%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU652^1 : 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:53 AM UTC 2026
% Result : Theorem 0.26s 0.40s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU652^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:05:22 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.27 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.54TzWYQXzh/E---3.1_1339228.p
% 0.26/0.40 % Version: 3.5.1-ho
% 0.26/0.40 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.26/0.40 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.40 % Starting ehoh_best5 with 300s (1) cores
% 0.26/0.40 % Starting almost_fo_3_lam with 300s (1) cores
% 0.26/0.40 % Starting new_bool_5 with 300s (1) cores
% 0.26/0.40 % Starting pre_casc_3 with 300s (1) cores
% 0.26/0.40 % Starting ho_unfolding_8 with 300s (1) cores
% 0.26/0.40 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.26/0.40 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.40 % Starting new_ho_5 with 300s (1) cores
% 0.26/0.40 % new_bool_5 with pid 1339243 completed with status 0
% 0.26/0.40 % Result found by new_bool_5
% 0.26/0.40 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.26/0.40 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.40 % Starting ehoh_best5 with 300s (1) cores
% 0.26/0.40 % Starting almost_fo_3_lam with 300s (1) cores
% 0.26/0.40 % Starting new_bool_5 with 300s (1) cores
% 0.26/0.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.26/0.40 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.26/0.40 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.26/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.40 % SubtermCWHack with pid 1339251 completed with status 0
% 0.26/0.40 % Result found by SubtermCWHack
% 0.26/0.40 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.26/0.40 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.40 % Starting ehoh_best5 with 300s (1) cores
% 0.26/0.40 % Starting almost_fo_3_lam with 300s (1) cores
% 0.26/0.40 % Starting new_bool_5 with 300s (1) cores
% 0.26/0.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.26/0.40 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.26/0.40 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.26/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.40 % Preprocessing time : 0.005 s
% 0.26/0.40
% 0.26/0.40 % Proof found!
% 0.26/0.40 % SZS status Theorem
% 0.26/0.40 % SZS output start CNFRefutation
% 0.26/0.40 thf(decl_23, type, in: $i > $i > $o).
% 0.26/0.40 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.26/0.40 thf(decl_25, type, setextAx: $o).
% 0.26/0.40 thf(decl_26, type, emptyset: $i).
% 0.26/0.40 thf(decl_27, type, emptysetAx: $o).
% 0.26/0.40 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.26/0.40 thf(decl_29, type, setadjoinAx: $o).
% 0.26/0.40 thf(decl_30, type, powerset: $i > $i).
% 0.26/0.40 thf(decl_31, type, powersetAx: $o).
% 0.26/0.40 thf(decl_32, type, setunion: $i > $i).
% 0.26/0.40 thf(decl_33, type, setunionAx: $o).
% 0.26/0.40 thf(decl_34, type, omega: $i).
% 0.26/0.40 thf(decl_35, type, omega0Ax: $o).
% 0.26/0.40 thf(decl_36, type, omegaSAx: $o).
% 0.26/0.40 thf(decl_37, type, omegaIndAx: $o).
% 0.26/0.40 thf(decl_38, type, replAx: $o).
% 0.26/0.40 thf(decl_39, type, foundationAx: $o).
% 0.26/0.40 thf(decl_40, type, wellorderingAx: $o).
% 0.26/0.40 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.26/0.40 thf(decl_42, type, descrp: $o).
% 0.26/0.40 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.26/0.40 thf(decl_44, type, dsetconstrI: $o).
% 0.26/0.40 thf(decl_45, type, dsetconstrEL: $o).
% 0.26/0.40 thf(decl_46, type, dsetconstrER: $o).
% 0.26/0.40 thf(decl_47, type, exuE1: $o).
% 0.26/0.40 thf(decl_48, type, prop2set: $o > $i).
% 0.26/0.40 thf(decl_49, type, prop2setE: $o).
% 0.26/0.40 thf(decl_50, type, emptysetE: $o).
% 0.26/0.40 thf(decl_51, type, emptysetimpfalse: $o).
% 0.26/0.40 thf(decl_52, type, notinemptyset: $o).
% 0.26/0.40 thf(decl_53, type, exuE3e: $o).
% 0.26/0.40 thf(decl_54, type, setext: $o).
% 0.26/0.40 thf(decl_55, type, emptyI: $o).
% 0.26/0.40 thf(decl_56, type, noeltsimpempty: $o).
% 0.26/0.40 thf(decl_57, type, setbeta: $o).
% 0.26/0.40 thf(decl_58, type, nonempty: $i > $o).
% 0.26/0.40 thf(decl_59, type, nonemptyE1: $o).
% 0.26/0.40 thf(decl_60, type, nonemptyI: $o).
% 0.26/0.40 thf(decl_61, type, nonemptyI1: $o).
% 0.26/0.40 thf(decl_62, type, setadjoinIL: $o).
% 0.26/0.40 thf(decl_63, type, emptyinunitempty: $o).
% 0.26/0.40 thf(decl_64, type, setadjoinIR: $o).
% 0.26/0.40 thf(decl_65, type, setadjoinE: $o).
% 0.26/0.40 thf(decl_66, type, setadjoinOr: $o).
% 0.26/0.40 thf(decl_67, type, setoftrueEq: $o).
% 0.26/0.40 thf(decl_68, type, powersetI: $o).
% 0.26/0.40 thf(decl_69, type, emptyinPowerset: $o).
% 0.26/0.40 thf(decl_70, type, emptyInPowerset: $o).
% 0.26/0.40 thf(decl_71, type, powersetE: $o).
% 0.26/0.40 thf(decl_72, type, setunionI: $o).
% 0.26/0.40 thf(decl_73, type, setunionE: $o).
% 0.26/0.40 thf(decl_74, type, subPowSU: $o).
% 0.26/0.40 thf(decl_75, type, exuE2: $o).
% 0.26/0.40 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.26/0.40 thf(decl_77, type, uniqinunit: $o).
% 0.26/0.40 thf(decl_78, type, notinsingleton: $o).
% 0.26/0.40 thf(decl_79, type, eqinunit: $o).
% 0.26/0.40 thf(decl_80, type, singletonsswitch: $o).
% 0.26/0.40 thf(decl_81, type, upairsetE: $o).
% 0.26/0.40 thf(decl_82, type, upairsetIL: $o).
% 0.26/0.40 thf(decl_83, type, upairsetIR: $o).
% 0.26/0.40 thf(decl_84, type, emptyE1: $o).
% 0.26/0.40 thf(decl_85, type, vacuousDall: $o).
% 0.26/0.40 thf(decl_86, type, quantDeMorgan1: $o).
% 0.26/0.40 thf(decl_87, type, quantDeMorgan2: $o).
% 0.26/0.40 thf(decl_88, type, quantDeMorgan3: $o).
% 0.26/0.40 thf(decl_89, type, quantDeMorgan4: $o).
% 0.26/0.40 thf(decl_90, type, prop2setI: $o).
% 0.26/0.40 thf(decl_92, type, prop2set2propI: $o).
% 0.26/0.40 thf(decl_93, type, notdexE: $o).
% 0.26/0.40 thf(decl_94, type, notdallE: $o).
% 0.26/0.40 thf(decl_95, type, exuI1: $o).
% 0.26/0.40 thf(decl_96, type, exuI3: $o).
% 0.26/0.40 thf(decl_97, type, exuI2: $o).
% 0.26/0.40 thf(decl_98, type, inCongP: $o).
% 0.26/0.40 thf(decl_99, type, in__Cong: $o).
% 0.26/0.40 thf(decl_100, type, exuE3u: $o).
% 0.26/0.40 thf(decl_101, type, exu__Cong: $o).
% 0.26/0.40 thf(decl_102, type, emptyset__Cong: $o).
% 0.26/0.40 thf(decl_103, type, setadjoin__Cong: $o).
% 0.26/0.40 thf(decl_104, type, powerset__Cong: $o).
% 0.26/0.40 thf(decl_105, type, setunion__Cong: $o).
% 0.26/0.40 thf(decl_106, type, omega__Cong: $o).
% 0.26/0.40 thf(decl_107, type, exuEu: $o).
% 0.26/0.40 thf(decl_108, type, descr__Cong: $o).
% 0.26/0.40 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.26/0.40 thf(decl_110, type, subset: $i > $i > $o).
% 0.26/0.40 thf(decl_113, type, subsetI1: $o).
% 0.26/0.40 thf(decl_114, type, eqimpsubset2: $o).
% 0.26/0.40 thf(decl_115, type, eqimpsubset1: $o).
% 0.26/0.40 thf(decl_116, type, subsetI2: $o).
% 0.26/0.40 thf(decl_117, type, emptysetsubset: $o).
% 0.26/0.40 thf(decl_118, type, subsetE: $o).
% 0.26/0.40 thf(decl_119, type, subsetE2: $o).
% 0.26/0.40 thf(decl_120, type, notsubsetI: $o).
% 0.26/0.40 thf(decl_121, type, notequalI1: $o).
% 0.26/0.40 thf(decl_122, type, notequalI2: $o).
% 0.26/0.40 thf(decl_123, type, subsetRefl: $o).
% 0.26/0.40 thf(decl_124, type, subsetTrans: $o).
% 0.26/0.40 thf(decl_125, type, setadjoinSub: $o).
% 0.26/0.40 thf(decl_126, type, setadjoinSub2: $o).
% 0.26/0.40 thf(decl_127, type, subset2powerset: $o).
% 0.26/0.40 thf(decl_128, type, setextsub: $o).
% 0.26/0.40 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.26/0.40 thf(decl_130, type, powersetI1: $o).
% 0.26/0.40 thf(decl_131, type, powersetE1: $o).
% 0.26/0.40 thf(decl_132, type, inPowerset: $o).
% 0.26/0.40 thf(decl_133, type, powersetsubset: $o).
% 0.26/0.40 thf(decl_134, type, sepInPowerset: $o).
% 0.26/0.40 thf(decl_135, type, sepSubset: $o).
% 0.26/0.40 thf(decl_136, type, binunion: $i > $i > $i).
% 0.26/0.40 thf(decl_137, type, binunionIL: $o).
% 0.26/0.40 thf(decl_138, type, upairset2IR: $o).
% 0.26/0.40 thf(decl_139, type, binunionIR: $o).
% 0.26/0.40 thf(decl_140, type, binunionEcases: $o).
% 0.26/0.41 thf(decl_141, type, binunionE: $o).
% 0.26/0.41 thf(decl_142, type, binunionLsub: $o).
% 0.26/0.41 thf(decl_143, type, binunionRsub: $o).
% 0.26/0.41 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.26/0.41 thf(decl_145, type, binintersectI: $o).
% 0.26/0.41 thf(decl_146, type, binintersectSubset5: $o).
% 0.26/0.41 thf(decl_147, type, binintersectEL: $o).
% 0.26/0.41 thf(decl_148, type, binintersectLsub: $o).
% 0.26/0.41 thf(decl_149, type, binintersectSubset2: $o).
% 0.26/0.41 thf(decl_150, type, binintersectSubset3: $o).
% 0.26/0.41 thf(decl_151, type, binintersectER: $o).
% 0.26/0.41 thf(decl_152, type, disjointsetsI1: $o).
% 0.26/0.41 thf(decl_153, type, binintersectRsub: $o).
% 0.26/0.41 thf(decl_154, type, binintersectSubset4: $o).
% 0.26/0.41 thf(decl_155, type, binintersectSubset1: $o).
% 0.26/0.41 thf(decl_156, type, bs114d: $o).
% 0.26/0.41 thf(decl_158, type, setminus: $i > $i > $i).
% 0.26/0.41 thf(decl_159, type, setminusI: $o).
% 0.26/0.41 thf(decl_160, type, setminusEL: $o).
% 0.26/0.41 thf(decl_161, type, setminusER: $o).
% 0.26/0.41 thf(decl_162, type, setminusSubset2: $o).
% 0.26/0.41 thf(decl_163, type, setminusERneg: $o).
% 0.26/0.41 thf(decl_164, type, setminusELneg: $o).
% 0.26/0.41 thf(decl_165, type, setminusILneg: $o).
% 0.26/0.41 thf(decl_166, type, setminusIRneg: $o).
% 0.26/0.41 thf(decl_167, type, setminusLsub: $o).
% 0.26/0.41 thf(decl_168, type, setminusSubset1: $o).
% 0.26/0.41 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.26/0.41 thf(decl_170, type, symdiffE: $o).
% 0.26/0.41 thf(decl_171, type, symdiffI1: $o).
% 0.26/0.41 thf(decl_172, type, symdiffI2: $o).
% 0.26/0.41 thf(decl_173, type, symdiffIneg1: $o).
% 0.26/0.41 thf(decl_174, type, symdiffIneg2: $o).
% 0.26/0.41 thf(decl_175, type, iskpair: $i > $o).
% 0.26/0.41 thf(decl_176, type, secondinupair: $o).
% 0.26/0.41 thf(decl_177, type, setukpairIL: $o).
% 0.26/0.41 thf(decl_178, type, setukpairIR: $o).
% 0.26/0.41 thf(decl_179, type, kpairiskpair: $o).
% 0.26/0.41 thf(decl_180, type, kpair: $i > $i > $i).
% 0.26/0.41 thf(decl_181, type, kpairp: $o).
% 0.26/0.41 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.26/0.41 thf(decl_183, type, singletonsubset: $o).
% 0.26/0.41 thf(decl_184, type, singletoninpowerset: $o).
% 0.26/0.41 thf(decl_185, type, singletoninpowunion: $o).
% 0.26/0.41 thf(decl_186, type, upairset2E: $o).
% 0.26/0.41 thf(decl_187, type, upairsubunion: $o).
% 0.26/0.41 thf(decl_188, type, upairinpowunion: $o).
% 0.26/0.41 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.26/0.41 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.26/0.41 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.26/0.41 thf(decl_192, type, cartprodpairin: $o).
% 0.26/0.41 thf(decl_193, type, cartprodmempair1: $o).
% 0.26/0.41 thf(decl_194, type, cartprodmempair: $o).
% 0.26/0.41 thf(decl_195, type, setunionE2: $o).
% 0.26/0.41 thf(decl_196, type, setunionsingleton1: $o).
% 0.26/0.41 thf(decl_197, type, setunionsingleton2: $o).
% 0.26/0.41 thf(decl_198, type, setunionsingleton: $o).
% 0.26/0.41 thf(decl_199, type, singleton: $i > $o).
% 0.26/0.41 thf(decl_200, type, singletonprop: $o).
% 0.26/0.41 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 0.26/0.41 thf(decl_202, type, ex1E1: $o).
% 0.26/0.41 thf(decl_203, type, ex1I: $o).
% 0.26/0.41 thf(decl_204, type, ex1I2: $o).
% 0.26/0.41 thf(decl_205, type, singletonsuniq: $o).
% 0.26/0.41 thf(decl_210, type, setukpairinjL1: $o).
% 0.26/0.41 thf(decl_211, type, kfstsingleton: $o).
% 0.26/0.41 thf(decl_212, type, theprop: $o).
% 0.26/0.41 thf(decl_213, type, kfst: $i > $i).
% 0.26/0.41 thf(decl_214, type, kfstpairEq: $o).
% 0.26/0.41 thf(decl_215, type, cartprodfstin: $o).
% 0.26/0.41 thf(decl_216, type, setukpairinjL2: $o).
% 0.26/0.41 thf(decl_217, type, setukpairinjL: $o).
% 0.26/0.41 thf(decl_218, type, setukpairinjR11: $o).
% 0.26/0.41 thf(decl_219, type, setukpairinjR12: $o).
% 0.26/0.41 thf(decl_220, type, setukpairinjR1: $o).
% 0.26/0.41 thf(decl_221, type, epred1_0: $o).
% 0.26/0.41 thf(decl_222, type, esk1_2: $i > $i > $i).
% 0.26/0.41 thf(decl_223, type, esk2_2: $i > $i > $i).
% 0.26/0.41 thf(decl_224, type, esk3_2: $i > $i > $i).
% 0.26/0.41 thf(decl_225, type, esk4_1: $i > $i).
% 0.26/0.41 thf(decl_226, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.26/0.41 thf(decl_227, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.26/0.41 thf(decl_228, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.26/0.41 thf(decl_229, type, esk8_1: $i > $i).
% 0.26/0.41 thf(decl_230, type, esk9_1: ($i > $o) > $i).
% 0.26/0.41 thf(decl_231, type, esk10_1: ($i > $o) > $i).
% 0.26/0.41 thf(decl_232, type, esk11_2: $i > $i > $i).
% 0.26/0.41 thf(decl_233, type, esk12_2: $i > $i > $i).
% 0.26/0.41 thf(decl_234, type, esk13_1: $i > $i).
% 0.26/0.41 thf(decl_235, type, esk14_1: $i > $i).
% 0.26/0.41 thf(decl_236, type, esk15_1: $i > $i).
% 0.26/0.41 thf(decl_237, type, esk16_2: $i > $i > $i).
% 0.26/0.41 thf(decl_238, type, esk17_3: $i > $i > $o > $i).
% 0.26/0.41 thf(decl_239, type, esk18_1: ($i > $o) > $i).
% 0.26/0.41 thf(decl_240, type, esk19_1: $i > $i).
% 0.26/0.41 thf(decl_241, type, esk20_2: $i > ($i > $o) > $i).
% 0.26/0.41 thf(decl_242, type, esk21_2: $i > ($i > $o) > $i).
% 0.26/0.41 thf(decl_243, type, esk22_2: $i > ($i > $o) > $i).
% 0.26/0.41 thf(decl_244, type, esk23_2: $i > ($i > $o) > $i).
% 0.26/0.41 thf(decl_245, type, esk24_2: $i > ($i > $o) > $i).
% 0.26/0.41 thf(decl_246, type, esk25_2: $i > ($i > $o) > $i).
% 0.26/0.41 thf(decl_247, type, esk26_2: ($i > $o) > $i > $i).
% 0.26/0.41 thf(decl_248, type, esk27_1: ($i > $o) > $i).
% 0.26/0.41 thf(decl_249, type, esk28_1: ($i > $o) > $i).
% 0.26/0.41 thf(decl_250, type, esk29_2: ($i > $o) > $i > $i).
% 0.26/0.41 thf(decl_251, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 0.26/0.41 thf(decl_252, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 0.26/0.41 thf(decl_253, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 0.26/0.41 thf(decl_254, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 0.26/0.41 thf(decl_255, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.26/0.41 thf(decl_256, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.26/0.41 thf(decl_257, type, esk36_2: $i > $i > $i).
% 0.26/0.41 thf(decl_258, type, esk37_2: $i > $i > $i).
% 0.26/0.41 thf(decl_259, type, esk38_2: $i > $i > $i).
% 0.26/0.41 thf(decl_260, type, esk39_3: $i > $i > $i > $i).
% 0.26/0.41 thf(decl_261, type, esk40_3: $i > $i > $i > $i).
% 0.26/0.41 thf(decl_262, type, esk41_2: $i > $i > $i).
% 0.26/0.41 thf(decl_263, type, esk42_2: $i > ($i > $o) > $i).
% 0.26/0.41 thf(decl_264, type, esk43_2: $i > ($i > $o) > $i).
% 0.26/0.41 thf(decl_265, type, esk44_2: $i > ($i > $o) > $i).
% 0.26/0.41 thf(decl_266, type, esk45_3: $i > ($i > $o) > $i > $i).
% 0.26/0.41 thf(decl_267, type, esk46_2: $i > ($i > $o) > $i).
% 0.26/0.41 thf(decl_268, type, esk47_2: $i > ($i > $o) > $i).
% 0.26/0.41 thf(decl_269, type, esk48_0: $i).
% 0.26/0.41 thf(decl_270, type, esk49_0: $i).
% 0.26/0.41 thf(decl_271, type, esk50_0: $i).
% 0.26/0.41 thf(upairequniteq, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', upairequniteq)).
% 0.26/0.41 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setbeta)).
% 0.26/0.41 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', exuE3e)).
% 0.26/0.41 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', nonemptyI)).
% 0.26/0.41 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setoftrueEq)).
% 0.26/0.41 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', singletonprop)).
% 0.26/0.41 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', ex1E1)).
% 0.26/0.41 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', ex1I)).
% 0.26/0.41 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', ex1I2)).
% 0.26/0.41 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', kfstsingleton)).
% 0.26/0.41 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', exuE2)).
% 0.26/0.41 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.54TzWYQXzh/E---3.1_1339228.p', emptyE1)).
% 0.26/0.41 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', exu__Cong)).
% 0.26/0.41 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', exuE3u)).
% 0.26/0.41 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.54TzWYQXzh/E---3.1_1339228.p', exuI2)).
% 0.26/0.41 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', exuI3)).
% 0.26/0.41 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', exuI1)).
% 0.26/0.41 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', dsetconstr__Cong)).
% 0.26/0.41 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', descr__Cong)).
% 0.26/0.41 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', exuEu)).
% 0.26/0.41 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', sepSubset)).
% 0.26/0.41 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', sepInPowerset)).
% 0.26/0.41 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.54TzWYQXzh/E---3.1_1339228.p', exuE1)).
% 0.26/0.41 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', dsetconstrER)).
% 0.26/0.41 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', dsetconstrEL)).
% 0.26/0.41 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', dsetconstrI)).
% 0.26/0.41 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', descrp)).
% 0.26/0.41 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', replAx)).
% 0.26/0.41 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', symdiffIneg1)).
% 0.26/0.41 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', symdiffI1)).
% 0.26/0.41 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', symdiffI2)).
% 0.26/0.41 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', symdiffIneg2)).
% 0.26/0.41 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', secondinupair)).
% 0.26/0.41 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', nonemptyE1)).
% 0.26/0.41 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setukpairIL)).
% 0.26/0.41 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setukpairIR)).
% 0.26/0.41 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', noeltsimpempty)).
% 0.26/0.41 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', kpairiskpair)).
% 0.26/0.41 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', emptyI)).
% 0.26/0.41 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', kpairp)).
% 0.26/0.41 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setext)).
% 0.26/0.41 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', singletonsubset)).
% 0.26/0.41 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', singletoninpowerset)).
% 0.26/0.41 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', singletoninpowunion)).
% 0.26/0.41 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', upairset2E)).
% 0.26/0.41 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', upairsubunion)).
% 0.26/0.41 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', upairinpowunion)).
% 0.26/0.41 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', ubforcartprodlem1)).
% 0.26/0.41 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', ubforcartprodlem2)).
% 0.26/0.41 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', ubforcartprodlem3)).
% 0.26/0.41 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', cartprodpairin)).
% 0.26/0.41 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', cartprodmempair1)).
% 0.26/0.41 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', cartprodmempair)).
% 0.26/0.41 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setunionE2)).
% 0.26/0.41 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setunionsingleton1)).
% 0.26/0.41 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setunionsingleton2)).
% 0.26/0.41 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setunionsingleton)).
% 0.26/0.41 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setadjoinOr)).
% 0.26/0.41 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.54TzWYQXzh/E---3.1_1339228.p', setadjoinE)).
% 0.26/0.41 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setadjoinIR)).
% 0.26/0.41 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', emptyinunitempty)).
% 0.26/0.41 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', singletonsuniq)).
% 0.26/0.41 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setadjoinIL)).
% 0.26/0.41 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setukpairinjL1)).
% 0.26/0.41 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', nonemptyI1)).
% 0.26/0.41 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', powersetI)).
% 0.26/0.41 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', theprop)).
% 0.26/0.41 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', kfstpairEq)).
% 0.26/0.41 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', cartprodfstin)).
% 0.26/0.41 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setukpairinjL2)).
% 0.26/0.41 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setukpairinjL)).
% 0.26/0.41 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setukpairinjR11)).
% 0.26/0.41 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setukpairinjR12)).
% 0.26/0.41 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setukpairinjR1)).
% 0.26/0.41 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', subPowSU)).
% 0.26/0.41 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setunionE)).
% 0.26/0.41 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setunionI)).
% 0.26/0.41 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', powersetE)).
% 0.26/0.41 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', emptyInPowerset)).
% 0.26/0.41 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', emptyinPowerset)).
% 0.26/0.41 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', nonemptyImpWitness)).
% 0.26/0.41 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', notsubsetI)).
% 0.26/0.41 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', subsetE2)).
% 0.26/0.41 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', upairsetIR)).
% 0.26/0.41 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', upairsetIL)).
% 0.26/0.41 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', upairsetE)).
% 0.26/0.41 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', singletonsswitch)).
% 0.26/0.41 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', eqinunit)).
% 0.26/0.41 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', notinsingleton)).
% 0.26/0.41 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', uniqinunit)).
% 0.26/0.41 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', notdexE)).
% 0.26/0.41 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', prop2setI)).
% 0.26/0.41 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', quantDeMorgan4)).
% 0.26/0.41 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', quantDeMorgan3)).
% 0.26/0.41 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', quantDeMorgan2)).
% 0.26/0.41 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', quantDeMorgan1)).
% 0.26/0.41 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', vacuousDall)).
% 0.26/0.41 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', notdallE)).
% 0.26/0.41 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', in__Cong)).
% 0.26/0.41 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', inCongP)).
% 0.26/0.41 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', emptyset__Cong)).
% 0.26/0.41 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', omega__Cong)).
% 0.26/0.41 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setunion__Cong)).
% 0.26/0.41 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', powerset__Cong)).
% 0.26/0.41 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setadjoin__Cong)).
% 0.26/0.41 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', subsetI1)).
% 0.26/0.41 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', subsetE)).
% 0.26/0.41 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', emptysetsubset)).
% 0.26/0.41 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', subsetI2)).
% 0.26/0.41 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', eqimpsubset1)).
% 0.26/0.41 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', eqimpsubset2)).
% 0.26/0.41 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', notequalI1)).
% 0.26/0.41 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setextsub)).
% 0.26/0.41 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', subset2powerset)).
% 0.26/0.41 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setadjoinSub2)).
% 0.26/0.41 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setadjoinSub)).
% 0.26/0.41 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', subsetTrans)).
% 0.26/0.41 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', subsetRefl)).
% 0.26/0.41 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', notequalI2)).
% 0.26/0.41 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', subsetemptysetimpeq)).
% 0.26/0.41 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binunionIL)).
% 0.26/0.41 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', powersetsubset)).
% 0.26/0.41 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', inPowerset)).
% 0.26/0.41 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', powersetE1)).
% 0.26/0.41 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', powersetI1)).
% 0.26/0.41 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', upairset2IR)).
% 0.26/0.41 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binintersectSubset5)).
% 0.26/0.41 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binintersectI)).
% 0.26/0.41 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binunionRsub)).
% 0.26/0.41 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binunionLsub)).
% 0.26/0.41 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binunionE)).
% 0.26/0.41 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binunionEcases)).
% 0.26/0.41 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binunionIR)).
% 0.26/0.41 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binintersectEL)).
% 0.26/0.41 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binintersectSubset4)).
% 0.26/0.41 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binintersectRsub)).
% 0.26/0.41 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', disjointsetsI1)).
% 0.26/0.41 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binintersectER)).
% 0.26/0.41 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binintersectSubset3)).
% 0.26/0.41 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binintersectSubset2)).
% 0.26/0.41 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binintersectLsub)).
% 0.26/0.41 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', binintersectSubset1)).
% 0.26/0.41 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setminusELneg)).
% 0.26/0.41 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setminusERneg)).
% 0.26/0.41 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setminusSubset2)).
% 0.26/0.41 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setminusER)).
% 0.26/0.41 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setminusEL)).
% 0.26/0.41 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setminusI)).
% 0.26/0.41 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', bs114d)).
% 0.26/0.41 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setminusIRneg)).
% 0.26/0.41 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setminusLsub)).
% 0.26/0.41 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setminusSubset1)).
% 0.26/0.41 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.54TzWYQXzh/E---3.1_1339228.p', symdiffE)).
% 0.26/0.41 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setminusILneg)).
% 0.26/0.41 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', notinemptyset)).
% 0.26/0.41 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', emptysetimpfalse)).
% 0.26/0.41 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', emptysetE)).
% 0.26/0.41 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', prop2setE)).
% 0.26/0.41 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', wellorderingAx)).
% 0.26/0.41 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', foundationAx)).
% 0.26/0.41 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.54TzWYQXzh/E---3.1_1339228.p', omegaIndAx)).
% 0.26/0.41 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', omegaSAx)).
% 0.26/0.41 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', omega0Ax)).
% 0.26/0.41 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setunionAx)).
% 0.26/0.41 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', powersetAx)).
% 0.26/0.41 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setadjoinAx)).
% 0.26/0.41 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', emptysetAx)).
% 0.26/0.41 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.54TzWYQXzh/E---3.1_1339228.p', setextAx)).
% 0.26/0.41 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)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[upairequniteq])).
% 0.26/0.41 thf(c_0_169, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.26/0.41 thf(c_0_170, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.26/0.41 thf(c_0_171, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.26/0.41 thf(c_0_172, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.26/0.41 thf(c_0_173, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 0.26/0.41 thf(c_0_174, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 0.26/0.41 thf(c_0_175, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 0.26/0.41 thf(c_0_176, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 0.26/0.41 thf(c_0_177, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 0.26/0.41 thf(c_0_178, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.26/0.41 thf(c_0_179, 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])).
% 0.26/0.41 thf(c_0_180, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.26/0.41 thf(c_0_181, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.26/0.41 thf(c_0_182, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.26/0.41 thf(c_0_183, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.26/0.41 thf(c_0_184, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.26/0.41 thf(c_0_185, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.26/0.41 thf(c_0_186, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.26/0.41 thf(c_0_187, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.26/0.41 thf(c_0_188, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.26/0.41 thf(c_0_189, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.26/0.41 thf(c_0_190, 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])).
% 0.26/0.41 thf(c_0_191, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.26/0.41 thf(c_0_192, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.26/0.41 thf(c_0_193, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.26/0.41 thf(c_0_194, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.26/0.41 thf(c_0_195, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.26/0.41 thf(c_0_196, plain, ((epred1_0)<=>![X508:$i]:(?[X509:$i]:((((![X510:$i]:(((in @ X510 @ X509)=>![X511:$i]:(((in @ X511 @ X510)=>(in @ X511 @ X508)))))&![X512:$i, X513:$i]:((((in @ X512 @ X508)&(in @ X513 @ X508))=>(![X514:$i]:(((in @ X514 @ X509)=>((in @ X512 @ X514)<=>(in @ X513 @ X514))))=>((X512)=(X513))))))&![X515:$i, X516:$i]:((((in @ X515 @ X509)&(in @ X516 @ X509))=>(![X517:$i]:(((in @ X517 @ X515)=>(in @ X517 @ X516)))|![X518:$i]:(((in @ X518 @ X516)=>(in @ X518 @ X515)))))))&![X519:$i]:(((![X520:$i]:(((in @ X520 @ X519)=>(in @ X520 @ X508)))&?[X521:$i]:((in @ X521 @ X519)))=>?[X522:$i, X523:$i]:(((((in @ X522 @ X509)&(in @ X523 @ X519))&~(?[X524:$i]:(((in @ X524 @ X522)&(in @ X524 @ X519)))))&![X525:$i]:(((in @ X525 @ X509)=>(![X526:$i]:(((in @ X526 @ X525)=>(in @ X526 @ X522)))|(in @ X523 @ X525)))))))))))), introduced(definition)).
% 0.26/0.41 thf(c_0_197, negated_conjecture, ~((![X481:$i, X482:$i]:((![X483:$i]:(((in @ X483 @ X481)<=>(in @ X483 @ X482)))=>((X481)=(X482))))=>(![X484:$i]:(~(in @ X484 @ emptyset))=>(![X485:$i, X486:$i, X487:$i]:(((in @ X487 @ (setadjoin @ X485 @ X486))<=>(((X487)=(X485))|(in @ X487 @ X486))))=>(![X488:$i, X489:$i]:(((in @ X489 @ (powerset @ X488))<=>![X490:$i]:(((in @ X490 @ X489)=>(in @ X490 @ X488)))))=>(![X491:$i, X492:$i]:(((in @ X492 @ (setunion @ X491))<=>?[X493:$i]:(((in @ X492 @ X493)&(in @ X493 @ X491)))))=>((in @ emptyset @ omega)=>(![X494:$i]:(((in @ X494 @ omega)=>(in @ (setadjoin @ X494 @ X494) @ omega)))=>(![X495:$i]:((((in @ emptyset @ X495)&![X496:$i]:((((in @ X496 @ omega)&(in @ X496 @ X495))=>(in @ (setadjoin @ X496 @ X496) @ X495))))=>![X497:$i]:(((in @ X497 @ omega)=>(in @ X497 @ X495)))))=>(![X498:$i > $i > $o, X499:$i]:((![X500:$i]:(((in @ X500 @ X499)=>(exu @ (X498 @ X500))))=>?[X501:$i]:(![X502:$i]:(((in @ X502 @ X501)<=>?[X503:$i]:(((in @ X503 @ X499)&(X498 @ X503 @ X502))))))))=>(![X504:$i]:((?[X505:$i]:((in @ X505 @ X504))=>?[X506:$i]:(((in @ X506 @ X504)&~(?[X507:$i]:(((in @ X507 @ X506)&(in @ X507 @ X504))))))))=>((epred1_0)=>(![X527:$i > $o]:(((exu @ X527)=>(X527 @ (descr @ (^[Z0:$i]:(X527 @ Z0))))))=>(![X528:$i, X529:$i > $o, X530:$i]:(((in @ X530 @ X528)=>((X529 @ X530)=>(in @ X530 @ (dsetconstr @ X528 @ X529)))))=>(![X531:$i, X532:$i > $o, X533:$i]:(((in @ X533 @ (dsetconstr @ X531 @ X532))=>(in @ X533 @ X531)))=>(![X534:$i, X535:$i > $o, X536:$i]:(((in @ X536 @ (dsetconstr @ X534 @ X535))=>(X535 @ X536)))=>(![X537:$i > $o]:(((exu @ X537)=>?[X538:$i]:(((X537 @ X538)&![X539:$i]:(((X537 @ X539)=>((X538)=(X539))))))))=>(![X540:$o, X541:$i]:(((in @ X541 @ (prop2set @ ((X540))))=>(X540)))=>(![X542:$i]:(((in @ X542 @ emptyset)=>![X543:$o]:((X543))))=>(![X544:$i]:(((in @ X544 @ emptyset)=>~($true)))=>(![X545:$i]:(~(in @ X545 @ emptyset))=>(![X546:$i > $o]:(((exu @ X546)=>?[X547:$i]:((X546 @ X547))))=>(![X548:$i, X549:$i]:((![X550:$i]:(((in @ X550 @ X548)=>(in @ X550 @ X549)))=>(![X551:$i]:(((in @ X551 @ X549)=>(in @ X551 @ X548)))=>((X548)=(X549)))))=>(![X552:$i]:((![X553:$i]:(~(in @ X553 @ X552))=>((X552)=(emptyset))))=>(![X554:$i]:((![X555:$i]:(~(in @ X555 @ X554))=>((X554)=(emptyset))))=>(![X556:$i, X557:$i > $o, X558:$i]:(((in @ X558 @ X556)=>((in @ X558 @ (dsetconstr @ X556 @ X557))<=>(X557 @ X558))))=>(![X559:$i]:(((nonempty @ X559)=>?[X560:$i]:((in @ X560 @ X559))))=>(![X561:$i, X562:$i > $o, X563:$i]:(((in @ X563 @ X561)=>((X562 @ X563)=>(nonempty @ (dsetconstr @ X561 @ X562)))))=>(![X564:$i]:((?[X565:$i]:((in @ X565 @ X564))=>(nonempty @ X564)))=>(![X566:$i, X567:$i]:((in @ X566 @ (setadjoin @ X566 @ X567)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X568:$i, X569:$i, X570:$i]:(((in @ X570 @ X569)=>(in @ X570 @ (setadjoin @ X568 @ X569))))=>(![X571:$i, X572:$i, X573:$i]:(((in @ X573 @ (setadjoin @ X571 @ X572))=>![X574:$o]:(((((X573)=(X571))=>(X574))=>(((in @ X573 @ X572)=>(X574))=>(X574))))))=>(![X575:$i, X576:$i, X577:$i]:(((in @ X577 @ (setadjoin @ X575 @ X576))=>(((X577)=(X575))|(in @ X577 @ X576))))=>(![X578:$i]:(((dsetconstr @ X578 @ (^[Z0:$i]:($true)))=(X578)))=>(![X579:$i, X580:$i]:((![X581:$i]:(((in @ X581 @ X580)=>(in @ X581 @ X579)))=>(in @ X580 @ (powerset @ X579))))=>(![X582:$i]:((in @ emptyset @ (powerset @ X582)))=>(![X583:$i]:((in @ emptyset @ (powerset @ X583)))=>(![X584:$i, X585:$i, X586:$i]:(((in @ X585 @ (powerset @ X584))=>((in @ X586 @ X585)=>(in @ X586 @ X584))))=>(![X587:$i, X588:$i, X589:$i]:(((in @ X588 @ X589)=>((in @ X589 @ X587)=>(in @ X588 @ (setunion @ X587)))))=>(![X590:$i, X591:$i]:(((in @ X591 @ (setunion @ X590))=>![X592:$o]:((![X593:$i]:(((in @ X591 @ X593)=>((in @ X593 @ X590)=>(X592))))=>(X592)))))=>(![X594:$i, X595:$i]:(((in @ X595 @ X594)=>(in @ X595 @ (powerset @ (setunion @ X594)))))=>(![X596:$i > $o]:(((exu @ X596)=>?[X597:$i]:(![X598:$i]:(((X596 @ X598)<=>((X598)=(X597)))))))=>(![X599:$i]:(((nonempty @ X599)=>?[X600:$i]:(((in @ X600 @ X599)&$true))))=>(![X601:$i, X602:$i]:(((in @ X601 @ (setadjoin @ X602 @ emptyset))=>((X601)=(X602))))=>(![X603:$i, X604:$i]:((((X603)!=(X604))=>~(in @ X604 @ (setadjoin @ X603 @ emptyset))))=>(![X605:$i, X606:$i]:((((X605)=(X606))=>(in @ X605 @ (setadjoin @ X606 @ emptyset))))=>(![X607:$i, X608:$i]:(((in @ X607 @ (setadjoin @ X608 @ emptyset))=>(in @ X608 @ (setadjoin @ X607 @ emptyset))))=>(![X609:$i, X610:$i, X611:$i]:(((in @ X611 @ (setadjoin @ X609 @ (setadjoin @ X610 @ emptyset)))=>(((X611)=(X609))|((X611)=(X610)))))=>(![X612:$i, X613:$i]:((in @ X612 @ (setadjoin @ X612 @ (setadjoin @ X613 @ emptyset))))=>(![X614:$i, X615:$i]:((in @ X615 @ (setadjoin @ X614 @ (setadjoin @ X615 @ emptyset))))=>(![X616:$i, X617:$i > $o]:((?[X618:$i]:(((in @ X618 @ X616)&(X617 @ X618)))=>(((dsetconstr @ X616 @ X617)=(emptyset))=>~($true))))=>(![X619:$i > $o, X620:$i]:(((in @ X620 @ emptyset)=>(X619 @ X620)))=>(![X621:$i, X622:$i > $o]:((~(![X623:$i]:(((in @ X623 @ X621)=>(X622 @ X623))))=>?[X624:$i]:(((in @ X624 @ X621)&~((X622 @ X624))))))=>(![X625:$i, X626:$i > $o]:((![X627:$i]:(((in @ X627 @ X625)=>~((X626 @ X627))))=>~(?[X628:$i]:(((in @ X628 @ X625)&(X626 @ X628))))))=>(![X629:$i, X630:$i > $o]:((~(?[X631:$i]:(((in @ X631 @ X629)&(X630 @ X631))))=>![X632:$i]:(((in @ X632 @ X629)=>~((X630 @ X632))))))=>(![X633:$i, X634:$i > $o]:((?[X635:$i]:(((in @ X635 @ X633)&~((X634 @ X635))))=>~(![X636:$i]:(((in @ X636 @ X633)=>(X634 @ X636))))))=>(![X637:$o]:(((X637)=>(in @ emptyset @ (prop2set @ ((X637))))))=>((prop2set2propI)=>(![X638:$i, X639:$i > $o]:((~(?[X640:$i]:(((in @ X640 @ X638)&(X639 @ X640))))=>![X641:$i]:(((in @ X641 @ X638)=>~((X639 @ X641))))))=>(![X642:$i, X643:$i > $o]:((~(![X644:$i]:(((in @ X644 @ X642)=>(X643 @ X644))))=>?[X645:$i]:(((in @ X645 @ X642)&~((X643 @ X645))))))=>(![X646:$i > $o]:((?[X647:$i]:(((X646 @ X647)&![X648:$i]:(((X646 @ X648)=>((X647)=(X648))))))=>(exu @ X646)))=>(![X649:$i > $o]:((?[X650:$i]:((X649 @ 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X932:$i]:((((X931)=(X932))=>((setadjoin @ (setadjoin @ X931 @ emptyset) @ (setadjoin @ (setadjoin @ X931 @ (setadjoin @ X932 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X931 @ emptyset) @ emptyset))))=>(![X933:$i, X934:$i, X935:$i, X936:$i]:((((setadjoin @ (setadjoin @ X933 @ emptyset) @ (setadjoin @ (setadjoin @ X933 @ (setadjoin @ X934 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X935 @ emptyset) @ (setadjoin @ (setadjoin @ X935 @ (setadjoin @ X936 @ emptyset)) @ emptyset)))=>(((X935)=(X936))=>((X934)=(X936)))))=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_168, symdiffIneg1]), symdiffI1]), symdiffI2]), symdiffIneg2]), secondinupair]), nonemptyE1]), setukpairIL]), c_0_169]), setukpairIR]), noeltsimpempty]), kpairiskpair]), emptyI]), kpairp]), setext]), singletonsubset]), c_0_170]), singletoninpowerset]), c_0_171]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_172]), c_0_173]), setadjoinOr]), c_0_174]), setadjoinE]), c_0_175]), setadjoinIR]), c_0_176]), emptyinunitempty]), singletonsuniq]), setadjoinIL]), setukpairinjL1]), nonemptyI1]), c_0_177]), powersetI]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), c_0_178]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), nonemptyImpWitness]), notsubsetI]), subsetE2]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_179]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), notdallE]), c_0_180]), c_0_181]), in__Cong]), inCongP]), c_0_182]), c_0_183]), c_0_184]), emptyset__Cong]), c_0_185]), c_0_186]), c_0_187]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), subsetI1]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), notequalI1]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), subsetemptysetimpeq]), binunionIL]), c_0_188]), c_0_189]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), upairset2IR]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), binintersectEL]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectSubset1]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), setminusEL]), setminusI]), bs114d]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), setminusILneg]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_190]), c_0_191]), c_0_192]), c_0_193]), c_0_194]), wellorderingAx]), foundationAx]), c_0_195]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_196])).
% 0.26/0.41 thf(c_0_198, negated_conjecture, ![X937:$i, X938:$i, X940:$i, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X950:$i, X951:$i, X953:$i, X954:$i, X955:$i, X956:$i, X957:$i, X959:$i, X960:$i > $i > $o, X961:$i, X964:$i, X966:$i, X967:$i, X968:$i, X969:$i, X971:$i, X972:$i > $o, X973:$i, X974:$i > $o, X975:$i, X976:$i, X977:$i > $o, X978:$i, X979:$i, X980:$i > $o, X981:$i, X982:$i > $o, X984:$i, X985:$o, X986:$i, X987:$i, X988:$o, X989:$i, X990:$i, X991:$i > $o, X993:$i, X994:$i, X997:$i, X999:$i, X1001:$i, X1002:$i > $o, X1003:$i, X1004:$i, X1006:$i, X1007:$i > $o, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$o, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$o, X1039:$i, X1040:$i, X1041:$i > $o, X1043:$i, X1044:$i, X1045:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i > $o, X1064:$i, X1065:$i > $o, X1066:$i, X1067:$i, X1068:$i > $o, X1069:$i, X1071:$i, X1072:$i > $o, X1074:$i, X1075:$i, X1076:$i > $o, X1078:$i, X1079:$i, X1080:$i > $o, X1081:$i, X1083:$o, X1084:$i, X1085:$i > $o, X1087:$i, X1088:$i, X1089:$i > $o, X1090:$i, X1092:$i > $o, X1093:$i, X1095:$i > $o, X1096:$i, X1099:$i > $o, X1100:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i > $o, X1111:$i, X1112:$i, X1113:$i > $o, X1114:$i > $o, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i > $o, X1126:$i, X1127:$i, X1128:$i > $o, X1129:$i > $o, X1132:$i, X1133:$i, X1134:$i > $o, X1135:$i > $o, X1138:$i, X1139:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1148:$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:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i > $o, X1186:$i, X1187:$i > $o, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1199:$o, X1200:$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, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$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:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$o, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i > $o, X1342:$i, X1343:$i, X1344:$i > $o, X1346:$i, X1347:$i > $o, X1348:$i, X1350:$i, X1351:$i > $o, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i]:((((~(in @ (esk1_2 @ X937 @ X938) @ X937)|~(in @ (esk1_2 @ X937 @ X938) @ X938)|((X937)=(X938)))&((in @ (esk1_2 @ X937 @ X938) @ X937)|(in @ (esk1_2 @ X937 @ X938) @ X938)|((X937)=(X938))))&(~(in @ X940 @ emptyset)&(((~(in @ X943 @ (setadjoin @ X941 @ X942))|(((X943)=(X941))|(in @ X943 @ X942)))&((((X943)!=(X941))|(in @ X943 @ (setadjoin @ X941 @ X942)))&(~(in @ X943 @ X942)|(in @ X943 @ (setadjoin @ X941 @ X942)))))&(((~(in @ X945 @ (powerset @ X944))|(~(in @ X946 @ X945)|(in @ X946 @ X944)))&(((in @ (esk2_2 @ X947 @ X948) @ X948)|(in @ X948 @ (powerset @ X947)))&(~(in @ (esk2_2 @ X947 @ X948) @ X947)|(in @ X948 @ (powerset @ X947)))))&(((((in @ X951 @ (esk3_2 @ X950 @ X951))|~(in @ X951 @ (setunion @ X950)))&((in @ (esk3_2 @ X950 @ X951) @ X950)|~(in @ X951 @ (setunion @ X950))))&(~(in @ X954 @ X955)|~(in @ X955 @ X953)|(in @ X954 @ (setunion @ X953))))&((in @ emptyset @ omega)&((~(in @ X956 @ omega)|(in @ (setadjoin @ X956 @ X956) @ omega))&(((((in @ (esk4_1 @ X957) @ omega)|~(in @ emptyset @ X957)|(~(in @ X959 @ omega)|(in @ X959 @ X957)))&((in @ (esk4_1 @ X957) @ X957)|~(in @ emptyset @ X957)|(~(in @ X959 @ omega)|(in @ X959 @ X957))))&(~(in @ (setadjoin @ (esk4_1 @ X957) @ (esk4_1 @ X957)) @ X957)|~(in @ emptyset @ X957)|(~(in @ X959 @ omega)|(in @ X959 @ X957))))&((((((in @ (esk7_3 @ X960 @ X961 @ X964) @ X961)|~(in @ X964 @ (esk6_2 @ X960 @ X961))|(in @ (esk5_2 @ X960 @ X961) @ X961))&((X960 @ (esk7_3 @ X960 @ X961 @ X964) @ X964)|~(in @ X964 @ (esk6_2 @ X960 @ X961))|(in @ (esk5_2 @ X960 @ X961) @ X961)))&(~(in @ X967 @ X961)|~(X960 @ X967 @ X966)|(in @ X966 @ (esk6_2 @ X960 @ X961))|(in @ (esk5_2 @ X960 @ X961) @ X961)))&((((in @ (esk7_3 @ X960 @ X961 @ X964) @ X961)|~(in @ X964 @ (esk6_2 @ X960 @ X961))|~(exu @ (X960 @ (esk5_2 @ X960 @ X961))))&((X960 @ (esk7_3 @ X960 @ X961 @ X964) @ X964)|~(in @ X964 @ (esk6_2 @ X960 @ X961))|~(exu @ (X960 @ (esk5_2 @ X960 @ X961)))))&(~(in @ X967 @ X961)|~(X960 @ X967 @ X966)|(in @ X966 @ (esk6_2 @ X960 @ X961))|~(exu @ (X960 @ (esk5_2 @ X960 @ X961))))))&((((in @ (esk8_1 @ X968) @ X968)|~(in @ X969 @ X968))&(~(in @ X971 @ (esk8_1 @ X968))|~(in @ X971 @ X968)|~(in @ X969 @ X968)))&((epred1_0)&((~(exu @ X972)|(X972 @ (descr @ X972)))&((~(in @ X975 @ X973)|(~(X974 @ X975)|(in @ X975 @ (dsetconstr @ X973 @ X974))))&((~(in @ X978 @ (dsetconstr @ X976 @ X977))|(in @ X978 @ X976))&((~(in @ X981 @ (dsetconstr @ X979 @ X980))|(X980 @ X981))&((((X982 @ (esk9_1 @ X982))|~(exu @ X982))&(~(X982 @ X984)|((esk9_1 @ X982)=(X984))|~(exu @ X982)))&((~(in @ X986 @ (prop2set @ ((X985))))|(X985))&((~(in @ X987 @ emptyset)|(X988))&((~(in @ X989 @ emptyset)|~($true))&(~(in @ X990 @ emptyset)&((~(exu @ X991)|(X991 @ (esk10_1 @ X991)))&(((((in @ (esk12_2 @ X993 @ X994) @ X994)|((X993)=(X994))|(in @ (esk11_2 @ X993 @ X994) @ X993))&(~(in @ (esk12_2 @ X993 @ X994) @ X993)|((X993)=(X994))|(in @ (esk11_2 @ X993 @ X994) @ X993)))&(((in @ (esk12_2 @ X993 @ X994) @ X994)|((X993)=(X994))|~(in @ (esk11_2 @ X993 @ X994) @ X994))&(~(in @ (esk12_2 @ X993 @ X994) @ X993)|((X993)=(X994))|~(in @ (esk11_2 @ X993 @ X994) @ X994))))&(((in @ (esk13_1 @ X997) @ X997)|((X997)=(emptyset)))&(((in @ (esk14_1 @ X999) @ X999)|((X999)=(emptyset)))&(((~(in @ X1003 @ (dsetconstr @ X1001 @ X1002))|(X1002 @ X1003)|~(in @ X1003 @ X1001))&(~(X1002 @ X1003)|(in @ X1003 @ (dsetconstr @ X1001 @ X1002))|~(in @ X1003 @ X1001)))&((~(nonempty @ X1004)|(in @ (esk15_1 @ X1004) @ X1004))&((~(in @ X1008 @ X1006)|(~(X1007 @ X1008)|(nonempty @ (dsetconstr @ X1006 @ X1007))))&((~(in @ X1010 @ X1009)|(nonempty @ X1009))&((in @ X1011 @ (setadjoin @ X1011 @ X1012))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1015 @ X1014)|(in @ X1015 @ (setadjoin @ X1013 @ X1014)))&(((((in @ X1018 @ X1017)|(X1019)|((X1018)=(X1016))|~(in @ X1018 @ (setadjoin @ X1016 @ 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emptyset)) @ (powerset @ (powerset @ (binunion @ X1312 @ X1313))))))&((~(in @ X1318 @ X1316)|(~(in @ X1319 @ X1317)|(in @ (kpair @ X1318 @ X1319) @ (powerset @ (powerset @ (binunion @ X1316 @ X1317))))))&((~(in @ X1322 @ X1320)|(~(in @ X1323 @ X1321)|(in @ (kpair @ X1322 @ X1323) @ (cartprod @ X1320 @ X1321))))&((((in @ (esk39_3 @ X1324 @ X1325 @ X1326) @ X1324)|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))&(((in @ (esk40_3 @ X1324 @ X1325 @ X1326) @ X1325)|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))&(((X1326)=(kpair @ (esk39_3 @ X1324 @ X1325 @ X1326) @ (esk40_3 @ X1324 @ X1325 @ X1326)))|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))))&((~(in @ X1331 @ (cartprod @ X1329 @ X1330))|(iskpair @ X1331))&((((in @ (esk41_2 @ X1332 @ X1333) @ X1332)|~(in @ X1333 @ (setunion @ X1332)))&((in @ X1333 @ (esk41_2 @ X1332 @ X1333))|~(in @ X1333 @ (setunion @ X1332))))&((subset @ (setunion @ (setadjoin @ X1335 @ emptyset)) @ X1335)&((subset @ X1336 @ (setunion @ (setadjoin @ X1336 @ emptyset)))&(((setunion @ (setadjoin @ X1337 @ emptyset))=(X1337))&((((in @ (esk42_2 @ X1338 @ X1339) @ X1338)|(~(in @ X1342 @ X1338)|~(X1339 @ X1342)|(singleton @ (dsetconstr @ X1338 @ X1339))))&(((in @ (esk43_2 @ X1338 @ X1339) @ X1338)|(~(in @ X1342 @ X1338)|~(X1339 @ X1342)|(singleton @ (dsetconstr @ X1338 @ X1339))))&(((X1339 @ (esk42_2 @ X1338 @ X1339))|(~(in @ X1342 @ X1338)|~(X1339 @ X1342)|(singleton @ (dsetconstr @ X1338 @ X1339))))&(((X1339 @ (esk43_2 @ X1338 @ X1339))|(~(in @ X1342 @ X1338)|~(X1339 @ X1342)|(singleton @ (dsetconstr @ X1338 @ X1339))))&(((esk42_2 @ X1338 @ X1339)!=(esk43_2 @ X1338 @ X1339))|(~(in @ X1342 @ X1338)|~(X1339 @ X1342)|(singleton @ (dsetconstr @ X1338 @ X1339))))))))&((((in @ (esk44_2 @ X1343 @ X1344) @ X1343)|~(ex1 @ X1343 @ X1344))&((X1344 @ (esk44_2 @ X1343 @ X1344))|~(ex1 @ X1343 @ X1344)))&((((in @ (esk45_3 @ X1346 @ X1347 @ X1348) @ X1346)|(ex1 @ X1346 @ X1347)|~(X1347 @ X1348)|~(in @ X1348 @ X1346))&(((X1347 @ (esk45_3 @ X1346 @ X1347 @ X1348))|(ex1 @ X1346 @ X1347)|~(X1347 @ X1348)|~(in @ X1348 @ X1346))&(((esk45_3 @ X1346 @ X1347 @ X1348)!=(X1348))|(ex1 @ X1346 @ X1347)|~(X1347 @ X1348)|~(in @ X1348 @ X1346))))&((((in @ (esk46_2 @ X1350 @ X1351) @ X1350)|(~(in @ X1354 @ X1350)|~(X1351 @ X1354)|(ex1 @ X1350 @ X1351)))&(((in @ (esk47_2 @ X1350 @ X1351) @ X1350)|(~(in @ X1354 @ X1350)|~(X1351 @ X1354)|(ex1 @ X1350 @ X1351)))&(((X1351 @ (esk46_2 @ X1350 @ X1351))|(~(in @ X1354 @ X1350)|~(X1351 @ X1354)|(ex1 @ X1350 @ X1351)))&(((X1351 @ (esk47_2 @ X1350 @ X1351))|(~(in @ X1354 @ X1350)|~(X1351 @ X1354)|(ex1 @ X1350 @ X1351)))&(((esk46_2 @ X1350 @ X1351)!=(esk47_2 @ X1350 @ X1351))|(~(in @ X1354 @ X1350)|~(X1351 @ X1354)|(ex1 @ X1350 @ X1351)))))))&((((setadjoin @ X1355 @ emptyset)!=(setadjoin @ X1356 @ emptyset))|((X1355)=(X1356)))&((~(in @ (setadjoin @ X1359 @ emptyset) @ (setadjoin @ (setadjoin @ X1357 @ emptyset) @ (setadjoin @ (setadjoin @ X1357 @ (setadjoin @ X1358 @ emptyset)) @ emptyset)))|((X1357)=(X1359)))&((~(iskpair @ X1360)|(singleton @ (dsetconstr @ (setunion @ X1360) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1360))))))&((~(singleton @ X1361)|(in @ (setunion @ X1361) @ X1361))&(((kfst @ (kpair @ X1362 @ X1363))=(X1362))&((~(in @ X1366 @ (cartprod @ X1364 @ X1365))|(in @ (kfst @ X1366) @ X1364))&((((setadjoin @ (setadjoin @ X1367 @ emptyset) @ (setadjoin @ (setadjoin @ X1367 @ (setadjoin @ X1368 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1369 @ emptyset) @ (setadjoin @ (setadjoin @ X1369 @ (setadjoin @ X1370 @ emptyset)) @ emptyset)))|((X1367)=(X1369)))&((((kpair @ X1371 @ X1372)!=(kpair @ X1373 @ X1374))|((X1371)=(X1373)))&((((X1375)!=(X1376))|((setadjoin @ X1375 @ (setadjoin @ X1376 @ emptyset))=(setadjoin @ X1375 @ emptyset)))&((((X1377)!=(X1378))|((setadjoin @ (setadjoin @ X1377 @ emptyset) @ (setadjoin @ (setadjoin @ X1377 @ (setadjoin @ X1378 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1377 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1379 @ emptyset) @ (setadjoin @ (setadjoin @ X1379 @ (setadjoin @ X1380 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1381 @ emptyset) @ (setadjoin @ (setadjoin @ X1381 @ (setadjoin @ X1382 @ emptyset)) @ emptyset)))|(((X1381)!=(X1382))|((X1380)=(X1382))))&(((setadjoin @ esk48_0 @ (setadjoin @ esk49_0 @ emptyset))=(setadjoin @ esk50_0 @ emptyset))&((esk48_0)!=(esk49_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_197])])])])])])])).
% 0.26/0.41 thf(c_0_199, negated_conjecture, ![X3:$i, X2:$i]:((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_198])).
% 0.26/0.41 thf(c_0_200, negated_conjecture, ((setadjoin @ esk48_0 @ (setadjoin @ esk49_0 @ emptyset))=(setadjoin @ esk50_0 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_198])).
% 0.26/0.41 thf(c_0_201, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_198])).
% 0.26/0.41 thf(c_0_202, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((in @ X3 @ (setadjoin @ X2 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_198])).
% 0.26/0.41 thf(c_0_203, negated_conjecture, (in @ esk49_0 @ (setadjoin @ esk50_0 @ emptyset)), inference(spm,[status(thm)],[c_0_199, c_0_200])).
% 0.26/0.41 thf(c_0_204, negated_conjecture, (in @ esk48_0 @ (setadjoin @ esk50_0 @ emptyset)), inference(spm,[status(thm)],[c_0_201, c_0_200])).
% 0.26/0.41 thf(c_0_205, negated_conjecture, ((esk50_0)=(esk49_0)), inference(spm,[status(thm)],[c_0_202, c_0_203])).
% 0.26/0.41 thf(c_0_206, negated_conjecture, ((esk48_0)!=(esk49_0)), inference(split_conjunct,[status(thm)],[c_0_198])).
% 0.26/0.41 thf(c_0_207, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202, c_0_204]), c_0_205]), c_0_206]), ['proof']).
% 0.26/0.41 % SZS output end CNFRefutation
% 0.26/0.41 % Parsed axioms : 373
% 0.26/0.41 % Removed by relevancy pruning/SinE : 205
% 0.26/0.41 % Initial clauses : 265
% 0.26/0.41 % Removed in clause preprocessing : 25
% 0.26/0.41 % Initial clauses in saturation : 240
% 0.26/0.41 % Processed clauses : 361
% 0.26/0.41 % ...of these trivial : 10
% 0.26/0.41 % ...subsumed : 166
% 0.26/0.41 % ...remaining for further processing : 184
% 0.26/0.41 % Other redundant clauses eliminated : 15
% 0.26/0.41 % Clauses deleted for lack of memory : 0
% 0.26/0.41 % Backward-subsumed : 2
% 0.26/0.41 % Backward-rewritten : 4
% 0.26/0.41 % Generated clauses : 918
% 0.26/0.41 % ...of the previous two non-redundant : 762
% 0.26/0.41 % ...aggressively subsumed : 0
% 0.26/0.41 % Contextual simplify-reflections : 0
% 0.26/0.41 % Paramodulations : 901
% 0.26/0.41 % Factorizations : 0
% 0.26/0.41 % NegExts : 0
% 0.26/0.41 % Equation resolutions : 17
% 0.26/0.41 % Disequality decompositions : 0
% 0.26/0.41 % Total rewrite steps : 157
% 0.26/0.41 % ...of those cached : 115
% 0.26/0.41 % Propositional unsat checks : 0
% 0.26/0.41 % Propositional check models : 0
% 0.26/0.41 % Propositional check unsatisfiable : 0
% 0.26/0.41 % Propositional clauses : 0
% 0.26/0.41 % Propositional clauses after purity: 0
% 0.26/0.41 % Propositional unsat core size : 0
% 0.26/0.41 % Propositional preprocessing time : 0.000
% 0.26/0.41 % Propositional encoding time : 0.000
% 0.26/0.41 % Propositional solver time : 0.000
% 0.26/0.41 % Success case prop preproc time : 0.000
% 0.26/0.41 % Success case prop encoding time : 0.000
% 0.26/0.41 % Success case prop solver time : 0.000
% 0.26/0.41 % Current number of processed clauses : 171
% 0.26/0.41 % Positive orientable unit clauses : 45
% 0.26/0.41 % Positive unorientable unit clauses: 0
% 0.26/0.41 % Negative unit clauses : 3
% 0.26/0.41 % Non-unit-clauses : 123
% 0.26/0.41 % Current number of unprocessed clauses: 611
% 0.26/0.41 % ...number of literals in the above : 1642
% 0.26/0.41 % Current number of archived formulas : 0
% 0.26/0.41 % Current number of archived clauses : 6
% 0.26/0.41 % Clause-clause subsumption calls (NU) : 1857
% 0.26/0.41 % Rec. Clause-clause subsumption calls : 1784
% 0.26/0.41 % Non-unit clause-clause subsumptions : 160
% 0.26/0.41 % Unit Clause-clause subsumption calls : 133
% 0.26/0.41 % Rewrite failures with RHS unbound : 0
% 0.26/0.41 % BW rewrite match attempts : 8
% 0.26/0.41 % BW rewrite match successes : 4
% 0.26/0.41 % Condensation attempts : 0
% 0.26/0.41 % Condensation successes : 0
% 0.26/0.41 % Termbank termtop insertions : 46154
% 0.26/0.41 % Search garbage collected termcells : 14776
% 0.26/0.41
% 0.26/0.41 % -------------------------------------------------
% 0.26/0.41 % User time : 0.082 s
% 0.26/0.41 % System time : 0.009 s
% 0.26/0.41 % Total time : 0.091 s
% 0.26/0.41 % Maximum resident set size: 7332 pages
% 0.26/0.41
% 0.26/0.41 % -------------------------------------------------
% 0.26/0.41 % User time : 0.094 s
% 0.26/0.41 % System time : 0.013 s
% 0.26/0.41 % Total time : 0.107 s
% 0.26/0.41 % Maximum resident set size: 4864 pages
% 0.26/0.41 % E exiting
%------------------------------------------------------------------------------