%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU784^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:25:37 AM UTC 2026
% Result : Theorem 1.96s 0.59s
% Output : CNFRefutation 1.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU784^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n003.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 14:30:13 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.21/0.26 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p
% 1.96/0.59 % Version: 3.5.1-ho
% 1.96/0.59 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.96/0.59 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.96/0.59 % Starting ehoh_best5 with 300s (1) cores
% 1.96/0.59 % Starting almost_fo_3_lam with 300s (1) cores
% 1.96/0.59 % Starting new_bool_5 with 300s (1) cores
% 1.96/0.59 % Starting pre_casc_3 with 300s (1) cores
% 1.96/0.59 % Starting ho_unfolding_8 with 300s (1) cores
% 1.96/0.59 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.96/0.59 % Starting new_bool_3 with 300s (1) cores
% 1.96/0.59 % Starting new_ho_5 with 300s (1) cores
% 1.96/0.59 % pre_casc_3 with pid 2585886 completed with status 9
% 1.96/0.59 % new_ho_5 with pid 2585890 completed with status 9
% 1.96/0.59 % new_bool_3 with pid 2585889 completed with status 0
% 1.96/0.59 % Result found by new_bool_3
% 1.96/0.59 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.96/0.59 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.96/0.59 % Starting ehoh_best5 with 300s (1) cores
% 1.96/0.59 % Starting almost_fo_3_lam with 300s (1) cores
% 1.96/0.59 % Starting new_bool_5 with 300s (1) cores
% 1.96/0.59 % Starting pre_casc_3 with 300s (1) cores
% 1.96/0.59 % Starting ho_unfolding_8 with 300s (1) cores
% 1.96/0.59 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.96/0.59 % Starting new_bool_3 with 300s (1) cores
% 1.96/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.96/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.96/0.59 % Search class: HGHSM-FSLM32-MHFMMSBN
% 1.96/0.59 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 1.96/0.59 % Starting SubtermCWHack with 31s (1) cores
% 1.96/0.59 % SubtermCWHack with pid 2585919 completed with status 0
% 1.96/0.59 % Result found by SubtermCWHack
% 1.96/0.59 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.96/0.59 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.96/0.59 % Starting ehoh_best5 with 300s (1) cores
% 1.96/0.59 % Starting almost_fo_3_lam with 300s (1) cores
% 1.96/0.59 % Starting new_bool_5 with 300s (1) cores
% 1.96/0.59 % Starting pre_casc_3 with 300s (1) cores
% 1.96/0.59 % Starting ho_unfolding_8 with 300s (1) cores
% 1.96/0.59 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.96/0.59 % Starting new_bool_3 with 300s (1) cores
% 1.96/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.96/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.96/0.59 % Search class: HGHSM-FSLM32-MHFMMSBN
% 1.96/0.59 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 1.96/0.59 % Starting SubtermCWHack with 31s (1) cores
% 1.96/0.59 % Preprocessing time : 0.009 s
% 1.96/0.59
% 1.96/0.59 % Proof found!
% 1.96/0.59 % SZS status Theorem
% 1.96/0.59 % SZS output start CNFRefutation
% 1.96/0.59 thf(decl_23, type, in: $i > $i > $o).
% 1.96/0.59 thf(decl_24, type, exu: ($i > $o) > $o).
% 1.96/0.59 thf(decl_25, type, setextAx: $o).
% 1.96/0.59 thf(decl_26, type, emptyset: $i).
% 1.96/0.59 thf(decl_27, type, emptysetAx: $o).
% 1.96/0.59 thf(decl_28, type, setadjoin: $i > $i > $i).
% 1.96/0.59 thf(decl_29, type, setadjoinAx: $o).
% 1.96/0.59 thf(decl_30, type, powerset: $i > $i).
% 1.96/0.59 thf(decl_31, type, powersetAx: $o).
% 1.96/0.59 thf(decl_32, type, setunion: $i > $i).
% 1.96/0.59 thf(decl_33, type, setunionAx: $o).
% 1.96/0.59 thf(decl_34, type, omega: $i).
% 1.96/0.59 thf(decl_35, type, omega0Ax: $o).
% 1.96/0.59 thf(decl_36, type, omegaSAx: $o).
% 1.96/0.59 thf(decl_37, type, omegaIndAx: $o).
% 1.96/0.59 thf(decl_38, type, replAx: $o).
% 1.96/0.59 thf(decl_39, type, foundationAx: $o).
% 1.96/0.59 thf(decl_40, type, wellorderingAx: $o).
% 1.96/0.59 thf(decl_41, type, descr: ($i > $o) > $i).
% 1.96/0.59 thf(decl_42, type, descrp: $o).
% 1.96/0.59 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_44, type, dsetconstrI: $o).
% 1.96/0.59 thf(decl_45, type, dsetconstrEL: $o).
% 1.96/0.59 thf(decl_46, type, dsetconstrER: $o).
% 1.96/0.59 thf(decl_47, type, exuE1: $o).
% 1.96/0.59 thf(decl_48, type, prop2set: $o > $i).
% 1.96/0.59 thf(decl_49, type, prop2setE: $o).
% 1.96/0.59 thf(decl_50, type, emptysetE: $o).
% 1.96/0.59 thf(decl_51, type, emptysetimpfalse: $o).
% 1.96/0.59 thf(decl_52, type, notinemptyset: $o).
% 1.96/0.59 thf(decl_53, type, exuE3e: $o).
% 1.96/0.59 thf(decl_54, type, setext: $o).
% 1.96/0.59 thf(decl_55, type, emptyI: $o).
% 1.96/0.59 thf(decl_56, type, noeltsimpempty: $o).
% 1.96/0.59 thf(decl_57, type, setbeta: $o).
% 1.96/0.59 thf(decl_58, type, nonempty: $i > $o).
% 1.96/0.59 thf(decl_59, type, nonemptyE1: $o).
% 1.96/0.59 thf(decl_60, type, nonemptyI: $o).
% 1.96/0.59 thf(decl_61, type, nonemptyI1: $o).
% 1.96/0.59 thf(decl_62, type, setadjoinIL: $o).
% 1.96/0.59 thf(decl_63, type, emptyinunitempty: $o).
% 1.96/0.59 thf(decl_64, type, setadjoinIR: $o).
% 1.96/0.59 thf(decl_65, type, setadjoinE: $o).
% 1.96/0.59 thf(decl_66, type, setadjoinOr: $o).
% 1.96/0.59 thf(decl_67, type, setoftrueEq: $o).
% 1.96/0.59 thf(decl_68, type, powersetI: $o).
% 1.96/0.59 thf(decl_69, type, emptyinPowerset: $o).
% 1.96/0.59 thf(decl_70, type, emptyInPowerset: $o).
% 1.96/0.59 thf(decl_71, type, powersetE: $o).
% 1.96/0.59 thf(decl_72, type, setunionI: $o).
% 1.96/0.59 thf(decl_73, type, setunionE: $o).
% 1.96/0.59 thf(decl_74, type, subPowSU: $o).
% 1.96/0.59 thf(decl_75, type, exuE2: $o).
% 1.96/0.59 thf(decl_76, type, nonemptyImpWitness: $o).
% 1.96/0.59 thf(decl_77, type, uniqinunit: $o).
% 1.96/0.59 thf(decl_78, type, notinsingleton: $o).
% 1.96/0.59 thf(decl_79, type, eqinunit: $o).
% 1.96/0.59 thf(decl_80, type, singletonsswitch: $o).
% 1.96/0.59 thf(decl_81, type, upairsetE: $o).
% 1.96/0.59 thf(decl_82, type, upairsetIL: $o).
% 1.96/0.59 thf(decl_83, type, upairsetIR: $o).
% 1.96/0.59 thf(decl_84, type, emptyE1: $o).
% 1.96/0.59 thf(decl_85, type, vacuousDall: $o).
% 1.96/0.59 thf(decl_86, type, quantDeMorgan1: $o).
% 1.96/0.59 thf(decl_87, type, quantDeMorgan2: $o).
% 1.96/0.59 thf(decl_88, type, quantDeMorgan3: $o).
% 1.96/0.59 thf(decl_89, type, quantDeMorgan4: $o).
% 1.96/0.59 thf(decl_90, type, prop2setI: $o).
% 1.96/0.59 thf(decl_92, type, prop2set2propI: $o).
% 1.96/0.59 thf(decl_93, type, notdexE: $o).
% 1.96/0.59 thf(decl_94, type, notdallE: $o).
% 1.96/0.59 thf(decl_95, type, exuI1: $o).
% 1.96/0.59 thf(decl_96, type, exuI3: $o).
% 1.96/0.59 thf(decl_97, type, exuI2: $o).
% 1.96/0.59 thf(decl_98, type, inCongP: $o).
% 1.96/0.59 thf(decl_99, type, in__Cong: $o).
% 1.96/0.59 thf(decl_100, type, exuE3u: $o).
% 1.96/0.59 thf(decl_101, type, exu__Cong: $o).
% 1.96/0.59 thf(decl_102, type, emptyset__Cong: $o).
% 1.96/0.59 thf(decl_103, type, setadjoin__Cong: $o).
% 1.96/0.59 thf(decl_104, type, powerset__Cong: $o).
% 1.96/0.59 thf(decl_105, type, setunion__Cong: $o).
% 1.96/0.59 thf(decl_106, type, omega__Cong: $o).
% 1.96/0.59 thf(decl_107, type, exuEu: $o).
% 1.96/0.59 thf(decl_108, type, descr__Cong: $o).
% 1.96/0.59 thf(decl_109, type, dsetconstr__Cong: $o).
% 1.96/0.59 thf(decl_110, type, subset: $i > $i > $o).
% 1.96/0.59 thf(decl_113, type, subsetI1: $o).
% 1.96/0.59 thf(decl_114, type, eqimpsubset2: $o).
% 1.96/0.59 thf(decl_115, type, eqimpsubset1: $o).
% 1.96/0.59 thf(decl_116, type, subsetI2: $o).
% 1.96/0.59 thf(decl_117, type, emptysetsubset: $o).
% 1.96/0.59 thf(decl_118, type, subsetE: $o).
% 1.96/0.59 thf(decl_119, type, subsetE2: $o).
% 1.96/0.59 thf(decl_120, type, notsubsetI: $o).
% 1.96/0.59 thf(decl_121, type, notequalI1: $o).
% 1.96/0.59 thf(decl_122, type, notequalI2: $o).
% 1.96/0.59 thf(decl_123, type, subsetRefl: $o).
% 1.96/0.59 thf(decl_124, type, subsetTrans: $o).
% 1.96/0.59 thf(decl_125, type, setadjoinSub: $o).
% 1.96/0.59 thf(decl_126, type, setadjoinSub2: $o).
% 1.96/0.59 thf(decl_127, type, subset2powerset: $o).
% 1.96/0.59 thf(decl_128, type, setextsub: $o).
% 1.96/0.59 thf(decl_129, type, subsetemptysetimpeq: $o).
% 1.96/0.59 thf(decl_130, type, powersetI1: $o).
% 1.96/0.59 thf(decl_131, type, powersetE1: $o).
% 1.96/0.59 thf(decl_132, type, inPowerset: $o).
% 1.96/0.59 thf(decl_133, type, powersetsubset: $o).
% 1.96/0.59 thf(decl_134, type, sepInPowerset: $o).
% 1.96/0.59 thf(decl_135, type, sepSubset: $o).
% 1.96/0.59 thf(decl_136, type, binunion: $i > $i > $i).
% 1.96/0.59 thf(decl_137, type, binunionIL: $o).
% 1.96/0.59 thf(decl_138, type, upairset2IR: $o).
% 1.96/0.59 thf(decl_139, type, binunionIR: $o).
% 1.96/0.59 thf(decl_140, type, binunionEcases: $o).
% 1.96/0.59 thf(decl_141, type, binunionE: $o).
% 1.96/0.59 thf(decl_142, type, binunionLsub: $o).
% 1.96/0.59 thf(decl_143, type, binunionRsub: $o).
% 1.96/0.59 thf(decl_144, type, binintersect: $i > $i > $i).
% 1.96/0.59 thf(decl_145, type, binintersectI: $o).
% 1.96/0.59 thf(decl_146, type, binintersectSubset5: $o).
% 1.96/0.59 thf(decl_147, type, binintersectEL: $o).
% 1.96/0.59 thf(decl_148, type, binintersectLsub: $o).
% 1.96/0.59 thf(decl_149, type, binintersectSubset2: $o).
% 1.96/0.59 thf(decl_150, type, binintersectSubset3: $o).
% 1.96/0.59 thf(decl_151, type, binintersectER: $o).
% 1.96/0.59 thf(decl_152, type, disjointsetsI1: $o).
% 1.96/0.59 thf(decl_153, type, binintersectRsub: $o).
% 1.96/0.59 thf(decl_154, type, binintersectSubset4: $o).
% 1.96/0.59 thf(decl_155, type, binintersectSubset1: $o).
% 1.96/0.59 thf(decl_156, type, bs114d: $o).
% 1.96/0.59 thf(decl_158, type, setminus: $i > $i > $i).
% 1.96/0.59 thf(decl_159, type, setminusI: $o).
% 1.96/0.59 thf(decl_160, type, setminusEL: $o).
% 1.96/0.59 thf(decl_161, type, setminusER: $o).
% 1.96/0.59 thf(decl_162, type, setminusSubset2: $o).
% 1.96/0.59 thf(decl_163, type, setminusERneg: $o).
% 1.96/0.59 thf(decl_164, type, setminusELneg: $o).
% 1.96/0.59 thf(decl_165, type, setminusILneg: $o).
% 1.96/0.59 thf(decl_166, type, setminusIRneg: $o).
% 1.96/0.59 thf(decl_167, type, setminusLsub: $o).
% 1.96/0.59 thf(decl_168, type, setminusSubset1: $o).
% 1.96/0.59 thf(decl_169, type, symdiff: $i > $i > $i).
% 1.96/0.59 thf(decl_170, type, symdiffE: $o).
% 1.96/0.59 thf(decl_171, type, symdiffI1: $o).
% 1.96/0.59 thf(decl_172, type, symdiffI2: $o).
% 1.96/0.59 thf(decl_173, type, symdiffIneg1: $o).
% 1.96/0.59 thf(decl_174, type, symdiffIneg2: $o).
% 1.96/0.59 thf(decl_175, type, iskpair: $i > $o).
% 1.96/0.59 thf(decl_176, type, secondinupair: $o).
% 1.96/0.59 thf(decl_177, type, setukpairIL: $o).
% 1.96/0.59 thf(decl_178, type, setukpairIR: $o).
% 1.96/0.59 thf(decl_179, type, kpairiskpair: $o).
% 1.96/0.59 thf(decl_180, type, kpair: $i > $i > $i).
% 1.96/0.59 thf(decl_181, type, kpairp: $o).
% 1.96/0.59 thf(decl_182, type, cartprod: $i > $i > $i).
% 1.96/0.59 thf(decl_183, type, singletonsubset: $o).
% 1.96/0.59 thf(decl_184, type, singletoninpowerset: $o).
% 1.96/0.59 thf(decl_185, type, singletoninpowunion: $o).
% 1.96/0.59 thf(decl_186, type, upairset2E: $o).
% 1.96/0.59 thf(decl_187, type, upairsubunion: $o).
% 1.96/0.59 thf(decl_188, type, upairinpowunion: $o).
% 1.96/0.59 thf(decl_189, type, ubforcartprodlem1: $o).
% 1.96/0.59 thf(decl_190, type, ubforcartprodlem2: $o).
% 1.96/0.59 thf(decl_191, type, ubforcartprodlem3: $o).
% 1.96/0.59 thf(decl_192, type, cartprodpairin: $o).
% 1.96/0.59 thf(decl_193, type, cartprodmempair1: $o).
% 1.96/0.59 thf(decl_194, type, cartprodmempair: $o).
% 1.96/0.59 thf(decl_195, type, setunionE2: $o).
% 1.96/0.59 thf(decl_196, type, setunionsingleton1: $o).
% 1.96/0.59 thf(decl_197, type, setunionsingleton2: $o).
% 1.96/0.59 thf(decl_198, type, setunionsingleton: $o).
% 1.96/0.59 thf(decl_199, type, singleton: $i > $o).
% 1.96/0.59 thf(decl_200, type, singletonprop: $o).
% 1.96/0.59 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 1.96/0.59 thf(decl_202, type, ex1E1: $o).
% 1.96/0.59 thf(decl_203, type, ex1I: $o).
% 1.96/0.59 thf(decl_204, type, ex1I2: $o).
% 1.96/0.59 thf(decl_205, type, singletonsuniq: $o).
% 1.96/0.59 thf(decl_210, type, setukpairinjL1: $o).
% 1.96/0.59 thf(decl_211, type, kfstsingleton: $o).
% 1.96/0.59 thf(decl_212, type, theprop: $o).
% 1.96/0.59 thf(decl_213, type, kfst: $i > $i).
% 1.96/0.59 thf(decl_214, type, kfstpairEq: $o).
% 1.96/0.59 thf(decl_215, type, cartprodfstin: $o).
% 1.96/0.59 thf(decl_216, type, setukpairinjL2: $o).
% 1.96/0.59 thf(decl_217, type, setukpairinjL: $o).
% 1.96/0.59 thf(decl_218, type, setukpairinjR11: $o).
% 1.96/0.59 thf(decl_219, type, setukpairinjR12: $o).
% 1.96/0.59 thf(decl_220, type, setukpairinjR1: $o).
% 1.96/0.59 thf(decl_221, type, upairequniteq: $o).
% 1.96/0.59 thf(decl_222, type, setukpairinjR2: $o).
% 1.96/0.59 thf(decl_223, type, setukpairinjR: $o).
% 1.96/0.59 thf(decl_224, type, ksndsingleton: $o).
% 1.96/0.59 thf(decl_225, type, ksnd: $i > $i).
% 1.96/0.59 thf(decl_226, type, ksndpairEq: $o).
% 1.96/0.59 thf(decl_227, type, kpairsurjEq: $o).
% 1.96/0.59 thf(decl_228, type, cartprodsndin: $o).
% 1.96/0.59 thf(decl_229, type, cartprodpairmemEL: $o).
% 1.96/0.59 thf(decl_230, type, cartprodpairmemER: $o).
% 1.96/0.59 thf(decl_231, type, cartprodmempaircEq: $o).
% 1.96/0.59 thf(decl_232, type, cartprodfstpairEq: $o).
% 1.96/0.59 thf(decl_233, type, cartprodsndpairEq: $o).
% 1.96/0.59 thf(decl_234, type, cartprodpairsurjEq: $o).
% 1.96/0.59 thf(decl_235, type, breln: $i > $i > $i > $o).
% 1.96/0.59 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.96/0.59 thf(decl_237, type, dpsetconstrI: $o).
% 1.96/0.59 thf(decl_238, type, dpsetconstrSub: $o).
% 1.96/0.59 thf(decl_239, type, setOfPairsIsBReln: $o).
% 1.96/0.59 thf(decl_240, type, dpsetconstrERa: $o).
% 1.96/0.59 thf(decl_241, type, dpsetconstrEL1: $o).
% 1.96/0.59 thf(decl_242, type, dpsetconstrEL2: $o).
% 1.96/0.59 thf(decl_243, type, dpsetconstrER: $o).
% 1.96/0.59 thf(decl_244, type, func: $i > $i > $i > $o).
% 1.96/0.59 thf(decl_245, type, funcSet: $i > $i > $i).
% 1.96/0.59 thf(decl_246, type, funcImageSingleton: $o).
% 1.96/0.59 thf(decl_247, type, apProp: $o).
% 1.96/0.59 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 1.96/0.59 thf(decl_249, type, app: $o).
% 1.96/0.59 thf(decl_250, type, infuncsetfunc: $o).
% 1.96/0.59 thf(decl_251, type, ap2p: $o).
% 1.96/0.59 thf(decl_252, type, funcinfuncset: $o).
% 1.96/0.59 thf(decl_253, type, lamProp: $o).
% 1.96/0.59 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 1.96/0.59 thf(decl_255, type, lamp: $o).
% 1.96/0.59 thf(decl_256, type, lam2p: $o).
% 1.96/0.59 thf(decl_257, type, brelnall1: $o).
% 1.96/0.59 thf(decl_258, type, brelnall2: $o).
% 1.96/0.59 thf(decl_259, type, ex1E2: $o).
% 1.96/0.59 thf(decl_260, type, funcGraphProp1: $o).
% 1.96/0.59 thf(decl_261, type, funcGraphProp3: $o).
% 1.96/0.59 thf(decl_262, type, funcGraphProp2: $o).
% 1.96/0.59 thf(decl_263, type, funcextLem: $o).
% 1.96/0.59 thf(decl_264, type, funcGraphProp4: $o).
% 1.96/0.59 thf(decl_265, type, subbreln: $o).
% 1.96/0.59 thf(decl_266, type, eqbreln: $o).
% 1.96/0.59 thf(decl_267, type, funcext: $o).
% 1.96/0.59 thf(decl_268, type, funcext2: $o).
% 1.96/0.59 thf(decl_269, type, ap2apEq1: $o).
% 1.96/0.59 thf(decl_270, type, ap2apEq2: $o).
% 1.96/0.59 thf(decl_271, type, beta1: $o).
% 1.96/0.59 thf(decl_272, type, eta1: $o).
% 1.96/0.59 thf(decl_273, type, lam2lamEq: $o).
% 1.96/0.59 thf(decl_274, type, beta2: $o).
% 1.96/0.59 thf(decl_275, type, eta2: $o).
% 1.96/0.59 thf(decl_276, type, iffalseProp1: $o).
% 1.96/0.59 thf(decl_277, type, iffalseProp2: $o).
% 1.96/0.59 thf(decl_278, type, iftrueProp1: $o).
% 1.96/0.59 thf(decl_279, type, iftrueProp2: $o).
% 1.96/0.59 thf(decl_280, type, ifSingleton: $o).
% 1.96/0.59 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 1.96/0.59 thf(decl_282, type, ifp: $o).
% 1.96/0.59 thf(decl_283, type, theeq: $o).
% 1.96/0.59 thf(decl_284, type, iftrue: $o).
% 1.96/0.59 thf(decl_285, type, iffalse: $o).
% 1.96/0.59 thf(decl_286, type, iftrueorfalse: $o).
% 1.96/0.59 thf(decl_287, type, binintersectT_lem: $o).
% 1.96/0.59 thf(decl_288, type, binunionT_lem: $o).
% 1.96/0.59 thf(decl_289, type, powersetT_lem: $o).
% 1.96/0.59 thf(decl_290, type, setminusT_lem: $o).
% 1.96/0.59 thf(decl_291, type, complementT_lem: $o).
% 1.96/0.59 thf(decl_292, type, setextT: $o).
% 1.96/0.59 thf(decl_293, type, subsetTI: $o).
% 1.96/0.59 thf(decl_294, type, powersetTI1: $o).
% 1.96/0.59 thf(decl_295, type, powersetTE1: $o).
% 1.96/0.59 thf(decl_296, type, complementTI1: $o).
% 1.96/0.59 thf(decl_297, type, complementTE1: $o).
% 1.96/0.59 thf(decl_298, type, binintersectTELcontra: $o).
% 1.96/0.59 thf(decl_299, type, binintersectTERcontra: $o).
% 1.96/0.59 thf(decl_300, type, contrasubsetT: $o).
% 1.96/0.59 thf(decl_301, type, contrasubsetT1: $o).
% 1.96/0.59 thf(decl_302, type, contrasubsetT2: $o).
% 1.96/0.59 thf(decl_303, type, contrasubsetT3: $o).
% 1.96/0.59 thf(decl_304, type, doubleComplementI1: $o).
% 1.96/0.59 thf(decl_305, type, doubleComplementE1: $o).
% 1.96/0.59 thf(decl_306, type, doubleComplementSub1: $o).
% 1.96/0.59 thf(decl_307, type, doubleComplementSub2: $o).
% 1.96/0.59 thf(decl_308, type, doubleComplementEq: $o).
% 1.96/0.59 thf(decl_309, type, complementTnotintersectT: $o).
% 1.96/0.59 thf(decl_310, type, complementImpComplementIntersect: $o).
% 1.96/0.59 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 1.96/0.59 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 1.96/0.59 thf(decl_313, type, contraSubsetComplement: $o).
% 1.96/0.59 thf(decl_314, type, complementTcontraSubset: $o).
% 1.96/0.59 thf(decl_315, type, binunionTILcontra: $o).
% 1.96/0.59 thf(decl_316, type, binunionTIRcontra: $o).
% 1.96/0.59 thf(decl_317, type, inIntersectImpInUnion: $o).
% 1.96/0.59 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 1.96/0.59 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 1.96/0.59 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 1.96/0.59 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 1.96/0.59 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 1.96/0.59 thf(decl_323, type, binunionTE: $o).
% 1.96/0.59 thf(decl_324, type, binunionTEcontra: $o).
% 1.96/0.59 thf(decl_325, type, demorgan2a1: $o).
% 1.96/0.59 thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 1.96/0.59 thf(decl_327, type, demorgan2a2: $o).
% 1.96/0.59 thf(decl_328, type, demorgan1a: $o).
% 1.96/0.59 thf(decl_329, type, demorgan1b: $o).
% 1.96/0.59 thf(decl_330, type, demorgan1: $o).
% 1.96/0.59 thf(decl_331, type, demorgan2a: $o).
% 1.96/0.59 thf(decl_332, type, demorgan2b2: $o).
% 1.96/0.59 thf(decl_333, type, demorgan2b: $o).
% 1.96/0.59 thf(decl_334, type, demorgan2: $o).
% 1.96/0.59 thf(decl_335, type, woz13rule0: $o).
% 1.96/0.59 thf(decl_336, type, woz13rule1: $o).
% 1.96/0.59 thf(decl_337, type, woz13rule2: $o).
% 1.96/0.59 thf(decl_338, type, woz13rule3: $o).
% 1.96/0.59 thf(decl_339, type, woz13rule4: $o).
% 1.96/0.59 thf(decl_340, type, woz1_1: $o).
% 1.96/0.59 thf(decl_341, type, woz1_2: $o).
% 1.96/0.59 thf(decl_342, type, woz1_3: $o).
% 1.96/0.59 thf(decl_343, type, woz1_4: $o).
% 1.96/0.59 thf(decl_344, type, woz1_5: $o).
% 1.96/0.59 thf(decl_345, type, breln1: $i > $i > $o).
% 1.96/0.59 thf(decl_346, type, breln1all2: $o).
% 1.96/0.59 thf(decl_347, type, breln1Set: $i > $i).
% 1.96/0.59 thf(decl_348, type, breln1SetBreln1: $o).
% 1.96/0.59 thf(decl_355, type, choice2fnsingleton: $o).
% 1.96/0.59 thf(decl_356, type, setOfPairsIsBReln1: $o).
% 1.96/0.59 thf(decl_357, type, breln1all1: $o).
% 1.96/0.59 thf(decl_358, type, subbreln1: $o).
% 1.96/0.59 thf(decl_359, type, eqbreln1: $o).
% 1.96/0.59 thf(decl_360, type, breln1invset: $i > $i > $i).
% 1.96/0.59 thf(decl_361, type, breln1invprop: $o).
% 1.96/0.59 thf(decl_362, type, breln1invI: $o).
% 1.96/0.59 thf(decl_363, type, breln1invE: $o).
% 1.96/0.59 thf(decl_364, type, breln1compset: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_365, type, breln1compprop: $o).
% 1.96/0.59 thf(decl_366, type, breln1compI: $o).
% 1.96/0.59 thf(decl_367, type, breln1compE: $o).
% 1.96/0.59 thf(decl_368, type, breln1compEex: $o).
% 1.96/0.59 thf(decl_369, type, breln1unionprop: $o).
% 1.96/0.59 thf(decl_370, type, breln1unionIL: $o).
% 1.96/0.59 thf(decl_371, type, epred1_0: $o).
% 1.96/0.59 thf(decl_372, type, esk1_2: $i > $i > $i).
% 1.96/0.59 thf(decl_373, type, esk2_2: $i > $i > $i).
% 1.96/0.59 thf(decl_374, type, esk3_2: $i > $i > $i).
% 1.96/0.59 thf(decl_375, type, esk4_1: $i > $i).
% 1.96/0.59 thf(decl_376, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.96/0.59 thf(decl_377, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 1.96/0.59 thf(decl_378, type, esk7_2: ($i > $i > $o) > $i > $i).
% 1.96/0.59 thf(decl_379, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 1.96/0.59 thf(decl_380, type, esk9_1: $i > $i).
% 1.96/0.59 thf(decl_381, type, esk10_2: ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_382, type, esk11_2: ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_383, type, esk12_1: ($i > $o) > $i).
% 1.96/0.59 thf(decl_384, type, esk13_2: ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_385, type, esk14_1: ($i > $o) > $i).
% 1.96/0.59 thf(decl_386, type, esk15_2: $i > $i > $i).
% 1.96/0.59 thf(decl_387, type, esk16_2: $i > $i > $i).
% 1.96/0.59 thf(decl_388, type, esk17_1: $i > $i).
% 1.96/0.59 thf(decl_389, type, esk18_1: $i > $i).
% 1.96/0.59 thf(decl_390, type, esk19_1: $i > $i).
% 1.96/0.59 thf(decl_391, type, esk20_2: $i > $i > $i).
% 1.96/0.59 thf(decl_392, type, esk21_3: $i > $i > $o > $i).
% 1.96/0.59 thf(decl_393, type, esk22_2: ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_394, type, esk23_1: ($i > $o) > $i).
% 1.96/0.59 thf(decl_395, type, esk24_1: $i > $i).
% 1.96/0.59 thf(decl_396, type, esk25_2: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_397, type, esk26_2: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_398, type, esk27_2: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_399, type, esk28_2: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_400, type, esk29_2: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_401, type, esk30_2: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_402, type, esk31_2: ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_403, type, esk32_1: ($i > $o) > $i).
% 1.96/0.59 thf(decl_404, type, esk33_1: ($i > $o) > $i).
% 1.96/0.59 thf(decl_405, type, esk34_1: ($i > $o) > $i).
% 1.96/0.59 thf(decl_406, type, esk35_1: ($i > $o) > $i).
% 1.96/0.59 thf(decl_407, type, esk36_2: ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_408, type, esk37_1: ($i > $o) > $i).
% 1.96/0.59 thf(decl_409, type, esk38_2: ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_410, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 1.96/0.59 thf(decl_411, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 1.96/0.59 thf(decl_412, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_413, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 1.96/0.59 thf(decl_414, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_415, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 1.96/0.59 thf(decl_416, type, esk45_2: ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_417, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 1.96/0.59 thf(decl_418, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 1.96/0.59 thf(decl_419, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_420, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_421, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.96/0.59 thf(decl_422, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.96/0.59 thf(decl_423, type, esk52_2: $i > $i > $i).
% 1.96/0.59 thf(decl_424, type, esk53_2: $i > $i > $i).
% 1.96/0.59 thf(decl_425, type, esk54_2: $i > $i > $i).
% 1.96/0.59 thf(decl_426, type, esk55_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_427, type, esk56_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_428, type, esk57_2: $i > $i > $i).
% 1.96/0.59 thf(decl_429, type, esk58_2: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_430, type, esk59_2: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_431, type, esk60_2: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_432, type, esk61_3: $i > ($i > $o) > $i > $i).
% 1.96/0.59 thf(decl_433, type, esk62_2: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_434, type, esk63_2: $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_435, type, esk64_3: $i > $i > ($i > $i) > $i).
% 1.96/0.59 thf(decl_436, type, esk65_3: $i > $i > ($i > $i) > $i).
% 1.96/0.59 thf(decl_437, type, esk66_3: $i > $i > ($i > $i) > $i).
% 1.96/0.59 thf(decl_438, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_439, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_440, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_441, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_442, type, esk71_4: $i > $i > $i > $i > $i).
% 1.96/0.59 thf(decl_443, type, esk72_4: $i > $i > $i > $i > $i).
% 1.96/0.59 thf(decl_444, type, esk73_4: $i > $i > $i > $i > $i).
% 1.96/0.59 thf(decl_445, type, esk74_4: $i > $i > $i > $i > $i).
% 1.96/0.59 thf(decl_446, type, esk75_4: $i > $i > $i > $i > $i).
% 1.96/0.59 thf(decl_447, type, esk76_4: $i > $i > $i > $i > $i).
% 1.96/0.59 thf(decl_448, type, esk77_4: $i > $i > $i > $i > $i).
% 1.96/0.59 thf(decl_449, type, esk78_4: $i > $i > $i > $i > $i).
% 1.96/0.59 thf(decl_450, type, esk79_4: $i > $i > $i > $i > $i).
% 1.96/0.59 thf(decl_451, type, esk80_3: $i > $i > ($i > $i) > $i).
% 1.96/0.59 thf(decl_452, type, esk81_3: $i > $i > ($i > $i) > $i).
% 1.96/0.59 thf(decl_453, type, esk82_3: $i > $i > ($i > $i) > $i).
% 1.96/0.59 thf(decl_454, type, esk83_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_455, type, esk84_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_456, type, esk85_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_457, type, esk86_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_458, type, esk87_3: $i > $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_459, type, esk88_3: $i > $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_460, type, esk89_3: $i > $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_461, type, esk90_3: $i > $i > ($i > $o) > $i).
% 1.96/0.59 thf(decl_462, type, esk91_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_463, type, esk92_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_464, type, esk93_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_465, type, esk94_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_466, type, esk95_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_467, type, esk96_3: $i > $i > $i > $i).
% 1.96/0.59 thf(decl_468, type, esk97_5: $i > $i > $i > $i > $i > $i).
% 1.96/0.59 thf(decl_469, type, esk98_6: $i > $i > $i > $i > $i > $o > $i).
% 1.96/0.59 thf(decl_470, type, esk99_0: $i).
% 1.96/0.59 thf(decl_471, type, esk100_0: $i).
% 1.96/0.59 thf(decl_472, type, esk101_0: $i).
% 1.96/0.59 thf(decl_473, type, esk102_0: $i).
% 1.96/0.59 thf(decl_474, type, esk103_0: $i).
% 1.96/0.59 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', exu__Cong)).
% 1.96/0.59 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', exu)).
% 1.96/0.59 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', exuE3u)).
% 1.96/0.59 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', descr__Cong)).
% 1.96/0.59 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', exuEu)).
% 1.96/0.59 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', exuI2)).
% 1.96/0.59 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', exuI3)).
% 1.96/0.59 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', exuI1)).
% 1.96/0.59 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', nonempty)).
% 1.96/0.59 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', exuE2)).
% 1.96/0.59 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', nonemptyI)).
% 1.96/0.59 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', exuE3e)).
% 1.96/0.59 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', exuE1)).
% 1.96/0.59 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', descrp)).
% 1.96/0.59 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', replAx)).
% 1.96/0.59 thf(breln1unionIR, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>((breln1compprop)=>((breln1compI)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1unionIR)).
% 1.96/0.59 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', dsetconstr__Cong)).
% 1.96/0.59 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setOfPairsIsBReln1)).
% 1.96/0.59 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', sepSubset)).
% 1.96/0.59 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', sepInPowerset)).
% 1.96/0.59 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', apProp)).
% 1.96/0.59 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', lam2p)).
% 1.96/0.59 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ex1E2)).
% 1.96/0.59 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ex1I)).
% 1.96/0.59 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ex1E1)).
% 1.96/0.59 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', singletonprop)).
% 1.96/0.59 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ex1I2)).
% 1.96/0.59 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', kfstsingleton)).
% 1.96/0.59 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ksndsingleton)).
% 1.96/0.59 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', dpsetconstrER)).
% 1.96/0.59 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', dpsetconstrEL2)).
% 1.96/0.59 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', dpsetconstrEL1)).
% 1.96/0.59 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', dpsetconstrERa)).
% 1.96/0.59 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setOfPairsIsBReln)).
% 1.96/0.59 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', dpsetconstrSub)).
% 1.96/0.59 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', dpsetconstrI)).
% 1.96/0.59 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', funcImageSingleton)).
% 1.96/0.59 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', lamp)).
% 1.96/0.59 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', lamProp)).
% 1.96/0.59 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', beta1)).
% 1.96/0.59 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', eta1)).
% 1.96/0.59 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', iftrueProp2)).
% 1.96/0.59 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', iftrueProp1)).
% 1.96/0.59 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', iffalseProp2)).
% 1.96/0.59 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', iffalseProp1)).
% 1.96/0.59 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', eta2)).
% 1.96/0.59 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', beta2)).
% 1.96/0.59 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', lam2lamEq)).
% 1.96/0.59 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ifSingleton)).
% 1.96/0.59 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', emptyE1)).
% 1.96/0.59 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', nonemptyImpWitness)).
% 1.96/0.59 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setoftrueEq)).
% 1.96/0.59 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', nonemptyI1)).
% 1.96/0.59 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', nonemptyE1)).
% 1.96/0.59 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setbeta)).
% 1.96/0.59 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', dsetconstrER)).
% 1.96/0.59 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', dsetconstrEL)).
% 1.96/0.59 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', dsetconstrI)).
% 1.96/0.59 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', complementImpComplementIntersect)).
% 1.96/0.59 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', complementSubsetComplementIntersect)).
% 1.96/0.59 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', complementInPowersetComplementIntersect)).
% 1.96/0.59 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', emptyset__Cong)).
% 1.96/0.59 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', contraSubsetComplement)).
% 1.96/0.59 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', complementTcontraSubset)).
% 1.96/0.59 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binunionTILcontra)).
% 1.96/0.59 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', in__Cong)).
% 1.96/0.59 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binunionTIRcontra)).
% 1.96/0.59 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', inCongP)).
% 1.96/0.59 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', inIntersectImpInUnion)).
% 1.96/0.59 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setadjoin__Cong)).
% 1.96/0.59 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', inIntersectImpInUnion2)).
% 1.96/0.59 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', inIntersectImpInIntersectUnions)).
% 1.96/0.59 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', intersectInPowersetIntersectUnions)).
% 1.96/0.59 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', inComplementUnionImpNotIn1)).
% 1.96/0.59 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', inComplementUnionImpInComplement1)).
% 1.96/0.59 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binunionTE)).
% 1.96/0.59 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binunionTEcontra)).
% 1.96/0.59 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', demorgan2a1)).
% 1.96/0.59 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', complementUnionInPowersetComplement)).
% 1.96/0.59 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', demorgan2a2)).
% 1.96/0.59 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', demorgan1a)).
% 1.96/0.59 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', demorgan1b)).
% 1.96/0.59 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', demorgan1)).
% 1.96/0.59 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', demorgan2a)).
% 1.96/0.59 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subsetI1)).
% 1.96/0.59 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', demorgan2b2)).
% 1.96/0.59 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', demorgan2b)).
% 1.96/0.59 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', demorgan2)).
% 1.96/0.59 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', woz13rule0)).
% 1.96/0.59 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', omega__Cong)).
% 1.96/0.59 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', woz13rule1)).
% 1.96/0.59 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setunion__Cong)).
% 1.96/0.59 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', woz13rule2)).
% 1.96/0.59 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', powerset__Cong)).
% 1.96/0.59 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', woz13rule3)).
% 1.96/0.59 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', eqimpsubset2)).
% 1.96/0.59 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', woz13rule4)).
% 1.96/0.59 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', woz1_1)).
% 1.96/0.59 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', woz1_2)).
% 1.96/0.59 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', woz1_3)).
% 1.96/0.59 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', woz1_4)).
% 1.96/0.59 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', woz1_5)).
% 1.96/0.59 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1all2)).
% 1.96/0.59 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1SetBreln1)).
% 1.96/0.59 thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1all1)).
% 1.96/0.59 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subbreln1)).
% 1.96/0.59 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', eqbreln1)).
% 1.96/0.59 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1invprop)).
% 1.96/0.59 thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1invI)).
% 1.96/0.59 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', notequalI1)).
% 1.96/0.59 thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1invE)).
% 1.96/0.59 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', notsubsetI)).
% 1.96/0.59 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1compprop)).
% 1.96/0.59 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subsetE2)).
% 1.96/0.59 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1compI)).
% 1.96/0.59 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subsetE)).
% 1.96/0.59 thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1compE)).
% 1.96/0.59 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', emptysetsubset)).
% 1.96/0.59 thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1compEex)).
% 1.96/0.59 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subsetI2)).
% 1.96/0.59 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1unionprop)).
% 1.96/0.59 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', eqimpsubset1)).
% 1.96/0.59 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', breln1unionIL)).
% 1.96/0.59 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', notequalI2)).
% 1.96/0.59 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setminusILneg)).
% 1.96/0.59 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subsetemptysetimpeq)).
% 1.96/0.59 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setextsub)).
% 1.96/0.59 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subset2powerset)).
% 1.96/0.59 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setadjoinSub2)).
% 1.96/0.59 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setadjoinSub)).
% 1.96/0.59 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subsetTrans)).
% 1.96/0.59 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subsetRefl)).
% 1.96/0.59 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', powersetI1)).
% 1.96/0.59 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', upairset2IR)).
% 1.96/0.59 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binunionIL)).
% 1.96/0.59 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', powersetsubset)).
% 1.96/0.59 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', inPowerset)).
% 1.96/0.59 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', powersetE1)).
% 1.96/0.59 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binunionIR)).
% 1.96/0.59 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectEL)).
% 1.96/0.59 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectSubset5)).
% 1.96/0.59 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectI)).
% 1.96/0.59 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binunionRsub)).
% 1.96/0.59 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binunionLsub)).
% 1.96/0.59 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binunionE)).
% 1.96/0.59 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binunionEcases)).
% 1.96/0.59 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectLsub)).
% 1.96/0.59 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectSubset1)).
% 1.96/0.59 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectSubset4)).
% 1.96/0.59 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectRsub)).
% 1.96/0.59 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', disjointsetsI1)).
% 1.96/0.59 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectER)).
% 1.96/0.59 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectSubset3)).
% 1.96/0.59 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectSubset2)).
% 1.96/0.59 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', bs114d)).
% 1.96/0.59 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', app)).
% 1.96/0.59 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', funcextLem)).
% 1.96/0.59 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', funcGraphProp2)).
% 1.96/0.59 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', funcGraphProp3)).
% 1.96/0.59 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', funcGraphProp1)).
% 1.96/0.59 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setminusELneg)).
% 1.96/0.59 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setminusERneg)).
% 1.96/0.59 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setminusSubset2)).
% 1.96/0.59 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setminusER)).
% 1.96/0.59 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setminusEL)).
% 1.96/0.59 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setminusI)).
% 1.96/0.59 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setminusIRneg)).
% 1.96/0.59 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', symdiffIneg2)).
% 1.96/0.59 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', symdiffIneg1)).
% 1.96/0.59 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', symdiffI2)).
% 1.96/0.59 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', symdiffI1)).
% 1.96/0.59 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', symdiffE)).
% 1.96/0.59 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setminusSubset1)).
% 1.96/0.59 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setminusLsub)).
% 1.96/0.59 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', secondinupair)).
% 1.96/0.59 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', singletoninpowunion)).
% 1.96/0.59 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', singletoninpowerset)).
% 1.96/0.59 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', singletonsubset)).
% 1.96/0.59 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', kpairp)).
% 1.96/0.59 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', kpairiskpair)).
% 1.96/0.59 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setukpairIR)).
% 1.96/0.59 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setukpairIL)).
% 1.96/0.59 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', upairset2E)).
% 1.96/0.59 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', cartprodmempair1)).
% 1.96/0.59 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', cartprodpairin)).
% 1.96/0.59 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ubforcartprodlem3)).
% 1.96/0.59 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ubforcartprodlem2)).
% 1.96/0.59 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ubforcartprodlem1)).
% 1.96/0.59 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', upairinpowunion)).
% 1.96/0.59 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', upairsubunion)).
% 1.96/0.59 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', cartprodmempair)).
% 1.96/0.59 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setunionsingleton)).
% 1.96/0.59 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setunionsingleton2)).
% 1.96/0.59 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setunionsingleton1)).
% 1.96/0.59 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setunionE2)).
% 1.96/0.59 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setukpairinjL2)).
% 1.96/0.59 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', cartprodfstin)).
% 1.96/0.59 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', kfstpairEq)).
% 1.96/0.59 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', theprop)).
% 1.96/0.59 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setukpairinjL1)).
% 1.96/0.59 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', singletonsuniq)).
% 1.96/0.59 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setukpairinjL)).
% 1.96/0.59 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setukpairinjR)).
% 1.96/0.59 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setukpairinjR2)).
% 1.96/0.59 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', upairequniteq)).
% 1.96/0.59 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setukpairinjR1)).
% 1.96/0.59 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setukpairinjR12)).
% 1.96/0.59 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setukpairinjR11)).
% 1.96/0.59 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ksndpairEq)).
% 1.96/0.59 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', cartprodsndpairEq)).
% 1.96/0.59 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', cartprodfstpairEq)).
% 1.96/0.59 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', cartprodmempaircEq)).
% 1.96/0.59 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', cartprodpairmemER)).
% 1.96/0.59 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', cartprodpairmemEL)).
% 1.96/0.59 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', cartprodsndin)).
% 1.96/0.59 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', kpairsurjEq)).
% 1.96/0.59 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', cartprodpairsurjEq)).
% 1.96/0.59 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', funcinfuncset)).
% 1.96/0.59 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ap2p)).
% 1.96/0.59 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', infuncsetfunc)).
% 1.96/0.59 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', brelnall2)).
% 1.96/0.59 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', brelnall1)).
% 1.96/0.60 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', funcGraphProp4)).
% 1.96/0.60 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ap2apEq2)).
% 1.96/0.60 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ap2apEq1)).
% 1.96/0.60 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', funcext2)).
% 1.96/0.60 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', funcext)).
% 1.96/0.60 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', eqbreln)).
% 1.96/0.60 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subbreln)).
% 1.96/0.60 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binunionT_lem)).
% 1.96/0.60 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectT_lem)).
% 1.96/0.60 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', iftrueorfalse)).
% 1.96/0.60 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', iffalse)).
% 1.96/0.60 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', iftrue)).
% 1.96/0.60 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', theeq)).
% 1.96/0.60 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', ifp)).
% 1.96/0.60 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', powersetT_lem)).
% 1.96/0.60 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', complementTI1)).
% 1.96/0.60 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', powersetTE1)).
% 1.96/0.60 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', powersetTI1)).
% 1.96/0.60 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subsetTI)).
% 1.96/0.60 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setextT)).
% 1.96/0.60 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', complementT_lem)).
% 1.96/0.60 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setminusT_lem)).
% 1.96/0.60 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', complementTE1)).
% 1.96/0.60 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', doubleComplementI1)).
% 1.96/0.60 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', contrasubsetT3)).
% 1.96/0.60 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', contrasubsetT2)).
% 1.96/0.60 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', contrasubsetT1)).
% 1.96/0.60 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', contrasubsetT)).
% 1.96/0.60 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectTERcontra)).
% 1.96/0.60 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', binintersectTELcontra)).
% 1.96/0.60 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', doubleComplementE1)).
% 1.96/0.60 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', doubleComplementSub1)).
% 1.96/0.60 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', doubleComplementSub2)).
% 1.96/0.60 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', doubleComplementEq)).
% 1.96/0.60 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', complementTnotintersectT)).
% 1.96/0.60 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', notdallE)).
% 1.96/0.60 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', notdexE)).
% 1.96/0.60 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', prop2setI)).
% 1.96/0.60 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', quantDeMorgan4)).
% 1.96/0.60 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', quantDeMorgan3)).
% 1.96/0.60 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', quantDeMorgan2)).
% 1.96/0.60 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', quantDeMorgan1)).
% 1.96/0.60 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', vacuousDall)).
% 1.96/0.60 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', upairsetIR)).
% 1.96/0.60 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', upairsetIL)).
% 1.96/0.60 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', upairsetE)).
% 1.96/0.60 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', singletonsswitch)).
% 1.96/0.60 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', eqinunit)).
% 1.96/0.60 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', notinsingleton)).
% 1.96/0.60 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', uniqinunit)).
% 1.96/0.60 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', subPowSU)).
% 1.96/0.60 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setunionE)).
% 1.96/0.60 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setunionI)).
% 1.96/0.60 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', powersetE)).
% 1.96/0.60 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', emptyInPowerset)).
% 1.96/0.60 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', emptyinPowerset)).
% 1.96/0.60 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', powersetI)).
% 1.96/0.60 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setadjoinOr)).
% 1.96/0.60 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setadjoinE)).
% 1.96/0.60 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setadjoinIR)).
% 1.96/0.60 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', emptyinunitempty)).
% 1.96/0.60 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setadjoinIL)).
% 1.96/0.60 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', noeltsimpempty)).
% 1.96/0.60 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', emptyI)).
% 1.96/0.60 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setext)).
% 1.96/0.60 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', notinemptyset)).
% 1.96/0.60 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', emptysetimpfalse)).
% 1.96/0.60 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', emptysetE)).
% 1.96/0.60 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', prop2setE)).
% 1.96/0.60 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', wellorderingAx)).
% 1.96/0.60 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', foundationAx)).
% 1.96/0.60 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', omegaIndAx)).
% 1.96/0.60 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', omegaSAx)).
% 1.96/0.60 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', omega0Ax)).
% 1.96/0.60 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setunionAx)).
% 1.96/0.60 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', powersetAx)).
% 1.96/0.60 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setadjoinAx)).
% 1.96/0.60 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', emptysetAx)).
% 1.96/0.60 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.suHUfLRoA7/E---3.1_2585870.p', setextAx)).
% 1.96/0.60 thf(c_0_301, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.96/0.60 thf(c_0_302, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 1.96/0.60 thf(c_0_303, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 1.96/0.60 thf(c_0_304, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.96/0.60 thf(c_0_305, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.96/0.60 thf(c_0_306, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.96/0.60 thf(c_0_307, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.96/0.60 thf(c_0_308, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 1.96/0.60 thf(c_0_309, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 1.96/0.60 thf(c_0_310, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.96/0.60 thf(c_0_311, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.96/0.60 thf(c_0_312, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.96/0.60 thf(c_0_313, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.96/0.60 thf(c_0_314, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.96/0.60 thf(c_0_315, plain, ((replAx)<=>![X6:$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])).
% 1.96/0.60 thf(c_0_316, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>((breln1compprop)=>((breln1compI)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[breln1unionIR])).
% 1.96/0.60 thf(c_0_317, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1052:$i]:(((((X1 @ X1052)))&(![X1053:$i]:(((((X1 @ X1053)))=>(((X1052)=(X1053))))))))))<=>((?[X1054:$i]:(((((X17 @ X1054)))&(![X1055:$i]:(((((X17 @ X1055)))=>(((X1054)=(X1055)))))))))))))))), inference(apply_def,[status(thm)],[c_0_301, c_0_302])).
% 1.96/0.60 thf(c_0_318, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X1050:$i]:(((((X1 @ X1050)))&(![X1051:$i]:(((((X1 @ X1051)))=>(((X1050)=(X1051))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_303, c_0_302])).
% 1.96/0.60 thf(c_0_319, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.96/0.60 thf(c_0_320, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1058:$i]:(((((X1 @ X1058)))&(![X1059:$i]:(((((X1 @ X1059)))=>(((X1058)=(X1059))))))))))=>((((?[X1060:$i]:(((((X17 @ X1060)))&(![X1061:$i]:(((((X17 @ X1061)))=>(((X1060)=(X1061))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_302])).
% 1.96/0.60 thf(c_0_321, plain, ((exuEu)=(![X1:$i > $o]:((((?[X1056:$i]:(((((X1 @ X1056)))&(![X1057:$i]:(((((X1 @ X1057)))=>(((X1056)=(X1057))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_305, c_0_302])).
% 1.96/0.60 thf(c_0_322, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
% 1.96/0.60 thf(c_0_323, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 1.96/0.60 thf(c_0_324, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 1.96/0.60 thf(c_0_325, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 1.96/0.60 thf(c_0_326, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 1.96/0.60 thf(c_0_327, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 1.96/0.60 thf(c_0_328, 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])).
% 1.96/0.60 thf(c_0_329, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 1.96/0.60 thf(c_0_330, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 1.96/0.60 thf(c_0_331, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 1.96/0.60 thf(c_0_332, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 1.96/0.60 thf(c_0_333, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 1.96/0.60 thf(c_0_334, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 1.96/0.60 thf(c_0_335, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 1.96/0.60 thf(c_0_336, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 1.96/0.60 thf(c_0_337, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 1.96/0.60 thf(c_0_338, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 1.96/0.60 thf(c_0_339, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 1.96/0.60 thf(c_0_340, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 1.96/0.60 thf(c_0_341, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 1.96/0.60 thf(c_0_342, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 1.96/0.60 thf(c_0_343, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 1.96/0.60 thf(c_0_344, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
% 1.96/0.60 thf(c_0_345, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
% 1.96/0.60 thf(c_0_346, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 1.96/0.60 thf(c_0_347, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 1.96/0.60 thf(c_0_348, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 1.96/0.60 thf(c_0_349, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 1.96/0.60 thf(c_0_350, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
% 1.96/0.60 thf(c_0_351, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
% 1.96/0.60 thf(c_0_352, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
% 1.96/0.60 thf(c_0_353, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 1.96/0.60 thf(c_0_354, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X1048:$i]:(((((X1 @ X1048)))&(![X1049:$i]:(((((X1 @ X1049)))=>(((X1048)=(X1049)))))))))))))), inference(apply_def,[status(thm)],[c_0_306, c_0_302])).
% 1.96/0.60 thf(c_0_355, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X1046:$i]:(((((X1 @ X1046)))&(![X1047:$i]:(((((X1 @ X1047)))=>(((X1046)=(X1047)))))))))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_302])).
% 1.96/0.60 thf(c_0_356, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X1044:$i]:(((((X1 @ X1044)))&(![X1045:$i]:(((((X1 @ X1045)))=>(((X1044)=(X1045)))))))))))))), inference(apply_def,[status(thm)],[c_0_308, c_0_302])).
% 1.96/0.60 thf(c_0_357, plain, ((emptyE1)<=>![X4:$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])).
% 1.96/0.60 thf(c_0_358, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_309])).
% 1.96/0.60 thf(c_0_359, plain, ((exuE2)=(![X1:$i > $o]:((((?[X1042:$i]:(((((X1 @ X1042)))&(![X1043:$i]:(((((X1 @ X1043)))=>(((X1042)=(X1043))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_310, c_0_302])).
% 1.96/0.60 thf(c_0_360, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.96/0.60 thf(c_0_361, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_309])).
% 1.96/0.60 thf(c_0_362, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_311, c_0_309])).
% 1.96/0.60 thf(c_0_363, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_309])).
% 1.96/0.60 thf(c_0_364, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.96/0.60 thf(c_0_365, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X1040:$i]:(((((X1 @ X1040)))&(![X1041:$i]:(((((X1 @ X1041)))=>(((X1040)=(X1041))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_312, c_0_302])).
% 1.96/0.60 thf(c_0_366, plain, ((exuE1)=(![X1:$i > $o]:((((?[X1038:$i]:(((((X1 @ X1038)))&(![X1039:$i]:(((((X1 @ X1039)))=>(((X1038)=(X1039))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_313, c_0_302])).
% 1.96/0.60 thf(c_0_367, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.96/0.60 thf(c_0_368, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.96/0.60 thf(c_0_369, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.96/0.60 thf(c_0_370, plain, ((descrp)=(![X1:$i > $o]:((((?[X1036:$i]:(((((X1 @ X1036)))&(![X1037:$i]:(((((X1 @ X1037)))=>(((X1036)=(X1037))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_314, c_0_302])).
% 1.96/0.60 thf(c_0_371, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X1034:$i]:(((((X6 @ X2 @ X1034)))&(![X1035:$i]:(((((X6 @ X2 @ X1035)))=>(((X1034)=(X1035)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_315, c_0_302])).
% 1.96/0.60 thf(c_0_372, plain, ((epred1_0)<=>![X1091:$i]:(?[X1092:$i]:((((![X1093:$i]:(((in @ X1093 @ X1092)=>![X1094:$i]:(((in @ X1094 @ X1093)=>(in @ X1094 @ X1091)))))&![X1095:$i, X1096:$i]:((((in @ X1095 @ X1091)&(in @ X1096 @ X1091))=>(![X1097:$i]:(((in @ X1097 @ X1092)=>((in @ X1095 @ X1097)<=>(in @ X1096 @ X1097))))=>((X1095)=(X1096))))))&![X1098:$i, X1099:$i]:((((in @ X1098 @ X1092)&(in @ X1099 @ X1092))=>(![X1100:$i]:(((in @ X1100 @ X1098)=>(in @ X1100 @ X1099)))|![X1101:$i]:(((in @ X1101 @ X1099)=>(in @ X1101 @ X1098)))))))&![X1102:$i]:(((![X1103:$i]:(((in @ X1103 @ X1102)=>(in @ X1103 @ X1091)))&?[X1104:$i]:((in @ X1104 @ X1102)))=>?[X1105:$i, X1106:$i]:(((((in @ X1105 @ X1092)&(in @ X1106 @ X1102))&~(?[X1107:$i]:(((in @ X1107 @ X1105)&(in @ X1107 @ X1102)))))&![X1108:$i]:(((in @ X1108 @ X1092)=>(![X1109:$i]:(((in @ X1109 @ X1108)=>(in @ X1109 @ X1105)))|(in @ X1106 @ X1108)))))))))))), introduced(definition)).
% 1.96/0.60 thf(c_0_373, negated_conjecture, ~((![X1062:$i, X1063:$i]:((![X1064:$i]:(((in @ X1064 @ X1062)<=>(in @ X1064 @ X1063)))=>((X1062)=(X1063))))=>(![X1065:$i]:(~(in @ X1065 @ emptyset))=>(![X1066:$i, X1067:$i, X1068:$i]:(((in @ X1068 @ (setadjoin @ X1066 @ X1067))<=>(((X1068)=(X1066))|(in @ X1068 @ X1067))))=>(![X1069:$i, X1070:$i]:(((in @ X1070 @ (powerset @ X1069))<=>![X1071:$i]:(((in @ X1071 @ X1070)=>(in @ X1071 @ X1069)))))=>(![X1072:$i, X1073:$i]:(((in @ X1073 @ (setunion @ X1072))<=>?[X1074:$i]:(((in @ X1073 @ X1074)&(in @ X1074 @ X1072)))))=>((in @ emptyset @ omega)=>(![X1075:$i]:(((in @ X1075 @ omega)=>(in @ (setadjoin @ X1075 @ X1075) @ omega)))=>(![X1076:$i]:((((in @ emptyset @ X1076)&![X1077:$i]:((((in @ X1077 @ omega)&(in @ X1077 @ X1076))=>(in @ (setadjoin @ X1077 @ X1077) @ X1076))))=>![X1078:$i]:(((in @ X1078 @ omega)=>(in @ X1078 @ X1076)))))=>(![X1079:$i > $i > $o, X1080:$i]:((![X1081:$i]:(((in @ X1081 @ X1080)=>?[X1082:$i]:(((X1079 @ X1081 @ X1082)&![X1083:$i]:(((X1079 @ X1081 @ X1083)=>((X1082)=(X1083))))))))=>?[X1084:$i]:(![X1085:$i]:(((in @ X1085 @ X1084)<=>?[X1086:$i]:(((in @ X1086 @ X1080)&(X1079 @ X1086 @ X1085))))))))=>(![X1087:$i]:((?[X1088:$i]:((in @ X1088 @ X1087))=>?[X1089:$i]:(((in @ X1089 @ X1087)&~(?[X1090:$i]:(((in @ X1090 @ X1089)&(in @ X1090 @ X1087))))))))=>((epred1_0)=>(![X1110:$i > $o]:((?[X1111:$i]:(((X1110 @ X1111)&![X1112:$i]:(((X1110 @ X1112)=>((X1111)=(X1112))))))=>(X1110 @ (descr @ (^[Z0:$i]:(X1110 @ Z0))))))=>(![X1113:$i, X1114:$i > $o, X1115:$i]:(((in @ X1115 @ X1113)=>((X1114 @ X1115)=>(in @ X1115 @ (dsetconstr @ X1113 @ X1114)))))=>(![X1116:$i, X1117:$i > $o, X1118:$i]:(((in @ X1118 @ (dsetconstr @ X1116 @ X1117))=>(in @ X1118 @ X1116)))=>(![X1119:$i, X1120:$i > $o, X1121:$i]:(((in @ X1121 @ (dsetconstr @ X1119 @ X1120))=>(X1120 @ X1121)))=>(![X1122:$i > $o]:((?[X1123:$i]:(((X1122 @ X1123)&![X1124:$i]:(((X1122 @ X1124)=>((X1123)=(X1124))))))=>?[X1125:$i]:(((X1122 @ X1125)&![X1126:$i]:(((X1122 @ X1126)=>((X1125)=(X1126))))))))=>(![X1127:$o, X1128:$i]:(((in @ X1128 @ (prop2set @ ((X1127))))=>(X1127)))=>(![X1129:$i]:(((in @ X1129 @ emptyset)=>![X1130:$o]:((X1130))))=>(![X1131:$i]:(((in @ X1131 @ emptyset)=>~($true)))=>(![X1132:$i]:(~(in @ X1132 @ emptyset))=>(![X1133:$i > $o]:((?[X1134:$i]:(((X1133 @ X1134)&![X1135:$i]:(((X1133 @ X1135)=>((X1134)=(X1135))))))=>?[X1136:$i]:((X1133 @ X1136))))=>(![X1137:$i, X1138:$i]:((![X1139:$i]:(((in @ X1139 @ X1137)=>(in @ X1139 @ X1138)))=>(![X1140:$i]:(((in @ X1140 @ X1138)=>(in @ X1140 @ X1137)))=>((X1137)=(X1138)))))=>(![X1141:$i]:((![X1142:$i]:(~(in @ X1142 @ X1141))=>((X1141)=(emptyset))))=>(![X1143:$i]:((![X1144:$i]:(~(in @ X1144 @ X1143))=>((X1143)=(emptyset))))=>(![X1145:$i, X1146:$i > $o, X1147:$i]:(((in @ X1147 @ X1145)=>((in @ X1147 @ (dsetconstr @ X1145 @ X1146))<=>(X1146 @ X1147))))=>(![X1148:$i]:((((X1148)!=(emptyset))=>?[X1149:$i]:((in @ X1149 @ X1148))))=>(![X1150:$i, X1151:$i > $o, X1152:$i]:(((in @ X1152 @ X1150)=>((X1151 @ X1152)=>((dsetconstr @ X1150 @ X1151)!=(emptyset)))))=>(![X1153:$i]:((?[X1154:$i]:((in @ X1154 @ X1153))=>((X1153)!=(emptyset))))=>(![X1155:$i, X1156:$i]:((in @ X1155 @ (setadjoin @ X1155 @ X1156)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1157:$i, X1158:$i, X1159:$i]:(((in @ X1159 @ X1158)=>(in @ X1159 @ (setadjoin @ X1157 @ X1158))))=>(![X1160:$i, X1161:$i, X1162:$i]:(((in @ X1162 @ (setadjoin @ X1160 @ X1161))=>![X1163:$o]:(((((X1162)=(X1160))=>(X1163))=>(((in @ X1162 @ X1161)=>(X1163))=>(X1163))))))=>(![X1164:$i, X1165:$i, X1166:$i]:(((in @ X1166 @ (setadjoin @ X1164 @ X1165))=>(((X1166)=(X1164))|(in @ X1166 @ X1165))))=>(![X1167:$i]:(((dsetconstr @ X1167 @ (^[Z0:$i]:($true)))=(X1167)))=>(![X1168:$i, X1169:$i]:((![X1170:$i]:(((in @ X1170 @ X1169)=>(in @ X1170 @ X1168)))=>(in @ X1169 @ (powerset @ X1168))))=>(![X1171:$i]:((in @ emptyset @ (powerset @ X1171)))=>(![X1172:$i]:((in @ emptyset @ (powerset @ X1172)))=>(![X1173:$i, X1174:$i, X1175:$i]:(((in @ X1174 @ (powerset @ X1173))=>((in @ X1175 @ X1174)=>(in @ X1175 @ X1173))))=>(![X1176:$i, X1177:$i, X1178:$i]:(((in @ X1177 @ X1178)=>((in @ X1178 @ X1176)=>(in @ X1177 @ (setunion @ X1176)))))=>(![X1179:$i, X1180:$i]:(((in @ X1180 @ (setunion @ X1179))=>![X1181:$o]:((![X1182:$i]:(((in @ X1180 @ X1182)=>((in @ X1182 @ X1179)=>(X1181))))=>(X1181)))))=>(![X1183:$i, X1184:$i]:(((in @ X1184 @ X1183)=>(in @ X1184 @ (powerset @ (setunion @ X1183)))))=>(![X1185:$i > $o]:((?[X1186:$i]:(((X1185 @ X1186)&![X1187:$i]:(((X1185 @ X1187)=>((X1186)=(X1187))))))=>?[X1188:$i]:(![X1189:$i]:(((X1185 @ X1189)<=>((X1189)=(X1188)))))))=>(![X1190:$i]:((((X1190)!=(emptyset))=>?[X1191:$i]:(((in @ X1191 @ X1190)&$true))))=>(![X1192:$i, X1193:$i]:(((in @ X1192 @ (setadjoin @ X1193 @ emptyset))=>((X1192)=(X1193))))=>(![X1194:$i, X1195:$i]:((((X1194)!=(X1195))=>~(in @ X1195 @ (setadjoin @ X1194 @ emptyset))))=>(![X1196:$i, X1197:$i]:((((X1196)=(X1197))=>(in @ X1196 @ (setadjoin @ X1197 @ emptyset))))=>(![X1198:$i, X1199:$i]:(((in @ X1198 @ (setadjoin @ X1199 @ emptyset))=>(in @ X1199 @ (setadjoin @ X1198 @ emptyset))))=>(![X1200:$i, X1201:$i, X1202:$i]:(((in @ X1202 @ (setadjoin @ X1200 @ (setadjoin @ X1201 @ emptyset)))=>(((X1202)=(X1200))|((X1202)=(X1201)))))=>(![X1203:$i, X1204:$i]:((in @ X1203 @ (setadjoin @ X1203 @ (setadjoin @ X1204 @ emptyset))))=>(![X1205:$i, X1206:$i]:((in @ X1206 @ (setadjoin @ X1205 @ (setadjoin @ X1206 @ emptyset))))=>(![X1207:$i, X1208:$i > $o]:((?[X1209:$i]:(((in @ X1209 @ X1207)&(X1208 @ X1209)))=>(((dsetconstr @ X1207 @ X1208)=(emptyset))=>~($true))))=>(![X1210:$i > $o, X1211:$i]:(((in @ X1211 @ emptyset)=>(X1210 @ X1211)))=>(![X1212:$i, X1213:$i > $o]:((~(![X1214:$i]:(((in @ X1214 @ X1212)=>(X1213 @ X1214))))=>?[X1215:$i]:(((in @ X1215 @ X1212)&~((X1213 @ X1215))))))=>(![X1216:$i, X1217:$i > $o]:((![X1218:$i]:(((in @ X1218 @ X1216)=>~((X1217 @ X1218))))=>~(?[X1219:$i]:(((in @ X1219 @ X1216)&(X1217 @ X1219))))))=>(![X1220:$i, X1221:$i > $o]:((~(?[X1222:$i]:(((in @ X1222 @ X1220)&(X1221 @ X1222))))=>![X1223:$i]:(((in @ X1223 @ X1220)=>~((X1221 @ X1223))))))=>(![X1224:$i, X1225:$i > $o]:((?[X1226:$i]:(((in @ X1226 @ X1224)&~((X1225 @ X1226))))=>~(![X1227:$i]:(((in @ X1227 @ X1224)=>(X1225 @ X1227))))))=>(![X1228:$o]:(((X1228)=>(in @ emptyset @ (prop2set @ ((X1228))))))=>((prop2set2propI)=>(![X1229:$i, X1230:$i > $o]:((~(?[X1231:$i]:(((in @ X1231 @ X1229)&(X1230 @ X1231))))=>![X1232:$i]:(((in @ X1232 @ X1229)=>~((X1230 @ X1232))))))=>(![X1233:$i, X1234:$i > $o]:((~(![X1235:$i]:(((in @ X1235 @ X1233)=>(X1234 @ X1235))))=>?[X1236:$i]:(((in @ X1236 @ X1233)&~((X1234 @ X1236))))))=>(![X1237:$i > $o]:((?[X1238:$i]:(((X1237 @ X1238)&![X1239:$i]:(((X1237 @ X1239)=>((X1238)=(X1239))))))=>?[X1240:$i]:(((X1237 @ X1240)&![X1241:$i]:(((X1237 @ X1241)=>((X1240)=(X1241))))))))=>(![X1242:$i > $o]:((?[X1243:$i]:((X1242 @ X1243))=>(![X1244:$i, X1245:$i]:(((X1242 @ X1244)=>((X1242 @ X1245)=>((X1244)=(X1245)))))=>?[X1246:$i]:(((X1242 @ X1246)&![X1247:$i]:(((X1242 @ X1247)=>((X1246)=(X1247)))))))))=>(![X1248:$i > $o]:((?[X1249:$i]:(![X1250:$i]:(((X1248 @ X1250)<=>((X1250)=(X1249)))))=>?[X1251:$i]:(((X1248 @ X1251)&![X1252:$i]:(((X1248 @ X1252)=>((X1251)=(X1252))))))))=>(![X1253:$i, X1254:$i]:((((X1253)=(X1254))=>![X1255:$i, X1256:$i]:((((X1255)=(X1256))=>((in @ X1255 @ X1253)=>(in @ X1256 @ X1254))))))=>(![X1257:$i, X1258:$i]:((((X1257)=(X1258))=>![X1259:$i, X1260:$i]:((((X1259)=(X1260))=>((in @ X1259 @ X1257)<=>(in @ X1260 @ X1258))))))=>(![X1261:$i > $o]:((?[X1262:$i]:(((X1261 @ X1262)&![X1263:$i]:(((X1261 @ X1263)=>((X1262)=(X1263))))))=>![X1264:$i, X1265:$i]:(((X1261 @ X1264)=>((X1261 @ X1265)=>((X1264)=(X1265)))))))=>(![X1266:$i > $o, X1267:$i > $o]:((![X1268:$i, X1269:$i]:((((X1268)=(X1269))=>((X1266 @ X1268)<=>(X1267 @ X1269))))=>(?[X1270:$i]:(((X1266 @ X1270)&![X1271:$i]:(((X1266 @ X1271)=>((X1270)=(X1271))))))<=>?[X1272:$i]:(((X1267 @ X1272)&![X1273:$i]:(((X1267 @ X1273)=>((X1272)=(X1273)))))))))=>(((emptyset)=(emptyset))=>(![X1274:$i, X1275:$i]:((((X1274)=(X1275))=>![X1276:$i, X1277:$i]:((((X1276)=(X1277))=>((setadjoin @ X1274 @ X1276)=(setadjoin @ X1275 @ X1277))))))=>(![X1278:$i, X1279:$i]:((((X1278)=(X1279))=>((powerset @ X1278)=(powerset @ X1279))))=>(![X1280:$i, X1281:$i]:((((X1280)=(X1281))=>((setunion @ X1280)=(setunion @ X1281))))=>(((omega)=(omega))=>(![X1282:$i > $o]:((?[X1283:$i]:(((X1282 @ X1283)&![X1284:$i]:(((X1282 @ X1284)=>((X1283)=(X1284))))))=>![X1285:$i, X1286:$i]:(((X1282 @ X1285)=>((X1282 @ X1286)=>((X1285)=(X1286)))))))=>(![X1287:$i > $o, X1288:$i > $o]:((![X1289:$i, X1290:$i]:((((X1289)=(X1290))=>((X1287 @ X1289)<=>(X1288 @ X1290))))=>(?[X1291:$i]:(((X1287 @ X1291)&![X1292:$i]:(((X1287 @ X1292)=>((X1291)=(X1292))))))=>(?[X1293:$i]:(((X1288 @ X1293)&![X1294:$i]:(((X1288 @ X1294)=>((X1293)=(X1294))))))=>((descr @ X1287)=(descr @ X1288))))))=>(![X1295:$i, X1296:$i]:((((X1295)=(X1296))=>![X1297:$i > $o, X1298:$i > $o]:((![X1299:$i]:(((in @ X1299 @ X1295)=>![X1300:$i]:(((in @ X1300 @ X1296)=>(((X1299)=(X1300))=>((X1297 @ X1299)<=>(X1298 @ X1300)))))))=>((dsetconstr @ X1295 @ X1297)=(dsetconstr @ X1296 @ X1298))))))=>(![X1301:$i, X1302:$i]:((![X1303:$i]:(((in @ X1303 @ X1301)=>(in @ X1303 @ X1302)))=>(subset @ X1301 @ X1302)))=>(![X1304:$i, X1305:$i]:((((X1304)=(X1305))=>(subset @ X1305 @ X1304)))=>(![X1306:$i, X1307:$i]:((((X1306)=(X1307))=>(subset @ X1306 @ X1307)))=>(![X1308:$i, X1309:$i]:((![X1310:$i]:(((in @ X1310 @ X1308)=>(in @ X1310 @ X1309)))=>(subset @ X1308 @ X1309)))=>(![X1311:$i]:((subset @ emptyset @ X1311))=>(![X1312:$i, X1313:$i, X1314:$i]:(((subset @ X1312 @ X1313)=>((in @ X1314 @ X1312)=>(in @ X1314 @ X1313))))=>(![X1315:$i, X1316:$i, X1317:$i]:(((subset @ X1315 @ X1316)=>(~(in @ X1317 @ X1316)=>~(in @ X1317 @ X1315))))=>(![X1318:$i, X1319:$i, X1320:$i]:(((in @ X1320 @ X1318)=>(~(in @ X1320 @ X1319)=>~(subset @ X1318 @ X1319))))=>(![X1321:$i, X1322:$i]:((~(subset @ X1321 @ X1322)=>((X1321)!=(X1322))))=>(![X1323:$i, X1324:$i, X1325:$i]:(((in @ X1325 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X1917:$i]:(((in @ X1917 @ (powerset @ X1916))=>![X1918:$i]:(((in @ X1918 @ (powerset @ X1916))=>![X1919:$i]:(((in @ X1919 @ X1916)=>(~(in @ X1919 @ X1917)=>(~(in @ X1919 @ X1918)=>~(in @ X1919 @ (binunion @ X1917 @ X1918))))))))))=>(![X1920:$i, X1921:$i]:(((in @ X1921 @ (powerset @ X1920))=>![X1922:$i]:(((in @ X1922 @ (powerset @ X1920))=>![X1923:$i]:(((in @ X1923 @ X1920)=>((in @ X1923 @ (setminus @ X1920 @ (binunion @ X1921 @ X1922)))=>(in @ X1923 @ (setminus @ X1920 @ X1921)))))))))=>(![X1924:$i, X1925:$i]:(((in @ X1925 @ (powerset @ X1924))=>![X1926:$i]:(((in @ X1926 @ (powerset @ X1924))=>(in @ (setminus @ X1924 @ (binunion @ X1925 @ X1926)) @ (powerset @ (setminus @ X1924 @ X1925)))))))=>(![X1927:$i, X1928:$i]:(((in @ X1928 @ (powerset @ X1927))=>![X1929:$i]:(((in @ X1929 @ (powerset @ X1927))=>![X1930:$i]:(((in @ X1930 @ X1927)=>((in @ X1930 @ (setminus @ X1927 @ (binunion @ X1928 @ X1929)))=>(in @ X1930 @ (setminus @ X1927 @ X1929)))))))))=>(![X1931:$i, X1932:$i]:(((in @ X1932 @ (powerset @ X1931))=>![X1933:$i]:(((in @ X1933 @ (powerset @ X1931))=>![X1934:$i]:(((in @ X1934 @ X1931)=>((in @ X1934 @ (setminus @ X1931 @ (binintersect @ X1932 @ X1933)))=>(in @ X1934 @ (binunion @ (setminus @ X1931 @ X1932) @ (setminus @ X1931 @ X1933))))))))))=>(![X1935:$i, X1936:$i]:(((in @ X1936 @ (powerset @ X1935))=>![X1937:$i]:(((in @ X1937 @ (powerset @ X1935))=>![X1938:$i]:(((in @ X1938 @ X1935)=>((in @ X1938 @ (binunion @ (setminus @ X1935 @ X1936) @ (setminus @ X1935 @ X1937)))=>(in @ X1938 @ (setminus @ X1935 @ (binintersect @ X1936 @ X1937))))))))))=>(![X1939:$i, X1940:$i]:(((in @ X1940 @ (powerset @ X1939))=>![X1941:$i]:(((in @ X1941 @ (powerset @ X1939))=>((setminus @ X1939 @ (binintersect @ X1940 @ X1941))=(binunion @ (setminus @ X1939 @ X1940) @ (setminus @ X1939 @ X1941)))))))=>(![X1942:$i, X1943:$i]:(((in @ X1943 @ (powerset @ X1942))=>![X1944:$i]:(((in @ X1944 @ (powerset @ X1942))=>![X1945:$i]:(((in @ X1945 @ X1942)=>((in @ X1945 @ (setminus @ X1942 @ 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X35)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_316, complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), emptyset__Cong]), contraSubsetComplement]), c_0_317]), complementTcontraSubset]), c_0_318]), binunionTILcontra]), in__Cong]), binunionTIRcontra]), inCongP]), inIntersectImpInUnion]), setadjoin__Cong]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), subsetI1]), demorgan2b2]), c_0_319]), demorgan2b]), c_0_320]), demorgan2]), c_0_321]), woz13rule0]), omega__Cong]), woz13rule1]), setunion__Cong]), woz13rule2]), powerset__Cong]), woz13rule3]), eqimpsubset2]), woz13rule4]), woz1_1]), woz1_2]), woz1_3]), woz1_4]), woz1_5]), breln1all2]), breln1SetBreln1]), c_0_322]), breln1all1]), subbreln1]), eqbreln1]), breln1invprop]), breln1invI]), notequalI1]), breln1invE]), notsubsetI]), breln1compprop]), subsetE2]), breln1compI]), subsetE]), breln1compE]), emptysetsubset]), breln1compEex]), subsetI2]), breln1unionprop]), eqimpsubset1]), breln1unionIL]), notequalI2]), setminusILneg]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), powersetI1]), upairset2IR]), binunionIL]), c_0_323]), c_0_324]), powersetsubset]), inPowerset]), powersetE1]), binunionIR]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), binunionEcases]), binintersectLsub]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), bs114d]), app]), c_0_325]), c_0_326]), funcextLem]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), c_0_327]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), setminusEL]), setminusI]), setminusIRneg]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), secondinupair]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), upairset2E]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), cartprodmempair]), c_0_328]), c_0_329]), c_0_330]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), c_0_331]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), theprop]), c_0_332]), setukpairinjL1]), singletonsuniq]), setukpairinjL]), c_0_333]), setukpairinjR]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), ksndpairEq]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), cartprodpairsurjEq]), c_0_334]), c_0_335]), c_0_336]), c_0_337]), c_0_338]), c_0_339]), c_0_340]), c_0_341]), c_0_342]), c_0_343]), funcinfuncset]), ap2p]), infuncsetfunc]), brelnall2]), brelnall1]), funcGraphProp4]), c_0_344]), ap2apEq2]), ap2apEq1]), funcext2]), funcext]), eqbreln]), subbreln]), c_0_345]), c_0_346]), c_0_347]), c_0_348]), c_0_349]), c_0_350]), c_0_351]), c_0_352]), c_0_353]), binunionT_lem]), binintersectT_lem]), iftrueorfalse]), iffalse]), iftrue]), theeq]), ifp]), powersetT_lem]), complementTI1]), powersetTE1]), powersetTI1]), subsetTI]), setextT]), complementT_lem]), setminusT_lem]), complementTE1]), doubleComplementI1]), contrasubsetT3]), contrasubsetT2]), contrasubsetT1]), contrasubsetT]), binintersectTERcontra]), binintersectTELcontra]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), c_0_354]), c_0_355]), c_0_356]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_357]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_358]), c_0_359]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_360]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_361]), c_0_362]), c_0_363]), c_0_364]), noeltsimpempty]), emptyI]), setext]), c_0_365]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_366]), c_0_367]), c_0_368]), c_0_369]), c_0_370]), wellorderingAx]), foundationAx]), c_0_371]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_372])).
% 1.96/0.60 thf(c_0_374, negated_conjecture, ![X2064:$i, X2065:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2077:$i, X2078:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2086:$i, X2087:$i > $i > $o, X2088:$i, X2090:$i, X2093:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2100:$i, X2101:$i > $o, X2102:$i, X2104:$i, X2105:$i > $o, X2106:$i, X2107:$i, X2108:$i > $o, X2109:$i, X2110:$i, X2111:$i > $o, X2112:$i, X2113:$i > $o, X2114:$i, X2117:$i, X2118:$o, X2119:$i, X2120:$i, X2121:$o, X2122:$i, X2123:$i, X2124:$i > $o, X2125:$i, X2128:$i, X2129:$i, X2132:$i, X2134:$i, X2136:$i, X2137:$i > $o, X2138:$i, X2139:$i, X2141:$i, X2142:$i > $o, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$o, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$o, X2174:$i, X2175:$i, X2176:$i > $o, X2177:$i, X2180:$i, X2181:$i, X2182:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i > $o, X2201:$i, X2202:$i > $o, X2203:$i, X2204:$i, X2205:$i > $o, X2206:$i, X2208:$i, X2209:$i > $o, X2211:$i, X2212:$i, X2213:$i > $o, X2215:$i, X2216:$i, X2217:$i > $o, X2218:$i, X2220:$o, X2221:$i, X2222:$i > $o, X2224:$i, X2225:$i, X2226:$i > $o, X2227:$i, X2229:$i > $o, X2230:$i, X2233:$i, X2234:$i > $o, X2235:$i, X2239:$i, X2240:$i > $o, X2241:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i > $o, X2254:$i, X2256:$i, X2257:$i, X2258:$i > $o, X2259:$i > $o, X2262:$i, X2265:$i, X2266:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i > $o, X2279:$i, X2281:$i, X2282:$i, X2283:$i > $o, X2284:$i > $o, X2287:$i, X2289:$i, X2291:$i, X2292:$i, X2293:$i > $o, X2294:$i > $o, X2297:$i, X2298:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i > $o, X2345:$i, X2346:$i > $o, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$o, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$o, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i > $o, X2501:$i, X2502:$i, X2503:$i > $o, X2505:$i, X2506:$i > $o, X2507:$i, X2509:$i, X2510:$i > $o, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i > $i > $o, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i > $i > $o, X2591:$i, X2592:$i, X2593:$i > $i > $o, X2594:$i, X2595:$i, X2596:$i > $i > $o, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i > $i > $o, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i > $i > $o, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i > $i > $o, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2623:$i, X2624:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i, X2630:$i, X2631:$i, X2632:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i > $i, X2640:$i, X2641:$i, X2642:$i > $i, X2644:$i, X2645:$i, X2646:$i > $i, X2648:$i, X2649:$i, X2650:$i, X2651:$i > $o, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i > $o, X2661:$i, X2662:$i, X2663:$i > $o, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$i, X2723:$i, X2724:$i, X2725:$i > $i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i > $i, X2735:$i, X2736:$i, X2737:$i > $i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$o, X2745:$i, X2746:$i, X2747:$i, X2748:$o, X2749:$i, X2750:$i, X2751:$i, X2752:$o, X2753:$i, X2754:$i, X2755:$i, X2756:$o, X2757:$i, X2758:$i, X2759:$i, X2760:$o, X2761:$i, X2762:$i, X2763:$i, X2764:$o, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$o, X2771:$i, X2772:$i, X2773:$i, X2774:$o, X2775:$i, X2776:$i, X2777:$i, X2778:$o, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2799:$i, X2800:$i, X2801:$i, X2803:$i, X2804:$i, X2805:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2851:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2856:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i, X2871:$i, X2872:$i, X2873:$i, X2874:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$i, X2885:$i, X2886:$i, X2887:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2901:$i, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$o, X2911:$i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$i, X2951:$i, X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i, X2976:$i, X2977:$i, X2978:$i, X2979:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i > $o, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i > $i > $o, X3002:$i, X3003:$i, X3004:$i > $o, X3007:$i, X3008:$i, X3009:$i, X3010:$i, X3013:$i, X3014:$i, X3015:$i, X3020:$i, X3021:$i, 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@ X3013 @ X3014 @ X3015) @ X3013)|((X3014)=(X3015))|~(in @ (kpair @ (esk93_3 @ X3013 @ X3014 @ X3015) @ (esk94_3 @ X3013 @ X3014 @ X3015)) @ X3015)|~(breln1 @ X3013 @ X3015)|~(breln1 @ X3013 @ X3014))&(((in @ (esk96_3 @ X3013 @ X3014 @ X3015) @ X3013)|((X3014)=(X3015))|~(in @ (kpair @ (esk93_3 @ X3013 @ X3014 @ X3015) @ (esk94_3 @ X3013 @ X3014 @ X3015)) @ X3015)|~(breln1 @ X3013 @ X3015)|~(breln1 @ X3013 @ X3014))&(((in @ (kpair @ (esk95_3 @ X3013 @ X3014 @ X3015) @ (esk96_3 @ X3013 @ X3014 @ X3015)) @ X3015)|((X3014)=(X3015))|~(in @ (kpair @ (esk93_3 @ X3013 @ X3014 @ X3015) @ (esk94_3 @ X3013 @ X3014 @ X3015)) @ X3015)|~(breln1 @ X3013 @ X3015)|~(breln1 @ X3013 @ X3014))&(~(in @ (kpair @ (esk95_3 @ X3013 @ X3014 @ X3015) @ (esk96_3 @ X3013 @ X3014 @ X3015)) @ X3014)|((X3014)=(X3015))|~(in @ (kpair @ (esk93_3 @ X3013 @ X3014 @ X3015) @ (esk94_3 @ X3013 @ X3014 @ X3015)) @ X3015)|~(breln1 @ X3013 @ X3015)|~(breln1 @ X3013 @ X3014))))))))&((~(breln1 @ X3020 @ X3021)|(breln1 @ X3020 @ (breln1invset @ X3020 @ X3021)))&((~(breln1 @ X3022 @ X3023)|(~(in @ X3024 @ X3022)|(~(in @ X3025 @ X3022)|(~(in @ (kpair @ X3024 @ X3025) @ X3023)|(in @ (kpair @ X3025 @ X3024) @ (breln1invset @ X3022 @ X3023))))))&((~(breln1 @ X3026 @ X3027)|(~(in @ X3028 @ X3026)|(~(in @ X3029 @ X3026)|(~(in @ (kpair @ X3029 @ X3028) @ (breln1invset @ X3026 @ X3027))|(in @ (kpair @ X3028 @ X3029) @ X3027)))))&((~(breln1 @ X3030 @ X3031)|(~(breln1 @ X3030 @ X3032)|(breln1 @ X3030 @ (breln1compset @ X3030 @ X3031 @ X3032))))&((~(breln1 @ X3033 @ X3034)|(~(breln1 @ X3033 @ X3035)|(~(in @ X3036 @ X3033)|(~(in @ X3037 @ X3033)|(~(in @ X3038 @ X3033)|(~(in @ (kpair @ X3036 @ X3038) @ X3034)|(~(in @ (kpair @ X3038 @ X3037) @ X3035)|(in @ (kpair @ X3036 @ X3037) @ (breln1compset @ X3033 @ X3034 @ X3035)))))))))&(((((in @ (esk97_5 @ X3039 @ X3040 @ X3041 @ X3042 @ X3043) @ X3039)|~(in @ (kpair @ X3042 @ X3043) @ (breln1compset @ X3039 @ X3040 @ X3041))|~(in @ X3043 @ X3039)|~(in @ X3042 @ X3039)|~(breln1 @ X3039 @ X3041)|~(breln1 @ X3039 @ X3040))&((in @ (kpair @ X3042 @ (esk97_5 @ X3039 @ X3040 @ X3041 @ X3042 @ X3043)) @ X3040)|~(in @ (kpair @ X3042 @ X3043) @ (breln1compset @ X3039 @ X3040 @ X3041))|~(in @ X3043 @ X3039)|~(in @ X3042 @ X3039)|~(breln1 @ X3039 @ X3041)|~(breln1 @ X3039 @ X3040)))&((in @ (kpair @ (esk97_5 @ X3039 @ X3040 @ X3041 @ X3042 @ X3043) @ X3043) @ X3041)|~(in @ (kpair @ X3042 @ X3043) @ (breln1compset @ X3039 @ X3040 @ X3041))|~(in @ X3043 @ X3039)|~(in @ X3042 @ X3039)|~(breln1 @ X3039 @ X3041)|~(breln1 @ X3039 @ X3040)))&((((in @ (esk98_6 @ X3045 @ X3046 @ X3047 @ X3048 @ X3049 @ X3050) @ X3045)|(X3050)|~(in @ (kpair @ X3048 @ X3049) @ (breln1compset @ X3045 @ X3046 @ X3047))|~(in @ X3049 @ X3045)|~(in @ X3048 @ X3045)|~(breln1 @ X3045 @ X3047)|~(breln1 @ X3045 @ X3046))&(((in @ (kpair @ X3048 @ (esk98_6 @ X3045 @ X3046 @ X3047 @ X3048 @ X3049 @ X3050)) @ X3046)|(X3050)|~(in @ (kpair @ X3048 @ X3049) @ (breln1compset @ X3045 @ X3046 @ X3047))|~(in @ X3049 @ X3045)|~(in @ X3048 @ X3045)|~(breln1 @ X3045 @ X3047)|~(breln1 @ X3045 @ X3046))&(((in @ (kpair @ (esk98_6 @ X3045 @ X3046 @ X3047 @ X3048 @ X3049 @ X3050) @ X3049) @ X3047)|(X3050)|~(in @ (kpair @ X3048 @ X3049) @ (breln1compset @ X3045 @ X3046 @ X3047))|~(in @ X3049 @ X3045)|~(in @ X3048 @ X3045)|~(breln1 @ X3045 @ X3047)|~(breln1 @ X3045 @ X3046))&(~(X3050)|(X3050)|~(in @ (kpair @ X3048 @ X3049) @ (breln1compset @ X3045 @ X3046 @ X3047))|~(in @ X3049 @ X3045)|~(in @ X3048 @ X3045)|~(breln1 @ X3045 @ X3047)|~(breln1 @ X3045 @ X3046)))))&((~(breln1 @ X3052 @ X3053)|(~(breln1 @ X3052 @ X3054)|(breln1 @ X3052 @ (binunion @ X3053 @ X3054))))&((~(breln1 @ X3055 @ X3056)|(~(breln1 @ X3055 @ X3057)|(~(in @ X3058 @ X3055)|(~(in @ X3059 @ X3055)|(~(in @ (kpair @ X3058 @ X3059) @ X3056)|(in @ (kpair @ X3058 @ X3059) @ (binunion @ X3056 @ X3057)))))))&((breln1 @ esk99_0 @ esk100_0)&((breln1 @ esk99_0 @ esk101_0)&((in @ esk102_0 @ esk99_0)&((in @ esk103_0 @ esk99_0)&((in @ (kpair @ esk102_0 @ esk103_0) @ esk101_0)&~(in @ (kpair @ esk102_0 @ esk103_0) @ (binunion @ esk100_0 @ esk101_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_373])])])])])])])).
% 1.96/0.60 thf(c_0_375, negated_conjecture, ~((in @ (kpair @ esk102_0 @ esk103_0) @ (binunion @ esk100_0 @ esk101_0))), inference(split_conjunct,[status(thm)],[c_0_374])).
% 1.96/0.60 thf(c_0_376, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X4 @ X3))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_374])).
% 1.96/0.60 thf(c_0_377, negated_conjecture, (in @ (kpair @ esk102_0 @ esk103_0) @ esk101_0), inference(split_conjunct,[status(thm)],[c_0_374])).
% 1.96/0.60 thf(c_0_378, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_375, c_0_376]), c_0_377])]), ['proof']).
% 1.96/0.60 % SZS output end CNFRefutation
% 1.96/0.60 % Parsed axioms : 651
% 1.96/0.60 % Removed by relevancy pruning/SinE : 350
% 1.96/0.60 % Initial clauses : 519
% 1.96/0.60 % Removed in clause preprocessing : 33
% 1.96/0.60 % Initial clauses in saturation : 486
% 1.96/0.60 % Processed clauses : 135
% 1.96/0.60 % ...of these trivial : 12
% 1.96/0.60 % ...subsumed : 24
% 1.96/0.60 % ...remaining for further processing : 99
% 1.96/0.60 % Other redundant clauses eliminated : 12
% 1.96/0.60 % Clauses deleted for lack of memory : 0
% 1.96/0.60 % Backward-subsumed : 0
% 1.96/0.60 % Backward-rewritten : 2
% 1.96/0.60 % Generated clauses : 210
% 1.96/0.60 % ...of the previous two non-redundant : 136
% 1.96/0.60 % ...aggressively subsumed : 0
% 1.96/0.60 % Contextual simplify-reflections : 0
% 1.96/0.60 % Paramodulations : 196
% 1.96/0.60 % Factorizations : 0
% 1.96/0.60 % NegExts : 0
% 1.96/0.60 % Equation resolutions : 14
% 1.96/0.60 % Disequality decompositions : 0
% 1.96/0.60 % Total rewrite steps : 80
% 1.96/0.60 % ...of those cached : 47
% 1.96/0.60 % Propositional unsat checks : 0
% 1.96/0.60 % Propositional check models : 0
% 1.96/0.60 % Propositional check unsatisfiable : 0
% 1.96/0.60 % Propositional clauses : 0
% 1.96/0.60 % Propositional clauses after purity: 0
% 1.96/0.60 % Propositional unsat core size : 0
% 1.96/0.60 % Propositional preprocessing time : 0.000
% 1.96/0.60 % Propositional encoding time : 0.000
% 1.96/0.60 % Propositional solver time : 0.000
% 1.96/0.60 % Success case prop preproc time : 0.000
% 1.96/0.60 % Success case prop encoding time : 0.000
% 1.96/0.60 % Success case prop solver time : 0.000
% 1.96/0.60 % Current number of processed clauses : 91
% 1.96/0.60 % Positive orientable unit clauses : 48
% 1.96/0.60 % Positive unorientable unit clauses: 0
% 1.96/0.60 % Negative unit clauses : 2
% 1.96/0.60 % Non-unit-clauses : 41
% 1.96/0.60 % Current number of unprocessed clauses: 487
% 1.96/0.60 % ...number of literals in the above : 1733
% 1.96/0.60 % Current number of archived formulas : 0
% 1.96/0.60 % Current number of archived clauses : 2
% 1.96/0.60 % Clause-clause subsumption calls (NU) : 180
% 1.96/0.60 % Rec. Clause-clause subsumption calls : 167
% 1.96/0.60 % Non-unit clause-clause subsumptions : 16
% 1.96/0.60 % Unit Clause-clause subsumption calls : 21
% 1.96/0.60 % Rewrite failures with RHS unbound : 0
% 1.96/0.60 % BW rewrite match attempts : 8
% 1.96/0.60 % BW rewrite match successes : 2
% 1.96/0.60 % Condensation attempts : 0
% 1.96/0.60 % Condensation successes : 0
% 1.96/0.60 % Termbank termtop insertions : 84828
% 1.96/0.60 % Search garbage collected termcells : 32928
% 1.96/0.60
% 1.96/0.60 % -------------------------------------------------
% 1.96/0.60 % User time : 0.232 s
% 1.96/0.60 % System time : 0.020 s
% 1.96/0.60 % Total time : 0.252 s
% 1.96/0.60 % Maximum resident set size: 11796 pages
% 1.96/0.60
% 1.96/0.60 % -------------------------------------------------
% 1.96/0.60 % User time : 0.499 s
% 1.96/0.60 % System time : 0.124 s
% 1.96/0.60 % Total time : 0.623 s
% 1.96/0.60 % Maximum resident set size: 5632 pages
% 1.96/0.60 % E exiting
%------------------------------------------------------------------------------