E---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SEU653^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:24:53 AM UTC 2026

% Result   : Theorem 201.52s 29.12s
% Output   : CNFRefutation 201.52s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01  % Problem  : SEU653^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10  % Computer : n012.cluster.edu
% 0.00/0.10  % Model    : x86_64 x86_64
% 0.00/0.10  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10  % Memory   : 8046.5625MB
% 0.00/0.10  % OS       : Linux 6.8.0-71-generic
% 0.00/0.10  % CPULimit : 300
% 0.00/0.10  % WCLimit  : 300
% 0.00/0.10  % DateTime : Tue Sep 29 14:02:33 UTC 2026
% 0.00/0.10  % CPUTime  : 
% 0.00/0.10  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13  Running higher-order theorem proving
% 0.08/0.15  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.S5vwxXPMTM/E---3.1_151674.p
% 201.52/29.12  % Version: 3.5.1-ho
% 201.52/29.12  % Preprocessing class: HSLMSLSSLLLCHFA.
% 201.52/29.12  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 201.52/29.12  % Starting ehoh_best5 with 300s (1) cores
% 201.52/29.12  % Starting almost_fo_3_lam with 300s (1) cores
% 201.52/29.12  % Starting new_bool_5 with 300s (1) cores
% 201.52/29.12  % Starting pre_casc_3 with 300s (1) cores
% 201.52/29.12  % Starting ho_unfolding_8 with 300s (1) cores
% 201.52/29.12  % Starting new_ho_10_cnf2 with 300s (1) cores
% 201.52/29.12  % Starting new_bool_3 with 300s (1) cores
% 201.52/29.12  % Starting new_ho_5 with 300s (1) cores
% 201.52/29.12  % ho_unfolding_8 with pid 151691 completed with status 0
% 201.52/29.12  % Result found by ho_unfolding_8
% 201.52/29.12  % Preprocessing class: HSLMSLSSLLLCHFA.
% 201.52/29.12  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 201.52/29.12  % Starting ehoh_best5 with 300s (1) cores
% 201.52/29.12  % Starting almost_fo_3_lam with 300s (1) cores
% 201.52/29.12  % Starting new_bool_5 with 300s (1) cores
% 201.52/29.12  % Starting pre_casc_3 with 300s (1) cores
% 201.52/29.12  % Starting ho_unfolding_8 with 300s (1) cores
% 201.52/29.12  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 201.52/29.12  % No SInE strategy applied
% 201.52/29.12  % Search class: HGHSM-FSLM31-MHFMMSBN
% 201.52/29.12  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 201.52/29.12  % Starting SubtermCWHack with 28s (1) cores
% 201.52/29.12  % SubtermCWHack with pid 151701 completed with status 8
% 201.52/29.12  % Starting ho_unfolding_8 with 31s (1) cores
% 201.52/29.12  % ho_unfolding_8 with pid 152432 completed with status 0
% 201.52/29.12  % Result found by ho_unfolding_8
% 201.52/29.12  % Preprocessing class: HSLMSLSSLLLCHFA.
% 201.52/29.12  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 201.52/29.12  % Starting ehoh_best5 with 300s (1) cores
% 201.52/29.12  % Starting almost_fo_3_lam with 300s (1) cores
% 201.52/29.12  % Starting new_bool_5 with 300s (1) cores
% 201.52/29.12  % Starting pre_casc_3 with 300s (1) cores
% 201.52/29.12  % Starting ho_unfolding_8 with 300s (1) cores
% 201.52/29.12  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 201.52/29.12  % No SInE strategy applied
% 201.52/29.12  % Search class: HGHSM-FSLM31-MHFMMSBN
% 201.52/29.12  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 201.52/29.12  % Starting SubtermCWHack with 28s (1) cores
% 201.52/29.12  % SubtermCWHack with pid 151701 completed with status 8
% 201.52/29.12  % Starting ho_unfolding_8 with 31s (1) cores
% 201.52/29.12  % Preprocessing time       : 0.102 s
% 201.52/29.12  % Presaturation interreduction done
% 201.52/29.12  
% 201.52/29.12  % Proof found!
% 201.52/29.12  % SZS status Theorem
% 201.52/29.12  % SZS output start CNFRefutation
% 201.52/29.12  thf(decl_23, type, in: $i > $i > $o).
% 201.52/29.12  thf(decl_24, type, exu: ($i > $o) > $o).
% 201.52/29.12  thf(decl_25, type, setextAx: $o).
% 201.52/29.12  thf(decl_26, type, emptyset: $i).
% 201.52/29.12  thf(decl_27, type, emptysetAx: $o).
% 201.52/29.12  thf(decl_28, type, setadjoin: $i > $i > $i).
% 201.52/29.12  thf(decl_29, type, setadjoinAx: $o).
% 201.52/29.12  thf(decl_30, type, powerset: $i > $i).
% 201.52/29.12  thf(decl_31, type, powersetAx: $o).
% 201.52/29.12  thf(decl_32, type, setunion: $i > $i).
% 201.52/29.12  thf(decl_33, type, setunionAx: $o).
% 201.52/29.12  thf(decl_34, type, omega: $i).
% 201.52/29.12  thf(decl_35, type, omega0Ax: $o).
% 201.52/29.12  thf(decl_36, type, omegaSAx: $o).
% 201.52/29.12  thf(decl_37, type, omegaIndAx: $o).
% 201.52/29.12  thf(decl_38, type, replAx: $o).
% 201.52/29.12  thf(decl_39, type, foundationAx: $o).
% 201.52/29.12  thf(decl_40, type, wellorderingAx: $o).
% 201.52/29.12  thf(decl_41, type, descr: ($i > $o) > $i).
% 201.52/29.12  thf(decl_42, type, descrp: $o).
% 201.52/29.12  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_44, type, dsetconstrI: $o).
% 201.52/29.12  thf(decl_45, type, dsetconstrEL: $o).
% 201.52/29.12  thf(decl_46, type, dsetconstrER: $o).
% 201.52/29.12  thf(decl_47, type, exuE1: $o).
% 201.52/29.12  thf(decl_48, type, prop2set: $o > $i).
% 201.52/29.12  thf(decl_49, type, prop2setE: $o).
% 201.52/29.12  thf(decl_50, type, emptysetE: $o).
% 201.52/29.12  thf(decl_51, type, emptysetimpfalse: $o).
% 201.52/29.12  thf(decl_52, type, notinemptyset: $o).
% 201.52/29.12  thf(decl_53, type, exuE3e: $o).
% 201.52/29.12  thf(decl_54, type, setext: $o).
% 201.52/29.12  thf(decl_55, type, emptyI: $o).
% 201.52/29.12  thf(decl_56, type, noeltsimpempty: $o).
% 201.52/29.12  thf(decl_57, type, setbeta: $o).
% 201.52/29.12  thf(decl_58, type, nonempty: $i > $o).
% 201.52/29.12  thf(decl_59, type, nonemptyE1: $o).
% 201.52/29.12  thf(decl_60, type, nonemptyI: $o).
% 201.52/29.12  thf(decl_61, type, nonemptyI1: $o).
% 201.52/29.12  thf(decl_62, type, setadjoinIL: $o).
% 201.52/29.12  thf(decl_63, type, emptyinunitempty: $o).
% 201.52/29.12  thf(decl_64, type, setadjoinIR: $o).
% 201.52/29.12  thf(decl_65, type, setadjoinE: $o).
% 201.52/29.12  thf(decl_66, type, setadjoinOr: $o).
% 201.52/29.12  thf(decl_67, type, setoftrueEq: $o).
% 201.52/29.12  thf(decl_68, type, powersetI: $o).
% 201.52/29.12  thf(decl_69, type, emptyinPowerset: $o).
% 201.52/29.12  thf(decl_70, type, emptyInPowerset: $o).
% 201.52/29.12  thf(decl_71, type, powersetE: $o).
% 201.52/29.12  thf(decl_72, type, setunionI: $o).
% 201.52/29.12  thf(decl_73, type, setunionE: $o).
% 201.52/29.12  thf(decl_74, type, subPowSU: $o).
% 201.52/29.12  thf(decl_75, type, exuE2: $o).
% 201.52/29.12  thf(decl_76, type, nonemptyImpWitness: $o).
% 201.52/29.12  thf(decl_77, type, uniqinunit: $o).
% 201.52/29.12  thf(decl_78, type, notinsingleton: $o).
% 201.52/29.12  thf(decl_79, type, eqinunit: $o).
% 201.52/29.12  thf(decl_80, type, singletonsswitch: $o).
% 201.52/29.12  thf(decl_81, type, upairsetE: $o).
% 201.52/29.12  thf(decl_82, type, upairsetIL: $o).
% 201.52/29.12  thf(decl_83, type, upairsetIR: $o).
% 201.52/29.12  thf(decl_84, type, emptyE1: $o).
% 201.52/29.12  thf(decl_85, type, vacuousDall: $o).
% 201.52/29.12  thf(decl_86, type, quantDeMorgan1: $o).
% 201.52/29.12  thf(decl_87, type, quantDeMorgan2: $o).
% 201.52/29.12  thf(decl_88, type, quantDeMorgan3: $o).
% 201.52/29.12  thf(decl_89, type, quantDeMorgan4: $o).
% 201.52/29.12  thf(decl_90, type, prop2setI: $o).
% 201.52/29.12  thf(decl_91, type, set2prop: $i > $o).
% 201.52/29.12  thf(decl_92, type, prop2set2propI: $o).
% 201.52/29.12  thf(decl_93, type, notdexE: $o).
% 201.52/29.12  thf(decl_94, type, notdallE: $o).
% 201.52/29.12  thf(decl_95, type, exuI1: $o).
% 201.52/29.12  thf(decl_96, type, exuI3: $o).
% 201.52/29.12  thf(decl_97, type, exuI2: $o).
% 201.52/29.12  thf(decl_98, type, inCongP: $o).
% 201.52/29.12  thf(decl_99, type, in__Cong: $o).
% 201.52/29.12  thf(decl_100, type, exuE3u: $o).
% 201.52/29.12  thf(decl_101, type, exu__Cong: $o).
% 201.52/29.12  thf(decl_102, type, emptyset__Cong: $o).
% 201.52/29.12  thf(decl_103, type, setadjoin__Cong: $o).
% 201.52/29.12  thf(decl_104, type, powerset__Cong: $o).
% 201.52/29.12  thf(decl_105, type, setunion__Cong: $o).
% 201.52/29.12  thf(decl_106, type, omega__Cong: $o).
% 201.52/29.12  thf(decl_107, type, exuEu: $o).
% 201.52/29.12  thf(decl_108, type, descr__Cong: $o).
% 201.52/29.12  thf(decl_109, type, dsetconstr__Cong: $o).
% 201.52/29.12  thf(decl_110, type, subset: $i > $i > $o).
% 201.52/29.12  thf(decl_113, type, subsetI1: $o).
% 201.52/29.12  thf(decl_114, type, eqimpsubset2: $o).
% 201.52/29.12  thf(decl_115, type, eqimpsubset1: $o).
% 201.52/29.12  thf(decl_116, type, subsetI2: $o).
% 201.52/29.12  thf(decl_117, type, emptysetsubset: $o).
% 201.52/29.12  thf(decl_118, type, subsetE: $o).
% 201.52/29.12  thf(decl_119, type, subsetE2: $o).
% 201.52/29.12  thf(decl_120, type, notsubsetI: $o).
% 201.52/29.12  thf(decl_121, type, notequalI1: $o).
% 201.52/29.12  thf(decl_122, type, notequalI2: $o).
% 201.52/29.12  thf(decl_123, type, subsetRefl: $o).
% 201.52/29.12  thf(decl_124, type, subsetTrans: $o).
% 201.52/29.12  thf(decl_125, type, setadjoinSub: $o).
% 201.52/29.12  thf(decl_126, type, setadjoinSub2: $o).
% 201.52/29.12  thf(decl_127, type, subset2powerset: $o).
% 201.52/29.12  thf(decl_128, type, setextsub: $o).
% 201.52/29.12  thf(decl_129, type, subsetemptysetimpeq: $o).
% 201.52/29.12  thf(decl_130, type, powersetI1: $o).
% 201.52/29.12  thf(decl_131, type, powersetE1: $o).
% 201.52/29.12  thf(decl_132, type, inPowerset: $o).
% 201.52/29.12  thf(decl_133, type, powersetsubset: $o).
% 201.52/29.12  thf(decl_134, type, sepInPowerset: $o).
% 201.52/29.12  thf(decl_135, type, sepSubset: $o).
% 201.52/29.12  thf(decl_136, type, binunion: $i > $i > $i).
% 201.52/29.12  thf(decl_137, type, binunionIL: $o).
% 201.52/29.12  thf(decl_138, type, upairset2IR: $o).
% 201.52/29.12  thf(decl_139, type, binunionIR: $o).
% 201.52/29.12  thf(decl_140, type, binunionEcases: $o).
% 201.52/29.12  thf(decl_141, type, binunionE: $o).
% 201.52/29.12  thf(decl_142, type, binunionLsub: $o).
% 201.52/29.12  thf(decl_143, type, binunionRsub: $o).
% 201.52/29.12  thf(decl_144, type, binintersect: $i > $i > $i).
% 201.52/29.12  thf(decl_145, type, binintersectI: $o).
% 201.52/29.12  thf(decl_146, type, binintersectSubset5: $o).
% 201.52/29.12  thf(decl_147, type, binintersectEL: $o).
% 201.52/29.12  thf(decl_148, type, binintersectLsub: $o).
% 201.52/29.12  thf(decl_149, type, binintersectSubset2: $o).
% 201.52/29.12  thf(decl_150, type, binintersectSubset3: $o).
% 201.52/29.12  thf(decl_151, type, binintersectER: $o).
% 201.52/29.12  thf(decl_152, type, disjointsetsI1: $o).
% 201.52/29.12  thf(decl_153, type, binintersectRsub: $o).
% 201.52/29.12  thf(decl_154, type, binintersectSubset4: $o).
% 201.52/29.12  thf(decl_155, type, binintersectSubset1: $o).
% 201.52/29.12  thf(decl_156, type, bs114d: $o).
% 201.52/29.12  thf(decl_158, type, setminus: $i > $i > $i).
% 201.52/29.12  thf(decl_159, type, setminusI: $o).
% 201.52/29.12  thf(decl_160, type, setminusEL: $o).
% 201.52/29.12  thf(decl_161, type, setminusER: $o).
% 201.52/29.12  thf(decl_162, type, setminusSubset2: $o).
% 201.52/29.12  thf(decl_163, type, setminusERneg: $o).
% 201.52/29.12  thf(decl_164, type, setminusELneg: $o).
% 201.52/29.12  thf(decl_165, type, setminusILneg: $o).
% 201.52/29.12  thf(decl_166, type, setminusIRneg: $o).
% 201.52/29.12  thf(decl_167, type, setminusLsub: $o).
% 201.52/29.12  thf(decl_168, type, setminusSubset1: $o).
% 201.52/29.12  thf(decl_169, type, symdiff: $i > $i > $i).
% 201.52/29.12  thf(decl_170, type, symdiffE: $o).
% 201.52/29.12  thf(decl_171, type, symdiffI1: $o).
% 201.52/29.12  thf(decl_172, type, symdiffI2: $o).
% 201.52/29.12  thf(decl_173, type, symdiffIneg1: $o).
% 201.52/29.12  thf(decl_174, type, symdiffIneg2: $o).
% 201.52/29.12  thf(decl_175, type, iskpair: $i > $o).
% 201.52/29.12  thf(decl_176, type, secondinupair: $o).
% 201.52/29.12  thf(decl_177, type, setukpairIL: $o).
% 201.52/29.12  thf(decl_178, type, setukpairIR: $o).
% 201.52/29.12  thf(decl_179, type, kpairiskpair: $o).
% 201.52/29.12  thf(decl_180, type, kpair: $i > $i > $i).
% 201.52/29.12  thf(decl_181, type, kpairp: $o).
% 201.52/29.12  thf(decl_182, type, cartprod: $i > $i > $i).
% 201.52/29.12  thf(decl_183, type, singletonsubset: $o).
% 201.52/29.12  thf(decl_184, type, singletoninpowerset: $o).
% 201.52/29.12  thf(decl_185, type, singletoninpowunion: $o).
% 201.52/29.12  thf(decl_186, type, upairset2E: $o).
% 201.52/29.12  thf(decl_187, type, upairsubunion: $o).
% 201.52/29.12  thf(decl_188, type, upairinpowunion: $o).
% 201.52/29.12  thf(decl_189, type, ubforcartprodlem1: $o).
% 201.52/29.12  thf(decl_190, type, ubforcartprodlem2: $o).
% 201.52/29.12  thf(decl_191, type, ubforcartprodlem3: $o).
% 201.52/29.12  thf(decl_192, type, cartprodpairin: $o).
% 201.52/29.12  thf(decl_193, type, cartprodmempair1: $o).
% 201.52/29.12  thf(decl_194, type, cartprodmempair: $o).
% 201.52/29.12  thf(decl_195, type, setunionE2: $o).
% 201.52/29.12  thf(decl_196, type, setunionsingleton1: $o).
% 201.52/29.12  thf(decl_197, type, setunionsingleton2: $o).
% 201.52/29.12  thf(decl_198, type, setunionsingleton: $o).
% 201.52/29.12  thf(decl_199, type, singleton: $i > $o).
% 201.52/29.12  thf(decl_200, type, singletonprop: $o).
% 201.52/29.12  thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 201.52/29.12  thf(decl_202, type, ex1E1: $o).
% 201.52/29.12  thf(decl_203, type, ex1I: $o).
% 201.52/29.12  thf(decl_204, type, ex1I2: $o).
% 201.52/29.12  thf(decl_205, type, singletonsuniq: $o).
% 201.52/29.12  thf(decl_210, type, setukpairinjL1: $o).
% 201.52/29.12  thf(decl_211, type, kfstsingleton: $o).
% 201.52/29.12  thf(decl_212, type, theprop: $o).
% 201.52/29.12  thf(decl_213, type, kfst: $i > $i).
% 201.52/29.12  thf(decl_214, type, kfstpairEq: $o).
% 201.52/29.12  thf(decl_215, type, cartprodfstin: $o).
% 201.52/29.12  thf(decl_216, type, setukpairinjL2: $o).
% 201.52/29.12  thf(decl_217, type, setukpairinjL: $o).
% 201.52/29.12  thf(decl_218, type, setukpairinjR11: $o).
% 201.52/29.12  thf(decl_219, type, setukpairinjR12: $o).
% 201.52/29.12  thf(decl_220, type, setukpairinjR1: $o).
% 201.52/29.12  thf(decl_221, type, upairequniteq: $o).
% 201.52/29.12  thf(decl_222, type, epred1_0: $o).
% 201.52/29.12  thf(decl_223, type, esk1_2: $i > $i > $i).
% 201.52/29.12  thf(decl_224, type, esk2_2: $i > $i > $i).
% 201.52/29.12  thf(decl_225, type, esk3_2: $i > $i > $i).
% 201.52/29.12  thf(decl_226, type, esk4_1: $i > $i).
% 201.52/29.12  thf(decl_227, type, esk5_2: ($i > $i > $o) > $i > $i).
% 201.52/29.12  thf(decl_228, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 201.52/29.12  thf(decl_229, type, esk7_2: ($i > $i > $o) > $i > $i).
% 201.52/29.12  thf(decl_230, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 201.52/29.12  thf(decl_231, type, esk9_1: $i > $i).
% 201.52/29.12  thf(decl_232, type, esk10_2: ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_233, type, esk11_2: ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_234, type, esk12_1: ($i > $o) > $i).
% 201.52/29.12  thf(decl_235, type, esk13_2: ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_236, type, esk14_1: ($i > $o) > $i).
% 201.52/29.12  thf(decl_237, type, esk15_2: $i > $i > $i).
% 201.52/29.12  thf(decl_238, type, esk16_2: $i > $i > $i).
% 201.52/29.12  thf(decl_239, type, esk17_1: $i > $i).
% 201.52/29.12  thf(decl_240, type, esk18_1: $i > $i).
% 201.52/29.12  thf(decl_241, type, esk19_1: $i > $i).
% 201.52/29.12  thf(decl_242, type, esk20_2: $i > $i > $i).
% 201.52/29.12  thf(decl_243, type, esk21_3: $i > $i > $o > $i).
% 201.52/29.12  thf(decl_244, type, esk22_2: ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_245, type, esk23_1: ($i > $o) > $i).
% 201.52/29.12  thf(decl_246, type, esk24_1: $i > $i).
% 201.52/29.12  thf(decl_247, type, esk25_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_248, type, esk26_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_249, type, esk27_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_250, type, esk28_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_251, type, esk29_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_252, type, esk30_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_253, type, esk31_2: ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_254, type, esk32_1: ($i > $o) > $i).
% 201.52/29.12  thf(decl_255, type, esk33_1: ($i > $o) > $i).
% 201.52/29.12  thf(decl_256, type, esk34_1: ($i > $o) > $i).
% 201.52/29.12  thf(decl_257, type, esk35_1: ($i > $o) > $i).
% 201.52/29.12  thf(decl_258, type, esk36_2: ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_259, type, esk37_1: ($i > $o) > $i).
% 201.52/29.12  thf(decl_260, type, esk38_2: ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_261, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 201.52/29.12  thf(decl_262, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 201.52/29.12  thf(decl_263, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_264, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 201.52/29.12  thf(decl_265, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_266, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 201.52/29.12  thf(decl_267, type, esk45_2: ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_268, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 201.52/29.12  thf(decl_269, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 201.52/29.12  thf(decl_270, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_271, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_272, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 201.52/29.12  thf(decl_273, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 201.52/29.12  thf(decl_274, type, esk52_2: $i > $i > $i).
% 201.52/29.12  thf(decl_275, type, esk53_2: $i > $i > $i).
% 201.52/29.12  thf(decl_276, type, esk54_2: $i > $i > $i).
% 201.52/29.12  thf(decl_277, type, esk55_2: $i > $i > $i).
% 201.52/29.12  thf(decl_278, type, esk56_2: $i > $i > $i).
% 201.52/29.12  thf(decl_279, type, esk57_2: $i > $i > $i).
% 201.52/29.12  thf(decl_280, type, esk58_2: $i > $i > $i).
% 201.52/29.12  thf(decl_281, type, esk59_3: $i > $i > $i > $i).
% 201.52/29.12  thf(decl_282, type, esk60_3: $i > $i > $i > $i).
% 201.52/29.12  thf(decl_283, type, esk61_3: $i > $i > $i > $i).
% 201.52/29.12  thf(decl_284, type, esk62_3: $i > $i > $i > $i).
% 201.52/29.12  thf(decl_285, type, esk63_2: $i > $i > $i).
% 201.52/29.12  thf(decl_286, type, esk64_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_287, type, esk65_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_288, type, esk66_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_289, type, esk67_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_290, type, esk68_3: $i > ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_291, type, esk69_3: $i > ($i > $o) > $i > $i).
% 201.52/29.12  thf(decl_292, type, esk70_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_293, type, esk71_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_294, type, esk72_2: $i > ($i > $o) > $i).
% 201.52/29.12  thf(decl_295, type, esk73_1: $i > $i).
% 201.52/29.12  thf(decl_296, type, esk74_0: $i).
% 201.52/29.12  thf(decl_297, type, esk75_0: $i).
% 201.52/29.12  thf(decl_298, type, esk76_0: $i).
% 201.52/29.12  thf(decl_299, type, esk77_0: $i).
% 201.52/29.12  thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', ex1)).
% 201.52/29.12  thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', singleton)).
% 201.52/29.12  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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', replAx)).
% 201.52/29.12  thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', exu)).
% 201.52/29.12  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', descrp)).
% 201.52/29.12  thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', exuE1)).
% 201.52/29.12  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', exuE3e)).
% 201.52/29.12  thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', nonempty)).
% 201.52/29.12  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', nonemptyI)).
% 201.52/29.12  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', exuE2)).
% 201.52/29.12  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.S5vwxXPMTM/E---3.1_151674.p', exuI1)).
% 201.52/29.12  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', exuI3)).
% 201.52/29.12  thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', exuI2)).
% 201.52/29.12  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.S5vwxXPMTM/E---3.1_151674.p', exuE3u)).
% 201.52/29.12  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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', exu__Cong)).
% 201.52/29.12  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', exuEu)).
% 201.52/29.12  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', descr__Cong)).
% 201.52/29.12  thf(iskpair, axiom, ((iskpair)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ (setunion @ X4)))&(?[X3:$i]:((((in @ X3 @ (setunion @ X4)))&(((X4)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', iskpair)).
% 201.52/29.12  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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', singletonprop)).
% 201.52/29.12  thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', ex1E1)).
% 201.52/29.12  thf(ex1I, axiom, ((ex1I)<=>![X4:$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.S5vwxXPMTM/E---3.1_151674.p', ex1I)).
% 201.52/29.12  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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', ex1I2)).
% 201.52/29.12  thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', kfstsingleton)).
% 201.52/29.12  thf(setukpairinjR2, 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)=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setukpairinjR2)).
% 201.52/29.12  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', dsetconstrI)).
% 201.52/29.12  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', dsetconstrEL)).
% 201.52/29.12  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', dsetconstrER)).
% 201.52/29.12  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setbeta)).
% 201.52/29.12  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', nonemptyE1)).
% 201.52/29.12  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', nonemptyI1)).
% 201.52/29.12  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setoftrueEq)).
% 201.52/29.12  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', nonemptyImpWitness)).
% 201.52/29.12  thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.S5vwxXPMTM/E---3.1_151674.p', emptyE1)).
% 201.52/29.12  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', dsetconstr__Cong)).
% 201.52/29.12  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', sepInPowerset)).
% 201.52/29.12  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', sepSubset)).
% 201.52/29.12  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.S5vwxXPMTM/E---3.1_151674.p', kpairiskpair)).
% 201.52/29.12  thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', kpairp)).
% 201.52/29.12  thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', cartprodmempair)).
% 201.52/29.12  thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', theprop)).
% 201.52/29.12  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setextAx)).
% 201.52/29.12  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', emptysetAx)).
% 201.52/29.12  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setadjoinAx)).
% 201.52/29.12  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', powersetAx)).
% 201.52/29.12  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setunionAx)).
% 201.52/29.12  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', omega0Ax)).
% 201.52/29.12  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', omegaSAx)).
% 201.52/29.12  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', omegaIndAx)).
% 201.52/29.12  thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', foundationAx)).
% 201.52/29.12  thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.S5vwxXPMTM/E---3.1_151674.p', wellorderingAx)).
% 201.52/29.12  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', prop2setE)).
% 201.52/29.12  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', emptysetE)).
% 201.52/29.12  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', emptysetimpfalse)).
% 201.52/29.12  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', notinemptyset)).
% 201.52/29.12  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setext)).
% 201.52/29.12  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', emptyI)).
% 201.52/29.12  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', noeltsimpempty)).
% 201.52/29.12  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setadjoinIL)).
% 201.52/29.12  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', emptyinunitempty)).
% 201.52/29.12  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setadjoinIR)).
% 201.52/29.12  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.S5vwxXPMTM/E---3.1_151674.p', setadjoinE)).
% 201.52/29.12  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setadjoinOr)).
% 201.52/29.12  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', powersetI)).
% 201.52/29.12  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', emptyinPowerset)).
% 201.52/29.12  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', emptyInPowerset)).
% 201.52/29.12  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', powersetE)).
% 201.52/29.12  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setunionI)).
% 201.52/29.12  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.S5vwxXPMTM/E---3.1_151674.p', setunionE)).
% 201.52/29.12  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', subPowSU)).
% 201.52/29.12  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', uniqinunit)).
% 201.52/29.12  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', notinsingleton)).
% 201.52/29.12  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', eqinunit)).
% 201.52/29.12  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', singletonsswitch)).
% 201.52/29.12  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', upairsetE)).
% 201.52/29.12  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', upairsetIL)).
% 201.52/29.12  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', upairsetIR)).
% 201.52/29.12  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', vacuousDall)).
% 201.52/29.12  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', quantDeMorgan1)).
% 201.52/29.12  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', quantDeMorgan2)).
% 201.52/29.12  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', quantDeMorgan3)).
% 201.52/29.12  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', quantDeMorgan4)).
% 201.52/29.12  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', prop2setI)).
% 201.52/29.12  thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', prop2set2propI)).
% 201.52/29.12  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', notdexE)).
% 201.52/29.12  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', notdallE)).
% 201.52/29.12  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', inCongP)).
% 201.52/29.12  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', in__Cong)).
% 201.52/29.12  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', emptyset__Cong)).
% 201.52/29.12  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setadjoin__Cong)).
% 201.52/29.12  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', powerset__Cong)).
% 201.52/29.12  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setunion__Cong)).
% 201.52/29.12  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', omega__Cong)).
% 201.52/29.12  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', subsetI1)).
% 201.52/29.12  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', eqimpsubset2)).
% 201.52/29.12  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', eqimpsubset1)).
% 201.52/29.12  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', subsetI2)).
% 201.52/29.12  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', emptysetsubset)).
% 201.52/29.12  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', subsetE)).
% 201.52/29.12  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', subsetE2)).
% 201.52/29.12  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', notsubsetI)).
% 201.52/29.12  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', notequalI1)).
% 201.52/29.12  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', notequalI2)).
% 201.52/29.12  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', subsetRefl)).
% 201.52/29.12  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', subsetTrans)).
% 201.52/29.12  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setadjoinSub)).
% 201.52/29.12  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setadjoinSub2)).
% 201.52/29.12  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', subset2powerset)).
% 201.52/29.12  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setextsub)).
% 201.52/29.12  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', subsetemptysetimpeq)).
% 201.52/29.12  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', powersetI1)).
% 201.52/29.12  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', powersetE1)).
% 201.52/29.12  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', inPowerset)).
% 201.52/29.12  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', powersetsubset)).
% 201.52/29.12  thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binunionIL)).
% 201.52/29.12  thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', upairset2IR)).
% 201.52/29.12  thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binunionIR)).
% 201.52/29.12  thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binunionEcases)).
% 201.52/29.12  thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binunionE)).
% 201.52/29.12  thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binunionLsub)).
% 201.52/29.12  thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binunionRsub)).
% 201.52/29.12  thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binintersectI)).
% 201.52/29.12  thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binintersectSubset5)).
% 201.52/29.12  thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binintersectEL)).
% 201.52/29.12  thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binintersectLsub)).
% 201.52/29.12  thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binintersectSubset2)).
% 201.52/29.12  thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binintersectSubset3)).
% 201.52/29.12  thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binintersectER)).
% 201.52/29.12  thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', disjointsetsI1)).
% 201.52/29.12  thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binintersectRsub)).
% 201.52/29.12  thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binintersectSubset4)).
% 201.52/29.12  thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', binintersectSubset1)).
% 201.52/29.12  thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', bs114d)).
% 201.52/29.12  thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setminusI)).
% 201.52/29.12  thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setminusEL)).
% 201.52/29.12  thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setminusER)).
% 201.52/29.12  thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setminusSubset2)).
% 201.52/29.12  thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setminusERneg)).
% 201.52/29.12  thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setminusELneg)).
% 201.52/29.12  thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setminusILneg)).
% 201.52/29.12  thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setminusIRneg)).
% 201.52/29.12  thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setminusLsub)).
% 201.52/29.12  thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setminusSubset1)).
% 201.52/29.12  thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', symdiffE)).
% 201.52/29.12  thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', symdiffI1)).
% 201.52/29.12  thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', symdiffI2)).
% 201.52/29.12  thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', symdiffIneg1)).
% 201.52/29.12  thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', symdiffIneg2)).
% 201.52/29.12  thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', secondinupair)).
% 201.52/29.12  thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setukpairIL)).
% 201.52/29.12  thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setukpairIR)).
% 201.52/29.12  thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', singletonsubset)).
% 201.52/29.12  thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', singletoninpowerset)).
% 201.52/29.12  thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', singletoninpowunion)).
% 201.52/29.12  thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', upairset2E)).
% 201.52/29.12  thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', upairsubunion)).
% 201.52/29.12  thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', upairinpowunion)).
% 201.52/29.12  thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', ubforcartprodlem1)).
% 201.52/29.12  thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', ubforcartprodlem2)).
% 201.52/29.12  thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', ubforcartprodlem3)).
% 201.52/29.12  thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', cartprodpairin)).
% 201.52/29.12  thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.S5vwxXPMTM/E---3.1_151674.p', cartprodmempair1)).
% 201.52/29.12  thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setunionE2)).
% 201.52/29.12  thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setunionsingleton1)).
% 201.52/29.12  thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setunionsingleton2)).
% 201.52/29.12  thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setunionsingleton)).
% 201.52/29.12  thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', singletonsuniq)).
% 201.52/29.12  thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setukpairinjL1)).
% 201.52/29.12  thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', kfstpairEq)).
% 201.52/29.12  thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', cartprodfstin)).
% 201.52/29.12  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.S5vwxXPMTM/E---3.1_151674.p', setukpairinjL2)).
% 201.52/29.12  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.S5vwxXPMTM/E---3.1_151674.p', setukpairinjL)).
% 201.52/29.12  thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', setukpairinjR11)).
% 201.52/29.12  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.S5vwxXPMTM/E---3.1_151674.p', setukpairinjR12)).
% 201.52/29.12  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.S5vwxXPMTM/E---3.1_151674.p', setukpairinjR1)).
% 201.52/29.12  thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', upairequniteq)).
% 201.52/29.12  thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.S5vwxXPMTM/E---3.1_151674.p', kpair)).
% 201.52/29.12  thf(c_0_176, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X521:$i]:((((in @ X521 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X521 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 201.52/29.12  thf(c_0_177, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 201.52/29.12  thf(c_0_178, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 201.52/29.12  thf(c_0_179, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 201.52/29.12  thf(c_0_180, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 201.52/29.12  thf(c_0_181, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 201.52/29.12  thf(c_0_182, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 201.52/29.12  thf(c_0_183, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 201.52/29.12  thf(c_0_184, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 201.52/29.12  thf(c_0_185, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 201.52/29.12  thf(c_0_186, 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])).
% 201.52/29.12  thf(c_0_187, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 201.52/29.12  thf(c_0_188, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 201.52/29.12  thf(c_0_189, 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])).
% 201.52/29.12  thf(c_0_190, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 201.52/29.12  thf(c_0_191, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 201.52/29.12  thf(c_0_192, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 201.52/29.12  thf(c_0_193, plain, ((iskpair)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ (setunion @ Z0)))&(?[X3:$i]:((((in @ X3 @ (setunion @ Z0)))&(((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))), inference(fof_simplification,[status(thm)],[iskpair])).
% 201.52/29.12  thf(c_0_194, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 201.52/29.12  thf(c_0_195, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 201.52/29.12  thf(c_0_196, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X521:$i]:((((in @ X521 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X521 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_176, c_0_177])).
% 201.52/29.12  thf(c_0_197, 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])).
% 201.52/29.12  thf(c_0_198, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 201.52/29.12  thf(c_0_199, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 201.52/29.12  thf(c_0_200, 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)=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setukpairinjR2])).
% 201.52/29.12  thf(c_0_201, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X486:$i]:(((((X6 @ X2 @ X486)))&(![X487:$i]:(((((X6 @ X2 @ X487)))=>(((X486)=(X487)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_178, c_0_179])).
% 201.52/29.12  thf(c_0_202, plain, ((descrp)=(![X1:$i > $o]:((((?[X488:$i]:(((((X1 @ X488)))&(![X489:$i]:(((((X1 @ X489)))=>(((X488)=(X489))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_180, c_0_179])).
% 201.52/29.12  thf(c_0_203, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 201.52/29.12  thf(c_0_204, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 201.52/29.12  thf(c_0_205, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 201.52/29.12  thf(c_0_206, plain, ((exuE1)=(![X1:$i > $o]:((((?[X490:$i]:(((((X1 @ X490)))&(![X491:$i]:(((((X1 @ X491)))=>(((X490)=(X491))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_181, c_0_179])).
% 201.52/29.12  thf(c_0_207, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X492:$i]:(((((X1 @ X492)))&(![X493:$i]:(((((X1 @ X493)))=>(((X492)=(X493))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_182, c_0_179])).
% 201.52/29.12  thf(c_0_208, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 201.52/29.12  thf(c_0_209, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_183])).
% 201.52/29.12  thf(c_0_210, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_184, c_0_183])).
% 201.52/29.12  thf(c_0_211, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_183])).
% 201.52/29.12  thf(c_0_212, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 201.52/29.12  thf(c_0_213, plain, ((exuE2)=(![X1:$i > $o]:((((?[X494:$i]:(((((X1 @ X494)))&(![X495:$i]:(((((X1 @ X495)))=>(((X494)=(X495))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_185, c_0_179])).
% 201.52/29.12  thf(c_0_214, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_183])).
% 201.52/29.12  thf(c_0_215, 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])).
% 201.52/29.12  thf(c_0_216, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X496:$i]:(((((X1 @ X496)))&(![X497:$i]:(((((X1 @ X497)))=>(((X496)=(X497)))))))))))))), inference(apply_def,[status(thm)],[c_0_186, c_0_179])).
% 201.52/29.12  thf(c_0_217, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X498:$i]:(((((X1 @ X498)))&(![X499:$i]:(((((X1 @ X499)))=>(((X498)=(X499)))))))))))))))), inference(apply_def,[status(thm)],[c_0_187, c_0_179])).
% 201.52/29.12  thf(c_0_218, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X500:$i]:(((((X1 @ X500)))&(![X501:$i]:(((((X1 @ X501)))=>(((X500)=(X501)))))))))))))), inference(apply_def,[status(thm)],[c_0_188, c_0_179])).
% 201.52/29.12  thf(c_0_219, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X502:$i]:(((((X1 @ X502)))&(![X503:$i]:(((((X1 @ X503)))=>(((X502)=(X503))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_189, c_0_179])).
% 201.52/29.12  thf(c_0_220, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X504:$i]:(((((X1 @ X504)))&(![X505:$i]:(((((X1 @ X505)))=>(((X504)=(X505))))))))))<=>((?[X506:$i]:(((((X17 @ X506)))&(![X507:$i]:(((((X17 @ X507)))=>(((X506)=(X507)))))))))))))))), inference(apply_def,[status(thm)],[c_0_190, c_0_179])).
% 201.52/29.12  thf(c_0_221, plain, ((exuEu)=(![X1:$i > $o]:((((?[X508:$i]:(((((X1 @ X508)))&(![X509:$i]:(((((X1 @ X509)))=>(((X508)=(X509))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_191, c_0_179])).
% 201.52/29.12  thf(c_0_222, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X510:$i]:(((((X1 @ X510)))&(![X511:$i]:(((((X1 @ X511)))=>(((X510)=(X511))))))))))=>((((?[X512:$i]:(((((X17 @ X512)))&(![X513:$i]:(((((X17 @ X513)))=>(((X512)=(X513))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_192, c_0_179])).
% 201.52/29.12  thf(c_0_223, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 201.52/29.12  thf(c_0_224, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 201.52/29.12  thf(c_0_225, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 201.52/29.12  thf(c_0_226, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X514:$i]:((((in @ X514 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X515:$i]:((((in @ X515 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X514 @ emptyset) @ (setadjoin @ (setadjoin @ X514 @ (setadjoin @ X515 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_193])).
% 201.52/29.12  thf(c_0_227, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X516:$i]:((((in @ X516 @ (setunion @ (kpair @ X2 @ X3))))&(?[X517:$i]:((((in @ X517 @ (setunion @ (kpair @ X2 @ X3))))&(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X516 @ emptyset) @ (setadjoin @ (setadjoin @ X516 @ (setadjoin @ X517 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_193])).
% 201.52/29.12  thf(c_0_228, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:((((in @ X18 @ (cartprod @ X4 @ X5)))=>((?[X518:$i]:((((in @ X518 @ (setunion @ X18)))&(?[X519:$i]:((((in @ X519 @ (setunion @ X18)))&(((X18)=(setadjoin @ (setadjoin @ X518 @ emptyset) @ (setadjoin @ (setadjoin @ X518 @ (setadjoin @ X519 @ emptyset)) @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_193])).
% 201.52/29.12  thf(c_0_229, plain, ((singletonprop)=(![X4:$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)))))=>((?[X520:$i]:((((in @ X520 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X520 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_194, c_0_177])).
% 201.52/29.12  thf(c_0_230, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X522:$i]:((((in @ X522 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X522 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_195, c_0_196])).
% 201.52/29.12  thf(c_0_231, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X523:$i]:((((in @ X523 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X523 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_197, c_0_196])).
% 201.52/29.12  thf(c_0_232, 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)))))=>((?[X524:$i]:((((in @ X524 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X524 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_198, c_0_196])).
% 201.52/29.12  thf(c_0_233, plain, ((kfstsingleton)=(![X18:$i]:((((?[X525:$i]:((((in @ X525 @ (setunion @ X18)))&(?[X526:$i]:((((in @ X526 @ (setunion @ X18)))&(((X18)=(setadjoin @ (setadjoin @ X525 @ emptyset) @ (setadjoin @ (setadjoin @ X525 @ (setadjoin @ X526 @ emptyset)) @ emptyset)))))))))))=>((?[X527:$i]:((((in @ X527 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X527 @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_199, c_0_193]), c_0_177])).
% 201.52/29.12  thf(c_0_234, axiom, ((theprop)=(![X21:$i]:((((?[X528:$i]:((((in @ X528 @ X21))&(((X21)=(setadjoin @ X528 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_177])).
% 201.52/29.12  thf(c_0_235, plain, ((epred1_0)<=>![X558:$i]:(?[X559:$i]:((((![X560:$i]:(((in @ X560 @ X559)=>![X561:$i]:(((in @ X561 @ X560)=>(in @ X561 @ X558)))))&![X562:$i, X563:$i]:((((in @ X562 @ X558)&(in @ X563 @ X558))=>(![X564:$i]:(((in @ X564 @ X559)=>((in @ X562 @ X564)<=>(in @ X563 @ X564))))=>((X562)=(X563))))))&![X565:$i, X566:$i]:((((in @ X565 @ X559)&(in @ X566 @ X559))=>(![X567:$i]:(((in @ X567 @ X565)=>(in @ X567 @ X566)))|![X568:$i]:(((in @ X568 @ X566)=>(in @ X568 @ X565)))))))&![X569:$i]:(((![X570:$i]:(((in @ X570 @ X569)=>(in @ X570 @ X558)))&?[X571:$i]:((in @ X571 @ X569)))=>?[X572:$i, X573:$i]:(((((in @ X572 @ X559)&(in @ X573 @ X569))&~(?[X574:$i]:(((in @ X574 @ X572)&(in @ X574 @ X569)))))&![X575:$i]:(((in @ X575 @ X559)=>(![X576:$i]:(((in @ X576 @ X575)=>(in @ X576 @ X572)))|(in @ X573 @ X575)))))))))))), introduced(definition)).
% 201.52/29.12  thf(c_0_236, negated_conjecture, ~((![X529:$i, X530:$i]:((![X531:$i]:(((in @ X531 @ X529)<=>(in @ X531 @ X530)))=>((X529)=(X530))))=>(![X532:$i]:(~(in @ X532 @ emptyset))=>(![X533:$i, X534:$i, X535:$i]:(((in @ X535 @ (setadjoin @ X533 @ X534))<=>(((X535)=(X533))|(in @ X535 @ X534))))=>(![X536:$i, X537:$i]:(((in @ X537 @ (powerset @ X536))<=>![X538:$i]:(((in @ X538 @ X537)=>(in @ X538 @ X536)))))=>(![X539:$i, X540:$i]:(((in @ X540 @ (setunion @ X539))<=>?[X541:$i]:(((in @ X540 @ X541)&(in @ X541 @ X539)))))=>((in @ emptyset @ omega)=>(![X542:$i]:(((in @ X542 @ omega)=>(in @ (setadjoin @ X542 @ X542) @ omega)))=>(![X543:$i]:((((in @ emptyset @ X543)&![X544:$i]:((((in @ X544 @ omega)&(in @ X544 @ X543))=>(in @ (setadjoin @ X544 @ X544) @ X543))))=>![X545:$i]:(((in @ X545 @ omega)=>(in @ X545 @ X543)))))=>(![X546:$i > $i > $o, X547:$i]:((![X548:$i]:(((in @ X548 @ X547)=>?[X549:$i]:(((X546 @ X548 @ X549)&![X550:$i]:(((X546 @ X548 @ X550)=>((X549)=(X550))))))))=>?[X551:$i]:(![X552:$i]:(((in @ X552 @ X551)<=>?[X553:$i]:(((in @ X553 @ X547)&(X546 @ X553 @ X552))))))))=>(![X554:$i]:((?[X555:$i]:((in @ X555 @ X554))=>?[X556:$i]:(((in @ X556 @ X554)&~(?[X557:$i]:(((in @ X557 @ X556)&(in @ X557 @ X554))))))))=>((epred1_0)=>(![X577:$i > $o]:((?[X578:$i]:(((X577 @ X578)&![X579:$i]:(((X577 @ X579)=>((X578)=(X579))))))=>(X577 @ (descr @ (^[Z0:$i]:(X577 @ Z0))))))=>(![X580:$i, X581:$i > $o, X582:$i]:(((in @ X582 @ X580)=>((X581 @ X582)=>(in @ X582 @ (dsetconstr @ X580 @ X581)))))=>(![X583:$i, X584:$i > $o, X585:$i]:(((in @ X585 @ (dsetconstr @ X583 @ X584))=>(in @ X585 @ X583)))=>(![X586:$i, X587:$i > $o, X588:$i]:(((in @ X588 @ (dsetconstr @ X586 @ X587))=>(X587 @ X588)))=>(![X589:$i > $o]:((?[X590:$i]:(((X589 @ X590)&![X591:$i]:(((X589 @ X591)=>((X590)=(X591))))))=>?[X592:$i]:(((X589 @ X592)&![X593:$i]:(((X589 @ X593)=>((X592)=(X593))))))))=>(![X594:$o, X595:$i]:(((in @ X595 @ (prop2set @ ((X594))))=>(X594)))=>(![X596:$i]:(((in @ X596 @ emptyset)=>![X597:$o]:((X597))))=>(![X598:$i]:(((in @ X598 @ emptyset)=>~($true)))=>(![X599:$i]:(~(in @ X599 @ emptyset))=>(![X600:$i > $o]:((?[X601:$i]:(((X600 @ X601)&![X602:$i]:(((X600 @ X602)=>((X601)=(X602))))))=>?[X603:$i]:((X600 @ X603))))=>(![X604:$i, X605:$i]:((![X606:$i]:(((in @ X606 @ X604)=>(in @ X606 @ X605)))=>(![X607:$i]:(((in @ X607 @ X605)=>(in @ X607 @ X604)))=>((X604)=(X605)))))=>(![X608:$i]:((![X609:$i]:(~(in @ X609 @ X608))=>((X608)=(emptyset))))=>(![X610:$i]:((![X611:$i]:(~(in @ X611 @ X610))=>((X610)=(emptyset))))=>(![X612:$i, X613:$i > $o, X614:$i]:(((in @ X614 @ X612)=>((in @ X614 @ (dsetconstr @ X612 @ X613))<=>(X613 @ X614))))=>(![X615:$i]:((((X615)!=(emptyset))=>?[X616:$i]:((in @ X616 @ X615))))=>(![X617:$i, X618:$i > $o, X619:$i]:(((in @ X619 @ X617)=>((X618 @ X619)=>((dsetconstr @ X617 @ X618)!=(emptyset)))))=>(![X620:$i]:((?[X621:$i]:((in @ X621 @ X620))=>((X620)!=(emptyset))))=>(![X622:$i, X623:$i]:((in @ X622 @ (setadjoin @ X622 @ X623)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X624:$i, X625:$i, X626:$i]:(((in @ X626 @ X625)=>(in @ X626 @ (setadjoin @ X624 @ X625))))=>(![X627:$i, X628:$i, X629:$i]:(((in @ X629 @ (setadjoin @ X627 @ X628))=>![X630:$o]:(((((X629)=(X627))=>(X630))=>(((in @ X629 @ X628)=>(X630))=>(X630))))))=>(![X631:$i, X632:$i, X633:$i]:(((in @ X633 @ (setadjoin @ X631 @ X632))=>(((X633)=(X631))|(in @ X633 @ X632))))=>(![X634:$i]:(((dsetconstr @ X634 @ (^[Z0:$i]:($true)))=(X634)))=>(![X635:$i, X636:$i]:((![X637:$i]:(((in @ X637 @ X636)=>(in @ X637 @ X635)))=>(in @ X636 @ (powerset @ X635))))=>(![X638:$i]:((in @ emptyset @ (powerset @ X638)))=>(![X639:$i]:((in @ emptyset @ (powerset @ X639)))=>(![X640:$i, X641:$i, X642:$i]:(((in @ X641 @ (powerset @ X640))=>((in @ X642 @ X641)=>(in @ X642 @ X640))))=>(![X643:$i, X644:$i, X645:$i]:(((in @ X644 @ X645)=>((in @ X645 @ X643)=>(in @ X644 @ (setunion @ X643)))))=>(![X646:$i, X647:$i]:(((in @ X647 @ (setunion @ X646))=>![X648:$o]:((![X649:$i]:(((in @ X647 @ X649)=>((in @ X649 @ X646)=>(X648))))=>(X648)))))=>(![X650:$i, X651:$i]:(((in @ X651 @ X650)=>(in @ X651 @ (powerset @ (setunion @ X650)))))=>(![X652:$i > $o]:((?[X653:$i]:(((X652 @ X653)&![X654:$i]:(((X652 @ X654)=>((X653)=(X654))))))=>?[X655:$i]:(![X656:$i]:(((X652 @ X656)<=>((X656)=(X655)))))))=>(![X657:$i]:((((X657)!=(emptyset))=>?[X658:$i]:(((in @ X658 @ X657)&$true))))=>(![X659:$i, X660:$i]:(((in @ X659 @ (setadjoin @ X660 @ emptyset))=>((X659)=(X660))))=>(![X661:$i, X662:$i]:((((X661)!=(X662))=>~(in @ X662 @ (setadjoin @ X661 @ emptyset))))=>(![X663:$i, X664:$i]:((((X663)=(X664))=>(in @ X663 @ (setadjoin @ X664 @ emptyset))))=>(![X665:$i, X666:$i]:(((in @ X665 @ (setadjoin @ X666 @ emptyset))=>(in @ X666 @ (setadjoin @ X665 @ emptyset))))=>(![X667:$i, X668:$i, X669:$i]:(((in @ X669 @ (setadjoin @ X667 @ (setadjoin @ X668 @ emptyset)))=>(((X669)=(X667))|((X669)=(X668)))))=>(![X670:$i, X671:$i]:((in @ X670 @ (setadjoin @ X670 @ (setadjoin @ X671 @ emptyset))))=>(![X672:$i, X673:$i]:((in @ X673 @ (setadjoin @ X672 @ (setadjoin @ X673 @ emptyset))))=>(![X674:$i, X675:$i > $o]:((?[X676:$i]:(((in @ X676 @ X674)&(X675 @ X676)))=>(((dsetconstr @ X674 @ X675)=(emptyset))=>~($true))))=>(![X677:$i > $o, X678:$i]:(((in @ X678 @ emptyset)=>(X677 @ X678)))=>(![X679:$i, X680:$i > $o]:((~(![X681:$i]:(((in @ X681 @ X679)=>(X680 @ X681))))=>?[X682:$i]:(((in @ X682 @ X679)&~((X680 @ X682))))))=>(![X683:$i, X684:$i > $o]:((![X685:$i]:(((in @ X685 @ X683)=>~((X684 @ X685))))=>~(?[X686:$i]:(((in @ X686 @ X683)&(X684 @ X686))))))=>(![X687:$i, X688:$i > $o]:((~(?[X689:$i]:(((in @ X689 @ X687)&(X688 @ X689))))=>![X690:$i]:(((in @ X690 @ X687)=>~((X688 @ X690))))))=>(![X691:$i, X692:$i > $o]:((?[X693:$i]:(((in @ X693 @ X691)&~((X692 @ X693))))=>~(![X694:$i]:(((in @ X694 @ X691)=>(X692 @ X694))))))=>(![X695:$o]:(((X695)=>(in @ emptyset @ (prop2set @ ((X695))))))=>(![X696:$o]:(((X696)=>(set2prop @ (prop2set @ ((X696))))))=>(![X697:$i, X698:$i > $o]:((~(?[X699:$i]:(((in @ X699 @ X697)&(X698 @ X699))))=>![X700:$i]:(((in @ X700 @ X697)=>~((X698 @ X700))))))=>(![X701:$i, X702:$i > $o]:((~(![X703:$i]:(((in @ X703 @ X701)=>(X702 @ X703))))=>?[X704:$i]:(((in @ X704 @ X701)&~((X702 @ X704))))))=>(![X705:$i > $o]:((?[X706:$i]:(((X705 @ X706)&![X707:$i]:(((X705 @ X707)=>((X706)=(X707))))))=>?[X708:$i]:(((X705 @ X708)&![X709:$i]:(((X705 @ X709)=>((X708)=(X709))))))))=>(![X710:$i > $o]:((?[X711:$i]:((X710 @ X711))=>(![X712:$i, X713:$i]:(((X710 @ X712)=>((X710 @ X713)=>((X712)=(X713)))))=>?[X714:$i]:(((X710 @ X714)&![X715:$i]:(((X710 @ X715)=>((X714)=(X715)))))))))=>(![X716:$i > $o]:((?[X717:$i]:(![X718:$i]:(((X716 @ X718)<=>((X718)=(X717)))))=>?[X719:$i]:(((X716 @ X719)&![X720:$i]:(((X716 @ X720)=>((X719)=(X720))))))))=>(![X721:$i, X722:$i]:((((X721)=(X722))=>![X723:$i, X724:$i]:((((X723)=(X724))=>((in @ X723 @ X721)=>(in @ X724 @ X722))))))=>(![X725:$i, X726:$i]:((((X725)=(X726))=>![X727:$i, X728:$i]:((((X727)=(X728))=>((in @ X727 @ X725)<=>(in @ X728 @ X726))))))=>(![X729:$i > $o]:((?[X730:$i]:(((X729 @ X730)&![X731:$i]:(((X729 @ X731)=>((X730)=(X731))))))=>![X732:$i, X733:$i]:(((X729 @ X732)=>((X729 @ X733)=>((X732)=(X733)))))))=>(![X734:$i > $o, X735:$i > $o]:((![X736:$i, X737:$i]:((((X736)=(X737))=>((X734 @ X736)<=>(X735 @ X737))))=>(?[X738:$i]:(((X734 @ X738)&![X739:$i]:(((X734 @ X739)=>((X738)=(X739))))))<=>?[X740:$i]:(((X735 @ X740)&![X741:$i]:(((X735 @ X741)=>((X740)=(X741)))))))))=>(((emptyset)=(emptyset))=>(![X742:$i, X743:$i]:((((X742)=(X743))=>![X744:$i, X745:$i]:((((X744)=(X745))=>((setadjoin @ X742 @ X744)=(setadjoin @ X743 @ X745))))))=>(![X746:$i, X747:$i]:((((X746)=(X747))=>((powerset @ X746)=(powerset @ X747))))=>(![X748:$i, X749:$i]:((((X748)=(X749))=>((setunion @ X748)=(setunion @ X749))))=>(((omega)=(omega))=>(![X750:$i > $o]:((?[X751:$i]:(((X750 @ X751)&![X752:$i]:(((X750 @ X752)=>((X751)=(X752))))))=>![X753:$i, X754:$i]:(((X750 @ X753)=>((X750 @ X754)=>((X753)=(X754)))))))=>(![X755:$i > $o, X756:$i > $o]:((![X757:$i, X758:$i]:((((X757)=(X758))=>((X755 @ X757)<=>(X756 @ X758))))=>(?[X759:$i]:(((X755 @ X759)&![X760:$i]:(((X755 @ X760)=>((X759)=(X760))))))=>(?[X761:$i]:(((X756 @ X761)&![X762:$i]:(((X756 @ X762)=>((X761)=(X762))))))=>((descr @ X755)=(descr @ X756))))))=>(![X763:$i, X764:$i]:((((X763)=(X764))=>![X765:$i > $o, X766:$i > $o]:((![X767:$i]:(((in @ X767 @ X763)=>![X768:$i]:(((in @ X768 @ X764)=>(((X767)=(X768))=>((X765 @ X767)<=>(X766 @ X768)))))))=>((dsetconstr @ X763 @ X765)=(dsetconstr @ X764 @ X766))))))=>(![X769:$i, X770:$i]:((![X771:$i]:(((in @ X771 @ X769)=>(in @ X771 @ X770)))=>(subset @ X769 @ X770)))=>(![X772:$i, X773:$i]:((((X772)=(X773))=>(subset @ X773 @ X772)))=>(![X774:$i, X775:$i]:((((X774)=(X775))=>(subset @ X774 @ X775)))=>(![X776:$i, X777:$i]:((![X778:$i]:(((in @ X778 @ X776)=>(in @ X778 @ X777)))=>(subset @ X776 @ X777)))=>(![X779:$i]:((subset @ emptyset @ X779))=>(![X780:$i, X781:$i, X782:$i]:(((subset @ X780 @ X781)=>((in @ X782 @ 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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)],[c_0_200, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_201]), foundationAx]), wellorderingAx]), c_0_202]), c_0_203]), c_0_204]), c_0_205]), c_0_206]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_207]), setext]), emptyI]), noeltsimpempty]), c_0_208]), c_0_209]), c_0_210]), c_0_211]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_212]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_213]), c_0_214]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_215]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_216]), c_0_217]), c_0_218]), inCongP]), in__Cong]), c_0_219]), c_0_220]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_221]), c_0_222]), c_0_223]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_224]), c_0_225]), 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]), c_0_226]), c_0_227]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), c_0_228]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_229]), c_0_230]), c_0_231]), c_0_232]), singletonsuniq]), setukpairinjL1]), c_0_233]), c_0_234]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq])])]), c_0_235])).
% 201.52/29.12  thf(c_0_237, plain, ![X1031:$i, X1032:$i]:(((kpair @ X1031 @ X1032)=(setadjoin @ (setadjoin @ X1031 @ emptyset) @ (setadjoin @ (setadjoin @ X1031 @ (setadjoin @ X1032 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])])).
% 201.52/29.12  thf(c_0_238, negated_conjecture, ![X1035:$i, X1036:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1048:$i, X1049:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1057:$i, X1058:$i > $i > $o, X1059:$i, X1061:$i, X1064:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1071:$i, X1072:$i > $o, X1073:$i, X1075:$i, X1076:$i > $o, X1077:$i, X1078:$i, X1079:$i > $o, X1080:$i, X1081:$i, X1082:$i > $o, X1083:$i, X1084:$i > $o, X1085:$i, X1088:$i, X1089:$o, X1090:$i, X1091:$i, X1092:$o, X1093:$i, X1094:$i, X1095:$i > $o, X1096:$i, X1099:$i, X1100:$i, X1103:$i, X1105:$i, X1107:$i, X1108:$i > $o, X1109:$i, X1110:$i, X1112:$i, X1113:$i > $o, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$o, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$o, X1145:$i, X1146:$i, X1147:$i > $o, X1148:$i, X1151:$i, X1152:$i, X1153:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i > $o, X1172:$i, X1173:$i > $o, X1174:$i, X1175:$i, X1176:$i > $o, X1177:$i, X1179:$i, X1180:$i > $o, X1182:$i, X1183:$i, X1184:$i > $o, X1186:$i, X1187:$i, X1188:$i > $o, X1189:$i, X1191:$o, X1192:$o, X1193:$i, X1194:$i > $o, X1196:$i, X1197:$i, X1198:$i > $o, X1199:$i, X1201:$i > $o, X1202:$i, X1205:$i, X1206:$i > $o, X1207:$i, X1211:$i, X1212:$i > $o, X1213:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i > $o, X1226:$i, X1228:$i, X1229:$i, X1230:$i > $o, X1231:$i > $o, X1234:$i, X1237:$i, X1238:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i > $o, X1251:$i, X1253:$i, X1254:$i, X1255:$i > $o, X1256:$i > $o, X1259:$i, X1261:$i, X1263:$i, X1264:$i, X1265:$i > $o, X1266:$i > $o, X1269:$i, X1270:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i > $o, X1317:$i, X1318:$i > $o, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$o, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$o, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1421:$i, X1422:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1464:$i, X1465:$i, X1466:$i, X1469:$i, X1470:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i > $o, X1479:$i, X1481:$i, X1482:$i > $o, X1483:$i, X1485:$i, X1486:$i > $o, X1487:$i, X1490:$i, X1491:$i > $o, X1494:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i]:((((~(in @ (esk1_2 @ X1035 @ X1036) @ X1035)|~(in @ (esk1_2 @ X1035 @ X1036) @ X1036)|((X1035)=(X1036)))&((in @ (esk1_2 @ X1035 @ X1036) @ X1035)|(in @ (esk1_2 @ X1035 @ X1036) @ X1036)|((X1035)=(X1036))))&(~(in @ X1038 @ emptyset)&(((~(in @ X1041 @ (setadjoin @ X1039 @ X1040))|(((X1041)=(X1039))|(in @ X1041 @ X1040)))&((((X1041)!=(X1039))|(in @ X1041 @ (setadjoin @ X1039 @ X1040)))&(~(in @ X1041 @ X1040)|(in @ X1041 @ (setadjoin @ X1039 @ X1040)))))&(((~(in @ X1043 @ (powerset @ X1042))|(~(in @ X1044 @ X1043)|(in @ X1044 @ X1042)))&(((in @ (esk2_2 @ X1045 @ X1046) @ X1046)|(in @ X1046 @ (powerset @ X1045)))&(~(in @ (esk2_2 @ X1045 @ X1046) @ X1045)|(in @ X1046 @ (powerset @ X1045)))))&(((((in @ X1049 @ (esk3_2 @ X1048 @ X1049))|~(in @ X1049 @ (setunion @ X1048)))&((in @ (esk3_2 @ X1048 @ X1049) @ X1048)|~(in @ X1049 @ (setunion @ X1048))))&(~(in @ X1052 @ X1053)|~(in @ X1053 @ X1051)|(in @ X1052 @ (setunion @ X1051))))&((in @ emptyset @ omega)&((~(in @ X1054 @ omega)|(in @ (setadjoin @ X1054 @ X1054) @ omega))&(((((in @ (esk4_1 @ X1055) @ omega)|~(in @ emptyset @ X1055)|(~(in @ X1057 @ omega)|(in @ X1057 @ X1055)))&((in @ (esk4_1 @ X1055) @ X1055)|~(in @ emptyset @ X1055)|(~(in @ X1057 @ omega)|(in @ X1057 @ X1055))))&(~(in @ (setadjoin @ (esk4_1 @ X1055) @ (esk4_1 @ X1055)) @ X1055)|~(in @ emptyset @ X1055)|(~(in @ X1057 @ omega)|(in @ X1057 @ X1055))))&((((((in @ (esk8_3 @ X1058 @ X1059 @ X1064) @ X1059)|~(in @ X1064 @ (esk7_2 @ X1058 @ X1059))|(in @ (esk5_2 @ X1058 @ X1059) @ X1059))&((X1058 @ (esk8_3 @ X1058 @ X1059 @ X1064) @ X1064)|~(in @ X1064 @ (esk7_2 @ X1058 @ X1059))|(in @ (esk5_2 @ X1058 @ X1059) @ X1059)))&(~(in @ X1067 @ X1059)|~(X1058 @ X1067 @ X1066)|(in @ X1066 @ (esk7_2 @ X1058 @ X1059))|(in @ (esk5_2 @ X1058 @ X1059) @ X1059)))&(((((in @ (esk8_3 @ X1058 @ X1059 @ X1064) @ X1059)|~(in @ X1064 @ (esk7_2 @ X1058 @ X1059))|((X1058 @ (esk5_2 @ X1058 @ X1059) @ (esk6_3 @ X1058 @ X1059 @ X1061))|~(X1058 @ (esk5_2 @ X1058 @ X1059) @ X1061)))&((X1058 @ (esk8_3 @ X1058 @ X1059 @ X1064) @ X1064)|~(in @ X1064 @ (esk7_2 @ X1058 @ X1059))|((X1058 @ (esk5_2 @ X1058 @ X1059) @ (esk6_3 @ X1058 @ X1059 @ X1061))|~(X1058 @ (esk5_2 @ X1058 @ X1059) @ X1061))))&(~(in @ X1067 @ X1059)|~(X1058 @ X1067 @ X1066)|(in @ X1066 @ (esk7_2 @ X1058 @ X1059))|((X1058 @ (esk5_2 @ X1058 @ X1059) @ (esk6_3 @ X1058 @ X1059 @ X1061))|~(X1058 @ (esk5_2 @ X1058 @ X1059) @ X1061))))&((((in @ (esk8_3 @ X1058 @ X1059 @ X1064) @ X1059)|~(in @ X1064 @ (esk7_2 @ X1058 @ X1059))|(((X1061)!=(esk6_3 @ X1058 @ X1059 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X1476))|(~(in @ X1479 @ X1475)|~(X1476 @ X1479))|((esk64_2 @ X1475 @ X1476)!=(esk65_2 @ X1475 @ X1476)))&(((dsetconstr @ X1475 @ X1476)=(setadjoin @ (esk66_2 @ X1475 @ X1476) @ emptyset))|(~(in @ X1479 @ X1475)|~(X1476 @ X1479))|((esk64_2 @ X1475 @ X1476)!=(esk65_2 @ X1475 @ X1476))))))))&((((in @ (esk67_2 @ X1481 @ X1482) @ X1481)|(~(in @ X1483 @ (dsetconstr @ X1481 @ X1482))|((dsetconstr @ X1481 @ X1482)!=(setadjoin @ X1483 @ emptyset))))&((X1482 @ (esk67_2 @ X1481 @ X1482))|(~(in @ X1483 @ (dsetconstr @ X1481 @ X1482))|((dsetconstr @ X1481 @ X1482)!=(setadjoin @ X1483 @ emptyset)))))&(((((in @ (esk69_3 @ X1485 @ X1486 @ X1487) @ (dsetconstr @ X1485 @ X1486))|(in @ (esk68_3 @ X1485 @ X1486 @ X1487) @ X1485)|~(X1486 @ X1487)|~(in @ X1487 @ X1485))&(((dsetconstr @ X1485 @ X1486)=(setadjoin @ (esk69_3 @ X1485 @ X1486 @ X1487) @ emptyset))|(in @ (esk68_3 @ X1485 @ X1486 @ X1487) @ X1485)|~(X1486 @ X1487)|~(in @ X1487 @ X1485)))&((((in @ (esk69_3 @ X1485 @ X1486 @ X1487) @ (dsetconstr @ X1485 @ X1486))|(X1486 @ (esk68_3 @ X1485 @ X1486 @ X1487))|~(X1486 @ X1487)|~(in @ X1487 @ X1485))&(((dsetconstr @ X1485 @ X1486)=(setadjoin @ (esk69_3 @ X1485 @ X1486 @ X1487) @ emptyset))|(X1486 @ (esk68_3 @ X1485 @ X1486 @ X1487))|~(X1486 @ X1487)|~(in @ X1487 @ X1485)))&(((in @ (esk69_3 @ X1485 @ X1486 @ X1487) @ (dsetconstr @ X1485 @ X1486))|((esk68_3 @ X1485 @ X1486 @ X1487)!=(X1487))|~(X1486 @ X1487)|~(in @ X1487 @ X1485))&(((dsetconstr @ X1485 @ X1486)=(setadjoin @ (esk69_3 @ X1485 @ X1486 @ X1487) @ emptyset))|((esk68_3 @ X1485 @ X1486 @ X1487)!=(X1487))|~(X1486 @ X1487)|~(in @ X1487 @ X1485)))))&(((((in @ (esk72_2 @ X1490 @ X1491) @ (dsetconstr @ X1490 @ X1491))|(~(in @ X1494 @ X1490)|~(X1491 @ X1494))|(in @ (esk70_2 @ X1490 @ X1491) @ X1490))&(((dsetconstr @ X1490 @ X1491)=(setadjoin @ (esk72_2 @ X1490 @ X1491) @ emptyset))|(~(in @ X1494 @ X1490)|~(X1491 @ X1494))|(in @ (esk70_2 @ X1490 @ X1491) @ X1490)))&((((in @ (esk72_2 @ X1490 @ X1491) @ (dsetconstr @ X1490 @ X1491))|(~(in @ X1494 @ X1490)|~(X1491 @ X1494))|(in @ (esk71_2 @ X1490 @ X1491) @ X1490))&(((dsetconstr @ X1490 @ X1491)=(setadjoin @ (esk72_2 @ X1490 @ X1491) @ emptyset))|(~(in @ X1494 @ X1490)|~(X1491 @ X1494))|(in @ (esk71_2 @ X1490 @ X1491) @ X1490)))&((((in @ (esk72_2 @ X1490 @ X1491) @ (dsetconstr @ X1490 @ X1491))|(~(in @ X1494 @ X1490)|~(X1491 @ X1494))|(X1491 @ (esk70_2 @ X1490 @ X1491)))&(((dsetconstr @ X1490 @ X1491)=(setadjoin @ (esk72_2 @ X1490 @ X1491) @ emptyset))|(~(in @ X1494 @ X1490)|~(X1491 @ X1494))|(X1491 @ (esk70_2 @ X1490 @ X1491))))&((((in @ (esk72_2 @ X1490 @ X1491) @ (dsetconstr @ X1490 @ X1491))|(~(in @ X1494 @ X1490)|~(X1491 @ X1494))|(X1491 @ (esk71_2 @ X1490 @ X1491)))&(((dsetconstr @ X1490 @ X1491)=(setadjoin @ (esk72_2 @ X1490 @ X1491) @ emptyset))|(~(in @ X1494 @ X1490)|~(X1491 @ X1494))|(X1491 @ (esk71_2 @ X1490 @ X1491))))&(((in @ (esk72_2 @ X1490 @ X1491) @ (dsetconstr @ X1490 @ X1491))|(~(in @ X1494 @ X1490)|~(X1491 @ X1494))|((esk70_2 @ X1490 @ X1491)!=(esk71_2 @ X1490 @ X1491)))&(((dsetconstr @ X1490 @ X1491)=(setadjoin @ (esk72_2 @ X1490 @ X1491) @ emptyset))|(~(in @ X1494 @ X1490)|~(X1491 @ X1494))|((esk70_2 @ X1490 @ X1491)!=(esk71_2 @ X1490 @ X1491))))))))&((((setadjoin @ X1496 @ emptyset)!=(setadjoin @ X1497 @ emptyset))|((X1496)=(X1497)))&((~(in @ (setadjoin @ X1500 @ emptyset) @ (setadjoin @ (setadjoin @ X1498 @ emptyset) @ (setadjoin @ (setadjoin @ X1498 @ (setadjoin @ X1499 @ emptyset)) @ emptyset)))|((X1498)=(X1500)))&((((in @ (esk73_1 @ X1501) @ (dsetconstr @ (setunion @ X1501) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1501)))))|(~(in @ X1502 @ (setunion @ X1501))|(~(in @ X1503 @ (setunion @ X1501))|((X1501)!=(setadjoin @ (setadjoin @ X1502 @ emptyset) @ (setadjoin @ (setadjoin @ X1502 @ (setadjoin @ X1503 @ emptyset)) @ emptyset))))))&(((dsetconstr @ (setunion @ X1501) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1501))))=(setadjoin @ (esk73_1 @ X1501) @ emptyset))|(~(in @ X1502 @ (setunion @ X1501))|(~(in @ X1503 @ (setunion @ X1501))|((X1501)!=(setadjoin @ (setadjoin @ X1502 @ emptyset) @ (setadjoin @ (setadjoin @ X1502 @ (setadjoin @ X1503 @ emptyset)) @ emptyset)))))))&((~(in @ X1506 @ X1505)|((X1505)!=(setadjoin @ X1506 @ emptyset))|(in @ (setunion @ X1505) @ X1505))&(((kfst @ (kpair @ X1507 @ X1508))=(X1507))&((~(in @ X1511 @ (cartprod @ X1509 @ X1510))|(in @ (kfst @ X1511) @ X1509))&((((setadjoin @ (setadjoin @ X1512 @ emptyset) @ (setadjoin @ (setadjoin @ X1512 @ (setadjoin @ X1513 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1514 @ emptyset) @ (setadjoin @ (setadjoin @ X1514 @ (setadjoin @ X1515 @ emptyset)) @ emptyset)))|((X1512)=(X1514)))&((((kpair @ X1516 @ X1517)!=(kpair @ X1518 @ X1519))|((X1516)=(X1518)))&((((X1520)!=(X1521))|((setadjoin @ X1520 @ (setadjoin @ X1521 @ emptyset))=(setadjoin @ X1520 @ emptyset)))&((((X1522)!=(X1523))|((setadjoin @ (setadjoin @ X1522 @ emptyset) @ (setadjoin @ (setadjoin @ X1522 @ (setadjoin @ X1523 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1522 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1524 @ emptyset) @ (setadjoin @ (setadjoin @ X1524 @ (setadjoin @ X1525 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1526 @ emptyset) @ (setadjoin @ (setadjoin @ X1526 @ (setadjoin @ X1527 @ emptyset)) @ emptyset)))|(((X1526)!=(X1527))|((X1525)=(X1527))))&((((setadjoin @ X1528 @ (setadjoin @ X1529 @ emptyset))!=(setadjoin @ X1530 @ emptyset))|((X1528)=(X1529)))&(((setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk74_0 @ (setadjoin @ esk75_0 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset)))&((esk75_0)!=(esk77_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_236])])])])])])])).
% 201.52/29.12  thf(c_0_239, plain, ![X1033:$i, X1034:$i]:(((kpair @ X1033 @ X1034)=(setadjoin @ (setadjoin @ X1033 @ emptyset) @ (setadjoin @ (setadjoin @ X1033 @ (setadjoin @ X1034 @ emptyset)) @ emptyset)))), inference(variable_rename,[status(thm)],[c_0_237])).
% 201.52/29.12  thf(c_0_240, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_238])).
% 201.52/29.12  thf(c_0_241, plain, ![X2:$i, X3:$i]:(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_239])).
% 201.52/29.12  thf(c_0_242, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=(X2))), inference(rw,[status(thm)],[c_0_240, c_0_241])).
% 201.52/29.12  thf(c_0_243, negated_conjecture, ((setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk74_0 @ (setadjoin @ esk75_0 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_238])).
% 201.52/29.12  thf(c_0_244, negated_conjecture, ![X3:$i, X2:$i]:((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_238])).
% 201.52/29.12  thf(c_0_245, negated_conjecture, ((esk74_0)=(esk76_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242, c_0_243]), c_0_242])).
% 201.52/29.12  thf(c_0_246, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(X3))|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)))))), inference(split_conjunct,[status(thm)],[c_0_238])).
% 201.52/29.12  thf(c_0_247, negated_conjecture, (in @ (setadjoin @ esk76_0 @ (setadjoin @ esk75_0 @ emptyset)) @ (setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244, c_0_243]), c_0_245])).
% 201.52/29.12  thf(c_0_248, negated_conjecture, (((setadjoin @ esk76_0 @ (setadjoin @ esk75_0 @ emptyset))=(setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)))|((setadjoin @ esk76_0 @ (setadjoin @ esk75_0 @ emptyset))=(setadjoin @ esk76_0 @ emptyset))), inference(spm,[status(thm)],[c_0_246, c_0_247])).
% 201.52/29.12  thf(c_0_249, negated_conjecture, (((setadjoin @ esk76_0 @ (setadjoin @ esk75_0 @ emptyset))=(setadjoin @ esk76_0 @ emptyset))|(in @ esk75_0 @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)))), inference(spm,[status(thm)],[c_0_244, c_0_248])).
% 201.52/29.12  thf(c_0_250, negated_conjecture, ((esk75_0)!=(esk77_0)), inference(split_conjunct,[status(thm)],[c_0_238])).
% 201.52/29.12  thf(c_0_251, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(X3))|((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))!=(setadjoin @ X4 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_238])).
% 201.52/29.12  thf(c_0_252, negated_conjecture, ![X2:$i, X3:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))|((X2)!=(X3)))), inference(split_conjunct,[status(thm)],[c_0_238])).
% 201.52/29.12  thf(c_0_253, negated_conjecture, ((esk75_0)=(esk76_0)), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_246, c_0_249]), c_0_250]), c_0_251])).
% 201.52/29.12  thf(c_0_254, negated_conjecture, ![X2:$i]:(((setadjoin @ X2 @ (setadjoin @ X2 @ emptyset))=(setadjoin @ X2 @ emptyset))), inference(er,[status(thm)],[c_0_252])).
% 201.52/29.12  thf(c_0_255, negated_conjecture, ![X2:$i]:((((X2)=(setadjoin @ esk76_0 @ emptyset))|~((in @ X2 @ (setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246, c_0_243]), c_0_245]), c_0_253]), c_0_254]), c_0_245])])).
% 201.52/29.12  thf(c_0_256, negated_conjecture, ((setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset))=(setadjoin @ esk76_0 @ emptyset)), inference(spm,[status(thm)],[c_0_255, c_0_244])).
% 201.52/29.12  thf(c_0_257, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_238])])])).
% 201.52/29.12  thf(c_0_258, negated_conjecture, (in @ esk77_0 @ (setadjoin @ esk76_0 @ emptyset)), inference(spm,[status(thm)],[c_0_244, c_0_256])).
% 201.52/29.12  thf(c_0_259, negated_conjecture, ((esk77_0)!=(esk76_0)), inference(rw,[status(thm)],[c_0_250, c_0_253])).
% 201.52/29.12  thf(c_0_260, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_238])).
% 201.52/29.12  thf(c_0_261, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_257, c_0_258]), c_0_259]), c_0_260]), ['proof']).
% 201.52/29.12  % SZS output end CNFRefutation
% 201.52/29.12  % Parsed axioms                        : 375
% 201.52/29.12  % Removed by relevancy pruning/SinE    : 0
% 201.52/29.12  % Initial clauses                      : 527
% 201.52/29.12  % Removed in clause preprocessing      : 224
% 201.52/29.12  % Initial clauses in saturation        : 303
% 201.52/29.12  % Processed clauses                    : 1639
% 201.52/29.12  % ...of these trivial                  : 31
% 201.52/29.12  % ...subsumed                          : 582
% 201.52/29.12  % ...remaining for further processing  : 1026
% 201.52/29.12  % Other redundant clauses eliminated   : 40
% 201.52/29.12  % Clauses deleted for lack of memory   : 0
% 201.52/29.12  % Backward-subsumed                    : 34
% 201.52/29.12  % Backward-rewritten                   : 67
% 201.52/29.12  % Generated clauses                    : 27928
% 201.52/29.12  % ...of the previous two non-redundant : 27042
% 201.52/29.12  % ...aggressively subsumed             : 0
% 201.52/29.12  % Contextual simplify-reflections      : 17
% 201.52/29.12  % Paramodulations                      : 27878
% 201.52/29.12  % Factorizations                       : 5
% 201.52/29.12  % NegExts                              : 0
% 201.52/29.13  % Equation resolutions                 : 44
% 201.52/29.13  % Disequality decompositions           : 0
% 201.52/29.13  % Total rewrite steps                  : 3497
% 201.52/29.13  % ...of those cached                   : 3282
% 201.52/29.13  % Propositional unsat checks           : 0
% 201.52/29.13  %    Propositional check models        : 0
% 201.52/29.13  %    Propositional check unsatisfiable : 0
% 201.52/29.13  %    Propositional clauses             : 0
% 201.52/29.13  %    Propositional clauses after purity: 0
% 201.52/29.13  %    Propositional unsat core size     : 0
% 201.52/29.13  %    Propositional preprocessing time  : 0.000
% 201.52/29.13  %    Propositional encoding time       : 0.000
% 201.52/29.13  %    Propositional solver time         : 0.000
% 201.52/29.13  %    Success case prop preproc time    : 0.000
% 201.52/29.13  %    Success case prop encoding time   : 0.000
% 201.52/29.13  %    Success case prop solver time     : 0.000
% 201.52/29.13  % Current number of processed clauses  : 645
% 201.52/29.13  %    Positive orientable unit clauses  : 67
% 201.52/29.13  %    Positive unorientable unit clauses: 0
% 201.52/29.13  %    Negative unit clauses             : 16
% 201.52/29.13  %    Non-unit-clauses                  : 562
% 201.52/29.13  % Current number of unprocessed clauses: 25800
% 201.52/29.13  % ...number of literals in the above   : 97725
% 201.52/29.13  % Current number of archived formulas  : 0
% 201.52/29.13  % Current number of archived clauses   : 363
% 201.52/29.13  % Clause-clause subsumption calls (NU) : 42409
% 201.52/29.13  % Rec. Clause-clause subsumption calls : 21957
% 201.52/29.13  % Non-unit clause-clause subsumptions  : 487
% 201.52/29.13  % Unit Clause-clause subsumption calls : 1217
% 201.52/29.13  % Rewrite failures with RHS unbound    : 0
% 201.52/29.13  % BW rewrite match attempts            : 57
% 201.52/29.13  % BW rewrite match successes           : 23
% 201.52/29.13  % Condensation attempts                : 0
% 201.52/29.13  % Condensation successes               : 0
% 201.52/29.13  % Termbank termtop insertions          : 663459
% 201.52/29.13  % Search garbage collected termcells   : 16740
% 201.52/29.13  
% 201.52/29.13  % -------------------------------------------------
% 201.52/29.13  % User time                : 27.816 s
% 201.52/29.13  % System time              : 0.989 s
% 201.52/29.13  % Total time               : 28.805 s
% 201.52/29.13  % Maximum resident set size: 7336 pages
% 201.52/29.13  
% 201.52/29.13  % -------------------------------------------------
% 201.52/29.13  % User time                : 27.821 s
% 201.52/29.13  % System time              : 0.994 s
% 201.52/29.13  % Total time               : 28.816 s
% 201.52/29.13  % Maximum resident set size: 5376 pages
% 201.52/29.13  % E exiting
%------------------------------------------------------------------------------