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

%------------------------------------------------------------------------------
% File     : E-SAT---3.5.1
% Problem  : SEU811^1 : 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 : n007.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 08:27:53 AM UTC 2026

% Result   : Theorem 83.50s 12.42s
% Output   : CNFRefutation 83.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU811^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17  % Computer : n007.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 14:31:26 UTC 2026
% 0.07/0.17  % CPUTime  : 
% 0.07/0.17  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22  Running higher-order theorem proving
% 0.07/0.26  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.7LvfJVf02x/E---3.1_3446945.p
% 83.50/12.42  % Version: 3.5.1-ho
% 83.50/12.42  % Preprocessing class: HSLMSLSSLLLCHFA.
% 83.50/12.42  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 83.50/12.42  % Starting ehoh_best5 with 300s (1) cores
% 83.50/12.42  % Starting almost_fo_3_lam with 300s (1) cores
% 83.50/12.42  % Starting new_bool_5 with 300s (1) cores
% 83.50/12.42  % Starting pre_casc_3 with 300s (1) cores
% 83.50/12.42  % Starting ho_unfolding_8 with 300s (1) cores
% 83.50/12.42  % Starting new_ho_10_cnf2 with 300s (1) cores
% 83.50/12.42  % Starting new_bool_3 with 300s (1) cores
% 83.50/12.42  % Starting new_ho_5 with 300s (1) cores
% 83.50/12.42  % new_ho_10_cnf2 with pid 3446999 completed with status 0
% 83.50/12.42  % Result found by new_ho_10_cnf2
% 83.50/12.42  % Preprocessing class: HSLMSLSSLLLCHFA.
% 83.50/12.42  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 83.50/12.42  % Starting ehoh_best5 with 300s (1) cores
% 83.50/12.42  % Starting almost_fo_3_lam with 300s (1) cores
% 83.50/12.42  % Starting new_bool_5 with 300s (1) cores
% 83.50/12.42  % Starting pre_casc_3 with 300s (1) cores
% 83.50/12.42  % Starting ho_unfolding_8 with 300s (1) cores
% 83.50/12.42  % Starting new_ho_10_cnf2 with 300s (1) cores
% 83.50/12.42  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 83.50/12.42  % No SInE strategy applied
% 83.50/12.42  % Search class: HGHSM-FSLM32-MHFMMSBN
% 83.50/12.42  % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 83.50/12.42  % Starting SubtermCWHack with 31s (1) cores
% 83.50/12.42  % SubtermCWHack with pid 3447052 completed with status 0
% 83.50/12.42  % Result found by SubtermCWHack
% 83.50/12.42  % Preprocessing class: HSLMSLSSLLLCHFA.
% 83.50/12.42  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 83.50/12.42  % Starting ehoh_best5 with 300s (1) cores
% 83.50/12.42  % Starting almost_fo_3_lam with 300s (1) cores
% 83.50/12.42  % Starting new_bool_5 with 300s (1) cores
% 83.50/12.42  % Starting pre_casc_3 with 300s (1) cores
% 83.50/12.42  % Starting ho_unfolding_8 with 300s (1) cores
% 83.50/12.42  % Starting new_ho_10_cnf2 with 300s (1) cores
% 83.50/12.42  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 83.50/12.42  % No SInE strategy applied
% 83.50/12.42  % Search class: HGHSM-FSLM32-MHFMMSBN
% 83.50/12.42  % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 83.50/12.42  % Starting SubtermCWHack with 31s (1) cores
% 83.50/12.42  % Preprocessing time       : 0.014 s
% 83.50/12.42  
% 83.50/12.42  % Proof found!
% 83.50/12.42  % SZS status Theorem
% 83.50/12.42  % SZS output start CNFRefutation
% 83.50/12.42  thf(decl_23, type, in: $i > $i > $o).
% 83.50/12.42  thf(decl_24, type, exu: ($i > $o) > $o).
% 83.50/12.42  thf(decl_25, type, setextAx: $o).
% 83.50/12.42  thf(decl_26, type, emptyset: $i).
% 83.50/12.42  thf(decl_27, type, emptysetAx: $o).
% 83.50/12.42  thf(decl_28, type, setadjoin: $i > $i > $i).
% 83.50/12.42  thf(decl_29, type, setadjoinAx: $o).
% 83.50/12.42  thf(decl_30, type, powerset: $i > $i).
% 83.50/12.42  thf(decl_31, type, powersetAx: $o).
% 83.50/12.42  thf(decl_32, type, setunion: $i > $i).
% 83.50/12.42  thf(decl_33, type, setunionAx: $o).
% 83.50/12.42  thf(decl_34, type, omega: $i).
% 83.50/12.42  thf(decl_35, type, omega0Ax: $o).
% 83.50/12.42  thf(decl_36, type, omegaSAx: $o).
% 83.50/12.42  thf(decl_37, type, omegaIndAx: $o).
% 83.50/12.42  thf(decl_38, type, replAx: $o).
% 83.50/12.42  thf(decl_39, type, foundationAx: $o).
% 83.50/12.42  thf(decl_40, type, wellorderingAx: $o).
% 83.50/12.42  thf(decl_41, type, descr: ($i > $o) > $i).
% 83.50/12.42  thf(decl_42, type, descrp: $o).
% 83.50/12.42  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_44, type, dsetconstrI: $o).
% 83.50/12.42  thf(decl_45, type, dsetconstrEL: $o).
% 83.50/12.42  thf(decl_46, type, dsetconstrER: $o).
% 83.50/12.42  thf(decl_47, type, exuE1: $o).
% 83.50/12.42  thf(decl_48, type, prop2set: $o > $i).
% 83.50/12.42  thf(decl_49, type, prop2setE: $o).
% 83.50/12.42  thf(decl_50, type, emptysetE: $o).
% 83.50/12.42  thf(decl_51, type, emptysetimpfalse: $o).
% 83.50/12.42  thf(decl_52, type, notinemptyset: $o).
% 83.50/12.42  thf(decl_53, type, exuE3e: $o).
% 83.50/12.42  thf(decl_54, type, setext: $o).
% 83.50/12.42  thf(decl_55, type, emptyI: $o).
% 83.50/12.42  thf(decl_56, type, noeltsimpempty: $o).
% 83.50/12.42  thf(decl_57, type, setbeta: $o).
% 83.50/12.42  thf(decl_58, type, nonempty: $i > $o).
% 83.50/12.42  thf(decl_59, type, nonemptyE1: $o).
% 83.50/12.42  thf(decl_60, type, nonemptyI: $o).
% 83.50/12.42  thf(decl_61, type, nonemptyI1: $o).
% 83.50/12.42  thf(decl_62, type, setadjoinIL: $o).
% 83.50/12.42  thf(decl_63, type, emptyinunitempty: $o).
% 83.50/12.42  thf(decl_64, type, setadjoinIR: $o).
% 83.50/12.42  thf(decl_65, type, setadjoinE: $o).
% 83.50/12.42  thf(decl_66, type, setadjoinOr: $o).
% 83.50/12.42  thf(decl_67, type, setoftrueEq: $o).
% 83.50/12.42  thf(decl_68, type, powersetI: $o).
% 83.50/12.42  thf(decl_69, type, emptyinPowerset: $o).
% 83.50/12.42  thf(decl_70, type, emptyInPowerset: $o).
% 83.50/12.42  thf(decl_71, type, powersetE: $o).
% 83.50/12.42  thf(decl_72, type, setunionI: $o).
% 83.50/12.42  thf(decl_73, type, setunionE: $o).
% 83.50/12.42  thf(decl_74, type, subPowSU: $o).
% 83.50/12.42  thf(decl_75, type, exuE2: $o).
% 83.50/12.42  thf(decl_76, type, nonemptyImpWitness: $o).
% 83.50/12.42  thf(decl_77, type, uniqinunit: $o).
% 83.50/12.42  thf(decl_78, type, notinsingleton: $o).
% 83.50/12.42  thf(decl_79, type, eqinunit: $o).
% 83.50/12.42  thf(decl_80, type, singletonsswitch: $o).
% 83.50/12.42  thf(decl_81, type, upairsetE: $o).
% 83.50/12.42  thf(decl_82, type, upairsetIL: $o).
% 83.50/12.42  thf(decl_83, type, upairsetIR: $o).
% 83.50/12.42  thf(decl_84, type, emptyE1: $o).
% 83.50/12.42  thf(decl_85, type, vacuousDall: $o).
% 83.50/12.42  thf(decl_86, type, quantDeMorgan1: $o).
% 83.50/12.42  thf(decl_87, type, quantDeMorgan2: $o).
% 83.50/12.42  thf(decl_88, type, quantDeMorgan3: $o).
% 83.50/12.42  thf(decl_89, type, quantDeMorgan4: $o).
% 83.50/12.42  thf(decl_90, type, prop2setI: $o).
% 83.50/12.42  thf(decl_91, type, set2prop: $i > $o).
% 83.50/12.42  thf(decl_92, type, prop2set2propI: $o).
% 83.50/12.42  thf(decl_93, type, notdexE: $o).
% 83.50/12.42  thf(decl_94, type, notdallE: $o).
% 83.50/12.42  thf(decl_95, type, exuI1: $o).
% 83.50/12.42  thf(decl_96, type, exuI3: $o).
% 83.50/12.42  thf(decl_97, type, exuI2: $o).
% 83.50/12.42  thf(decl_98, type, inCongP: $o).
% 83.50/12.42  thf(decl_99, type, in__Cong: $o).
% 83.50/12.42  thf(decl_100, type, exuE3u: $o).
% 83.50/12.42  thf(decl_101, type, exu__Cong: $o).
% 83.50/12.42  thf(decl_102, type, emptyset__Cong: $o).
% 83.50/12.42  thf(decl_103, type, setadjoin__Cong: $o).
% 83.50/12.42  thf(decl_104, type, powerset__Cong: $o).
% 83.50/12.42  thf(decl_105, type, setunion__Cong: $o).
% 83.50/12.42  thf(decl_106, type, omega__Cong: $o).
% 83.50/12.42  thf(decl_107, type, exuEu: $o).
% 83.50/12.42  thf(decl_108, type, descr__Cong: $o).
% 83.50/12.42  thf(decl_109, type, dsetconstr__Cong: $o).
% 83.50/12.42  thf(decl_110, type, subset: $i > $i > $o).
% 83.50/12.42  thf(decl_113, type, subsetI1: $o).
% 83.50/12.42  thf(decl_114, type, eqimpsubset2: $o).
% 83.50/12.42  thf(decl_115, type, eqimpsubset1: $o).
% 83.50/12.42  thf(decl_116, type, subsetI2: $o).
% 83.50/12.42  thf(decl_117, type, emptysetsubset: $o).
% 83.50/12.42  thf(decl_118, type, subsetE: $o).
% 83.50/12.42  thf(decl_119, type, subsetE2: $o).
% 83.50/12.42  thf(decl_120, type, notsubsetI: $o).
% 83.50/12.42  thf(decl_121, type, notequalI1: $o).
% 83.50/12.42  thf(decl_122, type, notequalI2: $o).
% 83.50/12.42  thf(decl_123, type, subsetRefl: $o).
% 83.50/12.42  thf(decl_124, type, subsetTrans: $o).
% 83.50/12.42  thf(decl_125, type, setadjoinSub: $o).
% 83.50/12.42  thf(decl_126, type, setadjoinSub2: $o).
% 83.50/12.42  thf(decl_127, type, subset2powerset: $o).
% 83.50/12.42  thf(decl_128, type, setextsub: $o).
% 83.50/12.42  thf(decl_129, type, subsetemptysetimpeq: $o).
% 83.50/12.42  thf(decl_130, type, powersetI1: $o).
% 83.50/12.42  thf(decl_131, type, powersetE1: $o).
% 83.50/12.42  thf(decl_132, type, inPowerset: $o).
% 83.50/12.42  thf(decl_133, type, powersetsubset: $o).
% 83.50/12.42  thf(decl_134, type, sepInPowerset: $o).
% 83.50/12.42  thf(decl_135, type, sepSubset: $o).
% 83.50/12.42  thf(decl_136, type, binunion: $i > $i > $i).
% 83.50/12.42  thf(decl_137, type, binunionIL: $o).
% 83.50/12.42  thf(decl_138, type, upairset2IR: $o).
% 83.50/12.42  thf(decl_139, type, binunionIR: $o).
% 83.50/12.42  thf(decl_140, type, binunionEcases: $o).
% 83.50/12.42  thf(decl_141, type, binunionE: $o).
% 83.50/12.42  thf(decl_142, type, binunionLsub: $o).
% 83.50/12.42  thf(decl_143, type, binunionRsub: $o).
% 83.50/12.42  thf(decl_144, type, binintersect: $i > $i > $i).
% 83.50/12.42  thf(decl_145, type, binintersectI: $o).
% 83.50/12.42  thf(decl_146, type, binintersectSubset5: $o).
% 83.50/12.42  thf(decl_147, type, binintersectEL: $o).
% 83.50/12.42  thf(decl_148, type, binintersectLsub: $o).
% 83.50/12.42  thf(decl_149, type, binintersectSubset2: $o).
% 83.50/12.42  thf(decl_150, type, binintersectSubset3: $o).
% 83.50/12.42  thf(decl_151, type, binintersectER: $o).
% 83.50/12.42  thf(decl_152, type, disjointsetsI1: $o).
% 83.50/12.42  thf(decl_153, type, binintersectRsub: $o).
% 83.50/12.42  thf(decl_154, type, binintersectSubset4: $o).
% 83.50/12.42  thf(decl_155, type, binintersectSubset1: $o).
% 83.50/12.42  thf(decl_156, type, bs114d: $o).
% 83.50/12.42  thf(decl_158, type, setminus: $i > $i > $i).
% 83.50/12.42  thf(decl_159, type, setminusI: $o).
% 83.50/12.42  thf(decl_160, type, setminusEL: $o).
% 83.50/12.42  thf(decl_161, type, setminusER: $o).
% 83.50/12.42  thf(decl_162, type, setminusSubset2: $o).
% 83.50/12.42  thf(decl_163, type, setminusERneg: $o).
% 83.50/12.42  thf(decl_164, type, setminusELneg: $o).
% 83.50/12.42  thf(decl_165, type, setminusILneg: $o).
% 83.50/12.42  thf(decl_166, type, setminusIRneg: $o).
% 83.50/12.42  thf(decl_167, type, setminusLsub: $o).
% 83.50/12.42  thf(decl_168, type, setminusSubset1: $o).
% 83.50/12.42  thf(decl_169, type, symdiff: $i > $i > $i).
% 83.50/12.42  thf(decl_170, type, symdiffE: $o).
% 83.50/12.42  thf(decl_171, type, symdiffI1: $o).
% 83.50/12.42  thf(decl_172, type, symdiffI2: $o).
% 83.50/12.42  thf(decl_173, type, symdiffIneg1: $o).
% 83.50/12.42  thf(decl_174, type, symdiffIneg2: $o).
% 83.50/12.42  thf(decl_175, type, iskpair: $i > $o).
% 83.50/12.42  thf(decl_176, type, secondinupair: $o).
% 83.50/12.42  thf(decl_177, type, setukpairIL: $o).
% 83.50/12.42  thf(decl_178, type, setukpairIR: $o).
% 83.50/12.42  thf(decl_179, type, kpairiskpair: $o).
% 83.50/12.42  thf(decl_180, type, kpair: $i > $i > $i).
% 83.50/12.42  thf(decl_181, type, kpairp: $o).
% 83.50/12.42  thf(decl_182, type, cartprod: $i > $i > $i).
% 83.50/12.42  thf(decl_183, type, singletonsubset: $o).
% 83.50/12.42  thf(decl_184, type, singletoninpowerset: $o).
% 83.50/12.42  thf(decl_185, type, singletoninpowunion: $o).
% 83.50/12.42  thf(decl_186, type, upairset2E: $o).
% 83.50/12.42  thf(decl_187, type, upairsubunion: $o).
% 83.50/12.42  thf(decl_188, type, upairinpowunion: $o).
% 83.50/12.42  thf(decl_189, type, ubforcartprodlem1: $o).
% 83.50/12.42  thf(decl_190, type, ubforcartprodlem2: $o).
% 83.50/12.42  thf(decl_191, type, ubforcartprodlem3: $o).
% 83.50/12.42  thf(decl_192, type, cartprodpairin: $o).
% 83.50/12.42  thf(decl_193, type, cartprodmempair1: $o).
% 83.50/12.42  thf(decl_194, type, cartprodmempair: $o).
% 83.50/12.42  thf(decl_195, type, setunionE2: $o).
% 83.50/12.42  thf(decl_196, type, setunionsingleton1: $o).
% 83.50/12.42  thf(decl_197, type, setunionsingleton2: $o).
% 83.50/12.42  thf(decl_198, type, setunionsingleton: $o).
% 83.50/12.42  thf(decl_199, type, singleton: $i > $o).
% 83.50/12.42  thf(decl_200, type, singletonprop: $o).
% 83.50/12.42  thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 83.50/12.42  thf(decl_202, type, ex1E1: $o).
% 83.50/12.42  thf(decl_203, type, ex1I: $o).
% 83.50/12.42  thf(decl_204, type, ex1I2: $o).
% 83.50/12.42  thf(decl_205, type, singletonsuniq: $o).
% 83.50/12.42  thf(decl_210, type, setukpairinjL1: $o).
% 83.50/12.42  thf(decl_211, type, kfstsingleton: $o).
% 83.50/12.42  thf(decl_212, type, theprop: $o).
% 83.50/12.42  thf(decl_213, type, kfst: $i > $i).
% 83.50/12.42  thf(decl_214, type, kfstpairEq: $o).
% 83.50/12.42  thf(decl_215, type, cartprodfstin: $o).
% 83.50/12.42  thf(decl_216, type, setukpairinjL2: $o).
% 83.50/12.42  thf(decl_217, type, setukpairinjL: $o).
% 83.50/12.42  thf(decl_218, type, setukpairinjR11: $o).
% 83.50/12.42  thf(decl_219, type, setukpairinjR12: $o).
% 83.50/12.42  thf(decl_220, type, setukpairinjR1: $o).
% 83.50/12.42  thf(decl_221, type, upairequniteq: $o).
% 83.50/12.42  thf(decl_222, type, setukpairinjR2: $o).
% 83.50/12.42  thf(decl_223, type, setukpairinjR: $o).
% 83.50/12.42  thf(decl_224, type, ksndsingleton: $o).
% 83.50/12.42  thf(decl_225, type, ksnd: $i > $i).
% 83.50/12.42  thf(decl_226, type, ksndpairEq: $o).
% 83.50/12.42  thf(decl_227, type, kpairsurjEq: $o).
% 83.50/12.42  thf(decl_228, type, cartprodsndin: $o).
% 83.50/12.42  thf(decl_229, type, cartprodpairmemEL: $o).
% 83.50/12.42  thf(decl_230, type, cartprodpairmemER: $o).
% 83.50/12.42  thf(decl_231, type, cartprodmempaircEq: $o).
% 83.50/12.42  thf(decl_232, type, cartprodfstpairEq: $o).
% 83.50/12.42  thf(decl_233, type, cartprodsndpairEq: $o).
% 83.50/12.42  thf(decl_234, type, cartprodpairsurjEq: $o).
% 83.50/12.42  thf(decl_235, type, breln: $i > $i > $i > $o).
% 83.50/12.42  thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 83.50/12.42  thf(decl_237, type, dpsetconstrI: $o).
% 83.50/12.42  thf(decl_238, type, dpsetconstrSub: $o).
% 83.50/12.42  thf(decl_239, type, setOfPairsIsBReln: $o).
% 83.50/12.42  thf(decl_240, type, dpsetconstrERa: $o).
% 83.50/12.42  thf(decl_241, type, dpsetconstrEL1: $o).
% 83.50/12.42  thf(decl_242, type, dpsetconstrEL2: $o).
% 83.50/12.42  thf(decl_243, type, dpsetconstrER: $o).
% 83.50/12.42  thf(decl_244, type, func: $i > $i > $i > $o).
% 83.50/12.42  thf(decl_245, type, funcSet: $i > $i > $i).
% 83.50/12.42  thf(decl_246, type, funcImageSingleton: $o).
% 83.50/12.42  thf(decl_247, type, apProp: $o).
% 83.50/12.42  thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 83.50/12.42  thf(decl_249, type, app: $o).
% 83.50/12.42  thf(decl_250, type, infuncsetfunc: $o).
% 83.50/12.42  thf(decl_251, type, ap2p: $o).
% 83.50/12.42  thf(decl_252, type, funcinfuncset: $o).
% 83.50/12.42  thf(decl_253, type, lamProp: $o).
% 83.50/12.42  thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 83.50/12.42  thf(decl_255, type, lamp: $o).
% 83.50/12.42  thf(decl_256, type, lam2p: $o).
% 83.50/12.42  thf(decl_257, type, brelnall1: $o).
% 83.50/12.42  thf(decl_258, type, brelnall2: $o).
% 83.50/12.42  thf(decl_259, type, ex1E2: $o).
% 83.50/12.42  thf(decl_260, type, funcGraphProp1: $o).
% 83.50/12.42  thf(decl_261, type, funcGraphProp3: $o).
% 83.50/12.42  thf(decl_262, type, funcGraphProp2: $o).
% 83.50/12.42  thf(decl_263, type, funcextLem: $o).
% 83.50/12.42  thf(decl_264, type, funcGraphProp4: $o).
% 83.50/12.42  thf(decl_265, type, subbreln: $o).
% 83.50/12.42  thf(decl_266, type, eqbreln: $o).
% 83.50/12.42  thf(decl_267, type, funcext: $o).
% 83.50/12.42  thf(decl_268, type, funcext2: $o).
% 83.50/12.42  thf(decl_269, type, ap2apEq1: $o).
% 83.50/12.42  thf(decl_270, type, ap2apEq2: $o).
% 83.50/12.42  thf(decl_271, type, beta1: $o).
% 83.50/12.42  thf(decl_272, type, eta1: $o).
% 83.50/12.42  thf(decl_273, type, lam2lamEq: $o).
% 83.50/12.42  thf(decl_274, type, beta2: $o).
% 83.50/12.42  thf(decl_275, type, eta2: $o).
% 83.50/12.42  thf(decl_276, type, iffalseProp1: $o).
% 83.50/12.42  thf(decl_277, type, iffalseProp2: $o).
% 83.50/12.42  thf(decl_278, type, iftrueProp1: $o).
% 83.50/12.42  thf(decl_279, type, iftrueProp2: $o).
% 83.50/12.42  thf(decl_280, type, ifSingleton: $o).
% 83.50/12.42  thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 83.50/12.42  thf(decl_282, type, ifp: $o).
% 83.50/12.42  thf(decl_283, type, theeq: $o).
% 83.50/12.42  thf(decl_284, type, iftrue: $o).
% 83.50/12.42  thf(decl_285, type, iffalse: $o).
% 83.50/12.42  thf(decl_286, type, iftrueorfalse: $o).
% 83.50/12.42  thf(decl_287, type, binintersectT_lem: $o).
% 83.50/12.42  thf(decl_288, type, binunionT_lem: $o).
% 83.50/12.42  thf(decl_289, type, powersetT_lem: $o).
% 83.50/12.42  thf(decl_290, type, setminusT_lem: $o).
% 83.50/12.42  thf(decl_291, type, complementT_lem: $o).
% 83.50/12.42  thf(decl_292, type, setextT: $o).
% 83.50/12.42  thf(decl_293, type, subsetTI: $o).
% 83.50/12.42  thf(decl_294, type, powersetTI1: $o).
% 83.50/12.42  thf(decl_295, type, powersetTE1: $o).
% 83.50/12.42  thf(decl_296, type, complementTI1: $o).
% 83.50/12.42  thf(decl_297, type, complementTE1: $o).
% 83.50/12.42  thf(decl_298, type, binintersectTELcontra: $o).
% 83.50/12.42  thf(decl_299, type, binintersectTERcontra: $o).
% 83.50/12.42  thf(decl_300, type, contrasubsetT: $o).
% 83.50/12.42  thf(decl_301, type, contrasubsetT1: $o).
% 83.50/12.42  thf(decl_302, type, contrasubsetT2: $o).
% 83.50/12.42  thf(decl_303, type, contrasubsetT3: $o).
% 83.50/12.42  thf(decl_304, type, doubleComplementI1: $o).
% 83.50/12.42  thf(decl_305, type, doubleComplementE1: $o).
% 83.50/12.42  thf(decl_306, type, doubleComplementSub1: $o).
% 83.50/12.42  thf(decl_307, type, doubleComplementSub2: $o).
% 83.50/12.42  thf(decl_308, type, doubleComplementEq: $o).
% 83.50/12.42  thf(decl_309, type, complementTnotintersectT: $o).
% 83.50/12.42  thf(decl_310, type, complementImpComplementIntersect: $o).
% 83.50/12.42  thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 83.50/12.42  thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 83.50/12.42  thf(decl_313, type, contraSubsetComplement: $o).
% 83.50/12.42  thf(decl_314, type, complementTcontraSubset: $o).
% 83.50/12.42  thf(decl_315, type, binunionTILcontra: $o).
% 83.50/12.42  thf(decl_316, type, binunionTIRcontra: $o).
% 83.50/12.42  thf(decl_317, type, inIntersectImpInUnion: $o).
% 83.50/12.42  thf(decl_318, type, inIntersectImpInUnion2: $o).
% 83.50/12.42  thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 83.50/12.42  thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 83.50/12.42  thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 83.50/12.42  thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 83.50/12.42  thf(decl_323, type, binunionTE: $o).
% 83.50/12.42  thf(decl_324, type, binunionTEcontra: $o).
% 83.50/12.42  thf(decl_325, type, demorgan2a1: $o).
% 83.50/12.42  thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 83.50/12.42  thf(decl_327, type, demorgan2a2: $o).
% 83.50/12.42  thf(decl_328, type, demorgan1a: $o).
% 83.50/12.42  thf(decl_329, type, demorgan1b: $o).
% 83.50/12.42  thf(decl_330, type, demorgan1: $o).
% 83.50/12.42  thf(decl_331, type, demorgan2a: $o).
% 83.50/12.42  thf(decl_332, type, demorgan2b2: $o).
% 83.50/12.42  thf(decl_333, type, demorgan2b: $o).
% 83.50/12.42  thf(decl_334, type, demorgan2: $o).
% 83.50/12.42  thf(decl_335, type, woz13rule0: $o).
% 83.50/12.42  thf(decl_336, type, woz13rule1: $o).
% 83.50/12.42  thf(decl_337, type, woz13rule2: $o).
% 83.50/12.42  thf(decl_338, type, woz13rule3: $o).
% 83.50/12.42  thf(decl_339, type, woz13rule4: $o).
% 83.50/12.42  thf(decl_340, type, woz1_1: $o).
% 83.50/12.42  thf(decl_341, type, woz1_2: $o).
% 83.50/12.42  thf(decl_342, type, woz1_3: $o).
% 83.50/12.42  thf(decl_343, type, woz1_4: $o).
% 83.50/12.42  thf(decl_344, type, woz1_5: $o).
% 83.50/12.42  thf(decl_345, type, breln1: $i > $i > $o).
% 83.50/12.42  thf(decl_346, type, breln1all2: $o).
% 83.50/12.42  thf(decl_347, type, breln1Set: $i > $i).
% 83.50/12.42  thf(decl_348, type, breln1SetBreln1: $o).
% 83.50/12.42  thf(decl_354, type, reflwellordering: $i > $i > $o).
% 83.50/12.42  thf(decl_355, type, choice2fnsingleton: $o).
% 83.50/12.42  thf(decl_356, type, setOfPairsIsBReln1: $o).
% 83.50/12.42  thf(decl_357, type, breln1all1: $o).
% 83.50/12.42  thf(decl_358, type, subbreln1: $o).
% 83.50/12.42  thf(decl_359, type, eqbreln1: $o).
% 83.50/12.42  thf(decl_360, type, breln1invset: $i > $i > $i).
% 83.50/12.42  thf(decl_361, type, breln1invprop: $o).
% 83.50/12.42  thf(decl_362, type, breln1invI: $o).
% 83.50/12.42  thf(decl_363, type, breln1invE: $o).
% 83.50/12.42  thf(decl_364, type, breln1compset: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_365, type, breln1compprop: $o).
% 83.50/12.42  thf(decl_366, type, breln1compI: $o).
% 83.50/12.42  thf(decl_367, type, breln1compE: $o).
% 83.50/12.42  thf(decl_368, type, breln1compEex: $o).
% 83.50/12.42  thf(decl_369, type, breln1unionprop: $o).
% 83.50/12.42  thf(decl_370, type, breln1unionIL: $o).
% 83.50/12.42  thf(decl_371, type, breln1unionIR: $o).
% 83.50/12.42  thf(decl_372, type, breln1unionI: $o).
% 83.50/12.42  thf(decl_373, type, breln1unionE: $o).
% 83.50/12.42  thf(decl_374, type, breln1unionEcases: $o).
% 83.50/12.42  thf(decl_375, type, breln1unionCommutes: $o).
% 83.50/12.42  thf(decl_376, type, woz2Ex: $o).
% 83.50/12.42  thf(decl_377, type, woz2W: $o).
% 83.50/12.42  thf(decl_378, type, woz2A: $o).
% 83.50/12.42  thf(decl_379, type, woz2B: $o).
% 83.50/12.42  thf(decl_380, type, image1Ex: $o).
% 83.50/12.42  thf(decl_381, type, image1Ex1: $o).
% 83.50/12.42  thf(decl_382, type, image1: $i > ($i > $i) > $i).
% 83.50/12.42  thf(decl_383, type, image1Equiv: $o).
% 83.50/12.42  thf(decl_384, type, image1E: $o).
% 83.50/12.42  thf(decl_385, type, image1I: $o).
% 83.50/12.42  thf(decl_386, type, injective: $i > $i > $i > $o).
% 83.50/12.42  thf(decl_387, type, injFuncSet: $i > $i > $i).
% 83.50/12.42  thf(decl_388, type, injFuncInInjFuncSet: $o).
% 83.50/12.42  thf(decl_389, type, injFuncSetFuncIn: $o).
% 83.50/12.42  thf(decl_390, type, injFuncSetFuncInj: $o).
% 83.50/12.42  thf(decl_391, type, surjective: $i > $i > $i > $o).
% 83.50/12.42  thf(decl_392, type, surjFuncSet: $i > $i > $i).
% 83.50/12.42  thf(decl_393, type, surjFuncSetFuncIn: $o).
% 83.50/12.42  thf(decl_394, type, surjFuncSetFuncSurj: $o).
% 83.50/12.42  thf(decl_395, type, leftInvIsSurj: $o).
% 83.50/12.42  thf(decl_396, type, surjCantorThm: $o).
% 83.50/12.42  thf(decl_397, type, foundation2: $o).
% 83.50/12.42  thf(decl_398, type, notinself: $o).
% 83.50/12.42  thf(decl_399, type, notinself2: $o).
% 83.50/12.42  thf(decl_400, type, omegaS: $i > $i).
% 83.50/12.42  thf(decl_401, type, omegaSp: $o).
% 83.50/12.42  thf(decl_402, type, omegaSclos: $o).
% 83.50/12.42  thf(decl_403, type, peano0notS: $o).
% 83.50/12.42  thf(decl_407, type, epred1_0: $o).
% 83.50/12.42  thf(decl_408, type, esk1_2: $i > $i > $i).
% 83.50/12.42  thf(decl_409, type, esk2_2: $i > $i > $i).
% 83.50/12.42  thf(decl_410, type, esk3_2: $i > $i > $i).
% 83.50/12.42  thf(decl_411, type, esk4_1: $i > $i).
% 83.50/12.42  thf(decl_412, type, esk5_2: ($i > $i > $o) > $i > $i).
% 83.50/12.42  thf(decl_413, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 83.50/12.42  thf(decl_414, type, esk7_2: ($i > $i > $o) > $i > $i).
% 83.50/12.42  thf(decl_415, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 83.50/12.42  thf(decl_416, type, esk9_1: $i > $i).
% 83.50/12.42  thf(decl_417, type, esk10_2: ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_418, type, esk11_2: ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_419, type, esk12_1: ($i > $o) > $i).
% 83.50/12.42  thf(decl_420, type, esk13_2: ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_421, type, esk14_1: ($i > $o) > $i).
% 83.50/12.42  thf(decl_422, type, esk15_2: $i > $i > $i).
% 83.50/12.42  thf(decl_423, type, esk16_2: $i > $i > $i).
% 83.50/12.42  thf(decl_424, type, esk17_1: $i > $i).
% 83.50/12.42  thf(decl_425, type, esk18_1: $i > $i).
% 83.50/12.42  thf(decl_426, type, esk19_1: $i > $i).
% 83.50/12.42  thf(decl_427, type, esk20_2: $i > $i > $i).
% 83.50/12.42  thf(decl_428, type, esk21_3: $i > $i > $o > $i).
% 83.50/12.42  thf(decl_429, type, esk22_2: ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_430, type, esk23_1: ($i > $o) > $i).
% 83.50/12.42  thf(decl_431, type, esk24_1: $i > $i).
% 83.50/12.42  thf(decl_432, type, esk25_2: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_433, type, esk26_2: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_434, type, esk27_2: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_435, type, esk28_2: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_436, type, esk29_2: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_437, type, esk30_2: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_438, type, esk31_2: ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_439, type, esk32_1: ($i > $o) > $i).
% 83.50/12.42  thf(decl_440, type, esk33_1: ($i > $o) > $i).
% 83.50/12.42  thf(decl_441, type, esk34_1: ($i > $o) > $i).
% 83.50/12.42  thf(decl_442, type, esk35_1: ($i > $o) > $i).
% 83.50/12.42  thf(decl_443, type, esk36_2: ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_444, type, esk37_1: ($i > $o) > $i).
% 83.50/12.42  thf(decl_445, type, esk38_2: ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_446, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 83.50/12.42  thf(decl_447, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 83.50/12.42  thf(decl_448, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_449, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 83.50/12.42  thf(decl_450, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_451, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 83.50/12.42  thf(decl_452, type, esk45_2: ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_453, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 83.50/12.42  thf(decl_454, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 83.50/12.42  thf(decl_455, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_456, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_457, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 83.50/12.42  thf(decl_458, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 83.50/12.42  thf(decl_459, type, esk52_2: $i > $i > $i).
% 83.50/12.42  thf(decl_460, type, esk53_2: $i > $i > $i).
% 83.50/12.42  thf(decl_461, type, esk54_2: $i > $i > $i).
% 83.50/12.42  thf(decl_462, type, esk55_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_463, type, esk56_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_464, type, esk57_2: $i > $i > $i).
% 83.50/12.42  thf(decl_465, type, esk58_2: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_466, type, esk59_2: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_467, type, esk60_2: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_468, type, esk61_3: $i > ($i > $o) > $i > $i).
% 83.50/12.42  thf(decl_469, type, esk62_2: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_470, type, esk63_2: $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_471, type, esk64_3: $i > $i > ($i > $i) > $i).
% 83.50/12.42  thf(decl_472, type, esk65_3: $i > $i > ($i > $i) > $i).
% 83.50/12.42  thf(decl_473, type, esk66_3: $i > $i > ($i > $i) > $i).
% 83.50/12.42  thf(decl_474, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_475, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_476, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_477, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_478, type, esk71_4: $i > $i > $i > $i > $i).
% 83.50/12.42  thf(decl_479, type, esk72_4: $i > $i > $i > $i > $i).
% 83.50/12.42  thf(decl_480, type, esk73_4: $i > $i > $i > $i > $i).
% 83.50/12.42  thf(decl_481, type, esk74_4: $i > $i > $i > $i > $i).
% 83.50/12.42  thf(decl_482, type, esk75_4: $i > $i > $i > $i > $i).
% 83.50/12.42  thf(decl_483, type, esk76_4: $i > $i > $i > $i > $i).
% 83.50/12.42  thf(decl_484, type, esk77_4: $i > $i > $i > $i > $i).
% 83.50/12.42  thf(decl_485, type, esk78_4: $i > $i > $i > $i > $i).
% 83.50/12.42  thf(decl_486, type, esk79_4: $i > $i > $i > $i > $i).
% 83.50/12.42  thf(decl_487, type, esk80_3: $i > $i > ($i > $i) > $i).
% 83.50/12.42  thf(decl_488, type, esk81_3: $i > $i > ($i > $i) > $i).
% 83.50/12.42  thf(decl_489, type, esk82_3: $i > $i > ($i > $i) > $i).
% 83.50/12.42  thf(decl_490, type, esk83_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_491, type, esk84_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_492, type, esk85_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_493, type, esk86_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_494, type, esk87_3: $i > $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_495, type, esk88_3: $i > $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_496, type, esk89_3: $i > $i > ($i > $i > $o) > $i).
% 83.50/12.42  thf(decl_497, type, esk90_3: $i > $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_498, type, esk91_3: $i > $i > ($i > $o) > $i).
% 83.50/12.42  thf(decl_499, type, esk92_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_500, type, esk93_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_501, type, esk94_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_502, type, esk95_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_503, type, esk96_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_504, type, esk97_3: $i > $i > $i > $i).
% 83.50/12.42  thf(decl_505, type, esk98_5: $i > $i > $i > $i > $i > $i).
% 83.50/12.42  thf(decl_506, type, esk99_6: $i > $i > $i > $i > $i > $o > $i).
% 83.50/12.42  thf(decl_507, type, esk100_2: $i > ($i > $i) > $i).
% 83.50/12.42  thf(decl_508, type, esk101_3: $i > ($i > $i) > $i > $i).
% 83.50/12.42  thf(decl_509, type, esk102_2: $i > ($i > $i) > $i).
% 83.50/12.42  thf(decl_510, type, esk103_3: $i > ($i > $i) > $i > $i).
% 83.50/12.42  thf(decl_511, type, esk104_3: $i > ($i > $i) > $i > $i).
% 83.50/12.42  thf(decl_512, type, esk105_3: $i > ($i > $i) > $i > $i).
% 83.50/12.42  thf(decl_513, type, esk106_3: $i > ($i > $i) > $i > $i).
% 83.50/12.42  thf(decl_514, type, esk107_3: $i > ($i > $i) > $i > $i).
% 83.50/12.42  thf(decl_515, type, esk108_3: $i > $i > ($i > $i) > $i).
% 83.50/12.42  thf(decl_516, type, esk109_4: $i > $i > ($i > $i) > $i > $i).
% 83.50/12.42  thf(decl_517, type, esk110_1: $i > $i).
% 83.50/12.42  thf(decl_518, type, esk111_0: $i).
% 83.50/12.42  thf(decl_519, type, esk112_0: $i).
% 83.50/12.42  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', replAx)).
% 83.50/12.42  thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', exu)).
% 83.50/12.42  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', descrp)).
% 83.50/12.42  thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', exuE1)).
% 83.50/12.42  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', exuE3e)).
% 83.50/12.42  thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', nonempty)).
% 83.50/12.42  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', nonemptyI)).
% 83.50/12.42  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', exuE2)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', exuI1)).
% 83.50/12.42  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', exuI3)).
% 83.50/12.42  thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', exuI2)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', exuE3u)).
% 83.50/12.42  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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', exu__Cong)).
% 83.50/12.42  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', exuEu)).
% 83.50/12.42  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', descr__Cong)).
% 83.50/12.42  thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', image1Ex1)).
% 83.50/12.42  thf(peanoSinj, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>((breln1compprop)=>((breln1compI)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>((breln1unionIR)=>((breln1unionI)=>((breln1unionE)=>((breln1unionEcases)=>((breln1unionCommutes)=>((woz2Ex)=>((woz2W)=>((woz2A)=>((woz2B)=>((image1Ex)=>((image1Ex1)=>((image1Equiv)=>((image1E)=>((image1I)=>((injFuncInInjFuncSet)=>((injFuncSetFuncIn)=>((injFuncSetFuncInj)=>((surjFuncSetFuncIn)=>((surjFuncSetFuncSurj)=>((leftInvIsSurj)=>((surjCantorThm)=>((foundation2)=>((notinself)=>((notinself2)=>((omegaSp)=>((omegaSclos)=>((peano0notS)=>![X2:$i]:(((in @ X2 @ omega)=>![X3:$i]:(((in @ X3 @ omega)=>(((omegaS @ X2)=(omegaS @ X3))=>((X2)=(X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', peanoSinj)).
% 83.50/12.42  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', dsetconstrI)).
% 83.50/12.42  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', dsetconstrEL)).
% 83.50/12.42  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', dsetconstrER)).
% 83.50/12.42  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setbeta)).
% 83.50/12.42  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', nonemptyE1)).
% 83.50/12.42  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', nonemptyI1)).
% 83.50/12.42  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setoftrueEq)).
% 83.50/12.42  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', nonemptyImpWitness)).
% 83.50/12.42  thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', emptyE1)).
% 83.50/12.42  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', dsetconstr__Cong)).
% 83.50/12.42  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', sepInPowerset)).
% 83.50/12.42  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', sepSubset)).
% 83.50/12.42  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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', singletonprop)).
% 83.50/12.42  thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ex1E1)).
% 83.50/12.42  thf(ex1I, axiom, ((ex1I)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', ex1I)).
% 83.50/12.42  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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ex1I2)).
% 83.50/12.42  thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', kfstsingleton)).
% 83.50/12.42  thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ksndsingleton)).
% 83.50/12.42  thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', dpsetconstrI)).
% 83.50/12.42  thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', dpsetconstrSub)).
% 83.50/12.42  thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setOfPairsIsBReln)).
% 83.50/12.42  thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', dpsetconstrERa)).
% 83.50/12.42  thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', dpsetconstrEL1)).
% 83.50/12.42  thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', dpsetconstrEL2)).
% 83.50/12.42  thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', dpsetconstrER)).
% 83.50/12.42  thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', funcImageSingleton)).
% 83.50/12.42  thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', apProp)).
% 83.50/12.42  thf(lamProp, axiom, ((lamProp)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', lamProp)).
% 83.50/12.42  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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', lamp)).
% 83.50/12.42  thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', lam2p)).
% 83.50/12.42  thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', ex1E2)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', beta1)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', eta1)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', lam2lamEq)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', beta2)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', eta2)).
% 83.50/12.42  thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', iffalseProp1)).
% 83.50/12.42  thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', iffalseProp2)).
% 83.50/12.42  thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', iftrueProp1)).
% 83.50/12.42  thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', iftrueProp2)).
% 83.50/12.42  thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ifSingleton)).
% 83.50/12.42  thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((((X52 @ X2 @ X3))&(![X14:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ X3 @ X14) @ X33)))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', choice2fnsingleton)).
% 83.50/12.42  thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setOfPairsIsBReln1)).
% 83.50/12.42  thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', image1Equiv)).
% 83.50/12.42  thf(image1E, axiom, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', image1E)).
% 83.50/12.42  thf(image1I, axiom, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X61 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', image1I)).
% 83.50/12.42  thf(foundation2, axiom, ((foundation2)<=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', foundation2)).
% 83.50/12.42  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setextAx)).
% 83.50/12.42  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', emptysetAx)).
% 83.50/12.42  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setadjoinAx)).
% 83.50/12.42  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', powersetAx)).
% 83.50/12.42  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setunionAx)).
% 83.50/12.42  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', omega0Ax)).
% 83.50/12.42  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', omegaSAx)).
% 83.50/12.42  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', omegaIndAx)).
% 83.50/12.42  thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', foundationAx)).
% 83.50/12.42  thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', wellorderingAx)).
% 83.50/12.42  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', prop2setE)).
% 83.50/12.42  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', emptysetE)).
% 83.50/12.42  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', emptysetimpfalse)).
% 83.50/12.42  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', notinemptyset)).
% 83.50/12.42  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setext)).
% 83.50/12.42  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', emptyI)).
% 83.50/12.42  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', noeltsimpempty)).
% 83.50/12.42  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setadjoinIL)).
% 83.50/12.42  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', emptyinunitempty)).
% 83.50/12.42  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setadjoinIR)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', setadjoinE)).
% 83.50/12.42  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setadjoinOr)).
% 83.50/12.42  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', powersetI)).
% 83.50/12.42  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', emptyinPowerset)).
% 83.50/12.42  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', emptyInPowerset)).
% 83.50/12.42  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', powersetE)).
% 83.50/12.42  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setunionI)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', setunionE)).
% 83.50/12.42  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subPowSU)).
% 83.50/12.42  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', uniqinunit)).
% 83.50/12.42  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', notinsingleton)).
% 83.50/12.42  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', eqinunit)).
% 83.50/12.42  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', singletonsswitch)).
% 83.50/12.42  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', upairsetE)).
% 83.50/12.42  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', upairsetIL)).
% 83.50/12.42  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', upairsetIR)).
% 83.50/12.42  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', vacuousDall)).
% 83.50/12.42  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', quantDeMorgan1)).
% 83.50/12.42  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', quantDeMorgan2)).
% 83.50/12.42  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', quantDeMorgan3)).
% 83.50/12.42  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', quantDeMorgan4)).
% 83.50/12.42  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', prop2setI)).
% 83.50/12.42  thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', prop2set2propI)).
% 83.50/12.42  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', notdexE)).
% 83.50/12.42  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', notdallE)).
% 83.50/12.42  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', inCongP)).
% 83.50/12.42  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', in__Cong)).
% 83.50/12.42  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', emptyset__Cong)).
% 83.50/12.42  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setadjoin__Cong)).
% 83.50/12.42  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', powerset__Cong)).
% 83.50/12.42  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setunion__Cong)).
% 83.50/12.42  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', omega__Cong)).
% 83.50/12.42  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subsetI1)).
% 83.50/12.42  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', eqimpsubset2)).
% 83.50/12.42  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', eqimpsubset1)).
% 83.50/12.42  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subsetI2)).
% 83.50/12.42  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', emptysetsubset)).
% 83.50/12.42  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subsetE)).
% 83.50/12.42  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subsetE2)).
% 83.50/12.42  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', notsubsetI)).
% 83.50/12.42  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', notequalI1)).
% 83.50/12.42  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', notequalI2)).
% 83.50/12.42  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subsetRefl)).
% 83.50/12.42  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subsetTrans)).
% 83.50/12.42  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setadjoinSub)).
% 83.50/12.42  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setadjoinSub2)).
% 83.50/12.42  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subset2powerset)).
% 83.50/12.42  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setextsub)).
% 83.50/12.42  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subsetemptysetimpeq)).
% 83.50/12.42  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', powersetI1)).
% 83.50/12.42  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', powersetE1)).
% 83.50/12.42  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', inPowerset)).
% 83.50/12.42  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', powersetsubset)).
% 83.50/12.42  thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binunionIL)).
% 83.50/12.42  thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', upairset2IR)).
% 83.50/12.42  thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binunionIR)).
% 83.50/12.42  thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binunionEcases)).
% 83.50/12.42  thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binunionE)).
% 83.50/12.42  thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binunionLsub)).
% 83.50/12.42  thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binunionRsub)).
% 83.50/12.42  thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectI)).
% 83.50/12.42  thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectSubset5)).
% 83.50/12.42  thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectEL)).
% 83.50/12.42  thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectLsub)).
% 83.50/12.42  thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectSubset2)).
% 83.50/12.42  thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectSubset3)).
% 83.50/12.42  thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectER)).
% 83.50/12.42  thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', disjointsetsI1)).
% 83.50/12.42  thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectRsub)).
% 83.50/12.42  thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectSubset4)).
% 83.50/12.42  thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectSubset1)).
% 83.50/12.42  thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', bs114d)).
% 83.50/12.42  thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setminusI)).
% 83.50/12.42  thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setminusEL)).
% 83.50/12.42  thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setminusER)).
% 83.50/12.42  thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setminusSubset2)).
% 83.50/12.42  thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setminusERneg)).
% 83.50/12.42  thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setminusELneg)).
% 83.50/12.42  thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setminusILneg)).
% 83.50/12.42  thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setminusIRneg)).
% 83.50/12.42  thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setminusLsub)).
% 83.50/12.42  thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setminusSubset1)).
% 83.50/12.42  thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', symdiffE)).
% 83.50/12.42  thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', symdiffI1)).
% 83.50/12.42  thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', symdiffI2)).
% 83.50/12.42  thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', symdiffIneg1)).
% 83.50/12.42  thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', symdiffIneg2)).
% 83.50/12.42  thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', secondinupair)).
% 83.50/12.42  thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setukpairIL)).
% 83.50/12.42  thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setukpairIR)).
% 83.50/12.42  thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', kpairiskpair)).
% 83.50/12.42  thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', kpairp)).
% 83.50/12.42  thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', singletonsubset)).
% 83.50/12.42  thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', singletoninpowerset)).
% 83.50/12.42  thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', singletoninpowunion)).
% 83.50/12.42  thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', upairset2E)).
% 83.50/12.42  thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', upairsubunion)).
% 83.50/12.42  thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', upairinpowunion)).
% 83.50/12.42  thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ubforcartprodlem1)).
% 83.50/12.42  thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ubforcartprodlem2)).
% 83.50/12.42  thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ubforcartprodlem3)).
% 83.50/12.42  thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', cartprodpairin)).
% 83.50/12.42  thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', cartprodmempair1)).
% 83.50/12.42  thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', cartprodmempair)).
% 83.50/12.42  thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setunionE2)).
% 83.50/12.42  thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setunionsingleton1)).
% 83.50/12.42  thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setunionsingleton2)).
% 83.50/12.42  thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setunionsingleton)).
% 83.50/12.42  thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', singletonsuniq)).
% 83.50/12.42  thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.7LvfJVf02x/E---3.1_3446945.p', setukpairinjL1)).
% 83.50/12.42  thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', theprop)).
% 83.50/12.42  thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', kfstpairEq)).
% 83.50/12.42  thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', cartprodfstin)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', setukpairinjL2)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', setukpairinjL)).
% 83.50/12.42  thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setukpairinjR11)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', setukpairinjR12)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', setukpairinjR1)).
% 83.50/12.42  thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', upairequniteq)).
% 83.50/12.42  thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setukpairinjR2)).
% 83.50/12.42  thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setukpairinjR)).
% 83.50/12.42  thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ksndpairEq)).
% 83.50/12.42  thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', kpairsurjEq)).
% 83.50/12.42  thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', cartprodsndin)).
% 83.50/12.42  thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', cartprodpairmemEL)).
% 83.50/12.42  thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', cartprodpairmemER)).
% 83.50/12.42  thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', cartprodmempaircEq)).
% 83.50/12.42  thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', cartprodfstpairEq)).
% 83.50/12.42  thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', cartprodsndpairEq)).
% 83.50/12.42  thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', cartprodpairsurjEq)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', app)).
% 83.50/12.42  thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', infuncsetfunc)).
% 83.50/12.42  thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ap2p)).
% 83.50/12.42  thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', funcinfuncset)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', brelnall1)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', brelnall2)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', funcGraphProp1)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', funcGraphProp3)).
% 83.50/12.42  thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', funcGraphProp2)).
% 83.50/12.42  thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', funcextLem)).
% 83.50/12.42  thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', funcGraphProp4)).
% 83.50/12.42  thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subbreln)).
% 83.50/12.42  thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', eqbreln)).
% 83.50/12.42  thf(funcext, axiom, ((funcext)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', funcext)).
% 83.50/12.42  thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', funcext2)).
% 83.50/12.42  thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ap2apEq1)).
% 83.50/12.42  thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ap2apEq2)).
% 83.50/12.42  thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', ifp)).
% 83.50/12.42  thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', theeq)).
% 83.50/12.42  thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', iftrue)).
% 83.50/12.42  thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', iffalse)).
% 83.50/12.42  thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', iftrueorfalse)).
% 83.50/12.42  thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', binintersectT_lem)).
% 83.50/12.42  thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binunionT_lem)).
% 83.50/12.42  thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', powersetT_lem)).
% 83.50/12.42  thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', setminusT_lem)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', complementT_lem)).
% 83.50/12.42  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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', setextT)).
% 83.50/12.42  thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subsetTI)).
% 83.50/12.42  thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', powersetTI1)).
% 83.50/12.42  thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', powersetTE1)).
% 83.50/12.42  thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', complementTI1)).
% 83.50/12.42  thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', complementTE1)).
% 83.50/12.42  thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectTELcontra)).
% 83.50/12.42  thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', binintersectTERcontra)).
% 83.50/12.42  thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', contrasubsetT)).
% 83.50/12.42  thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', contrasubsetT1)).
% 83.50/12.42  thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', contrasubsetT2)).
% 83.50/12.42  thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', contrasubsetT3)).
% 83.50/12.42  thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', doubleComplementI1)).
% 83.50/12.42  thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', doubleComplementE1)).
% 83.50/12.42  thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', doubleComplementSub1)).
% 83.50/12.42  thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', doubleComplementSub2)).
% 83.50/12.42  thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', doubleComplementEq)).
% 83.50/12.42  thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', complementTnotintersectT)).
% 83.50/12.42  thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', complementImpComplementIntersect)).
% 83.50/12.42  thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', complementSubsetComplementIntersect)).
% 83.50/12.42  thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', complementInPowersetComplementIntersect)).
% 83.50/12.42  thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', contraSubsetComplement)).
% 83.50/12.42  thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', complementTcontraSubset)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', binunionTILcontra)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', binunionTIRcontra)).
% 83.50/12.42  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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', inIntersectImpInUnion)).
% 83.50/12.42  thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', inIntersectImpInUnion2)).
% 83.50/12.42  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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', inIntersectImpInIntersectUnions)).
% 83.50/12.42  thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', intersectInPowersetIntersectUnions)).
% 83.50/12.42  thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', inComplementUnionImpNotIn1)).
% 83.50/12.42  thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', inComplementUnionImpInComplement1)).
% 83.50/12.42  thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', binunionTE)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', binunionTEcontra)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', demorgan2a1)).
% 83.50/12.42  thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', complementUnionInPowersetComplement)).
% 83.50/12.42  thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', demorgan2a2)).
% 83.50/12.42  thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', demorgan1a)).
% 83.50/12.42  thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', demorgan1b)).
% 83.50/12.42  thf(demorgan1, axiom, ((demorgan1)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', demorgan1)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', demorgan2a)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', demorgan2b2)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', demorgan2b)).
% 83.50/12.42  thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', demorgan2)).
% 83.50/12.42  thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', woz13rule0)).
% 83.50/12.42  thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', woz13rule1)).
% 83.50/12.42  thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', woz13rule2)).
% 83.50/12.42  thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', woz13rule3)).
% 83.50/12.42  thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', woz13rule4)).
% 83.50/12.42  thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', woz1_1)).
% 83.50/12.42  thf(woz1_2, axiom, ((woz1_2)<=>![X4:$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.7LvfJVf02x/E---3.1_3446945.p', woz1_2)).
% 83.50/12.42  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.7LvfJVf02x/E---3.1_3446945.p', woz1_3)).
% 83.50/12.42  thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', woz1_4)).
% 83.50/12.42  thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', woz1_5)).
% 83.50/12.42  thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1all2)).
% 83.50/12.42  thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1SetBreln1)).
% 83.50/12.42  thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1all1)).
% 83.50/12.42  thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', subbreln1)).
% 83.50/12.42  thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', eqbreln1)).
% 83.50/12.42  thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1invprop)).
% 83.50/12.42  thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1invI)).
% 83.50/12.42  thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1invE)).
% 83.50/12.42  thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1compprop)).
% 83.50/12.42  thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1compI)).
% 83.50/12.42  thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1compE)).
% 83.50/12.42  thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1compEex)).
% 83.50/12.42  thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1unionprop)).
% 83.50/12.42  thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1unionIL)).
% 83.50/12.42  thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1unionIR)).
% 83.50/12.42  thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1unionI)).
% 83.50/12.42  thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1unionE)).
% 83.50/12.42  thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1unionEcases)).
% 83.50/12.42  thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', breln1unionCommutes)).
% 83.50/12.42  thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', woz2Ex)).
% 83.50/12.43  thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', woz2W)).
% 83.50/12.43  thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', woz2A)).
% 83.50/12.43  thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', woz2B)).
% 83.50/12.43  thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', image1Ex)).
% 83.50/12.43  thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', injFuncInInjFuncSet)).
% 83.50/12.43  thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', injFuncSetFuncIn)).
% 83.50/12.43  thf(injFuncSetFuncInj, axiom, ((injFuncSetFuncInj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', injFuncSetFuncInj)).
% 83.50/12.43  thf(surjFuncSetFuncIn, axiom, ((surjFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', surjFuncSetFuncIn)).
% 83.50/12.43  thf(surjFuncSetFuncSurj, axiom, ((surjFuncSetFuncSurj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X2 @ X3))=>(surjective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', surjFuncSetFuncSurj)).
% 83.50/12.43  thf(leftInvIsSurj, axiom, ((leftInvIsSurj)<=>![X4:$i, X5:$i, X62:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X62 @ X2) @ X5)))=>![X34:$i]:(((in @ X34 @ (funcSet @ X5 @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X5 @ X4 @ X34 @ (X62 @ X2))=(X2))))=>(surjective @ X5 @ X4 @ X34))))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', leftInvIsSurj)).
% 83.50/12.43  thf(surjCantorThm, axiom, ((surjCantorThm)<=>![X4:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ (powerset @ X4)))=>~((surjective @ X4 @ (powerset @ X4) @ X29))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', surjCantorThm)).
% 83.50/12.43  thf(notinself, axiom, ((notinself)<=>![X4:$i]:(~((in @ X4 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', notinself)).
% 83.50/12.43  thf(notinself2, axiom, ((notinself2)<=>![X4:$i, X5:$i]:(((in @ X4 @ X5)=>~((in @ X5 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', notinself2)).
% 83.50/12.43  thf(omegaSp, axiom, ((omegaSp)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (omegaS @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', omegaSp)).
% 83.50/12.43  thf(omegaSclos, axiom, ((omegaSclos)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', omegaSclos)).
% 83.50/12.43  thf(peano0notS, axiom, ((peano0notS)<=>![X2:$i]:(((in @ X2 @ omega)=>((omegaS @ X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', peano0notS)).
% 83.50/12.43  thf(omegaS, axiom, ((omegaS)=(^[X2:$i]:(setadjoin @ X2 @ X2))), file('/export/starexec/sandbox2/tmp/tmp.7LvfJVf02x/E---3.1_3446945.p', omegaS)).
% 83.50/12.43  thf(c_0_331, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 83.50/12.43  thf(c_0_332, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 83.50/12.43  thf(c_0_333, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 83.50/12.43  thf(c_0_334, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 83.50/12.43  thf(c_0_335, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 83.50/12.43  thf(c_0_336, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 83.50/12.43  thf(c_0_337, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 83.50/12.43  thf(c_0_338, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 83.50/12.43  thf(c_0_339, 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])).
% 83.50/12.43  thf(c_0_340, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 83.50/12.43  thf(c_0_341, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 83.50/12.43  thf(c_0_342, 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])).
% 83.50/12.43  thf(c_0_343, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 83.50/12.43  thf(c_0_344, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 83.50/12.43  thf(c_0_345, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 83.50/12.43  thf(c_0_346, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0:$i]:(![X2:$i]:((((in @ X2 @ Z0))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])).
% 83.50/12.43  thf(c_0_347, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>((breln1compprop)=>((breln1compI)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>((breln1unionIR)=>((breln1unionI)=>((breln1unionE)=>((breln1unionEcases)=>((breln1unionCommutes)=>((woz2Ex)=>((woz2W)=>((woz2A)=>((woz2B)=>((image1Ex)=>((image1Ex1)=>((image1Equiv)=>((image1E)=>((image1I)=>((injFuncInInjFuncSet)=>((injFuncSetFuncIn)=>((injFuncSetFuncInj)=>((surjFuncSetFuncIn)=>((surjFuncSetFuncSurj)=>((leftInvIsSurj)=>((surjCantorThm)=>((foundation2)=>((notinself)=>((notinself2)=>((omegaSp)=>((omegaSclos)=>((peano0notS)=>![X2:$i]:(((in @ X2 @ omega)=>![X3:$i]:(((in @ X3 @ omega)=>(((omegaS @ X2)=(omegaS @ X3))=>((X2)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[peanoSinj])).
% 83.50/12.43  thf(c_0_348, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X1134:$i]:(((((X6 @ X2 @ X1134)))&(![X1135:$i]:(((((X6 @ X2 @ X1135)))=>(((X1134)=(X1135)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_331, c_0_332])).
% 83.50/12.43  thf(c_0_349, plain, ((descrp)=(![X1:$i > $o]:((((?[X1136:$i]:(((((X1 @ X1136)))&(![X1137:$i]:(((((X1 @ X1137)))=>(((X1136)=(X1137))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_333, c_0_332])).
% 83.50/12.43  thf(c_0_350, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 83.50/12.43  thf(c_0_351, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 83.50/12.43  thf(c_0_352, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 83.50/12.43  thf(c_0_353, plain, ((exuE1)=(![X1:$i > $o]:((((?[X1138:$i]:(((((X1 @ X1138)))&(![X1139:$i]:(((((X1 @ X1139)))=>(((X1138)=(X1139))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_334, c_0_332])).
% 83.50/12.43  thf(c_0_354, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X1140:$i]:(((((X1 @ X1140)))&(![X1141:$i]:(((((X1 @ X1141)))=>(((X1140)=(X1141))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_335, c_0_332])).
% 83.50/12.43  thf(c_0_355, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 83.50/12.43  thf(c_0_356, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_336])).
% 83.50/12.43  thf(c_0_357, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_337, c_0_336])).
% 83.50/12.43  thf(c_0_358, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_336])).
% 83.50/12.43  thf(c_0_359, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 83.50/12.43  thf(c_0_360, plain, ((exuE2)=(![X1:$i > $o]:((((?[X1142:$i]:(((((X1 @ X1142)))&(![X1143:$i]:(((((X1 @ X1143)))=>(((X1142)=(X1143))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_338, c_0_332])).
% 83.50/12.43  thf(c_0_361, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_336])).
% 83.50/12.43  thf(c_0_362, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 83.50/12.43  thf(c_0_363, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X1144:$i]:(((((X1 @ X1144)))&(![X1145:$i]:(((((X1 @ X1145)))=>(((X1144)=(X1145)))))))))))))), inference(apply_def,[status(thm)],[c_0_339, c_0_332])).
% 83.50/12.43  thf(c_0_364, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X1146:$i]:(((((X1 @ X1146)))&(![X1147:$i]:(((((X1 @ X1147)))=>(((X1146)=(X1147)))))))))))))))), inference(apply_def,[status(thm)],[c_0_340, c_0_332])).
% 83.50/12.43  thf(c_0_365, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X1148:$i]:(((((X1 @ X1148)))&(![X1149:$i]:(((((X1 @ X1149)))=>(((X1148)=(X1149)))))))))))))), inference(apply_def,[status(thm)],[c_0_341, c_0_332])).
% 83.50/12.43  thf(c_0_366, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X1150:$i]:(((((X1 @ X1150)))&(![X1151:$i]:(((((X1 @ X1151)))=>(((X1150)=(X1151))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_342, c_0_332])).
% 83.50/12.43  thf(c_0_367, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1152:$i]:(((((X1 @ X1152)))&(![X1153:$i]:(((((X1 @ X1153)))=>(((X1152)=(X1153))))))))))<=>((?[X1154:$i]:(((((X17 @ X1154)))&(![X1155:$i]:(((((X17 @ X1155)))=>(((X1154)=(X1155)))))))))))))))), inference(apply_def,[status(thm)],[c_0_343, c_0_332])).
% 83.50/12.43  thf(c_0_368, plain, ((exuEu)=(![X1:$i > $o]:((((?[X1156:$i]:(((((X1 @ X1156)))&(![X1157:$i]:(((((X1 @ X1157)))=>(((X1156)=(X1157))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_344, c_0_332])).
% 83.50/12.43  thf(c_0_369, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1158:$i]:(((((X1 @ X1158)))&(![X1159:$i]:(((((X1 @ X1159)))=>(((X1158)=(X1159))))))))))=>((((?[X1160:$i]:(((((X17 @ X1160)))&(![X1161:$i]:(((((X17 @ X1161)))=>(((X1160)=(X1161))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_345, c_0_332])).
% 83.50/12.43  thf(c_0_370, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 83.50/12.43  thf(c_0_371, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 83.50/12.43  thf(c_0_372, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 83.50/12.43  thf(c_0_373, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 83.50/12.43  thf(c_0_374, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 83.50/12.43  thf(c_0_375, plain, ((ex1I)<=>![X4:$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])).
% 83.50/12.43  thf(c_0_376, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 83.50/12.43  thf(c_0_377, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 83.50/12.43  thf(c_0_378, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 83.50/12.43  thf(c_0_379, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 83.50/12.43  thf(c_0_380, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 83.50/12.43  thf(c_0_381, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 83.50/12.43  thf(c_0_382, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 83.50/12.43  thf(c_0_383, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 83.50/12.43  thf(c_0_384, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 83.50/12.43  thf(c_0_385, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 83.50/12.43  thf(c_0_386, plain, ((funcImageSingleton)<=>![X4:$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])).
% 83.50/12.43  thf(c_0_387, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 83.50/12.43  thf(c_0_388, plain, ((lamProp)<=>![X4:$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])).
% 83.50/12.43  thf(c_0_389, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 83.50/12.43  thf(c_0_390, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 83.50/12.43  thf(c_0_391, plain, ((ex1E2)<=>![X4:$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])).
% 83.50/12.43  thf(c_0_392, 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])).
% 83.50/12.43  thf(c_0_393, 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])).
% 83.50/12.43  thf(c_0_394, 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])).
% 83.50/12.43  thf(c_0_395, 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])).
% 83.50/12.43  thf(c_0_396, 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])).
% 83.50/12.43  thf(c_0_397, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 83.50/12.43  thf(c_0_398, plain, ((iffalseProp2)<=>![X4:$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])).
% 83.50/12.43  thf(c_0_399, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 83.50/12.43  thf(c_0_400, plain, ((iftrueProp2)<=>![X4:$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])).
% 83.50/12.43  thf(c_0_401, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 83.50/12.43  thf(c_0_402, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((((X52 @ X2 @ Z0))&(![X14:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ Z0 @ X14) @ X33)))))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])).
% 83.50/12.43  thf(c_0_403, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
% 83.50/12.43  thf(c_0_404, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1162:$i]:((((![X2:$i]:((((in @ X2 @ X1162))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))&(![X1163:$i]:((((![X2:$i]:((((in @ X2 @ X1163))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))=>(((X1162)=(X1163)))))))))))), inference(apply_def,[status(thm)],[c_0_346, c_0_332])).
% 83.50/12.43  thf(c_0_405, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])).
% 83.50/12.43  thf(c_0_406, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])).
% 83.50/12.43  thf(c_0_407, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])).
% 83.50/12.43  thf(c_0_408, axiom, ((foundation2)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X21:$i]:((((in @ X21 @ X4))&(((binintersect @ X21 @ X4)=(emptyset)))))))))), inference(apply_def,[status(thm)],[foundation2, c_0_336])).
% 83.50/12.43  thf(c_0_409, plain, ((epred1_0)<=>![X1193:$i]:(?[X1194:$i]:((((![X1195:$i]:(((in @ X1195 @ X1194)=>![X1196:$i]:(((in @ X1196 @ X1195)=>(in @ X1196 @ X1193)))))&![X1197:$i, X1198:$i]:((((in @ X1197 @ X1193)&(in @ X1198 @ X1193))=>(![X1199:$i]:(((in @ X1199 @ X1194)=>((in @ X1197 @ X1199)<=>(in @ X1198 @ X1199))))=>((X1197)=(X1198))))))&![X1200:$i, X1201:$i]:((((in @ X1200 @ X1194)&(in @ X1201 @ X1194))=>(![X1202:$i]:(((in @ X1202 @ X1200)=>(in @ X1202 @ X1201)))|![X1203:$i]:(((in @ X1203 @ X1201)=>(in @ X1203 @ X1200)))))))&![X1204:$i]:(((![X1205:$i]:(((in @ X1205 @ X1204)=>(in @ X1205 @ X1193)))&?[X1206:$i]:((in @ X1206 @ X1204)))=>?[X1207:$i, X1208:$i]:(((((in @ X1207 @ X1194)&(in @ X1208 @ X1204))&~(?[X1209:$i]:(((in @ X1209 @ X1207)&(in @ X1209 @ X1204)))))&![X1210:$i]:(((in @ X1210 @ X1194)=>(![X1211:$i]:(((in @ X1211 @ X1210)=>(in @ X1211 @ X1207)))|(in @ X1208 @ X1210)))))))))))), introduced(definition)).
% 83.50/12.43  thf(c_0_410, negated_conjecture, ~((![X1164:$i, X1165:$i]:((![X1166:$i]:(((in @ X1166 @ X1164)<=>(in @ X1166 @ X1165)))=>((X1164)=(X1165))))=>(![X1167:$i]:(~(in @ X1167 @ emptyset))=>(![X1168:$i, X1169:$i, X1170:$i]:(((in @ X1170 @ (setadjoin @ X1168 @ X1169))<=>(((X1170)=(X1168))|(in @ X1170 @ X1169))))=>(![X1171:$i, X1172:$i]:(((in @ X1172 @ (powerset @ X1171))<=>![X1173:$i]:(((in @ X1173 @ X1172)=>(in @ X1173 @ X1171)))))=>(![X1174:$i, X1175:$i]:(((in @ X1175 @ (setunion @ X1174))<=>?[X1176:$i]:(((in @ X1175 @ X1176)&(in @ X1176 @ X1174)))))=>((in @ emptyset @ omega)=>(![X1177:$i]:(((in @ X1177 @ omega)=>(in @ (setadjoin @ X1177 @ X1177) @ omega)))=>(![X1178:$i]:((((in @ emptyset @ X1178)&![X1179:$i]:((((in @ X1179 @ omega)&(in @ X1179 @ X1178))=>(in @ (setadjoin @ X1179 @ X1179) @ X1178))))=>![X1180:$i]:(((in @ X1180 @ omega)=>(in @ X1180 @ X1178)))))=>(![X1181:$i > $i > $o, X1182:$i]:((![X1183:$i]:(((in @ X1183 @ X1182)=>?[X1184:$i]:(((X1181 @ X1183 @ X1184)&![X1185:$i]:(((X1181 @ X1183 @ X1185)=>((X1184)=(X1185))))))))=>?[X1186:$i]:(![X1187:$i]:(((in @ X1187 @ X1186)<=>?[X1188:$i]:(((in @ X1188 @ X1182)&(X1181 @ X1188 @ X1187))))))))=>(![X1189:$i]:((?[X1190:$i]:((in @ X1190 @ X1189))=>?[X1191:$i]:(((in @ X1191 @ X1189)&~(?[X1192:$i]:(((in @ X1192 @ X1191)&(in @ X1192 @ X1189))))))))=>((epred1_0)=>(![X1212:$i > $o]:((?[X1213:$i]:(((X1212 @ X1213)&![X1214:$i]:(((X1212 @ X1214)=>((X1213)=(X1214))))))=>(X1212 @ (descr @ (^[Z0:$i]:(X1212 @ Z0))))))=>(![X1215:$i, X1216:$i > $o, X1217:$i]:(((in @ X1217 @ X1215)=>((X1216 @ X1217)=>(in @ X1217 @ (dsetconstr @ X1215 @ X1216)))))=>(![X1218:$i, X1219:$i > $o, X1220:$i]:(((in @ X1220 @ (dsetconstr @ X1218 @ X1219))=>(in @ X1220 @ X1218)))=>(![X1221:$i, X1222:$i > $o, X1223:$i]:(((in @ X1223 @ (dsetconstr @ X1221 @ X1222))=>(X1222 @ X1223)))=>(![X1224:$i > $o]:((?[X1225:$i]:(((X1224 @ X1225)&![X1226:$i]:(((X1224 @ X1226)=>((X1225)=(X1226))))))=>?[X1227:$i]:(((X1224 @ X1227)&![X1228:$i]:(((X1224 @ X1228)=>((X1227)=(X1228))))))))=>(![X1229:$o, X1230:$i]:(((in @ X1230 @ (prop2set @ ((X1229))))=>(X1229)))=>(![X1231:$i]:(((in @ X1231 @ emptyset)=>![X1232:$o]:((X1232))))=>(![X1233:$i]:(((in @ X1233 @ emptyset)=>~($true)))=>(![X1234:$i]:(~(in @ X1234 @ emptyset))=>(![X1235:$i > $o]:((?[X1236:$i]:(((X1235 @ X1236)&![X1237:$i]:(((X1235 @ X1237)=>((X1236)=(X1237))))))=>?[X1238:$i]:((X1235 @ X1238))))=>(![X1239:$i, X1240:$i]:((![X1241:$i]:(((in @ X1241 @ X1239)=>(in @ X1241 @ X1240)))=>(![X1242:$i]:(((in @ X1242 @ X1240)=>(in @ X1242 @ X1239)))=>((X1239)=(X1240)))))=>(![X1243:$i]:((![X1244:$i]:(~(in @ X1244 @ X1243))=>((X1243)=(emptyset))))=>(![X1245:$i]:((![X1246:$i]:(~(in @ X1246 @ X1245))=>((X1245)=(emptyset))))=>(![X1247:$i, X1248:$i > $o, X1249:$i]:(((in @ X1249 @ X1247)=>((in @ X1249 @ (dsetconstr @ X1247 @ X1248))<=>(X1248 @ X1249))))=>(![X1250:$i]:((((X1250)!=(emptyset))=>?[X1251:$i]:((in @ X1251 @ X1250))))=>(![X1252:$i, X1253:$i > $o, X1254:$i]:(((in @ X1254 @ X1252)=>((X1253 @ X1254)=>((dsetconstr @ X1252 @ X1253)!=(emptyset)))))=>(![X1255:$i]:((?[X1256:$i]:((in @ X1256 @ X1255))=>((X1255)!=(emptyset))))=>(![X1257:$i, X1258:$i]:((in @ X1257 @ (setadjoin @ X1257 @ X1258)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1259:$i, X1260:$i, X1261:$i]:(((in @ X1261 @ X1260)=>(in @ X1261 @ (setadjoin @ X1259 @ X1260))))=>(![X1262:$i, X1263:$i, X1264:$i]:(((in @ X1264 @ (setadjoin @ X1262 @ X1263))=>![X1265:$o]:(((((X1264)=(X1262))=>(X1265))=>(((in @ X1264 @ X1263)=>(X1265))=>(X1265))))))=>(![X1266:$i, X1267:$i, X1268:$i]:(((in @ X1268 @ (setadjoin @ X1266 @ X1267))=>(((X1268)=(X1266))|(in @ X1268 @ X1267))))=>(![X1269:$i]:(((dsetconstr @ X1269 @ (^[Z0:$i]:($true)))=(X1269)))=>(![X1270:$i, X1271:$i]:((![X1272:$i]:(((in @ X1272 @ X1271)=>(in @ X1272 @ X1270)))=>(in @ X1271 @ (powerset @ X1270))))=>(![X1273:$i]:((in @ emptyset @ (powerset @ X1273)))=>(![X1274:$i]:((in @ emptyset @ (powerset @ X1274)))=>(![X1275:$i, X1276:$i, X1277:$i]:(((in @ X1276 @ (powerset @ X1275))=>((in @ X1277 @ X1276)=>(in @ X1277 @ X1275))))=>(![X1278:$i, X1279:$i, X1280:$i]:(((in @ X1279 @ X1280)=>((in @ X1280 @ X1278)=>(in @ X1279 @ (setunion @ X1278)))))=>(![X1281:$i, X1282:$i]:(((in @ X1282 @ (setunion @ X1281))=>![X1283:$o]:((![X1284:$i]:(((in @ X1282 @ X1284)=>((in @ X1284 @ X1281)=>(X1283))))=>(X1283)))))=>(![X1285:$i, X1286:$i]:(((in @ X1286 @ X1285)=>(in @ X1286 @ (powerset @ (setunion @ X1285)))))=>(![X1287:$i > $o]:((?[X1288:$i]:(((X1287 @ X1288)&![X1289:$i]:(((X1287 @ X1289)=>((X1288)=(X1289))))))=>?[X1290:$i]:(![X1291:$i]:(((X1287 @ X1291)<=>((X1291)=(X1290)))))))=>(![X1292:$i]:((((X1292)!=(emptyset))=>?[X1293:$i]:(((in @ X1293 @ X1292)&$true))))=>(![X1294:$i, X1295:$i]:(((in @ X1294 @ (setadjoin @ X1295 @ emptyset))=>((X1294)=(X1295))))=>(![X1296:$i, X1297:$i]:((((X1296)!=(X1297))=>~(in @ X1297 @ (setadjoin @ X1296 @ emptyset))))=>(![X1298:$i, X1299:$i]:((((X1298)=(X1299))=>(in @ X1298 @ (setadjoin @ X1299 @ emptyset))))=>(![X1300:$i, X1301:$i]:(((in @ X1300 @ (setadjoin @ X1301 @ emptyset))=>(in @ X1301 @ (setadjoin @ X1300 @ emptyset))))=>(![X1302:$i, X1303:$i, X1304:$i]:(((in @ X1304 @ (setadjoin @ X1302 @ (setadjoin @ X1303 @ emptyset)))=>(((X1304)=(X1302))|((X1304)=(X1303)))))=>(![X1305:$i, X1306:$i]:((in @ X1305 @ (setadjoin @ X1305 @ (setadjoin @ X1306 @ emptyset))))=>(![X1307:$i, X1308:$i]:((in @ X1308 @ (setadjoin @ X1307 @ (setadjoin @ X1308 @ emptyset))))=>(![X1309:$i, X1310:$i > $o]:((?[X1311:$i]:(((in @ X1311 @ X1309)&(X1310 @ X1311)))=>(((dsetconstr @ X1309 @ X1310)=(emptyset))=>~($true))))=>(![X1312:$i > $o, X1313:$i]:(((in @ X1313 @ emptyset)=>(X1312 @ X1313)))=>(![X1314:$i, X1315:$i > $o]:((~(![X1316:$i]:(((in @ X1316 @ X1314)=>(X1315 @ X1316))))=>?[X1317:$i]:(((in @ X1317 @ X1314)&~((X1315 @ X1317))))))=>(![X1318:$i, X1319:$i > $o]:((![X1320:$i]:(((in @ X1320 @ X1318)=>~((X1319 @ X1320))))=>~(?[X1321:$i]:(((in @ X1321 @ X1318)&(X1319 @ X1321))))))=>(![X1322:$i, X1323:$i > $o]:((~(?[X1324:$i]:(((in @ X1324 @ X1322)&(X1323 @ X1324))))=>![X1325:$i]:(((in @ X1325 @ X1322)=>~((X1323 @ X1325))))))=>(![X1326:$i, X1327:$i > $o]:((?[X1328:$i]:(((in @ X1328 @ X1326)&~((X1327 @ X1328))))=>~(![X1329:$i]:(((in @ X1329 @ X1326)=>(X1327 @ X1329))))))=>(![X1330:$o]:(((X1330)=>(in @ emptyset @ (prop2set @ ((X1330))))))=>(![X1331:$o]:(((X1331)=>(set2prop @ (prop2set @ ((X1331))))))=>(![X1332:$i, X1333:$i > $o]:((~(?[X1334:$i]:(((in @ X1334 @ X1332)&(X1333 @ X1334))))=>![X1335:$i]:(((in @ X1335 @ X1332)=>~((X1333 @ X1335))))))=>(![X1336:$i, X1337:$i > $o]:((~(![X1338:$i]:(((in @ X1338 @ X1336)=>(X1337 @ X1338))))=>?[X1339:$i]:(((in @ X1339 @ X1336)&~((X1337 @ X1339))))))=>(![X1340:$i > $o]:((?[X1341:$i]:(((X1340 @ X1341)&![X1342:$i]:(((X1340 @ X1342)=>((X1341)=(X1342))))))=>?[X1343:$i]:(((X1340 @ X1343)&![X1344:$i]:(((X1340 @ X1344)=>((X1343)=(X1344))))))))=>(![X1345:$i > $o]:((?[X1346:$i]:((X1345 @ X1346))=>(![X1347:$i, X1348:$i]:(((X1345 @ X1347)=>((X1345 @ X1348)=>((X1347)=(X1348)))))=>?[X1349:$i]:(((X1345 @ X1349)&![X1350:$i]:(((X1345 @ X1350)=>((X1349)=(X1350)))))))))=>(![X1351:$i > $o]:((?[X1352:$i]:(![X1353:$i]:(((X1351 @ X1353)<=>((X1353)=(X1352)))))=>?[X1354:$i]:(((X1351 @ X1354)&![X1355:$i]:(((X1351 @ X1355)=>((X1354)=(X1355))))))))=>(![X1356:$i, X1357:$i]:((((X1356)=(X1357))=>![X1358:$i, X1359:$i]:((((X1358)=(X1359))=>((in @ X1358 @ X1356)=>(in @ X1359 @ X1357))))))=>(![X1360:$i, X1361:$i]:((((X1360)=(X1361))=>![X1362:$i, X1363:$i]:((((X1362)=(X1363))=>((in @ X1362 @ X1360)<=>(in @ X1363 @ X1361))))))=>(![X1364:$i > $o]:((?[X1365:$i]:(((X1364 @ X1365)&![X1366:$i]:(((X1364 @ X1366)=>((X1365)=(X1366))))))=>![X1367:$i, X1368:$i]:(((X1364 @ X1367)=>((X1364 @ X1368)=>((X1367)=(X1368)))))))=>(![X1369:$i > $o, X1370:$i > $o]:((![X1371:$i, X1372:$i]:((((X1371)=(X1372))=>((X1369 @ X1371)<=>(X1370 @ X1372))))=>(?[X1373:$i]:(((X1369 @ X1373)&![X1374:$i]:(((X1369 @ X1374)=>((X1373)=(X1374))))))<=>?[X1375:$i]:(((X1370 @ 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X2190 @ X2192)=>![X2193:$i]:(((in @ X2193 @ X2190)=>![X2194:$i]:(((in @ X2194 @ X2190)=>((in @ (kpair @ X2193 @ X2194) @ (binunion @ X2191 @ X2192))=>![X2195:$o]:((((in @ (kpair @ X2193 @ X2194) @ X2191)=>(X2195))=>(((in @ (kpair @ X2193 @ X2194) @ X2192)=>(X2195))=>(X2195)))))))))))))=>(![X2196:$i, X2197:$i]:(((breln1 @ X2196 @ X2197)=>![X2198:$i]:(((breln1 @ X2196 @ X2198)=>((binunion @ X2197 @ X2198)=(binunion @ X2198 @ X2197))))))=>(![X2199:$i, X2200:$i]:(((breln1 @ X2199 @ X2200)=>((X2200)=(breln1invset @ X2199 @ (breln1invset @ X2199 @ X2200)))))=>(![X2201:$i, X2202:$i]:(((breln1 @ X2201 @ X2202)=>![X2203:$i]:(((breln1 @ X2201 @ X2203)=>((breln1invset @ X2201 @ (breln1compset @ X2201 @ X2202 @ X2203))=(breln1compset @ X2201 @ (breln1invset @ X2201 @ X2203) @ (breln1invset @ X2201 @ X2202)))))))=>(![X2204:$i, X2205:$i]:(((breln1 @ X2204 @ X2205)=>![X2206:$i]:(((breln1 @ X2204 @ X2206)=>![X2207:$i]:(((breln1 @ X2204 @ X2207)=>((breln1compset @ X2204 @ (binunion @ X2205 @ X2206) @ X2207)=(binunion @ (breln1compset @ X2204 @ X2205 @ X2207) @ (breln1compset @ X2204 @ X2206 @ X2207)))))))))=>(![X2208:$i, X2209:$i]:(((breln1 @ X2208 @ X2209)=>![X2210:$i]:(((breln1 @ X2208 @ X2210)=>![X2211:$i]:(((breln1 @ X2208 @ X2211)=>((breln1compset @ X2208 @ (binunion @ X2209 @ X2210) @ X2211)=(binunion @ (breln1invset @ X2208 @ (breln1compset @ X2208 @ (breln1invset @ X2208 @ X2211) @ (breln1invset @ X2208 @ X2210))) @ (breln1invset @ X2208 @ (breln1compset @ X2208 @ (breln1invset @ X2208 @ X2211) @ (breln1invset @ X2208 @ X2209)))))))))))=>(![X2212:$i, X2213:$i > $i]:(?[X2214:$i]:(![X2215:$i]:(((in @ X2215 @ X2214)<=>?[X2216:$i]:(((in @ X2216 @ X2212)&((X2215)=(X2213 @ X2216))))))))=>(![X2217:$i, X2218:$i > $i]:(?[X2219:$i]:((![X2220:$i]:(((in @ X2220 @ X2219)<=>?[X2221:$i]:(((in @ X2221 @ X2217)&((X2220)=(X2218 @ X2221))))))&![X2222:$i]:((![X2223:$i]:(((in @ X2223 @ X2222)<=>?[X2224:$i]:(((in @ X2224 @ X2217)&((X2223)=(X2218 @ X2224))))))=>((X2219)=(X2222)))))))=>(![X2225:$i, X2226:$i > $i, X2227:$i]:(((in @ X2227 @ (image1 @ X2225 @ X2226))<=>?[X2228:$i]:(((in @ X2228 @ X2225)&((X2227)=(X2226 @ X2228))))))=>(![X2229:$i, X2230:$i > $i, X2231:$i]:(((in @ X2231 @ (image1 @ X2229 @ X2230))=>?[X2232:$i]:(((in @ X2232 @ X2229)&((X2231)=(X2230 @ X2232))))))=>(![X2233:$i, X2234:$i > $i, X2235:$i]:((?[X2236:$i]:(((in @ X2236 @ X2233)&((X2235)=(X2234 @ X2236))))=>(in @ X2235 @ (image1 @ X2233 @ X2234))))=>(![X2237:$i, X2238:$i, X2239:$i]:(((in @ X2239 @ (funcSet @ X2237 @ X2238))=>((injective @ X2237 @ X2238 @ X2239)=>(in @ X2239 @ (injFuncSet @ X2237 @ X2238)))))=>(![X2240:$i, X2241:$i, X2242:$i]:(((in @ X2242 @ (injFuncSet @ X2240 @ X2241))=>(in @ X2242 @ (funcSet @ X2240 @ X2241))))=>(![X2243:$i, X2244:$i, X2245:$i]:(((in @ X2245 @ (injFuncSet @ X2243 @ X2244))=>(injective @ X2243 @ X2244 @ X2245)))=>(![X2246:$i, X2247:$i, X2248:$i]:(((in @ X2248 @ (surjFuncSet @ X2246 @ X2247))=>(in @ X2248 @ (funcSet @ X2246 @ X2247))))=>(![X2249:$i, X2250:$i, X2251:$i]:(((in @ X2251 @ (surjFuncSet @ X2249 @ X2250))=>(surjective @ X2249 @ X2250 @ X2251)))=>(![X2252:$i, X2253:$i, X2254:$i > $i]:((![X2255:$i]:(((in @ X2255 @ X2252)=>(in @ (X2254 @ X2255) @ X2253)))=>![X2256:$i]:(((in @ X2256 @ (funcSet @ X2253 @ X2252))=>(![X2257:$i]:(((in @ X2257 @ X2252)=>((ap @ X2253 @ X2252 @ X2256 @ (X2254 @ X2257))=(X2257))))=>(surjective @ X2253 @ X2252 @ X2256))))))=>(![X2258:$i, X2259:$i]:(((in @ X2259 @ (funcSet @ X2258 @ (powerset @ X2258)))=>~(surjective @ X2258 @ (powerset @ X2258) @ X2259)))=>(![X2260:$i]:((((X2260)!=(emptyset))=>?[X2261:$i]:(((in @ X2261 @ X2260)&((binintersect @ X2261 @ X2260)=(emptyset))))))=>(![X2262:$i]:(~(in @ X2262 @ X2262))=>(![X2263:$i, X2264:$i]:(((in @ X2263 @ X2264)=>~(in @ X2264 @ X2263)))=>(![X2265:$i]:(((in @ X2265 @ omega)=>(in @ (omegaS @ X2265) @ omega)))=>(![X2266:$i]:(((in @ X2266 @ omega)=>(in @ (setadjoin @ X2266 @ X2266) @ omega)))=>(![X2267:$i]:(((in @ X2267 @ omega)=>((omegaS @ X2267)!=(emptyset))))=>![X2:$i]:(((in @ X2 @ omega)=>![X3:$i]:(((in @ X3 @ omega)=>(((omegaS @ X2)=(omegaS @ X3))=>((X2)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_347, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_348]), foundationAx]), wellorderingAx]), c_0_349]), c_0_350]), c_0_351]), c_0_352]), c_0_353]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_354]), setext]), emptyI]), noeltsimpempty]), c_0_355]), c_0_356]), c_0_357]), c_0_358]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_359]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_360]), c_0_361]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_362]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_363]), c_0_364]), c_0_365]), inCongP]), in__Cong]), c_0_366]), c_0_367]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_368]), c_0_369]), c_0_370]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_371]), c_0_372]), 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_373]), c_0_374]), c_0_375]), c_0_376]), singletonsuniq]), setukpairinjL1]), c_0_377]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_378]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_379]), c_0_380]), c_0_381]), c_0_382]), c_0_383]), c_0_384]), c_0_385]), c_0_386]), c_0_387]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_388]), c_0_389]), c_0_390]), brelnall1]), brelnall2]), c_0_391]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), subbreln]), eqbreln]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_392]), c_0_393]), c_0_394]), c_0_395]), c_0_396]), c_0_397]), c_0_398]), c_0_399]), c_0_400]), c_0_401]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3]), woz1_4]), woz1_5]), breln1all2]), breln1SetBreln1]), c_0_402]), c_0_403]), breln1all1]), subbreln1]), eqbreln1]), breln1invprop]), breln1invI]), breln1invE]), breln1compprop]), breln1compI]), breln1compE]), breln1compEex]), breln1unionprop]), breln1unionIL]), breln1unionIR]), breln1unionI]), breln1unionE]), breln1unionEcases]), breln1unionCommutes]), woz2Ex]), woz2W]), woz2A]), woz2B]), image1Ex]), c_0_404]), c_0_405]), c_0_406]), c_0_407]), injFuncInInjFuncSet]), injFuncSetFuncIn]), injFuncSetFuncInj]), surjFuncSetFuncIn]), surjFuncSetFuncSurj]), leftInvIsSurj]), surjCantorThm]), c_0_408]), notinself]), notinself2]), omegaSp]), omegaSclos]), peano0notS])])]), c_0_409])).
% 83.50/12.43  thf(c_0_411, plain, ![X2268:$i]:(((omegaS @ X2268)=(setadjoin @ X2268 @ X2268))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[omegaS])])).
% 83.50/12.43  thf(c_0_412, negated_conjecture, ![X2270:$i, X2271:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2283:$i, X2284:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2292:$i, X2293:$i > $i > $o, X2294:$i, X2296:$i, X2299:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2306:$i, X2307:$i > $o, X2308:$i, X2310:$i, X2311:$i > $o, X2312:$i, X2313:$i, X2314:$i > $o, X2315:$i, X2316:$i, X2317:$i > $o, X2318:$i, X2319:$i > $o, X2320:$i, X2323:$i, X2324:$o, X2325:$i, X2326:$i, X2327:$o, X2328:$i, X2329:$i, X2330:$i > $o, X2331:$i, X2334:$i, X2335:$i, X2338:$i, X2340:$i, X2342:$i, X2343:$i > $o, X2344:$i, X2345:$i, X2347:$i, X2348:$i > $o, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$o, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$o, X2380:$i, X2381:$i, X2382:$i > $o, X2383:$i, X2386:$i, X2387:$i, X2388:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i > $o, X2407:$i, X2408:$i > $o, X2409:$i, X2410:$i, X2411:$i > $o, X2412:$i, X2414:$i, X2415:$i > $o, X2417:$i, X2418:$i, X2419:$i > $o, X2421:$i, X2422:$i, X2423:$i > $o, X2424:$i, X2426:$o, X2427:$o, X2428:$i, X2429:$i > $o, X2431:$i, X2432:$i, X2433:$i > $o, X2434:$i, X2436:$i > $o, X2437:$i, X2440:$i, X2441:$i > $o, X2442:$i, X2446:$i, X2447:$i > $o, X2448:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i > $o, X2461:$i, X2463:$i, X2464:$i, X2465:$i > $o, X2466:$i > $o, X2469:$i, X2472:$i, X2473:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i > $o, X2486:$i, X2488:$i, X2489:$i, X2490:$i > $o, X2491:$i > $o, X2494:$i, X2496:$i, X2498:$i, X2499:$i, X2500:$i > $o, X2501:$i > $o, X2504:$i, X2505:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i > $o, X2552:$i, X2553:$i > $o, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$o, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i, X2591:$i, X2592:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2623:$i, X2624:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i, X2630:$i, X2631:$i, X2632:$i, X2633:$o, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i > $o, X2708:$i, X2709:$i, X2710:$i > $o, X2712:$i, X2713:$i > $o, X2714:$i, X2716:$i, X2717:$i > $o, X2720:$i, X2721:$i, X2722:$i, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2791:$i, X2792:$i > $i > $o, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i > $i > $o, X2798:$i, X2799:$i, X2800:$i > $i > $o, X2801:$i, X2802:$i, X2803:$i > $i > $o, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i > $i > $o, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i > $i > $o, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i > $i > $o, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i > $i, X2847:$i, X2848:$i, X2849:$i > $i, X2851:$i, X2852:$i, X2853:$i > $i, X2855:$i, X2856:$i, X2857:$i, X2858:$i > $o, X2861:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i > $o, X2868:$i, X2869:$i, X2870:$i > $o, X2871:$i, X2872:$i, X2873:$i, X2874:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$i, X2885:$i, X2886:$i, X2887:$i, X2888:$i, X2889:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2901:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i > $i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i, X2939:$i, X2940:$i > $i, X2942:$i, X2943:$i, X2944:$i > $i, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$i, X2951:$o, X2952:$i, X2953:$i, X2954:$i, X2955:$o, X2956:$i, X2957:$i, X2958:$i, X2959:$o, X2960:$i, X2961:$i, X2962:$i, X2963:$o, X2964:$i, X2965:$i, X2966:$i, X2967:$o, X2968:$i, X2969:$i, X2970:$i, X2971:$o, X2972:$i, X2973:$i, X2974:$i, X2975:$i, X2976:$i, X2977:$o, X2978:$i, X2979:$i, X2980:$i, X2981:$o, X2982:$i, X2983:$i, X2984:$i, X2985:$o, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3002:$i, X3003:$i, X3006:$i, X3007:$i, X3008:$i, X3010:$i, X3011:$i, X3012:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i, X3023:$i, X3024:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i, X3037:$i, X3038:$i, X3039:$i, X3040:$i, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3047:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3059:$i, X3060:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i, X3068:$i, X3069:$i, X3070:$i, X3071:$i, X3072:$i, X3073:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i, X3079:$i, X3080:$i, X3081:$i, X3082:$i, X3083:$i, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i, X3090:$i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$i, X3115:$i, X3116:$i, X3117:$o, X3118:$i, X3119:$i, X3120:$i, X3121:$i, X3122:$i, X3123:$i, X3124:$i, X3125:$i, X3126:$i, X3127:$i, X3128:$i, X3129:$i, X3130:$i, X3131:$i, X3132:$i, X3133:$i, X3134:$i, X3135:$i, X3136:$i, X3137:$i, X3138:$i, X3139:$i, X3140:$i, X3141:$i, X3142:$i, X3143:$i, X3144:$i, X3145:$i, X3146:$i, X3147:$i, X3148:$i, X3149:$i, X3150:$i, X3151:$i, X3152:$i, X3153:$i, X3154:$i, X3155:$i, X3156:$i, X3157:$i, X3158:$i, X3159:$i, X3160:$i, X3161:$i, X3162:$i, X3163:$i, X3164:$i, X3165:$i, X3166:$i, X3167:$i, X3168:$i, X3169:$i, X3170:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i, X3176:$i, X3177:$i, X3178:$i, X3179:$i, X3180:$i, X3181:$i, X3182:$i, X3183:$i, X3184:$i, X3185:$i, X3186:$i, X3187:$i, X3188:$i, X3189:$i, X3190:$i, X3191:$i, X3192:$i, X3193:$i, X3194:$i, X3195:$i, X3196:$i, X3197:$i, X3198:$i, X3199:$i, X3200:$i, X3201:$i > $o, X3204:$i, X3205:$i, X3206:$i, X3207:$i, X3208:$i, X3209:$i > $i > $o, X3211:$i, X3212:$i, X3213:$i, X3214:$i, X3215:$i > $i > $o, X3216:$i, X3217:$i, X3218:$i > $o, X3221:$i, X3222:$i, X3223:$i, X3224:$i, X3227:$i, X3228:$i, X3229:$i, X3234:$i, X3235:$i, X3236:$i, X3237:$i, X3238:$i, X3239:$i, X3240:$i, X3241:$i, X3242:$i, X3243:$i, X3244:$i, X3245:$i, X3246:$i, X3247:$i, X3248:$i, X3249:$i, X3250:$i, X3251:$i, X3252:$i, X3253:$i, X3254:$i, X3255:$i, X3256:$i, X3257:$i, X3259:$i, X3260:$i, X3261:$i, X3262:$i, X3263:$i, X3264:$o, X3266:$i, X3267:$i, X3268:$i, X3269:$i, X3270:$i, X3271:$i, X3272:$i, X3273:$i, X3274:$i, X3275:$i, X3276:$i, X3277:$i, X3278:$i, X3279:$i, X3280:$i, X3281:$i, X3282:$i, X3283:$i, X3284:$i, X3285:$i, X3286:$i, X3287:$i, X3288:$i, X3289:$i, X3290:$i, X3291:$i, X3292:$i, X3293:$i, X3294:$o, X3295:$i, X3296:$i, X3297:$i, X3298:$i, X3299:$i, X3300:$i, X3301:$i, X3302:$i, X3303:$i, X3304:$i, X3305:$i, X3306:$i, X3307:$i, X3308:$i, X3309:$i, X3310:$i, X3311:$i, X3312:$i > $i, X3314:$i, X3316:$i, X3317:$i, X3318:$i, X3319:$i > $i, X3321:$i, X3323:$i, X3324:$i, X3325:$i, X3327:$i, X3329:$i, X3330:$i > $i, X3331:$i, X3333:$i, X3334:$i > $i, X3335:$i, X3336:$i, X3337:$i, X3338:$i > $i, X3339:$i, X3341:$i, X3342:$i > $i, X3343:$i, X3344:$i, X3345:$i, X3346:$i, X3347:$i, X3348:$i, X3349:$i, X3350:$i, X3351:$i, X3352:$i, X3353:$i, X3354:$i, X3355:$i, X3356:$i, X3357:$i, X3358:$i, X3359:$i, X3360:$i, X3361:$i, X3362:$i > $i, X3364:$i, X3366:$i, X3367:$i, X3368:$i, X3370:$i, X3371:$i, X3372:$i, X3373:$i, X3374:$i, X3375:$i]:((((~(in @ (esk1_2 @ X2270 @ X2271) @ X2270)|~(in @ (esk1_2 @ X2270 @ X2271) @ X2271)|((X2270)=(X2271)))&((in @ (esk1_2 @ X2270 @ X2271) @ X2270)|(in @ (esk1_2 @ X2270 @ X2271) @ X2271)|((X2270)=(X2271))))&(~(in @ X2273 @ emptyset)&(((~(in @ X2276 @ (setadjoin @ X2274 @ X2275))|(((X2276)=(X2274))|(in @ X2276 @ X2275)))&((((X2276)!=(X2274))|(in @ X2276 @ (setadjoin @ X2274 @ X2275)))&(~(in @ X2276 @ X2275)|(in @ X2276 @ (setadjoin @ X2274 @ X2275)))))&(((~(in @ X2278 @ (powerset @ X2277))|(~(in @ X2279 @ X2278)|(in @ X2279 @ X2277)))&(((in @ (esk2_2 @ X2280 @ X2281) @ X2281)|(in @ X2281 @ (powerset @ X2280)))&(~(in @ (esk2_2 @ X2280 @ X2281) @ X2280)|(in @ X2281 @ (powerset @ X2280)))))&(((((in @ X2284 @ (esk3_2 @ X2283 @ X2284))|~(in @ X2284 @ (setunion @ X2283)))&((in @ (esk3_2 @ X2283 @ X2284) @ X2283)|~(in @ X2284 @ (setunion @ X2283))))&(~(in @ X2287 @ X2288)|~(in @ X2288 @ X2286)|(in @ X2287 @ (setunion @ X2286))))&((in @ emptyset @ omega)&((~(in @ X2289 @ omega)|(in @ (setadjoin @ X2289 @ X2289) @ omega))&(((((in @ (esk4_1 @ X2290) @ omega)|~(in @ emptyset @ X2290)|(~(in @ X2292 @ omega)|(in @ X2292 @ X2290)))&((in @ (esk4_1 @ X2290) @ X2290)|~(in @ emptyset @ X2290)|(~(in @ X2292 @ omega)|(in @ X2292 @ X2290))))&(~(in @ (setadjoin @ (esk4_1 @ X2290) @ (esk4_1 @ X2290)) @ X2290)|~(in @ emptyset @ X2290)|(~(in @ X2292 @ omega)|(in @ X2292 @ X2290))))&((((((in @ (esk8_3 @ X2293 @ X2294 @ X2299) @ X2294)|~(in @ X2299 @ (esk7_2 @ X2293 @ X2294))|(in @ (esk5_2 @ X2293 @ X2294) @ X2294))&((X2293 @ (esk8_3 @ X2293 @ X2294 @ X2299) @ X2299)|~(in @ X2299 @ (esk7_2 @ X2293 @ X2294))|(in @ (esk5_2 @ X2293 @ X2294) @ X2294)))&(~(in @ X2302 @ X2294)|~(X2293 @ X2302 @ X2301)|(in @ X2301 @ (esk7_2 @ X2293 @ X2294))|(in @ (esk5_2 @ X2293 @ X2294) @ X2294)))&(((((in @ (esk8_3 @ X2293 @ X2294 @ X2299) @ X2294)|~(in @ X2299 @ (esk7_2 @ X2293 @ X2294))|((X2293 @ (esk5_2 @ X2293 @ X2294) @ (esk6_3 @ X2293 @ X2294 @ X2296))|~(X2293 @ (esk5_2 @ X2293 @ X2294) @ X2296)))&((X2293 @ (esk8_3 @ X2293 @ X2294 @ X2299) @ X2299)|~(in @ X2299 @ (esk7_2 @ X2293 @ X2294))|((X2293 @ (esk5_2 @ X2293 @ X2294) @ (esk6_3 @ X2293 @ X2294 @ X2296))|~(X2293 @ (esk5_2 @ X2293 @ X2294) @ X2296))))&(~(in @ X2302 @ X2294)|~(X2293 @ X2302 @ X2301)|(in @ X2301 @ (esk7_2 @ X2293 @ X2294))|((X2293 @ (esk5_2 @ X2293 @ X2294) @ (esk6_3 @ X2293 @ X2294 @ X2296))|~(X2293 @ (esk5_2 @ X2293 @ X2294) @ X2296))))&((((in @ (esk8_3 @ X2293 @ X2294 @ X2299) @ X2294)|~(in @ X2299 @ (esk7_2 @ X2293 @ X2294))|(((X2296)!=(esk6_3 @ X2293 @ X2294 @ X2296))|~(X2293 @ (esk5_2 @ X2293 @ X2294) @ X2296)))&((X2293 @ (esk8_3 @ X2293 @ X2294 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X3334))))&((((in @ (esk107_3 @ X3337 @ X3338 @ X3339) @ X3337)|~(in @ X3339 @ (image1 @ X3337 @ X3338)))&(((X3339)=(X3338 @ (esk107_3 @ X3337 @ X3338 @ X3339)))|~(in @ X3339 @ (image1 @ X3337 @ X3338))))&((~(in @ X3344 @ X3341)|((X3343)!=(X3342 @ X3344))|(in @ X3343 @ (image1 @ X3341 @ X3342)))&((~(in @ X3347 @ (funcSet @ X3345 @ X3346))|(~(injective @ X3345 @ X3346 @ X3347)|(in @ X3347 @ (injFuncSet @ X3345 @ X3346))))&((~(in @ X3350 @ (injFuncSet @ X3348 @ X3349))|(in @ X3350 @ (funcSet @ X3348 @ X3349)))&((~(in @ X3353 @ (injFuncSet @ X3351 @ X3352))|(injective @ X3351 @ X3352 @ X3353))&((~(in @ X3356 @ (surjFuncSet @ X3354 @ X3355))|(in @ X3356 @ (funcSet @ X3354 @ X3355)))&((~(in @ X3359 @ (surjFuncSet @ X3357 @ X3358))|(surjective @ X3357 @ X3358 @ X3359))&(((((in @ (esk109_4 @ X3360 @ X3361 @ X3362 @ X3364) @ X3360)|(surjective @ X3361 @ X3360 @ X3364)|~(in @ X3364 @ (funcSet @ X3361 @ X3360))|(in @ (esk108_3 @ X3360 @ X3361 @ X3362) @ X3360))&(((ap @ X3361 @ X3360 @ X3364 @ (X3362 @ (esk109_4 @ X3360 @ X3361 @ X3362 @ X3364)))!=(esk109_4 @ X3360 @ X3361 @ X3362 @ X3364))|(surjective @ X3361 @ X3360 @ X3364)|~(in @ X3364 @ (funcSet @ X3361 @ X3360))|(in @ (esk108_3 @ X3360 @ X3361 @ X3362) @ X3360)))&(((in @ (esk109_4 @ X3360 @ X3361 @ X3362 @ X3364) @ X3360)|(surjective @ X3361 @ X3360 @ X3364)|~(in @ X3364 @ (funcSet @ X3361 @ X3360))|~(in @ (X3362 @ (esk108_3 @ X3360 @ X3361 @ X3362)) @ X3361))&(((ap @ X3361 @ X3360 @ X3364 @ (X3362 @ (esk109_4 @ X3360 @ X3361 @ X3362 @ X3364)))!=(esk109_4 @ X3360 @ X3361 @ X3362 @ X3364))|(surjective @ X3361 @ X3360 @ X3364)|~(in @ X3364 @ (funcSet @ X3361 @ X3360))|~(in @ (X3362 @ (esk108_3 @ X3360 @ X3361 @ X3362)) @ X3361))))&((~(in @ X3367 @ (funcSet @ X3366 @ (powerset @ X3366)))|~(surjective @ X3366 @ (powerset @ X3366) @ X3367))&((((in @ (esk110_1 @ X3368) @ X3368)|((X3368)=(emptyset)))&(((binintersect @ (esk110_1 @ X3368) @ X3368)=(emptyset))|((X3368)=(emptyset))))&(~(in @ X3370 @ X3370)&((~(in @ X3371 @ X3372)|~(in @ X3372 @ X3371))&((~(in @ X3373 @ omega)|(in @ (omegaS @ X3373) @ omega))&((~(in @ X3374 @ omega)|(in @ (setadjoin @ X3374 @ X3374) @ omega))&((~(in @ X3375 @ omega)|((omegaS @ X3375)!=(emptyset)))&((in @ esk111_0 @ omega)&((in @ esk112_0 @ omega)&(((omegaS @ esk111_0)=(omegaS @ esk112_0))&((esk111_0)!=(esk112_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_410])])])])])])])).
% 83.50/12.43  thf(c_0_413, plain, ![X2269:$i]:(((omegaS @ X2269)=(setadjoin @ X2269 @ X2269))), inference(variable_rename,[status(thm)],[c_0_411])).
% 83.50/12.43  thf(c_0_414, negated_conjecture, ((omegaS @ esk111_0)=(omegaS @ esk112_0)), inference(split_conjunct,[status(thm)],[c_0_412])).
% 83.50/12.43  thf(c_0_415, plain, ![X2:$i]:(((omegaS @ X2)=(setadjoin @ X2 @ X2))), inference(split_conjunct,[status(thm)],[c_0_413])).
% 83.50/12.43  thf(c_0_416, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_412])).
% 83.50/12.43  thf(c_0_417, negated_conjecture, ((setadjoin @ esk111_0 @ esk111_0)=(setadjoin @ esk112_0 @ esk112_0)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_414, c_0_415]), c_0_415])).
% 83.50/12.43  thf(c_0_418, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_412])])])).
% 83.50/12.43  thf(c_0_419, negated_conjecture, (in @ esk111_0 @ (setadjoin @ esk112_0 @ esk112_0)), inference(spm,[status(thm)],[c_0_416, c_0_417])).
% 83.50/12.43  thf(c_0_420, negated_conjecture, ((esk111_0)!=(esk112_0)), inference(split_conjunct,[status(thm)],[c_0_412])).
% 83.50/12.43  thf(c_0_421, negated_conjecture, ![X3:$i, X2:$i]:((~((in @ X2 @ X3))|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_412])).
% 83.50/12.43  thf(c_0_422, negated_conjecture, (in @ esk111_0 @ esk112_0), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_418, c_0_419]), c_0_420])).
% 83.50/12.43  thf(c_0_423, negated_conjecture, ![X2:$i]:((((X2)=(esk111_0))|(in @ X2 @ esk111_0)|~((in @ X2 @ (setadjoin @ esk112_0 @ esk112_0))))), inference(spm,[status(thm)],[c_0_418, c_0_417])).
% 83.50/12.43  thf(c_0_424, negated_conjecture, ~((in @ esk112_0 @ esk111_0)), inference(spm,[status(thm)],[c_0_421, c_0_422])).
% 83.50/12.43  thf(c_0_425, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_423, c_0_416]), c_0_420]), c_0_424]), ['proof']).
% 83.50/12.43  % SZS output end CNFRefutation
% 83.50/12.43  % Parsed axioms                        : 715
% 83.50/12.43  % Removed by relevancy pruning/SinE    : 0
% 83.50/12.43  % Initial clauses                      : 974
% 83.50/12.43  % Removed in clause preprocessing      : 425
% 83.50/12.43  % Initial clauses in saturation        : 549
% 83.50/12.43  % Processed clauses                    : 27324
% 83.50/12.43  % ...of these trivial                  : 195
% 83.50/12.43  % ...subsumed                          : 16870
% 83.50/12.43  % ...remaining for further processing  : 10259
% 83.50/12.43  % Other redundant clauses eliminated   : 127
% 83.50/12.43  % Clauses deleted for lack of memory   : 0
% 83.50/12.43  % Backward-subsumed                    : 483
% 83.50/12.43  % Backward-rewritten                   : 30
% 83.50/12.43  % Generated clauses                    : 804863
% 83.50/12.43  % ...of the previous two non-redundant : 792571
% 83.50/12.43  % ...aggressively subsumed             : 0
% 83.50/12.43  % Contextual simplify-reflections      : 23
% 83.50/12.43  % Paramodulations                      : 804708
% 83.50/12.43  % Factorizations                       : 18
% 83.50/12.43  % NegExts                              : 0
% 83.50/12.43  % Equation resolutions                 : 134
% 83.50/12.43  % Disequality decompositions           : 0
% 83.50/12.43  % Total rewrite steps                  : 58819
% 83.50/12.43  % ...of those cached                   : 56276
% 83.50/12.43  % Propositional unsat checks           : 0
% 83.50/12.43  %    Propositional check models        : 0
% 83.50/12.43  %    Propositional check unsatisfiable : 0
% 83.50/12.43  %    Propositional clauses             : 0
% 83.50/12.43  %    Propositional clauses after purity: 0
% 83.50/12.43  %    Propositional unsat core size     : 0
% 83.50/12.43  %    Propositional preprocessing time  : 0.000
% 83.50/12.43  %    Propositional encoding time       : 0.000
% 83.50/12.43  %    Propositional solver time         : 0.000
% 83.50/12.43  %    Success case prop preproc time    : 0.000
% 83.50/12.43  %    Success case prop encoding time   : 0.000
% 83.50/12.43  %    Success case prop solver time     : 0.000
% 83.50/12.43  % Current number of processed clauses  : 9723
% 83.50/12.43  %    Positive orientable unit clauses  : 488
% 83.50/12.43  %    Positive unorientable unit clauses: 1
% 83.50/12.43  %    Negative unit clauses             : 6701
% 83.50/12.43  %    Non-unit-clauses                  : 2533
% 83.50/12.43  % Current number of unprocessed clauses: 754779
% 83.50/12.43  % ...number of literals in the above   : 1875299
% 83.50/12.43  % Current number of archived formulas  : 0
% 83.50/12.43  % Current number of archived clauses   : 514
% 83.50/12.43  % Clause-clause subsumption calls (NU) : 861004
% 83.50/12.43  % Rec. Clause-clause subsumption calls : 632917
% 83.50/12.43  % Non-unit clause-clause subsumptions  : 3692
% 83.50/12.43  % Unit Clause-clause subsumption calls : 4500849
% 83.50/12.43  % Rewrite failures with RHS unbound    : 0
% 83.50/12.43  % BW rewrite match attempts            : 800
% 83.50/12.43  % BW rewrite match successes           : 33
% 83.50/12.43  % Condensation attempts                : 0
% 83.50/12.43  % Condensation successes               : 0
% 83.50/12.43  % Termbank termtop insertions          : 12195707
% 83.50/12.43  % Search garbage collected termcells   : 36942
% 83.50/12.43  
% 83.50/12.43  % -------------------------------------------------
% 83.50/12.43  % User time                : 11.468 s
% 83.50/12.43  % System time              : 0.431 s
% 83.50/12.43  % Total time               : 11.899 s
% 83.50/12.43  % Maximum resident set size: 12136 pages
% 83.50/12.43  
% 83.50/12.43  % -------------------------------------------------
% 83.50/12.43  % User time                : 11.490 s
% 83.50/12.43  % System time              : 0.438 s
% 83.50/12.43  % Total time               : 11.928 s
% 83.50/12.43  % Maximum resident set size: 5888 pages
% 83.50/12.43  % E exiting
%------------------------------------------------------------------------------