%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU674^1 : 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 : n016.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 08:24:59 AM UTC 2026
% Result : Theorem 4.86s 1.02s
% Output : CNFRefutation 4.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU674^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.16 % Computer : n016.cluster.edu
% 0.13/0.16 % Model : x86_64 x86_64
% 0.13/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.16 % Memory : 8046.5625MB
% 0.13/0.16 % OS : Linux 6.8.0-71-generic
% 0.13/0.16 % CPULimit : 300
% 0.13/0.16 % WCLimit : 300
% 0.13/0.16 % DateTime : Tue Sep 29 14:12:04 UTC 2026
% 0.13/0.17 % CPUTime :
% 0.13/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.23 Running higher-order theorem proving
% 0.13/0.27 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.iYtLh2Sxg7/E---3.1_411641.p
% 4.86/1.02 % Version: 3.5.1-ho
% 4.86/1.02 % Preprocessing class: HSLMSLSSLLLCHFA.
% 4.86/1.02 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 4.86/1.02 % Starting ehoh_best5 with 300s (1) cores
% 4.86/1.02 % Starting almost_fo_3_lam with 300s (1) cores
% 4.86/1.02 % Starting new_bool_5 with 300s (1) cores
% 4.86/1.02 % Starting pre_casc_3 with 300s (1) cores
% 4.86/1.02 % Starting ho_unfolding_8 with 300s (1) cores
% 4.86/1.02 % Starting new_ho_10_cnf2 with 300s (1) cores
% 4.86/1.02 % Starting new_bool_3 with 300s (1) cores
% 4.86/1.02 % Starting new_ho_5 with 300s (1) cores
% 4.86/1.02 % new_bool_3 with pid 411664 completed with status 0
% 4.86/1.02 % Result found by new_bool_3
% 4.86/1.02 % Preprocessing class: HSLMSLSSLLLCHFA.
% 4.86/1.02 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 4.86/1.02 % Starting ehoh_best5 with 300s (1) cores
% 4.86/1.02 % Starting almost_fo_3_lam with 300s (1) cores
% 4.86/1.02 % Starting new_bool_5 with 300s (1) cores
% 4.86/1.02 % Starting pre_casc_3 with 300s (1) cores
% 4.86/1.02 % Starting ho_unfolding_8 with 300s (1) cores
% 4.86/1.02 % Starting new_ho_10_cnf2 with 300s (1) cores
% 4.86/1.02 % Starting new_bool_3 with 300s (1) cores
% 4.86/1.02 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.86/1.02 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.86/1.02 % Search class: HGHSM-FSLM31-MHFMMSBN
% 4.86/1.02 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 4.86/1.02 % Starting SubtermCWHack with 28s (1) cores
% 4.86/1.02 % SubtermCWHack with pid 411691 completed with status 0
% 4.86/1.02 % Result found by SubtermCWHack
% 4.86/1.02 % Preprocessing class: HSLMSLSSLLLCHFA.
% 4.86/1.02 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 4.86/1.02 % Starting ehoh_best5 with 300s (1) cores
% 4.86/1.02 % Starting almost_fo_3_lam with 300s (1) cores
% 4.86/1.02 % Starting new_bool_5 with 300s (1) cores
% 4.86/1.02 % Starting pre_casc_3 with 300s (1) cores
% 4.86/1.02 % Starting ho_unfolding_8 with 300s (1) cores
% 4.86/1.02 % Starting new_ho_10_cnf2 with 300s (1) cores
% 4.86/1.02 % Starting new_bool_3 with 300s (1) cores
% 4.86/1.02 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.86/1.02 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.86/1.02 % Search class: HGHSM-FSLM31-MHFMMSBN
% 4.86/1.02 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 4.86/1.02 % Starting SubtermCWHack with 28s (1) cores
% 4.86/1.02 % Preprocessing time : 0.007 s
% 4.86/1.02
% 4.86/1.02 % Proof found!
% 4.86/1.02 % SZS status Theorem
% 4.86/1.02 % SZS output start CNFRefutation
% 4.86/1.02 thf(decl_23, type, in: $i > $i > $o).
% 4.86/1.02 thf(decl_24, type, exu: ($i > $o) > $o).
% 4.86/1.02 thf(decl_25, type, setextAx: $o).
% 4.86/1.02 thf(decl_26, type, emptyset: $i).
% 4.86/1.02 thf(decl_27, type, emptysetAx: $o).
% 4.86/1.02 thf(decl_28, type, setadjoin: $i > $i > $i).
% 4.86/1.02 thf(decl_29, type, setadjoinAx: $o).
% 4.86/1.02 thf(decl_30, type, powerset: $i > $i).
% 4.86/1.02 thf(decl_31, type, powersetAx: $o).
% 4.86/1.02 thf(decl_32, type, setunion: $i > $i).
% 4.86/1.02 thf(decl_33, type, setunionAx: $o).
% 4.86/1.02 thf(decl_34, type, omega: $i).
% 4.86/1.02 thf(decl_35, type, omega0Ax: $o).
% 4.86/1.02 thf(decl_36, type, omegaSAx: $o).
% 4.86/1.02 thf(decl_37, type, omegaIndAx: $o).
% 4.86/1.02 thf(decl_38, type, replAx: $o).
% 4.86/1.02 thf(decl_39, type, foundationAx: $o).
% 4.86/1.02 thf(decl_40, type, wellorderingAx: $o).
% 4.86/1.02 thf(decl_41, type, descr: ($i > $o) > $i).
% 4.86/1.02 thf(decl_42, type, descrp: $o).
% 4.86/1.02 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 4.86/1.02 thf(decl_44, type, dsetconstrI: $o).
% 4.86/1.02 thf(decl_45, type, dsetconstrEL: $o).
% 4.86/1.02 thf(decl_46, type, dsetconstrER: $o).
% 4.86/1.02 thf(decl_47, type, exuE1: $o).
% 4.86/1.02 thf(decl_48, type, prop2set: $o > $i).
% 4.86/1.02 thf(decl_49, type, prop2setE: $o).
% 4.86/1.02 thf(decl_50, type, emptysetE: $o).
% 4.86/1.02 thf(decl_51, type, emptysetimpfalse: $o).
% 4.86/1.02 thf(decl_52, type, notinemptyset: $o).
% 4.86/1.02 thf(decl_53, type, exuE3e: $o).
% 4.86/1.02 thf(decl_54, type, setext: $o).
% 4.86/1.02 thf(decl_55, type, emptyI: $o).
% 4.86/1.02 thf(decl_56, type, noeltsimpempty: $o).
% 4.86/1.02 thf(decl_57, type, setbeta: $o).
% 4.86/1.02 thf(decl_58, type, nonempty: $i > $o).
% 4.86/1.02 thf(decl_59, type, nonemptyE1: $o).
% 4.86/1.02 thf(decl_60, type, nonemptyI: $o).
% 4.86/1.02 thf(decl_61, type, nonemptyI1: $o).
% 4.86/1.02 thf(decl_62, type, setadjoinIL: $o).
% 4.86/1.02 thf(decl_63, type, emptyinunitempty: $o).
% 4.86/1.02 thf(decl_64, type, setadjoinIR: $o).
% 4.86/1.02 thf(decl_65, type, setadjoinE: $o).
% 4.86/1.02 thf(decl_66, type, setadjoinOr: $o).
% 4.86/1.02 thf(decl_67, type, setoftrueEq: $o).
% 4.86/1.02 thf(decl_68, type, powersetI: $o).
% 4.86/1.02 thf(decl_69, type, emptyinPowerset: $o).
% 4.86/1.02 thf(decl_70, type, emptyInPowerset: $o).
% 4.86/1.02 thf(decl_71, type, powersetE: $o).
% 4.86/1.02 thf(decl_72, type, setunionI: $o).
% 4.86/1.02 thf(decl_73, type, setunionE: $o).
% 4.86/1.03 thf(decl_74, type, subPowSU: $o).
% 4.86/1.03 thf(decl_75, type, exuE2: $o).
% 4.86/1.03 thf(decl_76, type, nonemptyImpWitness: $o).
% 4.86/1.03 thf(decl_77, type, uniqinunit: $o).
% 4.86/1.03 thf(decl_78, type, notinsingleton: $o).
% 4.86/1.03 thf(decl_79, type, eqinunit: $o).
% 4.86/1.03 thf(decl_80, type, singletonsswitch: $o).
% 4.86/1.03 thf(decl_81, type, upairsetE: $o).
% 4.86/1.03 thf(decl_82, type, upairsetIL: $o).
% 4.86/1.03 thf(decl_83, type, upairsetIR: $o).
% 4.86/1.03 thf(decl_84, type, emptyE1: $o).
% 4.86/1.03 thf(decl_85, type, vacuousDall: $o).
% 4.86/1.03 thf(decl_86, type, quantDeMorgan1: $o).
% 4.86/1.03 thf(decl_87, type, quantDeMorgan2: $o).
% 4.86/1.03 thf(decl_88, type, quantDeMorgan3: $o).
% 4.86/1.03 thf(decl_89, type, quantDeMorgan4: $o).
% 4.86/1.03 thf(decl_90, type, prop2setI: $o).
% 4.86/1.03 thf(decl_92, type, prop2set2propI: $o).
% 4.86/1.03 thf(decl_93, type, notdexE: $o).
% 4.86/1.03 thf(decl_94, type, notdallE: $o).
% 4.86/1.03 thf(decl_95, type, exuI1: $o).
% 4.86/1.03 thf(decl_96, type, exuI3: $o).
% 4.86/1.03 thf(decl_97, type, exuI2: $o).
% 4.86/1.03 thf(decl_98, type, inCongP: $o).
% 4.86/1.03 thf(decl_99, type, in__Cong: $o).
% 4.86/1.03 thf(decl_100, type, exuE3u: $o).
% 4.86/1.03 thf(decl_101, type, exu__Cong: $o).
% 4.86/1.03 thf(decl_102, type, emptyset__Cong: $o).
% 4.86/1.03 thf(decl_103, type, setadjoin__Cong: $o).
% 4.86/1.03 thf(decl_104, type, powerset__Cong: $o).
% 4.86/1.03 thf(decl_105, type, setunion__Cong: $o).
% 4.86/1.03 thf(decl_106, type, omega__Cong: $o).
% 4.86/1.03 thf(decl_107, type, exuEu: $o).
% 4.86/1.03 thf(decl_108, type, descr__Cong: $o).
% 4.86/1.03 thf(decl_109, type, dsetconstr__Cong: $o).
% 4.86/1.03 thf(decl_110, type, subset: $i > $i > $o).
% 4.86/1.03 thf(decl_113, type, subsetI1: $o).
% 4.86/1.03 thf(decl_114, type, eqimpsubset2: $o).
% 4.86/1.03 thf(decl_115, type, eqimpsubset1: $o).
% 4.86/1.03 thf(decl_116, type, subsetI2: $o).
% 4.86/1.03 thf(decl_117, type, emptysetsubset: $o).
% 4.86/1.03 thf(decl_118, type, subsetE: $o).
% 4.86/1.03 thf(decl_119, type, subsetE2: $o).
% 4.86/1.03 thf(decl_120, type, notsubsetI: $o).
% 4.86/1.03 thf(decl_121, type, notequalI1: $o).
% 4.86/1.03 thf(decl_122, type, notequalI2: $o).
% 4.86/1.03 thf(decl_123, type, subsetRefl: $o).
% 4.86/1.03 thf(decl_124, type, subsetTrans: $o).
% 4.86/1.03 thf(decl_125, type, setadjoinSub: $o).
% 4.86/1.03 thf(decl_126, type, setadjoinSub2: $o).
% 4.86/1.03 thf(decl_127, type, subset2powerset: $o).
% 4.86/1.03 thf(decl_128, type, setextsub: $o).
% 4.86/1.03 thf(decl_129, type, subsetemptysetimpeq: $o).
% 4.86/1.03 thf(decl_130, type, powersetI1: $o).
% 4.86/1.03 thf(decl_131, type, powersetE1: $o).
% 4.86/1.03 thf(decl_132, type, inPowerset: $o).
% 4.86/1.03 thf(decl_133, type, powersetsubset: $o).
% 4.86/1.03 thf(decl_134, type, sepInPowerset: $o).
% 4.86/1.03 thf(decl_135, type, sepSubset: $o).
% 4.86/1.03 thf(decl_136, type, binunion: $i > $i > $i).
% 4.86/1.03 thf(decl_137, type, binunionIL: $o).
% 4.86/1.03 thf(decl_138, type, upairset2IR: $o).
% 4.86/1.03 thf(decl_139, type, binunionIR: $o).
% 4.86/1.03 thf(decl_140, type, binunionEcases: $o).
% 4.86/1.03 thf(decl_141, type, binunionE: $o).
% 4.86/1.03 thf(decl_142, type, binunionLsub: $o).
% 4.86/1.03 thf(decl_143, type, binunionRsub: $o).
% 4.86/1.03 thf(decl_144, type, binintersect: $i > $i > $i).
% 4.86/1.03 thf(decl_145, type, binintersectI: $o).
% 4.86/1.03 thf(decl_146, type, binintersectSubset5: $o).
% 4.86/1.03 thf(decl_147, type, binintersectEL: $o).
% 4.86/1.03 thf(decl_148, type, binintersectLsub: $o).
% 4.86/1.03 thf(decl_149, type, binintersectSubset2: $o).
% 4.86/1.03 thf(decl_150, type, binintersectSubset3: $o).
% 4.86/1.03 thf(decl_151, type, binintersectER: $o).
% 4.86/1.03 thf(decl_152, type, disjointsetsI1: $o).
% 4.86/1.03 thf(decl_153, type, binintersectRsub: $o).
% 4.86/1.03 thf(decl_154, type, binintersectSubset4: $o).
% 4.86/1.03 thf(decl_155, type, binintersectSubset1: $o).
% 4.86/1.03 thf(decl_156, type, bs114d: $o).
% 4.86/1.03 thf(decl_158, type, setminus: $i > $i > $i).
% 4.86/1.03 thf(decl_159, type, setminusI: $o).
% 4.86/1.03 thf(decl_160, type, setminusEL: $o).
% 4.86/1.03 thf(decl_161, type, setminusER: $o).
% 4.86/1.03 thf(decl_162, type, setminusSubset2: $o).
% 4.86/1.03 thf(decl_163, type, setminusERneg: $o).
% 4.86/1.03 thf(decl_164, type, setminusELneg: $o).
% 4.86/1.03 thf(decl_165, type, setminusILneg: $o).
% 4.86/1.03 thf(decl_166, type, setminusIRneg: $o).
% 4.86/1.03 thf(decl_167, type, setminusLsub: $o).
% 4.86/1.03 thf(decl_168, type, setminusSubset1: $o).
% 4.86/1.03 thf(decl_169, type, symdiff: $i > $i > $i).
% 4.86/1.03 thf(decl_170, type, symdiffE: $o).
% 4.86/1.03 thf(decl_171, type, symdiffI1: $o).
% 4.86/1.03 thf(decl_172, type, symdiffI2: $o).
% 4.86/1.03 thf(decl_173, type, symdiffIneg1: $o).
% 4.86/1.03 thf(decl_174, type, symdiffIneg2: $o).
% 4.86/1.03 thf(decl_175, type, iskpair: $i > $o).
% 4.86/1.03 thf(decl_176, type, secondinupair: $o).
% 4.86/1.03 thf(decl_177, type, setukpairIL: $o).
% 4.86/1.03 thf(decl_178, type, setukpairIR: $o).
% 4.86/1.03 thf(decl_179, type, kpairiskpair: $o).
% 4.86/1.03 thf(decl_180, type, kpair: $i > $i > $i).
% 4.86/1.03 thf(decl_181, type, kpairp: $o).
% 4.86/1.03 thf(decl_182, type, cartprod: $i > $i > $i).
% 4.86/1.03 thf(decl_183, type, singletonsubset: $o).
% 4.86/1.03 thf(decl_184, type, singletoninpowerset: $o).
% 4.86/1.03 thf(decl_185, type, singletoninpowunion: $o).
% 4.86/1.03 thf(decl_186, type, upairset2E: $o).
% 4.86/1.03 thf(decl_187, type, upairsubunion: $o).
% 4.86/1.03 thf(decl_188, type, upairinpowunion: $o).
% 4.86/1.03 thf(decl_189, type, ubforcartprodlem1: $o).
% 4.86/1.03 thf(decl_190, type, ubforcartprodlem2: $o).
% 4.86/1.03 thf(decl_191, type, ubforcartprodlem3: $o).
% 4.86/1.03 thf(decl_192, type, cartprodpairin: $o).
% 4.86/1.03 thf(decl_193, type, cartprodmempair1: $o).
% 4.86/1.03 thf(decl_194, type, cartprodmempair: $o).
% 4.86/1.03 thf(decl_195, type, setunionE2: $o).
% 4.86/1.03 thf(decl_196, type, setunionsingleton1: $o).
% 4.86/1.03 thf(decl_197, type, setunionsingleton2: $o).
% 4.86/1.03 thf(decl_198, type, setunionsingleton: $o).
% 4.86/1.03 thf(decl_199, type, singleton: $i > $o).
% 4.86/1.03 thf(decl_200, type, singletonprop: $o).
% 4.86/1.03 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 4.86/1.03 thf(decl_202, type, ex1E1: $o).
% 4.86/1.03 thf(decl_203, type, ex1I: $o).
% 4.86/1.03 thf(decl_204, type, ex1I2: $o).
% 4.86/1.03 thf(decl_205, type, singletonsuniq: $o).
% 4.86/1.03 thf(decl_210, type, setukpairinjL1: $o).
% 4.86/1.03 thf(decl_211, type, kfstsingleton: $o).
% 4.86/1.03 thf(decl_212, type, theprop: $o).
% 4.86/1.03 thf(decl_213, type, kfst: $i > $i).
% 4.86/1.03 thf(decl_214, type, kfstpairEq: $o).
% 4.86/1.03 thf(decl_215, type, cartprodfstin: $o).
% 4.86/1.03 thf(decl_216, type, setukpairinjL2: $o).
% 4.86/1.03 thf(decl_217, type, setukpairinjL: $o).
% 4.86/1.03 thf(decl_218, type, setukpairinjR11: $o).
% 4.86/1.03 thf(decl_219, type, setukpairinjR12: $o).
% 4.86/1.03 thf(decl_220, type, setukpairinjR1: $o).
% 4.86/1.03 thf(decl_221, type, upairequniteq: $o).
% 4.86/1.03 thf(decl_222, type, setukpairinjR2: $o).
% 4.86/1.03 thf(decl_223, type, setukpairinjR: $o).
% 4.86/1.03 thf(decl_224, type, ksndsingleton: $o).
% 4.86/1.03 thf(decl_225, type, ksnd: $i > $i).
% 4.86/1.03 thf(decl_226, type, ksndpairEq: $o).
% 4.86/1.03 thf(decl_227, type, kpairsurjEq: $o).
% 4.86/1.03 thf(decl_228, type, cartprodsndin: $o).
% 4.86/1.03 thf(decl_229, type, cartprodpairmemEL: $o).
% 4.86/1.03 thf(decl_230, type, cartprodpairmemER: $o).
% 4.86/1.03 thf(decl_231, type, cartprodmempaircEq: $o).
% 4.86/1.03 thf(decl_232, type, cartprodfstpairEq: $o).
% 4.86/1.03 thf(decl_233, type, cartprodsndpairEq: $o).
% 4.86/1.03 thf(decl_234, type, cartprodpairsurjEq: $o).
% 4.86/1.03 thf(decl_235, type, breln: $i > $i > $i > $o).
% 4.86/1.03 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 4.86/1.03 thf(decl_237, type, dpsetconstrI: $o).
% 4.86/1.03 thf(decl_238, type, dpsetconstrSub: $o).
% 4.86/1.03 thf(decl_239, type, setOfPairsIsBReln: $o).
% 4.86/1.03 thf(decl_240, type, dpsetconstrERa: $o).
% 4.86/1.03 thf(decl_241, type, dpsetconstrEL1: $o).
% 4.86/1.03 thf(decl_242, type, dpsetconstrEL2: $o).
% 4.86/1.03 thf(decl_243, type, dpsetconstrER: $o).
% 4.86/1.03 thf(decl_244, type, func: $i > $i > $i > $o).
% 4.86/1.03 thf(decl_246, type, funcImageSingleton: $o).
% 4.86/1.03 thf(decl_247, type, apProp: $o).
% 4.86/1.03 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 4.86/1.03 thf(decl_249, type, epred1_0: $o).
% 4.86/1.03 thf(decl_250, type, esk1_2: $i > $i > $i).
% 4.86/1.03 thf(decl_251, type, esk2_2: $i > $i > $i).
% 4.86/1.03 thf(decl_252, type, esk3_2: $i > $i > $i).
% 4.86/1.03 thf(decl_253, type, esk4_1: $i > $i).
% 4.86/1.03 thf(decl_254, type, esk5_2: ($i > $i > $o) > $i > $i).
% 4.86/1.03 thf(decl_255, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 4.86/1.03 thf(decl_256, type, esk7_2: ($i > $i > $o) > $i > $i).
% 4.86/1.03 thf(decl_257, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 4.86/1.03 thf(decl_258, type, esk9_1: $i > $i).
% 4.86/1.03 thf(decl_259, type, esk10_2: ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_260, type, esk11_2: ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_261, type, esk12_1: ($i > $o) > $i).
% 4.86/1.03 thf(decl_262, type, esk13_2: ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_263, type, esk14_1: ($i > $o) > $i).
% 4.86/1.03 thf(decl_264, type, esk15_2: $i > $i > $i).
% 4.86/1.03 thf(decl_265, type, esk16_2: $i > $i > $i).
% 4.86/1.03 thf(decl_266, type, esk17_1: $i > $i).
% 4.86/1.03 thf(decl_267, type, esk18_1: $i > $i).
% 4.86/1.03 thf(decl_268, type, esk19_1: $i > $i).
% 4.86/1.03 thf(decl_269, type, esk20_2: $i > $i > $i).
% 4.86/1.03 thf(decl_270, type, esk21_3: $i > $i > $o > $i).
% 4.86/1.03 thf(decl_271, type, esk22_2: ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_272, type, esk23_1: ($i > $o) > $i).
% 4.86/1.03 thf(decl_273, type, esk24_1: $i > $i).
% 4.86/1.03 thf(decl_274, type, esk25_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_275, type, esk26_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_276, type, esk27_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_277, type, esk28_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_278, type, esk29_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_279, type, esk30_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_280, type, esk31_2: ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_281, type, esk32_1: ($i > $o) > $i).
% 4.86/1.03 thf(decl_282, type, esk33_1: ($i > $o) > $i).
% 4.86/1.03 thf(decl_283, type, esk34_1: ($i > $o) > $i).
% 4.86/1.03 thf(decl_284, type, esk35_1: ($i > $o) > $i).
% 4.86/1.03 thf(decl_285, type, esk36_2: ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_286, type, esk37_1: ($i > $o) > $i).
% 4.86/1.03 thf(decl_287, type, esk38_2: ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_288, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 4.86/1.03 thf(decl_289, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 4.86/1.03 thf(decl_290, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_291, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 4.86/1.03 thf(decl_292, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_293, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 4.86/1.03 thf(decl_294, type, esk45_2: ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_295, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 4.86/1.03 thf(decl_296, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 4.86/1.03 thf(decl_297, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_298, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_299, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 4.86/1.03 thf(decl_300, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 4.86/1.03 thf(decl_301, type, esk52_2: $i > $i > $i).
% 4.86/1.03 thf(decl_302, type, esk53_2: $i > $i > $i).
% 4.86/1.03 thf(decl_303, type, esk54_2: $i > $i > $i).
% 4.86/1.03 thf(decl_304, type, esk55_3: $i > $i > $i > $i).
% 4.86/1.03 thf(decl_305, type, esk56_3: $i > $i > $i > $i).
% 4.86/1.03 thf(decl_306, type, esk57_2: $i > $i > $i).
% 4.86/1.03 thf(decl_307, type, esk58_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_308, type, esk59_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_309, type, esk60_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_310, type, esk61_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_311, type, esk62_3: $i > ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_312, type, esk63_3: $i > ($i > $o) > $i > $i).
% 4.86/1.03 thf(decl_313, type, esk64_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_314, type, esk65_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_315, type, esk66_2: $i > ($i > $o) > $i).
% 4.86/1.03 thf(decl_316, type, esk67_1: $i > $i).
% 4.86/1.03 thf(decl_317, type, esk68_1: $i > $i).
% 4.86/1.03 thf(decl_318, type, esk69_3: $i > $i > $i > $i).
% 4.86/1.03 thf(decl_319, type, esk70_4: $i > $i > $i > $i > $i).
% 4.86/1.03 thf(decl_320, type, esk71_3: $i > $i > $i > $i).
% 4.86/1.03 thf(decl_321, type, esk72_0: $i).
% 4.86/1.03 thf(decl_322, type, esk73_0: $i).
% 4.86/1.03 thf(decl_323, type, esk74_0: $i).
% 4.86/1.03 thf(decl_324, type, esk75_1: $i > $i).
% 4.86/1.03 thf(decl_325, type, esk76_0: $i).
% 4.86/1.03 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', ex1)).
% 4.86/1.03 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', singleton)).
% 4.86/1.03 thf(func, axiom, ((func)=(^[X4:$i, X5:$i, X29:$i]:((((breln @ X4 @ X5 @ X29))&(![X2:$i]:((((in @ X2 @ X4))=>((ex1 @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', func)).
% 4.86/1.03 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', breln)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', kfstsingleton)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', exuE2)).
% 4.86/1.03 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', exu)).
% 4.86/1.03 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', nonempty)).
% 4.86/1.03 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', ksndsingleton)).
% 4.86/1.03 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setOfPairsIsBReln)).
% 4.86/1.03 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', funcImageSingleton)).
% 4.86/1.03 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', apProp)).
% 4.86/1.03 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', exu__Cong)).
% 4.86/1.03 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', exuE3u)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', exuI2)).
% 4.86/1.03 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', exuI3)).
% 4.86/1.03 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', exuI1)).
% 4.86/1.03 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', descr__Cong)).
% 4.86/1.03 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', exuEu)).
% 4.86/1.03 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', ex1E1)).
% 4.86/1.03 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', singletonprop)).
% 4.86/1.03 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.iYtLh2Sxg7/E---3.1_411641.p', ex1I)).
% 4.86/1.03 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', ex1I2)).
% 4.86/1.03 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', nonemptyI)).
% 4.86/1.03 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', exuE3e)).
% 4.86/1.03 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', exuE1)).
% 4.86/1.03 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', descrp)).
% 4.86/1.03 thf(replAx, axiom, ((replAx)<=>![X6:$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.iYtLh2Sxg7/E---3.1_411641.p', replAx)).
% 4.86/1.03 thf(app, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', app)).
% 4.86/1.03 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', theprop)).
% 4.86/1.03 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', nonemptyImpWitness)).
% 4.86/1.03 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', dpsetconstrI)).
% 4.86/1.03 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', dpsetconstrSub)).
% 4.86/1.03 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', dpsetconstrERa)).
% 4.86/1.03 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', dpsetconstrEL1)).
% 4.86/1.03 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.iYtLh2Sxg7/E---3.1_411641.p', emptyE1)).
% 4.86/1.03 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', dpsetconstrEL2)).
% 4.86/1.03 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', dpsetconstrER)).
% 4.86/1.03 thf(ap, axiom, ((ap)=(^[X4:$i, X5:$i, X30:$i, X2:$i]:(setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', ap)).
% 4.86/1.03 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', sepSubset)).
% 4.86/1.03 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', sepInPowerset)).
% 4.86/1.03 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', dsetconstr__Cong)).
% 4.86/1.03 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setoftrueEq)).
% 4.86/1.03 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', nonemptyI1)).
% 4.86/1.03 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', nonemptyE1)).
% 4.86/1.03 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setbeta)).
% 4.86/1.03 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', dsetconstrER)).
% 4.86/1.03 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', dsetconstrEL)).
% 4.86/1.03 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', dsetconstrI)).
% 4.86/1.03 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', kfstpairEq)).
% 4.86/1.03 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', cartprodfstin)).
% 4.86/1.03 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', subPowSU)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', setukpairinjL2)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', setunionE)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', setukpairinjL)).
% 4.86/1.03 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setukpairinjR11)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', setukpairinjR12)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', setukpairinjR1)).
% 4.86/1.03 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', upairequniteq)).
% 4.86/1.03 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setukpairinjR2)).
% 4.86/1.03 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setukpairinjR)).
% 4.86/1.03 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', ksndpairEq)).
% 4.86/1.03 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', kpairsurjEq)).
% 4.86/1.03 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', cartprodsndin)).
% 4.86/1.03 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', cartprodpairmemEL)).
% 4.86/1.03 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', cartprodpairmemER)).
% 4.86/1.03 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', cartprodmempaircEq)).
% 4.86/1.03 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', cartprodfstpairEq)).
% 4.86/1.03 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', upairsetIR)).
% 4.86/1.03 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', cartprodsndpairEq)).
% 4.86/1.03 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', upairsetIL)).
% 4.86/1.03 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', cartprodpairsurjEq)).
% 4.86/1.03 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', upairsetE)).
% 4.86/1.03 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', singletonsswitch)).
% 4.86/1.03 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', eqinunit)).
% 4.86/1.03 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', notinsingleton)).
% 4.86/1.03 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', uniqinunit)).
% 4.86/1.03 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', notdexE)).
% 4.86/1.03 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', prop2setI)).
% 4.86/1.03 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', quantDeMorgan4)).
% 4.86/1.03 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', quantDeMorgan3)).
% 4.86/1.03 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', quantDeMorgan2)).
% 4.86/1.03 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', quantDeMorgan1)).
% 4.86/1.03 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', vacuousDall)).
% 4.86/1.03 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', notdallE)).
% 4.86/1.03 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binunionIL)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', in__Cong)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', inCongP)).
% 4.86/1.03 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', emptyset__Cong)).
% 4.86/1.03 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', omega__Cong)).
% 4.86/1.03 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setunion__Cong)).
% 4.86/1.03 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', powerset__Cong)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', setadjoin__Cong)).
% 4.86/1.03 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', subsetI1)).
% 4.86/1.03 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', notsubsetI)).
% 4.86/1.03 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', subsetE2)).
% 4.86/1.03 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', subsetE)).
% 4.86/1.03 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', emptysetsubset)).
% 4.86/1.03 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', subsetI2)).
% 4.86/1.03 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', eqimpsubset1)).
% 4.86/1.03 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', eqimpsubset2)).
% 4.86/1.03 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', notequalI1)).
% 4.86/1.03 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setextsub)).
% 4.86/1.03 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', subset2powerset)).
% 4.86/1.03 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setadjoinSub2)).
% 4.86/1.03 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setadjoinSub)).
% 4.86/1.03 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', subsetTrans)).
% 4.86/1.03 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', subsetRefl)).
% 4.86/1.03 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', notequalI2)).
% 4.86/1.03 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', subsetemptysetimpeq)).
% 4.86/1.03 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', powersetsubset)).
% 4.86/1.03 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', inPowerset)).
% 4.86/1.03 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', powersetE1)).
% 4.86/1.03 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', powersetI1)).
% 4.86/1.03 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', upairset2IR)).
% 4.86/1.03 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binintersectSubset5)).
% 4.86/1.03 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binintersectI)).
% 4.86/1.03 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binunionRsub)).
% 4.86/1.03 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binunionLsub)).
% 4.86/1.03 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binunionE)).
% 4.86/1.03 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binunionEcases)).
% 4.86/1.03 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binunionIR)).
% 4.86/1.03 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binintersectEL)).
% 4.86/1.03 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binintersectSubset4)).
% 4.86/1.03 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binintersectRsub)).
% 4.86/1.03 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', disjointsetsI1)).
% 4.86/1.03 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binintersectER)).
% 4.86/1.03 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binintersectSubset3)).
% 4.86/1.03 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binintersectSubset2)).
% 4.86/1.03 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binintersectLsub)).
% 4.86/1.03 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', binintersectSubset1)).
% 4.86/1.03 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setminusELneg)).
% 4.86/1.03 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setminusERneg)).
% 4.86/1.03 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setminusSubset2)).
% 4.86/1.03 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setminusER)).
% 4.86/1.03 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setminusEL)).
% 4.86/1.03 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setminusI)).
% 4.86/1.03 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', bs114d)).
% 4.86/1.03 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setminusILneg)).
% 4.86/1.03 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', symdiffIneg1)).
% 4.86/1.03 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', symdiffI2)).
% 4.86/1.03 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', symdiffI1)).
% 4.86/1.03 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', symdiffE)).
% 4.86/1.03 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setminusSubset1)).
% 4.86/1.03 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setminusLsub)).
% 4.86/1.03 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setminusIRneg)).
% 4.86/1.03 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', symdiffIneg2)).
% 4.86/1.03 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', singletoninpowerset)).
% 4.86/1.03 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', singletonsubset)).
% 4.86/1.03 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', kpairp)).
% 4.86/1.03 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', kpairiskpair)).
% 4.86/1.03 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setukpairIR)).
% 4.86/1.03 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setukpairIL)).
% 4.86/1.03 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', secondinupair)).
% 4.86/1.03 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', singletoninpowunion)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', cartprodpairin)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', ubforcartprodlem3)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', ubforcartprodlem2)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', ubforcartprodlem1)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', upairinpowunion)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', upairsubunion)).
% 4.86/1.03 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', upairset2E)).
% 4.86/1.03 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.iYtLh2Sxg7/E---3.1_411641.p', cartprodmempair1)).
% 4.86/1.03 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setunionsingleton)).
% 4.86/1.03 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setunionsingleton2)).
% 4.86/1.03 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setunionsingleton1)).
% 4.86/1.03 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setunionE2)).
% 4.86/1.03 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', cartprodmempair)).
% 4.86/1.03 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', singletonsuniq)).
% 4.86/1.03 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.iYtLh2Sxg7/E---3.1_411641.p', setukpairinjL1)).
% 4.86/1.03 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setunionI)).
% 4.86/1.03 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', powersetE)).
% 4.86/1.03 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', emptyInPowerset)).
% 4.86/1.03 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', emptyinPowerset)).
% 4.86/1.03 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', powersetI)).
% 4.86/1.03 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setadjoinOr)).
% 4.86/1.03 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.iYtLh2Sxg7/E---3.1_411641.p', setadjoinE)).
% 4.86/1.03 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setadjoinIR)).
% 4.86/1.03 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', emptyinunitempty)).
% 4.86/1.03 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setadjoinIL)).
% 4.86/1.03 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', noeltsimpempty)).
% 4.86/1.03 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', emptyI)).
% 4.86/1.03 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setext)).
% 4.86/1.03 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', notinemptyset)).
% 4.86/1.03 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', emptysetimpfalse)).
% 4.86/1.03 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', emptysetE)).
% 4.86/1.03 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', prop2setE)).
% 4.86/1.03 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', wellorderingAx)).
% 4.86/1.03 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', foundationAx)).
% 4.86/1.03 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.iYtLh2Sxg7/E---3.1_411641.p', omegaIndAx)).
% 4.86/1.03 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', omegaSAx)).
% 4.86/1.03 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', omega0Ax)).
% 4.86/1.03 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setunionAx)).
% 4.86/1.03 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', powersetAx)).
% 4.86/1.03 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setadjoinAx)).
% 4.86/1.03 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', emptysetAx)).
% 4.86/1.03 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.iYtLh2Sxg7/E---3.1_411641.p', setextAx)).
% 4.86/1.03 thf(c_0_197, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X600:$i]:((((in @ X600 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X600 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 4.86/1.03 thf(c_0_198, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 4.86/1.03 thf(c_0_199, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X607:$i]:((((in @ X607 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X607 @ emptyset)))))))))))))), inference(fof_simplification,[status(thm)],[func])).
% 4.86/1.03 thf(c_0_200, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X600:$i]:((((in @ X600 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X600 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_197, c_0_198])).
% 4.86/1.03 thf(c_0_201, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 4.86/1.03 thf(c_0_202, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 4.86/1.03 thf(c_0_203, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 4.86/1.03 thf(c_0_204, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 4.86/1.03 thf(c_0_205, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 4.86/1.03 thf(c_0_206, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 4.86/1.03 thf(c_0_207, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 4.86/1.03 thf(c_0_208, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 4.86/1.03 thf(c_0_209, plain, ((func)=(^[Z0:$i, Z1:$i, Z2:$i]:(((((subset @ Z2 @ (cartprod @ Z0 @ Z1))))&(![X2:$i]:((((in @ X2 @ Z0))=>((?[X607:$i]:((((in @ X607 @ (dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))))&(((dsetconstr @ Z1 @ (^[Z3:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X607 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_199, c_0_200]), c_0_201])).
% 4.86/1.03 thf(c_0_210, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 4.86/1.03 thf(c_0_211, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 4.86/1.03 thf(c_0_212, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 4.86/1.03 thf(c_0_213, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 4.86/1.03 thf(c_0_214, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 4.86/1.03 thf(c_0_215, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 4.86/1.03 thf(c_0_216, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 4.86/1.03 thf(c_0_217, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 4.86/1.03 thf(c_0_218, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 4.86/1.03 thf(c_0_219, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 4.86/1.03 thf(c_0_220, plain, ((ex1I)<=>![X4:$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])).
% 4.86/1.03 thf(c_0_221, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 4.86/1.03 thf(c_0_222, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 4.86/1.03 thf(c_0_223, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 4.86/1.03 thf(c_0_224, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 4.86/1.03 thf(c_0_225, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 4.86/1.03 thf(c_0_226, plain, ((replAx)<=>![X6:$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])).
% 4.86/1.03 thf(c_0_227, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[app])).
% 4.86/1.03 thf(c_0_228, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X604:$i]:((((in @ X604 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X604 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_202, c_0_198])).
% 4.86/1.03 thf(c_0_229, axiom, ((theprop)=(![X21:$i]:((((?[X605:$i]:((((in @ X605 @ X21))&(((X21)=(setadjoin @ X605 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_198])).
% 4.86/1.03 thf(c_0_230, plain, ((exuE2)=(![X1:$i > $o]:((((?[X579:$i]:(((((X1 @ X579)))&(![X580:$i]:(((((X1 @ X580)))=>(((X579)=(X580))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_203, c_0_204])).
% 4.86/1.03 thf(c_0_231, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_205])).
% 4.86/1.03 thf(c_0_232, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X606:$i]:((((in @ X606 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X606 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_206, c_0_198])).
% 4.86/1.03 thf(c_0_233, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 4.86/1.03 thf(c_0_234, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 4.86/1.03 thf(c_0_235, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_207, c_0_201])).
% 4.86/1.03 thf(c_0_236, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 4.86/1.03 thf(c_0_237, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 4.86/1.03 thf(c_0_238, plain, ((emptyE1)<=>![X4:$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])).
% 4.86/1.03 thf(c_0_239, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 4.86/1.03 thf(c_0_240, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 4.86/1.03 thf(c_0_241, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X608:$i]:((((in @ X608 @ X4))=>((?[X609:$i]:((((in @ X609 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X608 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X608 @ Z0) @ X30)))))=(setadjoin @ X609 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X610:$i]:((((in @ X610 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))=(setadjoin @ X610 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_208, c_0_198]), c_0_209])).
% 4.86/1.03 thf(c_0_242, plain, ((apProp)=(![X4:$i, X5:$i, X30:$i]:((((((((subset @ X30 @ (cartprod @ X4 @ X5))))&(![X611:$i]:((((in @ X611 @ X4))=>((?[X612:$i]:((((in @ X612 @ (dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X611 @ Z0) @ X30)))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:(((in @ (kpair @ X611 @ Z0) @ X30)))))=(setadjoin @ X612 @ emptyset)))))))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>((in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5))))))))), inference(apply_def,[status(thm)],[c_0_210, c_0_209])).
% 4.86/1.03 thf(c_0_243, plain, ((ap)=(^[Z0:$i, Z1:$i, Z2:$i, Z3:$i]:(setunion @ (dsetconstr @ Z1 @ (^[Z4:$i]:((in @ (kpair @ Z3 @ Z4) @ Z2))))))), inference(fof_simplification,[status(thm)],[ap])).
% 4.86/1.03 thf(c_0_244, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 4.86/1.03 thf(c_0_245, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 4.86/1.03 thf(c_0_246, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X589:$i]:(((((X1 @ X589)))&(![X590:$i]:(((((X1 @ X590)))=>(((X589)=(X590))))))))))<=>((?[X591:$i]:(((((X17 @ X591)))&(![X592:$i]:(((((X17 @ X592)))=>(((X591)=(X592)))))))))))))))), inference(apply_def,[status(thm)],[c_0_211, c_0_204])).
% 4.86/1.03 thf(c_0_247, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X587:$i]:(((((X1 @ X587)))&(![X588:$i]:(((((X1 @ X588)))=>(((X587)=(X588))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_212, c_0_204])).
% 4.86/1.03 thf(c_0_248, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X585:$i]:(((((X1 @ X585)))&(![X586:$i]:(((((X1 @ X586)))=>(((X585)=(X586)))))))))))))), inference(apply_def,[status(thm)],[c_0_213, c_0_204])).
% 4.86/1.03 thf(c_0_249, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X583:$i]:(((((X1 @ X583)))&(![X584:$i]:(((((X1 @ X584)))=>(((X583)=(X584)))))))))))))))), inference(apply_def,[status(thm)],[c_0_214, c_0_204])).
% 4.86/1.03 thf(c_0_250, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X581:$i]:(((((X1 @ X581)))&(![X582:$i]:(((((X1 @ X582)))=>(((X581)=(X582)))))))))))))), inference(apply_def,[status(thm)],[c_0_215, c_0_204])).
% 4.86/1.03 thf(c_0_251, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 4.86/1.03 thf(c_0_252, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X595:$i]:(((((X1 @ X595)))&(![X596:$i]:(((((X1 @ X596)))=>(((X595)=(X596))))))))))=>((((?[X597:$i]:(((((X17 @ X597)))&(![X598:$i]:(((((X17 @ X598)))=>(((X597)=(X598))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_216, c_0_204])).
% 4.86/1.03 thf(c_0_253, plain, ((exuEu)=(![X1:$i > $o]:((((?[X593:$i]:(((((X1 @ X593)))&(![X594:$i]:(((((X1 @ X594)))=>(((X593)=(X594))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_217, c_0_204])).
% 4.86/1.03 thf(c_0_254, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X601:$i]:((((in @ X601 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X601 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_218, c_0_200])).
% 4.86/1.03 thf(c_0_255, plain, ((singletonprop)=(![X4:$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)))))=>((?[X599:$i]:((((in @ X599 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X599 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_219, c_0_198])).
% 4.86/1.03 thf(c_0_256, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X602:$i]:((((in @ X602 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X602 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_220, c_0_200])).
% 4.86/1.03 thf(c_0_257, 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)))))=>((?[X603:$i]:((((in @ X603 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X603 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_221, c_0_200])).
% 4.86/1.03 thf(c_0_258, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 4.86/1.03 thf(c_0_259, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_205])).
% 4.86/1.03 thf(c_0_260, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_222, c_0_205])).
% 4.86/1.03 thf(c_0_261, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_205])).
% 4.86/1.03 thf(c_0_262, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 4.86/1.03 thf(c_0_263, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X577:$i]:(((((X1 @ X577)))&(![X578:$i]:(((((X1 @ X578)))=>(((X577)=(X578))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_223, c_0_204])).
% 4.86/1.03 thf(c_0_264, plain, ((exuE1)=(![X1:$i > $o]:((((?[X575:$i]:(((((X1 @ X575)))&(![X576:$i]:(((((X1 @ X576)))=>(((X575)=(X576))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_224, c_0_204])).
% 4.86/1.03 thf(c_0_265, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 4.86/1.03 thf(c_0_266, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 4.86/1.03 thf(c_0_267, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 4.86/1.03 thf(c_0_268, plain, ((descrp)=(![X1:$i > $o]:((((?[X573:$i]:(((((X1 @ X573)))&(![X574:$i]:(((((X1 @ X574)))=>(((X573)=(X574))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_225, c_0_204])).
% 4.86/1.03 thf(c_0_269, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X571:$i]:(((((X6 @ X2 @ X571)))&(![X572:$i]:(((((X6 @ X2 @ X572)))=>(((X571)=(X572)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_204])).
% 4.86/1.03 thf(c_0_270, plain, ((epred1_0)<=>![X642:$i]:(?[X643:$i]:((((![X644:$i]:(((in @ X644 @ X643)=>![X645:$i]:(((in @ X645 @ X644)=>(in @ X645 @ X642)))))&![X646:$i, X647:$i]:((((in @ X646 @ X642)&(in @ X647 @ X642))=>(![X648:$i]:(((in @ X648 @ X643)=>((in @ X646 @ X648)<=>(in @ X647 @ X648))))=>((X646)=(X647))))))&![X649:$i, X650:$i]:((((in @ X649 @ X643)&(in @ X650 @ X643))=>(![X651:$i]:(((in @ X651 @ X649)=>(in @ X651 @ X650)))|![X652:$i]:(((in @ X652 @ X650)=>(in @ X652 @ X649)))))))&![X653:$i]:(((![X654:$i]:(((in @ X654 @ X653)=>(in @ X654 @ X642)))&?[X655:$i]:((in @ X655 @ X653)))=>?[X656:$i, X657:$i]:(((((in @ X656 @ X643)&(in @ X657 @ X653))&~(?[X658:$i]:(((in @ X658 @ X656)&(in @ X658 @ X653)))))&![X659:$i]:(((in @ X659 @ X643)=>(![X660:$i]:(((in @ X660 @ X659)=>(in @ X660 @ X656)))|(in @ X657 @ X659)))))))))))), introduced(definition)).
% 4.86/1.03 thf(c_0_271, negated_conjecture, ~((![X613:$i, X614:$i]:((![X615:$i]:(((in @ X615 @ X613)<=>(in @ X615 @ X614)))=>((X613)=(X614))))=>(![X616:$i]:(~(in @ X616 @ emptyset))=>(![X617:$i, X618:$i, X619:$i]:(((in @ X619 @ (setadjoin @ X617 @ X618))<=>(((X619)=(X617))|(in @ X619 @ X618))))=>(![X620:$i, X621:$i]:(((in @ X621 @ (powerset @ X620))<=>![X622:$i]:(((in @ X622 @ X621)=>(in @ X622 @ X620)))))=>(![X623:$i, X624:$i]:(((in @ X624 @ (setunion @ X623))<=>?[X625:$i]:(((in @ X624 @ X625)&(in @ X625 @ X623)))))=>((in @ emptyset @ omega)=>(![X626:$i]:(((in @ X626 @ omega)=>(in @ (setadjoin @ X626 @ X626) @ omega)))=>(![X627:$i]:((((in @ emptyset @ X627)&![X628:$i]:((((in @ X628 @ omega)&(in @ X628 @ X627))=>(in @ (setadjoin @ X628 @ X628) @ X627))))=>![X629:$i]:(((in @ X629 @ omega)=>(in @ X629 @ X627)))))=>(![X630:$i > $i > $o, X631:$i]:((![X632:$i]:(((in @ X632 @ X631)=>?[X633:$i]:(((X630 @ X632 @ X633)&![X634:$i]:(((X630 @ X632 @ X634)=>((X633)=(X634))))))))=>?[X635:$i]:(![X636:$i]:(((in @ X636 @ X635)<=>?[X637:$i]:(((in @ X637 @ X631)&(X630 @ X637 @ X636))))))))=>(![X638:$i]:((?[X639:$i]:((in @ X639 @ X638))=>?[X640:$i]:(((in @ X640 @ X638)&~(?[X641:$i]:(((in @ X641 @ X640)&(in @ X641 @ X638))))))))=>((epred1_0)=>(![X661:$i > $o]:((?[X662:$i]:(((X661 @ X662)&![X663:$i]:(((X661 @ X663)=>((X662)=(X663))))))=>(X661 @ (descr @ (^[Z0:$i]:(X661 @ Z0))))))=>(![X664:$i, X665:$i > $o, X666:$i]:(((in @ X666 @ X664)=>((X665 @ X666)=>(in @ X666 @ (dsetconstr @ X664 @ X665)))))=>(![X667:$i, X668:$i > $o, X669:$i]:(((in @ X669 @ (dsetconstr @ X667 @ X668))=>(in @ X669 @ X667)))=>(![X670:$i, X671:$i > $o, X672:$i]:(((in @ X672 @ (dsetconstr @ X670 @ X671))=>(X671 @ X672)))=>(![X673:$i > $o]:((?[X674:$i]:(((X673 @ X674)&![X675:$i]:(((X673 @ X675)=>((X674)=(X675))))))=>?[X676:$i]:(((X673 @ X676)&![X677:$i]:(((X673 @ X677)=>((X676)=(X677))))))))=>(![X678:$o, X679:$i]:(((in @ X679 @ (prop2set @ ((X678))))=>(X678)))=>(![X680:$i]:(((in @ X680 @ emptyset)=>![X681:$o]:((X681))))=>(![X682:$i]:(((in @ X682 @ emptyset)=>~($true)))=>(![X683:$i]:(~(in @ X683 @ emptyset))=>(![X684:$i > $o]:((?[X685:$i]:(((X684 @ X685)&![X686:$i]:(((X684 @ X686)=>((X685)=(X686))))))=>?[X687:$i]:((X684 @ X687))))=>(![X688:$i, X689:$i]:((![X690:$i]:(((in @ X690 @ X688)=>(in @ X690 @ X689)))=>(![X691:$i]:(((in @ X691 @ X689)=>(in @ X691 @ X688)))=>((X688)=(X689)))))=>(![X692:$i]:((![X693:$i]:(~(in @ X693 @ X692))=>((X692)=(emptyset))))=>(![X694:$i]:((![X695:$i]:(~(in @ X695 @ X694))=>((X694)=(emptyset))))=>(![X696:$i, X697:$i > $o, X698:$i]:(((in @ X698 @ X696)=>((in @ X698 @ (dsetconstr @ X696 @ X697))<=>(X697 @ X698))))=>(![X699:$i]:((((X699)!=(emptyset))=>?[X700:$i]:((in @ X700 @ X699))))=>(![X701:$i, X702:$i > $o, X703:$i]:(((in @ X703 @ X701)=>((X702 @ X703)=>((dsetconstr @ X701 @ X702)!=(emptyset)))))=>(![X704:$i]:((?[X705:$i]:((in @ X705 @ X704))=>((X704)!=(emptyset))))=>(![X706:$i, X707:$i]:((in @ X706 @ (setadjoin @ X706 @ X707)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X708:$i, X709:$i, X710:$i]:(((in @ X710 @ X709)=>(in @ X710 @ (setadjoin @ X708 @ X709))))=>(![X711:$i, X712:$i, X713:$i]:(((in @ X713 @ (setadjoin @ X711 @ X712))=>![X714:$o]:(((((X713)=(X711))=>(X714))=>(((in @ X713 @ X712)=>(X714))=>(X714))))))=>(![X715:$i, X716:$i, X717:$i]:(((in @ X717 @ (setadjoin @ X715 @ X716))=>(((X717)=(X715))|(in @ X717 @ X716))))=>(![X718:$i]:(((dsetconstr @ X718 @ (^[Z0:$i]:($true)))=(X718)))=>(![X719:$i, X720:$i]:((![X721:$i]:(((in @ X721 @ X720)=>(in @ X721 @ X719)))=>(in @ X720 @ (powerset @ X719))))=>(![X722:$i]:((in @ emptyset @ (powerset @ X722)))=>(![X723:$i]:((in @ emptyset @ (powerset @ X723)))=>(![X724:$i, X725:$i, X726:$i]:(((in @ X725 @ (powerset @ X724))=>((in @ X726 @ X725)=>(in @ X726 @ X724))))=>(![X727:$i, X728:$i, X729:$i]:(((in @ X728 @ X729)=>((in @ X729 @ X727)=>(in @ X728 @ (setunion @ X727)))))=>(![X730:$i, X731:$i]:(((in @ X731 @ (setunion @ X730))=>![X732:$o]:((![X733:$i]:(((in @ X731 @ X733)=>((in @ X733 @ X730)=>(X732))))=>(X732)))))=>(![X734:$i, X735:$i]:(((in @ X735 @ X734)=>(in @ X735 @ (powerset @ (setunion @ X734)))))=>(![X736:$i > $o]:((?[X737:$i]:(((X736 @ X737)&![X738:$i]:(((X736 @ X738)=>((X737)=(X738))))))=>?[X739:$i]:(![X740:$i]:(((X736 @ X740)<=>((X740)=(X739)))))))=>(![X741:$i]:((((X741)!=(emptyset))=>?[X742:$i]:(((in @ X742 @ X741)&$true))))=>(![X743:$i, X744:$i]:(((in @ X743 @ (setadjoin @ X744 @ emptyset))=>((X743)=(X744))))=>(![X745:$i, X746:$i]:((((X745)!=(X746))=>~(in @ X746 @ (setadjoin @ X745 @ emptyset))))=>(![X747:$i, X748:$i]:((((X747)=(X748))=>(in @ X747 @ (setadjoin @ X748 @ emptyset))))=>(![X749:$i, X750:$i]:(((in @ X749 @ (setadjoin @ X750 @ emptyset))=>(in @ X750 @ (setadjoin @ X749 @ emptyset))))=>(![X751:$i, X752:$i, X753:$i]:(((in @ X753 @ (setadjoin @ X751 @ (setadjoin @ X752 @ emptyset)))=>(((X753)=(X751))|((X753)=(X752)))))=>(![X754:$i, X755:$i]:((in @ X754 @ (setadjoin @ X754 @ (setadjoin @ X755 @ emptyset))))=>(![X756:$i, X757:$i]:((in @ X757 @ (setadjoin @ X756 @ (setadjoin @ X757 @ emptyset))))=>(![X758:$i, X759:$i > $o]:((?[X760:$i]:(((in @ X760 @ X758)&(X759 @ X760)))=>(((dsetconstr @ X758 @ X759)=(emptyset))=>~($true))))=>(![X761:$i > $o, X762:$i]:(((in @ X762 @ emptyset)=>(X761 @ X762)))=>(![X763:$i, X764:$i > $o]:((~(![X765:$i]:(((in @ X765 @ X763)=>(X764 @ X765))))=>?[X766:$i]:(((in @ X766 @ X763)&~((X764 @ X766))))))=>(![X767:$i, X768:$i > $o]:((![X769:$i]:(((in @ X769 @ X767)=>~((X768 @ X769))))=>~(?[X770:$i]:(((in @ X770 @ X767)&(X768 @ X770))))))=>(![X771:$i, X772:$i > $o]:((~(?[X773:$i]:(((in @ X773 @ X771)&(X772 @ X773))))=>![X774:$i]:(((in @ X774 @ X771)=>~((X772 @ X774))))))=>(![X775:$i, X776:$i > $o]:((?[X777:$i]:(((in @ X777 @ X775)&~((X776 @ X777))))=>~(![X778:$i]:(((in @ X778 @ X775)=>(X776 @ X778))))))=>(![X779:$o]:(((X779)=>(in @ emptyset @ (prop2set @ ((X779))))))=>((prop2set2propI)=>(![X780:$i, X781:$i > $o]:((~(?[X782:$i]:(((in @ X782 @ X780)&(X781 @ X782))))=>![X783:$i]:(((in @ X783 @ X780)=>~((X781 @ X783))))))=>(![X784:$i, X785:$i > $o]:((~(![X786:$i]:(((in @ X786 @ X784)=>(X785 @ X786))))=>?[X787:$i]:(((in @ X787 @ X784)&~((X785 @ X787))))))=>(![X788:$i > $o]:((?[X789:$i]:(((X788 @ X789)&![X790:$i]:(((X788 @ X790)=>((X789)=(X790))))))=>?[X791:$i]:(((X788 @ X791)&![X792:$i]:(((X788 @ X792)=>((X791)=(X792))))))))=>(![X793:$i > $o]:((?[X794:$i]:((X793 @ X794))=>(![X795:$i, X796:$i]:(((X793 @ X795)=>((X793 @ X796)=>((X795)=(X796)))))=>?[X797:$i]:(((X793 @ X797)&![X798:$i]:(((X793 @ X798)=>((X797)=(X798)))))))))=>(![X799:$i > $o]:((?[X800:$i]:(![X801:$i]:(((X799 @ X801)<=>((X801)=(X800)))))=>?[X802:$i]:(((X799 @ X802)&![X803:$i]:(((X799 @ X803)=>((X802)=(X803))))))))=>(![X804:$i, X805:$i]:((((X804)=(X805))=>![X806:$i, X807:$i]:((((X806)=(X807))=>((in @ X806 @ X804)=>(in @ X807 @ X805))))))=>(![X808:$i, X809:$i]:((((X808)=(X809))=>![X810:$i, X811:$i]:((((X810)=(X811))=>((in @ X810 @ X808)<=>(in @ X811 @ X809))))))=>(![X812:$i > $o]:((?[X813:$i]:(((X812 @ X813)&![X814:$i]:(((X812 @ X814)=>((X813)=(X814))))))=>![X815:$i, X816:$i]:(((X812 @ X815)=>((X812 @ X816)=>((X815)=(X816)))))))=>(![X817:$i > $o, X818:$i > $o]:((![X819:$i, X820:$i]:((((X819)=(X820))=>((X817 @ X819)<=>(X818 @ X820))))=>(?[X821:$i]:(((X817 @ X821)&![X822:$i]:(((X817 @ X822)=>((X821)=(X822))))))<=>?[X823:$i]:(((X818 @ X823)&![X824:$i]:(((X818 @ X824)=>((X823)=(X824)))))))))=>(((emptyset)=(emptyset))=>(![X825:$i, X826:$i]:((((X825)=(X826))=>![X827:$i, X828:$i]:((((X827)=(X828))=>((setadjoin @ X825 @ X827)=(setadjoin @ X826 @ X828))))))=>(![X829:$i, X830:$i]:((((X829)=(X830))=>((powerset @ X829)=(powerset @ X830))))=>(![X831:$i, X832:$i]:((((X831)=(X832))=>((setunion @ X831)=(setunion @ X832))))=>(((omega)=(omega))=>(![X833:$i > $o]:((?[X834:$i]:(((X833 @ X834)&![X835:$i]:(((X833 @ X835)=>((X834)=(X835))))))=>![X836:$i, X837:$i]:(((X833 @ X836)=>((X833 @ X837)=>((X836)=(X837)))))))=>(![X838:$i > $o, X839:$i > 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_227, c_0_228]), c_0_229]), kfstpairEq]), c_0_230]), cartprodfstin]), subPowSU]), setukpairinjL2]), setunionE]), setukpairinjL]), c_0_231]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_232]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), upairsetIR]), cartprodsndpairEq]), upairsetIL]), cartprodpairsurjEq]), upairsetE]), c_0_233]), singletonsswitch]), c_0_234]), eqinunit]), c_0_235]), notinsingleton]), c_0_236]), uniqinunit]), c_0_237]), c_0_238]), c_0_239]), c_0_240]), c_0_241]), c_0_242]), c_0_243]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), notdallE]), binunionIL]), c_0_244]), c_0_245]), c_0_246]), c_0_247]), in__Cong]), inCongP]), c_0_248]), c_0_249]), c_0_250]), emptyset__Cong]), c_0_251]), c_0_252]), c_0_253]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), subsetI1]), notsubsetI]), subsetE2]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), notequalI1]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), subsetemptysetimpeq]), 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]), setminusILneg]), symdiffIneg1]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), symdiffIneg2]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), singletoninpowunion]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), upairset2E]), cartprodmempair1]), c_0_254]), c_0_255]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair]), c_0_256]), c_0_257]), singletonsuniq]), setukpairinjL1]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_258]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), noeltsimpempty]), emptyI]), setext]), c_0_263]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_264]), c_0_265]), c_0_266]), c_0_267]), c_0_268]), wellorderingAx]), foundationAx]), c_0_269]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx]), c_0_209])])]), c_0_270])).
% 4.86/1.03 thf(c_0_272, negated_conjecture, ![X1191:$i, X1192:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1204:$i, X1205:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1213:$i, X1214:$i > $i > $o, X1215:$i, X1217:$i, X1220:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1227:$i, X1228:$i > $o, X1229:$i, X1231:$i, X1232:$i > $o, X1233:$i, X1234:$i, X1235:$i > $o, X1236:$i, X1237:$i, X1238:$i > $o, X1239:$i, X1240:$i > $o, X1241:$i, X1244:$i, X1245:$o, X1246:$i, X1247:$i, X1248:$o, X1249:$i, X1250:$i, X1251:$i > $o, X1252:$i, X1255:$i, X1256:$i, X1259:$i, X1261:$i, X1263:$i, X1264:$i > $o, X1265:$i, X1266:$i, X1268:$i, X1269:$i > $o, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$o, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$o, X1301:$i, X1302:$i, X1303:$i > $o, X1304:$i, X1307:$i, X1308:$i, X1309:$i, X1311:$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:$i, X1327:$i > $o, X1328:$i, X1329:$i > $o, X1330:$i, X1331:$i, X1332:$i > $o, X1333:$i, X1335:$i, X1336:$i > $o, X1338:$i, X1339:$i, X1340:$i > $o, X1342:$i, X1343:$i, X1344:$i > $o, X1345:$i, X1347:$o, X1348:$i, X1349:$i > $o, X1351:$i, X1352:$i, X1353:$i > $o, X1354:$i, X1356:$i > $o, X1357:$i, X1360:$i, X1361:$i > $o, X1362:$i, X1366:$i, X1367:$i > $o, X1368:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i > $o, X1381:$i, X1383:$i, X1384:$i, X1385:$i > $o, X1386:$i > $o, X1389:$i, X1392:$i, X1393:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i > $o, X1406:$i, X1408:$i, X1409:$i, X1410:$i > $o, X1411:$i > $o, X1414:$i, X1416:$i, X1418:$i, X1419:$i, X1420:$i > $o, X1421:$i > $o, X1424:$i, X1425:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i > $o, X1472:$i, X1473:$i > $o, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$o, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$o, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i > $o, X1628:$i, X1630:$i, X1631:$i > $o, X1632:$i, X1634:$i, X1635:$i > $o, X1636:$i, X1639:$i, X1640:$i > $o, X1643:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i > $i > $o, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i > $i > $o, X1725:$i, X1726:$i, X1727:$i > $i > $o, X1728:$i, X1729:$i, X1730:$i > $i > $o, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i > $i > $o, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i > $i > $o, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i > $i > $o, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1752:$i, X1753:$i, X1755:$i, X1756:$i, X1757:$i, X1759:$i, X1760:$i, X1764:$i]:((((~(in @ (esk1_2 @ X1191 @ X1192) @ X1191)|~(in @ (esk1_2 @ X1191 @ X1192) @ X1192)|((X1191)=(X1192)))&((in @ (esk1_2 @ X1191 @ X1192) @ X1191)|(in @ (esk1_2 @ X1191 @ X1192) @ X1192)|((X1191)=(X1192))))&(~(in @ X1194 @ emptyset)&(((~(in @ X1197 @ (setadjoin @ X1195 @ X1196))|(((X1197)=(X1195))|(in @ X1197 @ X1196)))&((((X1197)!=(X1195))|(in @ X1197 @ (setadjoin @ X1195 @ X1196)))&(~(in @ X1197 @ X1196)|(in @ X1197 @ (setadjoin @ X1195 @ X1196)))))&(((~(in @ X1199 @ (powerset @ X1198))|(~(in @ X1200 @ X1199)|(in @ X1200 @ X1198)))&(((in @ (esk2_2 @ X1201 @ X1202) @ X1202)|(in @ X1202 @ (powerset @ X1201)))&(~(in @ (esk2_2 @ X1201 @ X1202) @ X1201)|(in @ X1202 @ (powerset @ X1201)))))&(((((in @ X1205 @ (esk3_2 @ X1204 @ X1205))|~(in @ X1205 @ (setunion @ X1204)))&((in @ (esk3_2 @ X1204 @ X1205) @ X1204)|~(in @ X1205 @ (setunion @ X1204))))&(~(in @ X1208 @ X1209)|~(in @ X1209 @ X1207)|(in @ X1208 @ (setunion @ X1207))))&((in @ emptyset @ omega)&((~(in @ X1210 @ omega)|(in @ (setadjoin @ X1210 @ X1210) @ omega))&(((((in @ (esk4_1 @ X1211) @ omega)|~(in @ emptyset @ X1211)|(~(in @ X1213 @ omega)|(in @ X1213 @ X1211)))&((in @ (esk4_1 @ X1211) @ X1211)|~(in @ emptyset @ X1211)|(~(in @ X1213 @ omega)|(in @ X1213 @ X1211))))&(~(in @ (setadjoin @ (esk4_1 @ X1211) @ (esk4_1 @ X1211)) @ X1211)|~(in @ emptyset @ X1211)|(~(in @ X1213 @ omega)|(in @ X1213 @ X1211))))&((((((in @ (esk8_3 @ X1214 @ X1215 @ X1220) @ X1215)|~(in @ X1220 @ (esk7_2 @ X1214 @ X1215))|(in @ (esk5_2 @ X1214 @ X1215) @ X1215))&((X1214 @ (esk8_3 @ X1214 @ X1215 @ X1220) @ X1220)|~(in @ X1220 @ (esk7_2 @ X1214 @ X1215))|(in @ (esk5_2 @ X1214 @ X1215) @ X1215)))&(~(in @ X1223 @ X1215)|~(X1214 @ 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(esk57_2 @ X1618 @ X1619))|~(in @ X1619 @ (setunion @ X1618))))&((subset @ (setunion @ (setadjoin @ X1621 @ emptyset)) @ X1621)&((subset @ X1622 @ (setunion @ (setadjoin @ X1622 @ emptyset)))&(((setunion @ (setadjoin @ X1623 @ emptyset))=(X1623))&(((((in @ (esk60_2 @ X1624 @ X1625) @ (dsetconstr @ X1624 @ X1625))|(~(in @ X1628 @ X1624)|~(X1625 @ X1628))|(in @ (esk58_2 @ X1624 @ X1625) @ X1624))&(((dsetconstr @ X1624 @ X1625)=(setadjoin @ (esk60_2 @ X1624 @ X1625) @ emptyset))|(~(in @ X1628 @ X1624)|~(X1625 @ X1628))|(in @ (esk58_2 @ X1624 @ X1625) @ X1624)))&((((in @ (esk60_2 @ X1624 @ X1625) @ (dsetconstr @ X1624 @ X1625))|(~(in @ X1628 @ X1624)|~(X1625 @ X1628))|(in @ (esk59_2 @ X1624 @ X1625) @ X1624))&(((dsetconstr @ X1624 @ X1625)=(setadjoin @ (esk60_2 @ X1624 @ X1625) @ emptyset))|(~(in @ X1628 @ X1624)|~(X1625 @ X1628))|(in @ (esk59_2 @ X1624 @ X1625) @ X1624)))&((((in @ (esk60_2 @ X1624 @ X1625) @ (dsetconstr @ X1624 @ X1625))|(~(in @ X1628 @ X1624)|~(X1625 @ X1628))|(X1625 @ 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emptyset))))&((X1631 @ (esk61_2 @ X1630 @ X1631))|(~(in @ X1632 @ (dsetconstr @ X1630 @ X1631))|((dsetconstr @ X1630 @ X1631)!=(setadjoin @ X1632 @ emptyset)))))&(((((in @ (esk63_3 @ X1634 @ X1635 @ X1636) @ (dsetconstr @ X1634 @ X1635))|(in @ (esk62_3 @ X1634 @ X1635 @ X1636) @ X1634)|~(X1635 @ X1636)|~(in @ X1636 @ X1634))&(((dsetconstr @ X1634 @ X1635)=(setadjoin @ (esk63_3 @ X1634 @ X1635 @ X1636) @ emptyset))|(in @ (esk62_3 @ X1634 @ X1635 @ X1636) @ X1634)|~(X1635 @ X1636)|~(in @ X1636 @ X1634)))&((((in @ (esk63_3 @ X1634 @ X1635 @ X1636) @ (dsetconstr @ X1634 @ X1635))|(X1635 @ (esk62_3 @ X1634 @ X1635 @ X1636))|~(X1635 @ X1636)|~(in @ X1636 @ X1634))&(((dsetconstr @ X1634 @ X1635)=(setadjoin @ (esk63_3 @ X1634 @ X1635 @ X1636) @ emptyset))|(X1635 @ (esk62_3 @ X1634 @ X1635 @ X1636))|~(X1635 @ X1636)|~(in @ X1636 @ X1634)))&(((in @ (esk63_3 @ X1634 @ X1635 @ X1636) @ (dsetconstr @ X1634 @ X1635))|((esk62_3 @ X1634 @ X1635 @ X1636)!=(X1636))|~(X1635 @ X1636)|~(in @ X1636 @ X1634))&(((dsetconstr @ X1634 @ X1635)=(setadjoin @ (esk63_3 @ X1634 @ X1635 @ X1636) @ emptyset))|((esk62_3 @ X1634 @ X1635 @ X1636)!=(X1636))|~(X1635 @ X1636)|~(in @ X1636 @ X1634)))))&(((((in @ (esk66_2 @ X1639 @ X1640) @ (dsetconstr @ X1639 @ X1640))|(~(in @ X1643 @ X1639)|~(X1640 @ X1643))|(in @ (esk64_2 @ X1639 @ X1640) @ X1639))&(((dsetconstr @ X1639 @ X1640)=(setadjoin @ (esk66_2 @ X1639 @ X1640) @ emptyset))|(~(in @ X1643 @ X1639)|~(X1640 @ X1643))|(in @ (esk64_2 @ X1639 @ X1640) @ X1639)))&((((in @ (esk66_2 @ X1639 @ X1640) @ (dsetconstr @ X1639 @ X1640))|(~(in @ X1643 @ X1639)|~(X1640 @ X1643))|(in @ (esk65_2 @ X1639 @ X1640) @ X1639))&(((dsetconstr @ X1639 @ X1640)=(setadjoin @ (esk66_2 @ X1639 @ X1640) @ emptyset))|(~(in @ X1643 @ X1639)|~(X1640 @ X1643))|(in @ (esk65_2 @ X1639 @ X1640) @ X1639)))&((((in @ (esk66_2 @ X1639 @ X1640) @ (dsetconstr @ X1639 @ X1640))|(~(in @ X1643 @ X1639)|~(X1640 @ X1643))|(X1640 @ (esk64_2 @ X1639 @ X1640)))&(((dsetconstr @ X1639 @ X1640)=(setadjoin @ (esk66_2 @ X1639 @ X1640) @ emptyset))|(~(in @ X1643 @ X1639)|~(X1640 @ X1643))|(X1640 @ (esk64_2 @ X1639 @ X1640))))&((((in @ (esk66_2 @ X1639 @ X1640) @ (dsetconstr @ X1639 @ X1640))|(~(in @ X1643 @ X1639)|~(X1640 @ X1643))|(X1640 @ (esk65_2 @ X1639 @ X1640)))&(((dsetconstr @ X1639 @ X1640)=(setadjoin @ (esk66_2 @ X1639 @ X1640) @ emptyset))|(~(in @ X1643 @ X1639)|~(X1640 @ X1643))|(X1640 @ (esk65_2 @ X1639 @ X1640))))&(((in @ (esk66_2 @ X1639 @ X1640) @ (dsetconstr @ X1639 @ X1640))|(~(in @ X1643 @ X1639)|~(X1640 @ X1643))|((esk64_2 @ X1639 @ X1640)!=(esk65_2 @ X1639 @ X1640)))&(((dsetconstr @ X1639 @ X1640)=(setadjoin @ (esk66_2 @ X1639 @ X1640) @ emptyset))|(~(in @ X1643 @ X1639)|~(X1640 @ X1643))|((esk64_2 @ X1639 @ X1640)!=(esk65_2 @ X1639 @ X1640))))))))&((((setadjoin @ X1645 @ emptyset)!=(setadjoin @ X1646 @ emptyset))|((X1645)=(X1646)))&((~(in @ (setadjoin @ X1649 @ emptyset) @ (setadjoin @ (setadjoin @ X1647 @ emptyset) @ (setadjoin @ (setadjoin @ X1647 @ (setadjoin @ X1648 @ emptyset)) @ emptyset)))|((X1647)=(X1649)))&((((in @ (esk67_1 @ X1650) @ (dsetconstr @ (setunion @ X1650) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1650)))))|~(iskpair @ X1650))&(((dsetconstr @ (setunion @ X1650) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1650))))=(setadjoin @ (esk67_1 @ X1650) @ emptyset))|~(iskpair @ X1650)))&((~(in @ X1653 @ X1652)|((X1652)!=(setadjoin @ X1653 @ emptyset))|(in @ (setunion @ X1652) @ X1652))&(((kfst @ (kpair @ X1654 @ X1655))=(X1654))&((~(in @ X1658 @ (cartprod @ X1656 @ X1657))|(in @ (kfst @ X1658) @ X1656))&((((setadjoin @ (setadjoin @ X1659 @ emptyset) @ (setadjoin @ (setadjoin @ X1659 @ (setadjoin @ X1660 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1661 @ emptyset) @ (setadjoin @ (setadjoin @ X1661 @ (setadjoin @ X1662 @ emptyset)) @ emptyset)))|((X1659)=(X1661)))&((((kpair @ X1663 @ X1664)!=(kpair @ X1665 @ X1666))|((X1663)=(X1665)))&((((X1667)!=(X1668))|((setadjoin @ X1667 @ (setadjoin @ X1668 @ emptyset))=(setadjoin @ X1667 @ emptyset)))&((((X1669)!=(X1670))|((setadjoin @ (setadjoin @ X1669 @ emptyset) @ (setadjoin @ (setadjoin @ X1669 @ (setadjoin @ X1670 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1669 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1671 @ emptyset) @ (setadjoin @ (setadjoin @ X1671 @ (setadjoin @ X1672 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1673 @ emptyset) @ (setadjoin @ (setadjoin @ X1673 @ (setadjoin @ X1674 @ emptyset)) @ emptyset)))|(((X1673)!=(X1674))|((X1672)=(X1674))))&((((setadjoin @ X1675 @ (setadjoin @ X1676 @ emptyset))!=(setadjoin @ X1677 @ emptyset))|((X1675)=(X1676)))&((((setadjoin @ (setadjoin @ X1678 @ emptyset) @ (setadjoin @ (setadjoin @ X1678 @ (setadjoin @ X1679 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1680 @ emptyset) @ (setadjoin @ (setadjoin @ X1680 @ (setadjoin @ X1681 @ emptyset)) @ emptyset)))|((X1679)=(X1681)))&((((kpair @ X1682 @ X1683)!=(kpair @ X1684 @ X1685))|((X1683)=(X1685)))&((((in @ (esk68_1 @ X1686) @ (dsetconstr @ (setunion @ X1686) @ (^[Z0:$i]:(((X1686)=(kpair @ (kfst @ X1686) @ Z0))))))|~(iskpair @ X1686))&(((dsetconstr @ (setunion @ X1686) @ (^[Z0:$i]:(((X1686)=(kpair @ (kfst @ X1686) @ Z0)))))=(setadjoin @ (esk68_1 @ X1686) @ emptyset))|~(iskpair @ X1686)))&(((ksnd @ (kpair @ X1688 @ X1689))=(X1689))&((~(iskpair @ X1690)|((kpair @ (kfst @ X1690) @ (ksnd @ X1690))=(X1690)))&((~(in @ X1693 @ (cartprod @ X1691 @ X1692))|(in @ (ksnd @ X1693) @ X1692))&((~(in @ (kpair @ X1696 @ X1697) @ (cartprod @ X1694 @ X1695))|(in @ X1696 @ X1694))&((~(in @ (kpair @ X1700 @ X1701) @ (cartprod @ X1698 @ X1699))|(in @ X1701 @ X1699))&((~(in @ X1704 @ X1702)|(~(in @ X1705 @ X1703)|((kpair @ X1704 @ X1705)=(kpair @ X1704 @ X1705))))&((~(in @ X1708 @ X1706)|(~(in @ X1709 @ X1707)|((kfst @ (kpair @ X1708 @ X1709))=(X1708))))&((~(in @ X1712 @ X1710)|(~(in @ X1713 @ X1711)|((ksnd @ (kpair @ X1712 @ X1713))=(X1713))))&((~(in @ X1716 @ (cartprod @ X1714 @ X1715))|((kpair @ (kfst @ X1716) @ (ksnd @ X1716))=(X1716)))&((~(in @ X1720 @ X1717)|(~(in @ X1721 @ X1718)|(~(X1719 @ X1720 @ X1721)|(in @ (kpair @ X1720 @ X1721) @ (dpsetconstr @ X1717 @ X1718 @ X1719)))))&((subset @ (dpsetconstr @ X1722 @ X1723 @ X1724) @ (cartprod @ X1722 @ X1723))&((subset @ (dpsetconstr @ X1725 @ X1726 @ X1727) @ (cartprod @ X1725 @ X1726))&((~(in @ X1731 @ X1728)|(~(in @ X1732 @ X1729)|(~(in @ (kpair @ X1731 @ X1732) @ (dpsetconstr @ X1728 @ X1729 @ X1730))|(X1730 @ X1731 @ X1732))))&((~(in @ (kpair @ X1736 @ X1737) @ (dpsetconstr @ X1733 @ X1734 @ X1735))|(in @ X1736 @ X1733))&((~(in @ (kpair @ X1741 @ X1742) @ (dpsetconstr @ X1738 @ X1739 @ X1740))|(in @ X1742 @ X1739))&((~(in @ (kpair @ X1746 @ X1747) @ (dpsetconstr @ X1743 @ X1744 @ X1745))|(X1745 @ X1746 @ X1747))&(((((in @ (esk70_4 @ X1748 @ X1749 @ X1750 @ X1753) @ (dsetconstr @ X1749 @ (^[Z0:$i]:((in @ (kpair @ X1753 @ Z0) @ X1750)))))|~(in @ X1753 @ X1748)|((in @ (esk69_3 @ X1748 @ X1749 @ X1750) @ X1748)|~(subset @ X1750 @ (cartprod @ X1748 @ X1749))))&(((dsetconstr @ X1749 @ (^[Z0:$i]:((in @ (kpair @ X1753 @ Z0) @ X1750))))=(setadjoin @ (esk70_4 @ X1748 @ X1749 @ X1750 @ X1753) @ emptyset))|~(in @ X1753 @ X1748)|((in @ (esk69_3 @ X1748 @ X1749 @ X1750) @ X1748)|~(subset @ X1750 @ (cartprod @ X1748 @ X1749)))))&(((in @ (esk70_4 @ X1748 @ X1749 @ X1750 @ X1753) @ (dsetconstr @ X1749 @ (^[Z0:$i]:((in @ (kpair @ X1753 @ Z0) @ X1750)))))|~(in @ X1753 @ X1748)|(~(in @ X1752 @ (dsetconstr @ X1749 @ (^[Z0:$i]:((in @ (kpair @ (esk69_3 @ X1748 @ X1749 @ X1750) @ Z0) @ X1750)))))|((dsetconstr @ X1749 @ (^[Z0:$i]:((in @ (kpair @ (esk69_3 @ X1748 @ X1749 @ X1750) @ Z0) @ X1750))))!=(setadjoin @ X1752 @ emptyset))|~(subset @ X1750 @ (cartprod @ X1748 @ X1749))))&(((dsetconstr @ X1749 @ (^[Z0:$i]:((in @ (kpair @ X1753 @ Z0) @ X1750))))=(setadjoin @ (esk70_4 @ X1748 @ X1749 @ X1750 @ X1753) @ emptyset))|~(in @ X1753 @ X1748)|(~(in @ X1752 @ (dsetconstr @ X1749 @ (^[Z0:$i]:((in @ (kpair @ (esk69_3 @ X1748 @ X1749 @ X1750) @ Z0) @ X1750)))))|((dsetconstr @ X1749 @ (^[Z0:$i]:((in @ (kpair @ (esk69_3 @ X1748 @ X1749 @ X1750) @ Z0) @ X1750))))!=(setadjoin @ X1752 @ emptyset))|~(subset @ X1750 @ (cartprod @ X1748 @ X1749))))))&((((in @ (esk71_3 @ X1755 @ X1756 @ X1757) @ X1755)|~(subset @ X1757 @ (cartprod @ X1755 @ X1756))|(~(in @ X1760 @ X1755)|(in @ (setunion @ (dsetconstr @ X1756 @ (^[Z0:$i]:((in @ (kpair @ X1760 @ Z0) @ X1757))))) @ X1756)))&(~(in @ X1759 @ (dsetconstr @ X1756 @ (^[Z0:$i]:((in @ (kpair @ (esk71_3 @ X1755 @ X1756 @ X1757) @ Z0) @ X1757)))))|((dsetconstr @ X1756 @ (^[Z0:$i]:((in @ (kpair @ (esk71_3 @ X1755 @ X1756 @ X1757) @ Z0) @ X1757))))!=(setadjoin @ X1759 @ emptyset))|~(subset @ X1757 @ (cartprod @ X1755 @ X1756))|(~(in @ X1760 @ X1755)|(in @ (setunion @ (dsetconstr @ X1756 @ (^[Z0:$i]:((in @ (kpair @ X1760 @ Z0) @ X1757))))) @ X1756))))&(((subset @ esk74_0 @ (cartprod @ esk72_0 @ esk73_0))&(((in @ (esk75_1 @ X1764) @ (dsetconstr @ esk73_0 @ (^[Z0:$i]:((in @ (kpair @ X1764 @ Z0) @ esk74_0)))))|~(in @ X1764 @ esk72_0))&(((dsetconstr @ esk73_0 @ (^[Z0:$i]:((in @ (kpair @ X1764 @ Z0) @ esk74_0))))=(setadjoin @ (esk75_1 @ X1764) @ emptyset))|~(in @ X1764 @ esk72_0))))&((in @ esk76_0 @ esk72_0)&~(in @ (setunion @ (dsetconstr @ esk73_0 @ (^[Z0:$i]:((in @ (kpair @ esk76_0 @ Z0) @ esk74_0))))) @ esk73_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_271])])])])])])])).
% 4.86/1.03 thf(c_0_273, negated_conjecture, ~((in @ (setunion @ (dsetconstr @ esk73_0 @ (^[Z0:$i]:((in @ (kpair @ esk76_0 @ Z0) @ esk74_0))))) @ esk73_0)), inference(split_conjunct,[status(thm)],[c_0_272])).
% 4.86/1.03 thf(c_0_274, negated_conjecture, ![X2:$i]:((((dsetconstr @ esk73_0 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ esk74_0))))=(setadjoin @ (esk75_1 @ X2) @ emptyset))|~((in @ X2 @ esk72_0)))), inference(split_conjunct,[status(thm)],[c_0_272])).
% 4.86/1.03 thf(c_0_275, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_272])).
% 4.86/1.03 thf(c_0_276, negated_conjecture, (in @ esk76_0 @ esk72_0), inference(split_conjunct,[status(thm)],[c_0_272])).
% 4.86/1.03 thf(c_0_277, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ X2 @ X3)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_272])).
% 4.86/1.03 thf(c_0_278, negated_conjecture, ![X2:$i]:(((in @ (esk75_1 @ X2) @ (dsetconstr @ esk73_0 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ esk74_0)))))|~((in @ X2 @ esk72_0)))), inference(split_conjunct,[status(thm)],[c_0_272])).
% 4.86/1.03 thf(c_0_279, negated_conjecture, ~((in @ (esk75_1 @ esk76_0) @ esk73_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_273, c_0_274]), c_0_275]), c_0_276])])).
% 4.86/1.03 thf(c_0_280, negated_conjecture, ![X2:$i]:(((in @ (esk75_1 @ X2) @ esk73_0)|~((in @ X2 @ esk72_0)))), inference(spm,[status(thm)],[c_0_277, c_0_278])).
% 4.86/1.03 thf(c_0_281, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279, c_0_280]), c_0_276])]), ['proof']).
% 4.86/1.03 % SZS output end CNFRefutation
% 4.86/1.03 % Parsed axioms : 425
% 4.86/1.03 % Removed by relevancy pruning/SinE : 228
% 4.86/1.03 % Initial clauses : 350
% 4.86/1.03 % Removed in clause preprocessing : 25
% 4.86/1.03 % Initial clauses in saturation : 325
% 4.86/1.03 % Processed clauses : 2378
% 4.86/1.03 % ...of these trivial : 17
% 4.86/1.03 % ...subsumed : 1590
% 4.86/1.03 % ...remaining for further processing : 771
% 4.86/1.03 % Other redundant clauses eliminated : 262
% 4.86/1.03 % Clauses deleted for lack of memory : 0
% 4.86/1.03 % Backward-subsumed : 26
% 4.86/1.03 % Backward-rewritten : 24
% 4.86/1.03 % Generated clauses : 35126
% 4.86/1.03 % ...of the previous two non-redundant : 32006
% 4.86/1.03 % ...aggressively subsumed : 0
% 4.86/1.03 % Contextual simplify-reflections : 1
% 4.86/1.03 % Paramodulations : 34853
% 4.86/1.03 % Factorizations : 6
% 4.86/1.03 % NegExts : 0
% 4.86/1.03 % Equation resolutions : 267
% 4.86/1.03 % Disequality decompositions : 0
% 4.86/1.03 % Total rewrite steps : 7981
% 4.86/1.03 % ...of those cached : 7691
% 4.86/1.03 % Propositional unsat checks : 0
% 4.86/1.03 % Propositional check models : 0
% 4.86/1.03 % Propositional check unsatisfiable : 0
% 4.86/1.03 % Propositional clauses : 0
% 4.86/1.03 % Propositional clauses after purity: 0
% 4.86/1.03 % Propositional unsat core size : 0
% 4.86/1.03 % Propositional preprocessing time : 0.000
% 4.86/1.03 % Propositional encoding time : 0.000
% 4.86/1.03 % Propositional solver time : 0.000
% 4.86/1.03 % Success case prop preproc time : 0.000
% 4.86/1.03 % Success case prop encoding time : 0.000
% 4.86/1.03 % Success case prop solver time : 0.000
% 4.86/1.03 % Current number of processed clauses : 707
% 4.86/1.03 % Positive orientable unit clauses : 210
% 4.86/1.03 % Positive unorientable unit clauses: 0
% 4.86/1.03 % Negative unit clauses : 18
% 4.86/1.03 % Non-unit-clauses : 479
% 4.86/1.03 % Current number of unprocessed clauses: 27322
% 4.86/1.03 % ...number of literals in the above : 96016
% 4.86/1.03 % Current number of archived formulas : 0
% 4.86/1.03 % Current number of archived clauses : 50
% 4.86/1.03 % Clause-clause subsumption calls (NU) : 38189
% 4.86/1.03 % Rec. Clause-clause subsumption calls : 22847
% 4.86/1.03 % Non-unit clause-clause subsumptions : 957
% 4.86/1.03 % Unit Clause-clause subsumption calls : 1583
% 4.86/1.03 % Rewrite failures with RHS unbound : 0
% 4.86/1.03 % BW rewrite match attempts : 961
% 4.86/1.03 % BW rewrite match successes : 17
% 4.86/1.03 % Condensation attempts : 0
% 4.86/1.03 % Condensation successes : 0
% 4.86/1.03 % Termbank termtop insertions : 598404
% 4.86/1.03 % Search garbage collected termcells : 18886
% 4.86/1.03
% 4.86/1.03 % -------------------------------------------------
% 4.86/1.03 % User time : 0.634 s
% 4.86/1.03 % System time : 0.038 s
% 4.86/1.03 % Total time : 0.672 s
% 4.86/1.03 % Maximum resident set size: 8168 pages
% 4.86/1.03
% 4.86/1.03 % -------------------------------------------------
% 4.86/1.03 % User time : 0.647 s
% 4.86/1.03 % System time : 0.043 s
% 4.86/1.03 % Total time : 0.690 s
% 4.86/1.03 % Maximum resident set size: 5632 pages
% 4.86/1.03 % E exiting
%------------------------------------------------------------------------------