E---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SEU737^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:25:25 AM UTC 2026

% Result   : Theorem 223.79s 32.86s
% Output   : CNFRefutation 223.79s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01  % Problem  : SEU737^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10  % Computer : n012.cluster.edu
% 0.00/0.10  % Model    : x86_64 x86_64
% 0.00/0.10  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10  % Memory   : 8046.5625MB
% 0.00/0.10  % OS       : Linux 6.8.0-71-generic
% 0.00/0.10  % CPULimit : 300
% 0.00/0.10  % WCLimit  : 300
% 0.00/0.10  % DateTime : Tue Sep 29 14:18:33 UTC 2026
% 0.00/0.10  % CPUTime  : 
% 0.00/0.10  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.13  Running higher-order theorem proving
% 0.09/0.16  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p
% 223.79/32.86  % Version: 3.5.1-ho
% 223.79/32.86  % Preprocessing class: HSLMSLSSLLLCHFA.
% 223.79/32.86  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 223.79/32.86  % Starting ehoh_best5 with 300s (1) cores
% 223.79/32.86  % Starting almost_fo_3_lam with 300s (1) cores
% 223.79/32.86  % Starting new_bool_5 with 300s (1) cores
% 223.79/32.86  % Starting pre_casc_3 with 300s (1) cores
% 223.79/32.86  % Starting ho_unfolding_8 with 300s (1) cores
% 223.79/32.86  % Starting new_ho_10_cnf2 with 300s (1) cores
% 223.79/32.86  % Starting new_bool_3 with 300s (1) cores
% 223.79/32.86  % Starting new_ho_5 with 300s (1) cores
% 223.79/32.86  % new_ho_5 with pid 172967 completed with status 9
% 223.79/32.86  % almost_fo_3_lam with pid 172961 completed with status 0
% 223.79/32.86  % Result found by almost_fo_3_lam
% 223.79/32.86  % Preprocessing class: HSLMSLSSLLLCHFA.
% 223.79/32.86  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 223.79/32.86  % Starting ehoh_best5 with 300s (1) cores
% 223.79/32.86  % Starting almost_fo_3_lam with 300s (1) cores
% 223.79/32.86  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 223.79/32.86  % No SInE strategy applied
% 223.79/32.86  % Search class: HGHSM-FSLM32-MHFMMSBN
% 223.79/32.86  % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 223.79/32.86  % Starting SubtermCWHack with 28s (1) cores
% 223.79/32.86  % SubtermCWHack with pid 172974 completed with status 8
% 223.79/32.86  % Starting almost_fo_3_lam with 31s (1) cores
% 223.79/32.86  % almost_fo_3_lam with pid 173729 completed with status 0
% 223.79/32.86  % Result found by almost_fo_3_lam
% 223.79/32.86  % Preprocessing class: HSLMSLSSLLLCHFA.
% 223.79/32.86  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 223.79/32.86  % Starting ehoh_best5 with 300s (1) cores
% 223.79/32.86  % Starting almost_fo_3_lam with 300s (1) cores
% 223.79/32.86  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 223.79/32.86  % No SInE strategy applied
% 223.79/32.86  % Search class: HGHSM-FSLM32-MHFMMSBN
% 223.79/32.86  % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 223.79/32.86  % Starting SubtermCWHack with 28s (1) cores
% 223.79/32.86  % SubtermCWHack with pid 172974 completed with status 8
% 223.79/32.86  % Starting almost_fo_3_lam with 31s (1) cores
% 223.79/32.86  % Preprocessing time       : 0.006 s
% 223.79/32.86  % Presaturation interreduction done
% 223.79/32.86  
% 223.79/32.86  % Proof found!
% 223.79/32.86  % SZS status Theorem
% 223.79/32.86  % SZS output start CNFRefutation
% 223.79/32.86  thf(decl_23, type, in: $i > $i > $o).
% 223.79/32.86  thf(decl_24, type, exu: ($i > $o) > $o).
% 223.79/32.86  thf(decl_25, type, setextAx: $o).
% 223.79/32.86  thf(decl_26, type, emptyset: $i).
% 223.79/32.86  thf(decl_27, type, emptysetAx: $o).
% 223.79/32.86  thf(decl_28, type, setadjoin: $i > $i > $i).
% 223.79/32.86  thf(decl_29, type, setadjoinAx: $o).
% 223.79/32.86  thf(decl_30, type, powerset: $i > $i).
% 223.79/32.86  thf(decl_31, type, powersetAx: $o).
% 223.79/32.86  thf(decl_32, type, setunion: $i > $i).
% 223.79/32.86  thf(decl_33, type, setunionAx: $o).
% 223.79/32.86  thf(decl_34, type, omega: $i).
% 223.79/32.86  thf(decl_35, type, omega0Ax: $o).
% 223.79/32.86  thf(decl_36, type, omegaSAx: $o).
% 223.79/32.86  thf(decl_37, type, omegaIndAx: $o).
% 223.79/32.86  thf(decl_38, type, replAx: $o).
% 223.79/32.86  thf(decl_39, type, foundationAx: $o).
% 223.79/32.86  thf(decl_40, type, wellorderingAx: $o).
% 223.79/32.86  thf(decl_41, type, descr: ($i > $o) > $i).
% 223.79/32.86  thf(decl_42, type, descrp: $o).
% 223.79/32.86  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_44, type, dsetconstrI: $o).
% 223.79/32.86  thf(decl_45, type, dsetconstrEL: $o).
% 223.79/32.86  thf(decl_46, type, dsetconstrER: $o).
% 223.79/32.86  thf(decl_47, type, exuE1: $o).
% 223.79/32.86  thf(decl_48, type, prop2set: $o > $i).
% 223.79/32.86  thf(decl_49, type, prop2setE: $o).
% 223.79/32.86  thf(decl_50, type, emptysetE: $o).
% 223.79/32.86  thf(decl_51, type, emptysetimpfalse: $o).
% 223.79/32.86  thf(decl_52, type, notinemptyset: $o).
% 223.79/32.86  thf(decl_53, type, exuE3e: $o).
% 223.79/32.86  thf(decl_54, type, setext: $o).
% 223.79/32.86  thf(decl_55, type, emptyI: $o).
% 223.79/32.86  thf(decl_56, type, noeltsimpempty: $o).
% 223.79/32.86  thf(decl_57, type, setbeta: $o).
% 223.79/32.86  thf(decl_58, type, nonempty: $i > $o).
% 223.79/32.86  thf(decl_59, type, nonemptyE1: $o).
% 223.79/32.86  thf(decl_60, type, nonemptyI: $o).
% 223.79/32.86  thf(decl_61, type, nonemptyI1: $o).
% 223.79/32.86  thf(decl_62, type, setadjoinIL: $o).
% 223.79/32.86  thf(decl_63, type, emptyinunitempty: $o).
% 223.79/32.86  thf(decl_64, type, setadjoinIR: $o).
% 223.79/32.86  thf(decl_65, type, setadjoinE: $o).
% 223.79/32.86  thf(decl_66, type, setadjoinOr: $o).
% 223.79/32.86  thf(decl_67, type, setoftrueEq: $o).
% 223.79/32.86  thf(decl_68, type, powersetI: $o).
% 223.79/32.86  thf(decl_69, type, emptyinPowerset: $o).
% 223.79/32.86  thf(decl_70, type, emptyInPowerset: $o).
% 223.79/32.86  thf(decl_71, type, powersetE: $o).
% 223.79/32.86  thf(decl_72, type, setunionI: $o).
% 223.79/32.86  thf(decl_73, type, setunionE: $o).
% 223.79/32.86  thf(decl_74, type, subPowSU: $o).
% 223.79/32.86  thf(decl_75, type, exuE2: $o).
% 223.79/32.86  thf(decl_76, type, nonemptyImpWitness: $o).
% 223.79/32.86  thf(decl_77, type, uniqinunit: $o).
% 223.79/32.86  thf(decl_78, type, notinsingleton: $o).
% 223.79/32.86  thf(decl_79, type, eqinunit: $o).
% 223.79/32.86  thf(decl_80, type, singletonsswitch: $o).
% 223.79/32.86  thf(decl_81, type, upairsetE: $o).
% 223.79/32.86  thf(decl_82, type, upairsetIL: $o).
% 223.79/32.86  thf(decl_83, type, upairsetIR: $o).
% 223.79/32.86  thf(decl_84, type, emptyE1: $o).
% 223.79/32.86  thf(decl_85, type, vacuousDall: $o).
% 223.79/32.86  thf(decl_86, type, quantDeMorgan1: $o).
% 223.79/32.86  thf(decl_87, type, quantDeMorgan2: $o).
% 223.79/32.86  thf(decl_88, type, quantDeMorgan3: $o).
% 223.79/32.86  thf(decl_89, type, quantDeMorgan4: $o).
% 223.79/32.86  thf(decl_90, type, prop2setI: $o).
% 223.79/32.86  thf(decl_91, type, set2prop: $i > $o).
% 223.79/32.86  thf(decl_92, type, prop2set2propI: $o).
% 223.79/32.86  thf(decl_93, type, notdexE: $o).
% 223.79/32.86  thf(decl_94, type, notdallE: $o).
% 223.79/32.86  thf(decl_95, type, exuI1: $o).
% 223.79/32.86  thf(decl_96, type, exuI3: $o).
% 223.79/32.86  thf(decl_97, type, exuI2: $o).
% 223.79/32.86  thf(decl_98, type, inCongP: $o).
% 223.79/32.86  thf(decl_99, type, in__Cong: $o).
% 223.79/32.86  thf(decl_100, type, exuE3u: $o).
% 223.79/32.86  thf(decl_101, type, exu__Cong: $o).
% 223.79/32.86  thf(decl_102, type, emptyset__Cong: $o).
% 223.79/32.86  thf(decl_103, type, setadjoin__Cong: $o).
% 223.79/32.86  thf(decl_104, type, powerset__Cong: $o).
% 223.79/32.86  thf(decl_105, type, setunion__Cong: $o).
% 223.79/32.86  thf(decl_106, type, omega__Cong: $o).
% 223.79/32.86  thf(decl_107, type, exuEu: $o).
% 223.79/32.86  thf(decl_108, type, descr__Cong: $o).
% 223.79/32.86  thf(decl_109, type, dsetconstr__Cong: $o).
% 223.79/32.86  thf(decl_110, type, subset: $i > $i > $o).
% 223.79/32.86  thf(decl_113, type, subsetI1: $o).
% 223.79/32.86  thf(decl_114, type, eqimpsubset2: $o).
% 223.79/32.86  thf(decl_115, type, eqimpsubset1: $o).
% 223.79/32.86  thf(decl_116, type, subsetI2: $o).
% 223.79/32.86  thf(decl_117, type, emptysetsubset: $o).
% 223.79/32.86  thf(decl_118, type, subsetE: $o).
% 223.79/32.86  thf(decl_119, type, subsetE2: $o).
% 223.79/32.86  thf(decl_120, type, notsubsetI: $o).
% 223.79/32.86  thf(decl_121, type, notequalI1: $o).
% 223.79/32.86  thf(decl_122, type, notequalI2: $o).
% 223.79/32.86  thf(decl_123, type, subsetRefl: $o).
% 223.79/32.86  thf(decl_124, type, subsetTrans: $o).
% 223.79/32.86  thf(decl_125, type, setadjoinSub: $o).
% 223.79/32.86  thf(decl_126, type, setadjoinSub2: $o).
% 223.79/32.86  thf(decl_127, type, subset2powerset: $o).
% 223.79/32.86  thf(decl_128, type, setextsub: $o).
% 223.79/32.86  thf(decl_129, type, subsetemptysetimpeq: $o).
% 223.79/32.86  thf(decl_130, type, powersetI1: $o).
% 223.79/32.86  thf(decl_131, type, powersetE1: $o).
% 223.79/32.86  thf(decl_132, type, inPowerset: $o).
% 223.79/32.86  thf(decl_133, type, powersetsubset: $o).
% 223.79/32.86  thf(decl_134, type, sepInPowerset: $o).
% 223.79/32.86  thf(decl_135, type, sepSubset: $o).
% 223.79/32.86  thf(decl_136, type, binunion: $i > $i > $i).
% 223.79/32.86  thf(decl_137, type, binunionIL: $o).
% 223.79/32.86  thf(decl_138, type, upairset2IR: $o).
% 223.79/32.86  thf(decl_139, type, binunionIR: $o).
% 223.79/32.86  thf(decl_140, type, binunionEcases: $o).
% 223.79/32.86  thf(decl_141, type, binunionE: $o).
% 223.79/32.86  thf(decl_142, type, binunionLsub: $o).
% 223.79/32.86  thf(decl_143, type, binunionRsub: $o).
% 223.79/32.86  thf(decl_144, type, binintersect: $i > $i > $i).
% 223.79/32.86  thf(decl_145, type, binintersectI: $o).
% 223.79/32.86  thf(decl_146, type, binintersectSubset5: $o).
% 223.79/32.86  thf(decl_147, type, binintersectEL: $o).
% 223.79/32.86  thf(decl_148, type, binintersectLsub: $o).
% 223.79/32.86  thf(decl_149, type, binintersectSubset2: $o).
% 223.79/32.86  thf(decl_150, type, binintersectSubset3: $o).
% 223.79/32.86  thf(decl_151, type, binintersectER: $o).
% 223.79/32.86  thf(decl_152, type, disjointsetsI1: $o).
% 223.79/32.86  thf(decl_153, type, binintersectRsub: $o).
% 223.79/32.86  thf(decl_154, type, binintersectSubset4: $o).
% 223.79/32.86  thf(decl_155, type, binintersectSubset1: $o).
% 223.79/32.86  thf(decl_156, type, bs114d: $o).
% 223.79/32.86  thf(decl_158, type, setminus: $i > $i > $i).
% 223.79/32.86  thf(decl_159, type, setminusI: $o).
% 223.79/32.86  thf(decl_160, type, setminusEL: $o).
% 223.79/32.86  thf(decl_161, type, setminusER: $o).
% 223.79/32.86  thf(decl_162, type, setminusSubset2: $o).
% 223.79/32.86  thf(decl_163, type, setminusERneg: $o).
% 223.79/32.86  thf(decl_164, type, setminusELneg: $o).
% 223.79/32.86  thf(decl_165, type, setminusILneg: $o).
% 223.79/32.86  thf(decl_166, type, setminusIRneg: $o).
% 223.79/32.86  thf(decl_167, type, setminusLsub: $o).
% 223.79/32.86  thf(decl_168, type, setminusSubset1: $o).
% 223.79/32.86  thf(decl_169, type, symdiff: $i > $i > $i).
% 223.79/32.86  thf(decl_170, type, symdiffE: $o).
% 223.79/32.86  thf(decl_171, type, symdiffI1: $o).
% 223.79/32.86  thf(decl_172, type, symdiffI2: $o).
% 223.79/32.86  thf(decl_173, type, symdiffIneg1: $o).
% 223.79/32.86  thf(decl_174, type, symdiffIneg2: $o).
% 223.79/32.86  thf(decl_175, type, iskpair: $i > $o).
% 223.79/32.86  thf(decl_176, type, secondinupair: $o).
% 223.79/32.86  thf(decl_177, type, setukpairIL: $o).
% 223.79/32.86  thf(decl_178, type, setukpairIR: $o).
% 223.79/32.86  thf(decl_179, type, kpairiskpair: $o).
% 223.79/32.86  thf(decl_180, type, kpair: $i > $i > $i).
% 223.79/32.86  thf(decl_181, type, kpairp: $o).
% 223.79/32.86  thf(decl_182, type, cartprod: $i > $i > $i).
% 223.79/32.86  thf(decl_183, type, singletonsubset: $o).
% 223.79/32.86  thf(decl_184, type, singletoninpowerset: $o).
% 223.79/32.86  thf(decl_185, type, singletoninpowunion: $o).
% 223.79/32.86  thf(decl_186, type, upairset2E: $o).
% 223.79/32.86  thf(decl_187, type, upairsubunion: $o).
% 223.79/32.86  thf(decl_188, type, upairinpowunion: $o).
% 223.79/32.86  thf(decl_189, type, ubforcartprodlem1: $o).
% 223.79/32.86  thf(decl_190, type, ubforcartprodlem2: $o).
% 223.79/32.86  thf(decl_191, type, ubforcartprodlem3: $o).
% 223.79/32.86  thf(decl_192, type, cartprodpairin: $o).
% 223.79/32.86  thf(decl_193, type, cartprodmempair1: $o).
% 223.79/32.86  thf(decl_194, type, cartprodmempair: $o).
% 223.79/32.86  thf(decl_195, type, setunionE2: $o).
% 223.79/32.86  thf(decl_196, type, setunionsingleton1: $o).
% 223.79/32.86  thf(decl_197, type, setunionsingleton2: $o).
% 223.79/32.86  thf(decl_198, type, setunionsingleton: $o).
% 223.79/32.86  thf(decl_199, type, singleton: $i > $o).
% 223.79/32.86  thf(decl_200, type, singletonprop: $o).
% 223.79/32.86  thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 223.79/32.86  thf(decl_202, type, ex1E1: $o).
% 223.79/32.86  thf(decl_203, type, ex1I: $o).
% 223.79/32.86  thf(decl_204, type, ex1I2: $o).
% 223.79/32.86  thf(decl_205, type, singletonsuniq: $o).
% 223.79/32.86  thf(decl_210, type, setukpairinjL1: $o).
% 223.79/32.86  thf(decl_211, type, kfstsingleton: $o).
% 223.79/32.86  thf(decl_212, type, theprop: $o).
% 223.79/32.86  thf(decl_213, type, kfst: $i > $i).
% 223.79/32.86  thf(decl_214, type, kfstpairEq: $o).
% 223.79/32.86  thf(decl_215, type, cartprodfstin: $o).
% 223.79/32.86  thf(decl_216, type, setukpairinjL2: $o).
% 223.79/32.86  thf(decl_217, type, setukpairinjL: $o).
% 223.79/32.86  thf(decl_218, type, setukpairinjR11: $o).
% 223.79/32.86  thf(decl_219, type, setukpairinjR12: $o).
% 223.79/32.86  thf(decl_220, type, setukpairinjR1: $o).
% 223.79/32.86  thf(decl_221, type, upairequniteq: $o).
% 223.79/32.86  thf(decl_222, type, setukpairinjR2: $o).
% 223.79/32.86  thf(decl_223, type, setukpairinjR: $o).
% 223.79/32.86  thf(decl_224, type, ksndsingleton: $o).
% 223.79/32.86  thf(decl_225, type, ksnd: $i > $i).
% 223.79/32.86  thf(decl_226, type, ksndpairEq: $o).
% 223.79/32.86  thf(decl_227, type, kpairsurjEq: $o).
% 223.79/32.86  thf(decl_228, type, cartprodsndin: $o).
% 223.79/32.86  thf(decl_229, type, cartprodpairmemEL: $o).
% 223.79/32.86  thf(decl_230, type, cartprodpairmemER: $o).
% 223.79/32.86  thf(decl_231, type, cartprodmempaircEq: $o).
% 223.79/32.86  thf(decl_232, type, cartprodfstpairEq: $o).
% 223.79/32.86  thf(decl_233, type, cartprodsndpairEq: $o).
% 223.79/32.86  thf(decl_234, type, cartprodpairsurjEq: $o).
% 223.79/32.86  thf(decl_235, type, breln: $i > $i > $i > $o).
% 223.79/32.86  thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 223.79/32.86  thf(decl_237, type, dpsetconstrI: $o).
% 223.79/32.86  thf(decl_238, type, dpsetconstrSub: $o).
% 223.79/32.86  thf(decl_239, type, setOfPairsIsBReln: $o).
% 223.79/32.86  thf(decl_240, type, dpsetconstrERa: $o).
% 223.79/32.86  thf(decl_241, type, dpsetconstrEL1: $o).
% 223.79/32.86  thf(decl_242, type, dpsetconstrEL2: $o).
% 223.79/32.86  thf(decl_243, type, dpsetconstrER: $o).
% 223.79/32.86  thf(decl_244, type, func: $i > $i > $i > $o).
% 223.79/32.86  thf(decl_245, type, funcSet: $i > $i > $i).
% 223.79/32.86  thf(decl_246, type, funcImageSingleton: $o).
% 223.79/32.86  thf(decl_247, type, apProp: $o).
% 223.79/32.86  thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 223.79/32.86  thf(decl_249, type, app: $o).
% 223.79/32.86  thf(decl_250, type, infuncsetfunc: $o).
% 223.79/32.86  thf(decl_251, type, ap2p: $o).
% 223.79/32.86  thf(decl_252, type, funcinfuncset: $o).
% 223.79/32.86  thf(decl_253, type, lamProp: $o).
% 223.79/32.86  thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 223.79/32.86  thf(decl_255, type, lamp: $o).
% 223.79/32.86  thf(decl_256, type, lam2p: $o).
% 223.79/32.86  thf(decl_257, type, brelnall1: $o).
% 223.79/32.86  thf(decl_258, type, brelnall2: $o).
% 223.79/32.86  thf(decl_259, type, ex1E2: $o).
% 223.79/32.86  thf(decl_260, type, funcGraphProp1: $o).
% 223.79/32.86  thf(decl_261, type, funcGraphProp3: $o).
% 223.79/32.86  thf(decl_262, type, funcGraphProp2: $o).
% 223.79/32.86  thf(decl_263, type, funcextLem: $o).
% 223.79/32.86  thf(decl_264, type, funcGraphProp4: $o).
% 223.79/32.86  thf(decl_265, type, subbreln: $o).
% 223.79/32.86  thf(decl_266, type, eqbreln: $o).
% 223.79/32.86  thf(decl_267, type, funcext: $o).
% 223.79/32.86  thf(decl_268, type, funcext2: $o).
% 223.79/32.86  thf(decl_269, type, ap2apEq1: $o).
% 223.79/32.86  thf(decl_270, type, ap2apEq2: $o).
% 223.79/32.86  thf(decl_271, type, beta1: $o).
% 223.79/32.86  thf(decl_272, type, eta1: $o).
% 223.79/32.86  thf(decl_273, type, lam2lamEq: $o).
% 223.79/32.86  thf(decl_274, type, beta2: $o).
% 223.79/32.86  thf(decl_275, type, eta2: $o).
% 223.79/32.86  thf(decl_276, type, iffalseProp1: $o).
% 223.79/32.86  thf(decl_277, type, iffalseProp2: $o).
% 223.79/32.86  thf(decl_278, type, iftrueProp1: $o).
% 223.79/32.86  thf(decl_279, type, iftrueProp2: $o).
% 223.79/32.86  thf(decl_280, type, ifSingleton: $o).
% 223.79/32.86  thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 223.79/32.86  thf(decl_282, type, ifp: $o).
% 223.79/32.86  thf(decl_283, type, theeq: $o).
% 223.79/32.86  thf(decl_284, type, iftrue: $o).
% 223.79/32.86  thf(decl_285, type, iffalse: $o).
% 223.79/32.86  thf(decl_286, type, iftrueorfalse: $o).
% 223.79/32.86  thf(decl_287, type, binintersectT_lem: $o).
% 223.79/32.86  thf(decl_288, type, binunionT_lem: $o).
% 223.79/32.86  thf(decl_289, type, powersetT_lem: $o).
% 223.79/32.86  thf(decl_290, type, setminusT_lem: $o).
% 223.79/32.86  thf(decl_291, type, complementT_lem: $o).
% 223.79/32.86  thf(decl_292, type, setextT: $o).
% 223.79/32.86  thf(decl_293, type, subsetTI: $o).
% 223.79/32.86  thf(decl_294, type, powersetTI1: $o).
% 223.79/32.86  thf(decl_295, type, powersetTE1: $o).
% 223.79/32.86  thf(decl_296, type, complementTI1: $o).
% 223.79/32.86  thf(decl_297, type, complementTE1: $o).
% 223.79/32.86  thf(decl_298, type, binintersectTELcontra: $o).
% 223.79/32.86  thf(decl_299, type, binintersectTERcontra: $o).
% 223.79/32.86  thf(decl_300, type, contrasubsetT: $o).
% 223.79/32.86  thf(decl_301, type, contrasubsetT1: $o).
% 223.79/32.86  thf(decl_302, type, contrasubsetT2: $o).
% 223.79/32.86  thf(decl_303, type, contrasubsetT3: $o).
% 223.79/32.86  thf(decl_304, type, doubleComplementI1: $o).
% 223.79/32.86  thf(decl_305, type, doubleComplementE1: $o).
% 223.79/32.86  thf(decl_306, type, doubleComplementSub1: $o).
% 223.79/32.86  thf(decl_307, type, doubleComplementSub2: $o).
% 223.79/32.86  thf(decl_308, type, doubleComplementEq: $o).
% 223.79/32.86  thf(decl_309, type, complementTnotintersectT: $o).
% 223.79/32.86  thf(decl_310, type, complementImpComplementIntersect: $o).
% 223.79/32.86  thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 223.79/32.86  thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 223.79/32.86  thf(decl_313, type, contraSubsetComplement: $o).
% 223.79/32.86  thf(decl_314, type, epred1_0: $o).
% 223.79/32.86  thf(decl_315, type, esk1_2: $i > $i > $i).
% 223.79/32.86  thf(decl_316, type, esk2_2: $i > $i > $i).
% 223.79/32.86  thf(decl_317, type, esk3_2: $i > $i > $i).
% 223.79/32.86  thf(decl_318, type, esk4_1: $i > $i).
% 223.79/32.86  thf(decl_319, type, esk5_2: ($i > $i > $o) > $i > $i).
% 223.79/32.86  thf(decl_320, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 223.79/32.86  thf(decl_321, type, esk7_2: ($i > $i > $o) > $i > $i).
% 223.79/32.86  thf(decl_322, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 223.79/32.86  thf(decl_323, type, esk9_1: $i > $i).
% 223.79/32.86  thf(decl_324, type, esk10_2: ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_325, type, esk11_2: ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_326, type, esk12_1: ($i > $o) > $i).
% 223.79/32.86  thf(decl_327, type, esk13_2: ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_328, type, esk14_1: ($i > $o) > $i).
% 223.79/32.86  thf(decl_329, type, esk15_2: $i > $i > $i).
% 223.79/32.86  thf(decl_330, type, esk16_2: $i > $i > $i).
% 223.79/32.86  thf(decl_331, type, esk17_1: $i > $i).
% 223.79/32.86  thf(decl_332, type, esk18_1: $i > $i).
% 223.79/32.86  thf(decl_333, type, esk19_1: $i > $i).
% 223.79/32.86  thf(decl_334, type, esk20_2: $i > $i > $i).
% 223.79/32.86  thf(decl_335, type, esk21_3: $i > $i > $o > $i).
% 223.79/32.86  thf(decl_336, type, esk22_2: ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_337, type, esk23_1: ($i > $o) > $i).
% 223.79/32.86  thf(decl_338, type, esk24_1: $i > $i).
% 223.79/32.86  thf(decl_339, type, esk25_2: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_340, type, esk26_2: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_341, type, esk27_2: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_342, type, esk28_2: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_343, type, esk29_2: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_344, type, esk30_2: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_345, type, esk31_2: ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_346, type, esk32_1: ($i > $o) > $i).
% 223.79/32.86  thf(decl_347, type, esk33_1: ($i > $o) > $i).
% 223.79/32.86  thf(decl_348, type, esk34_1: ($i > $o) > $i).
% 223.79/32.86  thf(decl_349, type, esk35_1: ($i > $o) > $i).
% 223.79/32.86  thf(decl_350, type, esk36_2: ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_351, type, esk37_1: ($i > $o) > $i).
% 223.79/32.86  thf(decl_352, type, esk38_2: ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_353, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 223.79/32.86  thf(decl_354, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 223.79/32.86  thf(decl_355, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_356, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 223.79/32.86  thf(decl_357, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_358, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 223.79/32.86  thf(decl_359, type, esk45_2: ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_360, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 223.79/32.86  thf(decl_361, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 223.79/32.86  thf(decl_362, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_363, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_364, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 223.79/32.86  thf(decl_365, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 223.79/32.86  thf(decl_366, type, esk52_2: $i > $i > $i).
% 223.79/32.86  thf(decl_367, type, esk53_2: $i > $i > $i).
% 223.79/32.86  thf(decl_368, type, esk54_2: $i > $i > $i).
% 223.79/32.86  thf(decl_369, type, esk55_3: $i > $i > $i > $i).
% 223.79/32.86  thf(decl_370, type, esk56_3: $i > $i > $i > $i).
% 223.79/32.86  thf(decl_371, type, esk57_2: $i > $i > $i).
% 223.79/32.86  thf(decl_372, type, esk58_2: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_373, type, esk59_2: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_374, type, esk60_2: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_375, type, esk61_3: $i > ($i > $o) > $i > $i).
% 223.79/32.86  thf(decl_376, type, esk62_2: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_377, type, esk63_2: $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_378, type, esk64_3: $i > $i > ($i > $i) > $i).
% 223.79/32.86  thf(decl_379, type, esk65_3: $i > $i > ($i > $i) > $i).
% 223.79/32.86  thf(decl_380, type, esk66_3: $i > $i > ($i > $i) > $i).
% 223.79/32.86  thf(decl_381, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_382, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_383, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_384, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
% 223.79/32.86  thf(decl_385, type, esk71_4: $i > $i > $i > $i > $i).
% 223.79/32.86  thf(decl_386, type, esk72_4: $i > $i > $i > $i > $i).
% 223.79/32.86  thf(decl_387, type, esk73_4: $i > $i > $i > $i > $i).
% 223.79/32.86  thf(decl_388, type, esk74_4: $i > $i > $i > $i > $i).
% 223.79/32.86  thf(decl_389, type, esk75_4: $i > $i > $i > $i > $i).
% 223.79/32.86  thf(decl_390, type, esk76_4: $i > $i > $i > $i > $i).
% 223.79/32.86  thf(decl_391, type, esk77_4: $i > $i > $i > $i > $i).
% 223.79/32.86  thf(decl_392, type, esk78_4: $i > $i > $i > $i > $i).
% 223.79/32.86  thf(decl_393, type, esk79_4: $i > $i > $i > $i > $i).
% 223.79/32.86  thf(decl_394, type, esk80_3: $i > $i > ($i > $i) > $i).
% 223.79/32.86  thf(decl_395, type, esk81_3: $i > $i > ($i > $i) > $i).
% 223.79/32.86  thf(decl_396, type, esk82_3: $i > $i > ($i > $i) > $i).
% 223.79/32.86  thf(decl_397, type, esk83_3: $i > $i > $i > $i).
% 223.79/32.86  thf(decl_398, type, esk84_3: $i > $i > $i > $i).
% 223.79/32.86  thf(decl_399, type, esk85_3: $i > $i > $i > $i).
% 223.79/32.86  thf(decl_400, type, esk86_3: $i > $i > $i > $i).
% 223.79/32.86  thf(decl_401, type, esk87_0: $i).
% 223.79/32.86  thf(decl_402, type, esk88_0: $i).
% 223.79/32.86  thf(decl_403, type, esk89_0: $i).
% 223.79/32.86  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', replAx)).
% 223.79/32.86  thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', exu)).
% 223.79/32.86  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', descrp)).
% 223.79/32.86  thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', exuE1)).
% 223.79/32.86  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', exuE3e)).
% 223.79/32.86  thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', nonempty)).
% 223.79/32.86  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', nonemptyI)).
% 223.79/32.86  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', exuE2)).
% 223.79/32.86  thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', exuI1)).
% 223.79/32.86  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', exuI3)).
% 223.79/32.86  thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', exuI2)).
% 223.79/32.86  thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', exuE3u)).
% 223.79/32.86  thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', exu__Cong)).
% 223.79/32.86  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', exuEu)).
% 223.79/32.86  thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', descr__Cong)).
% 223.79/32.86  thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ex1E1)).
% 223.79/32.86  thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ex1)).
% 223.79/32.86  thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ex1I)).
% 223.79/32.86  thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ex1I2)).
% 223.79/32.86  thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setOfPairsIsBReln)).
% 223.79/32.86  thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', breln)).
% 223.79/32.86  thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ex1E2)).
% 223.79/32.86  thf(complementTcontraSubset, 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)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', complementTcontraSubset)).
% 223.79/32.86  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', dsetconstrI)).
% 223.79/32.86  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', dsetconstrEL)).
% 223.79/32.86  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', dsetconstrER)).
% 223.79/32.86  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setbeta)).
% 223.79/32.86  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', nonemptyE1)).
% 223.79/32.86  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', nonemptyI1)).
% 223.79/32.86  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setoftrueEq)).
% 223.79/32.86  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', nonemptyImpWitness)).
% 223.79/32.86  thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', emptyE1)).
% 223.79/32.86  thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', dsetconstr__Cong)).
% 223.79/32.86  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', sepInPowerset)).
% 223.79/32.86  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', sepSubset)).
% 223.79/32.86  thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', singletonprop)).
% 223.79/32.86  thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', kfstsingleton)).
% 223.79/32.86  thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ksndsingleton)).
% 223.79/32.86  thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', dpsetconstrI)).
% 223.79/32.86  thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', dpsetconstrSub)).
% 223.79/32.86  thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', dpsetconstrERa)).
% 223.79/32.86  thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', dpsetconstrEL1)).
% 223.79/32.86  thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', dpsetconstrEL2)).
% 223.79/32.86  thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', dpsetconstrER)).
% 223.79/32.86  thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', funcImageSingleton)).
% 223.79/32.86  thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', apProp)).
% 223.79/32.86  thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', lamProp)).
% 223.79/32.86  thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', lamp)).
% 223.79/32.86  thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', lam2p)).
% 223.79/32.86  thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', brelnall1)).
% 223.79/32.86  thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', brelnall2)).
% 223.79/32.86  thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', subbreln)).
% 223.79/32.86  thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', eqbreln)).
% 223.79/32.86  thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', beta1)).
% 223.79/32.86  thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', eta1)).
% 223.79/32.86  thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', lam2lamEq)).
% 223.79/32.86  thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', beta2)).
% 223.79/32.86  thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', eta2)).
% 223.79/32.86  thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', iffalseProp1)).
% 223.79/32.86  thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', iffalseProp2)).
% 223.79/32.86  thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', iftrueProp1)).
% 223.79/32.86  thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', iftrueProp2)).
% 223.79/32.86  thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ifSingleton)).
% 223.79/32.86  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setextAx)).
% 223.79/32.86  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', emptysetAx)).
% 223.79/32.86  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setadjoinAx)).
% 223.79/32.86  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', powersetAx)).
% 223.79/32.86  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setunionAx)).
% 223.79/32.86  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', omega0Ax)).
% 223.79/32.86  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', omegaSAx)).
% 223.79/32.86  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', omegaIndAx)).
% 223.79/32.86  thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', foundationAx)).
% 223.79/32.86  thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', wellorderingAx)).
% 223.79/32.86  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', prop2setE)).
% 223.79/32.86  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', emptysetE)).
% 223.79/32.86  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', emptysetimpfalse)).
% 223.79/32.86  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', notinemptyset)).
% 223.79/32.86  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setext)).
% 223.79/32.86  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', emptyI)).
% 223.79/32.86  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', noeltsimpempty)).
% 223.79/32.86  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setadjoinIL)).
% 223.79/32.86  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', emptyinunitempty)).
% 223.79/32.86  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setadjoinIR)).
% 223.79/32.86  thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setadjoinE)).
% 223.79/32.86  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setadjoinOr)).
% 223.79/32.86  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', powersetI)).
% 223.79/32.86  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', emptyinPowerset)).
% 223.79/32.86  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', emptyInPowerset)).
% 223.79/32.86  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', powersetE)).
% 223.79/32.86  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setunionI)).
% 223.79/32.86  thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setunionE)).
% 223.79/32.86  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', subPowSU)).
% 223.79/32.86  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', uniqinunit)).
% 223.79/32.86  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', notinsingleton)).
% 223.79/32.86  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', eqinunit)).
% 223.79/32.86  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', singletonsswitch)).
% 223.79/32.86  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', upairsetE)).
% 223.79/32.86  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', upairsetIL)).
% 223.79/32.86  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', upairsetIR)).
% 223.79/32.86  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', vacuousDall)).
% 223.79/32.86  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', quantDeMorgan1)).
% 223.79/32.86  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', quantDeMorgan2)).
% 223.79/32.86  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', quantDeMorgan3)).
% 223.79/32.86  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', quantDeMorgan4)).
% 223.79/32.86  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', prop2setI)).
% 223.79/32.86  thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', prop2set2propI)).
% 223.79/32.86  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', notdexE)).
% 223.79/32.86  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', notdallE)).
% 223.79/32.86  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', inCongP)).
% 223.79/32.86  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', in__Cong)).
% 223.79/32.86  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', emptyset__Cong)).
% 223.79/32.86  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setadjoin__Cong)).
% 223.79/32.86  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', powerset__Cong)).
% 223.79/32.86  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setunion__Cong)).
% 223.79/32.86  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', omega__Cong)).
% 223.79/32.86  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', subsetI1)).
% 223.79/32.86  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', eqimpsubset2)).
% 223.79/32.86  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', eqimpsubset1)).
% 223.79/32.86  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', subsetI2)).
% 223.79/32.86  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', emptysetsubset)).
% 223.79/32.86  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', subsetE)).
% 223.79/32.86  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', subsetE2)).
% 223.79/32.86  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', notsubsetI)).
% 223.79/32.86  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', notequalI1)).
% 223.79/32.86  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', notequalI2)).
% 223.79/32.86  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', subsetRefl)).
% 223.79/32.86  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', subsetTrans)).
% 223.79/32.86  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setadjoinSub)).
% 223.79/32.86  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setadjoinSub2)).
% 223.79/32.86  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', subset2powerset)).
% 223.79/32.86  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setextsub)).
% 223.79/32.86  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', subsetemptysetimpeq)).
% 223.79/32.86  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', powersetI1)).
% 223.79/32.86  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', powersetE1)).
% 223.79/32.86  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', inPowerset)).
% 223.79/32.86  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', powersetsubset)).
% 223.79/32.87  thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binunionIL)).
% 223.79/32.87  thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', upairset2IR)).
% 223.79/32.87  thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binunionIR)).
% 223.79/32.87  thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binunionEcases)).
% 223.79/32.87  thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binunionE)).
% 223.79/32.87  thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binunionLsub)).
% 223.79/32.87  thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binunionRsub)).
% 223.79/32.87  thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectI)).
% 223.79/32.87  thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectSubset5)).
% 223.79/32.87  thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectEL)).
% 223.79/32.87  thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectLsub)).
% 223.79/32.87  thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectSubset2)).
% 223.79/32.87  thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectSubset3)).
% 223.79/32.87  thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectER)).
% 223.79/32.87  thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', disjointsetsI1)).
% 223.79/32.87  thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectRsub)).
% 223.79/32.87  thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectSubset4)).
% 223.79/32.87  thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectSubset1)).
% 223.79/32.87  thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', bs114d)).
% 223.79/32.87  thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setminusI)).
% 223.79/32.87  thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setminusEL)).
% 223.79/32.87  thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setminusER)).
% 223.79/32.87  thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setminusSubset2)).
% 223.79/32.87  thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setminusERneg)).
% 223.79/32.87  thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setminusELneg)).
% 223.79/32.87  thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setminusILneg)).
% 223.79/32.87  thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setminusIRneg)).
% 223.79/32.87  thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setminusLsub)).
% 223.79/32.87  thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setminusSubset1)).
% 223.79/32.87  thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', symdiffE)).
% 223.79/32.87  thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', symdiffI1)).
% 223.79/32.87  thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', symdiffI2)).
% 223.79/32.87  thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', symdiffIneg1)).
% 223.79/32.87  thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', symdiffIneg2)).
% 223.79/32.87  thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', secondinupair)).
% 223.79/32.87  thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setukpairIL)).
% 223.79/32.87  thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setukpairIR)).
% 223.79/32.87  thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', kpairiskpair)).
% 223.79/32.87  thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', kpairp)).
% 223.79/32.87  thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', singletonsubset)).
% 223.79/32.87  thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', singletoninpowerset)).
% 223.79/32.87  thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', singletoninpowunion)).
% 223.79/32.87  thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', upairset2E)).
% 223.79/32.87  thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', upairsubunion)).
% 223.79/32.87  thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', upairinpowunion)).
% 223.79/32.87  thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ubforcartprodlem1)).
% 223.79/32.87  thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ubforcartprodlem2)).
% 223.79/32.87  thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ubforcartprodlem3)).
% 223.79/32.87  thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', cartprodpairin)).
% 223.79/32.87  thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', cartprodmempair1)).
% 223.79/32.87  thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', cartprodmempair)).
% 223.79/32.87  thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setunionE2)).
% 223.79/32.87  thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setunionsingleton1)).
% 223.79/32.87  thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setunionsingleton2)).
% 223.79/32.87  thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setunionsingleton)).
% 223.79/32.87  thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', singletonsuniq)).
% 223.79/32.87  thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setukpairinjL1)).
% 223.79/32.87  thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', theprop)).
% 223.79/32.87  thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', kfstpairEq)).
% 223.79/32.87  thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', cartprodfstin)).
% 223.79/32.87  thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setukpairinjL2)).
% 223.79/32.87  thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setukpairinjL)).
% 223.79/32.87  thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setukpairinjR11)).
% 223.79/32.87  thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setukpairinjR12)).
% 223.79/32.87  thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setukpairinjR1)).
% 223.79/32.87  thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', upairequniteq)).
% 223.79/32.87  thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setukpairinjR2)).
% 223.79/32.87  thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setukpairinjR)).
% 223.79/32.87  thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ksndpairEq)).
% 223.79/32.87  thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', kpairsurjEq)).
% 223.79/32.87  thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', cartprodsndin)).
% 223.79/32.87  thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', cartprodpairmemEL)).
% 223.79/32.87  thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', cartprodpairmemER)).
% 223.79/32.87  thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', cartprodmempaircEq)).
% 223.79/32.87  thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', cartprodfstpairEq)).
% 223.79/32.87  thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', cartprodsndpairEq)).
% 223.79/32.87  thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', cartprodpairsurjEq)).
% 223.79/32.87  thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', app)).
% 223.79/32.87  thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', infuncsetfunc)).
% 223.79/32.87  thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ap2p)).
% 223.79/32.87  thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', funcinfuncset)).
% 223.79/32.87  thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', funcGraphProp1)).
% 223.79/32.87  thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', funcGraphProp3)).
% 223.79/32.87  thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', funcGraphProp2)).
% 223.79/32.87  thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', funcextLem)).
% 223.79/32.87  thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', funcGraphProp4)).
% 223.79/32.87  thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', funcext)).
% 223.79/32.87  thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', funcext2)).
% 223.79/32.87  thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ap2apEq1)).
% 223.79/32.87  thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ap2apEq2)).
% 223.79/32.87  thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', ifp)).
% 223.79/32.87  thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', theeq)).
% 223.79/32.87  thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', iftrue)).
% 223.79/32.87  thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', iffalse)).
% 223.79/32.87  thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', iftrueorfalse)).
% 223.79/32.87  thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectT_lem)).
% 223.79/32.87  thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binunionT_lem)).
% 223.79/32.87  thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', powersetT_lem)).
% 223.79/32.87  thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setminusT_lem)).
% 223.79/32.87  thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', complementT_lem)).
% 223.79/32.87  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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', setextT)).
% 223.79/32.87  thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', subsetTI)).
% 223.79/32.87  thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', powersetTI1)).
% 223.79/32.87  thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', powersetTE1)).
% 223.79/32.87  thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', complementTI1)).
% 223.79/32.87  thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', complementTE1)).
% 223.79/32.87  thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectTELcontra)).
% 223.79/32.87  thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', binintersectTERcontra)).
% 223.79/32.87  thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', contrasubsetT)).
% 223.79/32.87  thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', contrasubsetT1)).
% 223.79/32.87  thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', contrasubsetT2)).
% 223.79/32.87  thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', contrasubsetT3)).
% 223.79/32.87  thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', doubleComplementI1)).
% 223.79/32.87  thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', doubleComplementE1)).
% 223.79/32.87  thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', doubleComplementSub1)).
% 223.79/32.87  thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', doubleComplementSub2)).
% 223.79/32.87  thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', doubleComplementEq)).
% 223.79/32.87  thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', complementTnotintersectT)).
% 223.79/32.87  thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', complementImpComplementIntersect)).
% 223.79/32.87  thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', complementSubsetComplementIntersect)).
% 223.79/32.87  thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', complementInPowersetComplementIntersect)).
% 223.79/32.87  thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.MNB4CJHXXh/E---3.1_172947.p', contraSubsetComplement)).
% 223.79/32.87  thf(c_0_258, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 223.79/32.87  thf(c_0_259, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 223.79/32.87  thf(c_0_260, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 223.79/32.87  thf(c_0_261, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 223.79/32.87  thf(c_0_262, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 223.79/32.87  thf(c_0_263, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 223.79/32.87  thf(c_0_264, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 223.79/32.87  thf(c_0_265, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 223.79/32.87  thf(c_0_266, 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])).
% 223.79/32.87  thf(c_0_267, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 223.79/32.87  thf(c_0_268, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 223.79/32.87  thf(c_0_269, 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])).
% 223.79/32.87  thf(c_0_270, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 223.79/32.87  thf(c_0_271, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 223.79/32.87  thf(c_0_272, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 223.79/32.87  thf(c_0_273, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 223.79/32.87  thf(c_0_274, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 223.79/32.87  thf(c_0_275, 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])).
% 223.79/32.87  thf(c_0_276, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 223.79/32.87  thf(c_0_277, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 223.79/32.87  thf(c_0_278, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 223.79/32.87  thf(c_0_279, 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])).
% 223.79/32.87  thf(c_0_280, 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)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[complementTcontraSubset])).
% 223.79/32.87  thf(c_0_281, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X836:$i]:(((((X6 @ X2 @ X836)))&(![X837:$i]:(((((X6 @ X2 @ X837)))=>(((X836)=(X837)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_258, c_0_259])).
% 223.79/32.87  thf(c_0_282, plain, ((descrp)=(![X1:$i > $o]:((((?[X838:$i]:(((((X1 @ X838)))&(![X839:$i]:(((((X1 @ X839)))=>(((X838)=(X839))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_260, c_0_259])).
% 223.79/32.87  thf(c_0_283, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 223.79/32.87  thf(c_0_284, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 223.79/32.87  thf(c_0_285, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 223.79/32.87  thf(c_0_286, plain, ((exuE1)=(![X1:$i > $o]:((((?[X840:$i]:(((((X1 @ X840)))&(![X841:$i]:(((((X1 @ X841)))=>(((X840)=(X841))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_261, c_0_259])).
% 223.79/32.87  thf(c_0_287, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X842:$i]:(((((X1 @ X842)))&(![X843:$i]:(((((X1 @ X843)))=>(((X842)=(X843))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_262, c_0_259])).
% 223.79/32.87  thf(c_0_288, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 223.79/32.87  thf(c_0_289, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_263])).
% 223.79/32.87  thf(c_0_290, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_264, c_0_263])).
% 223.79/32.87  thf(c_0_291, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_263])).
% 223.79/32.87  thf(c_0_292, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 223.79/32.87  thf(c_0_293, plain, ((exuE2)=(![X1:$i > $o]:((((?[X844:$i]:(((((X1 @ X844)))&(![X845:$i]:(((((X1 @ X845)))=>(((X844)=(X845))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_265, c_0_259])).
% 223.79/32.87  thf(c_0_294, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_263])).
% 223.79/32.87  thf(c_0_295, 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])).
% 223.79/32.87  thf(c_0_296, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X846:$i]:(((((X1 @ X846)))&(![X847:$i]:(((((X1 @ X847)))=>(((X846)=(X847)))))))))))))), inference(apply_def,[status(thm)],[c_0_266, c_0_259])).
% 223.79/32.87  thf(c_0_297, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X848:$i]:(((((X1 @ X848)))&(![X849:$i]:(((((X1 @ X849)))=>(((X848)=(X849)))))))))))))))), inference(apply_def,[status(thm)],[c_0_267, c_0_259])).
% 223.79/32.87  thf(c_0_298, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X850:$i]:(((((X1 @ X850)))&(![X851:$i]:(((((X1 @ X851)))=>(((X850)=(X851)))))))))))))), inference(apply_def,[status(thm)],[c_0_268, c_0_259])).
% 223.79/32.87  thf(c_0_299, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X852:$i]:(((((X1 @ X852)))&(![X853:$i]:(((((X1 @ X853)))=>(((X852)=(X853))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_269, c_0_259])).
% 223.79/32.87  thf(c_0_300, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X854:$i]:(((((X1 @ X854)))&(![X855:$i]:(((((X1 @ X855)))=>(((X854)=(X855))))))))))<=>((?[X856:$i]:(((((X17 @ X856)))&(![X857:$i]:(((((X17 @ X857)))=>(((X856)=(X857)))))))))))))))), inference(apply_def,[status(thm)],[c_0_270, c_0_259])).
% 223.79/32.87  thf(c_0_301, plain, ((exuEu)=(![X1:$i > $o]:((((?[X858:$i]:(((((X1 @ X858)))&(![X859:$i]:(((((X1 @ X859)))=>(((X858)=(X859))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_271, c_0_259])).
% 223.79/32.87  thf(c_0_302, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X860:$i]:(((((X1 @ X860)))&(![X861:$i]:(((((X1 @ X861)))=>(((X860)=(X861))))))))))=>((((?[X862:$i]:(((((X17 @ X862)))&(![X863:$i]:(((((X17 @ X863)))=>(((X862)=(X863))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_272, c_0_259])).
% 223.79/32.87  thf(c_0_303, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 223.79/32.87  thf(c_0_304, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 223.79/32.87  thf(c_0_305, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 223.79/32.87  thf(c_0_306, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 223.79/32.87  thf(c_0_307, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_273, c_0_274])).
% 223.79/32.87  thf(c_0_308, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))))), inference(apply_def,[status(thm)],[c_0_275, c_0_274])).
% 223.79/32.87  thf(c_0_309, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))))=>(((?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2)))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_276, c_0_274])).
% 223.79/32.87  thf(c_0_310, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 223.79/32.87  thf(c_0_311, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 223.79/32.87  thf(c_0_312, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 223.79/32.87  thf(c_0_313, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 223.79/32.87  thf(c_0_314, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_277, c_0_278])).
% 223.79/32.87  thf(c_0_315, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 223.79/32.87  thf(c_0_316, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 223.79/32.87  thf(c_0_317, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 223.79/32.87  thf(c_0_318, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 223.79/32.87  thf(c_0_319, plain, ((funcImageSingleton)<=>![X4:$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])).
% 223.79/32.87  thf(c_0_320, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 223.79/32.87  thf(c_0_321, plain, ((lamProp)<=>![X4:$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])).
% 223.79/32.87  thf(c_0_322, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 223.79/32.87  thf(c_0_323, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 223.79/32.87  thf(c_0_324, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_278])).
% 223.79/32.87  thf(c_0_325, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_278])).
% 223.79/32.87  thf(c_0_326, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_279, c_0_274])).
% 223.79/32.87  thf(c_0_327, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_278])).
% 223.79/32.87  thf(c_0_328, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_278])).
% 223.79/32.87  thf(c_0_329, 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])).
% 223.79/32.87  thf(c_0_330, 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])).
% 223.79/32.87  thf(c_0_331, 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])).
% 223.79/32.87  thf(c_0_332, 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])).
% 223.79/32.87  thf(c_0_333, 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])).
% 223.79/32.87  thf(c_0_334, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 223.79/32.87  thf(c_0_335, plain, ((iffalseProp2)<=>![X4:$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])).
% 223.79/32.87  thf(c_0_336, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 223.79/32.87  thf(c_0_337, plain, ((iftrueProp2)<=>![X4:$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])).
% 223.79/32.87  thf(c_0_338, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 223.79/32.87  thf(c_0_339, plain, ((epred1_0)<=>![X893:$i]:(?[X894:$i]:((((![X895:$i]:(((in @ X895 @ X894)=>![X896:$i]:(((in @ X896 @ X895)=>(in @ X896 @ X893)))))&![X897:$i, X898:$i]:((((in @ X897 @ X893)&(in @ X898 @ X893))=>(![X899:$i]:(((in @ X899 @ X894)=>((in @ X897 @ X899)<=>(in @ X898 @ X899))))=>((X897)=(X898))))))&![X900:$i, X901:$i]:((((in @ X900 @ X894)&(in @ X901 @ X894))=>(![X902:$i]:(((in @ X902 @ X900)=>(in @ X902 @ X901)))|![X903:$i]:(((in @ X903 @ X901)=>(in @ X903 @ X900)))))))&![X904:$i]:(((![X905:$i]:(((in @ X905 @ X904)=>(in @ X905 @ X893)))&?[X906:$i]:((in @ X906 @ X904)))=>?[X907:$i, X908:$i]:(((((in @ X907 @ X894)&(in @ X908 @ X904))&~(?[X909:$i]:(((in @ X909 @ X907)&(in @ X909 @ X904)))))&![X910:$i]:(((in @ X910 @ X894)=>(![X911:$i]:(((in @ X911 @ X910)=>(in @ X911 @ X907)))|(in @ X908 @ X910)))))))))))), introduced(definition)).
% 223.79/32.87  thf(c_0_340, negated_conjecture, ~((![X864:$i, X865:$i]:((![X866:$i]:(((in @ X866 @ X864)<=>(in @ X866 @ X865)))=>((X864)=(X865))))=>(![X867:$i]:(~(in @ X867 @ emptyset))=>(![X868:$i, X869:$i, X870:$i]:(((in @ X870 @ (setadjoin @ X868 @ X869))<=>(((X870)=(X868))|(in @ X870 @ X869))))=>(![X871:$i, X872:$i]:(((in @ X872 @ (powerset @ X871))<=>![X873:$i]:(((in @ X873 @ X872)=>(in @ X873 @ X871)))))=>(![X874:$i, X875:$i]:(((in @ X875 @ (setunion @ X874))<=>?[X876:$i]:(((in @ X875 @ X876)&(in @ X876 @ X874)))))=>((in @ emptyset @ omega)=>(![X877:$i]:(((in @ X877 @ omega)=>(in @ (setadjoin @ X877 @ X877) @ omega)))=>(![X878:$i]:((((in @ emptyset @ X878)&![X879:$i]:((((in @ X879 @ omega)&(in @ X879 @ X878))=>(in @ (setadjoin @ X879 @ X879) @ X878))))=>![X880:$i]:(((in @ X880 @ omega)=>(in @ X880 @ X878)))))=>(![X881:$i > $i > $o, X882:$i]:((![X883:$i]:(((in @ X883 @ X882)=>?[X884:$i]:(((X881 @ X883 @ X884)&![X885:$i]:(((X881 @ X883 @ X885)=>((X884)=(X885))))))))=>?[X886:$i]:(![X887:$i]:(((in @ X887 @ X886)<=>?[X888:$i]:(((in @ X888 @ X882)&(X881 @ X888 @ X887))))))))=>(![X889:$i]:((?[X890:$i]:((in @ X890 @ X889))=>?[X891:$i]:(((in @ X891 @ X889)&~(?[X892:$i]:(((in @ X892 @ X891)&(in @ X892 @ X889))))))))=>((epred1_0)=>(![X912:$i > $o]:((?[X913:$i]:(((X912 @ X913)&![X914:$i]:(((X912 @ X914)=>((X913)=(X914))))))=>(X912 @ (descr @ (^[Z0:$i]:(X912 @ Z0))))))=>(![X915:$i, X916:$i > $o, X917:$i]:(((in @ X917 @ X915)=>((X916 @ X917)=>(in @ X917 @ (dsetconstr @ X915 @ X916)))))=>(![X918:$i, X919:$i > $o, X920:$i]:(((in @ X920 @ (dsetconstr @ X918 @ X919))=>(in @ X920 @ X918)))=>(![X921:$i, X922:$i > $o, X923:$i]:(((in @ X923 @ (dsetconstr @ X921 @ X922))=>(X922 @ X923)))=>(![X924:$i > $o]:((?[X925:$i]:(((X924 @ X925)&![X926:$i]:(((X924 @ X926)=>((X925)=(X926))))))=>?[X927:$i]:(((X924 @ X927)&![X928:$i]:(((X924 @ X928)=>((X927)=(X928))))))))=>(![X929:$o, X930:$i]:(((in @ X930 @ (prop2set @ ((X929))))=>(X929)))=>(![X931:$i]:(((in @ X931 @ emptyset)=>![X932:$o]:((X932))))=>(![X933:$i]:(((in @ X933 @ emptyset)=>~($true)))=>(![X934:$i]:(~(in @ X934 @ emptyset))=>(![X935:$i > $o]:((?[X936:$i]:(((X935 @ X936)&![X937:$i]:(((X935 @ X937)=>((X936)=(X937))))))=>?[X938:$i]:((X935 @ X938))))=>(![X939:$i, X940:$i]:((![X941:$i]:(((in @ X941 @ X939)=>(in @ X941 @ X940)))=>(![X942:$i]:(((in @ X942 @ X940)=>(in @ X942 @ X939)))=>((X939)=(X940)))))=>(![X943:$i]:((![X944:$i]:(~(in @ X944 @ X943))=>((X943)=(emptyset))))=>(![X945:$i]:((![X946:$i]:(~(in @ X946 @ X945))=>((X945)=(emptyset))))=>(![X947:$i, X948:$i > $o, X949:$i]:(((in @ X949 @ X947)=>((in @ X949 @ (dsetconstr @ X947 @ X948))<=>(X948 @ X949))))=>(![X950:$i]:((((X950)!=(emptyset))=>?[X951:$i]:((in @ X951 @ X950))))=>(![X952:$i, X953:$i > $o, X954:$i]:(((in @ X954 @ X952)=>((X953 @ X954)=>((dsetconstr @ X952 @ X953)!=(emptyset)))))=>(![X955:$i]:((?[X956:$i]:((in @ X956 @ X955))=>((X955)!=(emptyset))))=>(![X957:$i, X958:$i]:((in @ X957 @ (setadjoin @ X957 @ X958)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X959:$i, X960:$i, X961:$i]:(((in @ X961 @ X960)=>(in @ X961 @ (setadjoin @ X959 @ X960))))=>(![X962:$i, X963:$i, X964:$i]:(((in @ X964 @ (setadjoin @ X962 @ X963))=>![X965:$o]:(((((X964)=(X962))=>(X965))=>(((in @ X964 @ X963)=>(X965))=>(X965))))))=>(![X966:$i, X967:$i, X968:$i]:(((in @ X968 @ (setadjoin @ X966 @ X967))=>(((X968)=(X966))|(in @ X968 @ X967))))=>(![X969:$i]:(((dsetconstr @ X969 @ (^[Z0:$i]:($true)))=(X969)))=>(![X970:$i, X971:$i]:((![X972:$i]:(((in @ X972 @ X971)=>(in @ X972 @ X970)))=>(in @ X971 @ (powerset @ X970))))=>(![X973:$i]:((in @ emptyset @ (powerset @ X973)))=>(![X974:$i]:((in @ emptyset @ (powerset @ X974)))=>(![X975:$i, X976:$i, X977:$i]:(((in @ X976 @ (powerset @ X975))=>((in @ X977 @ X976)=>(in @ X977 @ X975))))=>(![X978:$i, X979:$i, X980:$i]:(((in @ X979 @ X980)=>((in @ X980 @ X978)=>(in @ X979 @ (setunion @ X978)))))=>(![X981:$i, X982:$i]:(((in @ X982 @ (setunion @ X981))=>![X983:$o]:((![X984:$i]:(((in @ X982 @ X984)=>((in @ X984 @ X981)=>(X983))))=>(X983)))))=>(![X985:$i, X986:$i]:(((in @ X986 @ X985)=>(in @ X986 @ (powerset @ (setunion @ X985)))))=>(![X987:$i > $o]:((?[X988:$i]:(((X987 @ X988)&![X989:$i]:(((X987 @ X989)=>((X988)=(X989))))))=>?[X990:$i]:(![X991:$i]:(((X987 @ X991)<=>((X991)=(X990)))))))=>(![X992:$i]:((((X992)!=(emptyset))=>?[X993:$i]:(((in @ X993 @ X992)&$true))))=>(![X994:$i, X995:$i]:(((in @ X994 @ (setadjoin @ X995 @ emptyset))=>((X994)=(X995))))=>(![X996:$i, X997:$i]:((((X996)!=(X997))=>~(in @ X997 @ (setadjoin @ X996 @ emptyset))))=>(![X998:$i, X999:$i]:((((X998)=(X999))=>(in @ X998 @ (setadjoin @ X999 @ emptyset))))=>(![X1000:$i, X1001:$i]:(((in @ X1000 @ (setadjoin @ X1001 @ emptyset))=>(in @ X1001 @ (setadjoin @ X1000 @ emptyset))))=>(![X1002:$i, X1003:$i, X1004:$i]:(((in @ X1004 @ (setadjoin @ X1002 @ (setadjoin @ X1003 @ emptyset)))=>(((X1004)=(X1002))|((X1004)=(X1003)))))=>(![X1005:$i, X1006:$i]:((in @ X1005 @ (setadjoin @ X1005 @ (setadjoin @ X1006 @ emptyset))))=>(![X1007:$i, X1008:$i]:((in @ X1008 @ (setadjoin @ X1007 @ (setadjoin @ X1008 @ emptyset))))=>(![X1009:$i, X1010:$i > $o]:((?[X1011:$i]:(((in @ X1011 @ X1009)&(X1010 @ X1011)))=>(((dsetconstr @ X1009 @ X1010)=(emptyset))=>~($true))))=>(![X1012:$i > $o, X1013:$i]:(((in @ X1013 @ emptyset)=>(X1012 @ X1013)))=>(![X1014:$i, X1015:$i > $o]:((~(![X1016:$i]:(((in @ X1016 @ X1014)=>(X1015 @ X1016))))=>?[X1017:$i]:(((in @ X1017 @ X1014)&~((X1015 @ X1017))))))=>(![X1018:$i, X1019:$i > $o]:((![X1020:$i]:(((in @ X1020 @ X1018)=>~((X1019 @ X1020))))=>~(?[X1021:$i]:(((in @ X1021 @ X1018)&(X1019 @ X1021))))))=>(![X1022:$i, X1023:$i > $o]:((~(?[X1024:$i]:(((in @ X1024 @ X1022)&(X1023 @ X1024))))=>![X1025:$i]:(((in @ X1025 @ X1022)=>~((X1023 @ X1025))))))=>(![X1026:$i, X1027:$i > $o]:((?[X1028:$i]:(((in @ X1028 @ X1026)&~((X1027 @ X1028))))=>~(![X1029:$i]:(((in @ X1029 @ X1026)=>(X1027 @ X1029))))))=>(![X1030:$o]:(((X1030)=>(in @ emptyset @ (prop2set @ ((X1030))))))=>(![X1031:$o]:(((X1031)=>(set2prop @ (prop2set @ ((X1031))))))=>(![X1032:$i, X1033:$i > $o]:((~(?[X1034:$i]:(((in @ X1034 @ X1032)&(X1033 @ X1034))))=>![X1035:$i]:(((in @ X1035 @ X1032)=>~((X1033 @ X1035))))))=>(![X1036:$i, X1037:$i > $o]:((~(![X1038:$i]:(((in @ X1038 @ X1036)=>(X1037 @ X1038))))=>?[X1039:$i]:(((in @ X1039 @ X1036)&~((X1037 @ X1039))))))=>(![X1040:$i > $o]:((?[X1041:$i]:(((X1040 @ X1041)&![X1042:$i]:(((X1040 @ X1042)=>((X1041)=(X1042))))))=>?[X1043:$i]:(((X1040 @ X1043)&![X1044:$i]:(((X1040 @ X1044)=>((X1043)=(X1044))))))))=>(![X1045:$i > $o]:((?[X1046:$i]:((X1045 @ X1046))=>(![X1047:$i, X1048:$i]:(((X1045 @ X1047)=>((X1045 @ X1048)=>((X1047)=(X1048)))))=>?[X1049:$i]:(((X1045 @ X1049)&![X1050:$i]:(((X1045 @ X1050)=>((X1049)=(X1050)))))))))=>(![X1051:$i > $o]:((?[X1052:$i]:(![X1053:$i]:(((X1051 @ X1053)<=>((X1053)=(X1052)))))=>?[X1054:$i]:(((X1051 @ X1054)&![X1055:$i]:(((X1051 @ X1055)=>((X1054)=(X1055))))))))=>(![X1056:$i, X1057:$i]:((((X1056)=(X1057))=>![X1058:$i, X1059:$i]:((((X1058)=(X1059))=>((in @ X1058 @ X1056)=>(in @ X1059 @ X1057))))))=>(![X1060:$i, X1061:$i]:((((X1060)=(X1061))=>![X1062:$i, X1063:$i]:((((X1062)=(X1063))=>((in @ X1062 @ X1060)<=>(in @ X1063 @ X1061))))))=>(![X1064:$i > $o]:((?[X1065:$i]:(((X1064 @ X1065)&![X1066:$i]:(((X1064 @ X1066)=>((X1065)=(X1066))))))=>![X1067:$i, X1068:$i]:(((X1064 @ X1067)=>((X1064 @ X1068)=>((X1067)=(X1068)))))))=>(![X1069:$i > $o, X1070:$i > $o]:((![X1071:$i, X1072:$i]:((((X1071)=(X1072))=>((X1069 @ X1071)<=>(X1070 @ X1072))))=>(?[X1073:$i]:(((X1069 @ X1073)&![X1074:$i]:(((X1069 @ X1074)=>((X1073)=(X1074))))))<=>?[X1075:$i]:(((X1070 @ X1075)&![X1076:$i]:(((X1070 @ X1076)=>((X1075)=(X1076)))))))))=>(((emptyset)=(emptyset))=>(![X1077:$i, X1078:$i]:((((X1077)=(X1078))=>![X1079:$i, X1080:$i]:((((X1079)=(X1080))=>((setadjoin @ X1077 @ X1079)=(setadjoin @ X1078 @ X1080))))))=>(![X1081:$i, X1082:$i]:((((X1081)=(X1082))=>((powerset @ X1081)=(powerset @ X1082))))=>(![X1083:$i, X1084:$i]:((((X1083)=(X1084))=>((setunion @ X1083)=(setunion @ X1084))))=>(((omega)=(omega))=>(![X1085:$i > $o]:((?[X1086:$i]:(((X1085 @ X1086)&![X1087:$i]:(((X1085 @ X1087)=>((X1086)=(X1087))))))=>![X1088:$i, X1089:$i]:(((X1085 @ X1088)=>((X1085 @ X1089)=>((X1088)=(X1089)))))))=>(![X1090:$i > $o, X1091:$i > $o]:((![X1092:$i, X1093:$i]:((((X1092)=(X1093))=>((X1090 @ X1092)<=>(X1091 @ X1093))))=>(?[X1094:$i]:(((X1090 @ X1094)&![X1095:$i]:(((X1090 @ X1095)=>((X1094)=(X1095))))))=>(?[X1096:$i]:(((X1091 @ X1096)&![X1097:$i]:(((X1091 @ X1097)=>((X1096)=(X1097))))))=>((descr @ X1090)=(descr @ X1091))))))=>(![X1098:$i, X1099:$i]:((((X1098)=(X1099))=>![X1100:$i > $o, X1101:$i > $o]:((![X1102:$i]:(((in @ X1102 @ X1098)=>![X1103:$i]:(((in @ X1103 @ X1099)=>(((X1102)=(X1103))=>((X1100 @ X1102)<=>(X1101 @ X1103)))))))=>((dsetconstr @ X1098 @ X1100)=(dsetconstr @ X1099 @ X1101))))))=>(![X1104:$i, X1105:$i]:((![X1106:$i]:(((in @ X1106 @ X1104)=>(in @ X1106 @ X1105)))=>(subset @ X1104 @ X1105)))=>(![X1107:$i, X1108:$i]:((((X1107)=(X1108))=>(subset @ X1108 @ X1107)))=>(![X1109:$i, X1110:$i]:((((X1109)=(X1110))=>(subset @ X1109 @ X1110)))=>(![X1111:$i, X1112:$i]:((![X1113:$i]:(((in @ X1113 @ X1111)=>(in @ X1113 @ X1112)))=>(subset @ X1111 @ X1112)))=>(![X1114:$i]:((subset @ emptyset @ X1114))=>(![X1115:$i, X1116:$i, X1117:$i]:(((subset @ X1115 @ X1116)=>((in @ X1117 @ X1115)=>(in @ X1117 @ X1116))))=>(![X1118:$i, X1119:$i, X1120:$i]:(((subset @ X1118 @ X1119)=>(~(in @ X1120 @ X1119)=>~(in @ X1120 @ X1118))))=>(![X1121:$i, X1122:$i, X1123:$i]:(((in @ X1123 @ X1121)=>(~(in @ X1123 @ X1122)=>~(subset @ X1121 @ X1122))))=>(![X1124:$i, X1125:$i]:((~(subset @ X1124 @ X1125)=>((X1124)!=(X1125))))=>(![X1126:$i, X1127:$i, X1128:$i]:(((in @ X1128 @ X1126)=>(~(in @ X1128 @ X1127)=>((X1126)!=(X1127)))))=>(![X1129:$i]:((subset @ X1129 @ X1129))=>(![X1130:$i, X1131:$i, X1132:$i]:(((subset @ X1130 @ X1131)=>((subset @ X1131 @ X1132)=>(subset @ X1130 @ X1132))))=>(![X1133:$i, X1134:$i]:((subset @ X1134 @ (setadjoin @ X1133 @ X1134)))=>(![X1135:$i, X1136:$i, X1137:$i]:(((subset @ X1135 @ X1137)=>(subset @ X1135 @ (setadjoin @ X1136 @ X1137))))=>(![X1138:$i, X1139:$i]:(((subset @ X1138 @ X1139)=>(in @ X1138 @ (powerset @ X1139))))=>(![X1140:$i, X1141:$i]:(((subset @ X1140 @ X1141)=>((subset @ X1141 @ X1140)=>((X1140)=(X1141)))))=>(![X1142:$i]:(((subset @ X1142 @ emptyset)=>((X1142)=(emptyset))))=>(![X1143:$i, X1144:$i]:(((subset @ X1144 @ X1143)=>(in @ X1144 @ (powerset @ X1143))))=>(![X1145:$i, X1146:$i]:(((in @ X1146 @ (powerset @ X1145))=>(subset @ X1146 @ X1145)))=>(![X1147:$i]:((in @ X1147 @ (powerset @ X1147)))=>(![X1148:$i, X1149:$i]:(((subset @ X1148 @ X1149)=>(subset @ (powerset @ X1148) @ (powerset @ X1149))))=>(![X1150:$i, X1151:$i > $o]:((in @ (dsetconstr @ X1150 @ X1151) @ (powerset @ X1150)))=>(![X1152:$i, X1153:$i > $o]:((subset @ (dsetconstr @ X1152 @ X1153) @ X1152))=>(![X1154:$i, X1155:$i, X1156:$i]:(((in @ X1156 @ X1154)=>(in @ X1156 @ (binunion @ X1154 @ X1155))))=>(![X1157:$i, X1158:$i]:((in @ X1158 @ (setadjoin @ X1157 @ (setadjoin @ X1158 @ emptyset))))=>(![X1159:$i, X1160:$i, X1161:$i]:(((in @ X1161 @ X1160)=>(in @ X1161 @ (binunion @ X1159 @ X1160))))=>(![X1162:$i, X1163:$i, X1164:$i, X1165:$o]:(((in @ X1164 @ (binunion @ X1162 @ X1163))=>(((in @ X1164 @ X1162)=>(X1165))=>(((in @ X1164 @ X1163)=>(X1165))=>(X1165)))))=>(![X1166:$i, X1167:$i, X1168:$i]:(((in @ X1168 @ (binunion @ X1166 @ X1167))=>((in @ X1168 @ X1166)|(in @ X1168 @ X1167))))=>(![X1169:$i, X1170:$i]:((subset @ X1169 @ (binunion @ X1169 @ X1170)))=>(![X1171:$i, X1172:$i]:((subset @ X1172 @ (binunion @ X1171 @ X1172)))=>(![X1173:$i, X1174:$i, X1175:$i]:(((in @ X1175 @ X1173)=>((in @ X1175 @ X1174)=>(in @ X1175 @ (binintersect @ X1173 @ X1174)))))=>(![X1176:$i, X1177:$i, X1178:$i]:(((subset @ X1178 @ X1176)=>((subset @ X1178 @ X1177)=>(subset @ X1178 @ (binintersect @ X1176 @ X1177)))))=>(![X1179:$i, X1180:$i, X1181:$i]:(((in @ X1181 @ (binintersect @ X1179 @ X1180))=>(in @ X1181 @ X1179)))=>(![X1182:$i, X1183:$i]:((subset @ (binintersect @ X1182 @ X1183) @ X1182))=>(![X1184:$i, X1185:$i]:(((subset @ X1184 @ X1185)=>((binintersect @ X1184 @ X1185)=(X1184))))=>(![X1186:$i, X1187:$i]:((((binintersect @ X1186 @ X1187)=(X1187))=>(subset @ X1187 @ X1186)))=>(![X1188:$i, X1189:$i, X1190:$i]:(((in @ X1190 @ (binintersect @ X1188 @ X1189))=>(in @ X1190 @ X1189)))=>(![X1191:$i, X1192:$i]:((~(?[X1193:$i]:(((in @ X1193 @ X1191)&(in @ X1193 @ X1192))))=>((binintersect @ X1191 @ X1192)=(emptyset))))=>(![X1194:$i, X1195:$i]:((subset @ (binintersect @ X1194 @ X1195) @ X1195))=>(![X1196:$i, X1197:$i]:(((subset @ X1197 @ X1196)=>((binintersect @ X1196 @ X1197)=(X1197))))=>(![X1198:$i, X1199:$i]:((((binintersect @ X1198 @ X1199)=(X1198))=>(subset @ X1198 @ X1199)))=>(![X1200:$i, X1201:$i, X1202:$i]:(((binintersect @ X1200 @ (binunion @ X1201 @ X1202))=(binunion @ (binintersect @ X1200 @ X1201) @ (binintersect @ X1200 @ X1202))))=>(![X1203:$i, 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_281]), foundationAx]), wellorderingAx]), c_0_282]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_287]), setext]), emptyI]), noeltsimpempty]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_292]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_293]), c_0_294]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_295]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_296]), c_0_297]), c_0_298]), inCongP]), in__Cong]), c_0_299]), c_0_300]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_301]), c_0_302]), c_0_303]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_304]), c_0_305]), 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_306]), c_0_307]), c_0_308]), c_0_309]), singletonsuniq]), setukpairinjL1]), c_0_310]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_311]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), c_0_318]), c_0_319]), c_0_320]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_321]), c_0_322]), c_0_323]), c_0_324]), c_0_325]), c_0_326]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_327]), c_0_328]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_329]), c_0_330]), c_0_331]), c_0_332]), c_0_333]), c_0_334]), c_0_335]), c_0_336]), c_0_337]), c_0_338]), 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])])]), c_0_339])).
% 223.79/32.87  thf(c_0_341, negated_conjecture, ![X1676:$i, X1677:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1689:$i, X1690:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1698:$i, X1699:$i > $i > $o, X1700:$i, X1702:$i, X1705:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1712:$i, X1713:$i > $o, X1714:$i, X1716:$i, X1717:$i > $o, X1718:$i, X1719:$i, X1720:$i > $o, X1721:$i, X1722:$i, X1723:$i > $o, X1724:$i, X1725:$i > $o, X1726:$i, X1729:$i, X1730:$o, X1731:$i, X1732:$i, X1733:$o, X1734:$i, X1735:$i, X1736:$i > $o, X1737:$i, X1740:$i, X1741:$i, X1744:$i, X1746:$i, X1748:$i, X1749:$i > $o, X1750:$i, X1751:$i, X1753:$i, X1754:$i > $o, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$o, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$o, X1786:$i, X1787:$i, X1788:$i > $o, X1789:$i, X1792:$i, X1793:$i, X1794:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i > $o, X1813:$i, X1814:$i > $o, X1815:$i, X1816:$i, X1817:$i > $o, X1818:$i, X1820:$i, X1821:$i > $o, X1823:$i, X1824:$i, X1825:$i > $o, X1827:$i, X1828:$i, X1829:$i > $o, X1830:$i, X1832:$o, X1833:$o, X1834:$i, X1835:$i > $o, X1837:$i, X1838:$i, X1839:$i > $o, X1840:$i, X1842:$i > $o, X1843:$i, X1846:$i, X1847:$i > $o, X1848:$i, X1852:$i, X1853:$i > $o, X1854:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i > $o, X1867:$i, X1869:$i, X1870:$i, X1871:$i > $o, X1872:$i > $o, X1875:$i, X1878:$i, X1879:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i > $o, X1892:$i, X1894:$i, X1895:$i, X1896:$i > $o, X1897:$i > $o, X1900:$i, X1902:$i, X1904:$i, X1905:$i, X1906:$i > $o, X1907:$i > $o, X1910:$i, X1911:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i > $o, X1958:$i, X1959:$i > $o, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$o, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$o, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i > $o, X2114:$i, X2115:$i, X2116:$i > $o, X2118:$i, X2119:$i > $o, X2120:$i, X2122:$i, X2123:$i > $o, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i > $i > $o, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i > $i > $o, X2204:$i, X2205:$i, X2206:$i > $i > $o, X2207:$i, X2208:$i, X2209:$i > $i > $o, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i > $i > $o, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i > $i > $o, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i > $i > $o, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i > $i, X2253:$i, X2254:$i, X2255:$i > $i, X2257:$i, X2258:$i, X2259:$i > $i, X2261:$i, X2262:$i, X2263:$i, X2264:$i > $o, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i > $o, X2274:$i, X2275:$i, X2276:$i > $o, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i > $i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i > $i, X2348:$i, X2349:$i, X2350:$i > $i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$o, X2358:$i, X2359:$i, X2360:$i, X2361:$o, X2362:$i, X2363:$i, X2364:$i, X2365:$o, X2366:$i, X2367:$i, X2368:$i, X2369:$o, X2370:$i, X2371:$i, X2372:$i, X2373:$o, X2374:$i, X2375:$i, X2376:$i, X2377:$o, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$o, X2384:$i, X2385:$i, X2386:$i, X2387:$o, X2388:$i, X2389:$i, X2390:$i, X2391:$o, X2392:$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, X2407:$i, X2408:$i, X2409:$i, X2412:$i, X2413:$i, X2414:$i, X2416:$i, X2417:$i, X2418:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, 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X2311 @ X2312 @ X2313) @ (esk77_4 @ X2310 @ X2311 @ X2312 @ X2313)) @ X2313)|((X2312)=(X2313))|~(in @ (kpair @ (esk74_4 @ X2310 @ X2311 @ X2312 @ X2313) @ (esk75_4 @ X2310 @ X2311 @ X2312 @ X2313)) @ X2313)|~(subset @ X2313 @ (cartprod @ X2310 @ X2311))|~(subset @ X2312 @ (cartprod @ X2310 @ X2311)))&(~(in @ (kpair @ (esk76_4 @ X2310 @ X2311 @ X2312 @ X2313) @ (esk77_4 @ X2310 @ X2311 @ X2312 @ X2313)) @ X2312)|((X2312)=(X2313))|~(in @ (kpair @ (esk74_4 @ X2310 @ X2311 @ X2312 @ X2313) @ (esk75_4 @ X2310 @ X2311 @ X2312 @ X2313)) @ X2313)|~(subset @ X2313 @ (cartprod @ X2310 @ X2311))|~(subset @ X2312 @ (cartprod @ X2310 @ X2311)))))))))&((((in @ (esk78_4 @ X2318 @ X2319 @ X2320 @ X2321) @ X2318)|((X2320)=(X2321))|~(func @ X2318 @ X2319 @ X2321)|~(func @ X2318 @ X2319 @ X2320))&(((ap @ X2318 @ X2319 @ X2320 @ (esk78_4 @ X2318 @ X2319 @ X2320 @ X2321))!=(ap @ X2318 @ X2319 @ X2321 @ (esk78_4 @ X2318 @ X2319 @ X2320 @ X2321)))|((X2320)=(X2321))|~(func @ X2318 @ X2319 @ X2321)|~(func @ X2318 @ X2319 @ X2320)))&((((in @ (esk79_4 @ X2323 @ X2324 @ X2325 @ X2326) @ X2323)|((X2325)=(X2326))|~(in @ X2326 @ (funcSet @ X2323 @ X2324))|~(in @ X2325 @ (funcSet @ X2323 @ X2324)))&(((ap @ X2323 @ X2324 @ X2325 @ (esk79_4 @ X2323 @ X2324 @ X2325 @ X2326))!=(ap @ X2323 @ X2324 @ X2326 @ (esk79_4 @ X2323 @ X2324 @ X2325 @ X2326)))|((X2325)=(X2326))|~(in @ X2326 @ (funcSet @ X2323 @ X2324))|~(in @ X2325 @ (funcSet @ X2323 @ X2324))))&((~(in @ X2330 @ (funcSet @ X2328 @ X2329))|(~(in @ X2331 @ X2328)|((ap @ X2328 @ X2329 @ X2330 @ X2331)=(ap @ X2328 @ X2329 @ X2330 @ X2331))))&((~(func @ X2332 @ X2333 @ X2334)|(~(in @ X2335 @ X2332)|((ap @ X2332 @ X2333 @ X2334 @ X2335)=(ap @ X2332 @ X2333 @ X2334 @ X2335))))&((((in @ (esk80_3 @ X2336 @ X2337 @ X2338) @ X2336)|(~(in @ X2340 @ X2336)|((ap @ X2336 @ X2337 @ (lam @ X2336 @ X2337 @ X2338) @ X2340)=(X2338 @ X2340))))&(~(in @ (X2338 @ (esk80_3 @ X2336 @ X2337 @ X2338)) @ X2337)|(~(in @ X2340 @ X2336)|((ap @ X2336 @ X2337 @ (lam @ X2336 @ X2337 @ X2338) @ X2340)=(X2338 @ X2340)))))&((~(func @ X2341 @ X2342 @ X2343)|((lam @ X2341 @ X2342 @ (ap @ X2341 @ X2342 @ X2343))=(X2343)))&((((in @ (esk81_3 @ X2344 @ X2345 @ X2346) @ X2344)|((lam @ X2344 @ X2345 @ X2346)=(lam @ X2344 @ X2345 @ X2346)))&(~(in @ (X2346 @ (esk81_3 @ X2344 @ X2345 @ X2346)) @ X2345)|((lam @ X2344 @ X2345 @ X2346)=(lam @ X2344 @ X2345 @ X2346))))&((((in @ (esk82_3 @ X2348 @ X2349 @ X2350) @ X2348)|(~(in @ X2352 @ X2348)|((ap @ X2348 @ X2349 @ (lam @ X2348 @ X2349 @ X2350) @ X2352)=(X2350 @ X2352))))&(~(in @ (X2350 @ (esk82_3 @ X2348 @ X2349 @ X2350)) @ X2349)|(~(in @ X2352 @ X2348)|((ap @ X2348 @ X2349 @ (lam @ X2348 @ X2349 @ X2350) @ X2352)=(X2350 @ X2352)))))&((~(in @ X2355 @ (funcSet @ X2353 @ X2354))|((lam @ X2353 @ X2354 @ (ap @ X2353 @ X2354 @ X2355))=(X2355)))&((~(in @ X2358 @ X2356)|(~(in @ X2359 @ X2356)|((X2357)|(in @ X2359 @ (dsetconstr @ X2356 @ (^[Z0:$i]:((((((X2357))&(((Z0)=(X2358)))))|(((~((X2357)))&(((Z0)=(X2359)))))))))))))&((~(in @ X2362 @ X2360)|(~(in @ X2363 @ X2360)|((X2361)|((dsetconstr @ X2360 @ (^[Z0:$i]:((((((X2361))&(((Z0)=(X2362)))))|(((~((X2361)))&(((Z0)=(X2363)))))))))=(setadjoin @ X2363 @ emptyset)))))&((~(in @ X2366 @ X2364)|(~(in @ X2367 @ X2364)|(~(X2365)|(in @ X2366 @ (dsetconstr @ X2364 @ (^[Z0:$i]:((((((X2365))&(((Z0)=(X2366)))))|(((~((X2365)))&(((Z0)=(X2367)))))))))))))&((~(in @ X2370 @ X2368)|(~(in @ X2371 @ X2368)|(~(X2369)|((dsetconstr @ X2368 @ (^[Z0:$i]:((((((X2369))&(((Z0)=(X2370)))))|(((~((X2369)))&(((Z0)=(X2371)))))))))=(setadjoin @ X2370 @ emptyset)))))&((~(in @ X2374 @ X2372)|(~(in @ X2375 @ X2372)|(singleton @ (dsetconstr @ X2372 @ (^[Z0:$i]:((((((X2373))&(((Z0)=(X2374)))))|(((~((X2373)))&(((Z0)=(X2375))))))))))))&((~(in @ X2378 @ X2376)|(~(in @ X2379 @ X2376)|(in @ (if @ X2376 @ ((X2377)) @ X2378 @ X2379) @ X2376)))&((~(singleton @ X2380)|(~(in @ X2381 @ X2380)|((setunion @ X2380)=(X2381))))&((~(in @ X2384 @ X2382)|(~(in @ X2385 @ X2382)|(~(X2383)|((if @ X2382 @ ((X2383)) @ X2384 @ X2385)=(X2384)))))&((~(in @ X2388 @ X2386)|(~(in @ X2389 @ X2386)|((X2387)|((if @ X2386 @ ((X2387)) @ X2388 @ X2389)=(X2389)))))&((~(in @ X2392 @ X2390)|(~(in @ X2393 @ X2390)|(in @ (if @ X2390 @ ((X2391)) @ X2392 @ X2393) @ (setadjoin @ X2392 @ (setadjoin @ X2393 @ emptyset)))))&((~(in @ X2395 @ (powerset @ X2394))|(~(in @ X2396 @ (powerset @ X2394))|(in @ (binintersect @ X2395 @ X2396) @ (powerset @ X2394))))&((~(in @ X2398 @ (powerset @ X2397))|(~(in @ X2399 @ (powerset @ X2397))|(in @ (binunion @ X2398 @ X2399) @ (powerset @ X2397))))&((~(in @ X2401 @ (powerset @ X2400))|(in @ (powerset @ X2401) @ (powerset @ (powerset @ X2400))))&((~(in @ X2403 @ (powerset @ X2402))|(~(in @ X2404 @ (powerset @ X2402))|(in @ (setminus @ X2403 @ X2404) @ (powerset @ X2402))))&((~(in @ X2406 @ (powerset @ X2405))|(in @ (setminus @ X2405 @ X2406) @ (powerset @ X2405)))&(((((in @ (esk84_3 @ X2407 @ X2408 @ X2409) @ X2407)|((X2408)=(X2409))|(in @ (esk83_3 @ X2407 @ X2408 @ X2409) @ X2407)|~(in @ X2409 @ (powerset @ X2407))|~(in @ X2408 @ (powerset @ X2407)))&(((in @ (esk84_3 @ X2407 @ X2408 @ X2409) @ X2409)|((X2408)=(X2409))|(in @ (esk83_3 @ X2407 @ X2408 @ X2409) @ X2407)|~(in @ X2409 @ (powerset @ X2407))|~(in @ X2408 @ (powerset @ X2407)))&(~(in @ (esk84_3 @ X2407 @ X2408 @ X2409) @ X2408)|((X2408)=(X2409))|(in @ (esk83_3 @ X2407 @ X2408 @ X2409) @ X2407)|~(in @ X2409 @ (powerset @ X2407))|~(in @ X2408 @ (powerset @ X2407)))))&((((in @ (esk84_3 @ X2407 @ X2408 @ X2409) @ X2407)|((X2408)=(X2409))|(in @ (esk83_3 @ X2407 @ X2408 @ X2409) @ X2408)|~(in @ X2409 @ (powerset @ X2407))|~(in @ X2408 @ (powerset @ X2407)))&(((in @ (esk84_3 @ X2407 @ X2408 @ X2409) @ X2409)|((X2408)=(X2409))|(in @ (esk83_3 @ X2407 @ X2408 @ X2409) @ X2408)|~(in @ X2409 @ (powerset @ X2407))|~(in @ X2408 @ (powerset @ X2407)))&(~(in @ (esk84_3 @ X2407 @ X2408 @ X2409) @ X2408)|((X2408)=(X2409))|(in @ (esk83_3 @ X2407 @ X2408 @ X2409) @ X2408)|~(in @ X2409 @ (powerset @ X2407))|~(in @ X2408 @ (powerset @ X2407)))))&(((in @ (esk84_3 @ X2407 @ X2408 @ X2409) @ X2407)|((X2408)=(X2409))|~(in @ (esk83_3 @ X2407 @ X2408 @ X2409) @ X2409)|~(in @ X2409 @ (powerset @ X2407))|~(in @ X2408 @ (powerset @ X2407)))&(((in @ (esk84_3 @ X2407 @ X2408 @ X2409) @ X2409)|((X2408)=(X2409))|~(in @ (esk83_3 @ X2407 @ X2408 @ X2409) @ X2409)|~(in @ X2409 @ (powerset @ X2407))|~(in @ X2408 @ (powerset @ X2407)))&(~(in @ (esk84_3 @ X2407 @ X2408 @ X2409) @ X2408)|((X2408)=(X2409))|~(in @ (esk83_3 @ X2407 @ X2408 @ X2409) @ X2409)|~(in @ X2409 @ (powerset @ X2407))|~(in @ X2408 @ (powerset @ X2407)))))))&((((in @ (esk85_3 @ X2412 @ X2413 @ X2414) @ X2412)|(subset @ X2413 @ X2414)|~(in @ X2414 @ (powerset @ X2412))|~(in @ X2413 @ (powerset @ X2412)))&(((in @ (esk85_3 @ X2412 @ X2413 @ X2414) @ X2413)|(subset @ X2413 @ X2414)|~(in @ X2414 @ (powerset @ X2412))|~(in @ X2413 @ (powerset @ X2412)))&(~(in @ (esk85_3 @ X2412 @ X2413 @ X2414) @ X2414)|(subset @ X2413 @ X2414)|~(in @ X2414 @ (powerset @ X2412))|~(in @ X2413 @ (powerset @ X2412)))))&((((in @ (esk86_3 @ X2416 @ X2417 @ X2418) @ X2416)|(in @ X2417 @ (powerset @ X2418))|~(in @ X2418 @ (powerset @ X2416))|~(in @ X2417 @ (powerset @ X2416)))&(((in @ (esk86_3 @ X2416 @ X2417 @ X2418) @ X2417)|(in @ X2417 @ (powerset @ X2418))|~(in @ X2418 @ (powerset @ X2416))|~(in @ X2417 @ (powerset @ X2416)))&(~(in @ (esk86_3 @ X2416 @ X2417 @ X2418) @ X2418)|(in @ X2417 @ (powerset @ X2418))|~(in @ X2418 @ (powerset @ X2416))|~(in @ X2417 @ (powerset @ X2416)))))&((~(in @ X2421 @ (powerset @ X2420))|(~(in @ X2422 @ (powerset @ X2420))|(~(in @ X2423 @ X2420)|(~(in @ X2421 @ (powerset @ X2422))|(~(in @ X2423 @ X2421)|(in @ X2423 @ X2422))))))&((~(in @ X2425 @ (powerset @ X2424))|(~(in @ X2426 @ X2424)|(~(in @ X2426 @ X2425)|~(in @ X2426 @ (setminus @ X2424 @ X2425)))))&((~(in @ X2428 @ (powerset @ X2427))|(~(in @ X2429 @ X2427)|((in @ X2429 @ (setminus @ X2427 @ X2428))|(in @ X2429 @ X2428))))&((~(in @ X2431 @ (powerset @ X2430))|(~(in @ X2432 @ (powerset @ X2430))|(~(in @ X2433 @ X2430)|((in @ X2433 @ X2431)|~(in @ X2433 @ (binintersect @ X2431 @ X2432))))))&((~(in @ X2435 @ (powerset @ X2434))|(~(in @ X2436 @ (powerset @ X2434))|(~(in @ X2437 @ X2434)|((in @ X2437 @ X2436)|~(in @ X2437 @ (binintersect @ X2435 @ X2436))))))&((~(in @ X2439 @ (powerset @ X2438))|(~(in @ X2440 @ (powerset @ X2438))|(~(in @ X2441 @ X2438)|(~(subset @ X2439 @ (setminus @ X2438 @ X2440))|(~(in @ X2441 @ X2440)|~(in @ X2441 @ X2439))))))&((~(in @ X2443 @ (powerset @ X2442))|(~(in @ X2444 @ (powerset @ X2442))|(~(in @ X2445 @ X2442)|(~(subset @ X2443 @ X2444)|((in @ X2445 @ X2444)|~(in @ X2445 @ X2443))))))&((~(in @ X2447 @ (powerset @ X2446))|(~(in @ X2448 @ (powerset @ X2446))|(~(subset @ X2447 @ X2448)|(subset @ (setminus @ X2446 @ X2448) @ (setminus @ X2446 @ X2447)))))&((~(in @ X2450 @ (powerset @ X2449))|(~(in @ X2451 @ (powerset @ X2449))|(~(subset @ (setminus @ X2449 @ X2451) @ (setminus @ X2449 @ X2450))|(subset @ X2450 @ X2451))))&((~(in @ X2453 @ (powerset @ X2452))|(~(in @ X2454 @ X2452)|(~(in @ X2454 @ X2453)|(in @ X2454 @ (setminus @ X2452 @ (setminus @ X2452 @ X2453))))))&((~(in @ X2456 @ (powerset @ X2455))|(~(in @ X2457 @ X2455)|(~(in @ X2457 @ (setminus @ X2455 @ (setminus @ X2455 @ X2456)))|(in @ X2457 @ X2456))))&((~(in @ X2459 @ (powerset @ X2458))|(subset @ X2459 @ (setminus @ X2458 @ (setminus @ X2458 @ X2459))))&((~(in @ X2461 @ (powerset @ X2460))|(subset @ (setminus @ X2460 @ (setminus @ X2460 @ X2461)) @ X2461))&((~(in @ X2463 @ (powerset @ X2462))|((X2463)=(setminus @ X2462 @ (setminus @ X2462 @ X2463))))&((~(in @ X2465 @ (powerset @ X2464))|(~(in @ X2466 @ (powerset @ X2464))|(~(in @ X2467 @ X2464)|(~(in @ X2467 @ (setminus @ X2464 @ X2465))|~(in @ X2467 @ (binintersect @ X2465 @ X2466))))))&((~(in @ X2469 @ (powerset @ X2468))|(~(in @ X2470 @ (powerset @ X2468))|(~(in @ X2471 @ X2468)|(~(in @ X2471 @ (setminus @ X2468 @ X2469))|(in @ X2471 @ (setminus @ X2468 @ (binintersect @ X2469 @ X2470)))))))&((~(in @ X2473 @ (powerset @ X2472))|(~(in @ X2474 @ (powerset @ X2472))|(subset @ (setminus @ X2472 @ X2473) @ (setminus @ X2472 @ (binintersect @ X2473 @ X2474)))))&((~(in @ X2476 @ (powerset @ X2475))|(~(in @ X2477 @ (powerset @ X2475))|(in @ (setminus @ X2475 @ X2476) @ (powerset @ (setminus @ X2475 @ (binintersect @ X2476 @ X2477))))))&((~(in @ X2479 @ (powerset @ X2478))|(~(in @ X2480 @ (powerset @ X2478))|(~(subset @ X2479 @ (setminus @ X2478 @ X2480))|(~(in @ X2481 @ X2478)|(~(in @ X2481 @ X2480)|(in @ X2481 @ (setminus @ X2478 @ X2479)))))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((subset @ esk88_0 @ (setminus @ esk87_0 @ esk89_0))&~(subset @ esk89_0 @ (setminus @ esk87_0 @ esk88_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_340])])])])])])])).
% 223.79/32.87  thf(c_0_342, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(setminus @ X3 @ (setminus @ X3 @ X2)))|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_343, negated_conjecture, (in @ esk89_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_344, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_345, negated_conjecture, ((setminus @ esk87_0 @ (setminus @ esk87_0 @ esk89_0))=(esk89_0)), inference(spm,[status(thm)],[c_0_342, c_0_343])).
% 223.79/32.87  thf(c_0_346, negated_conjecture, ~((subset @ esk89_0 @ (setminus @ esk87_0 @ esk88_0))), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_347, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_348, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_349, negated_conjecture, (subset @ esk88_0 @ (setminus @ esk87_0 @ esk89_0)), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_350, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk87_0)|~((in @ X2 @ esk89_0)))), inference(spm,[status(thm)],[c_0_344, c_0_345])).
% 223.79/32.87  thf(c_0_351, negated_conjecture, (in @ (esk53_2 @ esk89_0 @ (setminus @ esk87_0 @ esk88_0)) @ esk89_0), inference(spm,[status(thm)],[c_0_346, c_0_347])).
% 223.79/32.87  thf(c_0_352, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_353, negated_conjecture, ![X2:$i]:(((in @ X2 @ (setminus @ esk87_0 @ esk89_0))|~((in @ X2 @ esk88_0)))), inference(spm,[status(thm)],[c_0_348, c_0_349])).
% 223.79/32.87  thf(c_0_354, negated_conjecture, ![X2:$i, X3:$i]:((((binintersect @ X3 @ X2)=(X2))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_355, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_356, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_357, negated_conjecture, (in @ (esk53_2 @ esk89_0 @ (setminus @ esk87_0 @ esk88_0)) @ esk87_0), inference(spm,[status(thm)],[c_0_350, c_0_351])).
% 223.79/32.87  thf(c_0_358, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X3 @ X2)|((binintersect @ X2 @ X3)!=(X3)))), inference(split_conjunct,[status(thm)],[c_0_341])).
% 223.79/32.87  thf(c_0_359, negated_conjecture, ![X2:$i]:((~((in @ X2 @ esk89_0))|~((in @ X2 @ esk88_0)))), inference(spm,[status(thm)],[c_0_352, c_0_353])).
% 223.79/32.87  thf(c_0_360, negated_conjecture, ![X3:$i, X2:$i]:((((binintersect @ X2 @ X3)=(X3))|~((in @ (esk53_2 @ X3 @ X2) @ X2)))), inference(spm,[status(thm)],[c_0_354, c_0_355])).
% 223.79/32.87  thf(c_0_361, negated_conjecture, ![X2:$i]:(((in @ (esk53_2 @ esk89_0 @ (setminus @ esk87_0 @ esk88_0)) @ (setminus @ esk87_0 @ X2))|(in @ (esk53_2 @ esk89_0 @ (setminus @ esk87_0 @ esk88_0)) @ X2))), inference(spm,[status(thm)],[c_0_356, c_0_357])).
% 223.79/32.87  thf(c_0_362, negated_conjecture, ((binintersect @ (setminus @ esk87_0 @ esk88_0) @ esk89_0)!=(esk89_0)), inference(spm,[status(thm)],[c_0_346, c_0_358])).
% 223.79/32.87  thf(c_0_363, negated_conjecture, ~((in @ (esk53_2 @ esk89_0 @ (setminus @ esk87_0 @ esk88_0)) @ esk88_0)), inference(spm,[status(thm)],[c_0_359, c_0_351])).
% 223.79/32.87  thf(c_0_364, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_360, c_0_361]), c_0_362]), c_0_363]), ['proof']).
% 223.79/32.87  % SZS output end CNFRefutation
% 223.79/32.87  % Parsed axioms                        : 549
% 223.79/32.87  % Removed by relevancy pruning/SinE    : 0
% 223.79/32.87  % Initial clauses                      : 729
% 223.79/32.87  % Removed in clause preprocessing      : 320
% 223.79/32.87  % Initial clauses in saturation        : 409
% 223.79/32.87  % Processed clauses                    : 20961
% 223.79/32.87  % ...of these trivial                  : 556
% 223.79/32.87  % ...subsumed                          : 15463
% 223.79/32.87  % ...remaining for further processing  : 4942
% 223.79/32.87  % Other redundant clauses eliminated   : 333
% 223.79/32.87  % Clauses deleted for lack of memory   : 0
% 223.79/32.87  % Backward-subsumed                    : 321
% 223.79/32.87  % Backward-rewritten                   : 123
% 223.79/32.87  % Generated clauses                    : 314849
% 223.79/32.87  % ...of the previous two non-redundant : 288673
% 223.79/32.87  % ...aggressively subsumed             : 0
% 223.79/32.87  % Contextual simplify-reflections      : 44
% 223.79/32.87  % Paramodulations                      : 314441
% 223.79/32.87  % Factorizations                       : 46
% 223.79/32.87  % NegExts                              : 2
% 223.79/32.87  % Equation resolutions                 : 338
% 223.79/32.87  % Disequality decompositions           : 0
% 223.79/32.87  % Total rewrite steps                  : 49219
% 223.79/32.87  % ...of those cached                   : 46371
% 223.79/32.87  % Propositional unsat checks           : 0
% 223.79/32.87  %    Propositional check models        : 0
% 223.79/32.87  %    Propositional check unsatisfiable : 0
% 223.79/32.87  %    Propositional clauses             : 0
% 223.79/32.87  %    Propositional clauses after purity: 0
% 223.79/32.87  %    Propositional unsat core size     : 0
% 223.79/32.87  %    Propositional preprocessing time  : 0.000
% 223.79/32.87  %    Propositional encoding time       : 0.000
% 223.79/32.87  %    Propositional solver time         : 0.000
% 223.79/32.87  %    Success case prop preproc time    : 0.000
% 223.79/32.87  %    Success case prop encoding time   : 0.000
% 223.79/32.87  %    Success case prop solver time     : 0.000
% 223.79/32.87  % Current number of processed clauses  : 4119
% 223.79/32.87  %    Positive orientable unit clauses  : 685
% 223.79/32.87  %    Positive unorientable unit clauses: 0
% 223.79/32.87  %    Negative unit clauses             : 187
% 223.79/32.87  %    Non-unit-clauses                  : 3247
% 223.79/32.87  % Current number of unprocessed clauses: 267514
% 223.79/32.87  % ...number of literals in the above   : 803426
% 223.79/32.87  % Current number of archived formulas  : 0
% 223.79/32.87  % Current number of archived clauses   : 808
% 223.79/32.87  % Clause-clause subsumption calls (NU) : 530942
% 223.79/32.87  % Rec. Clause-clause subsumption calls : 369046
% 223.79/32.87  % Non-unit clause-clause subsumptions  : 9808
% 223.79/32.87  % Unit Clause-clause subsumption calls : 93794
% 223.79/32.87  % Rewrite failures with RHS unbound    : 0
% 223.79/32.87  % BW rewrite match attempts            : 343
% 223.79/32.87  % BW rewrite match successes           : 87
% 223.79/32.87  % Condensation attempts                : 0
% 223.79/32.87  % Condensation successes               : 0
% 223.79/32.87  % Termbank termtop insertions          : 8192265
% 223.79/32.87  % Search garbage collected termcells   : 26188
% 223.79/32.87  
% 223.79/32.87  % -------------------------------------------------
% 223.79/32.87  % User time                : 31.441 s
% 223.79/32.87  % System time              : 1.150 s
% 223.79/32.87  % Total time               : 32.591 s
% 223.79/32.87  % Maximum resident set size: 9872 pages
% 223.79/32.87  
% 223.79/32.87  % -------------------------------------------------
% 223.79/32.87  % User time                : 31.521 s
% 223.79/32.87  % System time              : 1.194 s
% 223.79/32.87  % Total time               : 32.714 s
% 223.79/32.87  % Maximum resident set size: 5120 pages
% 223.79/32.87  % E exiting
%------------------------------------------------------------------------------