
% 2.29/0.63  thf(decl_59, type, nonemptyE1: $o).
% 2.29/0.63  thf(decl_60, type, nonemptyI: $o).
% 2.29/0.63  thf(decl_61, type, nonemptyI1: $o).
% 2.29/0.63  thf(decl_62, type, setadjoinIL: $o).
% 2.29/0.63  thf(decl_63, type, emptyinunitempty: $o).
% 2.29/0.63  thf(decl_64, type, setadjoinIR: $o).
% 2.29/0.63  thf(decl_65, type, setadjoinE: $o).
% 2.29/0.63  thf(decl_66, type, setadjoinOr: $o).
% 2.29/0.63  thf(decl_67, type, setoftrueEq: $o).
% 2.29/0.63  thf(decl_68, type, powersetI: $o).
% 2.29/0.63  thf(decl_69, type, emptyinPowerset: $o).
% 2.29/0.63  thf(decl_70, type, emptyInPowerset: $o).
% 2.29/0.63  thf(decl_71, type, powersetE: $o).
% 2.29/0.63  thf(decl_72, type, setunionI: $o).
% 2.29/0.63  thf(decl_73, type, setunionE: $o).
% 2.29/0.63  thf(decl_74, type, subPowSU: $o).
% 2.29/0.63  thf(decl_75, type, exuE2: $o).
% 2.29/0.63  thf(decl_76, type, nonemptyImpWitness: $o).
% 2.29/0.63  thf(decl_77, type, uniqinunit: $o).
% 2.29/0.63  thf(decl_78, type, notinsingleton: $o).
% 2.29/0.63  thf(decl_79, type, eqinunit: $o).
% 2.29/0.63  thf(decl_80, type, singletonsswitch: $o).
% 2.29/0.63  thf(decl_81, type, upairsetE: $o).
% 2.29/0.63  thf(decl_82, type, upairsetIL: $o).
% 2.29/0.63  thf(decl_83, type, upairsetIR: $o).
% 2.29/0.63  thf(decl_84, type, emptyE1: $o).
% 2.29/0.63  thf(decl_85, type, vacuousDall: $o).
% 2.29/0.63  thf(decl_86, type, quantDeMorgan1: $o).
% 2.29/0.63  thf(decl_87, type, quantDeMorgan2: $o).
% 2.29/0.63  thf(decl_88, type, quantDeMorgan3: $o).
% 2.29/0.63  thf(decl_89, type, quantDeMorgan4: $o).
% 2.29/0.63  thf(decl_90, type, prop2setI: $o).
% 2.29/0.63  thf(decl_91, type, set2prop: $i > $o).
% 2.29/0.63  thf(decl_92, type, prop2set2propI: $o).
% 2.29/0.63  thf(decl_93, type, notdexE: $o).
% 2.29/0.63  thf(decl_94, type, notdallE: $o).
% 2.29/0.63  thf(decl_95, type, exuI1: $o).
% 2.29/0.63  thf(decl_96, type, exuI3: $o).
% 2.29/0.63  thf(decl_97, type, exuI2: $o).
% 2.29/0.63  thf(decl_98, type, inCongP: $o).
% 2.29/0.63  thf(decl_99, type, in__Cong: $o).
% 2.29/0.63  thf(decl_100, type, exuE3u: $o).
% 2.29/0.63  thf(decl_101, type, exu__Cong: $o).
% 2.29/0.63  thf(decl_102, type, emptyset__Cong: $o).
% 2.29/0.63  thf(decl_103, type, setadjoin__Cong: $o).
% 2.29/0.63  thf(decl_104, type, powerset__Cong: $o).
% 2.29/0.63  thf(decl_105, type, setunion__Cong: $o).
% 2.29/0.63  thf(decl_106, type, omega__Cong: $o).
% 2.29/0.63  thf(decl_107, type, exuEu: $o).
% 2.29/0.63  thf(decl_108, type, descr__Cong: $o).
% 2.29/0.63  thf(decl_109, type, dsetconstr__Cong: $o).
% 2.29/0.63  thf(decl_110, type, subset: $i > $i > $o).
% 2.29/0.63  thf(decl_113, type, subsetI1: $o).
% 2.29/0.63  thf(decl_114, type, eqimpsubset2: $o).
% 2.29/0.63  thf(decl_115, type, eqimpsubset1: $o).
% 2.29/0.63  thf(decl_116, type, subsetI2: $o).
% 2.29/0.63  thf(decl_117, type, emptysetsubset: $o).
% 2.29/0.63  thf(decl_118, type, subsetE: $o).
% 2.29/0.63  thf(decl_119, type, subsetE2: $o).
% 2.29/0.63  thf(decl_120, type, notsubsetI: $o).
% 2.29/0.63  thf(decl_121, type, notequalI1: $o).
% 2.29/0.63  thf(decl_122, type, notequalI2: $o).
% 2.29/0.63  thf(decl_123, type, subsetRefl: $o).
% 2.29/0.63  thf(decl_124, type, subsetTrans: $o).
% 2.29/0.63  thf(decl_125, type, setadjoinSub: $o).
% 2.29/0.63  thf(decl_126, type, setadjoinSub2: $o).
% 2.29/0.63  thf(decl_127, type, subset2powerset: $o).
% 2.29/0.63  thf(decl_128, type, setextsub: $o).
% 2.29/0.63  thf(decl_129, type, subsetemptysetimpeq: $o).
% 2.29/0.63  thf(decl_130, type, powersetI1: $o).
% 2.29/0.63  thf(decl_131, type, powersetE1: $o).
% 2.29/0.63  thf(decl_132, type, inPowerset: $o).
% 2.29/0.63  thf(decl_133, type, powersetsubset: $o).
% 2.29/0.63  thf(decl_134, type, sepInPowerset: $o).
% 2.29/0.63  thf(decl_135, type, sepSubset: $o).
% 2.29/0.63  thf(decl_136, type, binunion: $i > $i > $i).
% 2.29/0.63  thf(decl_137, type, binunionIL: $o).
% 2.29/0.63  thf(decl_138, type, upairset2IR: $o).
% 2.29/0.63  thf(decl_139, type, binunionIR: $o).
% 2.29/0.63  thf(decl_140, type, binunionEcases: $o).
% 2.29/0.63  thf(decl_141, type, binunionE: $o).
% 2.29/0.63  thf(decl_142, type, binunionLsub: $o).
% 2.29/0.63  thf(decl_143, type, binunionRsub: $o).
% 2.29/0.63  thf(decl_144, type, binintersect: $i > $i > $i).
% 2.29/0.63  thf(decl_145, type, binintersectI: $o).
% 2.29/0.63  thf(decl_146, type, binintersectSubset5: $o).
% 2.29/0.63  thf(decl_147, type, binintersectEL: $o).
% 2.29/0.63  thf(decl_148, type, binintersectLsub: $o).
% 2.29/0.63  thf(decl_149, type, binintersectSubset2: $o).
% 2.29/0.63  thf(decl_150, type, binintersectSubset3: $o).
% 2.29/0.63  thf(decl_151, type, binintersectER: $o).
% 2.29/0.63  thf(decl_152, type, disjointsetsI1: $o).
% 2.29/0.63  thf(decl_153, type, binintersectRsub: $o).
% 2.29/0.63  thf(decl_154, type, binintersectSubset4: $o).
% 2.29/0.63  thf(decl_155, type, binintersectSubset1: $o).
% 2.29/0.63  thf(decl_156, type, bs114d: $o).
% 2.29/0.63  thf(decl_158, type, setminus: $i > $i > $i).
% 2.29/0.63  thf(decl_159, type, setminusI: $o).
% 2.29/0.63  thf(decl_160, type, setminusEL: $o).
% 2.29/0.63  thf(decl_161, type, setminusER: $o).
% 2.29/0.63  thf(decl_162, type, setminusSubset2: $o).
% 2.29/0.63  thf(decl_163, type, setminusERneg: $o).
% 2.29/0.63  thf(decl_164, type, setminusELneg: $o).
% 2.29/0.63  thf(decl_165, type, setminusILneg: $o).
% 2.29/0.63  thf(decl_166, type, setminusIRneg: $o).
% 2.29/0.63  thf(decl_167, type, setminusLsub: $o).
% 2.29/0.63  thf(decl_168, type, setminusSubset1: $o).
% 2.29/0.63  thf(decl_169, type, symdiff: $i > $i > $i).
% 2.29/0.63  thf(decl_170, type, symdiffE: $o).
% 2.29/0.63  thf(decl_171, type, symdiffI1: $o).
% 2.29/0.63  thf(decl_172, type, symdiffI2: $o).
% 2.29/0.63  thf(decl_173, type, symdiffIneg1: $o).
% 2.29/0.63  thf(decl_174, type, symdiffIneg2: $o).
% 2.29/0.63  thf(decl_175, type, iskpair: $i > $o).
% 2.29/0.63  thf(decl_176, type, secondinupair: $o).
% 2.29/0.63  thf(decl_177, type, setukpairIL: $o).
% 2.29/0.63  thf(decl_178, type, setukpairIR: $o).
% 2.29/0.63  thf(decl_179, type, kpairiskpair: $o).
% 2.29/0.63  thf(decl_180, type, kpair: $i > $i > $i).
% 2.29/0.63  thf(decl_181, type, kpairp: $o).
% 2.29/0.63  thf(decl_182, type, cartprod: $i > $i > $i).
% 2.29/0.63  thf(decl_183, type, singletonsubset: $o).
% 2.29/0.63  thf(decl_184, type, singletoninpowerset: $o).
% 2.29/0.63  thf(decl_185, type, singletoninpowunion: $o).
% 2.29/0.63  thf(decl_186, type, upairset2E: $o).
% 2.29/0.63  thf(decl_187, type, upairsubunion: $o).
% 2.29/0.63  thf(decl_188, type, upairinpowunion: $o).
% 2.29/0.63  thf(decl_189, type, ubforcartprodlem1: $o).
% 2.29/0.63  thf(decl_190, type, ubforcartprodlem2: $o).
% 2.29/0.63  thf(decl_191, type, ubforcartprodlem3: $o).
% 2.29/0.63  thf(decl_192, type, cartprodpairin: $o).
% 2.29/0.63  thf(decl_193, type, cartprodmempair1: $o).
% 2.29/0.63  thf(decl_194, type, cartprodmempair: $o).
% 2.29/0.63  thf(decl_195, type, setunionE2: $o).
% 2.29/0.63  thf(decl_196, type, setunionsingleton1: $o).
% 2.29/0.63  thf(decl_197, type, setunionsingleton2: $o).
% 2.29/0.63  thf(decl_198, type, setunionsingleton: $o).
% 2.29/0.63  thf(decl_199, type, singleton: $i > $o).
% 2.29/0.63  thf(decl_200, type, singletonprop: $o).
% 2.29/0.63  thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 2.29/0.63  thf(decl_202, type, ex1E1: $o).
% 2.29/0.63  thf(decl_203, type, ex1I: $o).
% 2.29/0.63  thf(decl_204, type, ex1I2: $o).
% 2.29/0.63  thf(decl_205, type, singletonsuniq: $o).
% 2.29/0.63  thf(decl_210, type, setukpairinjL1: $o).
% 2.29/0.63  thf(decl_211, type, kfstsingleton: $o).
% 2.29/0.63  thf(decl_212, type, theprop: $o).
% 2.29/0.63  thf(decl_213, type, kfst: $i > $i).
% 2.29/0.63  thf(decl_214, type, kfstpairEq: $o).
% 2.29/0.63  thf(decl_215, type, cartprodfstin: $o).
% 2.29/0.63  thf(decl_216, type, setukpairinjL2: $o).
% 2.29/0.63  thf(decl_217, type, setukpairinjL: $o).
% 2.29/0.63  thf(decl_218, type, setukpairinjR11: $o).
% 2.29/0.63  thf(decl_219, type, setukpairinjR12: $o).
% 2.29/0.63  thf(decl_220, type, setukpairinjR1: $o).
% 2.29/0.63  thf(decl_221, type, upairequniteq: $o).
% 2.29/0.63  thf(decl_222, type, setukpairinjR2: $o).
% 2.29/0.63  thf(decl_223, type, setukpairinjR: $o).
% 2.29/0.63  thf(decl_224, type, ksndsingleton: $o).
% 2.29/0.63  thf(decl_225, type, ksnd: $i > $i).
% 2.29/0.63  thf(decl_226, type, ksndpairEq: $o).
% 2.29/0.63  thf(decl_227, type, kpairsurjEq: $o).
% 2.29/0.63  thf(decl_228, type, cartprodsndin: $o).
% 2.29/0.63  thf(decl_229, type, cartprodpairmemEL: $o).
% 2.29/0.63  thf(decl_230, type, cartprodpairmemER: $o).
% 2.29/0.63  thf(decl_231, type, cartprodmempaircEq: $o).
% 2.29/0.63  thf(decl_232, type, cartprodfstpairEq: $o).
% 2.29/0.63  thf(decl_233, type, cartprodsndpairEq: $o).
% 2.29/0.63  thf(decl_234, type, cartprodpairsurjEq: $o).
% 2.29/0.63  thf(decl_235, type, breln: $i > $i > $i > $o).
% 2.29/0.63  thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 2.29/0.63  thf(decl_237, type, dpsetconstrI: $o).
% 2.29/0.63  thf(decl_238, type, dpsetconstrSub: $o).
% 2.29/0.63  thf(decl_239, type, setOfPairsIsBReln: $o).
% 2.29/0.63  thf(decl_240, type, dpsetconstrERa: $o).
% 2.29/0.63  thf(decl_241, type, dpsetconstrEL1: $o).
% 2.29/0.63  thf(decl_242, type, dpsetconstrEL2: $o).
% 2.29/0.63  thf(decl_243, type, dpsetconstrER: $o).
% 2.29/0.63  thf(decl_244, type, func: $i > $i > $i > $o).
% 2.29/0.63  thf(decl_245, type, funcSet: $i > $i > $i).
% 2.29/0.63  thf(decl_246, type, funcImageSingleton: $o).
% 2.29/0.63  thf(decl_247, type, apProp: $o).
% 2.29/0.63  thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 2.29/0.63  thf(decl_249, type, app: $o).
% 2.29/0.63  thf(decl_250, type, infuncsetfunc: $o).
% 2.29/0.63  thf(decl_251, type, ap2p: $o).
% 2.29/0.63  thf(decl_252, type, funcinfuncset: $o).
% 2.29/0.63  thf(decl_253, type, lamProp: $o).
% 2.29/0.63  thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 2.29/0.63  thf(decl_255, type, lamp: $o).
% 2.29/0.63  thf(decl_256, type, lam2p: $o).
% 2.29/0.63  thf(decl_257, type, brelnall1: $o).
% 2.29/0.63  thf(decl_258, type, brelnall2: $o).
% 2.29/0.63  thf(decl_259, type, ex1E2: $o).
% 2.29/0.63  thf(decl_260, type, funcGraphProp1: $o).
% 2.29/0.63  thf(decl_261, type, funcGraphProp3: $o).
% 2.29/0.63  thf(decl_262, type, funcGraphProp2: $o).
% 2.29/0.63  thf(decl_263, type, funcextLem: $o).
% 2.29/0.63  thf(decl_264, type, funcGraphProp4: $o).
% 2.29/0.63  thf(decl_265, type, subbreln: $o).
% 2.29/0.63  thf(decl_266, type, eqbreln: $o).
% 2.29/0.63  thf(decl_267, type, funcext: $o).
% 2.29/0.63  thf(decl_268, type, funcext2: $o).
% 2.29/0.63  thf(decl_269, type, ap2apEq1: $o).
% 2.29/0.63  thf(decl_270, type, ap2apEq2: $o).
% 2.29/0.63  thf(decl_271, type, beta1: $o).
% 2.29/0.63  thf(decl_272, type, eta1: $o).
% 2.29/0.63  thf(decl_273, type, lam2lamEq: $o).
% 2.29/0.63  thf(decl_274, type, beta2: $o).
% 2.29/0.63  thf(decl_275, type, eta2: $o).
% 2.29/0.63  thf(decl_276, type, iffalseProp1: $o).
% 2.29/0.63  thf(decl_277, type, iffalseProp2: $o).
% 2.29/0.63  thf(decl_278, type, iftrueProp1: $o).
% 2.29/0.63  thf(decl_279, type, iftrueProp2: $o).
% 2.29/0.63  thf(decl_280, type, ifSingleton: $o).
% 2.29/0.63  thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 2.29/0.63  thf(decl_282, type, ifp: $o).
% 2.29/0.63  thf(decl_283, type, theeq: $o).
% 2.29/0.63  thf(decl_284, type, iftrue: $o).
% 2.29/0.63  thf(decl_285, type, iffalse: $o).
% 2.29/0.63  thf(decl_286, type, iftrueorfalse: $o).
% 2.29/0.63  thf(decl_287, type, binintersectT_lem: $o).
% 2.29/0.63  thf(decl_288, type, binunionT_lem: $o).
% 2.29/0.63  thf(decl_289, type, powersetT_lem: $o).
% 2.29/0.63  thf(decl_290, type, setminusT_lem: $o).
% 2.29/0.63  thf(decl_291, type, complementT_lem: $o).
% 2.29/0.63  thf(decl_292, type, setextT: $o).
% 2.29/0.63  thf(decl_293, type, subsetTI: $o).
% 2.29/0.63  thf(decl_294, type, powersetTI1: $o).
% 2.29/0.63  thf(decl_295, type, powersetTE1: $o).
% 2.29/0.63  thf(decl_296, type, complementTI1: $o).
% 2.29/0.63  thf(decl_297, type, complementTE1: $o).
% 2.29/0.64  thf(decl_298, type, binintersectTELcontra: $o).
% 2.29/0.64  thf(decl_299, type, binintersectTERcontra: $o).
% 2.29/0.64  thf(decl_300, type, contrasubsetT: $o).
% 2.29/0.64  thf(decl_301, type, contrasubsetT1: $o).
% 2.29/0.64  thf(decl_302, type, contrasubsetT2: $o).
% 2.29/0.64  thf(decl_303, type, contrasubsetT3: $o).
% 2.29/0.64  thf(decl_304, type, doubleComplementI1: $o).
% 2.29/0.64  thf(decl_305, type, doubleComplementE1: $o).
% 2.29/0.64  thf(decl_306, type, doubleComplementSub1: $o).
% 2.29/0.64  thf(decl_307, type, doubleComplementSub2: $o).
% 2.29/0.64  thf(decl_308, type, doubleComplementEq: $o).
% 2.29/0.64  thf(decl_309, type, complementTnotintersectT: $o).
% 2.29/0.64  thf(decl_310, type, complementImpComplementIntersect: $o).
% 2.29/0.64  thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 2.29/0.64  thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 2.29/0.64  thf(decl_313, type, contraSubsetComplement: $o).
% 2.29/0.64  thf(decl_314, type, complementTcontraSubset: $o).
% 2.29/0.64  thf(decl_315, type, binunionTILcontra: $o).
% 2.29/0.64  thf(decl_316, type, binunionTIRcontra: $o).
% 2.29/0.64  thf(decl_317, type, inIntersectImpInUnion: $o).
% 2.29/0.64  thf(decl_318, type, inIntersectImpInUnion2: $o).
% 2.29/0.64  thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 2.29/0.64  thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 2.29/0.64  thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 2.29/0.64  thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 2.29/0.64  thf(decl_323, type, binunionTE: $o).
% 2.29/0.64  thf(decl_324, type, binunionTEcontra: $o).
% 2.29/0.64  thf(decl_325, type, demorgan2a1: $o).
% 2.29/0.64  thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 2.29/0.64  thf(decl_327, type, demorgan2a2: $o).
% 2.29/0.64  thf(decl_328, type, demorgan1a: $o).
% 2.29/0.64  thf(decl_329, type, demorgan1b: $o).
% 2.29/0.64  thf(decl_330, type, demorgan1: $o).
% 2.29/0.64  thf(decl_331, type, demorgan2a: $o).
% 2.29/0.64  thf(decl_332, type, demorgan2b2: $o).
% 2.29/0.64  thf(decl_333, type, demorgan2b: $o).
% 2.29/0.64  thf(decl_334, type, demorgan2: $o).
% 2.29/0.64  thf(decl_335, type, woz13rule0: $o).
% 2.29/0.64  thf(decl_336, type, woz13rule1: $o).
% 2.29/0.64  thf(decl_337, type, woz13rule2: $o).
% 2.29/0.64  thf(decl_338, type, woz13rule3: $o).
% 2.29/0.64  thf(decl_339, type, woz13rule4: $o).
% 2.29/0.64  thf(decl_340, type, woz1_1: $o).
% 2.29/0.64  thf(decl_341, type, woz1_2: $o).
% 2.29/0.64  thf(decl_342, type, woz1_3: $o).
% 2.29/0.64  thf(decl_343, type, epred1_0: $o).
% 2.29/0.64  thf(decl_344, type, esk1_2: $i > $i > $i).
% 2.29/0.64  thf(decl_345, type, esk2_2: $i > $i > $i).
% 2.29/0.64  thf(decl_346, type, esk3_2: $i > $i > $i).
% 2.29/0.64  thf(decl_347, type, esk4_1: $i > $i).
% 2.29/0.64  thf(decl_348, type, esk5_2: ($i > $i > $o) > $i > $i).
% 2.29/0.64  thf(decl_349, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 2.29/0.64  thf(decl_350, type, esk7_2: ($i > $i > $o) > $i > $i).
% 2.29/0.64  thf(decl_351, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 2.29/0.64  thf(decl_352, type, esk9_1: $i > $i).
% 2.29/0.64  thf(decl_353, type, esk10_2: ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_354, type, esk11_2: ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_355, type, esk12_1: ($i > $o) > $i).
% 2.29/0.64  thf(decl_356, type, esk13_2: ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_357, type, esk14_1: ($i > $o) > $i).
% 2.29/0.64  thf(decl_358, type, esk15_2: $i > $i > $i).
% 2.29/0.64  thf(decl_359, type, esk16_2: $i > $i > $i).
% 2.29/0.64  thf(decl_360, type, esk17_1: $i > $i).
% 2.29/0.64  thf(decl_361, type, esk18_1: $i > $i).
% 2.29/0.64  thf(decl_362, type, esk19_1: $i > $i).
% 2.29/0.64  thf(decl_363, type, esk20_2: $i > $i > $i).
% 2.29/0.64  thf(decl_364, type, esk21_3: $i > $i > $o > $i).
% 2.29/0.64  thf(decl_365, type, esk22_2: ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_366, type, esk23_1: ($i > $o) > $i).
% 2.29/0.64  thf(decl_367, type, esk24_1: $i > $i).
% 2.29/0.64  thf(decl_368, type, esk25_2: $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_369, type, esk26_2: $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_370, type, esk27_2: $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_371, type, esk28_2: $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_372, type, esk29_2: $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_373, type, esk30_2: $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_374, type, esk31_2: ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_375, type, esk32_1: ($i > $o) > $i).
% 2.29/0.64  thf(decl_376, type, esk33_1: ($i > $o) > $i).
% 2.29/0.64  thf(decl_377, type, esk34_1: ($i > $o) > $i).
% 2.29/0.64  thf(decl_378, type, esk35_1: ($i > $o) > $i).
% 2.29/0.64  thf(decl_379, type, esk36_2: ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_380, type, esk37_1: ($i > $o) > $i).
% 2.29/0.64  thf(decl_381, type, esk38_2: ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_382, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 2.29/0.64  thf(decl_383, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 2.29/0.64  thf(decl_384, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_385, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 2.29/0.64  thf(decl_386, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_387, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 2.29/0.64  thf(decl_388, type, esk45_2: ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_389, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 2.29/0.64  thf(decl_390, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 2.29/0.64  thf(decl_391, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_392, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_393, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.29/0.64  thf(decl_394, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.29/0.64  thf(decl_395, type, esk52_2: $i > $i > $i).
% 2.29/0.64  thf(decl_396, type, esk53_2: $i > $i > $i).
% 2.29/0.64  thf(decl_397, type, esk54_2: $i > $i > $i).
% 2.29/0.64  thf(decl_398, type, esk55_3: $i > $i > $i > $i).
% 2.29/0.64  thf(decl_399, type, esk56_3: $i > $i > $i > $i).
% 2.29/0.64  thf(decl_400, type, esk57_2: $i > $i > $i).
% 2.29/0.64  thf(decl_401, type, esk58_2: $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_402, type, esk59_2: $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_403, type, esk60_2: $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_404, type, esk61_3: $i > ($i > $o) > $i > $i).
% 2.29/0.64  thf(decl_405, type, esk62_2: $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_406, type, esk63_2: $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_407, type, esk64_3: $i > $i > ($i > $i) > $i).
% 2.29/0.64  thf(decl_408, type, esk65_3: $i > $i > ($i > $i) > $i).
% 2.29/0.64  thf(decl_409, type, esk66_3: $i > $i > ($i > $i) > $i).
% 2.29/0.64  thf(decl_410, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_411, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_412, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_413, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
% 2.29/0.64  thf(decl_414, type, esk71_4: $i > $i > $i > $i > $i).
% 2.29/0.64  thf(decl_415, type, esk72_4: $i > $i > $i > $i > $i).
% 2.29/0.64  thf(decl_416, type, esk73_4: $i > $i > $i > $i > $i).
% 2.29/0.64  thf(decl_417, type, esk74_4: $i > $i > $i > $i > $i).
% 2.29/0.64  thf(decl_418, type, esk75_4: $i > $i > $i > $i > $i).
% 2.29/0.64  thf(decl_419, type, esk76_4: $i > $i > $i > $i > $i).
% 2.29/0.64  thf(decl_420, type, esk77_4: $i > $i > $i > $i > $i).
% 2.29/0.64  thf(decl_421, type, esk78_4: $i > $i > $i > $i > $i).
% 2.29/0.64  thf(decl_422, type, esk79_4: $i > $i > $i > $i > $i).
% 2.29/0.64  thf(decl_423, type, esk80_3: $i > $i > ($i > $i) > $i).
% 2.29/0.64  thf(decl_424, type, esk81_3: $i > $i > ($i > $i) > $i).
% 2.29/0.64  thf(decl_425, type, esk82_3: $i > $i > ($i > $i) > $i).
% 2.29/0.64  thf(decl_426, type, esk83_3: $i > $i > $i > $i).
% 2.29/0.64  thf(decl_427, type, esk84_3: $i > $i > $i > $i).
% 2.29/0.64  thf(decl_428, type, esk85_3: $i > $i > $i > $i).
% 2.29/0.64  thf(decl_429, type, esk86_3: $i > $i > $i > $i).
% 2.29/0.64  thf(decl_430, type, esk87_0: $i).
% 2.29/0.64  thf(decl_431, type, esk88_0: $i).
% 2.29/0.64  thf(decl_432, type, esk89_0: $i).
% 2.29/0.64  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', replAx)).
% 2.29/0.64  thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', exu)).
% 2.29/0.64  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', descrp)).
% 2.29/0.64  thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', exuE1)).
% 2.29/0.64  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', exuE3e)).
% 2.29/0.64  thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', nonempty)).
% 2.29/0.64  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', nonemptyI)).
% 2.29/0.64  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', exuE2)).
% 2.29/0.64  thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', exuI1)).
% 2.29/0.64  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', exuI3)).
% 2.29/0.64  thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', exuI2)).
% 2.29/0.64  thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', exuE3u)).
% 2.29/0.64  thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', exu__Cong)).
% 2.29/0.64  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', exuEu)).
% 2.29/0.64  thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', descr__Cong)).
% 2.29/0.64  thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ex1E1)).
% 2.29/0.64  thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ex1)).
% 2.29/0.64  thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ex1I)).
% 2.29/0.64  thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ex1I2)).
% 2.29/0.64  thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setOfPairsIsBReln)).
% 2.29/0.64  thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', breln)).
% 2.29/0.64  thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ex1E2)).
% 2.29/0.64  thf(woz1_4, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', woz1_4)).
% 2.29/0.64  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', dsetconstrI)).
% 2.29/0.64  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', dsetconstrEL)).
% 2.29/0.64  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', dsetconstrER)).
% 2.29/0.64  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setbeta)).
% 2.29/0.64  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', nonemptyE1)).
% 2.29/0.64  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', nonemptyI1)).
% 2.29/0.64  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setoftrueEq)).
% 2.29/0.64  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', nonemptyImpWitness)).
% 2.29/0.64  thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', emptyE1)).
% 2.29/0.64  thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', dsetconstr__Cong)).
% 2.29/0.64  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', sepInPowerset)).
% 2.29/0.64  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', sepSubset)).
% 2.29/0.64  thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', singletonprop)).
% 2.29/0.64  thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', kfstsingleton)).
% 2.29/0.64  thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ksndsingleton)).
% 2.29/0.64  thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', dpsetconstrI)).
% 2.29/0.64  thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', dpsetconstrSub)).
% 2.29/0.64  thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', dpsetconstrERa)).
% 2.29/0.64  thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', dpsetconstrEL1)).
% 2.29/0.64  thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', dpsetconstrEL2)).
% 2.29/0.64  thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', dpsetconstrER)).
% 2.29/0.64  thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', funcImageSingleton)).
% 2.29/0.64  thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', apProp)).
% 2.29/0.64  thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', lamProp)).
% 2.29/0.64  thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', lamp)).
% 2.29/0.64  thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', lam2p)).
% 2.29/0.64  thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', brelnall1)).
% 2.29/0.64  thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', brelnall2)).
% 2.29/0.64  thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', subbreln)).
% 2.29/0.64  thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', eqbreln)).
% 2.29/0.64  thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', beta1)).
% 2.29/0.64  thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', eta1)).
% 2.29/0.64  thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', lam2lamEq)).
% 2.29/0.64  thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', beta2)).
% 2.29/0.64  thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', eta2)).
% 2.29/0.64  thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', iffalseProp1)).
% 2.29/0.64  thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', iffalseProp2)).
% 2.29/0.64  thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', iftrueProp1)).
% 2.29/0.64  thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', iftrueProp2)).
% 2.29/0.64  thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ifSingleton)).
% 2.29/0.64  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setextAx)).
% 2.29/0.64  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', emptysetAx)).
% 2.29/0.64  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setadjoinAx)).
% 2.29/0.64  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', powersetAx)).
% 2.29/0.64  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setunionAx)).
% 2.29/0.64  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', omega0Ax)).
% 2.29/0.64  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', omegaSAx)).
% 2.29/0.64  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', omegaIndAx)).
% 2.29/0.64  thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', foundationAx)).
% 2.29/0.64  thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', wellorderingAx)).
% 2.29/0.64  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', prop2setE)).
% 2.29/0.64  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', emptysetE)).
% 2.29/0.64  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', emptysetimpfalse)).
% 2.29/0.64  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', notinemptyset)).
% 2.29/0.64  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setext)).
% 2.29/0.64  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', emptyI)).
% 2.29/0.64  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', noeltsimpempty)).
% 2.29/0.64  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setadjoinIL)).
% 2.29/0.64  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', emptyinunitempty)).
% 2.29/0.64  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setadjoinIR)).
% 2.29/0.64  thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setadjoinE)).
% 2.29/0.64  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setadjoinOr)).
% 2.29/0.64  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', powersetI)).
% 2.29/0.64  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', emptyinPowerset)).
% 2.29/0.64  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', emptyInPowerset)).
% 2.29/0.64  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', powersetE)).
% 2.29/0.64  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setunionI)).
% 2.29/0.64  thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setunionE)).
% 2.29/0.64  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', subPowSU)).
% 2.29/0.64  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', uniqinunit)).
% 2.29/0.64  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', notinsingleton)).
% 2.29/0.64  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', eqinunit)).
% 2.29/0.64  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', singletonsswitch)).
% 2.29/0.64  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', upairsetE)).
% 2.29/0.64  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', upairsetIL)).
% 2.29/0.64  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', upairsetIR)).
% 2.29/0.64  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', vacuousDall)).
% 2.29/0.64  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', quantDeMorgan1)).
% 2.29/0.64  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', quantDeMorgan2)).
% 2.29/0.64  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', quantDeMorgan3)).
% 2.29/0.64  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', quantDeMorgan4)).
% 2.29/0.64  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', prop2setI)).
% 2.29/0.64  thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', prop2set2propI)).
% 2.29/0.64  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', notdexE)).
% 2.29/0.64  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', notdallE)).
% 2.29/0.64  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', inCongP)).
% 2.29/0.64  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', in__Cong)).
% 2.29/0.64  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', emptyset__Cong)).
% 2.29/0.64  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setadjoin__Cong)).
% 2.29/0.64  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', powerset__Cong)).
% 2.29/0.64  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setunion__Cong)).
% 2.29/0.64  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', omega__Cong)).
% 2.29/0.64  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', subsetI1)).
% 2.29/0.64  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', eqimpsubset2)).
% 2.29/0.64  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', eqimpsubset1)).
% 2.29/0.64  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', subsetI2)).
% 2.29/0.64  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', emptysetsubset)).
% 2.29/0.64  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', subsetE)).
% 2.29/0.64  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', subsetE2)).
% 2.29/0.64  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', notsubsetI)).
% 2.29/0.64  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', notequalI1)).
% 2.29/0.64  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', notequalI2)).
% 2.29/0.64  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', subsetRefl)).
% 2.29/0.64  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', subsetTrans)).
% 2.29/0.64  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setadjoinSub)).
% 2.29/0.64  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setadjoinSub2)).
% 2.29/0.64  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', subset2powerset)).
% 2.29/0.64  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setextsub)).
% 2.29/0.64  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', subsetemptysetimpeq)).
% 2.29/0.64  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', powersetI1)).
% 2.29/0.64  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', powersetE1)).
% 2.29/0.64  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', inPowerset)).
% 2.29/0.64  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', powersetsubset)).
% 2.29/0.64  thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binunionIL)).
% 2.29/0.64  thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', upairset2IR)).
% 2.29/0.64  thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binunionIR)).
% 2.29/0.64  thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binunionEcases)).
% 2.29/0.64  thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binunionE)).
% 2.29/0.64  thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binunionLsub)).
% 2.29/0.64  thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binunionRsub)).
% 2.29/0.64  thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectI)).
% 2.29/0.64  thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectSubset5)).
% 2.29/0.64  thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectEL)).
% 2.29/0.64  thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectLsub)).
% 2.29/0.64  thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectSubset2)).
% 2.29/0.64  thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectSubset3)).
% 2.29/0.64  thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectER)).
% 2.29/0.64  thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', disjointsetsI1)).
% 2.29/0.64  thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectRsub)).
% 2.29/0.64  thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectSubset4)).
% 2.29/0.64  thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectSubset1)).
% 2.29/0.64  thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', bs114d)).
% 2.29/0.64  thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setminusI)).
% 2.29/0.64  thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setminusEL)).
% 2.29/0.64  thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setminusER)).
% 2.29/0.64  thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setminusSubset2)).
% 2.29/0.64  thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setminusERneg)).
% 2.29/0.64  thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setminusELneg)).
% 2.29/0.64  thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setminusILneg)).
% 2.29/0.64  thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setminusIRneg)).
% 2.29/0.64  thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setminusLsub)).
% 2.29/0.64  thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setminusSubset1)).
% 2.29/0.64  thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', symdiffE)).
% 2.29/0.64  thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', symdiffI1)).
% 2.29/0.64  thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', symdiffI2)).
% 2.29/0.64  thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', symdiffIneg1)).
% 2.29/0.64  thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', symdiffIneg2)).
% 2.29/0.64  thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', secondinupair)).
% 2.29/0.64  thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setukpairIL)).
% 2.29/0.64  thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setukpairIR)).
% 2.29/0.64  thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', kpairiskpair)).
% 2.29/0.64  thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', kpairp)).
% 2.29/0.64  thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', singletonsubset)).
% 2.29/0.64  thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', singletoninpowerset)).
% 2.29/0.64  thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', singletoninpowunion)).
% 2.29/0.64  thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', upairset2E)).
% 2.29/0.64  thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', upairsubunion)).
% 2.29/0.64  thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', upairinpowunion)).
% 2.29/0.64  thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ubforcartprodlem1)).
% 2.29/0.64  thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ubforcartprodlem2)).
% 2.29/0.64  thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ubforcartprodlem3)).
% 2.29/0.64  thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', cartprodpairin)).
% 2.29/0.64  thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', cartprodmempair1)).
% 2.29/0.64  thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', cartprodmempair)).
% 2.29/0.64  thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setunionE2)).
% 2.29/0.64  thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setunionsingleton1)).
% 2.29/0.64  thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setunionsingleton2)).
% 2.29/0.64  thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setunionsingleton)).
% 2.29/0.64  thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', singletonsuniq)).
% 2.29/0.64  thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setukpairinjL1)).
% 2.29/0.64  thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', theprop)).
% 2.29/0.64  thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', kfstpairEq)).
% 2.29/0.64  thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', cartprodfstin)).
% 2.29/0.64  thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setukpairinjL2)).
% 2.29/0.64  thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setukpairinjL)).
% 2.29/0.64  thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setukpairinjR11)).
% 2.29/0.64  thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setukpairinjR12)).
% 2.29/0.64  thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setukpairinjR1)).
% 2.29/0.64  thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', upairequniteq)).
% 2.29/0.64  thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setukpairinjR2)).
% 2.29/0.64  thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setukpairinjR)).
% 2.29/0.64  thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ksndpairEq)).
% 2.29/0.64  thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', kpairsurjEq)).
% 2.29/0.64  thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', cartprodsndin)).
% 2.29/0.64  thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', cartprodpairmemEL)).
% 2.29/0.64  thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', cartprodpairmemER)).
% 2.29/0.64  thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', cartprodmempaircEq)).
% 2.29/0.64  thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', cartprodfstpairEq)).
% 2.29/0.64  thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', cartprodsndpairEq)).
% 2.29/0.64  thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', cartprodpairsurjEq)).
% 2.29/0.64  thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', app)).
% 2.29/0.64  thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', infuncsetfunc)).
% 2.29/0.64  thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ap2p)).
% 2.29/0.64  thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', funcinfuncset)).
% 2.29/0.64  thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', funcGraphProp1)).
% 2.29/0.64  thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', funcGraphProp3)).
% 2.29/0.64  thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', funcGraphProp2)).
% 2.29/0.64  thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', funcextLem)).
% 2.29/0.64  thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', funcGraphProp4)).
% 2.29/0.64  thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', funcext)).
% 2.29/0.64  thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', funcext2)).
% 2.29/0.64  thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ap2apEq1)).
% 2.29/0.64  thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ap2apEq2)).
% 2.29/0.64  thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', ifp)).
% 2.29/0.64  thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', theeq)).
% 2.29/0.64  thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', iftrue)).
% 2.29/0.64  thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', iffalse)).
% 2.29/0.64  thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', iftrueorfalse)).
% 2.29/0.64  thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectT_lem)).
% 2.29/0.64  thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binunionT_lem)).
% 2.29/0.64  thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', powersetT_lem)).
% 2.29/0.64  thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setminusT_lem)).
% 2.29/0.64  thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', complementT_lem)).
% 2.29/0.64  thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', setextT)).
% 2.29/0.64  thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', subsetTI)).
% 2.29/0.64  thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', powersetTI1)).
% 2.29/0.64  thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', powersetTE1)).
% 2.29/0.64  thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', complementTI1)).
% 2.29/0.64  thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', complementTE1)).
% 2.29/0.64  thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectTELcontra)).
% 2.29/0.64  thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binintersectTERcontra)).
% 2.29/0.64  thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', contrasubsetT)).
% 2.29/0.64  thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', contrasubsetT1)).
% 2.29/0.64  thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', contrasubsetT2)).
% 2.29/0.64  thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', contrasubsetT3)).
% 2.29/0.64  thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', doubleComplementI1)).
% 2.29/0.64  thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', doubleComplementE1)).
% 2.29/0.64  thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', doubleComplementSub1)).
% 2.29/0.64  thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', doubleComplementSub2)).
% 2.29/0.64  thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', doubleComplementEq)).
% 2.29/0.64  thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', complementTnotintersectT)).
% 2.29/0.64  thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', complementImpComplementIntersect)).
% 2.29/0.64  thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', complementSubsetComplementIntersect)).
% 2.29/0.64  thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', complementInPowersetComplementIntersect)).
% 2.29/0.64  thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', contraSubsetComplement)).
% 2.29/0.64  thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', complementTcontraSubset)).
% 2.29/0.64  thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binunionTILcontra)).
% 2.29/0.64  thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binunionTIRcontra)).
% 2.29/0.64  thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', inIntersectImpInUnion)).
% 2.29/0.64  thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', inIntersectImpInUnion2)).
% 2.29/0.64  thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', inIntersectImpInIntersectUnions)).
% 2.29/0.64  thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', intersectInPowersetIntersectUnions)).
% 2.29/0.64  thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', inComplementUnionImpNotIn1)).
% 2.29/0.64  thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', inComplementUnionImpInComplement1)).
% 2.29/0.64  thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binunionTE)).
% 2.29/0.64  thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', binunionTEcontra)).
% 2.29/0.64  thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', demorgan2a1)).
% 2.29/0.64  thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', complementUnionInPowersetComplement)).
% 2.29/0.64  thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', demorgan2a2)).
% 2.29/0.64  thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', demorgan1a)).
% 2.29/0.64  thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', demorgan1b)).
% 2.29/0.64  thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', demorgan1)).
% 2.29/0.64  thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', demorgan2a)).
% 2.29/0.64  thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', demorgan2b2)).
% 2.29/0.64  thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', demorgan2b)).
% 2.29/0.64  thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', demorgan2)).
% 2.29/0.64  thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', woz13rule0)).
% 2.29/0.64  thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', woz13rule1)).
% 2.29/0.64  thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', woz13rule2)).
% 2.29/0.64  thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', woz13rule3)).
% 2.29/0.64  thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', woz13rule4)).
% 2.29/0.64  thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', woz1_1)).
% 2.29/0.64  thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', woz1_2)).
% 2.29/0.64  thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.r1KPT5FzpG/E---3.1_797879.p', woz1_3)).
% 2.29/0.64  thf(c_0_287, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 2.29/0.64  thf(c_0_288, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 2.29/0.64  thf(c_0_289, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 2.29/0.64  thf(c_0_290, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 2.29/0.64  thf(c_0_291, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 2.29/0.64  thf(c_0_292, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 2.29/0.64  thf(c_0_293, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 2.29/0.64  thf(c_0_294, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 2.29/0.64  thf(c_0_295, 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])).
% 2.29/0.64  thf(c_0_296, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 2.29/0.64  thf(c_0_297, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 2.29/0.64  thf(c_0_298, 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])).
% 2.29/0.64  thf(c_0_299, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 2.29/0.64  thf(c_0_300, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 2.29/0.64  thf(c_0_301, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 2.29/0.64  thf(c_0_302, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 2.29/0.64  thf(c_0_303, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 2.29/0.64  thf(c_0_304, 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])).
% 2.29/0.64  thf(c_0_305, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 2.29/0.64  thf(c_0_306, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 2.29/0.64  thf(c_0_307, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 2.29/0.64  thf(c_0_308, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 2.29/0.64  thf(c_0_309, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[woz1_4])).
% 2.29/0.64  thf(c_0_310, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X956:$i]:(((((X6 @ X2 @ X956)))&(![X957:$i]:(((((X6 @ X2 @ X957)))=>(((X956)=(X957)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_287, c_0_288])).
% 2.29/0.64  thf(c_0_311, plain, ((descrp)=(![X1:$i > $o]:((((?[X958:$i]:(((((X1 @ X958)))&(![X959:$i]:(((((X1 @ X959)))=>(((X958)=(X959))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_289, c_0_288])).
% 2.29/0.64  thf(c_0_312, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 2.29/0.64  thf(c_0_313, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 2.29/0.64  thf(c_0_314, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 2.29/0.64  thf(c_0_315, plain, ((exuE1)=(![X1:$i > $o]:((((?[X960:$i]:(((((X1 @ X960)))&(![X961:$i]:(((((X1 @ X961)))=>(((X960)=(X961))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_290, c_0_288])).
% 2.29/0.64  thf(c_0_316, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X962:$i]:(((((X1 @ X962)))&(![X963:$i]:(((((X1 @ X963)))=>(((X962)=(X963))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_291, c_0_288])).
% 2.29/0.64  thf(c_0_317, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 2.29/0.64  thf(c_0_318, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_292])).
% 2.29/0.64  thf(c_0_319, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_293, c_0_292])).
% 2.29/0.64  thf(c_0_320, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_292])).
% 2.29/0.64  thf(c_0_321, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 2.29/0.64  thf(c_0_322, plain, ((exuE2)=(![X1:$i > $o]:((((?[X964:$i]:(((((X1 @ X964)))&(![X965:$i]:(((((X1 @ X965)))=>(((X964)=(X965))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_294, c_0_288])).
% 2.29/0.64  thf(c_0_323, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_292])).
% 2.29/0.64  thf(c_0_324, 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])).
% 2.29/0.64  thf(c_0_325, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X966:$i]:(((((X1 @ X966)))&(![X967:$i]:(((((X1 @ X967)))=>(((X966)=(X967)))))))))))))), inference(apply_def,[status(thm)],[c_0_295, c_0_288])).
% 2.29/0.64  thf(c_0_326, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X968:$i]:(((((X1 @ X968)))&(![X969:$i]:(((((X1 @ X969)))=>(((X968)=(X969)))))))))))))))), inference(apply_def,[status(thm)],[c_0_296, c_0_288])).
% 2.29/0.64  thf(c_0_327, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X970:$i]:(((((X1 @ X970)))&(![X971:$i]:(((((X1 @ X971)))=>(((X970)=(X971)))))))))))))), inference(apply_def,[status(thm)],[c_0_297, c_0_288])).
% 2.29/0.64  thf(c_0_328, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X972:$i]:(((((X1 @ X972)))&(![X973:$i]:(((((X1 @ X973)))=>(((X972)=(X973))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_298, c_0_288])).
% 2.29/0.64  thf(c_0_329, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X974:$i]:(((((X1 @ X974)))&(![X975:$i]:(((((X1 @ X975)))=>(((X974)=(X975))))))))))<=>((?[X976:$i]:(((((X17 @ X976)))&(![X977:$i]:(((((X17 @ X977)))=>(((X976)=(X977)))))))))))))))), inference(apply_def,[status(thm)],[c_0_299, c_0_288])).
% 2.29/0.64  thf(c_0_330, plain, ((exuEu)=(![X1:$i > $o]:((((?[X978:$i]:(((((X1 @ X978)))&(![X979:$i]:(((((X1 @ X979)))=>(((X978)=(X979))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_300, c_0_288])).
% 2.29/0.64  thf(c_0_331, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X980:$i]:(((((X1 @ X980)))&(![X981:$i]:(((((X1 @ X981)))=>(((X980)=(X981))))))))))=>((((?[X982:$i]:(((((X17 @ X982)))&(![X983:$i]:(((((X17 @ X983)))=>(((X982)=(X983))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_301, c_0_288])).
% 2.29/0.64  thf(c_0_332, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 2.29/0.64  thf(c_0_333, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 2.29/0.64  thf(c_0_334, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 2.29/0.64  thf(c_0_335, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 2.29/0.64  thf(c_0_336, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_302, c_0_303])).
% 2.29/0.64  thf(c_0_337, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_303])).
% 2.29/0.64  thf(c_0_338, 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)))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_305, c_0_303])).
% 2.29/0.64  thf(c_0_339, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 2.29/0.64  thf(c_0_340, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 2.29/0.64  thf(c_0_341, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 2.29/0.64  thf(c_0_342, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 2.29/0.64  thf(c_0_343, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_306, c_0_307])).
% 2.29/0.64  thf(c_0_344, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 2.29/0.64  thf(c_0_345, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 2.29/0.64  thf(c_0_346, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 2.29/0.64  thf(c_0_347, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 2.29/0.64  thf(c_0_348, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 2.29/0.64  thf(c_0_349, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 2.29/0.64  thf(c_0_350, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 2.29/0.64  thf(c_0_351, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 2.29/0.64  thf(c_0_352, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 2.29/0.64  thf(c_0_353, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_307])).
% 2.29/0.64  thf(c_0_354, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_307])).
% 2.29/0.64  thf(c_0_355, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_308, c_0_303])).
% 2.29/0.64  thf(c_0_356, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_307])).
% 2.29/0.64  thf(c_0_357, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_307])).
% 2.29/0.64  thf(c_0_358, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
% 2.29/0.64  thf(c_0_359, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
% 2.29/0.64  thf(c_0_360, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
% 2.29/0.64  thf(c_0_361, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
% 2.29/0.64  thf(c_0_362, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
% 2.29/0.64  thf(c_0_363, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 2.29/0.64  thf(c_0_364, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 2.29/0.64  thf(c_0_365, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 2.29/0.64  thf(c_0_366, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 2.29/0.64  thf(c_0_367, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 2.29/0.64  thf(c_0_368, plain, ((epred1_0)<=>![X1013:$i]:(?[X1014:$i]:((((![X1015:$i]:(((in @ X1015 @ X1014)=>![X1016:$i]:(((in @ X1016 @ X1015)=>(in @ X1016 @ X1013)))))&![X1017:$i, X1018:$i]:((((in @ X1017 @ X1013)&(in @ X1018 @ X1013))=>(![X1019:$i]:(((in @ X1019 @ X1014)=>((in @ X1017 @ X1019)<=>(in @ X1018 @ X1019))))=>((X1017)=(X1018))))))&![X1020:$i, X1021:$i]:((((in @ X1020 @ X1014)&(in @ X1021 @ X1014))=>(![X1022:$i]:(((in @ X1022 @ X1020)=>(in @ X1022 @ X1021)))|![X1023:$i]:(((in @ X1023 @ X1021)=>(in @ X1023 @ X1020)))))))&![X1024:$i]:(((![X1025:$i]:(((in @ X1025 @ X1024)=>(in @ X1025 @ X1013)))&?[X1026:$i]:((in @ X1026 @ X1024)))=>?[X1027:$i, X1028:$i]:(((((in @ X1027 @ X1014)&(in @ X1028 @ X1024))&~(?[X1029:$i]:(((in @ X1029 @ X1027)&(in @ X1029 @ X1024)))))&![X1030:$i]:(((in @ X1030 @ X1014)=>(![X1031:$i]:(((in @ X1031 @ X1030)=>(in @ X1031 @ X1027)))|(in @ X1028 @ X1030)))))))))))), introduced(definition)).
% 2.29/0.64  thf(c_0_369, negated_conjecture, ~((![X984:$i, X985:$i]:((![X986:$i]:(((in @ X986 @ X984)<=>(in @ X986 @ X985)))=>((X984)=(X985))))=>(![X987:$i]:(~(in @ X987 @ emptyset))=>(![X988:$i, X989:$i, X990:$i]:(((in @ X990 @ (setadjoin @ X988 @ X989))<=>(((X990)=(X988))|(in @ X990 @ X989))))=>(![X991:$i, X992:$i]:(((in @ X992 @ (powerset @ X991))<=>![X993:$i]:(((in @ X993 @ X992)=>(in @ X993 @ X991)))))=>(![X994:$i, X995:$i]:(((in @ X995 @ (setunion @ X994))<=>?[X996:$i]:(((in @ X995 @ X996)&(in @ X996 @ X994)))))=>((in @ emptyset @ omega)=>(![X997:$i]:(((in @ X997 @ omega)=>(in @ (setadjoin @ X997 @ X997) @ omega)))=>(![X998:$i]:((((in @ emptyset @ X998)&![X999:$i]:((((in @ X999 @ omega)&(in @ X999 @ X998))=>(in @ (setadjoin @ X999 @ X999) @ X998))))=>![X1000:$i]:(((in @ X1000 @ omega)=>(in @ X1000 @ X998)))))=>(![X1001:$i > $i > $o, X1002:$i]:((![X1003:$i]:(((in @ X1003 @ X1002)=>?[X1004:$i]:(((X1001 @ X1003 @ X1004)&![X1005:$i]:(((X1001 @ X1003 @ X1005)=>((X1004)=(X1005))))))))=>?[X1006:$i]:(![X1007:$i]:(((in @ X1007 @ X1006)<=>?[X1008:$i]:(((in @ X1008 @ X1002)&(X1001 @ X1008 @ X1007))))))))=>(![X1009:$i]:((?[X1010:$i]:((in @ X1010 @ X1009))=>?[X1011:$i]:(((in @ X1011 @ X1009)&~(?[X1012:$i]:(((in @ X1012 @ X1011)&(in @ X1012 @ X1009))))))))=>((epred1_0)=>(![X1032:$i > $o]:((?[X1033:$i]:(((X1032 @ X1033)&![X1034:$i]:(((X1032 @ X1034)=>((X1033)=(X1034))))))=>(X1032 @ (descr @ (^[Z0:$i]:(X1032 @ Z0))))))=>(![X1035:$i, X1036:$i > $o, X1037:$i]:(((in @ X1037 @ X1035)=>((X1036 @ X1037)=>(in @ X1037 @ (dsetconstr @ X1035 @ X1036)))))=>(![X1038:$i, X1039:$i > $o, X1040:$i]:(((in @ X1040 @ (dsetconstr @ X1038 @ X1039))=>(in @ X1040 @ X1038)))=>(![X1041:$i, X1042:$i > $o, X1043:$i]:(((in @ X1043 @ (dsetconstr @ X1041 @ X1042))=>(X1042 @ X1043)))=>(![X1044:$i > $o]:((?[X1045:$i]:(((X1044 @ X1045)&![X1046:$i]:(((X1044 @ X1046)=>((X1045)=(X1046))))))=>?[X1047:$i]:(((X1044 @ X1047)&![X1048:$i]:(((X1044 @ X1048)=>((X1047)=(X1048))))))))=>(![X1049:$o, X1050:$i]:(((in @ X1050 @ (prop2set @ ((X1049))))=>(X1049)))=>(![X1051:$i]:(((in @ X1051 @ emptyset)=>![X1052:$o]:((X1052))))=>(![X1053:$i]:(((in @ X1053 @ emptyset)=>~($true)))=>(![X1054:$i]:(~(in @ X1054 @ emptyset))=>(![X1055:$i > $o]:((?[X1056:$i]:(((X1055 @ X1056)&![X1057:$i]:(((X1055 @ X1057)=>((X1056)=(X1057))))))=>?[X1058:$i]:((X1055 @ X1058))))=>(![X1059:$i, X1060:$i]:((![X1061:$i]:(((in @ X1061 @ X1059)=>(in @ X1061 @ X1060)))=>(![X1062:$i]:(((in @ X1062 @ X1060)=>(in @ X1062 @ X1059)))=>((X1059)=(X1060)))))=>(![X1063:$i]:((![X1064:$i]:(~(in @ X1064 @ X1063))=>((X1063)=(emptyset))))=>(![X1065:$i]:((![X1066:$i]:(~(in @ X1066 @ X1065))=>((X1065)=(emptyset))))=>(![X1067:$i, X1068:$i > $o, X1069:$i]:(((in @ X1069 @ X1067)=>((in @ X1069 @ (dsetconstr @ X1067 @ X1068))<=>(X1068 @ X1069))))=>(![X1070:$i]:((((X1070)!=(emptyset))=>?[X1071:$i]:((in @ X1071 @ X1070))))=>(![X1072:$i, X1073:$i > $o, X1074:$i]:(((in @ X1074 @ X1072)=>((X1073 @ X1074)=>((dsetconstr @ X1072 @ X1073)!=(emptyset)))))=>(![X1075:$i]:((?[X1076:$i]:((in @ X1076 @ X1075))=>((X1075)!=(emptyset))))=>(![X1077:$i, X1078:$i]:((in @ X1077 @ (setadjoin @ X1077 @ X1078)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1079:$i, X1080:$i, X1081:$i]:(((in @ X1081 @ X1080)=>(in @ X1081 @ (setadjoin @ X1079 @ X1080))))=>(![X1082:$i, X1083:$i, X1084:$i]:(((in @ X1084 @ (setadjoin @ X1082 @ X1083))=>![X1085:$o]:(((((X1084)=(X1082))=>(X1085))=>(((in @ X1084 @ X1083)=>(X1085))=>(X1085))))))=>(![X1086:$i, X1087:$i, X1088:$i]:(((in @ X1088 @ (setadjoin @ X1086 @ X1087))=>(((X1088)=(X1086))|(in @ X1088 @ X1087))))=>(![X1089:$i]:(((dsetconstr @ X1089 @ (^[Z0:$i]:($true)))=(X1089)))=>(![X1090:$i, X1091:$i]:((![X1092:$i]:(((in @ X1092 @ X1091)=>(in @ X1092 @ X1090)))=>(in @ X1091 @ (powerset @ X1090))))=>(![X1093:$i]:((in @ emptyset @ (powerset @ X1093)))=>(![X1094:$i]:((in @ emptyset @ (powerset @ X1094)))=>(![X1095:$i, X1096:$i, X1097:$i]:(((in @ X1096 @ (powerset @ X1095))=>((in @ X1097 @ X1096)=>(in @ X1097 @ X1095))))=>(![X1098:$i, X1099:$i, X1100:$i]:(((in @ X1099 @ X1100)=>((in @ X1100 @ X1098)=>(in @ X1099 @ (setunion @ X1098)))))=>(![X1101:$i, X1102:$i]:(((in @ X1102 @ (setunion @ X1101))=>![X1103:$o]:((![X1104:$i]:(((in @ X1102 @ X1104)=>((in @ X1104 @ X1101)=>(X1103))))=>(X1103)))))=>(![X1105:$i, X1106:$i]:(((in @ X1106 @ X1105)=>(in @ X1106 @ (powerset @ (setunion @ X1105)))))=>(![X1107:$i > $o]:((?[X1108:$i]:(((X1107 @ X1108)&![X1109:$i]:(((X1107 @ X1109)=>((X1108)=(X1109))))))=>?[X1110:$i]:(![X1111:$i]:(((X1107 @ X1111)<=>((X1111)=(X1110)))))))=>(![X1112:$i]:((((X1112)!=(emptyset))=>?[X1113:$i]:(((in @ X1113 @ X1112)&$true))))=>(![X1114:$i, X1115:$i]:(((in @ X1114 @ (setadjoin @ X1115 @ emptyset))=>((X1114)=(X1115))))=>(![X1116:$i, X1117:$i]:((((X1116)!=(X1117))=>~(in @ X1117 @ (setadjoin @ X1116 @ emptyset))))=>(![X1118:$i, X1119:$i]:((((X1118)=(X1119))=>(in @ X1118 @ (setadjoin @ X1119 @ emptyset))))=>(![X1120:$i, X1121:$i]:(((in @ X1120 @ (setadjoin @ X1121 @ emptyset))=>(in @ X1121 @ (setadjoin @ X1120 @ emptyset))))=>(![X1122:$i, X1123:$i, X1124:$i]:(((in @ X1124 @ (setadjoin @ X1122 @ (setadjoin @ X1123 @ emptyset)))=>(((X1124)=(X1122))|((X1124)=(X1123)))))=>(![X1125:$i, X1126:$i]:((in @ X1125 @ (setadjoin @ X1125 @ (setadjoin @ X1126 @ emptyset))))=>(![X1127:$i, X1128:$i]:((in @ X1128 @ (setadjoin @ X1127 @ (setadjoin @ X1128 @ emptyset))))=>(![X1129:$i, X1130:$i > $o]:((?[X1131:$i]:(((in @ X1131 @ X1129)&(X1130 @ X1131)))=>(((dsetconstr @ X1129 @ X1130)=(emptyset))=>~($true))))=>(![X1132:$i > $o, X1133:$i]:(((in @ X1133 @ emptyset)=>(X1132 @ X1133)))=>(![X1134:$i, X1135:$i > $o]:((~(![X1136:$i]:(((in @ X1136 @ X1134)=>(X1135 @ X1136))))=>?[X1137:$i]:(((in @ X1137 @ X1134)&~((X1135 @ X1137))))))=>(![X1138:$i, X1139:$i > $o]:((![X1140:$i]:(((in @ X1140 @ X1138)=>~((X1139 @ X1140))))=>~(?[X1141:$i]:(((in @ X1141 @ X1138)&(X1139 @ X1141))))))=>(![X1142:$i, X1143:$i > $o]:((~(?[X1144:$i]:(((in @ X1144 @ X1142)&(X1143 @ X1144))))=>![X1145:$i]:(((in @ X1145 @ X1142)=>~((X1143 @ X1145))))))=>(![X1146:$i, X1147:$i > $o]:((?[X1148:$i]:(((in @ X1148 @ X1146)&~((X1147 @ X1148))))=>~(![X1149:$i]:(((in @ X1149 @ X1146)=>(X1147 @ X1149))))))=>(![X1150:$o]:(((X1150)=>(in @ emptyset @ (prop2set @ ((X1150))))))=>(![X1151:$o]:(((X1151)=>(set2prop @ (prop2set @ ((X1151))))))=>(![X1152:$i, X1153:$i > $o]:((~(?[X1154:$i]:(((in @ X1154 @ X1152)&(X1153 @ X1154))))=>![X1155:$i]:(((in @ X1155 @ X1152)=>~((X1153 @ X1155))))))=>(![X1156:$i, X1157:$i > $o]:((~(![X1158:$i]:(((in @ X1158 @ X1156)=>(X1157 @ X1158))))=>?[X1159:$i]:(((in @ X1159 @ X1156)&~((X1157 @ X1159))))))=>(![X1160:$i > $o]:((?[X1161:$i]:(((X1160 @ X1161)&![X1162:$i]:(((X1160 @ X1162)=>((X1161)=(X1162))))))=>?[X1163:$i]:(((X1160 @ X1163)&![X1164:$i]:(((X1160 @ X1164)=>((X1163)=(X1164))))))))=>(![X1165:$i > $o]:((?[X1166:$i]:((X1165 @ X1166))=>(![X1167:$i, X1168:$i]:(((X1165 @ X1167)=>((X1165 @ X1168)=>((X1167)=(X1168)))))=>?[X1169:$i]:(((X1165 @ X1169)&![X1170:$i]:(((X1165 @ X1170)=>((X1169)=(X1170)))))))))=>(![X1171:$i > $o]:((?[X1172:$i]:(![X1173:$i]:(((X1171 @ X1173)<=>((X1173)=(X1172)))))=>?[X1174:$i]:(((X1171 @ X1174)&![X1175:$i]:(((X1171 @ X1175)=>((X1174)=(X1175))))))))=>(![X1176:$i, X1177:$i]:((((X1176)=(X1177))=>![X1178:$i, X1179:$i]:((((X1178)=(X1179))=>((in @ X1178 @ X1176)=>(in @ X1179 @ X1177))))))=>(![X1180:$i, X1181:$i]:((((X1180)=(X1181))=>![X1182:$i, X1183:$i]:((((X1182)=(X1183))=>((in @ X1182 @ X1180)<=>(in @ X1183 @ X1181))))))=>(![X1184:$i > $o]:((?[X1185:$i]:(((X1184 @ X1185)&![X1186:$i]:(((X1184 @ X1186)=>((X1185)=(X1186))))))=>![X1187:$i, X1188:$i]:(((X1184 @ X1187)=>((X1184 @ X1188)=>((X1187)=(X1188)))))))=>(![X1189:$i > $o, X1190:$i > $o]:((![X1191:$i, X1192:$i]:((((X1191)=(X1192))=>((X1189 @ X1191)<=>(X1190 @ X1192))))=>(?[X1193:$i]:(((X1189 @ X1193)&![X1194:$i]:(((X1189 @ X1194)=>((X1193)=(X1194))))))<=>?[X1195:$i]:(((X1190 @ X1195)&![X1196:$i]:(((X1190 @ X1196)=>((X1195)=(X1196)))))))))=>(((emptyset)=(emptyset))=>(![X1197:$i, X1198:$i]:((((X1197)=(X1198))=>![X1199:$i, X1200:$i]:((((X1199)=(X1200))=>((setadjoin @ X1197 @ X1199)=(setadjoin @ X1198 @ X1200))))))=>(![X1201:$i, X1202:$i]:((((X1201)=(X1202))=>((powerset @ X1201)=(powerset @ X1202))))=>(![X1203:$i, X1204:$i]:((((X1203)=(X1204))=>((setunion @ X1203)=(setunion @ X1204))))=>(((omega)=(omega))=>(![X1205:$i > $o]:((?[X1206:$i]:(((X1205 @ X1206)&![X1207:$i]:(((X1205 @ X1207)=>((X1206)=(X1207))))))=>![X1208:$i, X1209:$i]:(((X1205 @ X1208)=>((X1205 @ X1209)=>((X1208)=(X1209)))))))=>(![X1210:$i > $o, X1211:$i > $o]:((![X1212:$i, X1213:$i]:((((X1212)=(X1213))=>((X1210 @ X1212)<=>(X1211 @ X1213))))=>(?[X1214:$i]:(((X1210 @ X1214)&![X1215:$i]:(((X1210 @ X1215)=>((X1214)=(X1215))))))=>(?[X1216:$i]:(((X1211 @ X1216)&![X1217:$i]:(((X1211 @ X1217)=>((X1216)=(X1217))))))=>((descr @ X1210)=(descr @ X1211))))))=>(![X1218:$i, X1219:$i]:((((X1218)=(X1219))=>![X1220:$i > $o, X1221:$i > $o]:((![X1222:$i]:(((in @ X1222 @ X1218)=>![X1223:$i]:(((in @ X1223 @ X1219)=>(((X1222)=(X1223))=>((X1220 @ X1222)<=>(X1221 @ X1223)))))))=>((dsetconstr @ X1218 @ X1220)=(dsetconstr @ X1219 @ X1221))))))=>(![X1224:$i, X1225:$i]:((![X1226:$i]:(((in @ X1226 @ X1224)=>(in @ X1226 @ X1225)))=>(subset @ X1224 @ X1225)))=>(![X1227:$i, X1228:$i]:((((X1227)=(X1228))=>(subset @ X1228 @ X1227)))=>(![X1229:$i, X1230:$i]:((((X1229)=(X1230))=>(subset @ X1229 @ X1230)))=>(![X1231:$i, X1232:$i]:((![X1233:$i]:(((in @ X1233 @ X1231)=>(in @ X1233 @ X1232)))=>(subset @ X1231 @ X1232)))=>(![X1234:$i]:((subset @ emptyset @ X1234))=>(![X1235:$i, X1236:$i, X1237:$i]:(((subset @ X1235 @ X1236)=>((in @ X1237 @ X1235)=>(in @ X1237 @ X1236))))=>(![X1238:$i, X1239:$i, X1240:$i]:(((subset @ X1238 @ X1239)=>(~(in @ X1240 @ X1239)=>~(in @ X1240 @ X1238))))=>(![X1241:$i, X1242:$i, X1243:$i]:(((in @ X1243 @ X1241)=>(~(in @ X1243 @ X1242)=>~(subset @ X1241 @ X1242))))=>(![X1244:$i, X1245:$i]:((~(subset @ X1244 @ X1245)=>((X1244)!=(X1245))))=>(![X1246:$i, X1247:$i, X1248:$i]:(((in @ X1248 @ X1246)=>(~(in @ X1248 @ X1247)=>((X1246)!=(X1247)))))=>(![X1249:$i]:((subset @ X1249 @ X1249))=>(![X1250:$i, X1251:$i, X1252:$i]:(((subset @ X1250 @ X1251)=>((subset @ X1251 @ X1252)=>(subset @ X1250 @ X1252))))=>(![X1253:$i, X1254:$i]:((subset @ X1254 @ (setadjoin @ X1253 @ X1254)))=>(![X1255:$i, X1256:$i, X1257:$i]:(((subset @ X1255 @ X1257)=>(subset @ X1255 @ (setadjoin @ X1256 @ X1257))))=>(![X1258:$i, X1259:$i]:(((subset @ X1258 @ X1259)=>(in @ X1258 @ (powerset @ X1259))))=>(![X1260:$i, X1261:$i]:(((subset @ X1260 @ X1261)=>((subset @ X1261 @ X1260)=>((X1260)=(X1261)))))=>(![X1262:$i]:(((subset @ X1262 @ emptyset)=>((X1262)=(emptyset))))=>(![X1263:$i, X1264:$i]:(((subset @ X1264 @ X1263)=>(in @ X1264 @ (powerset @ X1263))))=>(![X1265:$i, X1266:$i]:(((in @ X1266 @ (powerset @ X1265))=>(subset @ X1266 @ X1265)))=>(![X1267:$i]:((in @ X1267 @ (powerset @ X1267)))=>(![X1268:$i, X1269:$i]:(((subset @ X1268 @ X1269)=>(subset @ (powerset @ X1268) @ (powerset @ X1269))))=>(![X1270:$i, X1271:$i > $o]:((in @ (dsetconstr @ X1270 @ X1271) @ (powerset @ X1270)))=>(![X1272:$i, X1273:$i > $o]:((subset @ (dsetconstr @ X1272 @ X1273) @ X1272))=>(![X1274:$i, X1275:$i, X1276:$i]:(((in @ X1276 @ X1274)=>(in @ X1276 @ (binunion @ X1274 @ X1275))))=>(![X1277:$i, X1278:$i]:((in @ X1278 @ (setadjoin @ X1277 @ (setadjoin @ X1278 @ emptyset))))=>(![X1279:$i, X1280:$i, X1281:$i]:(((in @ X1281 @ X1280)=>(in @ X1281 @ (binunion @ X1279 @ X1280))))=>(![X1282:$i, X1283:$i, X1284:$i, X1285:$o]:(((in @ X1284 @ (binunion @ X1282 @ X1283))=>(((in @ X1284 @ X1282)=>(X1285))=>(((in @ X1284 @ X1283)=>(X1285))=>(X1285)))))=>(![X1286:$i, X1287:$i, X1288:$i]:(((in @ X1288 @ (binunion @ X1286 @ X1287))=>((in @ X1288 @ X1286)|(in @ X1288 @ X1287))))=>(![X1289:$i, X1290:$i]:((subset @ X1289 @ (binunion @ X1289 @ X1290)))=>(![X1291:$i, X1292:$i]:((subset @ X1292 @ (binunion @ X1291 @ X1292)))=>(![X1293:$i, X1294:$i, X1295:$i]:(((in @ X1295 @ X1293)=>((in @ X1295 @ X1294)=>(in @ X1295 @ (binintersect @ X1293 @ X1294)))))=>(![X1296:$i, X1297:$i, X1298:$i]:(((subset @ X1298 @ X1296)=>((subset @ X1298 @ X1297)=>(subset @ X1298 @ (binintersect @ X1296 @ X1297)))))=>(![X1299:$i, X1300:$i, X1301:$i]:(((in @ X1301 @ (binintersect @ X1299 @ X1300))=>(in @ X1301 @ X1299)))=>(![X1302:$i, X1303:$i]:((subset @ (binintersect @ X1302 @ X1303) @ X1302))=>(![X1304:$i, X1305:$i]:(((subset @ X1304 @ X1305)=>((binintersect @ X1304 @ X1305)=(X1304))))=>(![X1306:$i, X1307:$i]:((((binintersect @ X1306 @ X1307)=(X1307))=>(subset @ X1307 @ X1306)))=>(![X1308:$i, X1309:$i, X1310:$i]:(((in @ X1310 @ (binintersect @ X1308 @ X1309))=>(in @ X1310 @ X1309)))=>(![X1311:$i, X1312:$i]:((~(?[X1313:$i]:(((in @ X1313 @ X1311)&(in @ X1313 @ X1312))))=>((binintersect @ X1311 @ X1312)=(emptyset))))=>(![X1314:$i, X1315:$i]:((subset @ (binintersect @ X1314 @ X1315) @ X1315))=>(![X1316:$i, 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X1905:$i]:(((in @ X1905 @ (powerset @ X1904))=>![X1906:$i]:(((in @ X1906 @ (powerset @ X1904))=>![X1907:$i]:(((in @ X1907 @ (powerset @ X1904))=>![X1908:$i]:(((in @ X1908 @ (powerset @ X1904))=>((setminus @ X1904 @ (binintersect @ (binunion @ X1905 @ X1906) @ (binunion @ X1907 @ X1908)))=(binunion @ (binintersect @ (setminus @ X1904 @ X1905) @ (setminus @ X1904 @ X1906)) @ (binintersect @ (setminus @ X1904 @ X1907) @ (setminus @ X1904 @ X1908))))))))))))=>(![X1909:$i, X1910:$i]:(((in @ X1910 @ (powerset @ X1909))=>![X1911:$i]:(((in @ X1911 @ (powerset @ X1909))=>![X1912:$i]:(((in @ X1912 @ (powerset @ X1909))=>(in @ (binintersect @ X1910 @ X1911) @ (powerset @ (binintersect @ (binunion @ X1910 @ X1912) @ (binunion @ X1911 @ X1912))))))))))=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[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_309, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_310]), foundationAx]), wellorderingAx]), c_0_311]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_316]), setext]), emptyI]), noeltsimpempty]), c_0_317]), c_0_318]), c_0_319]), c_0_320]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_321]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_322]), c_0_323]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_324]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_325]), c_0_326]), c_0_327]), inCongP]), in__Cong]), c_0_328]), c_0_329]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_330]), c_0_331]), c_0_332]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_333]), c_0_334]), 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]), c_0_335]), c_0_336]), c_0_337]), c_0_338]), singletonsuniq]), setukpairinjL1]), c_0_339]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_340]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_341]), c_0_342]), c_0_343]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), c_0_348]), c_0_349]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_350]), c_0_351]), c_0_352]), c_0_353]), c_0_354]), c_0_355]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_356]), c_0_357]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_358]), c_0_359]), c_0_360]), c_0_361]), c_0_362]), c_0_363]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3])])]), c_0_368])).
% 2.29/0.64  thf(c_0_370, negated_conjecture, ![X1913:$i, X1914:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1926:$i, X1927:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1935:$i, X1936:$i > $i > $o, X1937:$i, X1939:$i, X1942:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1949:$i, X1950:$i > $o, X1951:$i, X1953:$i, X1954:$i > $o, X1955:$i, X1956:$i, X1957:$i > $o, X1958:$i, X1959:$i, X1960:$i > $o, X1961:$i, X1962:$i > $o, X1963:$i, X1966:$i, X1967:$o, X1968:$i, X1969:$i, X1970:$o, X1971:$i, X1972:$i, X1973:$i > $o, X1974:$i, X1977:$i, X1978:$i, X1981:$i, X1983:$i, X1985:$i, X1986:$i > $o, X1987:$i, X1988:$i, X1990:$i, X1991:$i > $o, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$o, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$o, X2023:$i, X2024:$i, X2025:$i > $o, X2026:$i, X2029:$i, X2030:$i, X2031:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i > $o, X2050:$i, X2051:$i > $o, X2052:$i, X2053:$i, X2054:$i > $o, X2055:$i, X2057:$i, X2058:$i > $o, X2060:$i, X2061:$i, X2062:$i > $o, X2064:$i, X2065:$i, X2066:$i > $o, X2067:$i, X2069:$o, X2070:$o, X2071:$i, X2072:$i > $o, X2074:$i, X2075:$i, X2076:$i > $o, X2077:$i, X2079:$i > $o, X2080:$i, X2083:$i, X2084:$i > $o, X2085:$i, X2089:$i, X2090:$i > $o, X2091:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i > $o, X2104:$i, X2106:$i, X2107:$i, X2108:$i > $o, X2109:$i > $o, X2112:$i, X2115:$i, X2116:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i > $o, X2129:$i, X2131:$i, X2132:$i, X2133:$i > $o, X2134:$i > $o, X2137:$i, X2139:$i, X2141:$i, X2142:$i, X2143:$i > $o, X2144:$i > $o, X2147:$i, X2148:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i > $o, X2195:$i, X2196:$i > $o, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$o, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, 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@ X2686))|(~(in @ X2688 @ (powerset @ X2686))|(~(subset @ (setminus @ X2686 @ X2688) @ (setminus @ X2686 @ X2687))|(subset @ X2687 @ X2688))))&((~(in @ X2690 @ (powerset @ X2689))|(~(in @ X2691 @ X2689)|(~(in @ X2691 @ X2690)|(in @ X2691 @ (setminus @ X2689 @ (setminus @ X2689 @ X2690))))))&((~(in @ X2693 @ (powerset @ X2692))|(~(in @ X2694 @ X2692)|(~(in @ X2694 @ (setminus @ X2692 @ (setminus @ X2692 @ X2693)))|(in @ X2694 @ X2693))))&((~(in @ X2696 @ (powerset @ X2695))|(subset @ X2696 @ (setminus @ X2695 @ (setminus @ X2695 @ X2696))))&((~(in @ X2698 @ (powerset @ X2697))|(subset @ (setminus @ X2697 @ (setminus @ X2697 @ X2698)) @ X2698))&((~(in @ X2700 @ (powerset @ X2699))|((X2700)=(setminus @ X2699 @ (setminus @ X2699 @ X2700))))&((~(in @ X2702 @ (powerset @ X2701))|(~(in @ X2703 @ (powerset @ X2701))|(~(in @ X2704 @ X2701)|(~(in @ X2704 @ (setminus @ X2701 @ X2702))|~(in @ X2704 @ (binintersect @ X2702 @ X2703))))))&((~(in @ X2706 @ (powerset @ X2705))|(~(in @ X2707 @ (powerset @ X2705))|(~(in @ X2708 @ X2705)|(~(in @ X2708 @ (setminus @ X2705 @ X2706))|(in @ X2708 @ (setminus @ X2705 @ (binintersect @ X2706 @ X2707)))))))&((~(in @ X2710 @ (powerset @ X2709))|(~(in @ X2711 @ (powerset @ X2709))|(subset @ (setminus @ X2709 @ X2710) @ (setminus @ X2709 @ (binintersect @ X2710 @ X2711)))))&((~(in @ X2713 @ (powerset @ X2712))|(~(in @ X2714 @ (powerset @ X2712))|(in @ (setminus @ X2712 @ X2713) @ (powerset @ (setminus @ X2712 @ (binintersect @ X2713 @ X2714))))))&((~(in @ X2716 @ (powerset @ X2715))|(~(in @ X2717 @ (powerset @ X2715))|(~(subset @ X2716 @ (setminus @ X2715 @ X2717))|(~(in @ X2718 @ X2715)|(~(in @ X2718 @ X2717)|(in @ X2718 @ (setminus @ X2715 @ X2716)))))))&((~(in @ X2720 @ (powerset @ X2719))|(~(in @ X2721 @ (powerset @ X2719))|(~(subset @ X2720 @ (setminus @ X2719 @ X2721))|(subset @ X2721 @ (setminus @ X2719 @ X2720)))))&((~(in @ X2723 @ (powerset @ X2722))|(~(in @ X2724 @ (powerset @ X2722))|(~(in @ X2725 @ X2722)|((in @ X2725 @ (binunion @ X2723 @ X2724))|~(in @ X2725 @ X2723)))))&((~(in @ X2727 @ (powerset @ X2726))|(~(in @ X2728 @ (powerset @ X2726))|(~(in @ X2729 @ X2726)|((in @ X2729 @ (binunion @ X2727 @ X2728))|~(in @ X2729 @ X2728)))))&((~(in @ X2731 @ (powerset @ X2730))|(~(in @ X2732 @ (powerset @ X2730))|(~(in @ X2733 @ (powerset @ X2730))|(~(in @ X2734 @ X2730)|(~(in @ X2734 @ (binintersect @ X2731 @ X2732))|(in @ X2734 @ (binunion @ X2731 @ X2733)))))))&((~(in @ X2736 @ (powerset @ X2735))|(~(in @ X2737 @ (powerset @ X2735))|(~(in @ X2738 @ (powerset @ X2735))|(~(in @ X2739 @ X2735)|(~(in @ X2739 @ (binintersect @ X2736 @ X2737))|(in @ X2739 @ (binunion @ X2737 @ X2738)))))))&((~(in @ X2741 @ (powerset @ X2740))|(~(in @ X2742 @ (powerset @ X2740))|(~(in @ X2743 @ (powerset @ X2740))|(~(in @ X2744 @ X2740)|(~(in @ X2744 @ (binintersect @ X2741 @ X2742))|(in @ X2744 @ (binintersect @ (binunion @ X2741 @ X2743) @ (binunion @ X2742 @ X2743))))))))&((~(in @ X2746 @ (powerset @ X2745))|(~(in @ X2747 @ (powerset @ X2745))|(~(in @ X2748 @ (powerset @ X2745))|(in @ (binintersect @ X2746 @ X2747) @ (powerset @ (binintersect @ (binunion @ X2746 @ X2748) @ (binunion @ X2747 @ X2748)))))))&((~(in @ X2750 @ (powerset @ X2749))|(~(in @ X2751 @ (powerset @ X2749))|(~(in @ X2752 @ X2749)|(~(in @ X2752 @ (setminus @ X2749 @ (binunion @ X2750 @ X2751)))|~(in @ X2752 @ X2750)))))&((~(in @ X2754 @ (powerset @ X2753))|(~(in @ X2755 @ (powerset @ X2753))|(~(in @ X2756 @ X2753)|(~(in @ X2756 @ (setminus @ X2753 @ (binunion @ X2754 @ X2755)))|(in @ X2756 @ (setminus @ X2753 @ X2754))))))&(((((in @ X2761 @ X2759)|(X2760)|(in @ X2761 @ X2758)|~(in @ X2761 @ (binunion @ X2758 @ X2759))|~(in @ X2761 @ X2757)|~(in @ X2759 @ (powerset @ X2757))|~(in @ X2758 @ (powerset @ X2757)))&(~(X2760)|(X2760)|(in @ X2761 @ X2758)|~(in @ X2761 @ (binunion @ X2758 @ X2759))|~(in @ X2761 @ X2757)|~(in @ X2759 @ (powerset @ X2757))|~(in @ X2758 @ (powerset @ X2757))))&(((in @ X2761 @ X2759)|(X2760)|~(X2760)|~(in @ X2761 @ (binunion @ X2758 @ X2759))|~(in @ X2761 @ X2757)|~(in @ X2759 @ (powerset @ X2757))|~(in @ X2758 @ (powerset @ X2757)))&(~(X2760)|(X2760)|~(X2760)|~(in @ X2761 @ (binunion @ X2758 @ X2759))|~(in @ X2761 @ X2757)|~(in @ X2759 @ (powerset @ X2757))|~(in @ X2758 @ (powerset @ X2757)))))&((~(in @ X2763 @ (powerset @ X2762))|(~(in @ X2764 @ (powerset @ X2762))|(~(in @ X2765 @ X2762)|((in @ X2765 @ X2763)|((in @ X2765 @ X2764)|~(in @ X2765 @ (binunion @ X2763 @ X2764)))))))&((~(in @ X2767 @ (powerset @ X2766))|(~(in @ X2768 @ (powerset @ X2766))|(~(in @ X2769 @ X2766)|(~(in @ X2769 @ (setminus @ X2766 @ (binunion @ X2767 @ X2768)))|(in @ X2769 @ (setminus @ X2766 @ X2767))))))&((~(in @ X2771 @ (powerset @ X2770))|(~(in @ X2772 @ (powerset @ X2770))|(in @ (setminus @ X2770 @ (binunion @ X2771 @ X2772)) @ (powerset @ (setminus @ X2770 @ X2771)))))&((~(in @ X2774 @ (powerset @ X2773))|(~(in @ X2775 @ (powerset @ X2773))|(~(in @ X2776 @ X2773)|(~(in @ X2776 @ (setminus @ X2773 @ (binunion @ X2774 @ X2775)))|(in @ X2776 @ (setminus @ X2773 @ X2775))))))&((~(in @ X2778 @ (powerset @ X2777))|(~(in @ X2779 @ (powerset @ X2777))|(~(in @ X2780 @ X2777)|(~(in @ X2780 @ (setminus @ X2777 @ (binintersect @ X2778 @ X2779)))|(in @ X2780 @ (binunion @ (setminus @ X2777 @ X2778) @ (setminus @ X2777 @ X2779)))))))&((~(in @ X2782 @ (powerset @ X2781))|(~(in @ X2783 @ (powerset @ X2781))|(~(in @ X2784 @ X2781)|(~(in @ X2784 @ (binunion @ (setminus @ X2781 @ X2782) @ (setminus @ X2781 @ X2783)))|(in @ X2784 @ (setminus @ X2781 @ (binintersect @ X2782 @ X2783)))))))&((~(in @ X2786 @ (powerset @ X2785))|(~(in @ X2787 @ (powerset @ X2785))|((setminus @ X2785 @ (binintersect @ X2786 @ X2787))=(binunion @ (setminus @ X2785 @ X2786) @ (setminus @ X2785 @ X2787)))))&((~(in @ X2789 @ (powerset @ X2788))|(~(in @ X2790 @ (powerset @ X2788))|(~(in @ X2791 @ X2788)|(~(in @ X2791 @ (setminus @ X2788 @ (binunion @ X2789 @ X2790)))|(in @ X2791 @ (binintersect @ (setminus @ X2788 @ X2789) @ (setminus @ X2788 @ X2790)))))))&((~(in @ X2793 @ (powerset @ X2792))|(~(in @ X2794 @ (powerset @ X2792))|(~(in @ X2795 @ X2792)|(~(in @ X2795 @ (setminus @ X2792 @ X2793))|(~(in @ X2795 @ (setminus @ X2792 @ X2794))|(in @ X2795 @ (setminus @ X2792 @ (binunion @ X2793 @ X2794))))))))&((~(in @ X2797 @ (powerset @ X2796))|(~(in @ X2798 @ (powerset @ X2796))|(~(in @ X2799 @ X2796)|(~(in @ X2799 @ (binintersect @ (setminus @ X2796 @ X2797) @ (setminus @ X2796 @ X2798)))|(in @ X2799 @ (setminus @ X2796 @ (binunion @ X2797 @ X2798)))))))&((~(in @ X2801 @ (powerset @ X2800))|(~(in @ X2802 @ (powerset @ X2800))|((setminus @ X2800 @ (binunion @ X2801 @ X2802))=(binintersect @ (setminus @ X2800 @ X2801) @ (setminus @ X2800 @ X2802)))))&((~(in @ X2804 @ (powerset @ X2803))|(~(in @ X2805 @ (powerset @ X2803))|(~(in @ X2806 @ (binintersect @ X2804 @ X2805))|(in @ X2806 @ X2803))))&((~(in @ X2808 @ (powerset @ X2807))|(~(in @ X2809 @ (powerset @ X2807))|(~(in @ X2810 @ (powerset @ X2807))|(~(subset @ X2808 @ X2810)|(subset @ (binintersect @ X2808 @ X2809) @ X2810)))))&((~(in @ X2812 @ (powerset @ X2811))|(~(in @ X2813 @ (powerset @ X2811))|(~(in @ X2814 @ (powerset @ X2811))|(~(subset @ X2813 @ X2814)|(subset @ (binintersect @ X2812 @ X2813) @ X2814)))))&((~(in @ X2816 @ (powerset @ X2815))|(~(in @ X2817 @ (powerset @ X2815))|(~(in @ X2818 @ (powerset @ X2815))|(~(subset @ X2816 @ X2817)|(~(subset @ X2816 @ X2818)|(subset @ X2816 @ (binintersect @ X2817 @ X2818)))))))&((~(in @ X2820 @ (powerset @ X2819))|(~(in @ X2821 @ (powerset @ X2819))|(~(in @ X2822 @ (powerset @ X2819))|(~(in @ X2823 @ (powerset @ X2819))|(~(subset @ X2820 @ X2822)|(~(subset @ X2821 @ X2823)|(subset @ (binintersect @ X2820 @ X2821) @ (binintersect @ X2822 @ X2823))))))))&((~(in @ X2825 @ (powerset @ X2824))|(~(in @ X2826 @ (powerset @ X2824))|(in @ (setminus @ X2824 @ X2825) @ (powerset @ (setminus @ X2824 @ (binintersect @ X2825 @ X2826))))))&((~(in @ X2828 @ (powerset @ X2827))|(~(in @ X2829 @ (powerset @ X2827))|(~(in @ X2830 @ (powerset @ X2827))|(~(in @ X2831 @ (powerset @ X2827))|((setminus @ X2827 @ (binintersect @ (binunion @ X2828 @ X2829) @ (binunion @ X2830 @ X2831)))=(binunion @ (binintersect @ (setminus @ X2827 @ X2828) @ (setminus @ X2827 @ X2829)) @ (binintersect @ (setminus @ X2827 @ X2830) @ (setminus @ X2827 @ X2831))))))))&((~(in @ X2833 @ (powerset @ X2832))|(~(in @ X2834 @ (powerset @ X2832))|(~(in @ X2835 @ (powerset @ X2832))|(in @ (binintersect @ X2833 @ X2834) @ (powerset @ (binintersect @ (binunion @ X2833 @ X2835) @ (binunion @ X2834 @ X2835)))))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((subset @ esk88_0 @ (setminus @ esk87_0 @ esk89_0))&~(subset @ esk89_0 @ (setminus @ esk87_0 @ esk88_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_369])])])])])])])).
% 2.29/0.64  thf(c_0_371, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X4 @ (setminus @ X3 @ X2))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((subset @ X2 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_370])).
% 2.29/0.64  thf(c_0_372, negated_conjecture, (subset @ esk88_0 @ (setminus @ esk87_0 @ esk89_0)), inference(split_conjunct,[status(thm)],[c_0_370])).
% 2.29/0.64  thf(c_0_373, negated_conjecture, (in @ esk89_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_370])).
% 2.29/0.64  thf(c_0_374, negated_conjecture, (in @ esk88_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_370])).
% 2.29/0.64  thf(c_0_375, negated_conjecture, ~((subset @ esk89_0 @ (setminus @ esk87_0 @ esk88_0))), inference(split_conjunct,[status(thm)],[c_0_370])).
% 2.29/0.64  thf(c_0_376, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_371, c_0_372]), c_0_373]), c_0_374])]), c_0_375]), ['proof']).
% 2.29/0.64  % SZS output end CNFRefutation
% 2.29/0.64  % Parsed axioms                        : 607
% 2.29/0.64  % Removed by relevancy pruning/SinE    : 0
% 2.29/0.64  % Initial clauses                      : 790
% 2.29/0.64  % Removed in clause preprocessing      : 352
% 2.29/0.64  % Initial clauses in saturation        : 438
% 2.29/0.64  % Processed clauses                    : 1771
% 2.29/0.64  % ...of these trivial                  : 88
% 2.29/0.64  % ...subsumed                          : 875
% 2.29/0.64  % ...remaining for further processing  : 808
% 2.29/0.64  % Other redundant clauses eliminated   : 28
% 2.29/0.64  % Clauses deleted for lack of memory   : 0
% 2.29/0.64  % Backward-subsumed                    : 8
% 2.29/0.64  % Backward-rewritten                   : 8
% 2.29/0.64  % Generated clauses                    : 23476
% 2.29/0.64  % ...of the previous two non-redundant : 19254
% 2.29/0.64  % ...aggressively subsumed             : 0
% 2.29/0.64  % Contextual simplify-reflections      : 0
% 2.29/0.64  % Paramodulations                      : 23443
% 2.29/0.64  % Factorizations                       : 2
% 2.29/0.64  % NegExts                              : 0
% 2.29/0.64  % Equation resolutions                 : 31
% 2.29/0.64  % Disequality decompositions           : 0
% 2.29/0.64  % Total rewrite steps                  : 6773
% 2.29/0.64  % ...of those cached                   : 6359
% 2.29/0.64  % Propositional unsat checks           : 0
% 2.29/0.64  %    Propositional check models        : 0
% 2.29/0.64  %    Propositional check unsatisfiable : 0
% 2.29/0.64  %    Propositional clauses             : 0
% 2.29/0.64  %    Propositional clauses after purity: 0
% 2.29/0.64  %    Propositional unsat core size     : 0
% 2.29/0.64  %    Propositional preprocessing time  : 0.000
% 2.29/0.64  %    Propositional encoding time       : 0.000
% 2.29/0.64  %    Propositional solver time         : 0.000
% 2.29/0.64  %    Success case prop preproc time    : 0.000
% 2.29/0.64  %    Success case prop encoding time   : 0.000
% 2.29/0.64  %    Success case prop solver time     : 0.000
% 2.29/0.64  % Current number of processed clauses  : 783
% 2.29/0.64  %    Positive orientable unit clauses  : 337
% 2.29/0.64  %    Positive unorientable unit clauses: 0
% 2.29/0.64  %    Negative unit clauses             : 5
% 2.29/0.64  %    Non-unit-clauses                  : 441
% 2.29/0.64  % Current number of unprocessed clauses: 17880
% 2.29/0.64  % ...number of literals in the above   : 51714
% 2.29/0.64  % Current number of archived formulas  : 0
% 2.29/0.64  % Current number of archived clauses   : 16
% 2.29/0.64  % Clause-clause subsumption calls (NU) : 21598
% 2.29/0.64  % Rec. Clause-clause subsumption calls : 18121
% 2.29/0.64  % Non-unit clause-clause subsumptions  : 723
% 2.29/0.64  % Unit Clause-clause subsumption calls : 170
% 2.29/0.64  % Rewrite failures with RHS unbound    : 0
% 2.29/0.64  % BW rewrite match attempts            : 1059
% 2.29/0.64  % BW rewrite match successes           : 5
% 2.29/0.64  % Condensation attempts                : 0
% 2.29/0.64  % Condensation successes               : 0
% 2.29/0.64  % Termbank termtop insertions          : 402615
% 2.29/0.64  % Search garbage collected termcells   : 30040
% 2.29/0.64  
% 2.29/0.64  % -------------------------------------------------
% 2.29/0.64  % User time                : 0.283 s
% 2.29/0.64  % System time              : 0.028 s
% 2.29/0.64  % Total time               : 0.311 s
% 2.29/0.64  % Maximum resident set size: 10720 pages
% 2.29/0.64  
% 2.29/0.64  % -------------------------------------------------
% 2.29/0.64  % User time                : 0.451 s
% 2.29/0.64  % System time              : 0.086 s
% 2.29/0.64  % Total time               : 0.537 s
% 2.29/0.64  % Maximum resident set size: 5888 pages
% 2.29/0.64  % E exiting
%------------------------------------------------------------------------------