%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU765^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : 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 08:25:32 AM UTC 2026
% Result : Theorem 52.90s 10.87s
% Output : CNFRefutation 52.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU765^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n003.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 14:25:13 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p
% 52.90/10.87 % Version: 3.5.1-ho
% 52.90/10.87 % Preprocessing class: HSLMSLSSLLLCHFA.
% 52.90/10.87 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 52.90/10.87 % Starting ehoh_best5 with 300s (1) cores
% 52.90/10.87 % Starting almost_fo_3_lam with 300s (1) cores
% 52.90/10.87 % Starting new_bool_5 with 300s (1) cores
% 52.90/10.87 % Starting pre_casc_3 with 300s (1) cores
% 52.90/10.87 % Starting ho_unfolding_8 with 300s (1) cores
% 52.90/10.87 % Starting new_ho_10_cnf2 with 300s (1) cores
% 52.90/10.87 % Starting new_bool_3 with 300s (1) cores
% 52.90/10.87 % Starting new_ho_5 with 300s (1) cores
% 52.90/10.87 % pre_casc_3 with pid 2582263 completed with status 9
% 52.90/10.87 % new_ho_5 with pid 2582267 completed with status 9
% 52.90/10.87 % new_bool_5 with pid 2582262 completed with status 0
% 52.90/10.87 % Result found by new_bool_5
% 52.90/10.87 % Preprocessing class: HSLMSLSSLLLCHFA.
% 52.90/10.87 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 52.90/10.87 % Starting ehoh_best5 with 300s (1) cores
% 52.90/10.87 % Starting almost_fo_3_lam with 300s (1) cores
% 52.90/10.87 % Starting new_bool_5 with 300s (1) cores
% 52.90/10.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 52.90/10.87 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 52.90/10.87 % Search class: HGHSM-FSLM32-MHFMMSBN
% 52.90/10.87 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 52.90/10.87 % Starting SubtermCWHack with 28s (1) cores
% 52.90/10.87 % SubtermCWHack with pid 2582275 completed with status 0
% 52.90/10.87 % Result found by SubtermCWHack
% 52.90/10.87 % Preprocessing class: HSLMSLSSLLLCHFA.
% 52.90/10.87 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 52.90/10.87 % Starting ehoh_best5 with 300s (1) cores
% 52.90/10.87 % Starting almost_fo_3_lam with 300s (1) cores
% 52.90/10.87 % Starting new_bool_5 with 300s (1) cores
% 52.90/10.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 52.90/10.87 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 52.90/10.87 % Search class: HGHSM-FSLM32-MHFMMSBN
% 52.90/10.87 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 52.90/10.87 % Starting SubtermCWHack with 28s (1) cores
% 52.90/10.87 % Preprocessing time : 0.005 s
% 52.90/10.87
% 52.90/10.87 % Proof found!
% 52.90/10.87 % SZS status Theorem
% 52.90/10.87 % SZS output start CNFRefutation
% 52.90/10.87 thf(decl_23, type, in: $i > $i > $o).
% 52.90/10.87 thf(decl_24, type, exu: ($i > $o) > $o).
% 52.90/10.87 thf(decl_25, type, setextAx: $o).
% 52.90/10.87 thf(decl_26, type, emptyset: $i).
% 52.90/10.87 thf(decl_27, type, emptysetAx: $o).
% 52.90/10.87 thf(decl_28, type, setadjoin: $i > $i > $i).
% 52.90/10.87 thf(decl_29, type, setadjoinAx: $o).
% 52.90/10.87 thf(decl_30, type, powerset: $i > $i).
% 52.90/10.87 thf(decl_31, type, powersetAx: $o).
% 52.90/10.87 thf(decl_32, type, setunion: $i > $i).
% 52.90/10.87 thf(decl_33, type, setunionAx: $o).
% 52.90/10.87 thf(decl_34, type, omega: $i).
% 52.90/10.87 thf(decl_35, type, omega0Ax: $o).
% 52.90/10.87 thf(decl_36, type, omegaSAx: $o).
% 52.90/10.87 thf(decl_37, type, omegaIndAx: $o).
% 52.90/10.87 thf(decl_38, type, replAx: $o).
% 52.90/10.87 thf(decl_39, type, foundationAx: $o).
% 52.90/10.87 thf(decl_40, type, wellorderingAx: $o).
% 52.90/10.87 thf(decl_41, type, descr: ($i > $o) > $i).
% 52.90/10.87 thf(decl_42, type, descrp: $o).
% 52.90/10.87 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_44, type, dsetconstrI: $o).
% 52.90/10.87 thf(decl_45, type, dsetconstrEL: $o).
% 52.90/10.87 thf(decl_46, type, dsetconstrER: $o).
% 52.90/10.87 thf(decl_47, type, exuE1: $o).
% 52.90/10.87 thf(decl_48, type, prop2set: $o > $i).
% 52.90/10.87 thf(decl_49, type, prop2setE: $o).
% 52.90/10.87 thf(decl_50, type, emptysetE: $o).
% 52.90/10.87 thf(decl_51, type, emptysetimpfalse: $o).
% 52.90/10.87 thf(decl_52, type, notinemptyset: $o).
% 52.90/10.87 thf(decl_53, type, exuE3e: $o).
% 52.90/10.87 thf(decl_54, type, setext: $o).
% 52.90/10.87 thf(decl_55, type, emptyI: $o).
% 52.90/10.87 thf(decl_56, type, noeltsimpempty: $o).
% 52.90/10.87 thf(decl_57, type, setbeta: $o).
% 52.90/10.87 thf(decl_58, type, nonempty: $i > $o).
% 52.90/10.87 thf(decl_59, type, nonemptyE1: $o).
% 52.90/10.87 thf(decl_60, type, nonemptyI: $o).
% 52.90/10.87 thf(decl_61, type, nonemptyI1: $o).
% 52.90/10.87 thf(decl_62, type, setadjoinIL: $o).
% 52.90/10.87 thf(decl_63, type, emptyinunitempty: $o).
% 52.90/10.87 thf(decl_64, type, setadjoinIR: $o).
% 52.90/10.87 thf(decl_65, type, setadjoinE: $o).
% 52.90/10.87 thf(decl_66, type, setadjoinOr: $o).
% 52.90/10.87 thf(decl_67, type, setoftrueEq: $o).
% 52.90/10.87 thf(decl_68, type, powersetI: $o).
% 52.90/10.87 thf(decl_69, type, emptyinPowerset: $o).
% 52.90/10.87 thf(decl_70, type, emptyInPowerset: $o).
% 52.90/10.87 thf(decl_71, type, powersetE: $o).
% 52.90/10.87 thf(decl_72, type, setunionI: $o).
% 52.90/10.87 thf(decl_73, type, setunionE: $o).
% 52.90/10.87 thf(decl_74, type, subPowSU: $o).
% 52.90/10.87 thf(decl_75, type, exuE2: $o).
% 52.90/10.87 thf(decl_76, type, nonemptyImpWitness: $o).
% 52.90/10.87 thf(decl_77, type, uniqinunit: $o).
% 52.90/10.87 thf(decl_78, type, notinsingleton: $o).
% 52.90/10.87 thf(decl_79, type, eqinunit: $o).
% 52.90/10.87 thf(decl_80, type, singletonsswitch: $o).
% 52.90/10.87 thf(decl_81, type, upairsetE: $o).
% 52.90/10.87 thf(decl_82, type, upairsetIL: $o).
% 52.90/10.87 thf(decl_83, type, upairsetIR: $o).
% 52.90/10.87 thf(decl_84, type, emptyE1: $o).
% 52.90/10.87 thf(decl_85, type, vacuousDall: $o).
% 52.90/10.87 thf(decl_86, type, quantDeMorgan1: $o).
% 52.90/10.87 thf(decl_87, type, quantDeMorgan2: $o).
% 52.90/10.87 thf(decl_88, type, quantDeMorgan3: $o).
% 52.90/10.87 thf(decl_89, type, quantDeMorgan4: $o).
% 52.90/10.87 thf(decl_90, type, prop2setI: $o).
% 52.90/10.87 thf(decl_92, type, prop2set2propI: $o).
% 52.90/10.87 thf(decl_93, type, notdexE: $o).
% 52.90/10.87 thf(decl_94, type, notdallE: $o).
% 52.90/10.87 thf(decl_95, type, exuI1: $o).
% 52.90/10.87 thf(decl_96, type, exuI3: $o).
% 52.90/10.87 thf(decl_97, type, exuI2: $o).
% 52.90/10.87 thf(decl_98, type, inCongP: $o).
% 52.90/10.87 thf(decl_99, type, in__Cong: $o).
% 52.90/10.87 thf(decl_100, type, exuE3u: $o).
% 52.90/10.87 thf(decl_101, type, exu__Cong: $o).
% 52.90/10.87 thf(decl_102, type, emptyset__Cong: $o).
% 52.90/10.87 thf(decl_103, type, setadjoin__Cong: $o).
% 52.90/10.87 thf(decl_104, type, powerset__Cong: $o).
% 52.90/10.87 thf(decl_105, type, setunion__Cong: $o).
% 52.90/10.87 thf(decl_106, type, omega__Cong: $o).
% 52.90/10.87 thf(decl_107, type, exuEu: $o).
% 52.90/10.87 thf(decl_108, type, descr__Cong: $o).
% 52.90/10.87 thf(decl_109, type, dsetconstr__Cong: $o).
% 52.90/10.87 thf(decl_110, type, subset: $i > $i > $o).
% 52.90/10.87 thf(decl_113, type, subsetI1: $o).
% 52.90/10.87 thf(decl_114, type, eqimpsubset2: $o).
% 52.90/10.87 thf(decl_115, type, eqimpsubset1: $o).
% 52.90/10.87 thf(decl_116, type, subsetI2: $o).
% 52.90/10.87 thf(decl_117, type, emptysetsubset: $o).
% 52.90/10.87 thf(decl_118, type, subsetE: $o).
% 52.90/10.87 thf(decl_119, type, subsetE2: $o).
% 52.90/10.87 thf(decl_120, type, notsubsetI: $o).
% 52.90/10.87 thf(decl_121, type, notequalI1: $o).
% 52.90/10.87 thf(decl_122, type, notequalI2: $o).
% 52.90/10.87 thf(decl_123, type, subsetRefl: $o).
% 52.90/10.87 thf(decl_124, type, subsetTrans: $o).
% 52.90/10.87 thf(decl_125, type, setadjoinSub: $o).
% 52.90/10.87 thf(decl_126, type, setadjoinSub2: $o).
% 52.90/10.87 thf(decl_127, type, subset2powerset: $o).
% 52.90/10.87 thf(decl_128, type, setextsub: $o).
% 52.90/10.87 thf(decl_129, type, subsetemptysetimpeq: $o).
% 52.90/10.87 thf(decl_130, type, powersetI1: $o).
% 52.90/10.87 thf(decl_131, type, powersetE1: $o).
% 52.90/10.87 thf(decl_132, type, inPowerset: $o).
% 52.90/10.87 thf(decl_133, type, powersetsubset: $o).
% 52.90/10.87 thf(decl_134, type, sepInPowerset: $o).
% 52.90/10.87 thf(decl_135, type, sepSubset: $o).
% 52.90/10.87 thf(decl_136, type, binunion: $i > $i > $i).
% 52.90/10.87 thf(decl_137, type, binunionIL: $o).
% 52.90/10.87 thf(decl_138, type, upairset2IR: $o).
% 52.90/10.87 thf(decl_139, type, binunionIR: $o).
% 52.90/10.87 thf(decl_140, type, binunionEcases: $o).
% 52.90/10.87 thf(decl_141, type, binunionE: $o).
% 52.90/10.87 thf(decl_142, type, binunionLsub: $o).
% 52.90/10.87 thf(decl_143, type, binunionRsub: $o).
% 52.90/10.87 thf(decl_144, type, binintersect: $i > $i > $i).
% 52.90/10.87 thf(decl_145, type, binintersectI: $o).
% 52.90/10.87 thf(decl_146, type, binintersectSubset5: $o).
% 52.90/10.87 thf(decl_147, type, binintersectEL: $o).
% 52.90/10.87 thf(decl_148, type, binintersectLsub: $o).
% 52.90/10.87 thf(decl_149, type, binintersectSubset2: $o).
% 52.90/10.87 thf(decl_150, type, binintersectSubset3: $o).
% 52.90/10.87 thf(decl_151, type, binintersectER: $o).
% 52.90/10.87 thf(decl_152, type, disjointsetsI1: $o).
% 52.90/10.87 thf(decl_153, type, binintersectRsub: $o).
% 52.90/10.87 thf(decl_154, type, binintersectSubset4: $o).
% 52.90/10.87 thf(decl_155, type, binintersectSubset1: $o).
% 52.90/10.87 thf(decl_156, type, bs114d: $o).
% 52.90/10.87 thf(decl_158, type, setminus: $i > $i > $i).
% 52.90/10.87 thf(decl_159, type, setminusI: $o).
% 52.90/10.87 thf(decl_160, type, setminusEL: $o).
% 52.90/10.87 thf(decl_161, type, setminusER: $o).
% 52.90/10.87 thf(decl_162, type, setminusSubset2: $o).
% 52.90/10.87 thf(decl_163, type, setminusERneg: $o).
% 52.90/10.87 thf(decl_164, type, setminusELneg: $o).
% 52.90/10.87 thf(decl_165, type, setminusILneg: $o).
% 52.90/10.87 thf(decl_166, type, setminusIRneg: $o).
% 52.90/10.87 thf(decl_167, type, setminusLsub: $o).
% 52.90/10.87 thf(decl_168, type, setminusSubset1: $o).
% 52.90/10.87 thf(decl_169, type, symdiff: $i > $i > $i).
% 52.90/10.87 thf(decl_170, type, symdiffE: $o).
% 52.90/10.87 thf(decl_171, type, symdiffI1: $o).
% 52.90/10.87 thf(decl_172, type, symdiffI2: $o).
% 52.90/10.87 thf(decl_173, type, symdiffIneg1: $o).
% 52.90/10.87 thf(decl_174, type, symdiffIneg2: $o).
% 52.90/10.87 thf(decl_175, type, iskpair: $i > $o).
% 52.90/10.87 thf(decl_176, type, secondinupair: $o).
% 52.90/10.87 thf(decl_177, type, setukpairIL: $o).
% 52.90/10.87 thf(decl_178, type, setukpairIR: $o).
% 52.90/10.87 thf(decl_179, type, kpairiskpair: $o).
% 52.90/10.87 thf(decl_180, type, kpair: $i > $i > $i).
% 52.90/10.87 thf(decl_181, type, kpairp: $o).
% 52.90/10.87 thf(decl_182, type, cartprod: $i > $i > $i).
% 52.90/10.87 thf(decl_183, type, singletonsubset: $o).
% 52.90/10.87 thf(decl_184, type, singletoninpowerset: $o).
% 52.90/10.87 thf(decl_185, type, singletoninpowunion: $o).
% 52.90/10.87 thf(decl_186, type, upairset2E: $o).
% 52.90/10.87 thf(decl_187, type, upairsubunion: $o).
% 52.90/10.87 thf(decl_188, type, upairinpowunion: $o).
% 52.90/10.87 thf(decl_189, type, ubforcartprodlem1: $o).
% 52.90/10.87 thf(decl_190, type, ubforcartprodlem2: $o).
% 52.90/10.87 thf(decl_191, type, ubforcartprodlem3: $o).
% 52.90/10.87 thf(decl_192, type, cartprodpairin: $o).
% 52.90/10.87 thf(decl_193, type, cartprodmempair1: $o).
% 52.90/10.87 thf(decl_194, type, cartprodmempair: $o).
% 52.90/10.87 thf(decl_195, type, setunionE2: $o).
% 52.90/10.87 thf(decl_196, type, setunionsingleton1: $o).
% 52.90/10.87 thf(decl_197, type, setunionsingleton2: $o).
% 52.90/10.87 thf(decl_198, type, setunionsingleton: $o).
% 52.90/10.87 thf(decl_199, type, singleton: $i > $o).
% 52.90/10.87 thf(decl_200, type, singletonprop: $o).
% 52.90/10.87 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 52.90/10.87 thf(decl_202, type, ex1E1: $o).
% 52.90/10.87 thf(decl_203, type, ex1I: $o).
% 52.90/10.87 thf(decl_204, type, ex1I2: $o).
% 52.90/10.87 thf(decl_205, type, singletonsuniq: $o).
% 52.90/10.87 thf(decl_210, type, setukpairinjL1: $o).
% 52.90/10.87 thf(decl_211, type, kfstsingleton: $o).
% 52.90/10.87 thf(decl_212, type, theprop: $o).
% 52.90/10.87 thf(decl_213, type, kfst: $i > $i).
% 52.90/10.87 thf(decl_214, type, kfstpairEq: $o).
% 52.90/10.87 thf(decl_215, type, cartprodfstin: $o).
% 52.90/10.87 thf(decl_216, type, setukpairinjL2: $o).
% 52.90/10.87 thf(decl_217, type, setukpairinjL: $o).
% 52.90/10.87 thf(decl_218, type, setukpairinjR11: $o).
% 52.90/10.87 thf(decl_219, type, setukpairinjR12: $o).
% 52.90/10.87 thf(decl_220, type, setukpairinjR1: $o).
% 52.90/10.87 thf(decl_221, type, upairequniteq: $o).
% 52.90/10.87 thf(decl_222, type, setukpairinjR2: $o).
% 52.90/10.87 thf(decl_223, type, setukpairinjR: $o).
% 52.90/10.87 thf(decl_224, type, ksndsingleton: $o).
% 52.90/10.87 thf(decl_225, type, ksnd: $i > $i).
% 52.90/10.87 thf(decl_226, type, ksndpairEq: $o).
% 52.90/10.87 thf(decl_227, type, kpairsurjEq: $o).
% 52.90/10.87 thf(decl_228, type, cartprodsndin: $o).
% 52.90/10.87 thf(decl_229, type, cartprodpairmemEL: $o).
% 52.90/10.87 thf(decl_230, type, cartprodpairmemER: $o).
% 52.90/10.87 thf(decl_231, type, cartprodmempaircEq: $o).
% 52.90/10.87 thf(decl_232, type, cartprodfstpairEq: $o).
% 52.90/10.87 thf(decl_233, type, cartprodsndpairEq: $o).
% 52.90/10.87 thf(decl_234, type, cartprodpairsurjEq: $o).
% 52.90/10.87 thf(decl_235, type, breln: $i > $i > $i > $o).
% 52.90/10.87 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 52.90/10.87 thf(decl_237, type, dpsetconstrI: $o).
% 52.90/10.87 thf(decl_238, type, dpsetconstrSub: $o).
% 52.90/10.87 thf(decl_239, type, setOfPairsIsBReln: $o).
% 52.90/10.87 thf(decl_240, type, dpsetconstrERa: $o).
% 52.90/10.87 thf(decl_241, type, dpsetconstrEL1: $o).
% 52.90/10.87 thf(decl_242, type, dpsetconstrEL2: $o).
% 52.90/10.87 thf(decl_243, type, dpsetconstrER: $o).
% 52.90/10.87 thf(decl_244, type, func: $i > $i > $i > $o).
% 52.90/10.87 thf(decl_245, type, funcSet: $i > $i > $i).
% 52.90/10.87 thf(decl_246, type, funcImageSingleton: $o).
% 52.90/10.87 thf(decl_247, type, apProp: $o).
% 52.90/10.87 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 52.90/10.87 thf(decl_249, type, app: $o).
% 52.90/10.87 thf(decl_250, type, infuncsetfunc: $o).
% 52.90/10.87 thf(decl_251, type, ap2p: $o).
% 52.90/10.87 thf(decl_252, type, funcinfuncset: $o).
% 52.90/10.87 thf(decl_253, type, lamProp: $o).
% 52.90/10.87 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 52.90/10.87 thf(decl_255, type, lamp: $o).
% 52.90/10.87 thf(decl_256, type, lam2p: $o).
% 52.90/10.87 thf(decl_257, type, brelnall1: $o).
% 52.90/10.87 thf(decl_258, type, brelnall2: $o).
% 52.90/10.87 thf(decl_259, type, ex1E2: $o).
% 52.90/10.87 thf(decl_260, type, funcGraphProp1: $o).
% 52.90/10.87 thf(decl_261, type, funcGraphProp3: $o).
% 52.90/10.87 thf(decl_262, type, funcGraphProp2: $o).
% 52.90/10.87 thf(decl_263, type, funcextLem: $o).
% 52.90/10.87 thf(decl_264, type, funcGraphProp4: $o).
% 52.90/10.87 thf(decl_265, type, subbreln: $o).
% 52.90/10.87 thf(decl_266, type, eqbreln: $o).
% 52.90/10.87 thf(decl_267, type, funcext: $o).
% 52.90/10.87 thf(decl_268, type, funcext2: $o).
% 52.90/10.87 thf(decl_269, type, ap2apEq1: $o).
% 52.90/10.87 thf(decl_270, type, ap2apEq2: $o).
% 52.90/10.87 thf(decl_271, type, beta1: $o).
% 52.90/10.87 thf(decl_272, type, eta1: $o).
% 52.90/10.87 thf(decl_273, type, lam2lamEq: $o).
% 52.90/10.87 thf(decl_274, type, beta2: $o).
% 52.90/10.87 thf(decl_275, type, eta2: $o).
% 52.90/10.87 thf(decl_276, type, iffalseProp1: $o).
% 52.90/10.87 thf(decl_277, type, iffalseProp2: $o).
% 52.90/10.87 thf(decl_278, type, iftrueProp1: $o).
% 52.90/10.87 thf(decl_279, type, iftrueProp2: $o).
% 52.90/10.87 thf(decl_280, type, ifSingleton: $o).
% 52.90/10.87 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 52.90/10.87 thf(decl_282, type, ifp: $o).
% 52.90/10.87 thf(decl_283, type, theeq: $o).
% 52.90/10.87 thf(decl_284, type, iftrue: $o).
% 52.90/10.87 thf(decl_285, type, iffalse: $o).
% 52.90/10.87 thf(decl_286, type, iftrueorfalse: $o).
% 52.90/10.87 thf(decl_287, type, binintersectT_lem: $o).
% 52.90/10.87 thf(decl_288, type, binunionT_lem: $o).
% 52.90/10.87 thf(decl_289, type, powersetT_lem: $o).
% 52.90/10.87 thf(decl_290, type, setminusT_lem: $o).
% 52.90/10.87 thf(decl_291, type, complementT_lem: $o).
% 52.90/10.87 thf(decl_292, type, setextT: $o).
% 52.90/10.87 thf(decl_293, type, subsetTI: $o).
% 52.90/10.87 thf(decl_294, type, powersetTI1: $o).
% 52.90/10.87 thf(decl_295, type, powersetTE1: $o).
% 52.90/10.87 thf(decl_296, type, complementTI1: $o).
% 52.90/10.87 thf(decl_297, type, complementTE1: $o).
% 52.90/10.87 thf(decl_298, type, binintersectTELcontra: $o).
% 52.90/10.87 thf(decl_299, type, binintersectTERcontra: $o).
% 52.90/10.87 thf(decl_300, type, contrasubsetT: $o).
% 52.90/10.87 thf(decl_301, type, contrasubsetT1: $o).
% 52.90/10.87 thf(decl_302, type, contrasubsetT2: $o).
% 52.90/10.87 thf(decl_303, type, contrasubsetT3: $o).
% 52.90/10.87 thf(decl_304, type, doubleComplementI1: $o).
% 52.90/10.87 thf(decl_305, type, doubleComplementE1: $o).
% 52.90/10.87 thf(decl_306, type, doubleComplementSub1: $o).
% 52.90/10.87 thf(decl_307, type, doubleComplementSub2: $o).
% 52.90/10.87 thf(decl_308, type, doubleComplementEq: $o).
% 52.90/10.87 thf(decl_309, type, complementTnotintersectT: $o).
% 52.90/10.87 thf(decl_310, type, complementImpComplementIntersect: $o).
% 52.90/10.87 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 52.90/10.87 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 52.90/10.87 thf(decl_313, type, contraSubsetComplement: $o).
% 52.90/10.87 thf(decl_314, type, complementTcontraSubset: $o).
% 52.90/10.87 thf(decl_315, type, binunionTILcontra: $o).
% 52.90/10.87 thf(decl_316, type, binunionTIRcontra: $o).
% 52.90/10.87 thf(decl_317, type, inIntersectImpInUnion: $o).
% 52.90/10.87 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 52.90/10.87 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 52.90/10.87 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 52.90/10.87 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 52.90/10.87 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 52.90/10.87 thf(decl_323, type, binunionTE: $o).
% 52.90/10.87 thf(decl_324, type, binunionTEcontra: $o).
% 52.90/10.87 thf(decl_325, type, demorgan2a1: $o).
% 52.90/10.87 thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 52.90/10.87 thf(decl_327, type, demorgan2a2: $o).
% 52.90/10.87 thf(decl_328, type, demorgan1a: $o).
% 52.90/10.87 thf(decl_329, type, demorgan1b: $o).
% 52.90/10.87 thf(decl_330, type, demorgan1: $o).
% 52.90/10.87 thf(decl_331, type, demorgan2a: $o).
% 52.90/10.87 thf(decl_332, type, demorgan2b2: $o).
% 52.90/10.87 thf(decl_333, type, demorgan2b: $o).
% 52.90/10.87 thf(decl_334, type, demorgan2: $o).
% 52.90/10.87 thf(decl_335, type, woz13rule0: $o).
% 52.90/10.87 thf(decl_336, type, woz13rule1: $o).
% 52.90/10.87 thf(decl_337, type, woz13rule2: $o).
% 52.90/10.87 thf(decl_338, type, woz13rule3: $o).
% 52.90/10.87 thf(decl_339, type, woz13rule4: $o).
% 52.90/10.87 thf(decl_340, type, woz1_1: $o).
% 52.90/10.87 thf(decl_341, type, woz1_2: $o).
% 52.90/10.87 thf(decl_342, type, epred1_0: $o).
% 52.90/10.87 thf(decl_343, type, esk1_2: $i > $i > $i).
% 52.90/10.87 thf(decl_344, type, esk2_2: $i > $i > $i).
% 52.90/10.87 thf(decl_345, type, esk3_2: $i > $i > $i).
% 52.90/10.87 thf(decl_346, type, esk4_1: $i > $i).
% 52.90/10.87 thf(decl_347, type, esk5_2: ($i > $i > $o) > $i > $i).
% 52.90/10.87 thf(decl_348, type, esk6_2: ($i > $i > $o) > $i > $i).
% 52.90/10.87 thf(decl_349, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 52.90/10.87 thf(decl_350, type, esk8_1: $i > $i).
% 52.90/10.87 thf(decl_351, type, esk9_1: ($i > $o) > $i).
% 52.90/10.87 thf(decl_352, type, esk10_1: ($i > $o) > $i).
% 52.90/10.87 thf(decl_353, type, esk11_2: $i > $i > $i).
% 52.90/10.87 thf(decl_354, type, esk12_2: $i > $i > $i).
% 52.90/10.87 thf(decl_355, type, esk13_1: $i > $i).
% 52.90/10.87 thf(decl_356, type, esk14_1: $i > $i).
% 52.90/10.87 thf(decl_357, type, esk15_1: $i > $i).
% 52.90/10.87 thf(decl_358, type, esk16_2: $i > $i > $i).
% 52.90/10.87 thf(decl_359, type, esk17_3: $i > $i > $o > $i).
% 52.90/10.87 thf(decl_360, type, esk18_1: ($i > $o) > $i).
% 52.90/10.87 thf(decl_361, type, esk19_1: $i > $i).
% 52.90/10.87 thf(decl_362, type, esk20_2: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_363, type, esk21_2: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_364, type, esk22_2: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_365, type, esk23_2: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_366, type, esk24_2: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_367, type, esk25_2: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_368, type, esk26_2: ($i > $o) > $i > $i).
% 52.90/10.87 thf(decl_369, type, esk27_1: ($i > $o) > $i).
% 52.90/10.87 thf(decl_370, type, esk28_1: ($i > $o) > $i).
% 52.90/10.87 thf(decl_371, type, esk29_2: ($i > $o) > $i > $i).
% 52.90/10.87 thf(decl_372, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 52.90/10.87 thf(decl_373, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 52.90/10.87 thf(decl_374, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 52.90/10.87 thf(decl_375, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 52.90/10.87 thf(decl_376, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 52.90/10.87 thf(decl_377, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 52.90/10.87 thf(decl_378, type, esk36_2: $i > $i > $i).
% 52.90/10.87 thf(decl_379, type, esk37_2: $i > $i > $i).
% 52.90/10.87 thf(decl_380, type, esk38_2: $i > $i > $i).
% 52.90/10.87 thf(decl_381, type, esk39_3: $i > $i > $i > $i).
% 52.90/10.87 thf(decl_382, type, esk40_3: $i > $i > $i > $i).
% 52.90/10.87 thf(decl_383, type, esk41_2: $i > $i > $i).
% 52.90/10.87 thf(decl_384, type, esk42_2: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_385, type, esk43_2: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_386, type, esk44_2: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_387, type, esk45_3: $i > ($i > $o) > $i > $i).
% 52.90/10.87 thf(decl_388, type, esk46_2: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_389, type, esk47_2: $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_390, type, esk48_3: $i > $i > ($i > $i) > $i).
% 52.90/10.87 thf(decl_391, type, esk49_3: $i > $i > ($i > $i) > $i).
% 52.90/10.87 thf(decl_392, type, esk50_3: $i > $i > ($i > $i) > $i).
% 52.90/10.87 thf(decl_393, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_394, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_395, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_396, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 52.90/10.87 thf(decl_397, type, esk55_4: $i > $i > $i > $i > $i).
% 52.90/10.87 thf(decl_398, type, esk56_4: $i > $i > $i > $i > $i).
% 52.90/10.87 thf(decl_399, type, esk57_4: $i > $i > $i > $i > $i).
% 52.90/10.87 thf(decl_400, type, esk58_4: $i > $i > $i > $i > $i).
% 52.90/10.87 thf(decl_401, type, esk59_4: $i > $i > $i > $i > $i).
% 52.90/10.87 thf(decl_402, type, esk60_4: $i > $i > $i > $i > $i).
% 52.90/10.87 thf(decl_403, type, esk61_4: $i > $i > $i > $i > $i).
% 52.90/10.87 thf(decl_404, type, esk62_4: $i > $i > $i > $i > $i).
% 52.90/10.87 thf(decl_405, type, esk63_4: $i > $i > $i > $i > $i).
% 52.90/10.87 thf(decl_406, type, esk64_3: $i > $i > ($i > $i) > $i).
% 52.90/10.87 thf(decl_407, type, esk65_3: $i > $i > ($i > $i) > $i).
% 52.90/10.87 thf(decl_408, type, esk66_3: $i > $i > ($i > $i) > $i).
% 52.90/10.87 thf(decl_409, type, esk67_3: $i > $i > $i > $i).
% 52.90/10.87 thf(decl_410, type, esk68_3: $i > $i > $i > $i).
% 52.90/10.87 thf(decl_411, type, esk69_3: $i > $i > $i > $i).
% 52.90/10.87 thf(decl_412, type, esk70_3: $i > $i > $i > $i).
% 52.90/10.87 thf(decl_413, type, esk71_0: $i).
% 52.90/10.87 thf(decl_414, type, esk72_0: $i).
% 52.90/10.87 thf(decl_415, type, esk73_0: $i).
% 52.90/10.87 thf(decl_416, type, esk74_0: $i).
% 52.90/10.87 thf(woz1_3, 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)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', woz1_3)).
% 52.90/10.87 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', exu__Cong)).
% 52.90/10.87 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', exuE3u)).
% 52.90/10.87 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', dsetconstr__Cong)).
% 52.90/10.87 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', descr__Cong)).
% 52.90/10.87 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', exuEu)).
% 52.90/10.87 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', sepSubset)).
% 52.90/10.87 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', sepInPowerset)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', eta1)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', beta1)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', eta2)).
% 52.90/10.87 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ex1I2)).
% 52.90/10.87 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ex1I)).
% 52.90/10.87 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ex1E1)).
% 52.90/10.87 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', singletonprop)).
% 52.90/10.87 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', kfstsingleton)).
% 52.90/10.87 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ksndsingleton)).
% 52.90/10.87 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', dpsetconstrSub)).
% 52.90/10.87 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', dpsetconstrI)).
% 52.90/10.87 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setOfPairsIsBReln)).
% 52.90/10.87 thf(apProp, axiom, ((apProp)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', apProp)).
% 52.90/10.87 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', funcImageSingleton)).
% 52.90/10.87 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', dpsetconstrER)).
% 52.90/10.87 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', dpsetconstrEL2)).
% 52.90/10.87 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', dpsetconstrEL1)).
% 52.90/10.87 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', dpsetconstrERa)).
% 52.90/10.87 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', lam2p)).
% 52.90/10.87 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', lamp)).
% 52.90/10.87 thf(lamProp, axiom, ((lamProp)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', lamProp)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ex1E2)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', beta2)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', lam2lamEq)).
% 52.90/10.87 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ifSingleton)).
% 52.90/10.87 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', iftrueProp2)).
% 52.90/10.87 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', iftrueProp1)).
% 52.90/10.87 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', iffalseProp2)).
% 52.90/10.87 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', iffalseProp1)).
% 52.90/10.87 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', exuI2)).
% 52.90/10.87 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', exuI3)).
% 52.90/10.87 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', exuI1)).
% 52.90/10.87 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', emptyE1)).
% 52.90/10.87 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', exuE2)).
% 52.90/10.87 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setoftrueEq)).
% 52.90/10.87 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', nonemptyI)).
% 52.90/10.87 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setbeta)).
% 52.90/10.87 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', exuE3e)).
% 52.90/10.87 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', exuE1)).
% 52.90/10.87 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', dsetconstrER)).
% 52.90/10.87 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', dsetconstrEL)).
% 52.90/10.87 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', dsetconstrI)).
% 52.90/10.87 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', descrp)).
% 52.90/10.87 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', replAx)).
% 52.90/10.87 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectTELcontra)).
% 52.90/10.87 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', complementTE1)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectTERcontra)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', contrasubsetT)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', contrasubsetT1)).
% 52.90/10.87 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', contrasubsetT2)).
% 52.90/10.87 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', contrasubsetT3)).
% 52.90/10.87 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', doubleComplementI1)).
% 52.90/10.87 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', doubleComplementE1)).
% 52.90/10.87 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', doubleComplementSub1)).
% 52.90/10.87 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setunion__Cong)).
% 52.90/10.87 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', doubleComplementSub2)).
% 52.90/10.87 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', powerset__Cong)).
% 52.90/10.87 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', doubleComplementEq)).
% 52.90/10.87 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setadjoin__Cong)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', complementTnotintersectT)).
% 52.90/10.87 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', emptyset__Cong)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', complementImpComplementIntersect)).
% 52.90/10.87 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', complementSubsetComplementIntersect)).
% 52.90/10.87 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', complementInPowersetComplementIntersect)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', contraSubsetComplement)).
% 52.90/10.87 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', in__Cong)).
% 52.90/10.87 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', complementTcontraSubset)).
% 52.90/10.87 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', omega__Cong)).
% 52.90/10.87 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binunionTILcontra)).
% 52.90/10.87 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binunionTIRcontra)).
% 52.90/10.87 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', inIntersectImpInUnion)).
% 52.90/10.87 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', inIntersectImpInUnion2)).
% 52.90/10.87 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', inIntersectImpInIntersectUnions)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', intersectInPowersetIntersectUnions)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', inComplementUnionImpNotIn1)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', inComplementUnionImpInComplement1)).
% 52.90/10.87 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binunionTE)).
% 52.90/10.87 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binunionTEcontra)).
% 52.90/10.87 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', demorgan2a1)).
% 52.90/10.87 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', complementUnionInPowersetComplement)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', demorgan2a2)).
% 52.90/10.87 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', subsetI2)).
% 52.90/10.87 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', demorgan1a)).
% 52.90/10.87 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', eqimpsubset1)).
% 52.90/10.87 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', demorgan1b)).
% 52.90/10.87 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', eqimpsubset2)).
% 52.90/10.87 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', demorgan1)).
% 52.90/10.87 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', subsetI1)).
% 52.90/10.87 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', demorgan2a)).
% 52.90/10.87 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', demorgan2b2)).
% 52.90/10.87 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', demorgan2b)).
% 52.90/10.87 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', demorgan2)).
% 52.90/10.87 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', emptysetsubset)).
% 52.90/10.87 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', woz13rule0)).
% 52.90/10.87 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', woz13rule1)).
% 52.90/10.87 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', woz13rule2)).
% 52.90/10.87 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', woz13rule3)).
% 52.90/10.87 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', woz13rule4)).
% 52.90/10.87 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', woz1_1)).
% 52.90/10.87 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', woz1_2)).
% 52.90/10.87 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', subsetTrans)).
% 52.90/10.87 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', subsetRefl)).
% 52.90/10.87 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', notequalI2)).
% 52.90/10.87 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', notequalI1)).
% 52.90/10.87 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', notsubsetI)).
% 52.90/10.87 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', subsetE2)).
% 52.90/10.87 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', subsetE)).
% 52.90/10.87 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setadjoinSub)).
% 52.90/10.87 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', inPowerset)).
% 52.90/10.87 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', powersetE1)).
% 52.90/10.87 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', powersetI1)).
% 52.90/10.87 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', subsetemptysetimpeq)).
% 52.90/10.87 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setextsub)).
% 52.90/10.87 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', subset2powerset)).
% 52.90/10.87 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setadjoinSub2)).
% 52.90/10.87 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', powersetsubset)).
% 52.90/10.87 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binunionE)).
% 52.90/10.87 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binunionEcases)).
% 52.90/10.87 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binunionIR)).
% 52.90/10.87 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', upairset2IR)).
% 52.90/10.87 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binunionIL)).
% 52.90/10.87 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binunionLsub)).
% 52.90/10.87 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectSubset3)).
% 52.90/10.87 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectSubset2)).
% 52.90/10.87 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectLsub)).
% 52.90/10.87 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectEL)).
% 52.90/10.87 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectSubset5)).
% 52.90/10.87 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectI)).
% 52.90/10.87 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binunionRsub)).
% 52.90/10.87 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectER)).
% 52.90/10.87 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setminusEL)).
% 52.90/10.87 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setminusI)).
% 52.90/10.87 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', bs114d)).
% 52.90/10.87 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectSubset1)).
% 52.90/10.87 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectSubset4)).
% 52.90/10.87 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectRsub)).
% 52.90/10.87 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', disjointsetsI1)).
% 52.90/10.87 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setminusER)).
% 52.90/10.87 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ap2apEq2)).
% 52.90/10.87 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ap2apEq1)).
% 52.90/10.87 thf(funcext2, axiom, ((funcext2)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', funcext2)).
% 52.90/10.87 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', theeq)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ifp)).
% 52.90/10.87 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setminusSubset1)).
% 52.90/10.87 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setminusLsub)).
% 52.90/10.87 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setminusIRneg)).
% 52.90/10.87 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setminusILneg)).
% 52.90/10.87 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setminusELneg)).
% 52.90/10.87 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setminusERneg)).
% 52.90/10.87 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setminusSubset2)).
% 52.90/10.87 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', symdiffE)).
% 52.90/10.87 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setukpairIR)).
% 52.90/10.87 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setukpairIL)).
% 52.90/10.87 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', secondinupair)).
% 52.90/10.87 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', symdiffIneg2)).
% 52.90/10.87 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', symdiffIneg1)).
% 52.90/10.87 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', symdiffI2)).
% 52.90/10.87 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', symdiffI1)).
% 52.90/10.87 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', kpairiskpair)).
% 52.90/10.87 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', upairinpowunion)).
% 52.90/10.87 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', upairsubunion)).
% 52.90/10.87 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', upairset2E)).
% 52.90/10.87 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', singletoninpowunion)).
% 52.90/10.87 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', singletoninpowerset)).
% 52.90/10.87 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', singletonsubset)).
% 52.90/10.87 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', kpairp)).
% 52.90/10.87 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ubforcartprodlem1)).
% 52.90/10.87 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setunionsingleton1)).
% 52.90/10.87 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setunionE2)).
% 52.90/10.87 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', cartprodmempair)).
% 52.90/10.87 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', cartprodmempair1)).
% 52.90/10.87 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', cartprodpairin)).
% 52.90/10.87 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ubforcartprodlem3)).
% 52.90/10.87 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ubforcartprodlem2)).
% 52.90/10.87 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setunionsingleton2)).
% 52.90/10.87 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setukpairinjL1)).
% 52.90/10.87 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', singletonsuniq)).
% 52.90/10.87 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setunionsingleton)).
% 52.90/10.87 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setukpairinjR12)).
% 52.90/10.87 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setukpairinjR11)).
% 52.90/10.87 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setukpairinjL)).
% 52.90/10.87 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setukpairinjL2)).
% 52.90/10.87 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', cartprodfstin)).
% 52.90/10.87 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', kfstpairEq)).
% 52.90/10.87 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', theprop)).
% 52.90/10.87 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setukpairinjR1)).
% 52.90/10.87 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', cartprodsndin)).
% 52.90/10.87 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', kpairsurjEq)).
% 52.90/10.87 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ksndpairEq)).
% 52.90/10.87 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setukpairinjR)).
% 52.90/10.87 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setukpairinjR2)).
% 52.90/10.87 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', upairequniteq)).
% 52.90/10.87 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', cartprodpairmemEL)).
% 52.90/10.87 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', cartprodpairsurjEq)).
% 52.90/10.87 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', cartprodsndpairEq)).
% 52.90/10.87 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', cartprodfstpairEq)).
% 52.90/10.87 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', cartprodmempaircEq)).
% 52.90/10.87 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', cartprodpairmemER)).
% 52.90/10.87 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', app)).
% 52.90/10.87 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', infuncsetfunc)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', brelnall2)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', brelnall1)).
% 52.90/10.87 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', funcinfuncset)).
% 52.90/10.87 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', ap2p)).
% 52.90/10.87 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', eqbreln)).
% 52.90/10.87 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', subbreln)).
% 52.90/10.87 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', funcGraphProp4)).
% 52.90/10.87 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', funcextLem)).
% 52.90/10.87 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', funcGraphProp2)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', funcGraphProp3)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', funcGraphProp1)).
% 52.90/10.87 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', funcext)).
% 52.90/10.87 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', iftrue)).
% 52.90/10.87 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', complementT_lem)).
% 52.90/10.87 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setminusT_lem)).
% 52.90/10.87 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', powersetT_lem)).
% 52.90/10.87 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binunionT_lem)).
% 52.90/10.87 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', binintersectT_lem)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', iftrueorfalse)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', iffalse)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', subsetTI)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', powersetTI1)).
% 52.90/10.87 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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', powersetTE1)).
% 52.90/10.87 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', complementTI1)).
% 52.90/10.87 thf(setextT, axiom, ((setextT)<=>![X4:$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/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setextT)).
% 52.90/10.87 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', inCongP)).
% 52.90/10.87 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', notdallE)).
% 52.90/10.87 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', notdexE)).
% 52.90/10.87 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', prop2setI)).
% 52.90/10.87 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', quantDeMorgan4)).
% 52.90/10.87 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', quantDeMorgan3)).
% 52.90/10.87 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', quantDeMorgan2)).
% 52.90/10.87 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', quantDeMorgan1)).
% 52.90/10.87 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', vacuousDall)).
% 52.90/10.87 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', upairsetIR)).
% 52.90/10.87 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', upairsetIL)).
% 52.90/10.87 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', upairsetE)).
% 52.90/10.87 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', singletonsswitch)).
% 52.90/10.87 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', eqinunit)).
% 52.90/10.87 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', notinsingleton)).
% 52.90/10.87 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', uniqinunit)).
% 52.90/10.87 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', nonemptyImpWitness)).
% 52.90/10.87 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', subPowSU)).
% 52.90/10.87 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setunionE)).
% 52.90/10.87 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setunionI)).
% 52.90/10.87 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', powersetE)).
% 52.90/10.87 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', emptyInPowerset)).
% 52.90/10.87 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', emptyinPowerset)).
% 52.90/10.87 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', powersetI)).
% 52.90/10.87 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setadjoinOr)).
% 52.90/10.87 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setadjoinE)).
% 52.90/10.87 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setadjoinIR)).
% 52.90/10.87 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', emptyinunitempty)).
% 52.90/10.87 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setadjoinIL)).
% 52.90/10.87 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', nonemptyI1)).
% 52.90/10.87 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', nonemptyE1)).
% 52.90/10.87 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', noeltsimpempty)).
% 52.90/10.87 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', emptyI)).
% 52.90/10.87 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setext)).
% 52.90/10.87 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', notinemptyset)).
% 52.90/10.87 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', emptysetimpfalse)).
% 52.90/10.87 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', emptysetE)).
% 52.90/10.87 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', prop2setE)).
% 52.90/10.87 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', wellorderingAx)).
% 52.90/10.87 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', foundationAx)).
% 52.90/10.87 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', omegaIndAx)).
% 52.90/10.87 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', omegaSAx)).
% 52.90/10.87 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', omega0Ax)).
% 52.90/10.87 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setunionAx)).
% 52.90/10.87 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', powersetAx)).
% 52.90/10.87 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setadjoinAx)).
% 52.90/10.87 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', emptysetAx)).
% 52.90/10.87 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.PXBarFcFRZ/E---3.1_2582247.p', setextAx)).
% 52.90/10.87 thf(c_0_281, 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)=>![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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[woz1_3])).
% 52.90/10.87 thf(c_0_282, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 52.90/10.87 thf(c_0_283, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 52.90/10.87 thf(c_0_284, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 52.90/10.87 thf(c_0_285, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 52.90/10.87 thf(c_0_286, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 52.90/10.87 thf(c_0_287, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 52.90/10.87 thf(c_0_288, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 52.90/10.87 thf(c_0_289, 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])).
% 52.90/10.87 thf(c_0_290, 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])).
% 52.90/10.87 thf(c_0_291, 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])).
% 52.90/10.87 thf(c_0_292, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 52.90/10.87 thf(c_0_293, plain, ((ex1I)<=>![X4:$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])).
% 52.90/10.87 thf(c_0_294, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 52.90/10.87 thf(c_0_295, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 52.90/10.87 thf(c_0_296, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 52.90/10.87 thf(c_0_297, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 52.90/10.87 thf(c_0_298, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 52.90/10.87 thf(c_0_299, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 52.90/10.87 thf(c_0_300, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 52.90/10.87 thf(c_0_301, plain, ((apProp)<=>![X4:$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])).
% 52.90/10.87 thf(c_0_302, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 52.90/10.87 thf(c_0_303, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 52.90/10.87 thf(c_0_304, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 52.90/10.87 thf(c_0_305, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 52.90/10.87 thf(c_0_306, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 52.90/10.87 thf(c_0_307, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 52.90/10.87 thf(c_0_308, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 52.90/10.87 thf(c_0_309, plain, ((lamProp)<=>![X4:$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])).
% 52.90/10.87 thf(c_0_310, 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])).
% 52.90/10.87 thf(c_0_311, 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])).
% 52.90/10.87 thf(c_0_312, 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])).
% 52.90/10.87 thf(c_0_313, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 52.90/10.87 thf(c_0_314, plain, ((iftrueProp2)<=>![X4:$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])).
% 52.90/10.87 thf(c_0_315, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 52.90/10.87 thf(c_0_316, plain, ((iffalseProp2)<=>![X4:$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])).
% 52.90/10.87 thf(c_0_317, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 52.90/10.87 thf(c_0_318, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 52.90/10.87 thf(c_0_319, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 52.90/10.87 thf(c_0_320, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 52.90/10.87 thf(c_0_321, 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])).
% 52.90/10.87 thf(c_0_322, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 52.90/10.87 thf(c_0_323, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 52.90/10.87 thf(c_0_324, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 52.90/10.87 thf(c_0_325, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 52.90/10.87 thf(c_0_326, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 52.90/10.87 thf(c_0_327, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 52.90/10.87 thf(c_0_328, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 52.90/10.87 thf(c_0_329, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 52.90/10.87 thf(c_0_330, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 52.90/10.87 thf(c_0_331, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 52.90/10.87 thf(c_0_332, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 52.90/10.87 thf(c_0_333, plain, ((epred1_0)<=>![X979:$i]:(?[X980:$i]:((((![X981:$i]:(((in @ X981 @ X980)=>![X982:$i]:(((in @ X982 @ X981)=>(in @ X982 @ X979)))))&![X983:$i, X984:$i]:((((in @ X983 @ X979)&(in @ X984 @ X979))=>(![X985:$i]:(((in @ X985 @ X980)=>((in @ X983 @ X985)<=>(in @ X984 @ X985))))=>((X983)=(X984))))))&![X986:$i, X987:$i]:((((in @ X986 @ X980)&(in @ X987 @ X980))=>(![X988:$i]:(((in @ X988 @ X986)=>(in @ X988 @ X987)))|![X989:$i]:(((in @ X989 @ X987)=>(in @ X989 @ X986)))))))&![X990:$i]:(((![X991:$i]:(((in @ X991 @ X990)=>(in @ X991 @ X979)))&?[X992:$i]:((in @ X992 @ X990)))=>?[X993:$i, X994:$i]:(((((in @ X993 @ X980)&(in @ X994 @ X990))&~(?[X995:$i]:(((in @ X995 @ X993)&(in @ X995 @ X990)))))&![X996:$i]:(((in @ X996 @ X980)=>(![X997:$i]:(((in @ X997 @ X996)=>(in @ X997 @ X993)))|(in @ X994 @ X996)))))))))))), introduced(definition)).
% 52.90/10.87 thf(c_0_334, negated_conjecture, ~((![X952:$i, X953:$i]:((![X954:$i]:(((in @ X954 @ X952)<=>(in @ X954 @ X953)))=>((X952)=(X953))))=>(![X955:$i]:(~(in @ X955 @ emptyset))=>(![X956:$i, X957:$i, X958:$i]:(((in @ X958 @ (setadjoin @ X956 @ X957))<=>(((X958)=(X956))|(in @ X958 @ X957))))=>(![X959:$i, X960:$i]:(((in @ X960 @ (powerset @ X959))<=>![X961:$i]:(((in @ X961 @ X960)=>(in @ X961 @ X959)))))=>(![X962:$i, X963:$i]:(((in @ X963 @ (setunion @ X962))<=>?[X964:$i]:(((in @ X963 @ X964)&(in @ X964 @ X962)))))=>((in @ emptyset @ omega)=>(![X965:$i]:(((in @ X965 @ omega)=>(in @ (setadjoin @ X965 @ X965) @ omega)))=>(![X966:$i]:((((in @ emptyset @ X966)&![X967:$i]:((((in @ X967 @ omega)&(in @ X967 @ X966))=>(in @ (setadjoin @ X967 @ X967) @ X966))))=>![X968:$i]:(((in @ X968 @ omega)=>(in @ X968 @ X966)))))=>(![X969:$i > $i > $o, X970:$i]:((![X971:$i]:(((in @ X971 @ X970)=>(exu @ (X969 @ X971))))=>?[X972:$i]:(![X973:$i]:(((in @ X973 @ X972)<=>?[X974:$i]:(((in @ X974 @ X970)&(X969 @ X974 @ X973))))))))=>(![X975:$i]:((?[X976:$i]:((in @ X976 @ X975))=>?[X977:$i]:(((in @ X977 @ X975)&~(?[X978:$i]:(((in @ X978 @ X977)&(in @ X978 @ X975))))))))=>((epred1_0)=>(![X998:$i > $o]:(((exu @ X998)=>(X998 @ (descr @ (^[Z0:$i]:(X998 @ Z0))))))=>(![X999:$i, X1000:$i > $o, X1001:$i]:(((in @ X1001 @ X999)=>((X1000 @ X1001)=>(in @ X1001 @ (dsetconstr @ X999 @ X1000)))))=>(![X1002:$i, X1003:$i > $o, X1004:$i]:(((in @ X1004 @ (dsetconstr @ X1002 @ X1003))=>(in @ X1004 @ X1002)))=>(![X1005:$i, X1006:$i > $o, X1007:$i]:(((in @ X1007 @ (dsetconstr @ X1005 @ X1006))=>(X1006 @ X1007)))=>(![X1008:$i > $o]:(((exu @ X1008)=>?[X1009:$i]:(((X1008 @ X1009)&![X1010:$i]:(((X1008 @ X1010)=>((X1009)=(X1010))))))))=>(![X1011:$o, X1012:$i]:(((in @ X1012 @ (prop2set @ ((X1011))))=>(X1011)))=>(![X1013:$i]:(((in @ X1013 @ emptyset)=>![X1014:$o]:((X1014))))=>(![X1015:$i]:(((in @ X1015 @ emptyset)=>~($true)))=>(![X1016:$i]:(~(in @ X1016 @ emptyset))=>(![X1017:$i > $o]:(((exu @ X1017)=>?[X1018:$i]:((X1017 @ X1018))))=>(![X1019:$i, X1020:$i]:((![X1021:$i]:(((in @ X1021 @ X1019)=>(in @ X1021 @ X1020)))=>(![X1022:$i]:(((in @ X1022 @ X1020)=>(in @ X1022 @ X1019)))=>((X1019)=(X1020)))))=>(![X1023:$i]:((![X1024:$i]:(~(in @ X1024 @ X1023))=>((X1023)=(emptyset))))=>(![X1025:$i]:((![X1026:$i]:(~(in @ X1026 @ X1025))=>((X1025)=(emptyset))))=>(![X1027:$i, X1028:$i > $o, X1029:$i]:(((in @ X1029 @ X1027)=>((in @ X1029 @ (dsetconstr @ X1027 @ X1028))<=>(X1028 @ X1029))))=>(![X1030:$i]:(((nonempty @ X1030)=>?[X1031:$i]:((in @ X1031 @ X1030))))=>(![X1032:$i, X1033:$i > $o, X1034:$i]:(((in @ X1034 @ X1032)=>((X1033 @ X1034)=>(nonempty @ (dsetconstr @ X1032 @ X1033)))))=>(![X1035:$i]:((?[X1036:$i]:((in @ X1036 @ X1035))=>(nonempty @ X1035)))=>(![X1037:$i, X1038:$i]:((in @ X1037 @ (setadjoin @ X1037 @ X1038)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1039:$i, X1040:$i, X1041:$i]:(((in @ X1041 @ X1040)=>(in @ X1041 @ (setadjoin @ X1039 @ X1040))))=>(![X1042:$i, X1043:$i, X1044:$i]:(((in @ X1044 @ (setadjoin @ X1042 @ X1043))=>![X1045:$o]:(((((X1044)=(X1042))=>(X1045))=>(((in @ X1044 @ X1043)=>(X1045))=>(X1045))))))=>(![X1046:$i, X1047:$i, X1048:$i]:(((in @ X1048 @ (setadjoin @ X1046 @ X1047))=>(((X1048)=(X1046))|(in @ X1048 @ X1047))))=>(![X1049:$i]:(((dsetconstr @ X1049 @ (^[Z0:$i]:($true)))=(X1049)))=>(![X1050:$i, X1051:$i]:((![X1052:$i]:(((in @ X1052 @ X1051)=>(in @ X1052 @ X1050)))=>(in @ X1051 @ (powerset @ X1050))))=>(![X1053:$i]:((in @ emptyset @ (powerset @ X1053)))=>(![X1054:$i]:((in @ emptyset @ (powerset @ X1054)))=>(![X1055:$i, X1056:$i, X1057:$i]:(((in @ X1056 @ (powerset @ X1055))=>((in @ X1057 @ X1056)=>(in @ X1057 @ X1055))))=>(![X1058:$i, X1059:$i, X1060:$i]:(((in @ X1059 @ X1060)=>((in @ X1060 @ X1058)=>(in @ X1059 @ (setunion @ X1058)))))=>(![X1061:$i, X1062:$i]:(((in @ X1062 @ (setunion @ X1061))=>![X1063:$o]:((![X1064:$i]:(((in @ X1062 @ X1064)=>((in @ X1064 @ X1061)=>(X1063))))=>(X1063)))))=>(![X1065:$i, X1066:$i]:(((in @ X1066 @ X1065)=>(in @ X1066 @ (powerset @ (setunion @ X1065)))))=>(![X1067:$i > $o]:(((exu @ X1067)=>?[X1068:$i]:(![X1069:$i]:(((X1067 @ X1069)<=>((X1069)=(X1068)))))))=>(![X1070:$i]:(((nonempty @ X1070)=>?[X1071:$i]:(((in @ X1071 @ X1070)&$true))))=>(![X1072:$i, X1073:$i]:(((in @ X1072 @ (setadjoin @ X1073 @ emptyset))=>((X1072)=(X1073))))=>(![X1074:$i, X1075:$i]:((((X1074)!=(X1075))=>~(in @ X1075 @ (setadjoin @ X1074 @ emptyset))))=>(![X1076:$i, X1077:$i]:((((X1076)=(X1077))=>(in @ X1076 @ (setadjoin @ X1077 @ emptyset))))=>(![X1078:$i, X1079:$i]:(((in @ X1078 @ (setadjoin @ X1079 @ emptyset))=>(in @ X1079 @ (setadjoin @ X1078 @ emptyset))))=>(![X1080:$i, X1081:$i, X1082:$i]:(((in @ X1082 @ (setadjoin @ X1080 @ (setadjoin @ X1081 @ emptyset)))=>(((X1082)=(X1080))|((X1082)=(X1081)))))=>(![X1083:$i, X1084:$i]:((in @ X1083 @ (setadjoin @ X1083 @ (setadjoin @ X1084 @ emptyset))))=>(![X1085:$i, X1086:$i]:((in @ X1086 @ (setadjoin @ X1085 @ (setadjoin @ X1086 @ emptyset))))=>(![X1087:$i, X1088:$i > $o]:((?[X1089:$i]:(((in @ X1089 @ X1087)&(X1088 @ X1089)))=>(((dsetconstr @ X1087 @ X1088)=(emptyset))=>~($true))))=>(![X1090:$i > $o, X1091:$i]:(((in @ X1091 @ emptyset)=>(X1090 @ X1091)))=>(![X1092:$i, X1093:$i > $o]:((~(![X1094:$i]:(((in @ X1094 @ X1092)=>(X1093 @ X1094))))=>?[X1095:$i]:(((in @ X1095 @ X1092)&~((X1093 @ X1095))))))=>(![X1096:$i, X1097:$i > $o]:((![X1098:$i]:(((in @ X1098 @ X1096)=>~((X1097 @ X1098))))=>~(?[X1099:$i]:(((in @ X1099 @ X1096)&(X1097 @ X1099))))))=>(![X1100:$i, X1101:$i > $o]:((~(?[X1102:$i]:(((in @ X1102 @ X1100)&(X1101 @ X1102))))=>![X1103:$i]:(((in @ X1103 @ X1100)=>~((X1101 @ X1103))))))=>(![X1104:$i, X1105:$i > $o]:((?[X1106:$i]:(((in @ X1106 @ X1104)&~((X1105 @ X1106))))=>~(![X1107:$i]:(((in @ X1107 @ X1104)=>(X1105 @ X1107))))))=>(![X1108:$o]:(((X1108)=>(in @ emptyset @ (prop2set @ ((X1108))))))=>((prop2set2propI)=>(![X1109:$i, X1110:$i > $o]:((~(?[X1111:$i]:(((in @ X1111 @ X1109)&(X1110 @ X1111))))=>![X1112:$i]:(((in @ X1112 @ X1109)=>~((X1110 @ X1112))))))=>(![X1113:$i, X1114:$i > $o]:((~(![X1115:$i]:(((in @ X1115 @ X1113)=>(X1114 @ X1115))))=>?[X1116:$i]:(((in @ X1116 @ X1113)&~((X1114 @ X1116))))))=>(![X1117:$i > $o]:((?[X1118:$i]:(((X1117 @ X1118)&![X1119:$i]:(((X1117 @ X1119)=>((X1118)=(X1119))))))=>(exu @ X1117)))=>(![X1120:$i > $o]:((?[X1121:$i]:((X1120 @ X1121))=>(![X1122:$i, X1123:$i]:(((X1120 @ X1122)=>((X1120 @ X1123)=>((X1122)=(X1123)))))=>(exu @ X1120))))=>(![X1124:$i > $o]:((?[X1125:$i]:(![X1126:$i]:(((X1124 @ X1126)<=>((X1126)=(X1125)))))=>(exu @ X1124)))=>(![X1127:$i, X1128:$i]:((((X1127)=(X1128))=>![X1129:$i, X1130:$i]:((((X1129)=(X1130))=>((in @ X1129 @ X1127)=>(in @ X1130 @ X1128))))))=>(![X1131:$i, X1132:$i]:((((X1131)=(X1132))=>![X1133:$i, X1134:$i]:((((X1133)=(X1134))=>((in @ X1133 @ X1131)<=>(in @ X1134 @ X1132))))))=>(![X1135:$i > $o]:(((exu @ X1135)=>![X1136:$i, X1137:$i]:(((X1135 @ X1136)=>((X1135 @ X1137)=>((X1136)=(X1137)))))))=>(![X1138:$i > $o, X1139:$i > $o]:((![X1140:$i, X1141:$i]:((((X1140)=(X1141))=>((X1138 @ X1140)<=>(X1139 @ X1141))))=>((exu @ X1138)<=>(exu @ X1139))))=>(((emptyset)=(emptyset))=>(![X1142:$i, X1143:$i]:((((X1142)=(X1143))=>![X1144:$i, X1145:$i]:((((X1144)=(X1145))=>((setadjoin @ X1142 @ X1144)=(setadjoin @ X1143 @ X1145))))))=>(![X1146:$i, X1147:$i]:((((X1146)=(X1147))=>((powerset @ X1146)=(powerset @ X1147))))=>(![X1148:$i, X1149:$i]:((((X1148)=(X1149))=>((setunion @ X1148)=(setunion @ X1149))))=>(((omega)=(omega))=>(![X1150:$i > $o]:(((exu @ X1150)=>![X1151:$i, X1152:$i]:(((X1150 @ X1151)=>((X1150 @ X1152)=>((X1151)=(X1152)))))))=>(![X1153:$i > $o, X1154:$i > $o]:((![X1155:$i, X1156:$i]:((((X1155)=(X1156))=>((X1153 @ X1155)<=>(X1154 @ X1156))))=>((exu @ X1153)=>((exu @ X1154)=>((descr @ X1153)=(descr @ X1154))))))=>(![X1157:$i, X1158:$i]:((((X1157)=(X1158))=>![X1159:$i > $o, X1160:$i > $o]:((![X1161:$i]:(((in @ X1161 @ X1157)=>![X1162:$i]:(((in @ X1162 @ X1158)=>(((X1161)=(X1162))=>((X1159 @ X1161)<=>(X1160 @ X1162)))))))=>((dsetconstr @ X1157 @ X1159)=(dsetconstr @ X1158 @ X1160))))))=>(![X1163:$i, X1164:$i]:((![X1165:$i]:(((in @ X1165 @ X1163)=>(in @ X1165 @ X1164)))=>(subset @ X1163 @ X1164)))=>(![X1166:$i, X1167:$i]:((((X1166)=(X1167))=>(subset @ X1167 @ X1166)))=>(![X1168:$i, X1169:$i]:((((X1168)=(X1169))=>(subset @ X1168 @ X1169)))=>(![X1170:$i, X1171:$i]:((![X1172:$i]:(((in @ X1172 @ X1170)=>(in @ X1172 @ X1171)))=>(subset @ X1170 @ X1171)))=>(![X1173:$i]:((subset @ emptyset @ X1173))=>(![X1174:$i, X1175:$i, X1176:$i]:(((subset @ X1174 @ X1175)=>((in @ X1176 @ X1174)=>(in @ X1176 @ X1175))))=>(![X1177:$i, X1178:$i, X1179:$i]:(((subset @ X1177 @ X1178)=>(~(in @ X1179 @ X1178)=>~(in @ X1179 @ X1177))))=>(![X1180:$i, X1181:$i, X1182:$i]:(((in @ X1182 @ X1180)=>(~(in @ X1182 @ X1181)=>~(subset @ X1180 @ X1181))))=>(![X1183:$i, X1184:$i]:((~(subset @ X1183 @ X1184)=>((X1183)!=(X1184))))=>(![X1185:$i, X1186:$i, X1187:$i]:(((in @ X1187 @ X1185)=>(~(in @ X1187 @ X1186)=>((X1185)!=(X1186)))))=>(![X1188:$i]:((subset @ X1188 @ X1188))=>(![X1189:$i, X1190:$i, X1191:$i]:(((subset @ X1189 @ X1190)=>((subset @ X1190 @ X1191)=>(subset @ X1189 @ X1191))))=>(![X1192:$i, X1193:$i]:((subset @ X1193 @ (setadjoin @ X1192 @ X1193)))=>(![X1194:$i, X1195:$i, X1196:$i]:(((subset @ X1194 @ X1196)=>(subset @ X1194 @ (setadjoin @ X1195 @ X1196))))=>(![X1197:$i, X1198:$i]:(((subset @ X1197 @ X1198)=>(in @ X1197 @ (powerset @ X1198))))=>(![X1199:$i, X1200:$i]:(((subset @ X1199 @ X1200)=>((subset @ X1200 @ X1199)=>((X1199)=(X1200)))))=>(![X1201:$i]:(((subset @ X1201 @ emptyset)=>((X1201)=(emptyset))))=>(![X1202:$i, X1203:$i]:(((subset @ X1203 @ X1202)=>(in @ X1203 @ (powerset @ X1202))))=>(![X1204:$i, X1205:$i]:(((in @ X1205 @ (powerset @ X1204))=>(subset @ X1205 @ X1204)))=>(![X1206:$i]:((in @ X1206 @ (powerset @ X1206)))=>(![X1207:$i, X1208:$i]:(((subset @ X1207 @ X1208)=>(subset @ (powerset @ X1207) @ (powerset @ X1208))))=>(![X1209:$i, X1210:$i > $o]:((in @ (dsetconstr @ X1209 @ X1210) @ (powerset @ X1209)))=>(![X1211:$i, X1212:$i > $o]:((subset @ (dsetconstr @ X1211 @ X1212) @ X1211))=>(![X1213:$i, X1214:$i, X1215:$i]:(((in @ X1215 @ X1213)=>(in @ X1215 @ (binunion @ X1213 @ X1214))))=>(![X1216:$i, X1217:$i]:((in @ X1217 @ (setadjoin @ X1216 @ (setadjoin @ X1217 @ emptyset))))=>(![X1218:$i, X1219:$i, X1220:$i]:(((in @ X1220 @ X1219)=>(in @ X1220 @ (binunion @ X1218 @ X1219))))=>(![X1221:$i, X1222:$i, X1223:$i, X1224:$o]:(((in @ X1223 @ (binunion @ X1221 @ X1222))=>(((in @ X1223 @ X1221)=>(X1224))=>(((in @ X1223 @ X1222)=>(X1224))=>(X1224)))))=>(![X1225:$i, X1226:$i, X1227:$i]:(((in @ X1227 @ (binunion @ X1225 @ X1226))=>((in @ X1227 @ X1225)|(in @ X1227 @ X1226))))=>(![X1228:$i, X1229:$i]:((subset @ X1228 @ (binunion @ X1228 @ X1229)))=>(![X1230:$i, X1231:$i]:((subset @ X1231 @ (binunion @ X1230 @ X1231)))=>(![X1232:$i, X1233:$i, X1234:$i]:(((in @ X1234 @ X1232)=>((in @ X1234 @ X1233)=>(in @ X1234 @ (binintersect @ X1232 @ 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X1820:$i]:(((in @ X1820 @ (powerset @ X1819))=>![X1821:$i]:(((in @ X1821 @ (powerset @ X1819))=>![X1822:$i]:(((in @ X1822 @ (binintersect @ X1820 @ X1821))=>(in @ X1822 @ X1819)))))))=>(![X1823:$i, X1824:$i]:(((in @ X1824 @ (powerset @ X1823))=>![X1825:$i]:(((in @ X1825 @ (powerset @ X1823))=>![X1826:$i]:(((in @ X1826 @ (powerset @ X1823))=>((subset @ X1824 @ X1826)=>(subset @ (binintersect @ X1824 @ X1825) @ X1826))))))))=>(![X1827:$i, X1828:$i]:(((in @ X1828 @ (powerset @ X1827))=>![X1829:$i]:(((in @ X1829 @ (powerset @ X1827))=>![X1830:$i]:(((in @ X1830 @ (powerset @ X1827))=>((subset @ X1829 @ X1830)=>(subset @ (binintersect @ X1828 @ X1829) @ X1830))))))))=>(![X1831:$i, X1832:$i]:(((in @ X1832 @ (powerset @ X1831))=>![X1833:$i]:(((in @ X1833 @ (powerset @ X1831))=>![X1834:$i]:(((in @ X1834 @ (powerset @ X1831))=>((subset @ X1832 @ X1833)=>((subset @ X1832 @ X1834)=>(subset @ X1832 @ (binintersect @ X1833 @ X1834))))))))))=>(![X1835:$i, X1836:$i]:(((in @ X1836 @ (powerset @ X1835))=>![X1837:$i]:(((in @ X1837 @ (powerset @ X1835))=>![X1838:$i]:(((in @ X1838 @ (powerset @ X1835))=>![X1839:$i]:(((in @ X1839 @ (powerset @ X1835))=>((subset @ X1836 @ X1838)=>((subset @ X1837 @ X1839)=>(subset @ (binintersect @ X1836 @ X1837) @ (binintersect @ X1838 @ X1839))))))))))))=>(![X1840:$i, X1841:$i]:(((in @ X1841 @ (powerset @ X1840))=>![X1842:$i]:(((in @ X1842 @ (powerset @ X1840))=>(in @ (setminus @ X1840 @ X1841) @ (powerset @ (setminus @ X1840 @ (binintersect @ X1841 @ X1842))))))))=>(![X1843:$i, X1844:$i]:(((in @ X1844 @ (powerset @ X1843))=>![X1845:$i]:(((in @ X1845 @ (powerset @ X1843))=>![X1846:$i]:(((in @ X1846 @ (powerset @ X1843))=>![X1847:$i]:(((in @ X1847 @ (powerset @ X1843))=>((setminus @ X1843 @ (binintersect @ (binunion @ X1844 @ X1845) @ (binunion @ X1846 @ X1847)))=(binunion @ (binintersect @ (setminus @ X1843 @ X1844) @ (setminus @ X1843 @ X1845)) @ (binintersect @ (setminus @ X1843 @ X1846) @ (setminus @ X1843 @ X1847))))))))))))=>![X4:$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_281, binintersectTELcontra]), complementTE1]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), setunion__Cong]), doubleComplementSub2]), powerset__Cong]), doubleComplementEq]), setadjoin__Cong]), complementTnotintersectT]), emptyset__Cong]), complementImpComplementIntersect]), c_0_282]), complementSubsetComplementIntersect]), c_0_283]), complementInPowersetComplementIntersect]), contraSubsetComplement]), in__Cong]), complementTcontraSubset]), omega__Cong]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), subsetI2]), demorgan1a]), eqimpsubset1]), demorgan1b]), eqimpsubset2]), demorgan1]), subsetI1]), demorgan2a]), c_0_284]), demorgan2b2]), c_0_285]), demorgan2b]), c_0_286]), demorgan2]), emptysetsubset]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), setadjoinSub]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), powersetsubset]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_287]), c_0_288]), binunionLsub]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), binintersectER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), setminusER]), c_0_289]), c_0_290]), ap2apEq2]), ap2apEq1]), funcext2]), c_0_291]), theeq]), ifp]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), symdiffE]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), kpairiskpair]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), ubforcartprodlem1]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), setunionsingleton2]), setukpairinjL1]), singletonsuniq]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), setunionsingleton]), c_0_296]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), theprop]), setukpairinjR1]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), c_0_297]), setukpairinjR]), setukpairinjR2]), upairequniteq]), cartprodpairmemEL]), c_0_298]), c_0_299]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemER]), c_0_300]), app]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), c_0_306]), infuncsetfunc]), brelnall2]), brelnall1]), c_0_307]), c_0_308]), c_0_309]), funcinfuncset]), ap2p]), c_0_310]), eqbreln]), subbreln]), funcGraphProp4]), funcextLem]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), funcext]), c_0_311]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), iftrue]), complementT_lem]), setminusT_lem]), powersetT_lem]), binunionT_lem]), binintersectT_lem]), iftrueorfalse]), iffalse]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), setextT]), inCongP]), c_0_318]), c_0_319]), c_0_320]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_321]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), nonemptyImpWitness]), c_0_322]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_323]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_324]), nonemptyE1]), c_0_325]), noeltsimpempty]), emptyI]), setext]), c_0_326]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_327]), c_0_328]), c_0_329]), c_0_330]), c_0_331]), wellorderingAx]), foundationAx]), c_0_332]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_333])).
% 52.90/10.87 thf(c_0_335, negated_conjecture, ![X1848:$i, X1849:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1861:$i, X1862:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1870:$i, X1871:$i > $i > $o, X1872:$i, X1875:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1882:$i, X1883:$i > $o, X1884:$i, X1885:$i > $o, X1886:$i, X1887:$i, X1888:$i > $o, X1889:$i, X1890:$i, X1891:$i > $o, X1892:$i, X1893:$i > $o, X1895:$i, X1896:$o, X1897:$i, X1898:$i, X1899:$o, X1900:$i, X1901:$i, X1902:$i > $o, X1904:$i, X1905:$i, X1908:$i, X1910:$i, X1912:$i, X1913:$i > $o, X1914:$i, X1915:$i, X1917:$i, X1918:$i > $o, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$o, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$o, X1950:$i, X1951:$i, X1952:$i > $o, X1954:$i, X1955:$i, X1956:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i > $o, X1975:$i, X1976:$i > $o, X1977:$i, X1978:$i, X1979:$i > $o, X1980:$i, X1982:$i, X1983:$i > $o, X1985:$i, X1986:$i, X1987:$i > $o, X1989:$i, X1990:$i, X1991:$i > $o, X1992:$i, X1994:$o, X1995:$i, X1996:$i > $o, X1998:$i, X1999:$i, X2000:$i > $o, X2001:$i, X2003:$i > $o, X2004:$i, X2006:$i > $o, X2007:$i, X2010:$i > $o, X2011:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i > $o, X2022:$i, X2023:$i, X2024:$i > $o, X2025:$i > $o, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i > $o, X2037:$i, X2038:$i, X2039:$i > $o, X2040:$i > $o, X2043:$i, X2044:$i, X2045:$i > $o, X2046:$i > $o, X2049:$i, X2050:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i > $o, X2097:$i, X2098:$i > $o, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$o, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$o, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$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, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i > $o, X2253:$i, X2254:$i, X2255:$i > $o, X2257:$i, X2258:$i > $o, X2259:$i, X2261:$i, X2262:$i > $o, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$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 > $i > $o, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i > $i > $o, X2343:$i, X2344:$i, X2345:$i > $i > $o, X2346:$i, X2347:$i, X2348:$i > $i > $o, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i > $i > $o, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i > $i > $o, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i > $i > $o, X2364:$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:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i > $i, X2392:$i, X2393:$i, X2394:$i > $i, X2396:$i, X2397:$i, X2398:$i > $i, X2400:$i, X2401:$i, X2402:$i, X2403:$i > $o, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i > $o, X2413:$i, X2414:$i, X2415:$i > $o, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i > $i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i > $i, X2487:$i, X2488:$i, X2489:$i > $i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$o, X2497:$i, X2498:$i, X2499:$i, X2500:$o, X2501:$i, X2502:$i, X2503:$i, X2504:$o, X2505:$i, X2506:$i, X2507:$i, X2508:$o, X2509:$i, X2510:$i, X2511:$i, X2512:$o, X2513:$i, X2514:$i, X2515:$i, X2516:$o, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$o, X2523:$i, X2524:$i, X2525:$i, X2526:$o, X2527:$i, X2528:$i, X2529:$i, X2530:$o, X2531:$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:$i, X2551:$i, X2552:$i, X2553:$i, X2555:$i, X2556:$i, X2557:$i, X2559:$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, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, 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:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$o, X2663:$i, 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:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$i, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i]:((((~(in @ (esk1_2 @ X1848 @ X1849) @ X1848)|~(in @ (esk1_2 @ X1848 @ X1849) @ X1849)|((X1848)=(X1849)))&((in @ (esk1_2 @ X1848 @ X1849) @ X1848)|(in @ (esk1_2 @ X1848 @ X1849) @ X1849)|((X1848)=(X1849))))&(~(in @ X1851 @ emptyset)&(((~(in @ X1854 @ (setadjoin @ X1852 @ X1853))|(((X1854)=(X1852))|(in @ X1854 @ X1853)))&((((X1854)!=(X1852))|(in @ X1854 @ (setadjoin @ X1852 @ X1853)))&(~(in @ X1854 @ X1853)|(in @ X1854 @ (setadjoin @ X1852 @ X1853)))))&(((~(in @ X1856 @ (powerset @ X1855))|(~(in @ X1857 @ X1856)|(in @ X1857 @ X1855)))&(((in @ (esk2_2 @ X1858 @ X1859) @ X1859)|(in @ X1859 @ (powerset @ X1858)))&(~(in @ (esk2_2 @ X1858 @ X1859) @ X1858)|(in @ X1859 @ (powerset @ X1858)))))&(((((in @ X1862 @ (esk3_2 @ X1861 @ X1862))|~(in @ X1862 @ (setunion @ X1861)))&((in @ (esk3_2 @ X1861 @ X1862) @ X1861)|~(in @ X1862 @ (setunion @ X1861))))&(~(in @ X1865 @ X1866)|~(in @ X1866 @ X1864)|(in @ X1865 @ (setunion @ X1864))))&((in @ emptyset @ omega)&((~(in @ X1867 @ omega)|(in @ (setadjoin @ X1867 @ X1867) @ omega))&(((((in @ (esk4_1 @ X1868) @ omega)|~(in @ emptyset @ X1868)|(~(in @ X1870 @ omega)|(in @ X1870 @ X1868)))&((in @ (esk4_1 @ X1868) @ X1868)|~(in @ emptyset @ X1868)|(~(in @ X1870 @ omega)|(in @ X1870 @ X1868))))&(~(in @ (setadjoin @ (esk4_1 @ X1868) @ (esk4_1 @ X1868)) @ X1868)|~(in @ emptyset @ X1868)|(~(in @ X1870 @ omega)|(in @ X1870 @ X1868))))&((((((in @ (esk7_3 @ X1871 @ X1872 @ X1875) @ X1872)|~(in @ X1875 @ (esk6_2 @ X1871 @ X1872))|(in @ (esk5_2 @ X1871 @ X1872) @ X1872))&((X1871 @ (esk7_3 @ X1871 @ X1872 @ X1875) @ X1875)|~(in @ X1875 @ (esk6_2 @ X1871 @ X1872))|(in @ (esk5_2 @ X1871 @ X1872) @ X1872)))&(~(in @ X1878 @ X1872)|~(X1871 @ X1878 @ X1877)|(in @ X1877 @ (esk6_2 @ X1871 @ X1872))|(in @ (esk5_2 @ X1871 @ X1872) @ X1872)))&((((in @ (esk7_3 @ X1871 @ X1872 @ X1875) @ X1872)|~(in @ X1875 @ (esk6_2 @ X1871 @ X1872))|~(exu @ (X1871 @ (esk5_2 @ X1871 @ X1872))))&((X1871 @ (esk7_3 @ X1871 @ X1872 @ X1875) @ X1875)|~(in @ X1875 @ (esk6_2 @ X1871 @ X1872))|~(exu @ (X1871 @ (esk5_2 @ X1871 @ X1872)))))&(~(in @ X1878 @ X1872)|~(X1871 @ X1878 @ X1877)|(in @ X1877 @ (esk6_2 @ X1871 @ X1872))|~(exu @ (X1871 @ (esk5_2 @ X1871 @ X1872))))))&((((in @ (esk8_1 @ X1879) @ X1879)|~(in @ X1880 @ X1879))&(~(in @ X1882 @ (esk8_1 @ X1879))|~(in @ X1882 @ X1879)|~(in @ X1880 @ X1879)))&((epred1_0)&((~(exu @ X1883)|(X1883 @ (descr @ X1883)))&((~(in @ X1886 @ X1884)|(~(X1885 @ X1886)|(in @ X1886 @ (dsetconstr @ X1884 @ X1885))))&((~(in @ X1889 @ (dsetconstr @ X1887 @ X1888))|(in @ X1889 @ X1887))&((~(in @ X1892 @ (dsetconstr @ X1890 @ X1891))|(X1891 @ X1892))&((((X1893 @ (esk9_1 @ X1893))|~(exu @ X1893))&(~(X1893 @ X1895)|((esk9_1 @ X1893)=(X1895))|~(exu @ X1893)))&((~(in @ X1897 @ (prop2set @ ((X1896))))|(X1896))&((~(in @ X1898 @ emptyset)|(X1899))&((~(in @ X1900 @ emptyset)|~($true))&(~(in @ X1901 @ emptyset)&((~(exu @ X1902)|(X1902 @ (esk10_1 @ X1902)))&(((((in @ (esk12_2 @ X1904 @ X1905) @ X1905)|((X1904)=(X1905))|(in @ (esk11_2 @ X1904 @ X1905) @ X1904))&(~(in @ (esk12_2 @ X1904 @ X1905) @ X1904)|((X1904)=(X1905))|(in @ (esk11_2 @ X1904 @ X1905) @ X1904)))&(((in @ (esk12_2 @ X1904 @ X1905) @ X1905)|((X1904)=(X1905))|~(in @ (esk11_2 @ X1904 @ X1905) @ X1905))&(~(in @ (esk12_2 @ X1904 @ X1905) @ X1904)|((X1904)=(X1905))|~(in @ (esk11_2 @ X1904 @ X1905) @ X1905))))&(((in @ (esk13_1 @ X1908) @ X1908)|((X1908)=(emptyset)))&(((in @ (esk14_1 @ X1910) @ X1910)|((X1910)=(emptyset)))&(((~(in @ X1914 @ (dsetconstr @ X1912 @ X1913))|(X1913 @ X1914)|~(in @ X1914 @ X1912))&(~(X1913 @ X1914)|(in @ X1914 @ (dsetconstr @ X1912 @ X1913))|~(in @ X1914 @ X1912)))&((~(nonempty @ X1915)|(in @ (esk15_1 @ X1915) @ X1915))&((~(in @ X1919 @ X1917)|(~(X1918 @ X1919)|(nonempty @ (dsetconstr @ X1917 @ X1918))))&((~(in @ X1921 @ X1920)|(nonempty @ X1920))&((in @ X1922 @ (setadjoin @ X1922 @ X1923))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1926 @ X1925)|(in @ X1926 @ (setadjoin @ X1924 @ X1925)))&(((((in @ X1929 @ X1928)|(X1930)|((X1929)=(X1927))|~(in @ X1929 @ (setadjoin @ X1927 @ X1928)))&(~(X1930)|(X1930)|((X1929)=(X1927))|~(in @ X1929 @ (setadjoin @ X1927 @ X1928))))&(((in @ X1929 @ X1928)|(X1930)|~(X1930)|~(in @ X1929 @ (setadjoin @ X1927 @ X1928)))&(~(X1930)|(X1930)|~(X1930)|~(in @ X1929 @ (setadjoin @ X1927 @ X1928)))))&((~(in @ X1933 @ (setadjoin @ X1931 @ X1932))|(((X1933)=(X1931))|(in @ X1933 @ X1932)))&(((dsetconstr @ X1934 @ (^[Z0:$i]:($true)))=(X1934))&((((in @ (esk16_2 @ X1935 @ X1936) @ X1936)|(in @ X1936 @ (powerset @ X1935)))&(~(in @ (esk16_2 @ X1935 @ X1936) @ X1935)|(in @ X1936 @ (powerset @ X1935))))&((in @ emptyset @ (powerset @ X1938))&((in @ emptyset @ (powerset @ X1939))&((~(in @ X1941 @ (powerset @ X1940))|(~(in @ X1942 @ X1941)|(in @ X1942 @ X1940)))&((~(in @ X1944 @ X1945)|(~(in @ X1945 @ X1943)|(in @ X1944 @ (setunion @ X1943))))&((((in @ X1947 @ (esk17_3 @ X1946 @ X1947 @ X1948))|(X1948)|~(in @ X1947 @ (setunion @ X1946)))&(((in @ (esk17_3 @ X1946 @ X1947 @ X1948) @ X1946)|(X1948)|~(in @ X1947 @ (setunion @ X1946)))&(~(X1948)|(X1948)|~(in @ X1947 @ (setunion @ X1946)))))&((~(in @ X1951 @ X1950)|(in @ X1951 @ (powerset @ (setunion @ X1950))))&(((~(X1952 @ X1954)|((X1954)=(esk18_1 @ X1952))|~(exu @ X1952))&(((X1955)!=(esk18_1 @ X1952))|(X1952 @ X1955)|~(exu @ X1952)))&((((in @ (esk19_1 @ X1956) @ X1956)|~(nonempty @ X1956))&(($true)|~(nonempty @ X1956)))&((~(in @ X1958 @ (setadjoin @ X1959 @ emptyset))|((X1958)=(X1959)))&((((X1960)=(X1961))|~(in @ X1961 @ (setadjoin @ X1960 @ emptyset)))&((((X1962)!=(X1963))|(in @ X1962 @ (setadjoin @ X1963 @ emptyset)))&((~(in @ X1964 @ (setadjoin @ X1965 @ emptyset))|(in @ X1965 @ (setadjoin @ X1964 @ emptyset)))&((~(in @ X1968 @ (setadjoin @ X1966 @ (setadjoin @ X1967 @ emptyset)))|(((X1968)=(X1966))|((X1968)=(X1967))))&((in @ X1969 @ (setadjoin @ X1969 @ (setadjoin @ X1970 @ emptyset)))&((in @ X1972 @ (setadjoin @ X1971 @ (setadjoin @ X1972 @ emptyset)))&((~(in @ X1975 @ X1973)|~(X1974 @ X1975)|(((dsetconstr @ X1973 @ X1974)!=(emptyset))|~($true)))&((~(in @ X1977 @ emptyset)|(X1976 @ X1977))&((((in @ (esk20_2 @ X1978 @ X1979) @ X1978)|(~(in @ X1980 @ X1978)|(X1979 @ X1980)))&(~(X1979 @ (esk20_2 @ X1978 @ X1979))|(~(in @ X1980 @ X1978)|(X1979 @ X1980))))&((((in @ (esk21_2 @ X1982 @ X1983) @ X1982)|(~(in @ X1985 @ X1982)|~(X1983 @ X1985)))&((X1983 @ (esk21_2 @ X1982 @ X1983))|(~(in @ X1985 @ X1982)|~(X1983 @ X1985))))&((((in @ (esk22_2 @ 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@ (powerset @ X2624))|(~(in @ X2627 @ X2624)|((in @ X2627 @ (binunion @ X2625 @ X2626))|~(in @ X2627 @ X2625)))))&((~(in @ X2629 @ (powerset @ X2628))|(~(in @ X2630 @ (powerset @ X2628))|(~(in @ X2631 @ X2628)|((in @ X2631 @ (binunion @ X2629 @ X2630))|~(in @ X2631 @ X2630)))))&((~(in @ X2633 @ (powerset @ X2632))|(~(in @ X2634 @ (powerset @ X2632))|(~(in @ X2635 @ (powerset @ X2632))|(~(in @ X2636 @ X2632)|(~(in @ X2636 @ (binintersect @ X2633 @ X2634))|(in @ X2636 @ (binunion @ X2633 @ X2635)))))))&((~(in @ X2638 @ (powerset @ X2637))|(~(in @ X2639 @ (powerset @ X2637))|(~(in @ X2640 @ (powerset @ X2637))|(~(in @ X2641 @ X2637)|(~(in @ X2641 @ (binintersect @ X2638 @ X2639))|(in @ X2641 @ (binunion @ X2639 @ X2640)))))))&((~(in @ X2643 @ (powerset @ X2642))|(~(in @ X2644 @ (powerset @ X2642))|(~(in @ X2645 @ (powerset @ X2642))|(~(in @ X2646 @ X2642)|(~(in @ X2646 @ (binintersect @ X2643 @ X2644))|(in @ X2646 @ (binintersect @ (binunion @ X2643 @ X2645) @ (binunion @ X2644 @ X2645))))))))&((~(in @ X2648 @ (powerset @ X2647))|(~(in @ X2649 @ (powerset @ X2647))|(~(in @ X2650 @ (powerset @ X2647))|(in @ (binintersect @ X2648 @ X2649) @ (powerset @ (binintersect @ (binunion @ X2648 @ X2650) @ (binunion @ X2649 @ X2650)))))))&((~(in @ X2652 @ (powerset @ X2651))|(~(in @ X2653 @ (powerset @ X2651))|(~(in @ X2654 @ X2651)|(~(in @ X2654 @ (setminus @ X2651 @ (binunion @ X2652 @ X2653)))|~(in @ X2654 @ X2652)))))&((~(in @ X2656 @ (powerset @ X2655))|(~(in @ X2657 @ (powerset @ X2655))|(~(in @ X2658 @ X2655)|(~(in @ X2658 @ (setminus @ X2655 @ (binunion @ X2656 @ X2657)))|(in @ X2658 @ (setminus @ X2655 @ X2656))))))&(((((in @ X2663 @ X2661)|(X2662)|(in @ X2663 @ X2660)|~(in @ X2663 @ (binunion @ X2660 @ X2661))|~(in @ X2663 @ X2659)|~(in @ X2661 @ (powerset @ X2659))|~(in @ X2660 @ (powerset @ X2659)))&(~(X2662)|(X2662)|(in @ X2663 @ X2660)|~(in @ X2663 @ (binunion @ X2660 @ X2661))|~(in @ X2663 @ X2659)|~(in @ X2661 @ (powerset @ X2659))|~(in @ X2660 @ (powerset @ X2659))))&(((in @ X2663 @ X2661)|(X2662)|~(X2662)|~(in @ X2663 @ (binunion @ X2660 @ X2661))|~(in @ X2663 @ X2659)|~(in @ X2661 @ (powerset @ X2659))|~(in @ X2660 @ (powerset @ X2659)))&(~(X2662)|(X2662)|~(X2662)|~(in @ X2663 @ (binunion @ X2660 @ X2661))|~(in @ X2663 @ X2659)|~(in @ X2661 @ (powerset @ X2659))|~(in @ X2660 @ (powerset @ X2659)))))&((~(in @ X2665 @ (powerset @ X2664))|(~(in @ X2666 @ (powerset @ X2664))|(~(in @ X2667 @ X2664)|((in @ X2667 @ X2665)|((in @ X2667 @ X2666)|~(in @ X2667 @ (binunion @ X2665 @ X2666)))))))&((~(in @ X2669 @ (powerset @ X2668))|(~(in @ X2670 @ (powerset @ X2668))|(~(in @ X2671 @ X2668)|(~(in @ X2671 @ (setminus @ X2668 @ (binunion @ X2669 @ X2670)))|(in @ X2671 @ (setminus @ X2668 @ X2669))))))&((~(in @ X2673 @ (powerset @ X2672))|(~(in @ X2674 @ (powerset @ X2672))|(in @ (setminus @ X2672 @ (binunion @ X2673 @ X2674)) @ (powerset @ (setminus @ X2672 @ X2673)))))&((~(in @ X2676 @ (powerset @ X2675))|(~(in @ X2677 @ (powerset @ X2675))|(~(in @ X2678 @ X2675)|(~(in @ X2678 @ (setminus @ X2675 @ (binunion @ X2676 @ X2677)))|(in @ X2678 @ (setminus @ X2675 @ X2677))))))&((~(in @ X2680 @ (powerset @ X2679))|(~(in @ X2681 @ (powerset @ X2679))|(~(in @ X2682 @ X2679)|(~(in @ X2682 @ (setminus @ X2679 @ (binintersect @ X2680 @ X2681)))|(in @ X2682 @ (binunion @ (setminus @ X2679 @ X2680) @ (setminus @ X2679 @ X2681)))))))&((~(in @ X2684 @ (powerset @ X2683))|(~(in @ X2685 @ (powerset @ X2683))|(~(in @ X2686 @ X2683)|(~(in @ X2686 @ (binunion @ (setminus @ X2683 @ X2684) @ (setminus @ X2683 @ X2685)))|(in @ X2686 @ (setminus @ X2683 @ (binintersect @ X2684 @ X2685)))))))&((~(in @ X2688 @ (powerset @ X2687))|(~(in @ X2689 @ (powerset @ X2687))|((setminus @ X2687 @ (binintersect @ X2688 @ X2689))=(binunion @ (setminus @ X2687 @ X2688) @ (setminus @ X2687 @ X2689)))))&((~(in @ X2691 @ (powerset @ X2690))|(~(in @ X2692 @ (powerset @ X2690))|(~(in @ X2693 @ X2690)|(~(in @ X2693 @ (setminus @ X2690 @ (binunion @ X2691 @ X2692)))|(in @ X2693 @ (binintersect @ (setminus @ X2690 @ X2691) @ (setminus @ X2690 @ X2692)))))))&((~(in @ X2695 @ (powerset @ X2694))|(~(in @ X2696 @ (powerset @ X2694))|(~(in @ X2697 @ X2694)|(~(in @ X2697 @ (setminus @ X2694 @ X2695))|(~(in @ X2697 @ (setminus @ X2694 @ X2696))|(in @ X2697 @ (setminus @ X2694 @ (binunion @ X2695 @ X2696))))))))&((~(in @ X2699 @ (powerset @ X2698))|(~(in @ X2700 @ (powerset @ X2698))|(~(in @ X2701 @ X2698)|(~(in @ X2701 @ (binintersect @ (setminus @ X2698 @ X2699) @ (setminus @ X2698 @ X2700)))|(in @ X2701 @ (setminus @ X2698 @ (binunion @ X2699 @ X2700)))))))&((~(in @ X2703 @ (powerset @ X2702))|(~(in @ X2704 @ (powerset @ X2702))|((setminus @ X2702 @ (binunion @ X2703 @ X2704))=(binintersect @ (setminus @ X2702 @ X2703) @ (setminus @ X2702 @ X2704)))))&((~(in @ X2706 @ (powerset @ X2705))|(~(in @ X2707 @ (powerset @ X2705))|(~(in @ X2708 @ (binintersect @ X2706 @ X2707))|(in @ X2708 @ X2705))))&((~(in @ X2710 @ (powerset @ X2709))|(~(in @ X2711 @ (powerset @ X2709))|(~(in @ X2712 @ (powerset @ X2709))|(~(subset @ X2710 @ X2712)|(subset @ (binintersect @ X2710 @ X2711) @ X2712)))))&((~(in @ X2714 @ (powerset @ X2713))|(~(in @ X2715 @ (powerset @ X2713))|(~(in @ X2716 @ (powerset @ X2713))|(~(subset @ X2715 @ X2716)|(subset @ (binintersect @ X2714 @ X2715) @ X2716)))))&((~(in @ X2718 @ (powerset @ X2717))|(~(in @ X2719 @ (powerset @ X2717))|(~(in @ X2720 @ (powerset @ X2717))|(~(subset @ X2718 @ X2719)|(~(subset @ X2718 @ X2720)|(subset @ X2718 @ (binintersect @ X2719 @ X2720)))))))&((~(in @ X2722 @ (powerset @ X2721))|(~(in @ X2723 @ (powerset @ X2721))|(~(in @ X2724 @ (powerset @ X2721))|(~(in @ X2725 @ (powerset @ X2721))|(~(subset @ X2722 @ X2724)|(~(subset @ X2723 @ X2725)|(subset @ (binintersect @ X2722 @ X2723) @ (binintersect @ X2724 @ X2725))))))))&((~(in @ X2727 @ (powerset @ X2726))|(~(in @ X2728 @ (powerset @ X2726))|(in @ (setminus @ X2726 @ X2727) @ (powerset @ (setminus @ X2726 @ (binintersect @ X2727 @ X2728))))))&((~(in @ X2730 @ (powerset @ X2729))|(~(in @ X2731 @ (powerset @ X2729))|(~(in @ X2732 @ (powerset @ X2729))|(~(in @ X2733 @ (powerset @ X2729))|((setminus @ X2729 @ (binintersect @ (binunion @ X2730 @ X2731) @ (binunion @ X2732 @ X2733)))=(binunion @ (binintersect @ (setminus @ X2729 @ X2730) @ (setminus @ X2729 @ X2731)) @ (binintersect @ (setminus @ X2729 @ X2732) @ (setminus @ X2729 @ X2733))))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ (powerset @ esk71_0))&~(in @ (binintersect @ esk72_0 @ esk73_0) @ (powerset @ (binintersect @ (binunion @ esk72_0 @ esk74_0) @ (binunion @ esk73_0 @ esk74_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_334])])])])])])])).
% 52.90/10.87 thf(c_0_336, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk36_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_335])).
% 52.90/10.87 thf(c_0_337, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_335])).
% 52.90/10.87 thf(c_0_338, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X4)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_335])).
% 52.90/10.87 thf(c_0_339, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk36_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_335])).
% 52.90/10.87 thf(c_0_340, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_335])).
% 52.90/10.87 thf(c_0_341, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_335])).
% 52.90/10.87 thf(c_0_342, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X2 @ (binintersect @ X3 @ X4))|~((subset @ X2 @ X3))|~((subset @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_335])).
% 52.90/10.87 thf(c_0_343, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((subset @ X2 @ (binunion @ X3 @ X4))|~((in @ (esk36_2 @ X2 @ (binunion @ X3 @ X4)) @ X3)))), inference(spm,[status(thm)],[c_0_336, c_0_337])).
% 52.90/10.87 thf(c_0_344, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (esk36_2 @ (binintersect @ X2 @ X3) @ X4) @ X3)|(subset @ (binintersect @ X2 @ X3) @ X4))), inference(spm,[status(thm)],[c_0_338, c_0_339])).
% 52.90/10.87 thf(c_0_345, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (esk36_2 @ (binintersect @ X2 @ X3) @ X4) @ X2)|(subset @ (binintersect @ X2 @ X3) @ X4))), inference(spm,[status(thm)],[c_0_340, c_0_339])).
% 52.90/10.87 thf(c_0_346, negated_conjecture, ~((in @ (binintersect @ esk72_0 @ esk73_0) @ (powerset @ (binintersect @ (binunion @ esk72_0 @ esk74_0) @ (binunion @ esk73_0 @ esk74_0))))), inference(split_conjunct,[status(thm)],[c_0_335])).
% 52.90/10.87 thf(c_0_347, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (powerset @ (binintersect @ X3 @ X4)))|~((subset @ X2 @ X4))|~((subset @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_341, c_0_342])).
% 52.90/10.87 thf(c_0_348, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((subset @ (binintersect @ X2 @ X3) @ (binunion @ X3 @ X4))), inference(spm,[status(thm)],[c_0_343, c_0_344])).
% 52.90/10.87 thf(c_0_349, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((subset @ (binintersect @ X2 @ X3) @ (binunion @ X2 @ X4))), inference(spm,[status(thm)],[c_0_343, c_0_345])).
% 52.90/10.87 thf(c_0_350, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_346, c_0_347]), c_0_348]), c_0_349])]), ['proof']).
% 52.90/10.87 % SZS output end CNFRefutation
% 52.90/10.87 % Parsed axioms : 605
% 52.90/10.87 % Removed by relevancy pruning/SinE : 324
% 52.90/10.87 % Initial clauses : 445
% 52.90/10.87 % Removed in clause preprocessing : 37
% 52.90/10.87 % Initial clauses in saturation : 408
% 52.90/10.87 % Processed clauses : 33165
% 52.90/10.87 % ...of these trivial : 1281
% 52.90/10.87 % ...subsumed : 25423
% 52.90/10.87 % ...remaining for further processing : 6461
% 52.90/10.87 % Other redundant clauses eliminated : 293
% 52.90/10.87 % Clauses deleted for lack of memory : 0
% 52.90/10.87 % Backward-subsumed : 464
% 52.90/10.87 % Backward-rewritten : 176
% 52.90/10.87 % Generated clauses : 898433
% 52.90/10.87 % ...of the previous two non-redundant : 840350
% 52.90/10.87 % ...aggressively subsumed : 0
% 52.90/10.87 % Contextual simplify-reflections : 31
% 52.90/10.87 % Paramodulations : 898043
% 52.90/10.87 % Factorizations : 74
% 52.90/10.87 % NegExts : 0
% 52.90/10.87 % Equation resolutions : 300
% 52.90/10.87 % Disequality decompositions : 0
% 52.90/10.87 % Total rewrite steps : 97367
% 52.90/10.87 % ...of those cached : 91024
% 52.90/10.87 % Propositional unsat checks : 0
% 52.90/10.87 % Propositional check models : 0
% 52.90/10.87 % Propositional check unsatisfiable : 0
% 52.90/10.87 % Propositional clauses : 0
% 52.90/10.87 % Propositional clauses after purity: 0
% 52.90/10.87 % Propositional unsat core size : 0
% 52.90/10.87 % Propositional preprocessing time : 0.000
% 52.90/10.87 % Propositional encoding time : 0.000
% 52.90/10.87 % Propositional solver time : 0.000
% 52.90/10.87 % Success case prop preproc time : 0.000
% 52.90/10.87 % Success case prop encoding time : 0.000
% 52.90/10.87 % Success case prop solver time : 0.000
% 52.90/10.87 % Current number of processed clauses : 5790
% 52.90/10.87 % Positive orientable unit clauses : 1057
% 52.90/10.87 % Positive unorientable unit clauses: 0
% 52.90/10.87 % Negative unit clauses : 445
% 52.90/10.87 % Non-unit-clauses : 4288
% 52.90/10.87 % Current number of unprocessed clauses: 802549
% 52.90/10.87 % ...number of literals in the above : 2787255
% 52.90/10.87 % Current number of archived formulas : 0
% 52.90/10.87 % Current number of archived clauses : 654
% 52.90/10.87 % Clause-clause subsumption calls (NU) : 3352783
% 52.90/10.87 % Rec. Clause-clause subsumption calls : 2595705
% 52.90/10.87 % Non-unit clause-clause subsumptions : 12579
% 52.90/10.87 % Unit Clause-clause subsumption calls : 147800
% 52.90/10.87 % Rewrite failures with RHS unbound : 0
% 52.90/10.87 % BW rewrite match attempts : 3133
% 52.90/10.87 % BW rewrite match successes : 69
% 52.90/10.87 % Condensation attempts : 0
% 52.90/10.87 % Condensation successes : 0
% 52.90/10.87 % Termbank termtop insertions : 14016431
% 52.90/10.87 % Search garbage collected termcells : 28788
% 52.90/10.87
% 52.90/10.87 % -------------------------------------------------
% 52.90/10.87 % User time : 10.013 s
% 52.90/10.87 % System time : 0.369 s
% 52.90/10.87 % Total time : 10.382 s
% 52.90/10.87 % Maximum resident set size: 10716 pages
% 52.90/10.87
% 52.90/10.87 % -------------------------------------------------
% 52.90/10.87 % User time : 10.338 s
% 52.90/10.87 % System time : 0.499 s
% 52.90/10.87 % Total time : 10.838 s
% 52.90/10.87 % Maximum resident set size: 5888 pages
% 52.90/10.87 % E exiting
%------------------------------------------------------------------------------