%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU631^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:24:48 AM UTC 2026
% Result : Theorem 205.36s 29.99s
% Output : CNFRefutation 205.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU631^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n001.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 14:06:16 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p
% 205.36/29.99 % Version: 3.5.1-ho
% 205.36/29.99 % Preprocessing class: HSLMSLSSLLLCHFA.
% 205.36/29.99 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 205.36/29.99 % Starting ehoh_best5 with 300s (1) cores
% 205.36/29.99 % Starting almost_fo_3_lam with 300s (1) cores
% 205.36/29.99 % Starting new_bool_5 with 300s (1) cores
% 205.36/29.99 % Starting pre_casc_3 with 300s (1) cores
% 205.36/29.99 % Starting ho_unfolding_8 with 300s (1) cores
% 205.36/29.99 % Starting new_ho_10_cnf2 with 300s (1) cores
% 205.36/29.99 % Starting new_bool_3 with 300s (1) cores
% 205.36/29.99 % Starting new_ho_5 with 300s (1) cores
% 205.36/29.99 % ehoh_best5 with pid 1290010 completed with status 0
% 205.36/29.99 % Result found by ehoh_best5
% 205.36/29.99 % Preprocessing class: HSLMSLSSLLLCHFA.
% 205.36/29.99 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 205.36/29.99 % Starting ehoh_best5 with 300s (1) cores
% 205.36/29.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 205.36/29.99 % No SInE strategy applied
% 205.36/29.99 % Search class: HGHSM-FSLM31-MHFMMSBN
% 205.36/29.99 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 205.36/29.99 % Starting SubtermCWHack with 28s (1) cores
% 205.36/29.99 % SubtermCWHack with pid 1290022 completed with status 8
% 205.36/29.99 % Starting ehoh_best5 with 31s (1) cores
% 205.36/29.99 % ehoh_best5 with pid 1291149 completed with status 0
% 205.36/29.99 % Result found by ehoh_best5
% 205.36/29.99 % Preprocessing class: HSLMSLSSLLLCHFA.
% 205.36/29.99 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 205.36/29.99 % Starting ehoh_best5 with 300s (1) cores
% 205.36/29.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 205.36/29.99 % No SInE strategy applied
% 205.36/29.99 % Search class: HGHSM-FSLM31-MHFMMSBN
% 205.36/29.99 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 205.36/29.99 % Starting SubtermCWHack with 28s (1) cores
% 205.36/29.99 % SubtermCWHack with pid 1290022 completed with status 8
% 205.36/29.99 % Starting ehoh_best5 with 31s (1) cores
% 205.36/29.99 % Preprocessing time : 0.007 s
% 205.36/29.99 % Presaturation interreduction done
% 205.36/29.99
% 205.36/29.99 % Proof found!
% 205.36/29.99 % SZS status Theorem
% 205.36/29.99 % SZS output start CNFRefutation
% 205.36/29.99 thf(decl_23, type, in: $i > $i > $o).
% 205.36/29.99 thf(decl_24, type, exu: ($i > $o) > $o).
% 205.36/29.99 thf(decl_25, type, setextAx: $o).
% 205.36/29.99 thf(decl_26, type, emptyset: $i).
% 205.36/29.99 thf(decl_27, type, emptysetAx: $o).
% 205.36/29.99 thf(decl_28, type, setadjoin: $i > $i > $i).
% 205.36/29.99 thf(decl_29, type, setadjoinAx: $o).
% 205.36/29.99 thf(decl_30, type, powerset: $i > $i).
% 205.36/29.99 thf(decl_31, type, powersetAx: $o).
% 205.36/29.99 thf(decl_32, type, setunion: $i > $i).
% 205.36/29.99 thf(decl_33, type, setunionAx: $o).
% 205.36/29.99 thf(decl_34, type, omega: $i).
% 205.36/29.99 thf(decl_35, type, omega0Ax: $o).
% 205.36/29.99 thf(decl_36, type, omegaSAx: $o).
% 205.36/29.99 thf(decl_37, type, omegaIndAx: $o).
% 205.36/29.99 thf(decl_38, type, replAx: $o).
% 205.36/29.99 thf(decl_39, type, foundationAx: $o).
% 205.36/29.99 thf(decl_40, type, wellorderingAx: $o).
% 205.36/29.99 thf(decl_41, type, descr: ($i > $o) > $i).
% 205.36/29.99 thf(decl_42, type, descrp: $o).
% 205.36/29.99 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 205.36/29.99 thf(decl_44, type, dsetconstrI: $o).
% 205.36/29.99 thf(decl_45, type, dsetconstrEL: $o).
% 205.36/29.99 thf(decl_46, type, dsetconstrER: $o).
% 205.36/29.99 thf(decl_47, type, exuE1: $o).
% 205.36/29.99 thf(decl_48, type, prop2set: $o > $i).
% 205.36/29.99 thf(decl_49, type, prop2setE: $o).
% 205.36/29.99 thf(decl_50, type, emptysetE: $o).
% 205.36/29.99 thf(decl_51, type, emptysetimpfalse: $o).
% 205.36/29.99 thf(decl_52, type, notinemptyset: $o).
% 205.36/29.99 thf(decl_53, type, exuE3e: $o).
% 205.36/29.99 thf(decl_54, type, setext: $o).
% 205.36/29.99 thf(decl_55, type, emptyI: $o).
% 205.36/29.99 thf(decl_56, type, noeltsimpempty: $o).
% 205.36/29.99 thf(decl_57, type, setbeta: $o).
% 205.36/29.99 thf(decl_58, type, nonempty: $i > $o).
% 205.36/29.99 thf(decl_59, type, nonemptyE1: $o).
% 205.36/29.99 thf(decl_60, type, nonemptyI: $o).
% 205.36/29.99 thf(decl_61, type, nonemptyI1: $o).
% 205.36/29.99 thf(decl_62, type, setadjoinIL: $o).
% 205.36/29.99 thf(decl_63, type, emptyinunitempty: $o).
% 205.36/29.99 thf(decl_64, type, setadjoinIR: $o).
% 205.36/29.99 thf(decl_65, type, setadjoinE: $o).
% 205.36/29.99 thf(decl_66, type, setadjoinOr: $o).
% 205.36/29.99 thf(decl_67, type, setoftrueEq: $o).
% 205.36/29.99 thf(decl_68, type, powersetI: $o).
% 205.36/29.99 thf(decl_69, type, emptyinPowerset: $o).
% 205.36/29.99 thf(decl_70, type, emptyInPowerset: $o).
% 205.36/29.99 thf(decl_71, type, powersetE: $o).
% 205.36/29.99 thf(decl_72, type, setunionI: $o).
% 205.36/29.99 thf(decl_73, type, setunionE: $o).
% 205.36/29.99 thf(decl_74, type, subPowSU: $o).
% 205.36/29.99 thf(decl_75, type, exuE2: $o).
% 205.36/29.99 thf(decl_76, type, nonemptyImpWitness: $o).
% 205.36/29.99 thf(decl_77, type, uniqinunit: $o).
% 205.36/29.99 thf(decl_78, type, notinsingleton: $o).
% 205.36/29.99 thf(decl_79, type, eqinunit: $o).
% 205.36/29.99 thf(decl_80, type, singletonsswitch: $o).
% 205.36/29.99 thf(decl_81, type, upairsetE: $o).
% 205.36/29.99 thf(decl_82, type, upairsetIL: $o).
% 205.36/29.99 thf(decl_83, type, upairsetIR: $o).
% 205.36/29.99 thf(decl_84, type, emptyE1: $o).
% 205.36/29.99 thf(decl_85, type, vacuousDall: $o).
% 205.36/29.99 thf(decl_86, type, quantDeMorgan1: $o).
% 205.36/29.99 thf(decl_87, type, quantDeMorgan2: $o).
% 205.36/29.99 thf(decl_88, type, quantDeMorgan3: $o).
% 205.36/29.99 thf(decl_89, type, quantDeMorgan4: $o).
% 205.36/29.99 thf(decl_90, type, prop2setI: $o).
% 205.36/29.99 thf(decl_91, type, set2prop: $i > $o).
% 205.36/29.99 thf(decl_92, type, prop2set2propI: $o).
% 205.36/29.99 thf(decl_93, type, notdexE: $o).
% 205.36/29.99 thf(decl_94, type, notdallE: $o).
% 205.36/29.99 thf(decl_95, type, exuI1: $o).
% 205.36/29.99 thf(decl_96, type, exuI3: $o).
% 205.36/29.99 thf(decl_97, type, exuI2: $o).
% 205.36/29.99 thf(decl_98, type, inCongP: $o).
% 205.36/29.99 thf(decl_99, type, in__Cong: $o).
% 205.36/29.99 thf(decl_100, type, exuE3u: $o).
% 205.36/29.99 thf(decl_101, type, exu__Cong: $o).
% 205.36/29.99 thf(decl_102, type, emptyset__Cong: $o).
% 205.36/29.99 thf(decl_103, type, setadjoin__Cong: $o).
% 205.36/29.99 thf(decl_104, type, powerset__Cong: $o).
% 205.36/29.99 thf(decl_105, type, setunion__Cong: $o).
% 205.36/29.99 thf(decl_106, type, omega__Cong: $o).
% 205.36/29.99 thf(decl_107, type, exuEu: $o).
% 205.36/29.99 thf(decl_108, type, descr__Cong: $o).
% 205.36/29.99 thf(decl_109, type, dsetconstr__Cong: $o).
% 205.36/29.99 thf(decl_110, type, subset: $i > $i > $o).
% 205.36/29.99 thf(decl_113, type, subsetI1: $o).
% 205.36/29.99 thf(decl_114, type, eqimpsubset2: $o).
% 205.36/29.99 thf(decl_115, type, eqimpsubset1: $o).
% 205.36/29.99 thf(decl_116, type, subsetI2: $o).
% 205.36/29.99 thf(decl_117, type, emptysetsubset: $o).
% 205.36/29.99 thf(decl_118, type, subsetE: $o).
% 205.36/29.99 thf(decl_119, type, subsetE2: $o).
% 205.36/29.99 thf(decl_120, type, notsubsetI: $o).
% 205.36/29.99 thf(decl_121, type, notequalI1: $o).
% 205.36/29.99 thf(decl_122, type, notequalI2: $o).
% 205.36/29.99 thf(decl_123, type, subsetRefl: $o).
% 205.36/29.99 thf(decl_124, type, subsetTrans: $o).
% 205.36/29.99 thf(decl_125, type, setadjoinSub: $o).
% 205.36/29.99 thf(decl_126, type, setadjoinSub2: $o).
% 205.36/29.99 thf(decl_127, type, subset2powerset: $o).
% 205.36/29.99 thf(decl_128, type, setextsub: $o).
% 205.36/29.99 thf(decl_129, type, subsetemptysetimpeq: $o).
% 205.36/29.99 thf(decl_130, type, powersetI1: $o).
% 205.36/29.99 thf(decl_131, type, powersetE1: $o).
% 205.36/29.99 thf(decl_132, type, inPowerset: $o).
% 205.36/29.99 thf(decl_133, type, powersetsubset: $o).
% 205.36/29.99 thf(decl_134, type, sepInPowerset: $o).
% 205.36/29.99 thf(decl_135, type, sepSubset: $o).
% 205.36/29.99 thf(decl_136, type, binunion: $i > $i > $i).
% 205.36/29.99 thf(decl_137, type, binunionIL: $o).
% 205.36/29.99 thf(decl_138, type, upairset2IR: $o).
% 205.36/29.99 thf(decl_139, type, binunionIR: $o).
% 205.36/29.99 thf(decl_140, type, binunionEcases: $o).
% 205.36/29.99 thf(decl_141, type, binunionE: $o).
% 205.36/29.99 thf(decl_142, type, binunionLsub: $o).
% 205.36/29.99 thf(decl_143, type, binunionRsub: $o).
% 205.36/29.99 thf(decl_144, type, binintersect: $i > $i > $i).
% 205.36/29.99 thf(decl_145, type, binintersectI: $o).
% 205.36/29.99 thf(decl_146, type, binintersectSubset5: $o).
% 205.36/29.99 thf(decl_147, type, binintersectEL: $o).
% 205.36/29.99 thf(decl_148, type, binintersectLsub: $o).
% 205.36/29.99 thf(decl_149, type, binintersectSubset2: $o).
% 205.36/29.99 thf(decl_150, type, binintersectSubset3: $o).
% 205.36/29.99 thf(decl_151, type, binintersectER: $o).
% 205.36/29.99 thf(decl_152, type, disjointsetsI1: $o).
% 205.36/29.99 thf(decl_153, type, binintersectRsub: $o).
% 205.36/29.99 thf(decl_154, type, binintersectSubset4: $o).
% 205.36/29.99 thf(decl_155, type, binintersectSubset1: $o).
% 205.36/29.99 thf(decl_156, type, bs114d: $o).
% 205.36/29.99 thf(decl_158, type, setminus: $i > $i > $i).
% 205.36/29.99 thf(decl_159, type, setminusI: $o).
% 205.36/29.99 thf(decl_160, type, setminusEL: $o).
% 205.36/29.99 thf(decl_161, type, setminusER: $o).
% 205.36/29.99 thf(decl_162, type, setminusSubset2: $o).
% 205.36/29.99 thf(decl_163, type, setminusERneg: $o).
% 205.36/29.99 thf(decl_164, type, setminusELneg: $o).
% 205.36/29.99 thf(decl_165, type, setminusILneg: $o).
% 205.36/29.99 thf(decl_166, type, setminusIRneg: $o).
% 205.36/29.99 thf(decl_167, type, setminusLsub: $o).
% 205.36/29.99 thf(decl_168, type, setminusSubset1: $o).
% 205.36/29.99 thf(decl_169, type, symdiff: $i > $i > $i).
% 205.36/29.99 thf(decl_170, type, symdiffE: $o).
% 205.36/29.99 thf(decl_171, type, symdiffI1: $o).
% 205.36/29.99 thf(decl_172, type, symdiffI2: $o).
% 205.36/29.99 thf(decl_173, type, symdiffIneg1: $o).
% 205.36/29.99 thf(decl_174, type, symdiffIneg2: $o).
% 205.36/29.99 thf(decl_175, type, iskpair: $i > $o).
% 205.36/29.99 thf(decl_176, type, secondinupair: $o).
% 205.36/29.99 thf(decl_177, type, setukpairIL: $o).
% 205.36/29.99 thf(decl_178, type, setukpairIR: $o).
% 205.36/29.99 thf(decl_179, type, kpairiskpair: $o).
% 205.36/29.99 thf(decl_180, type, kpair: $i > $i > $i).
% 205.36/29.99 thf(decl_181, type, kpairp: $o).
% 205.36/29.99 thf(decl_182, type, cartprod: $i > $i > $i).
% 205.36/29.99 thf(decl_183, type, singletonsubset: $o).
% 205.36/29.99 thf(decl_184, type, singletoninpowerset: $o).
% 205.36/29.99 thf(decl_185, type, singletoninpowunion: $o).
% 205.36/29.99 thf(decl_186, type, upairset2E: $o).
% 205.36/29.99 thf(decl_187, type, upairsubunion: $o).
% 205.36/29.99 thf(decl_188, type, upairinpowunion: $o).
% 205.36/29.99 thf(decl_189, type, ubforcartprodlem1: $o).
% 205.36/29.99 thf(decl_190, type, ubforcartprodlem2: $o).
% 205.36/29.99 thf(decl_191, type, ubforcartprodlem3: $o).
% 205.36/29.99 thf(decl_192, type, cartprodpairin: $o).
% 205.36/29.99 thf(decl_193, type, epred1_0: $o).
% 205.36/29.99 thf(decl_194, type, esk1_2: $i > $i > $i).
% 205.36/29.99 thf(decl_195, type, esk2_2: $i > $i > $i).
% 205.36/29.99 thf(decl_196, type, esk3_2: $i > $i > $i).
% 205.36/29.99 thf(decl_197, type, esk4_1: $i > $i).
% 205.36/29.99 thf(decl_198, type, esk5_2: ($i > $i > $o) > $i > $i).
% 205.36/29.99 thf(decl_199, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 205.36/29.99 thf(decl_200, type, esk7_2: ($i > $i > $o) > $i > $i).
% 205.36/29.99 thf(decl_201, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 205.36/29.99 thf(decl_202, type, esk9_1: $i > $i).
% 205.36/29.99 thf(decl_203, type, esk10_2: ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_204, type, esk11_2: ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_205, type, esk12_1: ($i > $o) > $i).
% 205.36/29.99 thf(decl_206, type, esk13_2: ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_207, type, esk14_1: ($i > $o) > $i).
% 205.36/29.99 thf(decl_208, type, esk15_2: $i > $i > $i).
% 205.36/29.99 thf(decl_209, type, esk16_2: $i > $i > $i).
% 205.36/29.99 thf(decl_210, type, esk17_1: $i > $i).
% 205.36/29.99 thf(decl_211, type, esk18_1: $i > $i).
% 205.36/29.99 thf(decl_212, type, esk19_1: $i > $i).
% 205.36/29.99 thf(decl_213, type, esk20_2: $i > $i > $i).
% 205.36/29.99 thf(decl_214, type, esk21_3: $i > $i > $o > $i).
% 205.36/29.99 thf(decl_215, type, esk22_2: ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_216, type, esk23_1: ($i > $o) > $i).
% 205.36/29.99 thf(decl_217, type, esk24_1: $i > $i).
% 205.36/29.99 thf(decl_218, type, esk25_2: $i > ($i > $o) > $i).
% 205.36/29.99 thf(decl_219, type, esk26_2: $i > ($i > $o) > $i).
% 205.36/29.99 thf(decl_220, type, esk27_2: $i > ($i > $o) > $i).
% 205.36/29.99 thf(decl_221, type, esk28_2: $i > ($i > $o) > $i).
% 205.36/29.99 thf(decl_222, type, esk29_2: $i > ($i > $o) > $i).
% 205.36/29.99 thf(decl_223, type, esk30_2: $i > ($i > $o) > $i).
% 205.36/29.99 thf(decl_224, type, esk31_2: ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_225, type, esk32_1: ($i > $o) > $i).
% 205.36/29.99 thf(decl_226, type, esk33_1: ($i > $o) > $i).
% 205.36/29.99 thf(decl_227, type, esk34_1: ($i > $o) > $i).
% 205.36/29.99 thf(decl_228, type, esk35_1: ($i > $o) > $i).
% 205.36/29.99 thf(decl_229, type, esk36_2: ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_230, type, esk37_1: ($i > $o) > $i).
% 205.36/29.99 thf(decl_231, type, esk38_2: ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_232, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 205.36/29.99 thf(decl_233, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 205.36/29.99 thf(decl_234, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_235, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 205.36/29.99 thf(decl_236, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_237, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 205.36/29.99 thf(decl_238, type, esk45_2: ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_239, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 205.36/29.99 thf(decl_240, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 205.36/29.99 thf(decl_241, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_242, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 205.36/29.99 thf(decl_243, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 205.36/29.99 thf(decl_244, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 205.36/29.99 thf(decl_245, type, esk52_2: $i > $i > $i).
% 205.36/29.99 thf(decl_246, type, esk53_2: $i > $i > $i).
% 205.36/29.99 thf(decl_247, type, esk54_2: $i > $i > $i).
% 205.36/29.99 thf(decl_248, type, esk55_2: $i > $i > $i).
% 205.36/29.99 thf(decl_249, type, esk56_2: $i > $i > $i).
% 205.36/29.99 thf(decl_250, type, esk57_2: $i > $i > $i).
% 205.36/29.99 thf(decl_251, type, esk58_2: $i > $i > $i).
% 205.36/29.99 thf(decl_252, type, esk59_0: $i).
% 205.36/29.99 thf(decl_253, type, esk60_0: $i).
% 205.36/29.99 thf(decl_254, type, esk61_0: $i).
% 205.36/29.99 thf(decl_260, type, epred2_2: $i > $i > $i > $o).
% 205.36/29.99 thf(decl_262, type, esk67_3: $i > $i > $i > $i).
% 205.36/29.99 thf(decl_263, type, esk68_3: $i > $i > $i > $i).
% 205.36/29.99 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', replAx)).
% 205.36/29.99 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', exu)).
% 205.36/29.99 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', descrp)).
% 205.36/29.99 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', exuE1)).
% 205.36/29.99 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', exuE3e)).
% 205.36/29.99 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', nonempty)).
% 205.36/29.99 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', nonemptyI)).
% 205.36/29.99 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', exuE2)).
% 205.36/29.99 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', exuI1)).
% 205.36/29.99 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', exuI3)).
% 205.36/29.99 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', exuI2)).
% 205.36/29.99 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', exuE3u)).
% 205.36/29.99 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', exu__Cong)).
% 205.36/29.99 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', exuEu)).
% 205.36/29.99 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', descr__Cong)).
% 205.36/29.99 thf(iskpair, axiom, ((iskpair)=(^[X4:$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/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', iskpair)).
% 205.36/29.99 thf(cartprodmempair1, 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)=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', cartprodmempair1)).
% 205.36/29.99 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', dsetconstrI)).
% 205.36/29.99 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', dsetconstrEL)).
% 205.36/29.99 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', dsetconstrER)).
% 205.36/29.99 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setbeta)).
% 205.36/29.99 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', nonemptyE1)).
% 205.36/29.99 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', nonemptyI1)).
% 205.36/29.99 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setoftrueEq)).
% 205.36/29.99 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', nonemptyImpWitness)).
% 205.36/29.99 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', emptyE1)).
% 205.36/29.99 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', dsetconstr__Cong)).
% 205.36/29.99 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', sepInPowerset)).
% 205.36/29.99 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', sepSubset)).
% 205.36/29.99 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', kpairiskpair)).
% 205.36/29.99 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', kpairp)).
% 205.36/29.99 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setextAx)).
% 205.36/29.99 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', emptysetAx)).
% 205.36/29.99 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setadjoinAx)).
% 205.36/29.99 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', powersetAx)).
% 205.36/29.99 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setunionAx)).
% 205.36/29.99 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', omega0Ax)).
% 205.36/29.99 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', omegaSAx)).
% 205.36/29.99 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', omegaIndAx)).
% 205.36/29.99 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', foundationAx)).
% 205.36/29.99 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', wellorderingAx)).
% 205.36/29.99 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', prop2setE)).
% 205.36/29.99 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', emptysetE)).
% 205.36/29.99 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', emptysetimpfalse)).
% 205.36/29.99 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', notinemptyset)).
% 205.36/29.99 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setext)).
% 205.36/29.99 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', emptyI)).
% 205.36/29.99 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', noeltsimpempty)).
% 205.36/29.99 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setadjoinIL)).
% 205.36/29.99 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', emptyinunitempty)).
% 205.36/29.99 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setadjoinIR)).
% 205.36/29.99 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setadjoinE)).
% 205.36/29.99 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setadjoinOr)).
% 205.36/29.99 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', powersetI)).
% 205.36/29.99 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', emptyinPowerset)).
% 205.36/29.99 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', emptyInPowerset)).
% 205.36/29.99 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', powersetE)).
% 205.36/29.99 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setunionI)).
% 205.36/29.99 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setunionE)).
% 205.36/29.99 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', subPowSU)).
% 205.36/29.99 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', uniqinunit)).
% 205.36/29.99 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', notinsingleton)).
% 205.36/29.99 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', eqinunit)).
% 205.36/29.99 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', singletonsswitch)).
% 205.36/29.99 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', upairsetE)).
% 205.36/29.99 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', upairsetIL)).
% 205.36/29.99 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', upairsetIR)).
% 205.36/29.99 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', vacuousDall)).
% 205.36/29.99 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', quantDeMorgan1)).
% 205.36/29.99 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', quantDeMorgan2)).
% 205.36/29.99 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', quantDeMorgan3)).
% 205.36/29.99 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', quantDeMorgan4)).
% 205.36/29.99 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', prop2setI)).
% 205.36/29.99 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', prop2set2propI)).
% 205.36/29.99 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', notdexE)).
% 205.36/29.99 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', notdallE)).
% 205.36/29.99 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', inCongP)).
% 205.36/29.99 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', in__Cong)).
% 205.36/29.99 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', emptyset__Cong)).
% 205.36/29.99 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setadjoin__Cong)).
% 205.36/29.99 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', powerset__Cong)).
% 205.36/29.99 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setunion__Cong)).
% 205.36/29.99 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', omega__Cong)).
% 205.36/29.99 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', subsetI1)).
% 205.36/29.99 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', eqimpsubset2)).
% 205.36/29.99 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', eqimpsubset1)).
% 205.36/29.99 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', subsetI2)).
% 205.36/29.99 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', emptysetsubset)).
% 205.36/29.99 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', subsetE)).
% 205.36/29.99 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', subsetE2)).
% 205.36/29.99 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', notsubsetI)).
% 205.36/29.99 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', notequalI1)).
% 205.36/29.99 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', notequalI2)).
% 205.36/29.99 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', subsetRefl)).
% 205.36/29.99 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', subsetTrans)).
% 205.36/30.00 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setadjoinSub)).
% 205.36/30.00 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setadjoinSub2)).
% 205.36/30.00 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', subset2powerset)).
% 205.36/30.00 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setextsub)).
% 205.36/30.00 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', subsetemptysetimpeq)).
% 205.36/30.00 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', powersetI1)).
% 205.36/30.00 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', powersetE1)).
% 205.36/30.00 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', inPowerset)).
% 205.36/30.00 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', powersetsubset)).
% 205.36/30.00 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binunionIL)).
% 205.36/30.00 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', upairset2IR)).
% 205.36/30.00 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binunionIR)).
% 205.36/30.00 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binunionEcases)).
% 205.36/30.00 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binunionE)).
% 205.36/30.00 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binunionLsub)).
% 205.36/30.00 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binunionRsub)).
% 205.36/30.00 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binintersectI)).
% 205.36/30.00 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binintersectSubset5)).
% 205.36/30.00 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binintersectEL)).
% 205.36/30.00 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binintersectLsub)).
% 205.36/30.00 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binintersectSubset2)).
% 205.36/30.00 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binintersectSubset3)).
% 205.36/30.00 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binintersectER)).
% 205.36/30.00 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', disjointsetsI1)).
% 205.36/30.00 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binintersectRsub)).
% 205.36/30.00 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binintersectSubset4)).
% 205.36/30.00 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', binintersectSubset1)).
% 205.36/30.00 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', bs114d)).
% 205.36/30.00 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setminusI)).
% 205.36/30.00 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setminusEL)).
% 205.36/30.00 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setminusER)).
% 205.36/30.00 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setminusSubset2)).
% 205.36/30.00 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setminusERneg)).
% 205.36/30.00 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setminusELneg)).
% 205.36/30.00 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setminusILneg)).
% 205.36/30.00 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setminusIRneg)).
% 205.36/30.00 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setminusLsub)).
% 205.36/30.00 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setminusSubset1)).
% 205.36/30.00 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', symdiffE)).
% 205.36/30.00 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', symdiffI1)).
% 205.36/30.00 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', symdiffI2)).
% 205.36/30.00 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', symdiffIneg1)).
% 205.36/30.00 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', symdiffIneg2)).
% 205.36/30.00 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', secondinupair)).
% 205.36/30.00 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setukpairIL)).
% 205.36/30.00 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', setukpairIR)).
% 205.36/30.00 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', singletonsubset)).
% 205.36/30.00 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', singletoninpowerset)).
% 205.36/30.00 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', singletoninpowunion)).
% 205.36/30.00 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', upairset2E)).
% 205.36/30.00 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', upairsubunion)).
% 205.36/30.00 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', upairinpowunion)).
% 205.36/30.00 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', ubforcartprodlem1)).
% 205.36/30.00 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', ubforcartprodlem2)).
% 205.36/30.00 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', ubforcartprodlem3)).
% 205.36/30.00 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', cartprodpairin)).
% 205.36/30.00 thf(cartprod, axiom, ((cartprod)=(^[X4:$i, X5:$i]:(dsetconstr @ (powerset @ (powerset @ (binunion @ X4 @ X5))) @ (^[X2:$i]:(?[X3:$i]:((((in @ X3 @ X4))&(?[X14:$i]:((((in @ X14 @ X5))&(((X2)=(kpair @ X3 @ X14))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JmDny8Wk4Q/E---3.1_1289997.p', cartprod)).
% 205.36/30.00 thf(c_0_152, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 205.36/30.00 thf(c_0_153, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 205.36/30.00 thf(c_0_154, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 205.36/30.00 thf(c_0_155, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 205.36/30.00 thf(c_0_156, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 205.36/30.00 thf(c_0_157, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 205.36/30.00 thf(c_0_158, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 205.36/30.00 thf(c_0_159, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 205.36/30.00 thf(c_0_160, 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])).
% 205.36/30.00 thf(c_0_161, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 205.36/30.00 thf(c_0_162, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 205.36/30.00 thf(c_0_163, 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])).
% 205.36/30.00 thf(c_0_164, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 205.36/30.00 thf(c_0_165, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 205.36/30.00 thf(c_0_166, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 205.36/30.00 thf(c_0_167, plain, ((iskpair)=(^[Z0:$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])).
% 205.36/30.00 thf(c_0_168, 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)=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[cartprodmempair1])).
% 205.36/30.00 thf(c_0_169, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X424:$i]:(((((X6 @ X2 @ X424)))&(![X425:$i]:(((((X6 @ X2 @ X425)))=>(((X424)=(X425)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_152, c_0_153])).
% 205.36/30.00 thf(c_0_170, plain, ((descrp)=(![X1:$i > $o]:((((?[X426:$i]:(((((X1 @ X426)))&(![X427:$i]:(((((X1 @ X427)))=>(((X426)=(X427))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_154, c_0_153])).
% 205.36/30.00 thf(c_0_171, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 205.36/30.00 thf(c_0_172, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 205.36/30.00 thf(c_0_173, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 205.36/30.00 thf(c_0_174, plain, ((exuE1)=(![X1:$i > $o]:((((?[X428:$i]:(((((X1 @ X428)))&(![X429:$i]:(((((X1 @ X429)))=>(((X428)=(X429))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_155, c_0_153])).
% 205.36/30.00 thf(c_0_175, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X430:$i]:(((((X1 @ X430)))&(![X431:$i]:(((((X1 @ X431)))=>(((X430)=(X431))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_156, c_0_153])).
% 205.36/30.00 thf(c_0_176, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 205.36/30.00 thf(c_0_177, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_157])).
% 205.36/30.00 thf(c_0_178, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_158, c_0_157])).
% 205.36/30.00 thf(c_0_179, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_157])).
% 205.36/30.00 thf(c_0_180, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 205.36/30.00 thf(c_0_181, plain, ((exuE2)=(![X1:$i > $o]:((((?[X432:$i]:(((((X1 @ X432)))&(![X433:$i]:(((((X1 @ X433)))=>(((X432)=(X433))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_159, c_0_153])).
% 205.36/30.00 thf(c_0_182, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_157])).
% 205.36/30.00 thf(c_0_183, 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])).
% 205.36/30.00 thf(c_0_184, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X434:$i]:(((((X1 @ X434)))&(![X435:$i]:(((((X1 @ X435)))=>(((X434)=(X435)))))))))))))), inference(apply_def,[status(thm)],[c_0_160, c_0_153])).
% 205.36/30.00 thf(c_0_185, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X436:$i]:(((((X1 @ X436)))&(![X437:$i]:(((((X1 @ X437)))=>(((X436)=(X437)))))))))))))))), inference(apply_def,[status(thm)],[c_0_161, c_0_153])).
% 205.36/30.00 thf(c_0_186, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X438:$i]:(((((X1 @ X438)))&(![X439:$i]:(((((X1 @ X439)))=>(((X438)=(X439)))))))))))))), inference(apply_def,[status(thm)],[c_0_162, c_0_153])).
% 205.36/30.00 thf(c_0_187, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X440:$i]:(((((X1 @ X440)))&(![X441:$i]:(((((X1 @ X441)))=>(((X440)=(X441))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_163, c_0_153])).
% 205.36/30.00 thf(c_0_188, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X442:$i]:(((((X1 @ X442)))&(![X443:$i]:(((((X1 @ X443)))=>(((X442)=(X443))))))))))<=>((?[X444:$i]:(((((X17 @ X444)))&(![X445:$i]:(((((X17 @ X445)))=>(((X444)=(X445)))))))))))))))), inference(apply_def,[status(thm)],[c_0_164, c_0_153])).
% 205.36/30.00 thf(c_0_189, plain, ((exuEu)=(![X1:$i > $o]:((((?[X446:$i]:(((((X1 @ X446)))&(![X447:$i]:(((((X1 @ X447)))=>(((X446)=(X447))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_165, c_0_153])).
% 205.36/30.00 thf(c_0_190, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X448:$i]:(((((X1 @ X448)))&(![X449:$i]:(((((X1 @ X449)))=>(((X448)=(X449))))))))))=>((((?[X450:$i]:(((((X17 @ X450)))&(![X451:$i]:(((((X17 @ X451)))=>(((X450)=(X451))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_166, c_0_153])).
% 205.36/30.00 thf(c_0_191, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 205.36/30.00 thf(c_0_192, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 205.36/30.00 thf(c_0_193, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 205.36/30.00 thf(c_0_194, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X452:$i]:((((in @ X452 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X453:$i]:((((in @ X453 @ (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 @ X452 @ emptyset) @ (setadjoin @ (setadjoin @ X452 @ (setadjoin @ X453 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_167])).
% 205.36/30.00 thf(c_0_195, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X454:$i]:((((in @ X454 @ (setunion @ (kpair @ X2 @ X3))))&(?[X455:$i]:((((in @ X455 @ (setunion @ (kpair @ X2 @ X3))))&(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X454 @ emptyset) @ (setadjoin @ (setadjoin @ X454 @ (setadjoin @ X455 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_167])).
% 205.36/30.00 thf(c_0_196, plain, ((epred1_0)<=>![X485:$i]:(?[X486:$i]:((((![X487:$i]:(((in @ X487 @ X486)=>![X488:$i]:(((in @ X488 @ X487)=>(in @ X488 @ X485)))))&![X489:$i, X490:$i]:((((in @ X489 @ X485)&(in @ X490 @ X485))=>(![X491:$i]:(((in @ X491 @ X486)=>((in @ X489 @ X491)<=>(in @ X490 @ X491))))=>((X489)=(X490))))))&![X492:$i, X493:$i]:((((in @ X492 @ X486)&(in @ X493 @ X486))=>(![X494:$i]:(((in @ X494 @ X492)=>(in @ X494 @ X493)))|![X495:$i]:(((in @ X495 @ X493)=>(in @ X495 @ X492)))))))&![X496:$i]:(((![X497:$i]:(((in @ X497 @ X496)=>(in @ X497 @ X485)))&?[X498:$i]:((in @ X498 @ X496)))=>?[X499:$i, X500:$i]:(((((in @ X499 @ X486)&(in @ X500 @ X496))&~(?[X501:$i]:(((in @ X501 @ X499)&(in @ X501 @ X496)))))&![X502:$i]:(((in @ X502 @ X486)=>(![X503:$i]:(((in @ X503 @ X502)=>(in @ X503 @ X499)))|(in @ X500 @ X502)))))))))))), introduced(definition)).
% 205.36/30.00 thf(c_0_197, negated_conjecture, ~((![X456:$i, X457:$i]:((![X458:$i]:(((in @ X458 @ X456)<=>(in @ X458 @ X457)))=>((X456)=(X457))))=>(![X459:$i]:(~(in @ X459 @ emptyset))=>(![X460:$i, X461:$i, X462:$i]:(((in @ X462 @ (setadjoin @ X460 @ X461))<=>(((X462)=(X460))|(in @ X462 @ X461))))=>(![X463:$i, X464:$i]:(((in @ X464 @ (powerset @ X463))<=>![X465:$i]:(((in @ X465 @ X464)=>(in @ X465 @ X463)))))=>(![X466:$i, X467:$i]:(((in @ X467 @ (setunion @ X466))<=>?[X468:$i]:(((in @ X467 @ X468)&(in @ X468 @ X466)))))=>((in @ emptyset @ omega)=>(![X469:$i]:(((in @ X469 @ omega)=>(in @ (setadjoin @ X469 @ X469) @ omega)))=>(![X470:$i]:((((in @ emptyset @ X470)&![X471:$i]:((((in @ X471 @ omega)&(in @ X471 @ X470))=>(in @ (setadjoin @ X471 @ X471) @ X470))))=>![X472:$i]:(((in @ X472 @ omega)=>(in @ X472 @ X470)))))=>(![X473:$i > $i > $o, X474:$i]:((![X475:$i]:(((in @ X475 @ X474)=>?[X476:$i]:(((X473 @ X475 @ X476)&![X477:$i]:(((X473 @ X475 @ X477)=>((X476)=(X477))))))))=>?[X478:$i]:(![X479:$i]:(((in @ X479 @ X478)<=>?[X480:$i]:(((in @ X480 @ X474)&(X473 @ X480 @ X479))))))))=>(![X481:$i]:((?[X482:$i]:((in @ X482 @ X481))=>?[X483:$i]:(((in @ X483 @ X481)&~(?[X484:$i]:(((in @ X484 @ X483)&(in @ X484 @ X481))))))))=>((epred1_0)=>(![X504:$i > $o]:((?[X505:$i]:(((X504 @ X505)&![X506:$i]:(((X504 @ X506)=>((X505)=(X506))))))=>(X504 @ (descr @ (^[Z0:$i]:(X504 @ Z0))))))=>(![X507:$i, X508:$i > $o, X509:$i]:(((in @ X509 @ X507)=>((X508 @ X509)=>(in @ X509 @ (dsetconstr @ X507 @ X508)))))=>(![X510:$i, X511:$i > $o, X512:$i]:(((in @ X512 @ (dsetconstr @ X510 @ X511))=>(in @ X512 @ X510)))=>(![X513:$i, X514:$i > $o, X515:$i]:(((in @ X515 @ (dsetconstr @ X513 @ X514))=>(X514 @ X515)))=>(![X516:$i > $o]:((?[X517:$i]:(((X516 @ X517)&![X518:$i]:(((X516 @ X518)=>((X517)=(X518))))))=>?[X519:$i]:(((X516 @ X519)&![X520:$i]:(((X516 @ X520)=>((X519)=(X520))))))))=>(![X521:$o, X522:$i]:(((in @ X522 @ (prop2set @ ((X521))))=>(X521)))=>(![X523:$i]:(((in @ X523 @ emptyset)=>![X524:$o]:((X524))))=>(![X525:$i]:(((in @ X525 @ emptyset)=>~($true)))=>(![X526:$i]:(~(in @ X526 @ emptyset))=>(![X527:$i > $o]:((?[X528:$i]:(((X527 @ X528)&![X529:$i]:(((X527 @ X529)=>((X528)=(X529))))))=>?[X530:$i]:((X527 @ X530))))=>(![X531:$i, X532:$i]:((![X533:$i]:(((in @ X533 @ X531)=>(in @ X533 @ X532)))=>(![X534:$i]:(((in @ X534 @ X532)=>(in @ X534 @ X531)))=>((X531)=(X532)))))=>(![X535:$i]:((![X536:$i]:(~(in @ X536 @ X535))=>((X535)=(emptyset))))=>(![X537:$i]:((![X538:$i]:(~(in @ X538 @ X537))=>((X537)=(emptyset))))=>(![X539:$i, X540:$i > $o, X541:$i]:(((in @ X541 @ X539)=>((in @ X541 @ (dsetconstr @ X539 @ X540))<=>(X540 @ X541))))=>(![X542:$i]:((((X542)!=(emptyset))=>?[X543:$i]:((in @ X543 @ X542))))=>(![X544:$i, X545:$i > $o, X546:$i]:(((in @ X546 @ X544)=>((X545 @ X546)=>((dsetconstr @ X544 @ X545)!=(emptyset)))))=>(![X547:$i]:((?[X548:$i]:((in @ X548 @ X547))=>((X547)!=(emptyset))))=>(![X549:$i, X550:$i]:((in @ X549 @ (setadjoin @ X549 @ X550)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X551:$i, X552:$i, X553:$i]:(((in @ X553 @ X552)=>(in @ X553 @ (setadjoin @ X551 @ X552))))=>(![X554:$i, X555:$i, X556:$i]:(((in @ X556 @ (setadjoin @ X554 @ X555))=>![X557:$o]:(((((X556)=(X554))=>(X557))=>(((in @ X556 @ X555)=>(X557))=>(X557))))))=>(![X558:$i, X559:$i, X560:$i]:(((in @ X560 @ (setadjoin @ X558 @ X559))=>(((X560)=(X558))|(in @ X560 @ X559))))=>(![X561:$i]:(((dsetconstr @ X561 @ (^[Z0:$i]:($true)))=(X561)))=>(![X562:$i, X563:$i]:((![X564:$i]:(((in @ X564 @ X563)=>(in @ X564 @ X562)))=>(in @ X563 @ (powerset @ X562))))=>(![X565:$i]:((in @ emptyset @ (powerset @ X565)))=>(![X566:$i]:((in @ emptyset @ (powerset @ X566)))=>(![X567:$i, X568:$i, X569:$i]:(((in @ X568 @ (powerset @ X567))=>((in @ X569 @ X568)=>(in @ X569 @ X567))))=>(![X570:$i, X571:$i, X572:$i]:(((in @ X571 @ X572)=>((in @ X572 @ X570)=>(in @ X571 @ (setunion @ X570)))))=>(![X573:$i, X574:$i]:(((in @ X574 @ (setunion @ X573))=>![X575:$o]:((![X576:$i]:(((in @ X574 @ X576)=>((in @ X576 @ X573)=>(X575))))=>(X575)))))=>(![X577:$i, X578:$i]:(((in @ X578 @ X577)=>(in @ X578 @ (powerset @ (setunion @ X577)))))=>(![X579:$i > $o]:((?[X580:$i]:(((X579 @ X580)&![X581:$i]:(((X579 @ X581)=>((X580)=(X581))))))=>?[X582:$i]:(![X583:$i]:(((X579 @ X583)<=>((X583)=(X582)))))))=>(![X584:$i]:((((X584)!=(emptyset))=>?[X585:$i]:(((in @ X585 @ X584)&$true))))=>(![X586:$i, X587:$i]:(((in @ X586 @ (setadjoin @ X587 @ emptyset))=>((X586)=(X587))))=>(![X588:$i, X589:$i]:((((X588)!=(X589))=>~(in @ X589 @ (setadjoin @ X588 @ emptyset))))=>(![X590:$i, X591:$i]:((((X590)=(X591))=>(in @ X590 @ (setadjoin @ X591 @ emptyset))))=>(![X592:$i, X593:$i]:(((in @ X592 @ (setadjoin @ X593 @ emptyset))=>(in @ X593 @ (setadjoin @ X592 @ emptyset))))=>(![X594:$i, X595:$i, X596:$i]:(((in @ X596 @ (setadjoin @ X594 @ (setadjoin @ X595 @ emptyset)))=>(((X596)=(X594))|((X596)=(X595)))))=>(![X597:$i, X598:$i]:((in @ X597 @ (setadjoin @ X597 @ (setadjoin @ X598 @ emptyset))))=>(![X599:$i, X600:$i]:((in @ X600 @ (setadjoin @ X599 @ (setadjoin @ X600 @ emptyset))))=>(![X601:$i, X602:$i > $o]:((?[X603:$i]:(((in @ X603 @ X601)&(X602 @ X603)))=>(((dsetconstr @ X601 @ X602)=(emptyset))=>~($true))))=>(![X604:$i > $o, X605:$i]:(((in @ X605 @ emptyset)=>(X604 @ X605)))=>(![X606:$i, X607:$i > $o]:((~(![X608:$i]:(((in @ X608 @ X606)=>(X607 @ X608))))=>?[X609:$i]:(((in @ X609 @ X606)&~((X607 @ X609))))))=>(![X610:$i, X611:$i > $o]:((![X612:$i]:(((in @ X612 @ X610)=>~((X611 @ X612))))=>~(?[X613:$i]:(((in @ X613 @ X610)&(X611 @ X613))))))=>(![X614:$i, X615:$i > $o]:((~(?[X616:$i]:(((in @ X616 @ X614)&(X615 @ X616))))=>![X617:$i]:(((in @ X617 @ X614)=>~((X615 @ X617))))))=>(![X618:$i, X619:$i > $o]:((?[X620:$i]:(((in @ X620 @ X618)&~((X619 @ X620))))=>~(![X621:$i]:(((in @ X621 @ X618)=>(X619 @ X621))))))=>(![X622:$o]:(((X622)=>(in @ emptyset @ (prop2set @ ((X622))))))=>(![X623:$o]:(((X623)=>(set2prop @ (prop2set @ ((X623))))))=>(![X624:$i, X625:$i > $o]:((~(?[X626:$i]:(((in @ X626 @ X624)&(X625 @ X626))))=>![X627:$i]:(((in @ X627 @ X624)=>~((X625 @ X627))))))=>(![X628:$i, X629:$i > $o]:((~(![X630:$i]:(((in @ X630 @ X628)=>(X629 @ X630))))=>?[X631:$i]:(((in @ X631 @ X628)&~((X629 @ X631))))))=>(![X632:$i > $o]:((?[X633:$i]:(((X632 @ X633)&![X634:$i]:(((X632 @ X634)=>((X633)=(X634))))))=>?[X635:$i]:(((X632 @ X635)&![X636:$i]:(((X632 @ X636)=>((X635)=(X636))))))))=>(![X637:$i > $o]:((?[X638:$i]:((X637 @ X638))=>(![X639:$i, X640:$i]:(((X637 @ X639)=>((X637 @ X640)=>((X639)=(X640)))))=>?[X641:$i]:(((X637 @ X641)&![X642:$i]:(((X637 @ X642)=>((X641)=(X642)))))))))=>(![X643:$i > $o]:((?[X644:$i]:(![X645:$i]:(((X643 @ X645)<=>((X645)=(X644)))))=>?[X646:$i]:(((X643 @ X646)&![X647:$i]:(((X643 @ X647)=>((X646)=(X647))))))))=>(![X648:$i, X649:$i]:((((X648)=(X649))=>![X650:$i, X651:$i]:((((X650)=(X651))=>((in @ X650 @ X648)=>(in @ X651 @ X649))))))=>(![X652:$i, X653:$i]:((((X652)=(X653))=>![X654:$i, X655:$i]:((((X654)=(X655))=>((in @ X654 @ X652)<=>(in @ X655 @ X653))))))=>(![X656:$i > $o]:((?[X657:$i]:(((X656 @ X657)&![X658:$i]:(((X656 @ X658)=>((X657)=(X658))))))=>![X659:$i, X660:$i]:(((X656 @ X659)=>((X656 @ X660)=>((X659)=(X660)))))))=>(![X661:$i > $o, X662:$i > $o]:((![X663:$i, X664:$i]:((((X663)=(X664))=>((X661 @ X663)<=>(X662 @ X664))))=>(?[X665:$i]:(((X661 @ X665)&![X666:$i]:(((X661 @ X666)=>((X665)=(X666))))))<=>?[X667:$i]:(((X662 @ X667)&![X668:$i]:(((X662 @ X668)=>((X667)=(X668)))))))))=>(((emptyset)=(emptyset))=>(![X669:$i, X670:$i]:((((X669)=(X670))=>![X671:$i, X672:$i]:((((X671)=(X672))=>((setadjoin @ X669 @ X671)=(setadjoin @ X670 @ X672))))))=>(![X673:$i, X674:$i]:((((X673)=(X674))=>((powerset @ X673)=(powerset @ X674))))=>(![X675:$i, X676:$i]:((((X675)=(X676))=>((setunion @ X675)=(setunion @ X676))))=>(((omega)=(omega))=>(![X677:$i > $o]:((?[X678:$i]:(((X677 @ X678)&![X679:$i]:(((X677 @ X679)=>((X678)=(X679))))))=>![X680:$i, X681:$i]:(((X677 @ X680)=>((X677 @ X681)=>((X680)=(X681)))))))=>(![X682:$i > $o, X683:$i > $o]:((![X684:$i, X685:$i]:((((X684)=(X685))=>((X682 @ X684)<=>(X683 @ X685))))=>(?[X686:$i]:(((X682 @ X686)&![X687:$i]:(((X682 @ X687)=>((X686)=(X687))))))=>(?[X688:$i]:(((X683 @ X688)&![X689:$i]:(((X683 @ X689)=>((X688)=(X689))))))=>((descr @ X682)=(descr @ X683))))))=>(![X690:$i, X691:$i]:((((X690)=(X691))=>![X692:$i > $o, X693:$i > $o]:((![X694:$i]:(((in @ X694 @ X690)=>![X695:$i]:(((in @ X695 @ X691)=>(((X694)=(X695))=>((X692 @ X694)<=>(X693 @ X695)))))))=>((dsetconstr @ X690 @ X692)=(dsetconstr @ X691 @ X693))))))=>(![X696:$i, X697:$i]:((![X698:$i]:(((in @ X698 @ X696)=>(in @ X698 @ X697)))=>(subset @ X696 @ X697)))=>(![X699:$i, X700:$i]:((((X699)=(X700))=>(subset @ X700 @ X699)))=>(![X701:$i, X702:$i]:((((X701)=(X702))=>(subset @ X701 @ X702)))=>(![X703:$i, X704:$i]:((![X705:$i]:(((in @ X705 @ X703)=>(in @ X705 @ X704)))=>(subset @ X703 @ X704)))=>(![X706:$i]:((subset @ emptyset @ X706))=>(![X707:$i, X708:$i, X709:$i]:(((subset @ X707 @ X708)=>((in @ X709 @ X707)=>(in @ X709 @ X708))))=>(![X710:$i, X711:$i, X712:$i]:(((subset @ X710 @ X711)=>(~(in @ X712 @ X711)=>~(in @ X712 @ X710))))=>(![X713:$i, X714:$i, X715:$i]:(((in @ X715 @ X713)=>(~(in @ X715 @ X714)=>~(subset @ X713 @ X714))))=>(![X716:$i, X717:$i]:((~(subset @ X716 @ X717)=>((X716)!=(X717))))=>(![X718:$i, X719:$i, X720:$i]:(((in @ X720 @ X718)=>(~(in @ X720 @ X719)=>((X718)!=(X719)))))=>(![X721:$i]:((subset @ X721 @ X721))=>(![X722:$i, X723:$i, X724:$i]:(((subset @ X722 @ X723)=>((subset @ X723 @ X724)=>(subset @ X722 @ X724))))=>(![X725:$i, X726:$i]:((subset @ X726 @ (setadjoin @ X725 @ X726)))=>(![X727:$i, X728:$i, X729:$i]:(((subset @ X727 @ X729)=>(subset @ X727 @ (setadjoin @ X728 @ X729))))=>(![X730:$i, X731:$i]:(((subset @ X730 @ X731)=>(in @ X730 @ (powerset @ X731))))=>(![X732:$i, X733:$i]:(((subset @ X732 @ X733)=>((subset @ X733 @ X732)=>((X732)=(X733)))))=>(![X734:$i]:(((subset @ X734 @ emptyset)=>((X734)=(emptyset))))=>(![X735:$i, X736:$i]:(((subset @ X736 @ X735)=>(in @ X736 @ (powerset @ X735))))=>(![X737:$i, X738:$i]:(((in @ X738 @ (powerset @ X737))=>(subset @ X738 @ X737)))=>(![X739:$i]:((in @ X739 @ (powerset @ X739)))=>(![X740:$i, X741:$i]:(((subset @ X740 @ X741)=>(subset @ (powerset @ X740) @ (powerset @ X741))))=>(![X742:$i, X743:$i > $o]:((in @ (dsetconstr @ X742 @ X743) @ (powerset @ X742)))=>(![X744:$i, X745:$i > $o]:((subset @ (dsetconstr @ X744 @ X745) @ X744))=>(![X746:$i, X747:$i, X748:$i]:(((in @ X748 @ X746)=>(in @ X748 @ (binunion @ X746 @ X747))))=>(![X749:$i, X750:$i]:((in @ X750 @ (setadjoin @ X749 @ (setadjoin @ X750 @ emptyset))))=>(![X751:$i, X752:$i, X753:$i]:(((in @ X753 @ X752)=>(in @ X753 @ (binunion @ X751 @ X752))))=>(![X754:$i, X755:$i, X756:$i, X757:$o]:(((in @ X756 @ (binunion @ X754 @ X755))=>(((in @ X756 @ X754)=>(X757))=>(((in @ X756 @ X755)=>(X757))=>(X757)))))=>(![X758:$i, X759:$i, X760:$i]:(((in @ X760 @ (binunion @ X758 @ X759))=>((in @ X760 @ X758)|(in @ X760 @ X759))))=>(![X761:$i, X762:$i]:((subset @ X761 @ (binunion @ X761 @ X762)))=>(![X763:$i, X764:$i]:((subset @ X764 @ (binunion @ X763 @ X764)))=>(![X765:$i, X766:$i, X767:$i]:(((in @ X767 @ X765)=>((in @ X767 @ X766)=>(in @ X767 @ (binintersect @ X765 @ X766)))))=>(![X768:$i, X769:$i, X770:$i]:(((subset @ X770 @ X768)=>((subset @ X770 @ X769)=>(subset @ X770 @ (binintersect @ X768 @ X769)))))=>(![X771:$i, X772:$i, X773:$i]:(((in @ X773 @ (binintersect @ X771 @ X772))=>(in @ X773 @ X771)))=>(![X774:$i, X775:$i]:((subset @ (binintersect @ X774 @ X775) @ X774))=>(![X776:$i, X777:$i]:(((subset @ X776 @ X777)=>((binintersect @ X776 @ X777)=(X776))))=>(![X778:$i, X779:$i]:((((binintersect @ X778 @ X779)=(X779))=>(subset @ X779 @ X778)))=>(![X780:$i, X781:$i, X782:$i]:(((in @ X782 @ (binintersect @ X780 @ X781))=>(in @ X782 @ X781)))=>(![X783:$i, X784:$i]:((~(?[X785:$i]:(((in @ X785 @ X783)&(in @ X785 @ X784))))=>((binintersect @ X783 @ X784)=(emptyset))))=>(![X786:$i, X787:$i]:((subset @ (binintersect @ X786 @ X787) @ X787))=>(![X788:$i, X789:$i]:(((subset @ X789 @ X788)=>((binintersect @ X788 @ X789)=(X789))))=>(![X790:$i, X791:$i]:((((binintersect @ X790 @ X791)=(X790))=>(subset @ X790 @ X791)))=>(![X792:$i, X793:$i, X794:$i]:(((binintersect @ X792 @ (binunion @ X793 @ X794))=(binunion @ (binintersect @ X792 @ X793) @ (binintersect @ X792 @ X794))))=>(![X795:$i, X796:$i, X797:$i]:(((in @ X797 @ X795)=>(~(in @ X797 @ X796)=>(in @ X797 @ (setminus @ X795 @ X796)))))=>(![X798:$i, X799:$i, X800:$i]:(((in @ X800 @ (setminus @ X798 @ X799))=>(in @ X800 @ X798)))=>(![X801:$i, X802:$i, X803:$i]:(((in @ X803 @ (setminus @ X801 @ X802))=>~(in @ X803 @ X802)))=>(![X804:$i, X805:$i]:(((subset @ X804 @ X805)=>((setminus @ X804 @ X805)=(emptyset))))=>(![X806:$i, X807:$i, X808:$i]:((~(in @ X808 @ (setminus @ X806 @ X807))=>((in @ X808 @ X806)=>(in @ X808 @ X807))))=>(![X809:$i, X810:$i, X811:$i]:((~(in @ X811 @ (setminus @ X809 @ X810))=>(~(in @ X811 @ X810)=>~(in @ X811 @ X809))))=>(![X812:$i, X813:$i, X814:$i]:((~(in @ X814 @ X812)=>~(in @ X814 @ (setminus @ X812 @ X813))))=>(![X815:$i, X816:$i, X817:$i]:(((in @ X817 @ X816)=>~(in @ X817 @ (setminus @ X815 @ X816))))=>(![X818:$i, X819:$i]:((subset @ (setminus @ X818 @ X819) @ X818))=>(![X820:$i, X821:$i]:((((setminus @ X820 @ X821)=(emptyset))=>(subset @ X820 @ X821)))=>(![X822:$i, X823:$i, X824:$i]:(((in @ X824 @ (symdiff @ X822 @ X823))=>![X825:$o]:((((in @ X824 @ X822)=>(~(in @ X824 @ X823)=>(X825)))=>((~(in @ X824 @ X822)=>((in @ X824 @ X823)=>(X825)))=>(X825))))))=>(![X826:$i, X827:$i, X828:$i]:(((in @ X828 @ X826)=>(~(in @ X828 @ X827)=>(in @ X828 @ (symdiff @ X826 @ X827)))))=>(![X829:$i, X830:$i, X831:$i]:((~(in @ X831 @ X829)=>((in @ X831 @ X830)=>(in @ X831 @ (symdiff @ X829 @ X830)))))=>(![X832:$i, X833:$i, X834:$i]:(((in @ X834 @ X832)=>((in @ X834 @ X833)=>~(in @ X834 @ (symdiff @ X832 @ X833)))))=>(![X835:$i, X836:$i, X837:$i]:((~(in @ X837 @ X835)=>(~(in @ X837 @ X836)=>~(in @ X837 @ (symdiff @ X835 @ X836)))))=>(![X838:$i, X839:$i]:((in @ X839 @ (setadjoin @ X838 @ (setadjoin @ X839 @ emptyset))))=>(![X840:$i, X841:$i]:((in @ X840 @ (setunion @ (setadjoin @ (setadjoin @ X840 @ emptyset) @ (setadjoin @ (setadjoin @ X840 @ (setadjoin @ X841 @ emptyset)) @ emptyset)))))=>(![X842:$i, X843:$i]:((in @ X843 @ (setunion @ (setadjoin @ (setadjoin @ X842 @ emptyset) @ (setadjoin @ (setadjoin @ X842 @ (setadjoin @ X843 @ emptyset)) @ emptyset)))))=>(![X844:$i, X845:$i]:(?[X846:$i]:(((in @ X846 @ (setunion @ (setadjoin @ (setadjoin @ X844 @ emptyset) @ (setadjoin @ (setadjoin @ X844 @ (setadjoin @ X845 @ emptyset)) @ emptyset))))&?[X847:$i]:(((in @ X847 @ (setunion @ (setadjoin @ (setadjoin @ X844 @ emptyset) @ (setadjoin @ (setadjoin @ X844 @ (setadjoin @ X845 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X844 @ emptyset) @ (setadjoin @ (setadjoin @ X844 @ (setadjoin @ X845 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X846 @ emptyset) @ (setadjoin @ (setadjoin @ X846 @ (setadjoin @ X847 @ emptyset)) @ emptyset))))))))=>(![X848:$i, X849:$i]:(?[X850:$i]:(((in @ X850 @ (setunion @ (kpair @ X848 @ X849)))&?[X851:$i]:(((in @ X851 @ (setunion @ (kpair @ X848 @ X849)))&((kpair @ X848 @ X849)=(setadjoin @ (setadjoin @ X850 @ emptyset) @ (setadjoin @ (setadjoin @ X850 @ (setadjoin @ X851 @ emptyset)) @ emptyset))))))))=>(![X852:$i, X853:$i]:(((in @ X853 @ X852)=>(subset @ (setadjoin @ X853 @ emptyset) @ X852)))=>(![X854:$i, X855:$i]:(((in @ X855 @ X854)=>(in @ (setadjoin @ X855 @ emptyset) @ (powerset @ X854))))=>(![X856:$i, X857:$i, X858:$i]:(((in @ X858 @ X856)=>(in @ (setadjoin @ X858 @ emptyset) @ (powerset @ (binunion @ X856 @ X857)))))=>(![X859:$i, X860:$i, X861:$i]:(((in @ X861 @ (setadjoin @ X859 @ (setadjoin @ X860 @ emptyset)))=>(((X861)=(X859))|((X861)=(X860)))))=>(![X862:$i, X863:$i, X864:$i]:(((in @ X864 @ X862)=>![X865:$i]:(((in @ X865 @ X863)=>(subset @ (setadjoin @ X864 @ (setadjoin @ X865 @ emptyset)) @ (binunion @ X862 @ X863))))))=>(![X866:$i, X867:$i, X868:$i]:(((in @ X868 @ X866)=>![X869:$i]:(((in @ X869 @ X867)=>(in @ (setadjoin @ X868 @ (setadjoin @ X869 @ emptyset)) @ (powerset @ (binunion @ X866 @ X867)))))))=>(![X870:$i, X871:$i, X872:$i]:(((in @ X872 @ X870)=>![X873:$i]:(((in @ X873 @ X871)=>(subset @ (setadjoin @ (setadjoin @ X872 @ emptyset) @ (setadjoin @ (setadjoin @ X872 @ (setadjoin @ X873 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X870 @ X871)))))))=>(![X874:$i, X875:$i, X876:$i]:(((in @ X876 @ X874)=>![X877:$i]:(((in @ X877 @ X875)=>(in @ (setadjoin @ (setadjoin @ X876 @ emptyset) @ (setadjoin @ (setadjoin @ X876 @ (setadjoin @ X877 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X874 @ X875))))))))=>(![X878:$i, X879:$i, X880:$i]:(((in @ X880 @ X878)=>![X881:$i]:(((in @ X881 @ X879)=>(in @ (kpair @ X880 @ X881) @ (powerset @ (powerset @ (binunion @ X878 @ X879))))))))=>(![X882:$i, X883:$i, X884:$i]:(((in @ X884 @ X882)=>![X885:$i]:(((in @ X885 @ X883)=>(in @ (kpair @ X884 @ X885) @ (cartprod @ X882 @ X883))))))=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_168, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_169]), foundationAx]), wellorderingAx]), c_0_170]), c_0_171]), c_0_172]), c_0_173]), c_0_174]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_175]), setext]), emptyI]), noeltsimpempty]), c_0_176]), c_0_177]), c_0_178]), c_0_179]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_180]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_181]), c_0_182]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_183]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_184]), c_0_185]), c_0_186]), inCongP]), in__Cong]), c_0_187]), c_0_188]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_189]), c_0_190]), c_0_191]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_192]), c_0_193]), 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_194]), c_0_195]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin])])]), c_0_196])).
% 205.36/30.00 thf(c_0_198, negated_conjecture, ![X894:$i, X895:$i, X897:$i, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X904:$i, X905:$i, X907:$i, X908:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X916:$i, X917:$i > $i > $o, X918:$i, X920:$i, X923:$i, X925:$i, X926:$i, X927:$i, X928:$i, X930:$i, X931:$i > $o, X932:$i, X934:$i, X935:$i > $o, X936:$i, X937:$i, X938:$i > $o, X939:$i, X940:$i, X941:$i > $o, X942:$i, X943:$i > $o, X944:$i, X947:$i, X948:$o, X949:$i, X950:$i, X951:$o, X952:$i, X953:$i, X954:$i > $o, X955:$i, X958:$i, X959:$i, X962:$i, X964:$i, X966:$i, X967:$i > $o, X968:$i, X969:$i, X971:$i, X972:$i > $o, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i, X979:$i, X980:$i, X981:$i, X982:$i, X983:$i, X984:$o, X985:$i, X986:$i, X987:$i, X988:$i, X989:$i, X990:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$o, X1004:$i, X1005:$i, X1006:$i > $o, X1007:$i, X1010:$i, X1011:$i, X1012:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i > $o, X1031:$i, X1032:$i > $o, X1033:$i, X1034:$i, X1035:$i > $o, X1036:$i, X1038:$i, X1039:$i > $o, X1041:$i, X1042:$i, X1043:$i > $o, X1045:$i, X1046:$i, X1047:$i > $o, X1048:$i, X1050:$o, X1051:$o, X1052:$i, X1053:$i > $o, X1055:$i, X1056:$i, X1057:$i > $o, X1058:$i, X1060:$i > $o, X1061:$i, X1064:$i, X1065:$i > $o, X1066:$i, X1070:$i, X1071:$i > $o, X1072:$i, X1075:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i > $o, X1085:$i, X1087:$i, X1088:$i, X1089:$i > $o, X1090:$i > $o, X1093:$i, X1096:$i, X1097:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i > $o, X1110:$i, X1112:$i, X1113:$i, X1114:$i > $o, X1115:$i > $o, X1118:$i, X1120:$i, X1122:$i, X1123:$i, X1124:$i > $o, X1125:$i > $o, X1128:$i, X1129:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$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:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i > $o, X1176:$i, X1177:$i > $o, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$o, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$o, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1280:$i, X1281:$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:$i, X1317:$i, X1321:$i, X1322:$i]:((((~(in @ (esk1_2 @ X894 @ X895) @ X894)|~(in @ (esk1_2 @ X894 @ X895) @ X895)|((X894)=(X895)))&((in @ (esk1_2 @ X894 @ X895) @ X894)|(in @ (esk1_2 @ X894 @ X895) @ X895)|((X894)=(X895))))&(~(in @ X897 @ emptyset)&(((~(in @ X900 @ (setadjoin @ X898 @ X899))|(((X900)=(X898))|(in @ X900 @ X899)))&((((X900)!=(X898))|(in @ X900 @ (setadjoin @ X898 @ X899)))&(~(in @ X900 @ X899)|(in @ X900 @ (setadjoin @ X898 @ X899)))))&(((~(in @ X902 @ (powerset @ X901))|(~(in @ X903 @ X902)|(in @ X903 @ X901)))&(((in @ (esk2_2 @ X904 @ X905) @ X905)|(in @ X905 @ (powerset @ X904)))&(~(in @ (esk2_2 @ X904 @ X905) @ X904)|(in @ X905 @ (powerset @ X904)))))&(((((in @ X908 @ (esk3_2 @ X907 @ X908))|~(in @ X908 @ (setunion @ X907)))&((in @ (esk3_2 @ X907 @ X908) @ X907)|~(in @ X908 @ (setunion @ X907))))&(~(in @ X911 @ X912)|~(in @ X912 @ X910)|(in @ X911 @ (setunion @ X910))))&((in @ emptyset @ omega)&((~(in @ X913 @ omega)|(in @ (setadjoin @ X913 @ X913) @ omega))&(((((in @ (esk4_1 @ X914) @ omega)|~(in @ emptyset @ X914)|(~(in @ X916 @ omega)|(in @ X916 @ X914)))&((in @ (esk4_1 @ X914) @ X914)|~(in @ emptyset @ X914)|(~(in @ X916 @ omega)|(in @ X916 @ X914))))&(~(in @ (setadjoin @ (esk4_1 @ X914) @ (esk4_1 @ X914)) @ X914)|~(in @ emptyset @ X914)|(~(in @ X916 @ omega)|(in @ X916 @ X914))))&((((((in @ (esk8_3 @ X917 @ X918 @ X923) @ X918)|~(in @ X923 @ (esk7_2 @ X917 @ X918))|(in @ (esk5_2 @ X917 @ X918) @ X918))&((X917 @ (esk8_3 @ X917 @ X918 @ X923) @ X923)|~(in @ X923 @ (esk7_2 @ X917 @ X918))|(in @ (esk5_2 @ X917 @ X918) @ X918)))&(~(in @ X926 @ X918)|~(X917 @ X926 @ X925)|(in @ X925 @ (esk7_2 @ X917 @ X918))|(in @ (esk5_2 @ X917 @ X918) @ X918)))&(((((in @ (esk8_3 @ X917 @ X918 @ X923) @ X918)|~(in @ X923 @ (esk7_2 @ X917 @ X918))|((X917 @ (esk5_2 @ X917 @ X918) @ (esk6_3 @ X917 @ X918 @ X920))|~(X917 @ (esk5_2 @ X917 @ X918) @ X920)))&((X917 @ (esk8_3 @ X917 @ X918 @ X923) @ X923)|~(in @ X923 @ (esk7_2 @ X917 @ X918))|((X917 @ (esk5_2 @ X917 @ X918) @ (esk6_3 @ X917 @ X918 @ X920))|~(X917 @ (esk5_2 @ X917 @ X918) @ X920))))&(~(in @ X926 @ X918)|~(X917 @ X926 @ X925)|(in @ X925 @ (esk7_2 @ X917 @ X918))|((X917 @ (esk5_2 @ X917 @ X918) @ (esk6_3 @ X917 @ X918 @ X920))|~(X917 @ (esk5_2 @ X917 @ X918) @ X920))))&((((in @ (esk8_3 @ X917 @ X918 @ X923) @ X918)|~(in @ X923 @ (esk7_2 @ X917 @ X918))|(((X920)!=(esk6_3 @ X917 @ X918 @ X920))|~(X917 @ (esk5_2 @ X917 @ X918) @ X920)))&((X917 @ (esk8_3 @ X917 @ X918 @ X923) @ X923)|~(in @ X923 @ (esk7_2 @ X917 @ X918))|(((X920)!=(esk6_3 @ X917 @ X918 @ X920))|~(X917 @ (esk5_2 @ X917 @ X918) @ X920))))&(~(in @ X926 @ X918)|~(X917 @ X926 @ X925)|(in @ X925 @ (esk7_2 @ X917 @ X918))|(((X920)!=(esk6_3 @ X917 @ X918 @ X920))|~(X917 @ (esk5_2 @ X917 @ X918) @ X920))))))&((((in @ (esk9_1 @ X927) @ X927)|~(in @ X928 @ X927))&(~(in @ X930 @ (esk9_1 @ X927))|~(in @ X930 @ X927)|~(in @ X928 @ X927)))&((epred1_0)&((((X931 @ (esk10_2 @ X931 @ X932))|~(X931 @ X932)|(X931 @ (descr @ X931)))&(((X932)!=(esk10_2 @ X931 @ X932))|~(X931 @ X932)|(X931 @ (descr @ X931))))&((~(in @ X936 @ X934)|(~(X935 @ X936)|(in @ X936 @ (dsetconstr @ X934 @ X935))))&((~(in @ X939 @ (dsetconstr @ X937 @ X938))|(in @ X939 @ X937))&((~(in @ X942 @ (dsetconstr @ X940 @ X941))|(X941 @ X942))&(((((X943 @ (esk12_1 @ X943))|((X943 @ (esk11_2 @ X943 @ X944))|~(X943 @ X944)))&(~(X943 @ X947)|((esk12_1 @ X943)=(X947))|((X943 @ (esk11_2 @ X943 @ X944))|~(X943 @ X944))))&(((X943 @ (esk12_1 @ X943))|(((X944)!=(esk11_2 @ X943 @ X944))|~(X943 @ X944)))&(~(X943 @ X947)|((esk12_1 @ X943)=(X947))|(((X944)!=(esk11_2 @ X943 @ X944))|~(X943 @ X944)))))&((~(in @ X949 @ (prop2set @ ((X948))))|(X948))&((~(in @ X950 @ emptyset)|(X951))&((~(in @ X952 @ emptyset)|~($true))&(~(in @ X953 @ emptyset)&((((X954 @ (esk13_2 @ X954 @ X955))|~(X954 @ X955)|(X954 @ (esk14_1 @ X954)))&(((X955)!=(esk13_2 @ X954 @ X955))|~(X954 @ X955)|(X954 @ (esk14_1 @ X954))))&(((((in @ (esk16_2 @ X958 @ X959) @ X959)|((X958)=(X959))|(in @ (esk15_2 @ X958 @ X959) @ X958))&(~(in @ (esk16_2 @ X958 @ X959) @ X958)|((X958)=(X959))|(in @ (esk15_2 @ X958 @ X959) @ X958)))&(((in @ (esk16_2 @ X958 @ X959) @ X959)|((X958)=(X959))|~(in @ (esk15_2 @ X958 @ X959) @ X959))&(~(in @ (esk16_2 @ X958 @ X959) @ X958)|((X958)=(X959))|~(in @ (esk15_2 @ X958 @ X959) @ X959))))&(((in @ (esk17_1 @ X962) @ X962)|((X962)=(emptyset)))&(((in @ (esk18_1 @ X964) @ X964)|((X964)=(emptyset)))&(((~(in @ X968 @ (dsetconstr @ X966 @ X967))|(X967 @ X968)|~(in @ X968 @ X966))&(~(X967 @ X968)|(in @ X968 @ (dsetconstr @ X966 @ X967))|~(in @ X968 @ X966)))&((((X969)=(emptyset))|(in @ (esk19_1 @ X969) @ X969))&((~(in @ X973 @ X971)|(~(X972 @ X973)|((dsetconstr @ X971 @ X972)!=(emptyset))))&((~(in @ X975 @ X974)|((X974)!=(emptyset)))&((in @ X976 @ (setadjoin @ X976 @ X977))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X980 @ X979)|(in @ X980 @ (setadjoin @ X978 @ X979)))&(((((in @ X983 @ X982)|(X984)|((X983)=(X981))|~(in @ X983 @ (setadjoin @ X981 @ X982)))&(~(X984)|(X984)|((X983)=(X981))|~(in @ X983 @ (setadjoin @ X981 @ X982))))&(((in @ X983 @ X982)|(X984)|~(X984)|~(in @ X983 @ (setadjoin @ X981 @ X982)))&(~(X984)|(X984)|~(X984)|~(in @ X983 @ (setadjoin @ X981 @ X982)))))&((~(in @ X987 @ (setadjoin @ X985 @ X986))|(((X987)=(X985))|(in @ X987 @ X986)))&(((dsetconstr @ X988 @ (^[Z0:$i]:($true)))=(X988))&((((in @ (esk20_2 @ X989 @ X990) @ X990)|(in @ X990 @ (powerset @ X989)))&(~(in @ (esk20_2 @ X989 @ X990) @ X989)|(in @ X990 @ (powerset @ X989))))&((in @ emptyset @ (powerset @ X992))&((in @ emptyset @ (powerset @ X993))&((~(in @ X995 @ (powerset @ X994))|(~(in @ X996 @ X995)|(in @ X996 @ X994)))&((~(in @ X998 @ X999)|(~(in @ X999 @ X997)|(in @ X998 @ (setunion @ X997))))&((((in @ X1001 @ (esk21_3 @ X1000 @ X1001 @ X1002))|(X1002)|~(in @ X1001 @ (setunion @ X1000)))&(((in @ (esk21_3 @ X1000 @ X1001 @ X1002) @ X1000)|(X1002)|~(in @ X1001 @ (setunion @ X1000)))&(~(X1002)|(X1002)|~(in @ X1001 @ (setunion @ X1000)))))&((~(in @ X1005 @ X1004)|(in @ X1005 @ (powerset @ (setunion @ X1004))))&((((~(X1006 @ X1010)|((X1010)=(esk23_1 @ X1006))|((X1006 @ (esk22_2 @ X1006 @ X1007))|~(X1006 @ X1007)))&(((X1011)!=(esk23_1 @ X1006))|(X1006 @ X1011)|((X1006 @ (esk22_2 @ X1006 @ X1007))|~(X1006 @ X1007))))&((~(X1006 @ X1010)|((X1010)=(esk23_1 @ X1006))|(((X1007)!=(esk22_2 @ X1006 @ X1007))|~(X1006 @ X1007)))&(((X1011)!=(esk23_1 @ X1006))|(X1006 @ X1011)|(((X1007)!=(esk22_2 @ X1006 @ X1007))|~(X1006 @ X1007)))))&((((in @ (esk24_1 @ X1012) @ X1012)|((X1012)=(emptyset)))&(($true)|((X1012)=(emptyset))))&((~(in @ X1014 @ (setadjoin @ X1015 @ emptyset))|((X1014)=(X1015)))&((((X1016)=(X1017))|~(in @ X1017 @ (setadjoin @ X1016 @ emptyset)))&((((X1018)!=(X1019))|(in @ X1018 @ (setadjoin @ X1019 @ emptyset)))&((~(in @ X1020 @ (setadjoin @ X1021 @ emptyset))|(in @ X1021 @ (setadjoin @ X1020 @ emptyset)))&((~(in @ X1024 @ (setadjoin @ X1022 @ (setadjoin @ X1023 @ emptyset)))|(((X1024)=(X1022))|((X1024)=(X1023))))&((in @ X1025 @ (setadjoin @ X1025 @ (setadjoin @ X1026 @ emptyset)))&((in @ X1028 @ (setadjoin @ X1027 @ (setadjoin @ X1028 @ emptyset)))&((~(in @ X1031 @ X1029)|~(X1030 @ X1031)|(((dsetconstr @ X1029 @ X1030)!=(emptyset))|~($true)))&((~(in @ X1033 @ emptyset)|(X1032 @ X1033))&((((in @ (esk25_2 @ X1034 @ X1035) @ X1034)|(~(in @ X1036 @ X1034)|(X1035 @ X1036)))&(~(X1035 @ (esk25_2 @ X1034 @ X1035))|(~(in @ X1036 @ X1034)|(X1035 @ X1036))))&((((in @ (esk26_2 @ X1038 @ X1039) @ X1038)|(~(in @ X1041 @ X1038)|~(X1039 @ X1041)))&((X1039 @ (esk26_2 @ X1038 @ X1039))|(~(in @ X1041 @ X1038)|~(X1039 @ X1041))))&((((in @ (esk27_2 @ X1042 @ X1043) @ X1042)|(~(in @ X1045 @ X1042)|~(X1043 @ X1045)))&((X1043 @ (esk27_2 @ X1042 @ X1043))|(~(in @ X1045 @ X1042)|~(X1043 @ X1045))))&((((in @ (esk28_2 @ X1046 @ X1047) @ X1046)|(~(in @ X1048 @ X1046)|(X1047 @ X1048)))&(~(X1047 @ (esk28_2 @ X1046 @ X1047))|(~(in @ X1048 @ X1046)|(X1047 @ X1048))))&((~(X1050)|(in @ emptyset @ (prop2set @ ((X1050)))))&((~(X1051)|(set2prop @ (prop2set @ ((X1051)))))&((((in @ (esk29_2 @ X1052 @ X1053) @ X1052)|(~(in @ X1055 @ X1052)|~(X1053 @ X1055)))&((X1053 @ (esk29_2 @ X1052 @ X1053))|(~(in @ X1055 @ X1052)|~(X1053 @ X1055))))&((((in @ (esk30_2 @ X1056 @ X1057) @ X1056)|(~(in @ X1058 @ X1056)|(X1057 @ X1058)))&(~(X1057 @ (esk30_2 @ X1056 @ X1057))|(~(in @ X1058 @ X1056)|(X1057 @ X1058))))&(((((X1060 @ (esk32_1 @ X1060))|((X1060 @ (esk31_2 @ X1060 @ X1061))|~(X1060 @ X1061)))&(~(X1060 @ X1064)|((esk32_1 @ X1060)=(X1064))|((X1060 @ (esk31_2 @ X1060 @ X1061))|~(X1060 @ X1061))))&(((X1060 @ (esk32_1 @ X1060))|(((X1061)!=(esk31_2 @ X1060 @ X1061))|~(X1060 @ X1061)))&(~(X1060 @ X1064)|((esk32_1 @ X1060)=(X1064))|(((X1061)!=(esk31_2 @ X1060 @ X1061))|~(X1060 @ X1061)))))&(((((X1065 @ (esk35_1 @ X1065))|(X1065 @ (esk33_1 @ X1065))|~(X1065 @ X1066))&(~(X1065 @ X1070)|((esk35_1 @ X1065)=(X1070))|(X1065 @ (esk33_1 @ X1065))|~(X1065 @ X1066)))&((((X1065 @ (esk35_1 @ X1065))|(X1065 @ (esk34_1 @ X1065))|~(X1065 @ X1066))&(~(X1065 @ X1070)|((esk35_1 @ X1065)=(X1070))|(X1065 @ (esk34_1 @ X1065))|~(X1065 @ X1066)))&(((X1065 @ (esk35_1 @ X1065))|((esk33_1 @ X1065)!=(esk34_1 @ X1065))|~(X1065 @ X1066))&(~(X1065 @ 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X1255)|~(in @ X1256 @ (symdiff @ X1254 @ X1255)))&(~(X1257)|(X1257)|~(in @ X1256 @ X1255)|~(in @ X1256 @ (symdiff @ X1254 @ X1255)))))&((~(in @ X1256 @ X1254)|(X1257)|~(X1257)|~(in @ X1256 @ (symdiff @ X1254 @ X1255)))&(((in @ X1256 @ X1255)|(X1257)|~(X1257)|~(in @ X1256 @ (symdiff @ X1254 @ X1255)))&(~(X1257)|(X1257)|~(X1257)|~(in @ X1256 @ (symdiff @ X1254 @ X1255)))))))&((~(in @ X1260 @ X1258)|((in @ X1260 @ X1259)|(in @ X1260 @ (symdiff @ X1258 @ X1259))))&(((in @ X1263 @ X1261)|(~(in @ X1263 @ X1262)|(in @ X1263 @ (symdiff @ X1261 @ X1262))))&((~(in @ X1266 @ X1264)|(~(in @ X1266 @ X1265)|~(in @ X1266 @ (symdiff @ X1264 @ X1265))))&(((in @ X1269 @ X1267)|((in @ X1269 @ X1268)|~(in @ X1269 @ (symdiff @ X1267 @ X1268))))&((in @ X1271 @ (setadjoin @ X1270 @ (setadjoin @ X1271 @ emptyset)))&((in @ X1272 @ (setunion @ (setadjoin @ (setadjoin @ X1272 @ emptyset) @ (setadjoin @ (setadjoin @ X1272 @ (setadjoin @ X1273 @ emptyset)) @ emptyset))))&((in @ X1275 @ (setunion @ (setadjoin @ (setadjoin @ X1274 @ emptyset) @ (setadjoin @ (setadjoin @ X1274 @ (setadjoin @ X1275 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1276 @ X1277) @ (setunion @ (setadjoin @ (setadjoin @ X1276 @ emptyset) @ (setadjoin @ (setadjoin @ X1276 @ (setadjoin @ X1277 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1276 @ X1277) @ (setunion @ (setadjoin @ (setadjoin @ X1276 @ emptyset) @ (setadjoin @ (setadjoin @ X1276 @ (setadjoin @ X1277 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1276 @ emptyset) @ (setadjoin @ (setadjoin @ X1276 @ (setadjoin @ X1277 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1276 @ X1277) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1276 @ X1277) @ (setadjoin @ (esk56_2 @ X1276 @ X1277) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1280 @ X1281) @ (setunion @ (kpair @ X1280 @ X1281)))&((in @ (esk58_2 @ X1280 @ X1281) @ (setunion @ (kpair @ X1280 @ X1281)))&((kpair @ X1280 @ X1281)=(setadjoin @ (setadjoin @ (esk57_2 @ X1280 @ X1281) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1280 @ X1281) @ (setadjoin @ (esk58_2 @ X1280 @ X1281) @ emptyset)) @ emptyset)))))&((~(in @ X1285 @ X1284)|(subset @ (setadjoin @ X1285 @ emptyset) @ X1284))&((~(in @ X1287 @ X1286)|(in @ (setadjoin @ X1287 @ emptyset) @ (powerset @ X1286)))&((~(in @ X1290 @ X1288)|(in @ (setadjoin @ X1290 @ emptyset) @ (powerset @ (binunion @ X1288 @ X1289))))&((~(in @ X1293 @ (setadjoin @ X1291 @ (setadjoin @ X1292 @ emptyset)))|(((X1293)=(X1291))|((X1293)=(X1292))))&((~(in @ X1296 @ X1294)|(~(in @ X1297 @ X1295)|(subset @ (setadjoin @ X1296 @ (setadjoin @ X1297 @ emptyset)) @ (binunion @ X1294 @ X1295))))&((~(in @ X1300 @ X1298)|(~(in @ X1301 @ X1299)|(in @ (setadjoin @ X1300 @ (setadjoin @ X1301 @ emptyset)) @ (powerset @ (binunion @ X1298 @ X1299)))))&((~(in @ X1304 @ X1302)|(~(in @ X1305 @ X1303)|(subset @ (setadjoin @ (setadjoin @ X1304 @ emptyset) @ (setadjoin @ (setadjoin @ X1304 @ (setadjoin @ X1305 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1302 @ X1303)))))&((~(in @ X1308 @ X1306)|(~(in @ X1309 @ X1307)|(in @ (setadjoin @ (setadjoin @ X1308 @ emptyset) @ (setadjoin @ (setadjoin @ X1308 @ (setadjoin @ X1309 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1306 @ X1307))))))&((~(in @ X1312 @ X1310)|(~(in @ X1313 @ X1311)|(in @ (kpair @ X1312 @ X1313) @ (powerset @ (powerset @ (binunion @ X1310 @ X1311))))))&((~(in @ X1316 @ X1314)|(~(in @ X1317 @ X1315)|(in @ (kpair @ X1316 @ X1317) @ (cartprod @ X1314 @ X1315))))&((in @ esk61_0 @ (cartprod @ esk59_0 @ esk60_0))&(~(in @ X1321 @ esk59_0)|(~(in @ X1322 @ esk60_0)|((esk61_0)!=(kpair @ X1321 @ X1322))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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_197])])])])])])])).
% 205.36/30.00 thf(c_0_199, plain, ![X1346:$i, X1347:$i, X1348:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i]:(((((in @ (esk67_3 @ X1346 @ X1347 @ X1348) @ X1347)|~(epred2_2 @ X1348 @ X1347 @ X1346))&(((in @ (esk68_3 @ X1346 @ X1347 @ X1348) @ X1348)|~(epred2_2 @ X1348 @ X1347 @ X1346))&(((X1346)=(kpair @ (esk67_3 @ X1346 @ X1347 @ X1348) @ (esk68_3 @ X1346 @ X1347 @ X1348)))|~(epred2_2 @ X1348 @ X1347 @ X1346))))&(~(in @ X1354 @ X1352)|(~(in @ X1355 @ X1353)|((X1351)!=(kpair @ X1354 @ X1355)))|(epred2_2 @ X1353 @ X1352 @ X1351)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])])).
% 205.36/30.00 thf(c_0_200, plain, ![X888:$i, X889:$i]:(((cartprod @ X888 @ X889)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X888 @ X889))) @ (^[Z0:$i]:(?[X3:$i]:((((in @ X3 @ X888))&(?[X14:$i]:((((in @ X14 @ X889))&(((Z0)=(kpair @ X3 @ X14))))))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[cartprod])])).
% 205.36/30.00 thf(c_0_201, negated_conjecture, ![X2:$i, X3:$i]:((~((in @ X2 @ esk59_0))|~((in @ X3 @ esk60_0))|((esk61_0)!=(kpair @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_198])).
% 205.36/30.00 thf(c_0_202, plain, ![X4:$i, X3:$i, X2:$i]:((((X2)=(kpair @ (esk67_3 @ X2 @ X3 @ X4) @ (esk68_3 @ X2 @ X3 @ X4)))|~((epred2_2 @ X4 @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_199])).
% 205.36/30.00 thf(c_0_203, plain, ![X892:$i, X893:$i]:(((cartprod @ X892 @ X893)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X892 @ X893))) @ (^[Z0:$i]:(?[X3:$i]:((((in @ X3 @ X892))&(?[X14:$i]:((((in @ X14 @ X893))&(((Z0)=(kpair @ X3 @ X14))))))))))))), inference(variable_rename,[status(thm)],[c_0_200])).
% 205.36/30.00 thf(c_0_204, plain, ![X1344:$i, X2:$i, X3:$i]:(((epred2_2 @ X3 @ X2 @ X1344)<=>?[X1342:$i]:(((in @ X1342 @ X2)&?[X1343:$i]:(((in @ X1343 @ X3)&((X1344)=(kpair @ X1342 @ X1343)))))))), introduced(definition)).
% 205.36/30.00 thf(c_0_205, negated_conjecture, ![X3:$i, X2:$i]:((~((in @ (esk68_3 @ esk61_0 @ X2 @ X3) @ esk60_0))|~((in @ (esk67_3 @ esk61_0 @ X2 @ X3) @ esk59_0))|~((epred2_2 @ X3 @ X2 @ esk61_0)))), inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_201, c_0_202])])).
% 205.36/30.00 thf(c_0_206, plain, ![X4:$i, X3:$i, X2:$i]:(((in @ (esk68_3 @ X2 @ X3 @ X4) @ X4)|~((epred2_2 @ X4 @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_199])).
% 205.36/30.00 thf(c_0_207, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_198])).
% 205.36/30.00 thf(c_0_208, plain, ![X3:$i, X2:$i]:(((cartprod @ X2 @ X3)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X2 @ X3))) @ (epred2_2 @ X3 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_203]), c_0_204])).
% 205.36/30.00 thf(c_0_209, plain, ![X2:$i]:((~((in @ (esk67_3 @ esk61_0 @ X2 @ esk60_0) @ esk59_0))|~((epred2_2 @ esk60_0 @ X2 @ esk61_0)))), inference(spm,[status(thm)],[c_0_205, c_0_206])).
% 205.36/30.00 thf(c_0_210, plain, ![X4:$i, X3:$i, X2:$i]:(((in @ (esk67_3 @ X2 @ X3 @ X4) @ X3)|~((epred2_2 @ X4 @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_199])).
% 205.36/30.00 thf(c_0_211, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((epred2_2 @ X2 @ X3 @ X4)|~((in @ X4 @ (cartprod @ X3 @ X2))))), inference(spm,[status(thm)],[c_0_207, c_0_208])).
% 205.36/30.00 thf(c_0_212, negated_conjecture, (in @ esk61_0 @ (cartprod @ esk59_0 @ esk60_0)), inference(split_conjunct,[status(thm)],[c_0_198])).
% 205.36/30.00 thf(c_0_213, plain, ~((epred2_2 @ esk60_0 @ esk59_0 @ esk61_0)), inference(spm,[status(thm)],[c_0_209, c_0_210])).
% 205.36/30.00 thf(c_0_214, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_211, c_0_212]), c_0_213]), ['proof']).
% 205.36/30.00 % SZS output end CNFRefutation
% 205.36/30.00 % Parsed axioms : 323
% 205.36/30.00 % Removed by relevancy pruning/SinE : 0
% 205.36/30.00 % Initial clauses : 453
% 205.36/30.00 % Removed in clause preprocessing : 195
% 205.36/30.00 % Initial clauses in saturation : 258
% 205.36/30.00 % Processed clauses : 5594
% 205.36/30.00 % ...of these trivial : 29
% 205.36/30.00 % ...subsumed : 3650
% 205.36/30.00 % ...remaining for further processing : 1915
% 205.36/30.00 % Other redundant clauses eliminated : 56
% 205.36/30.00 % Clauses deleted for lack of memory : 0
% 205.36/30.00 % Backward-subsumed : 129
% 205.36/30.00 % Backward-rewritten : 10
% 205.36/30.00 % Generated clauses : 51689
% 205.36/30.00 % ...of the previous two non-redundant : 49867
% 205.36/30.00 % ...aggressively subsumed : 0
% 205.36/30.00 % Contextual simplify-reflections : 6
% 205.36/30.00 % Paramodulations : 51596
% 205.36/30.00 % Factorizations : 35
% 205.36/30.00 % NegExts : 0
% 205.36/30.00 % Equation resolutions : 56
% 205.36/30.00 % Disequality decompositions : 0
% 205.36/30.00 % Total rewrite steps : 2719
% 205.36/30.00 % ...of those cached : 2351
% 205.36/30.00 % Propositional unsat checks : 0
% 205.36/30.00 % Propositional check models : 0
% 205.36/30.00 % Propositional check unsatisfiable : 0
% 205.36/30.00 % Propositional clauses : 0
% 205.36/30.00 % Propositional clauses after purity: 0
% 205.36/30.00 % Propositional unsat core size : 0
% 205.36/30.00 % Propositional preprocessing time : 0.000
% 205.36/30.00 % Propositional encoding time : 0.000
% 205.36/30.00 % Propositional solver time : 0.000
% 205.36/30.00 % Success case prop preproc time : 0.000
% 205.36/30.00 % Success case prop encoding time : 0.000
% 205.36/30.00 % Success case prop solver time : 0.000
% 205.36/30.00 % Current number of processed clauses : 1540
% 205.36/30.00 % Positive orientable unit clauses : 109
% 205.36/30.00 % Positive unorientable unit clauses: 0
% 205.36/30.00 % Negative unit clauses : 244
% 205.36/30.00 % Non-unit-clauses : 1187
% 205.36/30.00 % Current number of unprocessed clauses: 44611
% 205.36/30.00 % ...number of literals in the above : 140433
% 205.36/30.00 % Current number of archived formulas : 0
% 205.36/30.00 % Current number of archived clauses : 361
% 205.36/30.00 % Clause-clause subsumption calls (NU) : 114210
% 205.36/30.00 % Rec. Clause-clause subsumption calls : 73190
% 205.36/30.00 % Non-unit clause-clause subsumptions : 2068
% 205.36/30.00 % Unit Clause-clause subsumption calls : 46964
% 205.36/30.00 % Rewrite failures with RHS unbound : 0
% 205.36/30.00 % BW rewrite match attempts : 98
% 205.36/30.00 % BW rewrite match successes : 9
% 205.36/30.00 % Condensation attempts : 0
% 205.36/30.00 % Condensation successes : 0
% 205.36/30.00 % Termbank termtop insertions : 904438
% 205.36/30.00 % Search garbage collected termcells : 14466
% 205.36/30.00
% 205.36/30.00 % -------------------------------------------------
% 205.36/30.00 % User time : 28.508 s
% 205.36/30.00 % System time : 0.951 s
% 205.36/30.00 % Total time : 29.459 s
% 205.36/30.00 % Maximum resident set size: 7028 pages
% 205.36/30.00
% 205.36/30.00 % -------------------------------------------------
% 205.36/30.00 % User time : 28.516 s
% 205.36/30.00 % System time : 0.961 s
% 205.36/30.00 % Total time : 29.477 s
% 205.36/30.00 % Maximum resident set size: 5120 pages
% 205.36/30.00 % E exiting
%------------------------------------------------------------------------------