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

%------------------------------------------------------------------------------
% File     : E-SAT---3.5.1
% Problem  : SEU767^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:27:43 AM UTC 2026

% Result   : Theorem 2.52s 0.76s
% Output   : CNFRefutation 2.52s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU767^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18  % Computer : n009.cluster.edu
% 0.09/0.18  % Model    : x86_64 x86_64
% 0.09/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18  % Memory   : 8046.5625MB
% 0.09/0.18  % OS       : Linux 6.8.0-71-generic
% 0.09/0.18  % CPULimit : 300
% 0.09/0.18  % WCLimit  : 300
% 0.09/0.18  % DateTime : Tue Sep 29 14:23:45 UTC 2026
% 0.09/0.18  % CPUTime  : 
% 0.09/0.18  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23  Running higher-order theorem proving
% 0.23/0.29  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.XjZ0hWvsML/E---3.1_4073238.p
% 2.52/0.76  % Version: 3.5.1-ho
% 2.52/0.76  % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.52/0.76  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.52/0.76  % Starting ehoh_best5 with 300s (1) cores
% 2.52/0.76  % Starting almost_fo_3_lam with 300s (1) cores
% 2.52/0.76  % Starting new_bool_5 with 300s (1) cores
% 2.52/0.76  % Starting pre_casc_3 with 300s (1) cores
% 2.52/0.76  % Starting ho_unfolding_8 with 300s (1) cores
% 2.52/0.76  % Starting new_ho_10_cnf2 with 300s (1) cores
% 2.52/0.76  % Starting new_bool_3 with 300s (1) cores
% 2.52/0.76  % Starting new_ho_5 with 300s (1) cores
% 2.52/0.76  % pre_casc_3 with pid 4073254 completed with status 9
% 2.52/0.76  % new_ho_5 with pid 4073258 completed with status 9
% 2.52/0.76  % almost_fo_3_lam with pid 4073252 completed with status 0
% 2.52/0.76  % Result found by almost_fo_3_lam
% 2.52/0.76  % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.52/0.76  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.52/0.76  % Starting ehoh_best5 with 300s (1) cores
% 2.52/0.76  % Starting almost_fo_3_lam with 300s (1) cores
% 2.52/0.76  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.52/0.76  % No SInE strategy applied
% 2.52/0.76  % Search class: HGHSM-FSLM32-MHFMMSBN
% 2.52/0.76  % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 2.52/0.76  % Starting SubtermCWHack with 28s (1) cores
% 2.52/0.76  % SubtermCWHack with pid 4073291 completed with status 0
% 2.52/0.76  % Result found by SubtermCWHack
% 2.52/0.76  % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.52/0.76  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.52/0.76  % Starting ehoh_best5 with 300s (1) cores
% 2.52/0.76  % Starting almost_fo_3_lam with 300s (1) cores
% 2.52/0.76  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.52/0.76  % No SInE strategy applied
% 2.52/0.76  % Search class: HGHSM-FSLM32-MHFMMSBN
% 2.52/0.76  % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 2.52/0.76  % Starting SubtermCWHack with 28s (1) cores
% 2.52/0.76  % Preprocessing time       : 0.005 s
% 2.52/0.76  
% 2.52/0.76  % Proof found!
% 2.52/0.76  % SZS status Theorem
% 2.52/0.76  % SZS output start CNFRefutation
% 2.52/0.76  thf(decl_23, type, in: $i > $i > $o).
% 2.52/0.76  thf(decl_24, type, exu: ($i > $o) > $o).
% 2.52/0.76  thf(decl_25, type, setextAx: $o).
% 2.52/0.76  thf(decl_26, type, emptyset: $i).
% 2.52/0.76  thf(decl_27, type, emptysetAx: $o).
% 2.52/0.76  thf(decl_28, type, setadjoin: $i > $i > $i).
% 2.52/0.76  thf(decl_29, type, setadjoinAx: $o).
% 2.52/0.76  thf(decl_30, type, powerset: $i > $i).
% 2.52/0.76  thf(decl_31, type, powersetAx: $o).
% 2.52/0.76  thf(decl_32, type, setunion: $i > $i).
% 2.52/0.76  thf(decl_33, type, setunionAx: $o).
% 2.52/0.76  thf(decl_34, type, omega: $i).
% 2.52/0.76  thf(decl_35, type, omega0Ax: $o).
% 2.52/0.76  thf(decl_36, type, omegaSAx: $o).
% 2.52/0.76  thf(decl_37, type, omegaIndAx: $o).
% 2.52/0.76  thf(decl_38, type, replAx: $o).
% 2.52/0.76  thf(decl_39, type, foundationAx: $o).
% 2.52/0.76  thf(decl_40, type, wellorderingAx: $o).
% 2.52/0.76  thf(decl_41, type, descr: ($i > $o) > $i).
% 2.52/0.76  thf(decl_42, type, descrp: $o).
% 2.52/0.76  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_44, type, dsetconstrI: $o).
% 2.52/0.76  thf(decl_45, type, dsetconstrEL: $o).
% 2.52/0.76  thf(decl_46, type, dsetconstrER: $o).
% 2.52/0.76  thf(decl_47, type, exuE1: $o).
% 2.52/0.76  thf(decl_48, type, prop2set: $o > $i).
% 2.52/0.76  thf(decl_49, type, prop2setE: $o).
% 2.52/0.76  thf(decl_50, type, emptysetE: $o).
% 2.52/0.76  thf(decl_51, type, emptysetimpfalse: $o).
% 2.52/0.76  thf(decl_52, type, notinemptyset: $o).
% 2.52/0.76  thf(decl_53, type, exuE3e: $o).
% 2.52/0.76  thf(decl_54, type, setext: $o).
% 2.52/0.76  thf(decl_55, type, emptyI: $o).
% 2.52/0.76  thf(decl_56, type, noeltsimpempty: $o).
% 2.52/0.76  thf(decl_57, type, setbeta: $o).
% 2.52/0.76  thf(decl_58, type, nonempty: $i > $o).
% 2.52/0.76  thf(decl_59, type, nonemptyE1: $o).
% 2.52/0.76  thf(decl_60, type, nonemptyI: $o).
% 2.52/0.76  thf(decl_61, type, nonemptyI1: $o).
% 2.52/0.76  thf(decl_62, type, setadjoinIL: $o).
% 2.52/0.76  thf(decl_63, type, emptyinunitempty: $o).
% 2.52/0.76  thf(decl_64, type, setadjoinIR: $o).
% 2.52/0.76  thf(decl_65, type, setadjoinE: $o).
% 2.52/0.76  thf(decl_66, type, setadjoinOr: $o).
% 2.52/0.76  thf(decl_67, type, setoftrueEq: $o).
% 2.52/0.76  thf(decl_68, type, powersetI: $o).
% 2.52/0.76  thf(decl_69, type, emptyinPowerset: $o).
% 2.52/0.76  thf(decl_70, type, emptyInPowerset: $o).
% 2.52/0.76  thf(decl_71, type, powersetE: $o).
% 2.52/0.76  thf(decl_72, type, setunionI: $o).
% 2.52/0.76  thf(decl_73, type, setunionE: $o).
% 2.52/0.76  thf(decl_74, type, subPowSU: $o).
% 2.52/0.76  thf(decl_75, type, exuE2: $o).
% 2.52/0.76  thf(decl_76, type, nonemptyImpWitness: $o).
% 2.52/0.76  thf(decl_77, type, uniqinunit: $o).
% 2.52/0.76  thf(decl_78, type, notinsingleton: $o).
% 2.52/0.76  thf(decl_79, type, eqinunit: $o).
% 2.52/0.76  thf(decl_80, type, singletonsswitch: $o).
% 2.52/0.76  thf(decl_81, type, upairsetE: $o).
% 2.52/0.76  thf(decl_82, type, upairsetIL: $o).
% 2.52/0.76  thf(decl_83, type, upairsetIR: $o).
% 2.52/0.76  thf(decl_84, type, emptyE1: $o).
% 2.52/0.76  thf(decl_85, type, vacuousDall: $o).
% 2.52/0.76  thf(decl_86, type, quantDeMorgan1: $o).
% 2.52/0.76  thf(decl_87, type, quantDeMorgan2: $o).
% 2.52/0.76  thf(decl_88, type, quantDeMorgan3: $o).
% 2.52/0.76  thf(decl_89, type, quantDeMorgan4: $o).
% 2.52/0.76  thf(decl_90, type, prop2setI: $o).
% 2.52/0.76  thf(decl_91, type, set2prop: $i > $o).
% 2.52/0.76  thf(decl_92, type, prop2set2propI: $o).
% 2.52/0.76  thf(decl_93, type, notdexE: $o).
% 2.52/0.76  thf(decl_94, type, notdallE: $o).
% 2.52/0.76  thf(decl_95, type, exuI1: $o).
% 2.52/0.76  thf(decl_96, type, exuI3: $o).
% 2.52/0.76  thf(decl_97, type, exuI2: $o).
% 2.52/0.76  thf(decl_98, type, inCongP: $o).
% 2.52/0.76  thf(decl_99, type, in__Cong: $o).
% 2.52/0.76  thf(decl_100, type, exuE3u: $o).
% 2.52/0.76  thf(decl_101, type, exu__Cong: $o).
% 2.52/0.76  thf(decl_102, type, emptyset__Cong: $o).
% 2.52/0.76  thf(decl_103, type, setadjoin__Cong: $o).
% 2.52/0.76  thf(decl_104, type, powerset__Cong: $o).
% 2.52/0.76  thf(decl_105, type, setunion__Cong: $o).
% 2.52/0.76  thf(decl_106, type, omega__Cong: $o).
% 2.52/0.76  thf(decl_107, type, exuEu: $o).
% 2.52/0.76  thf(decl_108, type, descr__Cong: $o).
% 2.52/0.76  thf(decl_109, type, dsetconstr__Cong: $o).
% 2.52/0.76  thf(decl_110, type, subset: $i > $i > $o).
% 2.52/0.76  thf(decl_113, type, subsetI1: $o).
% 2.52/0.76  thf(decl_114, type, eqimpsubset2: $o).
% 2.52/0.76  thf(decl_115, type, eqimpsubset1: $o).
% 2.52/0.76  thf(decl_116, type, subsetI2: $o).
% 2.52/0.76  thf(decl_117, type, emptysetsubset: $o).
% 2.52/0.76  thf(decl_118, type, subsetE: $o).
% 2.52/0.76  thf(decl_119, type, subsetE2: $o).
% 2.52/0.76  thf(decl_120, type, notsubsetI: $o).
% 2.52/0.76  thf(decl_121, type, notequalI1: $o).
% 2.52/0.76  thf(decl_122, type, notequalI2: $o).
% 2.52/0.76  thf(decl_123, type, subsetRefl: $o).
% 2.52/0.76  thf(decl_124, type, subsetTrans: $o).
% 2.52/0.76  thf(decl_125, type, setadjoinSub: $o).
% 2.52/0.76  thf(decl_126, type, setadjoinSub2: $o).
% 2.52/0.76  thf(decl_127, type, subset2powerset: $o).
% 2.52/0.76  thf(decl_128, type, setextsub: $o).
% 2.52/0.76  thf(decl_129, type, subsetemptysetimpeq: $o).
% 2.52/0.76  thf(decl_130, type, powersetI1: $o).
% 2.52/0.76  thf(decl_131, type, powersetE1: $o).
% 2.52/0.76  thf(decl_132, type, inPowerset: $o).
% 2.52/0.76  thf(decl_133, type, powersetsubset: $o).
% 2.52/0.76  thf(decl_134, type, sepInPowerset: $o).
% 2.52/0.76  thf(decl_135, type, sepSubset: $o).
% 2.52/0.76  thf(decl_136, type, binunion: $i > $i > $i).
% 2.52/0.76  thf(decl_137, type, binunionIL: $o).
% 2.52/0.76  thf(decl_138, type, upairset2IR: $o).
% 2.52/0.76  thf(decl_139, type, binunionIR: $o).
% 2.52/0.76  thf(decl_140, type, binunionEcases: $o).
% 2.52/0.76  thf(decl_141, type, binunionE: $o).
% 2.52/0.76  thf(decl_142, type, binunionLsub: $o).
% 2.52/0.76  thf(decl_143, type, binunionRsub: $o).
% 2.52/0.76  thf(decl_144, type, binintersect: $i > $i > $i).
% 2.52/0.76  thf(decl_145, type, binintersectI: $o).
% 2.52/0.76  thf(decl_146, type, binintersectSubset5: $o).
% 2.52/0.76  thf(decl_147, type, binintersectEL: $o).
% 2.52/0.76  thf(decl_148, type, binintersectLsub: $o).
% 2.52/0.76  thf(decl_149, type, binintersectSubset2: $o).
% 2.52/0.76  thf(decl_150, type, binintersectSubset3: $o).
% 2.52/0.76  thf(decl_151, type, binintersectER: $o).
% 2.52/0.76  thf(decl_152, type, disjointsetsI1: $o).
% 2.52/0.76  thf(decl_153, type, binintersectRsub: $o).
% 2.52/0.76  thf(decl_154, type, binintersectSubset4: $o).
% 2.52/0.76  thf(decl_155, type, binintersectSubset1: $o).
% 2.52/0.76  thf(decl_156, type, bs114d: $o).
% 2.52/0.76  thf(decl_158, type, setminus: $i > $i > $i).
% 2.52/0.76  thf(decl_159, type, setminusI: $o).
% 2.52/0.76  thf(decl_160, type, setminusEL: $o).
% 2.52/0.76  thf(decl_161, type, setminusER: $o).
% 2.52/0.76  thf(decl_162, type, setminusSubset2: $o).
% 2.52/0.76  thf(decl_163, type, setminusERneg: $o).
% 2.52/0.76  thf(decl_164, type, setminusELneg: $o).
% 2.52/0.76  thf(decl_165, type, setminusILneg: $o).
% 2.52/0.76  thf(decl_166, type, setminusIRneg: $o).
% 2.52/0.76  thf(decl_167, type, setminusLsub: $o).
% 2.52/0.76  thf(decl_168, type, setminusSubset1: $o).
% 2.52/0.76  thf(decl_169, type, symdiff: $i > $i > $i).
% 2.52/0.76  thf(decl_170, type, symdiffE: $o).
% 2.52/0.76  thf(decl_171, type, symdiffI1: $o).
% 2.52/0.76  thf(decl_172, type, symdiffI2: $o).
% 2.52/0.76  thf(decl_173, type, symdiffIneg1: $o).
% 2.52/0.76  thf(decl_174, type, symdiffIneg2: $o).
% 2.52/0.76  thf(decl_175, type, iskpair: $i > $o).
% 2.52/0.76  thf(decl_176, type, secondinupair: $o).
% 2.52/0.76  thf(decl_177, type, setukpairIL: $o).
% 2.52/0.76  thf(decl_178, type, setukpairIR: $o).
% 2.52/0.76  thf(decl_179, type, kpairiskpair: $o).
% 2.52/0.76  thf(decl_180, type, kpair: $i > $i > $i).
% 2.52/0.76  thf(decl_181, type, kpairp: $o).
% 2.52/0.76  thf(decl_182, type, cartprod: $i > $i > $i).
% 2.52/0.76  thf(decl_183, type, singletonsubset: $o).
% 2.52/0.76  thf(decl_184, type, singletoninpowerset: $o).
% 2.52/0.76  thf(decl_185, type, singletoninpowunion: $o).
% 2.52/0.76  thf(decl_186, type, upairset2E: $o).
% 2.52/0.76  thf(decl_187, type, upairsubunion: $o).
% 2.52/0.76  thf(decl_188, type, upairinpowunion: $o).
% 2.52/0.76  thf(decl_189, type, ubforcartprodlem1: $o).
% 2.52/0.76  thf(decl_190, type, ubforcartprodlem2: $o).
% 2.52/0.76  thf(decl_191, type, ubforcartprodlem3: $o).
% 2.52/0.76  thf(decl_192, type, cartprodpairin: $o).
% 2.52/0.76  thf(decl_193, type, cartprodmempair1: $o).
% 2.52/0.76  thf(decl_194, type, cartprodmempair: $o).
% 2.52/0.76  thf(decl_195, type, setunionE2: $o).
% 2.52/0.76  thf(decl_196, type, setunionsingleton1: $o).
% 2.52/0.76  thf(decl_197, type, setunionsingleton2: $o).
% 2.52/0.76  thf(decl_198, type, setunionsingleton: $o).
% 2.52/0.76  thf(decl_199, type, singleton: $i > $o).
% 2.52/0.76  thf(decl_200, type, singletonprop: $o).
% 2.52/0.76  thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 2.52/0.76  thf(decl_202, type, ex1E1: $o).
% 2.52/0.76  thf(decl_203, type, ex1I: $o).
% 2.52/0.76  thf(decl_204, type, ex1I2: $o).
% 2.52/0.76  thf(decl_205, type, singletonsuniq: $o).
% 2.52/0.76  thf(decl_210, type, setukpairinjL1: $o).
% 2.52/0.76  thf(decl_211, type, kfstsingleton: $o).
% 2.52/0.76  thf(decl_212, type, theprop: $o).
% 2.52/0.76  thf(decl_213, type, kfst: $i > $i).
% 2.52/0.76  thf(decl_214, type, kfstpairEq: $o).
% 2.52/0.76  thf(decl_215, type, cartprodfstin: $o).
% 2.52/0.76  thf(decl_216, type, setukpairinjL2: $o).
% 2.52/0.76  thf(decl_217, type, setukpairinjL: $o).
% 2.52/0.76  thf(decl_218, type, setukpairinjR11: $o).
% 2.52/0.76  thf(decl_219, type, setukpairinjR12: $o).
% 2.52/0.76  thf(decl_220, type, setukpairinjR1: $o).
% 2.52/0.76  thf(decl_221, type, upairequniteq: $o).
% 2.52/0.76  thf(decl_222, type, setukpairinjR2: $o).
% 2.52/0.76  thf(decl_223, type, setukpairinjR: $o).
% 2.52/0.76  thf(decl_224, type, ksndsingleton: $o).
% 2.52/0.76  thf(decl_225, type, ksnd: $i > $i).
% 2.52/0.76  thf(decl_226, type, ksndpairEq: $o).
% 2.52/0.76  thf(decl_227, type, kpairsurjEq: $o).
% 2.52/0.76  thf(decl_228, type, cartprodsndin: $o).
% 2.52/0.76  thf(decl_229, type, cartprodpairmemEL: $o).
% 2.52/0.76  thf(decl_230, type, cartprodpairmemER: $o).
% 2.52/0.76  thf(decl_231, type, cartprodmempaircEq: $o).
% 2.52/0.76  thf(decl_232, type, cartprodfstpairEq: $o).
% 2.52/0.76  thf(decl_233, type, cartprodsndpairEq: $o).
% 2.52/0.76  thf(decl_234, type, cartprodpairsurjEq: $o).
% 2.52/0.76  thf(decl_235, type, breln: $i > $i > $i > $o).
% 2.52/0.76  thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 2.52/0.76  thf(decl_237, type, dpsetconstrI: $o).
% 2.52/0.76  thf(decl_238, type, dpsetconstrSub: $o).
% 2.52/0.76  thf(decl_239, type, setOfPairsIsBReln: $o).
% 2.52/0.76  thf(decl_240, type, dpsetconstrERa: $o).
% 2.52/0.76  thf(decl_241, type, dpsetconstrEL1: $o).
% 2.52/0.76  thf(decl_242, type, dpsetconstrEL2: $o).
% 2.52/0.76  thf(decl_243, type, dpsetconstrER: $o).
% 2.52/0.76  thf(decl_244, type, func: $i > $i > $i > $o).
% 2.52/0.76  thf(decl_245, type, funcSet: $i > $i > $i).
% 2.52/0.76  thf(decl_246, type, funcImageSingleton: $o).
% 2.52/0.76  thf(decl_247, type, apProp: $o).
% 2.52/0.76  thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 2.52/0.76  thf(decl_249, type, app: $o).
% 2.52/0.76  thf(decl_250, type, infuncsetfunc: $o).
% 2.52/0.76  thf(decl_251, type, ap2p: $o).
% 2.52/0.76  thf(decl_252, type, funcinfuncset: $o).
% 2.52/0.76  thf(decl_253, type, lamProp: $o).
% 2.52/0.76  thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 2.52/0.76  thf(decl_255, type, lamp: $o).
% 2.52/0.76  thf(decl_256, type, lam2p: $o).
% 2.52/0.76  thf(decl_257, type, brelnall1: $o).
% 2.52/0.76  thf(decl_258, type, brelnall2: $o).
% 2.52/0.76  thf(decl_259, type, ex1E2: $o).
% 2.52/0.76  thf(decl_260, type, funcGraphProp1: $o).
% 2.52/0.76  thf(decl_261, type, funcGraphProp3: $o).
% 2.52/0.76  thf(decl_262, type, funcGraphProp2: $o).
% 2.52/0.76  thf(decl_263, type, funcextLem: $o).
% 2.52/0.76  thf(decl_264, type, funcGraphProp4: $o).
% 2.52/0.76  thf(decl_265, type, subbreln: $o).
% 2.52/0.76  thf(decl_266, type, eqbreln: $o).
% 2.52/0.76  thf(decl_267, type, funcext: $o).
% 2.52/0.76  thf(decl_268, type, funcext2: $o).
% 2.52/0.76  thf(decl_269, type, ap2apEq1: $o).
% 2.52/0.76  thf(decl_270, type, ap2apEq2: $o).
% 2.52/0.76  thf(decl_271, type, beta1: $o).
% 2.52/0.76  thf(decl_272, type, eta1: $o).
% 2.52/0.76  thf(decl_273, type, lam2lamEq: $o).
% 2.52/0.76  thf(decl_274, type, beta2: $o).
% 2.52/0.76  thf(decl_275, type, eta2: $o).
% 2.52/0.76  thf(decl_276, type, iffalseProp1: $o).
% 2.52/0.76  thf(decl_277, type, iffalseProp2: $o).
% 2.52/0.76  thf(decl_278, type, iftrueProp1: $o).
% 2.52/0.76  thf(decl_279, type, iftrueProp2: $o).
% 2.52/0.76  thf(decl_280, type, ifSingleton: $o).
% 2.52/0.76  thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 2.52/0.76  thf(decl_282, type, ifp: $o).
% 2.52/0.76  thf(decl_283, type, theeq: $o).
% 2.52/0.76  thf(decl_284, type, iftrue: $o).
% 2.52/0.76  thf(decl_285, type, iffalse: $o).
% 2.52/0.76  thf(decl_286, type, iftrueorfalse: $o).
% 2.52/0.76  thf(decl_287, type, binintersectT_lem: $o).
% 2.52/0.76  thf(decl_288, type, binunionT_lem: $o).
% 2.52/0.76  thf(decl_289, type, powersetT_lem: $o).
% 2.52/0.76  thf(decl_290, type, setminusT_lem: $o).
% 2.52/0.76  thf(decl_291, type, complementT_lem: $o).
% 2.52/0.76  thf(decl_292, type, setextT: $o).
% 2.52/0.76  thf(decl_293, type, subsetTI: $o).
% 2.52/0.76  thf(decl_294, type, powersetTI1: $o).
% 2.52/0.76  thf(decl_295, type, powersetTE1: $o).
% 2.52/0.76  thf(decl_296, type, complementTI1: $o).
% 2.52/0.76  thf(decl_297, type, complementTE1: $o).
% 2.52/0.76  thf(decl_298, type, binintersectTELcontra: $o).
% 2.52/0.76  thf(decl_299, type, binintersectTERcontra: $o).
% 2.52/0.76  thf(decl_300, type, contrasubsetT: $o).
% 2.52/0.76  thf(decl_301, type, contrasubsetT1: $o).
% 2.52/0.76  thf(decl_302, type, contrasubsetT2: $o).
% 2.52/0.76  thf(decl_303, type, contrasubsetT3: $o).
% 2.52/0.76  thf(decl_304, type, doubleComplementI1: $o).
% 2.52/0.76  thf(decl_305, type, doubleComplementE1: $o).
% 2.52/0.76  thf(decl_306, type, doubleComplementSub1: $o).
% 2.52/0.76  thf(decl_307, type, doubleComplementSub2: $o).
% 2.52/0.76  thf(decl_308, type, doubleComplementEq: $o).
% 2.52/0.76  thf(decl_309, type, complementTnotintersectT: $o).
% 2.52/0.76  thf(decl_310, type, complementImpComplementIntersect: $o).
% 2.52/0.76  thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 2.52/0.76  thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 2.52/0.76  thf(decl_313, type, contraSubsetComplement: $o).
% 2.52/0.76  thf(decl_314, type, complementTcontraSubset: $o).
% 2.52/0.76  thf(decl_315, type, binunionTILcontra: $o).
% 2.52/0.76  thf(decl_316, type, binunionTIRcontra: $o).
% 2.52/0.76  thf(decl_317, type, inIntersectImpInUnion: $o).
% 2.52/0.76  thf(decl_318, type, inIntersectImpInUnion2: $o).
% 2.52/0.76  thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 2.52/0.76  thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 2.52/0.76  thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 2.52/0.76  thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 2.52/0.76  thf(decl_323, type, binunionTE: $o).
% 2.52/0.76  thf(decl_324, type, binunionTEcontra: $o).
% 2.52/0.76  thf(decl_325, type, demorgan2a1: $o).
% 2.52/0.76  thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 2.52/0.76  thf(decl_327, type, demorgan2a2: $o).
% 2.52/0.76  thf(decl_328, type, demorgan1a: $o).
% 2.52/0.76  thf(decl_329, type, demorgan1b: $o).
% 2.52/0.76  thf(decl_330, type, demorgan1: $o).
% 2.52/0.76  thf(decl_331, type, demorgan2a: $o).
% 2.52/0.76  thf(decl_332, type, demorgan2b2: $o).
% 2.52/0.76  thf(decl_333, type, demorgan2b: $o).
% 2.52/0.76  thf(decl_334, type, demorgan2: $o).
% 2.52/0.76  thf(decl_335, type, woz13rule0: $o).
% 2.52/0.76  thf(decl_336, type, woz13rule1: $o).
% 2.52/0.76  thf(decl_337, type, woz13rule2: $o).
% 2.52/0.76  thf(decl_338, type, woz13rule3: $o).
% 2.52/0.76  thf(decl_339, type, woz13rule4: $o).
% 2.52/0.76  thf(decl_340, type, woz1_1: $o).
% 2.52/0.76  thf(decl_341, type, woz1_2: $o).
% 2.52/0.76  thf(decl_342, type, woz1_3: $o).
% 2.52/0.76  thf(decl_343, type, woz1_4: $o).
% 2.52/0.76  thf(decl_344, type, epred1_0: $o).
% 2.52/0.76  thf(decl_345, type, esk1_2: $i > $i > $i).
% 2.52/0.76  thf(decl_346, type, esk2_2: $i > $i > $i).
% 2.52/0.76  thf(decl_347, type, esk3_2: $i > $i > $i).
% 2.52/0.76  thf(decl_348, type, esk4_1: $i > $i).
% 2.52/0.76  thf(decl_349, type, esk5_2: ($i > $i > $o) > $i > $i).
% 2.52/0.76  thf(decl_350, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 2.52/0.76  thf(decl_351, type, esk7_2: ($i > $i > $o) > $i > $i).
% 2.52/0.76  thf(decl_352, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 2.52/0.76  thf(decl_353, type, esk9_1: $i > $i).
% 2.52/0.76  thf(decl_354, type, esk10_2: ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_355, type, esk11_2: ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_356, type, esk12_1: ($i > $o) > $i).
% 2.52/0.76  thf(decl_357, type, esk13_2: ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_358, type, esk14_1: ($i > $o) > $i).
% 2.52/0.76  thf(decl_359, type, esk15_2: $i > $i > $i).
% 2.52/0.76  thf(decl_360, type, esk16_2: $i > $i > $i).
% 2.52/0.76  thf(decl_361, type, esk17_1: $i > $i).
% 2.52/0.76  thf(decl_362, type, esk18_1: $i > $i).
% 2.52/0.76  thf(decl_363, type, esk19_1: $i > $i).
% 2.52/0.76  thf(decl_364, type, esk20_2: $i > $i > $i).
% 2.52/0.76  thf(decl_365, type, esk21_3: $i > $i > $o > $i).
% 2.52/0.76  thf(decl_366, type, esk22_2: ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_367, type, esk23_1: ($i > $o) > $i).
% 2.52/0.76  thf(decl_368, type, esk24_1: $i > $i).
% 2.52/0.76  thf(decl_369, type, esk25_2: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_370, type, esk26_2: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_371, type, esk27_2: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_372, type, esk28_2: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_373, type, esk29_2: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_374, type, esk30_2: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_375, type, esk31_2: ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_376, type, esk32_1: ($i > $o) > $i).
% 2.52/0.76  thf(decl_377, type, esk33_1: ($i > $o) > $i).
% 2.52/0.76  thf(decl_378, type, esk34_1: ($i > $o) > $i).
% 2.52/0.76  thf(decl_379, type, esk35_1: ($i > $o) > $i).
% 2.52/0.76  thf(decl_380, type, esk36_2: ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_381, type, esk37_1: ($i > $o) > $i).
% 2.52/0.76  thf(decl_382, type, esk38_2: ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_383, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 2.52/0.76  thf(decl_384, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 2.52/0.76  thf(decl_385, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_386, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 2.52/0.76  thf(decl_387, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_388, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 2.52/0.76  thf(decl_389, type, esk45_2: ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_390, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 2.52/0.76  thf(decl_391, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 2.52/0.76  thf(decl_392, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_393, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_394, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.52/0.76  thf(decl_395, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.52/0.76  thf(decl_396, type, esk52_2: $i > $i > $i).
% 2.52/0.76  thf(decl_397, type, esk53_2: $i > $i > $i).
% 2.52/0.76  thf(decl_398, type, esk54_2: $i > $i > $i).
% 2.52/0.76  thf(decl_399, type, esk55_3: $i > $i > $i > $i).
% 2.52/0.76  thf(decl_400, type, esk56_3: $i > $i > $i > $i).
% 2.52/0.76  thf(decl_401, type, esk57_2: $i > $i > $i).
% 2.52/0.76  thf(decl_402, type, esk58_2: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_403, type, esk59_2: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_404, type, esk60_2: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_405, type, esk61_3: $i > ($i > $o) > $i > $i).
% 2.52/0.76  thf(decl_406, type, esk62_2: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_407, type, esk63_2: $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_408, type, esk64_3: $i > $i > ($i > $i) > $i).
% 2.52/0.76  thf(decl_409, type, esk65_3: $i > $i > ($i > $i) > $i).
% 2.52/0.76  thf(decl_410, type, esk66_3: $i > $i > ($i > $i) > $i).
% 2.52/0.76  thf(decl_411, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_412, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_413, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_414, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
% 2.52/0.76  thf(decl_415, type, esk71_4: $i > $i > $i > $i > $i).
% 2.52/0.76  thf(decl_416, type, esk72_4: $i > $i > $i > $i > $i).
% 2.52/0.76  thf(decl_417, type, esk73_4: $i > $i > $i > $i > $i).
% 2.52/0.76  thf(decl_418, type, esk74_4: $i > $i > $i > $i > $i).
% 2.52/0.76  thf(decl_419, type, esk75_4: $i > $i > $i > $i > $i).
% 2.52/0.76  thf(decl_420, type, esk76_4: $i > $i > $i > $i > $i).
% 2.52/0.76  thf(decl_421, type, esk77_4: $i > $i > $i > $i > $i).
% 2.52/0.76  thf(decl_422, type, esk78_4: $i > $i > $i > $i > $i).
% 2.52/0.76  thf(decl_423, type, esk79_4: $i > $i > $i > $i > $i).
% 2.52/0.76  thf(decl_424, type, esk80_3: $i > $i > ($i > $i) > $i).
% 2.52/0.76  thf(decl_425, type, esk81_3: $i > $i > ($i > $i) > $i).
% 2.52/0.76  thf(decl_426, type, esk82_3: $i > $i > ($i > $i) > $i).
% 2.52/0.76  thf(decl_427, type, esk83_3: $i > $i > $i > $i).
% 2.52/0.76  thf(decl_428, type, esk84_3: $i > $i > $i > $i).
% 2.52/0.76  thf(decl_429, type, esk85_3: $i > $i > $i > $i).
% 2.52/0.76  thf(decl_430, type, esk86_3: $i > $i > $i > $i).
% 2.52/0.76  thf(decl_431, type, esk87_0: $i).
% 2.52/0.76  thf(decl_432, type, esk88_0: $i).
% 2.52/0.76  thf(decl_433, type, esk89_0: $i).
% 2.52/0.76  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', replAx)).
% 2.52/0.76  thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', exu)).
% 2.52/0.76  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', descrp)).
% 2.52/0.76  thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', exuE1)).
% 2.52/0.76  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', exuE3e)).
% 2.52/0.76  thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', nonempty)).
% 2.52/0.76  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', nonemptyI)).
% 2.52/0.76  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', exuE2)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', exuI1)).
% 2.52/0.76  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', exuI3)).
% 2.52/0.76  thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', exuI2)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', exuE3u)).
% 2.52/0.76  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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', exu__Cong)).
% 2.52/0.76  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', exuEu)).
% 2.52/0.76  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', descr__Cong)).
% 2.52/0.76  thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ex1E1)).
% 2.52/0.76  thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ex1)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', ex1I)).
% 2.52/0.76  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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ex1I2)).
% 2.52/0.76  thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setOfPairsIsBReln)).
% 2.52/0.76  thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', breln)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', ex1E2)).
% 2.52/0.76  thf(woz1_5, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', woz1_5)).
% 2.52/0.76  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', dsetconstrI)).
% 2.52/0.76  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', dsetconstrEL)).
% 2.52/0.76  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', dsetconstrER)).
% 2.52/0.76  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setbeta)).
% 2.52/0.76  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', nonemptyE1)).
% 2.52/0.76  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', nonemptyI1)).
% 2.52/0.76  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setoftrueEq)).
% 2.52/0.76  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', nonemptyImpWitness)).
% 2.52/0.76  thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', emptyE1)).
% 2.52/0.76  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', dsetconstr__Cong)).
% 2.52/0.76  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', sepInPowerset)).
% 2.52/0.76  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', sepSubset)).
% 2.52/0.76  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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', singletonprop)).
% 2.52/0.76  thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', kfstsingleton)).
% 2.52/0.76  thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ksndsingleton)).
% 2.52/0.76  thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', dpsetconstrI)).
% 2.52/0.76  thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', dpsetconstrSub)).
% 2.52/0.76  thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', dpsetconstrERa)).
% 2.52/0.76  thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', dpsetconstrEL1)).
% 2.52/0.76  thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', dpsetconstrEL2)).
% 2.52/0.76  thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', dpsetconstrER)).
% 2.52/0.76  thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', funcImageSingleton)).
% 2.52/0.76  thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', apProp)).
% 2.52/0.76  thf(lamProp, axiom, ((lamProp)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', lamProp)).
% 2.52/0.76  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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', lamp)).
% 2.52/0.76  thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', lam2p)).
% 2.52/0.76  thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', brelnall1)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', brelnall2)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', subbreln)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', eqbreln)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', beta1)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', eta1)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', lam2lamEq)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', beta2)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', eta2)).
% 2.52/0.76  thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', iffalseProp1)).
% 2.52/0.76  thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', iffalseProp2)).
% 2.52/0.76  thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', iftrueProp1)).
% 2.52/0.76  thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', iftrueProp2)).
% 2.52/0.76  thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ifSingleton)).
% 2.52/0.76  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setextAx)).
% 2.52/0.76  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', emptysetAx)).
% 2.52/0.76  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setadjoinAx)).
% 2.52/0.76  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', powersetAx)).
% 2.52/0.76  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setunionAx)).
% 2.52/0.76  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', omega0Ax)).
% 2.52/0.76  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', omegaSAx)).
% 2.52/0.76  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', omegaIndAx)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', foundationAx)).
% 2.52/0.76  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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', wellorderingAx)).
% 2.52/0.76  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', prop2setE)).
% 2.52/0.76  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', emptysetE)).
% 2.52/0.76  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', emptysetimpfalse)).
% 2.52/0.76  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', notinemptyset)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', setext)).
% 2.52/0.76  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', emptyI)).
% 2.52/0.76  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', noeltsimpempty)).
% 2.52/0.76  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setadjoinIL)).
% 2.52/0.76  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', emptyinunitempty)).
% 2.52/0.76  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setadjoinIR)).
% 2.52/0.76  thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setadjoinE)).
% 2.52/0.76  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setadjoinOr)).
% 2.52/0.76  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', powersetI)).
% 2.52/0.76  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', emptyinPowerset)).
% 2.52/0.76  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', emptyInPowerset)).
% 2.52/0.76  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', powersetE)).
% 2.52/0.76  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setunionI)).
% 2.52/0.76  thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setunionE)).
% 2.52/0.76  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', subPowSU)).
% 2.52/0.76  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', uniqinunit)).
% 2.52/0.76  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', notinsingleton)).
% 2.52/0.76  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', eqinunit)).
% 2.52/0.76  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', singletonsswitch)).
% 2.52/0.76  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', upairsetE)).
% 2.52/0.76  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', upairsetIL)).
% 2.52/0.76  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', upairsetIR)).
% 2.52/0.76  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', vacuousDall)).
% 2.52/0.76  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', quantDeMorgan1)).
% 2.52/0.76  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', quantDeMorgan2)).
% 2.52/0.76  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', quantDeMorgan3)).
% 2.52/0.76  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', quantDeMorgan4)).
% 2.52/0.76  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', prop2setI)).
% 2.52/0.76  thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', prop2set2propI)).
% 2.52/0.76  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', notdexE)).
% 2.52/0.76  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', notdallE)).
% 2.52/0.76  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', inCongP)).
% 2.52/0.76  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', in__Cong)).
% 2.52/0.76  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', emptyset__Cong)).
% 2.52/0.76  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setadjoin__Cong)).
% 2.52/0.76  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', powerset__Cong)).
% 2.52/0.76  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setunion__Cong)).
% 2.52/0.76  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', omega__Cong)).
% 2.52/0.76  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', subsetI1)).
% 2.52/0.76  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', eqimpsubset2)).
% 2.52/0.76  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', eqimpsubset1)).
% 2.52/0.76  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', subsetI2)).
% 2.52/0.76  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', emptysetsubset)).
% 2.52/0.76  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', subsetE)).
% 2.52/0.76  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', subsetE2)).
% 2.52/0.76  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', notsubsetI)).
% 2.52/0.76  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', notequalI1)).
% 2.52/0.76  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', notequalI2)).
% 2.52/0.76  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', subsetRefl)).
% 2.52/0.76  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', subsetTrans)).
% 2.52/0.76  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setadjoinSub)).
% 2.52/0.76  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setadjoinSub2)).
% 2.52/0.76  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', subset2powerset)).
% 2.52/0.76  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setextsub)).
% 2.52/0.76  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', subsetemptysetimpeq)).
% 2.52/0.76  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', powersetI1)).
% 2.52/0.76  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', powersetE1)).
% 2.52/0.76  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', inPowerset)).
% 2.52/0.76  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', powersetsubset)).
% 2.52/0.76  thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binunionIL)).
% 2.52/0.76  thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', upairset2IR)).
% 2.52/0.76  thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binunionIR)).
% 2.52/0.76  thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binunionEcases)).
% 2.52/0.76  thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binunionE)).
% 2.52/0.76  thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binunionLsub)).
% 2.52/0.76  thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binunionRsub)).
% 2.52/0.76  thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectI)).
% 2.52/0.76  thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectSubset5)).
% 2.52/0.76  thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectEL)).
% 2.52/0.76  thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectLsub)).
% 2.52/0.76  thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectSubset2)).
% 2.52/0.76  thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectSubset3)).
% 2.52/0.76  thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectER)).
% 2.52/0.76  thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', disjointsetsI1)).
% 2.52/0.76  thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectRsub)).
% 2.52/0.76  thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectSubset4)).
% 2.52/0.76  thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectSubset1)).
% 2.52/0.76  thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', bs114d)).
% 2.52/0.76  thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setminusI)).
% 2.52/0.76  thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setminusEL)).
% 2.52/0.76  thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setminusER)).
% 2.52/0.76  thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setminusSubset2)).
% 2.52/0.76  thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setminusERneg)).
% 2.52/0.76  thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setminusELneg)).
% 2.52/0.76  thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setminusILneg)).
% 2.52/0.76  thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setminusIRneg)).
% 2.52/0.76  thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setminusLsub)).
% 2.52/0.76  thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setminusSubset1)).
% 2.52/0.76  thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', symdiffE)).
% 2.52/0.76  thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', symdiffI1)).
% 2.52/0.76  thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', symdiffI2)).
% 2.52/0.76  thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', symdiffIneg1)).
% 2.52/0.76  thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', symdiffIneg2)).
% 2.52/0.76  thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', secondinupair)).
% 2.52/0.76  thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setukpairIL)).
% 2.52/0.76  thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setukpairIR)).
% 2.52/0.76  thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', kpairiskpair)).
% 2.52/0.76  thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', kpairp)).
% 2.52/0.76  thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', singletonsubset)).
% 2.52/0.76  thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', singletoninpowerset)).
% 2.52/0.76  thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', singletoninpowunion)).
% 2.52/0.76  thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', upairset2E)).
% 2.52/0.76  thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', upairsubunion)).
% 2.52/0.76  thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', upairinpowunion)).
% 2.52/0.76  thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ubforcartprodlem1)).
% 2.52/0.76  thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ubforcartprodlem2)).
% 2.52/0.76  thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ubforcartprodlem3)).
% 2.52/0.76  thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', cartprodpairin)).
% 2.52/0.76  thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', cartprodmempair1)).
% 2.52/0.76  thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', cartprodmempair)).
% 2.52/0.76  thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setunionE2)).
% 2.52/0.76  thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setunionsingleton1)).
% 2.52/0.76  thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setunionsingleton2)).
% 2.52/0.76  thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setunionsingleton)).
% 2.52/0.76  thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', singletonsuniq)).
% 2.52/0.76  thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.XjZ0hWvsML/E---3.1_4073238.p', setukpairinjL1)).
% 2.52/0.76  thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', theprop)).
% 2.52/0.76  thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', kfstpairEq)).
% 2.52/0.76  thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', cartprodfstin)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', setukpairinjL2)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', setukpairinjL)).
% 2.52/0.76  thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setukpairinjR11)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', setukpairinjR12)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', setukpairinjR1)).
% 2.52/0.76  thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', upairequniteq)).
% 2.52/0.76  thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setukpairinjR2)).
% 2.52/0.76  thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setukpairinjR)).
% 2.52/0.76  thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ksndpairEq)).
% 2.52/0.76  thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', kpairsurjEq)).
% 2.52/0.76  thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', cartprodsndin)).
% 2.52/0.76  thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', cartprodpairmemEL)).
% 2.52/0.76  thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', cartprodpairmemER)).
% 2.52/0.76  thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', cartprodmempaircEq)).
% 2.52/0.76  thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', cartprodfstpairEq)).
% 2.52/0.76  thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', cartprodsndpairEq)).
% 2.52/0.76  thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', cartprodpairsurjEq)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', app)).
% 2.52/0.76  thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', infuncsetfunc)).
% 2.52/0.76  thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ap2p)).
% 2.52/0.76  thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', funcinfuncset)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', funcGraphProp1)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', funcGraphProp3)).
% 2.52/0.76  thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', funcGraphProp2)).
% 2.52/0.76  thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', funcextLem)).
% 2.52/0.76  thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', funcGraphProp4)).
% 2.52/0.76  thf(funcext, axiom, ((funcext)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', funcext)).
% 2.52/0.76  thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', funcext2)).
% 2.52/0.76  thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ap2apEq1)).
% 2.52/0.76  thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ap2apEq2)).
% 2.52/0.76  thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', ifp)).
% 2.52/0.76  thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', theeq)).
% 2.52/0.76  thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', iftrue)).
% 2.52/0.76  thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', iffalse)).
% 2.52/0.76  thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', iftrueorfalse)).
% 2.52/0.76  thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', binintersectT_lem)).
% 2.52/0.76  thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binunionT_lem)).
% 2.52/0.76  thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', powersetT_lem)).
% 2.52/0.76  thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', setminusT_lem)).
% 2.52/0.76  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.XjZ0hWvsML/E---3.1_4073238.p', complementT_lem)).
% 2.52/0.76  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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', setextT)).
% 2.52/0.76  thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', subsetTI)).
% 2.52/0.76  thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', powersetTI1)).
% 2.52/0.76  thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', powersetTE1)).
% 2.52/0.76  thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', complementTI1)).
% 2.52/0.76  thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', complementTE1)).
% 2.52/0.76  thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectTELcontra)).
% 2.52/0.76  thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binintersectTERcontra)).
% 2.52/0.76  thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', contrasubsetT)).
% 2.52/0.76  thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', contrasubsetT1)).
% 2.52/0.76  thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', contrasubsetT2)).
% 2.52/0.76  thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', contrasubsetT3)).
% 2.52/0.76  thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', doubleComplementI1)).
% 2.52/0.76  thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', doubleComplementE1)).
% 2.52/0.76  thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', doubleComplementSub1)).
% 2.52/0.76  thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', doubleComplementSub2)).
% 2.52/0.76  thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', doubleComplementEq)).
% 2.52/0.76  thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', complementTnotintersectT)).
% 2.52/0.76  thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', complementImpComplementIntersect)).
% 2.52/0.76  thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.XjZ0hWvsML/E---3.1_4073238.p', complementSubsetComplementIntersect)).
% 2.52/0.76  thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', complementInPowersetComplementIntersect)).
% 2.52/0.76  thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', contraSubsetComplement)).
% 2.52/0.76  thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', complementTcontraSubset)).
% 2.52/0.76  thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binunionTILcontra)).
% 2.52/0.76  thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binunionTIRcontra)).
% 2.52/0.76  thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', inIntersectImpInUnion)).
% 2.52/0.76  thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', inIntersectImpInUnion2)).
% 2.52/0.76  thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', inIntersectImpInIntersectUnions)).
% 2.52/0.76  thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', intersectInPowersetIntersectUnions)).
% 2.52/0.76  thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', inComplementUnionImpNotIn1)).
% 2.52/0.76  thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', inComplementUnionImpInComplement1)).
% 2.52/0.76  thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binunionTE)).
% 2.52/0.76  thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', binunionTEcontra)).
% 2.52/0.76  thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', demorgan2a1)).
% 2.52/0.76  thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', complementUnionInPowersetComplement)).
% 2.52/0.76  thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', demorgan2a2)).
% 2.52/0.76  thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', demorgan1a)).
% 2.52/0.76  thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', demorgan1b)).
% 2.52/0.76  thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', demorgan1)).
% 2.52/0.76  thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', demorgan2a)).
% 2.52/0.76  thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', demorgan2b2)).
% 2.52/0.76  thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', demorgan2b)).
% 2.52/0.76  thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', demorgan2)).
% 2.52/0.76  thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', woz13rule0)).
% 2.52/0.76  thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', woz13rule1)).
% 2.52/0.76  thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', woz13rule2)).
% 2.52/0.76  thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', woz13rule3)).
% 2.52/0.76  thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', woz13rule4)).
% 2.52/0.76  thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', woz1_1)).
% 2.52/0.76  thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', woz1_2)).
% 2.52/0.76  thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', woz1_3)).
% 2.52/0.76  thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.XjZ0hWvsML/E---3.1_4073238.p', woz1_4)).
% 2.52/0.76  thf(c_0_288, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 2.52/0.76  thf(c_0_289, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 2.52/0.76  thf(c_0_290, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 2.52/0.76  thf(c_0_291, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 2.52/0.76  thf(c_0_292, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 2.52/0.76  thf(c_0_293, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 2.52/0.76  thf(c_0_294, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 2.52/0.76  thf(c_0_295, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 2.52/0.76  thf(c_0_296, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 2.52/0.76  thf(c_0_297, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 2.52/0.76  thf(c_0_298, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 2.52/0.76  thf(c_0_299, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 2.52/0.76  thf(c_0_300, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 2.52/0.76  thf(c_0_301, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 2.52/0.76  thf(c_0_302, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 2.52/0.76  thf(c_0_303, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 2.52/0.76  thf(c_0_304, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 2.52/0.76  thf(c_0_305, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 2.52/0.76  thf(c_0_306, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 2.52/0.76  thf(c_0_307, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 2.52/0.76  thf(c_0_308, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 2.52/0.76  thf(c_0_309, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 2.52/0.76  thf(c_0_310, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[woz1_5])).
% 2.52/0.76  thf(c_0_311, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X959:$i]:(((((X6 @ X2 @ X959)))&(![X960:$i]:(((((X6 @ X2 @ X960)))=>(((X959)=(X960)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_288, c_0_289])).
% 2.52/0.76  thf(c_0_312, plain, ((descrp)=(![X1:$i > $o]:((((?[X961:$i]:(((((X1 @ X961)))&(![X962:$i]:(((((X1 @ X962)))=>(((X961)=(X962))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_290, c_0_289])).
% 2.52/0.76  thf(c_0_313, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 2.52/0.76  thf(c_0_314, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 2.52/0.76  thf(c_0_315, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 2.52/0.76  thf(c_0_316, plain, ((exuE1)=(![X1:$i > $o]:((((?[X963:$i]:(((((X1 @ X963)))&(![X964:$i]:(((((X1 @ X964)))=>(((X963)=(X964))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_291, c_0_289])).
% 2.52/0.76  thf(c_0_317, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X965:$i]:(((((X1 @ X965)))&(![X966:$i]:(((((X1 @ X966)))=>(((X965)=(X966))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_292, c_0_289])).
% 2.52/0.76  thf(c_0_318, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 2.52/0.76  thf(c_0_319, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_293])).
% 2.52/0.76  thf(c_0_320, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_294, c_0_293])).
% 2.52/0.76  thf(c_0_321, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_293])).
% 2.52/0.76  thf(c_0_322, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 2.52/0.76  thf(c_0_323, plain, ((exuE2)=(![X1:$i > $o]:((((?[X967:$i]:(((((X1 @ X967)))&(![X968:$i]:(((((X1 @ X968)))=>(((X967)=(X968))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_295, c_0_289])).
% 2.52/0.76  thf(c_0_324, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_293])).
% 2.52/0.76  thf(c_0_325, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 2.52/0.76  thf(c_0_326, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X969:$i]:(((((X1 @ X969)))&(![X970:$i]:(((((X1 @ X970)))=>(((X969)=(X970)))))))))))))), inference(apply_def,[status(thm)],[c_0_296, c_0_289])).
% 2.52/0.76  thf(c_0_327, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X971:$i]:(((((X1 @ X971)))&(![X972:$i]:(((((X1 @ X972)))=>(((X971)=(X972)))))))))))))))), inference(apply_def,[status(thm)],[c_0_297, c_0_289])).
% 2.52/0.76  thf(c_0_328, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X973:$i]:(((((X1 @ X973)))&(![X974:$i]:(((((X1 @ X974)))=>(((X973)=(X974)))))))))))))), inference(apply_def,[status(thm)],[c_0_298, c_0_289])).
% 2.52/0.76  thf(c_0_329, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X975:$i]:(((((X1 @ X975)))&(![X976:$i]:(((((X1 @ X976)))=>(((X975)=(X976))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_299, c_0_289])).
% 2.52/0.76  thf(c_0_330, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X977:$i]:(((((X1 @ X977)))&(![X978:$i]:(((((X1 @ X978)))=>(((X977)=(X978))))))))))<=>((?[X979:$i]:(((((X17 @ X979)))&(![X980:$i]:(((((X17 @ X980)))=>(((X979)=(X980)))))))))))))))), inference(apply_def,[status(thm)],[c_0_300, c_0_289])).
% 2.52/0.76  thf(c_0_331, plain, ((exuEu)=(![X1:$i > $o]:((((?[X981:$i]:(((((X1 @ X981)))&(![X982:$i]:(((((X1 @ X982)))=>(((X981)=(X982))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_301, c_0_289])).
% 2.52/0.76  thf(c_0_332, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X983:$i]:(((((X1 @ X983)))&(![X984:$i]:(((((X1 @ X984)))=>(((X983)=(X984))))))))))=>((((?[X985:$i]:(((((X17 @ X985)))&(![X986:$i]:(((((X17 @ X986)))=>(((X985)=(X986))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_302, c_0_289])).
% 2.52/0.76  thf(c_0_333, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 2.52/0.76  thf(c_0_334, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 2.52/0.76  thf(c_0_335, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 2.52/0.76  thf(c_0_336, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 2.52/0.76  thf(c_0_337, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_303, c_0_304])).
% 2.52/0.76  thf(c_0_338, plain, ((ex1I)=(![X4:$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_305, c_0_304])).
% 2.52/0.76  thf(c_0_339, 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:$i]:(((X1 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_306, c_0_304])).
% 2.52/0.76  thf(c_0_340, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 2.52/0.76  thf(c_0_341, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 2.52/0.76  thf(c_0_342, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 2.52/0.76  thf(c_0_343, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 2.52/0.76  thf(c_0_344, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_307, c_0_308])).
% 2.52/0.76  thf(c_0_345, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 2.52/0.76  thf(c_0_346, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 2.52/0.76  thf(c_0_347, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 2.52/0.76  thf(c_0_348, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 2.52/0.76  thf(c_0_349, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 2.52/0.76  thf(c_0_350, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 2.52/0.76  thf(c_0_351, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 2.52/0.76  thf(c_0_352, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 2.52/0.76  thf(c_0_353, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 2.52/0.76  thf(c_0_354, axiom, ((brelnall1)=(![X4:$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_308])).
% 2.52/0.76  thf(c_0_355, 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_308])).
% 2.52/0.76  thf(c_0_356, 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_309, c_0_304])).
% 2.52/0.76  thf(c_0_357, 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_308])).
% 2.52/0.76  thf(c_0_358, 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_308])).
% 2.52/0.76  thf(c_0_359, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
% 2.52/0.76  thf(c_0_360, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
% 2.52/0.76  thf(c_0_361, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
% 2.52/0.76  thf(c_0_362, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
% 2.52/0.76  thf(c_0_363, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
% 2.52/0.76  thf(c_0_364, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 2.52/0.76  thf(c_0_365, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 2.52/0.76  thf(c_0_366, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 2.52/0.76  thf(c_0_367, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 2.52/0.76  thf(c_0_368, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 2.52/0.76  thf(c_0_369, plain, ((epred1_0)<=>![X1016:$i]:(?[X1017:$i]:((((![X1018:$i]:(((in @ X1018 @ X1017)=>![X1019:$i]:(((in @ X1019 @ X1018)=>(in @ X1019 @ X1016)))))&![X1020:$i, X1021:$i]:((((in @ X1020 @ X1016)&(in @ X1021 @ X1016))=>(![X1022:$i]:(((in @ X1022 @ X1017)=>((in @ X1020 @ X1022)<=>(in @ X1021 @ X1022))))=>((X1020)=(X1021))))))&![X1023:$i, X1024:$i]:((((in @ X1023 @ X1017)&(in @ X1024 @ X1017))=>(![X1025:$i]:(((in @ X1025 @ X1023)=>(in @ X1025 @ X1024)))|![X1026:$i]:(((in @ X1026 @ X1024)=>(in @ X1026 @ X1023)))))))&![X1027:$i]:(((![X1028:$i]:(((in @ X1028 @ X1027)=>(in @ X1028 @ X1016)))&?[X1029:$i]:((in @ X1029 @ X1027)))=>?[X1030:$i, X1031:$i]:(((((in @ X1030 @ X1017)&(in @ X1031 @ X1027))&~(?[X1032:$i]:(((in @ X1032 @ X1030)&(in @ X1032 @ X1027)))))&![X1033:$i]:(((in @ X1033 @ X1017)=>(![X1034:$i]:(((in @ X1034 @ X1033)=>(in @ X1034 @ X1030)))|(in @ X1031 @ X1033)))))))))))), introduced(definition)).
% 2.52/0.76  thf(c_0_370, negated_conjecture, ~((![X987:$i, X988:$i]:((![X989:$i]:(((in @ X989 @ X987)<=>(in @ X989 @ X988)))=>((X987)=(X988))))=>(![X990:$i]:(~(in @ X990 @ emptyset))=>(![X991:$i, X992:$i, X993:$i]:(((in @ X993 @ (setadjoin @ X991 @ X992))<=>(((X993)=(X991))|(in @ X993 @ X992))))=>(![X994:$i, X995:$i]:(((in @ X995 @ (powerset @ X994))<=>![X996:$i]:(((in @ X996 @ X995)=>(in @ X996 @ X994)))))=>(![X997:$i, X998:$i]:(((in @ X998 @ (setunion @ X997))<=>?[X999:$i]:(((in @ X998 @ X999)&(in @ X999 @ X997)))))=>((in @ emptyset @ omega)=>(![X1000:$i]:(((in @ X1000 @ omega)=>(in @ (setadjoin @ X1000 @ X1000) @ omega)))=>(![X1001:$i]:((((in @ emptyset @ X1001)&![X1002:$i]:((((in @ X1002 @ omega)&(in @ X1002 @ X1001))=>(in @ (setadjoin @ X1002 @ X1002) @ X1001))))=>![X1003:$i]:(((in @ X1003 @ omega)=>(in @ X1003 @ X1001)))))=>(![X1004:$i > $i > $o, X1005:$i]:((![X1006:$i]:(((in @ X1006 @ X1005)=>?[X1007:$i]:(((X1004 @ X1006 @ X1007)&![X1008:$i]:(((X1004 @ X1006 @ X1008)=>((X1007)=(X1008))))))))=>?[X1009:$i]:(![X1010:$i]:(((in @ X1010 @ X1009)<=>?[X1011:$i]:(((in @ X1011 @ X1005)&(X1004 @ X1011 @ X1010))))))))=>(![X1012:$i]:((?[X1013:$i]:((in @ X1013 @ X1012))=>?[X1014:$i]:(((in @ X1014 @ X1012)&~(?[X1015:$i]:(((in @ X1015 @ X1014)&(in @ X1015 @ X1012))))))))=>((epred1_0)=>(![X1035:$i > $o]:((?[X1036:$i]:(((X1035 @ X1036)&![X1037:$i]:(((X1035 @ X1037)=>((X1036)=(X1037))))))=>(X1035 @ (descr @ (^[Z0:$i]:(X1035 @ Z0))))))=>(![X1038:$i, X1039:$i > $o, X1040:$i]:(((in @ X1040 @ X1038)=>((X1039 @ X1040)=>(in @ X1040 @ (dsetconstr @ X1038 @ X1039)))))=>(![X1041:$i, X1042:$i > $o, X1043:$i]:(((in @ X1043 @ (dsetconstr @ X1041 @ X1042))=>(in @ X1043 @ X1041)))=>(![X1044:$i, X1045:$i > $o, X1046:$i]:(((in @ X1046 @ (dsetconstr @ X1044 @ X1045))=>(X1045 @ X1046)))=>(![X1047:$i > $o]:((?[X1048:$i]:(((X1047 @ X1048)&![X1049:$i]:(((X1047 @ X1049)=>((X1048)=(X1049))))))=>?[X1050:$i]:(((X1047 @ X1050)&![X1051:$i]:(((X1047 @ X1051)=>((X1050)=(X1051))))))))=>(![X1052:$o, X1053:$i]:(((in @ X1053 @ (prop2set @ ((X1052))))=>(X1052)))=>(![X1054:$i]:(((in @ X1054 @ emptyset)=>![X1055:$o]:((X1055))))=>(![X1056:$i]:(((in @ X1056 @ emptyset)=>~($true)))=>(![X1057:$i]:(~(in @ X1057 @ emptyset))=>(![X1058:$i > $o]:((?[X1059:$i]:(((X1058 @ X1059)&![X1060:$i]:(((X1058 @ X1060)=>((X1059)=(X1060))))))=>?[X1061:$i]:((X1058 @ X1061))))=>(![X1062:$i, X1063:$i]:((![X1064:$i]:(((in @ X1064 @ X1062)=>(in @ X1064 @ X1063)))=>(![X1065:$i]:(((in @ X1065 @ X1063)=>(in @ X1065 @ X1062)))=>((X1062)=(X1063)))))=>(![X1066:$i]:((![X1067:$i]:(~(in @ X1067 @ X1066))=>((X1066)=(emptyset))))=>(![X1068:$i]:((![X1069:$i]:(~(in @ X1069 @ X1068))=>((X1068)=(emptyset))))=>(![X1070:$i, X1071:$i > $o, X1072:$i]:(((in @ X1072 @ X1070)=>((in @ X1072 @ (dsetconstr @ X1070 @ X1071))<=>(X1071 @ X1072))))=>(![X1073:$i]:((((X1073)!=(emptyset))=>?[X1074:$i]:((in @ X1074 @ X1073))))=>(![X1075:$i, X1076:$i > $o, X1077:$i]:(((in @ X1077 @ X1075)=>((X1076 @ X1077)=>((dsetconstr @ X1075 @ X1076)!=(emptyset)))))=>(![X1078:$i]:((?[X1079:$i]:((in @ X1079 @ X1078))=>((X1078)!=(emptyset))))=>(![X1080:$i, X1081:$i]:((in @ X1080 @ (setadjoin @ X1080 @ X1081)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1082:$i, X1083:$i, X1084:$i]:(((in @ X1084 @ X1083)=>(in @ X1084 @ (setadjoin @ X1082 @ X1083))))=>(![X1085:$i, X1086:$i, X1087:$i]:(((in @ X1087 @ (setadjoin @ X1085 @ X1086))=>![X1088:$o]:(((((X1087)=(X1085))=>(X1088))=>(((in @ X1087 @ X1086)=>(X1088))=>(X1088))))))=>(![X1089:$i, X1090:$i, X1091:$i]:(((in @ X1091 @ (setadjoin @ X1089 @ X1090))=>(((X1091)=(X1089))|(in @ X1091 @ X1090))))=>(![X1092:$i]:(((dsetconstr @ X1092 @ (^[Z0:$i]:($true)))=(X1092)))=>(![X1093:$i, X1094:$i]:((![X1095:$i]:(((in @ X1095 @ X1094)=>(in @ X1095 @ X1093)))=>(in @ X1094 @ (powerset @ X1093))))=>(![X1096:$i]:((in @ emptyset @ (powerset @ X1096)))=>(![X1097:$i]:((in @ emptyset @ (powerset @ X1097)))=>(![X1098:$i, X1099:$i, X1100:$i]:(((in @ X1099 @ (powerset @ X1098))=>((in @ X1100 @ X1099)=>(in @ X1100 @ X1098))))=>(![X1101:$i, X1102:$i, X1103:$i]:(((in @ X1102 @ X1103)=>((in @ X1103 @ X1101)=>(in @ X1102 @ (setunion @ X1101)))))=>(![X1104:$i, X1105:$i]:(((in @ X1105 @ (setunion @ X1104))=>![X1106:$o]:((![X1107:$i]:(((in @ X1105 @ X1107)=>((in @ X1107 @ X1104)=>(X1106))))=>(X1106)))))=>(![X1108:$i, X1109:$i]:(((in @ X1109 @ X1108)=>(in @ X1109 @ (powerset @ (setunion @ X1108)))))=>(![X1110:$i > $o]:((?[X1111:$i]:(((X1110 @ X1111)&![X1112:$i]:(((X1110 @ X1112)=>((X1111)=(X1112))))))=>?[X1113:$i]:(![X1114:$i]:(((X1110 @ X1114)<=>((X1114)=(X1113)))))))=>(![X1115:$i]:((((X1115)!=(emptyset))=>?[X1116:$i]:(((in @ X1116 @ X1115)&$true))))=>(![X1117:$i, X1118:$i]:(((in @ X1117 @ (setadjoin @ X1118 @ emptyset))=>((X1117)=(X1118))))=>(![X1119:$i, X1120:$i]:((((X1119)!=(X1120))=>~(in @ X1120 @ (setadjoin @ X1119 @ emptyset))))=>(![X1121:$i, X1122:$i]:((((X1121)=(X1122))=>(in @ X1121 @ (setadjoin @ X1122 @ emptyset))))=>(![X1123:$i, X1124:$i]:(((in @ X1123 @ (setadjoin @ X1124 @ emptyset))=>(in @ X1124 @ (setadjoin @ X1123 @ emptyset))))=>(![X1125:$i, X1126:$i, X1127:$i]:(((in @ X1127 @ (setadjoin @ X1125 @ (setadjoin @ X1126 @ emptyset)))=>(((X1127)=(X1125))|((X1127)=(X1126)))))=>(![X1128:$i, X1129:$i]:((in @ X1128 @ (setadjoin @ X1128 @ (setadjoin @ X1129 @ emptyset))))=>(![X1130:$i, X1131:$i]:((in @ X1131 @ (setadjoin @ X1130 @ (setadjoin @ X1131 @ emptyset))))=>(![X1132:$i, X1133:$i > $o]:((?[X1134:$i]:(((in @ X1134 @ X1132)&(X1133 @ X1134)))=>(((dsetconstr @ X1132 @ X1133)=(emptyset))=>~($true))))=>(![X1135:$i > $o, X1136:$i]:(((in @ X1136 @ emptyset)=>(X1135 @ X1136)))=>(![X1137:$i, X1138:$i > $o]:((~(![X1139:$i]:(((in @ X1139 @ X1137)=>(X1138 @ X1139))))=>?[X1140:$i]:(((in @ X1140 @ X1137)&~((X1138 @ X1140))))))=>(![X1141:$i, X1142:$i > $o]:((![X1143:$i]:(((in @ X1143 @ X1141)=>~((X1142 @ X1143))))=>~(?[X1144:$i]:(((in @ X1144 @ X1141)&(X1142 @ X1144))))))=>(![X1145:$i, X1146:$i > $o]:((~(?[X1147:$i]:(((in @ X1147 @ X1145)&(X1146 @ X1147))))=>![X1148:$i]:(((in @ X1148 @ X1145)=>~((X1146 @ X1148))))))=>(![X1149:$i, X1150:$i > $o]:((?[X1151:$i]:(((in @ X1151 @ X1149)&~((X1150 @ X1151))))=>~(![X1152:$i]:(((in @ X1152 @ X1149)=>(X1150 @ X1152))))))=>(![X1153:$o]:(((X1153)=>(in @ emptyset @ (prop2set @ ((X1153))))))=>(![X1154:$o]:(((X1154)=>(set2prop @ (prop2set @ ((X1154))))))=>(![X1155:$i, X1156:$i > $o]:((~(?[X1157:$i]:(((in @ X1157 @ X1155)&(X1156 @ X1157))))=>![X1158:$i]:(((in @ X1158 @ X1155)=>~((X1156 @ X1158))))))=>(![X1159:$i, X1160:$i > $o]:((~(![X1161:$i]:(((in @ X1161 @ X1159)=>(X1160 @ X1161))))=>?[X1162:$i]:(((in @ X1162 @ X1159)&~((X1160 @ X1162))))))=>(![X1163:$i > $o]:((?[X1164:$i]:(((X1163 @ X1164)&![X1165:$i]:(((X1163 @ X1165)=>((X1164)=(X1165))))))=>?[X1166:$i]:(((X1163 @ X1166)&![X1167:$i]:(((X1163 @ X1167)=>((X1166)=(X1167))))))))=>(![X1168:$i > $o]:((?[X1169:$i]:((X1168 @ X1169))=>(![X1170:$i, X1171:$i]:(((X1168 @ X1170)=>((X1168 @ X1171)=>((X1170)=(X1171)))))=>?[X1172:$i]:(((X1168 @ X1172)&![X1173:$i]:(((X1168 @ X1173)=>((X1172)=(X1173)))))))))=>(![X1174:$i > $o]:((?[X1175:$i]:(![X1176:$i]:(((X1174 @ X1176)<=>((X1176)=(X1175)))))=>?[X1177:$i]:(((X1174 @ X1177)&![X1178:$i]:(((X1174 @ X1178)=>((X1177)=(X1178))))))))=>(![X1179:$i, X1180:$i]:((((X1179)=(X1180))=>![X1181:$i, X1182:$i]:((((X1181)=(X1182))=>((in @ X1181 @ X1179)=>(in @ X1182 @ X1180))))))=>(![X1183:$i, X1184:$i]:((((X1183)=(X1184))=>![X1185:$i, X1186:$i]:((((X1185)=(X1186))=>((in @ X1185 @ X1183)<=>(in @ X1186 @ X1184))))))=>(![X1187:$i > $o]:((?[X1188:$i]:(((X1187 @ X1188)&![X1189:$i]:(((X1187 @ X1189)=>((X1188)=(X1189))))))=>![X1190:$i, X1191:$i]:(((X1187 @ X1190)=>((X1187 @ X1191)=>((X1190)=(X1191)))))))=>(![X1192:$i > $o, X1193:$i > $o]:((![X1194:$i, X1195:$i]:((((X1194)=(X1195))=>((X1192 @ X1194)<=>(X1193 @ X1195))))=>(?[X1196:$i]:(((X1192 @ X1196)&![X1197:$i]:(((X1192 @ X1197)=>((X1196)=(X1197))))))<=>?[X1198:$i]:(((X1193 @ X1198)&![X1199:$i]:(((X1193 @ X1199)=>((X1198)=(X1199)))))))))=>(((emptyset)=(emptyset))=>(![X1200:$i, X1201:$i]:((((X1200)=(X1201))=>![X1202:$i, X1203:$i]:((((X1202)=(X1203))=>((setadjoin @ X1200 @ X1202)=(setadjoin @ X1201 @ X1203))))))=>(![X1204:$i, X1205:$i]:((((X1204)=(X1205))=>((powerset @ X1204)=(powerset @ X1205))))=>(![X1206:$i, X1207:$i]:((((X1206)=(X1207))=>((setunion @ X1206)=(setunion @ X1207))))=>(((omega)=(omega))=>(![X1208:$i > $o]:((?[X1209:$i]:(((X1208 @ X1209)&![X1210:$i]:(((X1208 @ X1210)=>((X1209)=(X1210))))))=>![X1211:$i, X1212:$i]:(((X1208 @ X1211)=>((X1208 @ X1212)=>((X1211)=(X1212)))))))=>(![X1213:$i > $o, X1214:$i > $o]:((![X1215:$i, X1216:$i]:((((X1215)=(X1216))=>((X1213 @ X1215)<=>(X1214 @ X1216))))=>(?[X1217:$i]:(((X1213 @ X1217)&![X1218:$i]:(((X1213 @ X1218)=>((X1217)=(X1218))))))=>(?[X1219:$i]:(((X1214 @ X1219)&![X1220:$i]:(((X1214 @ X1220)=>((X1219)=(X1220))))))=>((descr @ X1213)=(descr @ X1214))))))=>(![X1221:$i, X1222:$i]:((((X1221)=(X1222))=>![X1223:$i > $o, X1224:$i > $o]:((![X1225:$i]:(((in @ X1225 @ X1221)=>![X1226:$i]:(((in @ X1226 @ X1222)=>(((X1225)=(X1226))=>((X1223 @ X1225)<=>(X1224 @ X1226)))))))=>((dsetconstr @ X1221 @ X1223)=(dsetconstr @ X1222 @ X1224))))))=>(![X1227:$i, X1228:$i]:((![X1229:$i]:(((in @ X1229 @ X1227)=>(in @ X1229 @ X1228)))=>(subset @ X1227 @ X1228)))=>(![X1230:$i, X1231:$i]:((((X1230)=(X1231))=>(subset @ X1231 @ X1230)))=>(![X1232:$i, X1233:$i]:((((X1232)=(X1233))=>(subset @ X1232 @ X1233)))=>(![X1234:$i, X1235:$i]:((![X1236:$i]:(((in @ X1236 @ X1234)=>(in @ X1236 @ X1235)))=>(subset @ X1234 @ X1235)))=>(![X1237:$i]:((subset @ emptyset @ X1237))=>(![X1238:$i, X1239:$i, X1240:$i]:(((subset @ X1238 @ X1239)=>((in @ X1240 @ X1238)=>(in @ X1240 @ X1239))))=>(![X1241:$i, X1242:$i, X1243:$i]:(((subset @ X1241 @ X1242)=>(~(in @ X1243 @ X1242)=>~(in @ X1243 @ X1241))))=>(![X1244:$i, X1245:$i, X1246:$i]:(((in @ X1246 @ X1244)=>(~(in @ X1246 @ X1245)=>~(subset @ X1244 @ X1245))))=>(![X1247:$i, X1248:$i]:((~(subset @ X1247 @ X1248)=>((X1247)!=(X1248))))=>(![X1249:$i, X1250:$i, X1251:$i]:(((in @ X1251 @ X1249)=>(~(in @ X1251 @ X1250)=>((X1249)!=(X1250)))))=>(![X1252:$i]:((subset @ X1252 @ X1252))=>(![X1253:$i, X1254:$i, X1255:$i]:(((subset @ X1253 @ X1254)=>((subset @ X1254 @ X1255)=>(subset @ X1253 @ X1255))))=>(![X1256:$i, X1257:$i]:((subset @ X1257 @ (setadjoin @ X1256 @ X1257)))=>(![X1258:$i, X1259:$i, X1260:$i]:(((subset @ X1258 @ X1260)=>(subset @ X1258 @ (setadjoin @ X1259 @ X1260))))=>(![X1261:$i, X1262:$i]:(((subset @ X1261 @ X1262)=>(in @ X1261 @ (powerset @ X1262))))=>(![X1263:$i, X1264:$i]:(((subset @ X1263 @ X1264)=>((subset @ X1264 @ X1263)=>((X1263)=(X1264)))))=>(![X1265:$i]:(((subset @ X1265 @ emptyset)=>((X1265)=(emptyset))))=>(![X1266:$i, X1267:$i]:(((subset @ X1267 @ X1266)=>(in @ X1267 @ (powerset @ X1266))))=>(![X1268:$i, X1269:$i]:(((in @ X1269 @ (powerset @ X1268))=>(subset @ X1269 @ X1268)))=>(![X1270:$i]:((in @ X1270 @ (powerset @ X1270)))=>(![X1271:$i, X1272:$i]:(((subset @ X1271 @ X1272)=>(subset @ (powerset @ X1271) @ (powerset @ X1272))))=>(![X1273:$i, X1274:$i > $o]:((in @ (dsetconstr @ X1273 @ X1274) @ (powerset @ X1273)))=>(![X1275:$i, X1276:$i > $o]:((subset @ (dsetconstr @ X1275 @ X1276) @ X1275))=>(![X1277:$i, X1278:$i, X1279:$i]:(((in @ X1279 @ X1277)=>(in @ X1279 @ (binunion @ X1277 @ X1278))))=>(![X1280:$i, X1281:$i]:((in @ X1281 @ (setadjoin @ X1280 @ (setadjoin @ X1281 @ emptyset))))=>(![X1282:$i, X1283:$i, X1284:$i]:(((in @ X1284 @ X1283)=>(in @ X1284 @ (binunion @ X1282 @ X1283))))=>(![X1285:$i, X1286:$i, X1287:$i, X1288:$o]:(((in @ X1287 @ (binunion @ X1285 @ X1286))=>(((in @ X1287 @ X1285)=>(X1288))=>(((in @ X1287 @ X1286)=>(X1288))=>(X1288)))))=>(![X1289:$i, X1290:$i, X1291:$i]:(((in @ X1291 @ (binunion @ X1289 @ X1290))=>((in @ X1291 @ X1289)|(in @ X1291 @ X1290))))=>(![X1292:$i, X1293:$i]:((subset @ X1292 @ (binunion @ X1292 @ X1293)))=>(![X1294:$i, X1295:$i]:((subset @ X1295 @ (binunion @ X1294 @ X1295)))=>(![X1296:$i, X1297:$i, X1298:$i]:(((in @ X1298 @ X1296)=>((in @ X1298 @ X1297)=>(in @ X1298 @ (binintersect @ X1296 @ X1297)))))=>(![X1299:$i, X1300:$i, X1301:$i]:(((subset @ X1301 @ X1299)=>((subset @ X1301 @ X1300)=>(subset @ X1301 @ (binintersect @ X1299 @ X1300)))))=>(![X1302:$i, X1303:$i, X1304:$i]:(((in @ X1304 @ (binintersect @ X1302 @ X1303))=>(in @ X1304 @ X1302)))=>(![X1305:$i, X1306:$i]:((subset @ (binintersect @ X1305 @ X1306) @ X1305))=>(![X1307:$i, X1308:$i]:(((subset @ X1307 @ X1308)=>((binintersect @ X1307 @ X1308)=(X1307))))=>(![X1309:$i, X1310:$i]:((((binintersect @ X1309 @ X1310)=(X1310))=>(subset @ X1310 @ X1309)))=>(![X1311:$i, X1312:$i, X1313:$i]:(((in @ X1313 @ (binintersect @ X1311 @ X1312))=>(in @ X1313 @ X1312)))=>(![X1314:$i, X1315:$i]:((~(?[X1316:$i]:(((in @ X1316 @ X1314)&(in @ X1316 @ X1315))))=>((binintersect @ X1314 @ X1315)=(emptyset))))=>(![X1317:$i, X1318:$i]:((subset @ (binintersect @ X1317 @ X1318) @ X1318))=>(![X1319:$i, X1320:$i]:(((subset @ X1320 @ X1319)=>((binintersect @ X1319 @ X1320)=(X1320))))=>(![X1321:$i, X1322:$i]:((((binintersect @ X1321 @ X1322)=(X1321))=>(subset @ X1321 @ X1322)))=>(![X1323:$i, X1324:$i, X1325:$i]:(((binintersect @ X1323 @ (binunion @ X1324 @ X1325))=(binunion @ (binintersect @ X1323 @ X1324) @ (binintersect @ X1323 @ X1325))))=>(![X1326:$i, X1327:$i, X1328:$i]:(((in @ X1328 @ X1326)=>(~(in @ X1328 @ X1327)=>(in @ X1328 @ (setminus @ X1326 @ X1327)))))=>(![X1329:$i, X1330:$i, X1331:$i]:(((in @ X1331 @ (setminus @ X1329 @ X1330))=>(in @ X1331 @ X1329)))=>(![X1332:$i, X1333:$i, X1334:$i]:(((in @ X1334 @ (setminus @ X1332 @ X1333))=>~(in @ X1334 @ X1333)))=>(![X1335:$i, X1336:$i]:(((subset @ X1335 @ X1336)=>((setminus @ X1335 @ X1336)=(emptyset))))=>(![X1337:$i, X1338:$i, X1339:$i]:((~(in @ X1339 @ (setminus @ X1337 @ X1338))=>((in @ X1339 @ X1337)=>(in @ X1339 @ X1338))))=>(![X1340:$i, X1341:$i, X1342:$i]:((~(in @ X1342 @ (setminus @ X1340 @ X1341))=>(~(in @ X1342 @ 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X1908:$i]:(((in @ X1908 @ (powerset @ X1907))=>![X1909:$i]:(((in @ X1909 @ (powerset @ X1907))=>![X1910:$i]:(((in @ X1910 @ (powerset @ X1907))=>![X1911:$i]:(((in @ X1911 @ (powerset @ X1907))=>((setminus @ X1907 @ (binintersect @ (binunion @ X1908 @ X1909) @ (binunion @ X1910 @ X1911)))=(binunion @ (binintersect @ (setminus @ X1907 @ X1908) @ (setminus @ X1907 @ X1909)) @ (binintersect @ (setminus @ X1907 @ X1910) @ (setminus @ X1907 @ X1911))))))))))))=>(![X1912:$i, X1913:$i]:(((in @ X1913 @ (powerset @ X1912))=>![X1914:$i]:(((in @ X1914 @ (powerset @ X1912))=>![X1915:$i]:(((in @ X1915 @ (powerset @ X1912))=>(in @ (binintersect @ X1913 @ X1914) @ (powerset @ (binintersect @ (binunion @ X1913 @ X1915) @ (binunion @ X1914 @ X1915))))))))))=>(![X1916:$i, X1917:$i]:(((in @ X1917 @ (powerset @ X1916))=>![X1918:$i]:(((in @ X1918 @ (powerset @ X1916))=>((subset @ X1917 @ (setminus @ X1916 @ X1918))=>(subset @ X1918 @ (setminus @ X1916 @ X1917)))))))=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_310, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_311]), foundationAx]), wellorderingAx]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_317]), setext]), emptyI]), noeltsimpempty]), c_0_318]), c_0_319]), c_0_320]), c_0_321]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_322]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_323]), c_0_324]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_325]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_326]), c_0_327]), c_0_328]), inCongP]), in__Cong]), c_0_329]), c_0_330]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_331]), c_0_332]), c_0_333]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_334]), c_0_335]), 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_336]), c_0_337]), c_0_338]), c_0_339]), singletonsuniq]), setukpairinjL1]), c_0_340]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_341]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_342]), c_0_343]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), c_0_348]), c_0_349]), c_0_350]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_351]), c_0_352]), c_0_353]), c_0_354]), c_0_355]), c_0_356]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_357]), c_0_358]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_359]), c_0_360]), c_0_361]), c_0_362]), c_0_363]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), c_0_368]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3]), woz1_4])])]), c_0_369])).
% 2.52/0.76  thf(c_0_371, negated_conjecture, ![X1919:$i, X1920:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1932:$i, X1933:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1941:$i, X1942:$i > $i > $o, X1943:$i, X1945:$i, X1948:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1955:$i, X1956:$i > $o, X1957:$i, X1959:$i, X1960:$i > $o, X1961:$i, X1962:$i, X1963:$i > $o, X1964:$i, X1965:$i, X1966:$i > $o, X1967:$i, X1968:$i > $o, X1969:$i, X1972:$i, X1973:$o, X1974:$i, X1975:$i, X1976:$o, X1977:$i, X1978:$i, X1979:$i > $o, X1980:$i, X1983:$i, X1984:$i, X1987:$i, X1989:$i, X1991:$i, X1992:$i > $o, X1993:$i, X1994:$i, X1996:$i, X1997:$i > $o, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$o, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$o, X2029:$i, X2030:$i, X2031:$i > $o, X2032:$i, X2035:$i, X2036:$i, X2037:$i, X2039:$i, 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 > $o, X2056:$i, X2057:$i > $o, X2058:$i, X2059:$i, X2060:$i > $o, X2061:$i, X2063:$i, X2064:$i > $o, X2066:$i, X2067:$i, X2068:$i > $o, X2070:$i, X2071:$i, X2072:$i > $o, X2073:$i, X2075:$o, X2076:$o, X2077:$i, X2078:$i > $o, X2080:$i, X2081:$i, X2082:$i > $o, X2083:$i, X2085:$i > $o, X2086:$i, X2089:$i, X2090:$i > $o, X2091:$i, X2095:$i, X2096:$i > $o, X2097:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i > $o, X2110:$i, X2112:$i, X2113:$i, X2114:$i > $o, X2115:$i > $o, X2118:$i, X2121:$i, X2122:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i > $o, X2135:$i, X2137:$i, X2138:$i, X2139:$i > $o, X2140:$i > $o, X2143:$i, X2145:$i, X2147:$i, X2148:$i, X2149:$i > $o, X2150:$i > $o, X2153:$i, X2154:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2163:$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:$i, X2199:$i, X2200:$i > $o, X2201:$i, X2202:$i > $o, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$o, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$o, 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:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i > $o, X2357:$i, X2358:$i, X2359:$i > $o, X2361:$i, X2362:$i > $o, X2363:$i, X2365:$i, X2366:$i > $o, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i > $i > $o, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i > $i > $o, X2447:$i, X2448:$i, X2449:$i > $i > $o, X2450:$i, X2451:$i, X2452:$i > $i > $o, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i > $i > $o, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i > $i > $o, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i > $i > $o, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i > $i, X2496:$i, X2497:$i, X2498:$i > $i, X2500:$i, X2501:$i, X2502:$i > $i, X2504:$i, X2505:$i, X2506:$i, X2507:$i > $o, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i > $o, X2517:$i, X2518:$i, X2519:$i > $o, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i > $i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$i > $i, X2591:$i, X2592:$i, X2593:$i > $i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$o, X2601:$i, X2602:$i, X2603:$i, X2604:$o, X2605:$i, X2606:$i, X2607:$i, X2608:$o, X2609:$i, X2610:$i, X2611:$i, X2612:$o, X2613:$i, X2614:$i, X2615:$i, X2616:$o, X2617:$i, X2618:$i, X2619:$i, X2620:$o, X2621:$i, X2622:$i, X2623:$i, X2624:$i, X2625:$i, X2626:$o, X2627:$i, X2628:$i, X2629:$i, X2630:$o, X2631:$i, X2632:$i, X2633:$i, X2634:$o, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2655:$i, X2656:$i, X2657:$i, X2659:$i, X2660:$i, X2661:$i, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$i, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$o, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i]:((((~(in @ (esk1_2 @ X1919 @ X1920) @ X1919)|~(in @ (esk1_2 @ X1919 @ X1920) @ X1920)|((X1919)=(X1920)))&((in @ (esk1_2 @ X1919 @ X1920) @ X1919)|(in @ (esk1_2 @ X1919 @ X1920) @ X1920)|((X1919)=(X1920))))&(~(in @ X1922 @ emptyset)&(((~(in @ X1925 @ (setadjoin @ X1923 @ X1924))|(((X1925)=(X1923))|(in @ X1925 @ X1924)))&((((X1925)!=(X1923))|(in @ X1925 @ (setadjoin @ X1923 @ X1924)))&(~(in @ X1925 @ X1924)|(in @ X1925 @ (setadjoin @ X1923 @ X1924)))))&(((~(in @ X1927 @ (powerset @ X1926))|(~(in @ X1928 @ X1927)|(in @ X1928 @ X1926)))&(((in @ (esk2_2 @ X1929 @ X1930) @ X1930)|(in @ X1930 @ (powerset @ X1929)))&(~(in @ (esk2_2 @ X1929 @ X1930) @ X1929)|(in @ X1930 @ (powerset @ X1929)))))&(((((in @ X1933 @ (esk3_2 @ X1932 @ X1933))|~(in @ X1933 @ (setunion @ X1932)))&((in @ (esk3_2 @ X1932 @ X1933) @ X1932)|~(in @ X1933 @ (setunion @ X1932))))&(~(in @ X1936 @ X1937)|~(in @ X1937 @ X1935)|(in @ X1936 @ (setunion @ X1935))))&((in @ emptyset @ omega)&((~(in @ X1938 @ omega)|(in @ (setadjoin @ X1938 @ X1938) @ omega))&(((((in @ (esk4_1 @ X1939) @ omega)|~(in @ emptyset @ X1939)|(~(in @ X1941 @ omega)|(in @ X1941 @ X1939)))&((in @ (esk4_1 @ X1939) @ X1939)|~(in @ emptyset @ X1939)|(~(in @ X1941 @ omega)|(in @ X1941 @ X1939))))&(~(in @ (setadjoin @ (esk4_1 @ X1939) @ (esk4_1 @ X1939)) @ X1939)|~(in @ emptyset @ X1939)|(~(in @ X1941 @ omega)|(in @ X1941 @ X1939))))&((((((in @ (esk8_3 @ X1942 @ X1943 @ X1948) @ X1943)|~(in @ X1948 @ (esk7_2 @ X1942 @ X1943))|(in @ (esk5_2 @ X1942 @ X1943) @ X1943))&((X1942 @ (esk8_3 @ X1942 @ X1943 @ X1948) @ X1948)|~(in @ X1948 @ (esk7_2 @ X1942 @ X1943))|(in @ (esk5_2 @ X1942 @ X1943) @ X1943)))&(~(in @ X1951 @ X1943)|~(X1942 @ X1951 @ X1950)|(in @ X1950 @ (esk7_2 @ X1942 @ X1943))|(in @ (esk5_2 @ X1942 @ X1943) @ X1943)))&(((((in @ (esk8_3 @ X1942 @ X1943 @ X1948) @ X1943)|~(in @ X1948 @ (esk7_2 @ X1942 @ X1943))|((X1942 @ (esk5_2 @ X1942 @ X1943) @ (esk6_3 @ X1942 @ X1943 @ X1945))|~(X1942 @ (esk5_2 @ X1942 @ X1943) @ X1945)))&((X1942 @ (esk8_3 @ X1942 @ X1943 @ X1948) @ X1948)|~(in @ X1948 @ (esk7_2 @ X1942 @ X1943))|((X1942 @ (esk5_2 @ X1942 @ X1943) @ (esk6_3 @ X1942 @ X1943 @ X1945))|~(X1942 @ (esk5_2 @ X1942 @ X1943) @ X1945))))&(~(in @ X1951 @ X1943)|~(X1942 @ X1951 @ X1950)|(in @ X1950 @ (esk7_2 @ X1942 @ X1943))|((X1942 @ (esk5_2 @ X1942 @ X1943) @ (esk6_3 @ X1942 @ X1943 @ X1945))|~(X1942 @ (esk5_2 @ X1942 @ X1943) @ X1945))))&((((in @ (esk8_3 @ X1942 @ X1943 @ X1948) @ X1943)|~(in @ X1948 @ (esk7_2 @ X1942 @ X1943))|(((X1945)!=(esk6_3 @ X1942 @ X1943 @ X1945))|~(X1942 @ (esk5_2 @ X1942 @ X1943) @ X1945)))&((X1942 @ (esk8_3 @ X1942 @ X1943 @ X1948) @ X1948)|~(in @ X1948 @ (esk7_2 @ X1942 @ X1943))|(((X1945)!=(esk6_3 @ X1942 @ X1943 @ X1945))|~(X1942 @ (esk5_2 @ X1942 @ X1943) @ X1945))))&(~(in @ X1951 @ X1943)|~(X1942 @ X1951 @ X1950)|(in @ X1950 @ (esk7_2 @ X1942 @ X1943))|(((X1945)!=(esk6_3 @ X1942 @ X1943 @ X1945))|~(X1942 @ (esk5_2 @ X1942 @ X1943) @ X1945))))))&((((in @ (esk9_1 @ X1952) @ X1952)|~(in @ X1953 @ X1952))&(~(in @ X1955 @ (esk9_1 @ X1952))|~(in @ X1955 @ X1952)|~(in @ X1953 @ X1952)))&((epred1_0)&((((X1956 @ (esk10_2 @ X1956 @ X1957))|~(X1956 @ X1957)|(X1956 @ (descr @ X1956)))&(((X1957)!=(esk10_2 @ X1956 @ X1957))|~(X1956 @ X1957)|(X1956 @ (descr @ X1956))))&((~(in @ X1961 @ X1959)|(~(X1960 @ X1961)|(in @ X1961 @ (dsetconstr @ X1959 @ X1960))))&((~(in @ X1964 @ (dsetconstr @ X1962 @ X1963))|(in @ X1964 @ X1962))&((~(in @ X1967 @ (dsetconstr @ X1965 @ X1966))|(X1966 @ X1967))&(((((X1968 @ (esk12_1 @ X1968))|((X1968 @ (esk11_2 @ X1968 @ X1969))|~(X1968 @ X1969)))&(~(X1968 @ X1972)|((esk12_1 @ X1968)=(X1972))|((X1968 @ (esk11_2 @ X1968 @ X1969))|~(X1968 @ X1969))))&(((X1968 @ (esk12_1 @ X1968))|(((X1969)!=(esk11_2 @ X1968 @ X1969))|~(X1968 @ X1969)))&(~(X1968 @ X1972)|((esk12_1 @ X1968)=(X1972))|(((X1969)!=(esk11_2 @ X1968 @ X1969))|~(X1968 @ X1969)))))&((~(in @ X1974 @ (prop2set @ ((X1973))))|(X1973))&((~(in @ X1975 @ emptyset)|(X1976))&((~(in @ X1977 @ emptyset)|~($true))&(~(in @ X1978 @ emptyset)&((((X1979 @ (esk13_2 @ X1979 @ X1980))|~(X1979 @ X1980)|(X1979 @ (esk14_1 @ X1979)))&(((X1980)!=(esk13_2 @ X1979 @ X1980))|~(X1979 @ X1980)|(X1979 @ (esk14_1 @ X1979))))&(((((in @ (esk16_2 @ X1983 @ X1984) @ X1984)|((X1983)=(X1984))|(in @ (esk15_2 @ X1983 @ X1984) @ X1983))&(~(in @ (esk16_2 @ X1983 @ X1984) @ X1983)|((X1983)=(X1984))|(in @ (esk15_2 @ X1983 @ X1984) @ X1983)))&(((in @ (esk16_2 @ X1983 @ X1984) @ X1984)|((X1983)=(X1984))|~(in @ (esk15_2 @ X1983 @ X1984) @ X1984))&(~(in @ (esk16_2 @ X1983 @ X1984) @ X1983)|((X1983)=(X1984))|~(in @ (esk15_2 @ X1983 @ X1984) @ X1984))))&(((in @ (esk17_1 @ X1987) @ X1987)|((X1987)=(emptyset)))&(((in @ (esk18_1 @ X1989) @ X1989)|((X1989)=(emptyset)))&(((~(in @ X1993 @ (dsetconstr @ X1991 @ X1992))|(X1992 @ X1993)|~(in @ X1993 @ X1991))&(~(X1992 @ X1993)|(in @ X1993 @ (dsetconstr @ X1991 @ X1992))|~(in @ X1993 @ X1991)))&((((X1994)=(emptyset))|(in @ (esk19_1 @ X1994) @ X1994))&((~(in @ X1998 @ X1996)|(~(X1997 @ X1998)|((dsetconstr @ X1996 @ X1997)!=(emptyset))))&((~(in @ X2000 @ X1999)|((X1999)!=(emptyset)))&((in @ X2001 @ (setadjoin @ X2001 @ X2002))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X2005 @ X2004)|(in @ X2005 @ (setadjoin @ X2003 @ X2004)))&(((((in @ X2008 @ X2007)|(X2009)|((X2008)=(X2006))|~(in @ X2008 @ (setadjoin @ X2006 @ X2007)))&(~(X2009)|(X2009)|((X2008)=(X2006))|~(in @ X2008 @ (setadjoin @ X2006 @ X2007))))&(((in @ X2008 @ X2007)|(X2009)|~(X2009)|~(in @ X2008 @ (setadjoin @ X2006 @ X2007)))&(~(X2009)|(X2009)|~(X2009)|~(in @ X2008 @ (setadjoin @ X2006 @ X2007)))))&((~(in @ X2012 @ (setadjoin @ X2010 @ X2011))|(((X2012)=(X2010))|(in @ X2012 @ X2011)))&(((dsetconstr @ X2013 @ (^[Z0:$i]:($true)))=(X2013))&((((in @ (esk20_2 @ X2014 @ X2015) @ X2015)|(in @ X2015 @ (powerset @ X2014)))&(~(in @ (esk20_2 @ X2014 @ X2015) @ X2014)|(in @ X2015 @ (powerset @ X2014))))&((in @ emptyset @ (powerset @ X2017))&((in @ emptyset @ (powerset @ X2018))&((~(in @ X2020 @ (powerset @ X2019))|(~(in @ X2021 @ X2020)|(in @ X2021 @ X2019)))&((~(in @ X2023 @ X2024)|(~(in @ X2024 @ X2022)|(in @ X2023 @ (setunion @ X2022))))&((((in @ X2026 @ (esk21_3 @ X2025 @ X2026 @ X2027))|(X2027)|~(in @ X2026 @ (setunion @ 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@ X2670))|(~(in @ X2672 @ X2670)|((in @ X2672 @ (setminus @ X2670 @ X2671))|(in @ X2672 @ X2671))))&((~(in @ X2674 @ (powerset @ X2673))|(~(in @ X2675 @ (powerset @ X2673))|(~(in @ X2676 @ X2673)|((in @ X2676 @ X2674)|~(in @ X2676 @ (binintersect @ X2674 @ X2675))))))&((~(in @ X2678 @ (powerset @ X2677))|(~(in @ X2679 @ (powerset @ X2677))|(~(in @ X2680 @ X2677)|((in @ X2680 @ X2679)|~(in @ X2680 @ (binintersect @ X2678 @ X2679))))))&((~(in @ X2682 @ (powerset @ X2681))|(~(in @ X2683 @ (powerset @ X2681))|(~(in @ X2684 @ X2681)|(~(subset @ X2682 @ (setminus @ X2681 @ X2683))|(~(in @ X2684 @ X2683)|~(in @ X2684 @ X2682))))))&((~(in @ X2686 @ (powerset @ X2685))|(~(in @ X2687 @ (powerset @ X2685))|(~(in @ X2688 @ X2685)|(~(subset @ X2686 @ X2687)|((in @ X2688 @ X2687)|~(in @ X2688 @ X2686))))))&((~(in @ X2690 @ (powerset @ X2689))|(~(in @ X2691 @ (powerset @ X2689))|(~(subset @ X2690 @ X2691)|(subset @ (setminus @ X2689 @ X2691) @ (setminus @ X2689 @ X2690)))))&((~(in @ X2693 @ (powerset @ X2692))|(~(in @ X2694 @ (powerset @ X2692))|(~(subset @ (setminus @ X2692 @ X2694) @ (setminus @ X2692 @ X2693))|(subset @ X2693 @ X2694))))&((~(in @ X2696 @ (powerset @ X2695))|(~(in @ X2697 @ X2695)|(~(in @ X2697 @ X2696)|(in @ X2697 @ (setminus @ X2695 @ (setminus @ X2695 @ X2696))))))&((~(in @ X2699 @ (powerset @ X2698))|(~(in @ X2700 @ X2698)|(~(in @ X2700 @ (setminus @ X2698 @ (setminus @ X2698 @ X2699)))|(in @ X2700 @ X2699))))&((~(in @ X2702 @ (powerset @ X2701))|(subset @ X2702 @ (setminus @ X2701 @ (setminus @ X2701 @ X2702))))&((~(in @ X2704 @ (powerset @ X2703))|(subset @ (setminus @ X2703 @ (setminus @ X2703 @ X2704)) @ X2704))&((~(in @ X2706 @ (powerset @ X2705))|((X2706)=(setminus @ X2705 @ (setminus @ X2705 @ X2706))))&((~(in @ X2708 @ (powerset @ X2707))|(~(in @ X2709 @ (powerset @ X2707))|(~(in @ X2710 @ X2707)|(~(in @ X2710 @ (setminus @ X2707 @ X2708))|~(in @ X2710 @ (binintersect @ X2708 @ X2709))))))&((~(in @ X2712 @ (powerset @ X2711))|(~(in @ X2713 @ (powerset @ X2711))|(~(in @ X2714 @ X2711)|(~(in @ X2714 @ (setminus @ X2711 @ X2712))|(in @ X2714 @ (setminus @ X2711 @ (binintersect @ X2712 @ X2713)))))))&((~(in @ X2716 @ (powerset @ X2715))|(~(in @ X2717 @ (powerset @ X2715))|(subset @ (setminus @ X2715 @ X2716) @ (setminus @ X2715 @ (binintersect @ X2716 @ X2717)))))&((~(in @ X2719 @ (powerset @ X2718))|(~(in @ X2720 @ (powerset @ X2718))|(in @ (setminus @ X2718 @ X2719) @ (powerset @ (setminus @ X2718 @ (binintersect @ X2719 @ X2720))))))&((~(in @ X2722 @ (powerset @ X2721))|(~(in @ X2723 @ (powerset @ X2721))|(~(subset @ X2722 @ (setminus @ X2721 @ X2723))|(~(in @ X2724 @ X2721)|(~(in @ X2724 @ X2723)|(in @ X2724 @ (setminus @ X2721 @ X2722)))))))&((~(in @ X2726 @ (powerset @ X2725))|(~(in @ X2727 @ (powerset @ X2725))|(~(subset @ X2726 @ (setminus @ X2725 @ X2727))|(subset @ X2727 @ (setminus @ X2725 @ X2726)))))&((~(in @ X2729 @ (powerset @ X2728))|(~(in @ X2730 @ (powerset @ X2728))|(~(in @ X2731 @ X2728)|((in @ X2731 @ (binunion @ X2729 @ X2730))|~(in @ X2731 @ X2729)))))&((~(in @ X2733 @ (powerset @ X2732))|(~(in @ X2734 @ (powerset @ X2732))|(~(in @ X2735 @ X2732)|((in @ X2735 @ (binunion @ X2733 @ X2734))|~(in @ X2735 @ X2734)))))&((~(in @ X2737 @ (powerset @ X2736))|(~(in @ X2738 @ (powerset @ X2736))|(~(in @ X2739 @ (powerset @ X2736))|(~(in @ X2740 @ X2736)|(~(in @ X2740 @ (binintersect @ X2737 @ X2738))|(in @ X2740 @ (binunion @ X2737 @ X2739)))))))&((~(in @ X2742 @ (powerset @ X2741))|(~(in @ X2743 @ (powerset @ X2741))|(~(in @ X2744 @ (powerset @ X2741))|(~(in @ X2745 @ X2741)|(~(in @ X2745 @ (binintersect @ X2742 @ X2743))|(in @ X2745 @ (binunion @ X2743 @ X2744)))))))&((~(in @ X2747 @ (powerset @ X2746))|(~(in @ X2748 @ (powerset @ X2746))|(~(in @ X2749 @ (powerset @ X2746))|(~(in @ X2750 @ X2746)|(~(in @ X2750 @ (binintersect @ X2747 @ X2748))|(in @ X2750 @ (binintersect @ (binunion @ X2747 @ X2749) @ (binunion @ X2748 @ X2749))))))))&((~(in @ X2752 @ (powerset @ X2751))|(~(in @ X2753 @ (powerset @ X2751))|(~(in @ X2754 @ (powerset @ X2751))|(in @ (binintersect @ X2752 @ X2753) @ (powerset @ (binintersect @ (binunion @ X2752 @ X2754) @ (binunion @ X2753 @ X2754)))))))&((~(in @ X2756 @ (powerset @ X2755))|(~(in @ X2757 @ (powerset @ X2755))|(~(in @ X2758 @ X2755)|(~(in @ X2758 @ (setminus @ X2755 @ (binunion @ X2756 @ X2757)))|~(in @ X2758 @ X2756)))))&((~(in @ X2760 @ (powerset @ X2759))|(~(in @ X2761 @ (powerset @ X2759))|(~(in @ X2762 @ X2759)|(~(in @ X2762 @ (setminus @ X2759 @ (binunion @ X2760 @ X2761)))|(in @ X2762 @ (setminus @ X2759 @ X2760))))))&(((((in @ X2767 @ X2765)|(X2766)|(in @ X2767 @ X2764)|~(in @ X2767 @ (binunion @ X2764 @ X2765))|~(in @ X2767 @ X2763)|~(in @ X2765 @ (powerset @ X2763))|~(in @ X2764 @ (powerset @ X2763)))&(~(X2766)|(X2766)|(in @ X2767 @ X2764)|~(in @ X2767 @ (binunion @ X2764 @ X2765))|~(in @ X2767 @ X2763)|~(in @ X2765 @ (powerset @ X2763))|~(in @ X2764 @ (powerset @ X2763))))&(((in @ X2767 @ X2765)|(X2766)|~(X2766)|~(in @ X2767 @ (binunion @ X2764 @ X2765))|~(in @ X2767 @ X2763)|~(in @ X2765 @ (powerset @ X2763))|~(in @ X2764 @ (powerset @ X2763)))&(~(X2766)|(X2766)|~(X2766)|~(in @ X2767 @ (binunion @ X2764 @ X2765))|~(in @ X2767 @ X2763)|~(in @ X2765 @ (powerset @ X2763))|~(in @ X2764 @ (powerset @ X2763)))))&((~(in @ X2769 @ (powerset @ X2768))|(~(in @ X2770 @ (powerset @ X2768))|(~(in @ X2771 @ X2768)|((in @ X2771 @ X2769)|((in @ X2771 @ X2770)|~(in @ X2771 @ (binunion @ X2769 @ X2770)))))))&((~(in @ X2773 @ (powerset @ X2772))|(~(in @ X2774 @ (powerset @ X2772))|(~(in @ X2775 @ X2772)|(~(in @ X2775 @ (setminus @ X2772 @ (binunion @ X2773 @ X2774)))|(in @ X2775 @ (setminus @ X2772 @ X2773))))))&((~(in @ X2777 @ (powerset @ X2776))|(~(in @ X2778 @ (powerset @ X2776))|(in @ (setminus @ X2776 @ (binunion @ X2777 @ X2778)) @ (powerset @ (setminus @ X2776 @ X2777)))))&((~(in @ X2780 @ (powerset @ X2779))|(~(in @ X2781 @ (powerset @ X2779))|(~(in @ X2782 @ X2779)|(~(in @ X2782 @ (setminus @ X2779 @ (binunion @ X2780 @ X2781)))|(in @ X2782 @ (setminus @ X2779 @ X2781))))))&((~(in @ X2784 @ (powerset @ X2783))|(~(in @ X2785 @ (powerset @ X2783))|(~(in @ X2786 @ X2783)|(~(in @ X2786 @ (setminus @ X2783 @ (binintersect @ X2784 @ X2785)))|(in @ X2786 @ (binunion @ (setminus @ X2783 @ X2784) @ (setminus @ X2783 @ X2785)))))))&((~(in @ X2788 @ (powerset @ X2787))|(~(in @ X2789 @ (powerset @ X2787))|(~(in @ X2790 @ X2787)|(~(in @ X2790 @ (binunion @ (setminus @ X2787 @ X2788) @ (setminus @ X2787 @ X2789)))|(in @ X2790 @ (setminus @ X2787 @ (binintersect @ X2788 @ X2789)))))))&((~(in @ X2792 @ (powerset @ X2791))|(~(in @ X2793 @ (powerset @ X2791))|((setminus @ X2791 @ (binintersect @ X2792 @ X2793))=(binunion @ (setminus @ X2791 @ X2792) @ (setminus @ X2791 @ X2793)))))&((~(in @ X2795 @ (powerset @ X2794))|(~(in @ X2796 @ (powerset @ X2794))|(~(in @ X2797 @ X2794)|(~(in @ X2797 @ (setminus @ X2794 @ (binunion @ X2795 @ X2796)))|(in @ X2797 @ (binintersect @ (setminus @ X2794 @ X2795) @ (setminus @ X2794 @ X2796)))))))&((~(in @ X2799 @ (powerset @ X2798))|(~(in @ X2800 @ (powerset @ X2798))|(~(in @ X2801 @ X2798)|(~(in @ X2801 @ (setminus @ X2798 @ X2799))|(~(in @ X2801 @ (setminus @ X2798 @ X2800))|(in @ X2801 @ (setminus @ X2798 @ (binunion @ X2799 @ X2800))))))))&((~(in @ X2803 @ (powerset @ X2802))|(~(in @ X2804 @ (powerset @ X2802))|(~(in @ X2805 @ X2802)|(~(in @ X2805 @ (binintersect @ (setminus @ X2802 @ X2803) @ (setminus @ X2802 @ X2804)))|(in @ X2805 @ (setminus @ X2802 @ (binunion @ X2803 @ X2804)))))))&((~(in @ X2807 @ (powerset @ X2806))|(~(in @ X2808 @ (powerset @ X2806))|((setminus @ X2806 @ (binunion @ X2807 @ X2808))=(binintersect @ (setminus @ X2806 @ X2807) @ (setminus @ X2806 @ X2808)))))&((~(in @ X2810 @ (powerset @ X2809))|(~(in @ X2811 @ (powerset @ X2809))|(~(in @ X2812 @ (binintersect @ X2810 @ X2811))|(in @ X2812 @ X2809))))&((~(in @ X2814 @ (powerset @ X2813))|(~(in @ X2815 @ (powerset @ X2813))|(~(in @ X2816 @ (powerset @ X2813))|(~(subset @ X2814 @ X2816)|(subset @ (binintersect @ X2814 @ X2815) @ X2816)))))&((~(in @ X2818 @ (powerset @ X2817))|(~(in @ X2819 @ (powerset @ X2817))|(~(in @ X2820 @ (powerset @ X2817))|(~(subset @ X2819 @ X2820)|(subset @ (binintersect @ X2818 @ X2819) @ X2820)))))&((~(in @ X2822 @ (powerset @ X2821))|(~(in @ X2823 @ (powerset @ X2821))|(~(in @ X2824 @ (powerset @ X2821))|(~(subset @ X2822 @ X2823)|(~(subset @ X2822 @ X2824)|(subset @ X2822 @ (binintersect @ X2823 @ X2824)))))))&((~(in @ X2826 @ (powerset @ X2825))|(~(in @ X2827 @ (powerset @ X2825))|(~(in @ X2828 @ (powerset @ X2825))|(~(in @ X2829 @ (powerset @ X2825))|(~(subset @ X2826 @ X2828)|(~(subset @ X2827 @ X2829)|(subset @ (binintersect @ X2826 @ X2827) @ (binintersect @ X2828 @ X2829))))))))&((~(in @ X2831 @ (powerset @ X2830))|(~(in @ X2832 @ (powerset @ X2830))|(in @ (setminus @ X2830 @ X2831) @ (powerset @ (setminus @ X2830 @ (binintersect @ X2831 @ X2832))))))&((~(in @ X2834 @ (powerset @ X2833))|(~(in @ X2835 @ (powerset @ X2833))|(~(in @ X2836 @ (powerset @ X2833))|(~(in @ X2837 @ (powerset @ X2833))|((setminus @ X2833 @ (binintersect @ (binunion @ X2834 @ X2835) @ (binunion @ X2836 @ X2837)))=(binunion @ (binintersect @ (setminus @ X2833 @ X2834) @ (setminus @ X2833 @ X2835)) @ (binintersect @ (setminus @ X2833 @ X2836) @ (setminus @ X2833 @ X2837))))))))&((~(in @ X2839 @ (powerset @ X2838))|(~(in @ X2840 @ (powerset @ X2838))|(~(in @ X2841 @ (powerset @ X2838))|(in @ (binintersect @ X2839 @ X2840) @ (powerset @ (binintersect @ (binunion @ X2839 @ X2841) @ (binunion @ X2840 @ X2841)))))))&((~(in @ X2843 @ (powerset @ X2842))|(~(in @ X2844 @ (powerset @ X2842))|(~(subset @ X2843 @ (setminus @ X2842 @ X2844))|(subset @ X2844 @ (setminus @ X2842 @ X2843)))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&~(in @ (setminus @ esk87_0 @ (binunion @ esk88_0 @ esk89_0)) @ (powerset @ (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_370])])])])])])])).
% 2.52/0.76  thf(c_0_372, negated_conjecture, ~((in @ (setminus @ esk87_0 @ (binunion @ esk88_0 @ esk89_0)) @ (powerset @ (setminus @ esk87_0 @ esk88_0)))), inference(split_conjunct,[status(thm)],[c_0_371])).
% 2.52/0.76  thf(c_0_373, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ (setminus @ X3 @ (binunion @ X2 @ X4)) @ (powerset @ (setminus @ X3 @ X2)))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_371])).
% 2.52/0.76  thf(c_0_374, negated_conjecture, (in @ esk89_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_371])).
% 2.52/0.76  thf(c_0_375, negated_conjecture, (in @ esk88_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_371])).
% 2.52/0.76  thf(c_0_376, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_372, c_0_373]), c_0_374]), c_0_375])]), ['proof']).
% 2.52/0.76  % SZS output end CNFRefutation
% 2.52/0.76  % Parsed axioms                        : 609
% 2.52/0.76  % Removed by relevancy pruning/SinE    : 0
% 2.52/0.76  % Initial clauses                      : 791
% 2.52/0.76  % Removed in clause preprocessing      : 353
% 2.52/0.76  % Initial clauses in saturation        : 438
% 2.52/0.76  % Processed clauses                    : 2112
% 2.52/0.76  % ...of these trivial                  : 108
% 2.52/0.76  % ...subsumed                          : 1210
% 2.52/0.76  % ...remaining for further processing  : 794
% 2.52/0.76  % Other redundant clauses eliminated   : 29
% 2.52/0.76  % Clauses deleted for lack of memory   : 0
% 2.52/0.76  % Backward-subsumed                    : 8
% 2.52/0.76  % Backward-rewritten                   : 19
% 2.52/0.76  % Generated clauses                    : 27080
% 2.52/0.76  % ...of the previous two non-redundant : 23382
% 2.52/0.76  % ...aggressively subsumed             : 0
% 2.52/0.76  % Contextual simplify-reflections      : 8
% 2.52/0.76  % Paramodulations                      : 27046
% 2.52/0.76  % Factorizations                       : 2
% 2.52/0.76  % NegExts                              : 0
% 2.52/0.76  % Equation resolutions                 : 32
% 2.52/0.76  % Disequality decompositions           : 0
% 2.52/0.76  % Total rewrite steps                  : 7078
% 2.52/0.76  % ...of those cached                   : 6631
% 2.52/0.76  % Propositional unsat checks           : 0
% 2.52/0.76  %    Propositional check models        : 0
% 2.52/0.76  %    Propositional check unsatisfiable : 0
% 2.52/0.76  %    Propositional clauses             : 0
% 2.52/0.76  %    Propositional clauses after purity: 0
% 2.52/0.76  %    Propositional unsat core size     : 0
% 2.52/0.76  %    Propositional preprocessing time  : 0.000
% 2.52/0.76  %    Propositional encoding time       : 0.000
% 2.52/0.76  %    Propositional solver time         : 0.000
% 2.52/0.76  %    Success case prop preproc time    : 0.000
% 2.52/0.76  %    Success case prop encoding time   : 0.000
% 2.52/0.76  %    Success case prop solver time     : 0.000
% 2.52/0.76  % Current number of processed clauses  : 758
% 2.52/0.76  %    Positive orientable unit clauses  : 291
% 2.52/0.76  %    Positive unorientable unit clauses: 0
% 2.52/0.76  %    Negative unit clauses             : 15
% 2.52/0.76  %    Non-unit-clauses                  : 452
% 2.52/0.76  % Current number of unprocessed clauses: 21511
% 2.52/0.76  % ...number of literals in the above   : 66300
% 2.52/0.76  % Current number of archived formulas  : 0
% 2.52/0.76  % Current number of archived clauses   : 27
% 2.52/0.76  % Clause-clause subsumption calls (NU) : 26361
% 2.52/0.76  % Rec. Clause-clause subsumption calls : 19794
% 2.52/0.76  % Non-unit clause-clause subsumptions  : 839
% 2.52/0.76  % Unit Clause-clause subsumption calls : 702
% 2.52/0.76  % Rewrite failures with RHS unbound    : 0
% 2.52/0.76  % BW rewrite match attempts            : 808
% 2.52/0.76  % BW rewrite match successes           : 13
% 2.52/0.76  % Condensation attempts                : 0
% 2.52/0.76  % Condensation successes               : 0
% 2.52/0.76  % Termbank termtop insertions          : 474054
% 2.52/0.76  % Search garbage collected termcells   : 30129
% 2.52/0.76  
% 2.52/0.76  % -------------------------------------------------
% 2.52/0.76  % User time                : 0.387 s
% 2.52/0.76  % System time              : 0.023 s
% 2.52/0.76  % Total time               : 0.410 s
% 2.52/0.76  % Maximum resident set size: 10668 pages
% 2.52/0.76  
% 2.52/0.76  % -------------------------------------------------
% 2.52/0.76  % User time                : 0.605 s
% 2.52/0.76  % System time              : 0.110 s
% 2.52/0.76  % Total time               : 0.715 s
% 2.52/0.76  % Maximum resident set size: 5888 pages
% 2.52/0.76  % E exiting
%------------------------------------------------------------------------------