%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU801^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:27:51 AM UTC 2026
% Result : Theorem 13.00s 2.20s
% Output : CNFRefutation 14.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU801^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:31:46 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.20/0.30 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p
% 13.00/2.20 % Version: 3.5.1-ho
% 13.00/2.20 % Preprocessing class: HSLMSLSSLLLCHFA.
% 13.00/2.20 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 13.00/2.20 % Starting ehoh_best5 with 300s (1) cores
% 13.00/2.20 % Starting almost_fo_3_lam with 300s (1) cores
% 13.00/2.20 % Starting new_bool_5 with 300s (1) cores
% 13.00/2.20 % Starting pre_casc_3 with 300s (1) cores
% 13.00/2.20 % Starting ho_unfolding_8 with 300s (1) cores
% 13.00/2.20 % Starting new_ho_10_cnf2 with 300s (1) cores
% 13.00/2.20 % Starting new_bool_3 with 300s (1) cores
% 13.00/2.20 % Starting new_ho_5 with 300s (1) cores
% 13.00/2.20 % new_bool_3 with pid 1748365 completed with status 0
% 13.00/2.20 % Result found by new_bool_3
% 13.00/2.20 % Preprocessing class: HSLMSLSSLLLCHFA.
% 13.00/2.20 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 13.00/2.20 % Starting ehoh_best5 with 300s (1) cores
% 13.00/2.20 % Starting almost_fo_3_lam with 300s (1) cores
% 13.00/2.20 % Starting new_bool_5 with 300s (1) cores
% 13.00/2.20 % Starting pre_casc_3 with 300s (1) cores
% 13.00/2.20 % Starting ho_unfolding_8 with 300s (1) cores
% 13.00/2.20 % Starting new_ho_10_cnf2 with 300s (1) cores
% 13.00/2.20 % Starting new_bool_3 with 300s (1) cores
% 13.00/2.20 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 13.00/2.20 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 13.00/2.20 % Search class: HGHSM-FSLM32-DHFMMSBN
% 13.00/2.20 % partial match(1): HGHSM-FSLM32-MHFMMSBN
% 13.00/2.20 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 13.00/2.20 % Starting SubtermCWHack with 31s (1) cores
% 13.00/2.20 % SubtermCWHack with pid 1748392 completed with status 0
% 13.00/2.20 % Result found by SubtermCWHack
% 13.00/2.20 % Preprocessing class: HSLMSLSSLLLCHFA.
% 13.00/2.20 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 13.00/2.20 % Starting ehoh_best5 with 300s (1) cores
% 13.00/2.20 % Starting almost_fo_3_lam with 300s (1) cores
% 13.00/2.20 % Starting new_bool_5 with 300s (1) cores
% 13.00/2.20 % Starting pre_casc_3 with 300s (1) cores
% 13.00/2.20 % Starting ho_unfolding_8 with 300s (1) cores
% 13.00/2.20 % Starting new_ho_10_cnf2 with 300s (1) cores
% 13.00/2.20 % Starting new_bool_3 with 300s (1) cores
% 13.00/2.20 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 13.00/2.20 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 13.00/2.20 % Search class: HGHSM-FSLM32-DHFMMSBN
% 13.00/2.20 % partial match(1): HGHSM-FSLM32-MHFMMSBN
% 13.00/2.20 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 13.00/2.20 % Starting SubtermCWHack with 31s (1) cores
% 13.00/2.20 % Preprocessing time : 0.010 s
% 13.00/2.20
% 13.00/2.20 % Proof found!
% 13.00/2.20 % SZS status Theorem
% 13.00/2.20 % SZS output start CNFRefutation
% 13.00/2.20 thf(decl_23, type, in: $i > $i > $o).
% 13.00/2.20 thf(decl_24, type, exu: ($i > $o) > $o).
% 13.00/2.20 thf(decl_25, type, setextAx: $o).
% 13.00/2.20 thf(decl_26, type, emptyset: $i).
% 13.00/2.20 thf(decl_27, type, emptysetAx: $o).
% 13.00/2.20 thf(decl_28, type, setadjoin: $i > $i > $i).
% 13.00/2.20 thf(decl_29, type, setadjoinAx: $o).
% 13.00/2.20 thf(decl_30, type, powerset: $i > $i).
% 13.00/2.20 thf(decl_31, type, powersetAx: $o).
% 13.00/2.20 thf(decl_32, type, setunion: $i > $i).
% 13.00/2.20 thf(decl_33, type, setunionAx: $o).
% 13.00/2.20 thf(decl_34, type, omega: $i).
% 13.00/2.20 thf(decl_35, type, omega0Ax: $o).
% 13.00/2.20 thf(decl_36, type, omegaSAx: $o).
% 13.00/2.20 thf(decl_37, type, omegaIndAx: $o).
% 13.00/2.20 thf(decl_38, type, replAx: $o).
% 13.00/2.20 thf(decl_39, type, foundationAx: $o).
% 13.00/2.20 thf(decl_40, type, wellorderingAx: $o).
% 13.00/2.20 thf(decl_41, type, descr: ($i > $o) > $i).
% 13.00/2.20 thf(decl_42, type, descrp: $o).
% 13.00/2.20 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_44, type, dsetconstrI: $o).
% 14.84/2.20 thf(decl_45, type, dsetconstrEL: $o).
% 14.84/2.20 thf(decl_46, type, dsetconstrER: $o).
% 14.84/2.20 thf(decl_47, type, exuE1: $o).
% 14.84/2.20 thf(decl_48, type, prop2set: $o > $i).
% 14.84/2.20 thf(decl_49, type, prop2setE: $o).
% 14.84/2.20 thf(decl_50, type, emptysetE: $o).
% 14.84/2.20 thf(decl_51, type, emptysetimpfalse: $o).
% 14.84/2.20 thf(decl_52, type, notinemptyset: $o).
% 14.84/2.20 thf(decl_53, type, exuE3e: $o).
% 14.84/2.20 thf(decl_54, type, setext: $o).
% 14.84/2.20 thf(decl_55, type, emptyI: $o).
% 14.84/2.20 thf(decl_56, type, noeltsimpempty: $o).
% 14.84/2.20 thf(decl_57, type, setbeta: $o).
% 14.84/2.20 thf(decl_58, type, nonempty: $i > $o).
% 14.84/2.20 thf(decl_59, type, nonemptyE1: $o).
% 14.84/2.20 thf(decl_60, type, nonemptyI: $o).
% 14.84/2.20 thf(decl_61, type, nonemptyI1: $o).
% 14.84/2.20 thf(decl_62, type, setadjoinIL: $o).
% 14.84/2.20 thf(decl_63, type, emptyinunitempty: $o).
% 14.84/2.20 thf(decl_64, type, setadjoinIR: $o).
% 14.84/2.20 thf(decl_65, type, setadjoinE: $o).
% 14.84/2.20 thf(decl_66, type, setadjoinOr: $o).
% 14.84/2.20 thf(decl_67, type, setoftrueEq: $o).
% 14.84/2.20 thf(decl_68, type, powersetI: $o).
% 14.84/2.20 thf(decl_69, type, emptyinPowerset: $o).
% 14.84/2.20 thf(decl_70, type, emptyInPowerset: $o).
% 14.84/2.20 thf(decl_71, type, powersetE: $o).
% 14.84/2.20 thf(decl_72, type, setunionI: $o).
% 14.84/2.20 thf(decl_73, type, setunionE: $o).
% 14.84/2.20 thf(decl_74, type, subPowSU: $o).
% 14.84/2.20 thf(decl_75, type, exuE2: $o).
% 14.84/2.20 thf(decl_76, type, nonemptyImpWitness: $o).
% 14.84/2.20 thf(decl_77, type, uniqinunit: $o).
% 14.84/2.20 thf(decl_78, type, notinsingleton: $o).
% 14.84/2.20 thf(decl_79, type, eqinunit: $o).
% 14.84/2.20 thf(decl_80, type, singletonsswitch: $o).
% 14.84/2.20 thf(decl_81, type, upairsetE: $o).
% 14.84/2.20 thf(decl_82, type, upairsetIL: $o).
% 14.84/2.20 thf(decl_83, type, upairsetIR: $o).
% 14.84/2.20 thf(decl_84, type, emptyE1: $o).
% 14.84/2.20 thf(decl_85, type, vacuousDall: $o).
% 14.84/2.20 thf(decl_86, type, quantDeMorgan1: $o).
% 14.84/2.20 thf(decl_87, type, quantDeMorgan2: $o).
% 14.84/2.20 thf(decl_88, type, quantDeMorgan3: $o).
% 14.84/2.20 thf(decl_89, type, quantDeMorgan4: $o).
% 14.84/2.20 thf(decl_90, type, prop2setI: $o).
% 14.84/2.20 thf(decl_92, type, prop2set2propI: $o).
% 14.84/2.20 thf(decl_93, type, notdexE: $o).
% 14.84/2.20 thf(decl_94, type, notdallE: $o).
% 14.84/2.20 thf(decl_95, type, exuI1: $o).
% 14.84/2.20 thf(decl_96, type, exuI3: $o).
% 14.84/2.20 thf(decl_97, type, exuI2: $o).
% 14.84/2.20 thf(decl_98, type, inCongP: $o).
% 14.84/2.20 thf(decl_99, type, in__Cong: $o).
% 14.84/2.20 thf(decl_100, type, exuE3u: $o).
% 14.84/2.20 thf(decl_101, type, exu__Cong: $o).
% 14.84/2.20 thf(decl_102, type, emptyset__Cong: $o).
% 14.84/2.20 thf(decl_103, type, setadjoin__Cong: $o).
% 14.84/2.20 thf(decl_104, type, powerset__Cong: $o).
% 14.84/2.20 thf(decl_105, type, setunion__Cong: $o).
% 14.84/2.20 thf(decl_106, type, omega__Cong: $o).
% 14.84/2.20 thf(decl_107, type, exuEu: $o).
% 14.84/2.20 thf(decl_108, type, descr__Cong: $o).
% 14.84/2.20 thf(decl_109, type, dsetconstr__Cong: $o).
% 14.84/2.20 thf(decl_110, type, subset: $i > $i > $o).
% 14.84/2.20 thf(decl_113, type, subsetI1: $o).
% 14.84/2.20 thf(decl_114, type, eqimpsubset2: $o).
% 14.84/2.20 thf(decl_115, type, eqimpsubset1: $o).
% 14.84/2.20 thf(decl_116, type, subsetI2: $o).
% 14.84/2.20 thf(decl_117, type, emptysetsubset: $o).
% 14.84/2.20 thf(decl_118, type, subsetE: $o).
% 14.84/2.20 thf(decl_119, type, subsetE2: $o).
% 14.84/2.20 thf(decl_120, type, notsubsetI: $o).
% 14.84/2.20 thf(decl_121, type, notequalI1: $o).
% 14.84/2.20 thf(decl_122, type, notequalI2: $o).
% 14.84/2.20 thf(decl_123, type, subsetRefl: $o).
% 14.84/2.20 thf(decl_124, type, subsetTrans: $o).
% 14.84/2.20 thf(decl_125, type, setadjoinSub: $o).
% 14.84/2.20 thf(decl_126, type, setadjoinSub2: $o).
% 14.84/2.20 thf(decl_127, type, subset2powerset: $o).
% 14.84/2.20 thf(decl_128, type, setextsub: $o).
% 14.84/2.20 thf(decl_129, type, subsetemptysetimpeq: $o).
% 14.84/2.20 thf(decl_130, type, powersetI1: $o).
% 14.84/2.20 thf(decl_131, type, powersetE1: $o).
% 14.84/2.20 thf(decl_132, type, inPowerset: $o).
% 14.84/2.20 thf(decl_133, type, powersetsubset: $o).
% 14.84/2.20 thf(decl_134, type, sepInPowerset: $o).
% 14.84/2.20 thf(decl_135, type, sepSubset: $o).
% 14.84/2.20 thf(decl_136, type, binunion: $i > $i > $i).
% 14.84/2.20 thf(decl_137, type, binunionIL: $o).
% 14.84/2.20 thf(decl_138, type, upairset2IR: $o).
% 14.84/2.20 thf(decl_139, type, binunionIR: $o).
% 14.84/2.20 thf(decl_140, type, binunionEcases: $o).
% 14.84/2.20 thf(decl_141, type, binunionE: $o).
% 14.84/2.20 thf(decl_142, type, binunionLsub: $o).
% 14.84/2.20 thf(decl_143, type, binunionRsub: $o).
% 14.84/2.20 thf(decl_144, type, binintersect: $i > $i > $i).
% 14.84/2.20 thf(decl_145, type, binintersectI: $o).
% 14.84/2.20 thf(decl_146, type, binintersectSubset5: $o).
% 14.84/2.20 thf(decl_147, type, binintersectEL: $o).
% 14.84/2.20 thf(decl_148, type, binintersectLsub: $o).
% 14.84/2.20 thf(decl_149, type, binintersectSubset2: $o).
% 14.84/2.20 thf(decl_150, type, binintersectSubset3: $o).
% 14.84/2.20 thf(decl_151, type, binintersectER: $o).
% 14.84/2.20 thf(decl_152, type, disjointsetsI1: $o).
% 14.84/2.20 thf(decl_153, type, binintersectRsub: $o).
% 14.84/2.20 thf(decl_154, type, binintersectSubset4: $o).
% 14.84/2.20 thf(decl_155, type, binintersectSubset1: $o).
% 14.84/2.20 thf(decl_156, type, bs114d: $o).
% 14.84/2.20 thf(decl_158, type, setminus: $i > $i > $i).
% 14.84/2.20 thf(decl_159, type, setminusI: $o).
% 14.84/2.20 thf(decl_160, type, setminusEL: $o).
% 14.84/2.20 thf(decl_161, type, setminusER: $o).
% 14.84/2.20 thf(decl_162, type, setminusSubset2: $o).
% 14.84/2.20 thf(decl_163, type, setminusERneg: $o).
% 14.84/2.20 thf(decl_164, type, setminusELneg: $o).
% 14.84/2.20 thf(decl_165, type, setminusILneg: $o).
% 14.84/2.20 thf(decl_166, type, setminusIRneg: $o).
% 14.84/2.20 thf(decl_167, type, setminusLsub: $o).
% 14.84/2.20 thf(decl_168, type, setminusSubset1: $o).
% 14.84/2.20 thf(decl_169, type, symdiff: $i > $i > $i).
% 14.84/2.20 thf(decl_170, type, symdiffE: $o).
% 14.84/2.20 thf(decl_171, type, symdiffI1: $o).
% 14.84/2.20 thf(decl_172, type, symdiffI2: $o).
% 14.84/2.20 thf(decl_173, type, symdiffIneg1: $o).
% 14.84/2.20 thf(decl_174, type, symdiffIneg2: $o).
% 14.84/2.20 thf(decl_175, type, iskpair: $i > $o).
% 14.84/2.20 thf(decl_176, type, secondinupair: $o).
% 14.84/2.20 thf(decl_177, type, setukpairIL: $o).
% 14.84/2.20 thf(decl_178, type, setukpairIR: $o).
% 14.84/2.20 thf(decl_179, type, kpairiskpair: $o).
% 14.84/2.20 thf(decl_180, type, kpair: $i > $i > $i).
% 14.84/2.20 thf(decl_181, type, kpairp: $o).
% 14.84/2.20 thf(decl_182, type, cartprod: $i > $i > $i).
% 14.84/2.20 thf(decl_183, type, singletonsubset: $o).
% 14.84/2.20 thf(decl_184, type, singletoninpowerset: $o).
% 14.84/2.20 thf(decl_185, type, singletoninpowunion: $o).
% 14.84/2.20 thf(decl_186, type, upairset2E: $o).
% 14.84/2.20 thf(decl_187, type, upairsubunion: $o).
% 14.84/2.20 thf(decl_188, type, upairinpowunion: $o).
% 14.84/2.20 thf(decl_189, type, ubforcartprodlem1: $o).
% 14.84/2.20 thf(decl_190, type, ubforcartprodlem2: $o).
% 14.84/2.20 thf(decl_191, type, ubforcartprodlem3: $o).
% 14.84/2.20 thf(decl_192, type, cartprodpairin: $o).
% 14.84/2.20 thf(decl_193, type, cartprodmempair1: $o).
% 14.84/2.20 thf(decl_194, type, cartprodmempair: $o).
% 14.84/2.20 thf(decl_195, type, setunionE2: $o).
% 14.84/2.20 thf(decl_196, type, setunionsingleton1: $o).
% 14.84/2.20 thf(decl_197, type, setunionsingleton2: $o).
% 14.84/2.20 thf(decl_198, type, setunionsingleton: $o).
% 14.84/2.20 thf(decl_199, type, singleton: $i > $o).
% 14.84/2.20 thf(decl_200, type, singletonprop: $o).
% 14.84/2.20 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 14.84/2.20 thf(decl_202, type, ex1E1: $o).
% 14.84/2.20 thf(decl_203, type, ex1I: $o).
% 14.84/2.20 thf(decl_204, type, ex1I2: $o).
% 14.84/2.20 thf(decl_205, type, singletonsuniq: $o).
% 14.84/2.20 thf(decl_210, type, setukpairinjL1: $o).
% 14.84/2.20 thf(decl_211, type, kfstsingleton: $o).
% 14.84/2.20 thf(decl_212, type, theprop: $o).
% 14.84/2.20 thf(decl_213, type, kfst: $i > $i).
% 14.84/2.20 thf(decl_214, type, kfstpairEq: $o).
% 14.84/2.20 thf(decl_215, type, cartprodfstin: $o).
% 14.84/2.20 thf(decl_216, type, setukpairinjL2: $o).
% 14.84/2.20 thf(decl_217, type, setukpairinjL: $o).
% 14.84/2.20 thf(decl_218, type, setukpairinjR11: $o).
% 14.84/2.20 thf(decl_219, type, setukpairinjR12: $o).
% 14.84/2.20 thf(decl_220, type, setukpairinjR1: $o).
% 14.84/2.20 thf(decl_221, type, upairequniteq: $o).
% 14.84/2.20 thf(decl_222, type, setukpairinjR2: $o).
% 14.84/2.20 thf(decl_223, type, setukpairinjR: $o).
% 14.84/2.20 thf(decl_224, type, ksndsingleton: $o).
% 14.84/2.20 thf(decl_225, type, ksnd: $i > $i).
% 14.84/2.20 thf(decl_226, type, ksndpairEq: $o).
% 14.84/2.20 thf(decl_227, type, kpairsurjEq: $o).
% 14.84/2.20 thf(decl_228, type, cartprodsndin: $o).
% 14.84/2.20 thf(decl_229, type, cartprodpairmemEL: $o).
% 14.84/2.20 thf(decl_230, type, cartprodpairmemER: $o).
% 14.84/2.20 thf(decl_231, type, cartprodmempaircEq: $o).
% 14.84/2.20 thf(decl_232, type, cartprodfstpairEq: $o).
% 14.84/2.20 thf(decl_233, type, cartprodsndpairEq: $o).
% 14.84/2.20 thf(decl_234, type, cartprodpairsurjEq: $o).
% 14.84/2.20 thf(decl_235, type, breln: $i > $i > $i > $o).
% 14.84/2.20 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 14.84/2.20 thf(decl_237, type, dpsetconstrI: $o).
% 14.84/2.20 thf(decl_238, type, dpsetconstrSub: $o).
% 14.84/2.20 thf(decl_239, type, setOfPairsIsBReln: $o).
% 14.84/2.20 thf(decl_240, type, dpsetconstrERa: $o).
% 14.84/2.20 thf(decl_241, type, dpsetconstrEL1: $o).
% 14.84/2.20 thf(decl_242, type, dpsetconstrEL2: $o).
% 14.84/2.20 thf(decl_243, type, dpsetconstrER: $o).
% 14.84/2.20 thf(decl_244, type, func: $i > $i > $i > $o).
% 14.84/2.20 thf(decl_245, type, funcSet: $i > $i > $i).
% 14.84/2.20 thf(decl_246, type, funcImageSingleton: $o).
% 14.84/2.20 thf(decl_247, type, apProp: $o).
% 14.84/2.20 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 14.84/2.20 thf(decl_249, type, app: $o).
% 14.84/2.20 thf(decl_250, type, infuncsetfunc: $o).
% 14.84/2.20 thf(decl_251, type, ap2p: $o).
% 14.84/2.20 thf(decl_252, type, funcinfuncset: $o).
% 14.84/2.20 thf(decl_253, type, lamProp: $o).
% 14.84/2.20 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 14.84/2.20 thf(decl_255, type, lamp: $o).
% 14.84/2.20 thf(decl_256, type, lam2p: $o).
% 14.84/2.20 thf(decl_257, type, brelnall1: $o).
% 14.84/2.20 thf(decl_258, type, brelnall2: $o).
% 14.84/2.20 thf(decl_259, type, ex1E2: $o).
% 14.84/2.20 thf(decl_260, type, funcGraphProp1: $o).
% 14.84/2.20 thf(decl_261, type, funcGraphProp3: $o).
% 14.84/2.20 thf(decl_262, type, funcGraphProp2: $o).
% 14.84/2.20 thf(decl_263, type, funcextLem: $o).
% 14.84/2.20 thf(decl_264, type, funcGraphProp4: $o).
% 14.84/2.20 thf(decl_265, type, subbreln: $o).
% 14.84/2.20 thf(decl_266, type, eqbreln: $o).
% 14.84/2.20 thf(decl_267, type, funcext: $o).
% 14.84/2.20 thf(decl_268, type, funcext2: $o).
% 14.84/2.20 thf(decl_269, type, ap2apEq1: $o).
% 14.84/2.20 thf(decl_270, type, ap2apEq2: $o).
% 14.84/2.20 thf(decl_271, type, beta1: $o).
% 14.84/2.20 thf(decl_272, type, eta1: $o).
% 14.84/2.20 thf(decl_273, type, lam2lamEq: $o).
% 14.84/2.20 thf(decl_274, type, beta2: $o).
% 14.84/2.20 thf(decl_275, type, eta2: $o).
% 14.84/2.20 thf(decl_276, type, iffalseProp1: $o).
% 14.84/2.20 thf(decl_277, type, iffalseProp2: $o).
% 14.84/2.20 thf(decl_278, type, iftrueProp1: $o).
% 14.84/2.20 thf(decl_279, type, iftrueProp2: $o).
% 14.84/2.20 thf(decl_280, type, ifSingleton: $o).
% 14.84/2.20 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 14.84/2.20 thf(decl_282, type, ifp: $o).
% 14.84/2.20 thf(decl_283, type, theeq: $o).
% 14.84/2.20 thf(decl_284, type, iftrue: $o).
% 14.84/2.20 thf(decl_285, type, iffalse: $o).
% 14.84/2.20 thf(decl_286, type, iftrueorfalse: $o).
% 14.84/2.20 thf(decl_287, type, binintersectT_lem: $o).
% 14.84/2.20 thf(decl_288, type, binunionT_lem: $o).
% 14.84/2.20 thf(decl_289, type, powersetT_lem: $o).
% 14.84/2.20 thf(decl_290, type, setminusT_lem: $o).
% 14.84/2.20 thf(decl_291, type, complementT_lem: $o).
% 14.84/2.20 thf(decl_292, type, setextT: $o).
% 14.84/2.20 thf(decl_293, type, subsetTI: $o).
% 14.84/2.20 thf(decl_294, type, powersetTI1: $o).
% 14.84/2.20 thf(decl_295, type, powersetTE1: $o).
% 14.84/2.20 thf(decl_296, type, complementTI1: $o).
% 14.84/2.20 thf(decl_297, type, complementTE1: $o).
% 14.84/2.20 thf(decl_298, type, binintersectTELcontra: $o).
% 14.84/2.20 thf(decl_299, type, binintersectTERcontra: $o).
% 14.84/2.20 thf(decl_300, type, contrasubsetT: $o).
% 14.84/2.20 thf(decl_301, type, contrasubsetT1: $o).
% 14.84/2.20 thf(decl_302, type, contrasubsetT2: $o).
% 14.84/2.20 thf(decl_303, type, contrasubsetT3: $o).
% 14.84/2.20 thf(decl_304, type, doubleComplementI1: $o).
% 14.84/2.20 thf(decl_305, type, doubleComplementE1: $o).
% 14.84/2.20 thf(decl_306, type, doubleComplementSub1: $o).
% 14.84/2.20 thf(decl_307, type, doubleComplementSub2: $o).
% 14.84/2.20 thf(decl_308, type, doubleComplementEq: $o).
% 14.84/2.20 thf(decl_309, type, complementTnotintersectT: $o).
% 14.84/2.20 thf(decl_310, type, complementImpComplementIntersect: $o).
% 14.84/2.20 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 14.84/2.20 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 14.84/2.20 thf(decl_313, type, contraSubsetComplement: $o).
% 14.84/2.20 thf(decl_314, type, complementTcontraSubset: $o).
% 14.84/2.20 thf(decl_315, type, binunionTILcontra: $o).
% 14.84/2.20 thf(decl_316, type, binunionTIRcontra: $o).
% 14.84/2.20 thf(decl_317, type, inIntersectImpInUnion: $o).
% 14.84/2.20 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 14.84/2.20 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 14.84/2.20 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 14.84/2.20 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 14.84/2.20 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 14.84/2.20 thf(decl_323, type, binunionTE: $o).
% 14.84/2.20 thf(decl_324, type, binunionTEcontra: $o).
% 14.84/2.20 thf(decl_325, type, demorgan2a1: $o).
% 14.84/2.20 thf(decl_326, type, complementUnionInPowersetComplement: $o).
% 14.84/2.20 thf(decl_327, type, demorgan2a2: $o).
% 14.84/2.20 thf(decl_328, type, demorgan1a: $o).
% 14.84/2.20 thf(decl_329, type, demorgan1b: $o).
% 14.84/2.20 thf(decl_330, type, demorgan1: $o).
% 14.84/2.20 thf(decl_331, type, demorgan2a: $o).
% 14.84/2.20 thf(decl_332, type, demorgan2b2: $o).
% 14.84/2.20 thf(decl_333, type, demorgan2b: $o).
% 14.84/2.20 thf(decl_334, type, demorgan2: $o).
% 14.84/2.20 thf(decl_335, type, woz13rule0: $o).
% 14.84/2.20 thf(decl_336, type, woz13rule1: $o).
% 14.84/2.20 thf(decl_337, type, woz13rule2: $o).
% 14.84/2.20 thf(decl_338, type, woz13rule3: $o).
% 14.84/2.20 thf(decl_339, type, woz13rule4: $o).
% 14.84/2.20 thf(decl_340, type, woz1_1: $o).
% 14.84/2.20 thf(decl_341, type, woz1_2: $o).
% 14.84/2.20 thf(decl_342, type, woz1_3: $o).
% 14.84/2.20 thf(decl_343, type, woz1_4: $o).
% 14.84/2.20 thf(decl_344, type, woz1_5: $o).
% 14.84/2.20 thf(decl_345, type, breln1: $i > $i > $o).
% 14.84/2.20 thf(decl_346, type, breln1all2: $o).
% 14.84/2.20 thf(decl_347, type, breln1Set: $i > $i).
% 14.84/2.20 thf(decl_348, type, breln1SetBreln1: $o).
% 14.84/2.20 thf(decl_355, type, choice2fnsingleton: $o).
% 14.84/2.20 thf(decl_356, type, setOfPairsIsBReln1: $o).
% 14.84/2.20 thf(decl_357, type, breln1all1: $o).
% 14.84/2.20 thf(decl_358, type, subbreln1: $o).
% 14.84/2.20 thf(decl_359, type, eqbreln1: $o).
% 14.84/2.20 thf(decl_360, type, breln1invset: $i > $i > $i).
% 14.84/2.20 thf(decl_361, type, breln1invprop: $o).
% 14.84/2.20 thf(decl_362, type, breln1invI: $o).
% 14.84/2.20 thf(decl_363, type, breln1invE: $o).
% 14.84/2.20 thf(decl_364, type, breln1compset: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_365, type, breln1compprop: $o).
% 14.84/2.20 thf(decl_366, type, breln1compI: $o).
% 14.84/2.20 thf(decl_367, type, breln1compE: $o).
% 14.84/2.20 thf(decl_368, type, breln1compEex: $o).
% 14.84/2.20 thf(decl_369, type, breln1unionprop: $o).
% 14.84/2.20 thf(decl_370, type, breln1unionIL: $o).
% 14.84/2.20 thf(decl_371, type, breln1unionIR: $o).
% 14.84/2.20 thf(decl_372, type, breln1unionI: $o).
% 14.84/2.20 thf(decl_373, type, breln1unionE: $o).
% 14.84/2.20 thf(decl_374, type, breln1unionEcases: $o).
% 14.84/2.20 thf(decl_375, type, breln1unionCommutes: $o).
% 14.84/2.20 thf(decl_376, type, woz2Ex: $o).
% 14.84/2.20 thf(decl_377, type, woz2W: $o).
% 14.84/2.20 thf(decl_378, type, woz2A: $o).
% 14.84/2.20 thf(decl_379, type, woz2B: $o).
% 14.84/2.20 thf(decl_380, type, image1Ex: $o).
% 14.84/2.20 thf(decl_381, type, image1Ex1: $o).
% 14.84/2.20 thf(decl_382, type, image1: $i > ($i > $i) > $i).
% 14.84/2.20 thf(decl_383, type, image1Equiv: $o).
% 14.84/2.20 thf(decl_384, type, image1E: $o).
% 14.84/2.20 thf(decl_385, type, image1I: $o).
% 14.84/2.20 thf(decl_386, type, injective: $i > $i > $i > $o).
% 14.84/2.20 thf(decl_387, type, injFuncSet: $i > $i > $i).
% 14.84/2.20 thf(decl_388, type, injFuncInInjFuncSet: $o).
% 14.84/2.20 thf(decl_389, type, injFuncSetFuncIn: $o).
% 14.84/2.20 thf(decl_390, type, injFuncSetFuncInj: $o).
% 14.84/2.20 thf(decl_391, type, surjective: $i > $i > $i > $o).
% 14.84/2.20 thf(decl_392, type, surjFuncSet: $i > $i > $i).
% 14.84/2.20 thf(decl_393, type, epred1_0: $o).
% 14.84/2.20 thf(decl_394, type, esk1_2: $i > $i > $i).
% 14.84/2.20 thf(decl_395, type, esk2_2: $i > $i > $i).
% 14.84/2.20 thf(decl_396, type, esk3_2: $i > $i > $i).
% 14.84/2.20 thf(decl_397, type, esk4_1: $i > $i).
% 14.84/2.20 thf(decl_398, type, esk5_2: ($i > $i > $o) > $i > $i).
% 14.84/2.20 thf(decl_399, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 14.84/2.20 thf(decl_400, type, esk7_2: ($i > $i > $o) > $i > $i).
% 14.84/2.20 thf(decl_401, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 14.84/2.20 thf(decl_402, type, esk9_1: $i > $i).
% 14.84/2.20 thf(decl_403, type, esk10_2: ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_404, type, esk11_2: ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_405, type, esk12_1: ($i > $o) > $i).
% 14.84/2.20 thf(decl_406, type, esk13_2: ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_407, type, esk14_1: ($i > $o) > $i).
% 14.84/2.20 thf(decl_408, type, esk15_2: $i > $i > $i).
% 14.84/2.20 thf(decl_409, type, esk16_2: $i > $i > $i).
% 14.84/2.20 thf(decl_410, type, esk17_1: $i > $i).
% 14.84/2.20 thf(decl_411, type, esk18_1: $i > $i).
% 14.84/2.20 thf(decl_412, type, esk19_1: $i > $i).
% 14.84/2.20 thf(decl_413, type, esk20_2: $i > $i > $i).
% 14.84/2.20 thf(decl_414, type, esk21_3: $i > $i > $o > $i).
% 14.84/2.20 thf(decl_415, type, esk22_2: ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_416, type, esk23_1: ($i > $o) > $i).
% 14.84/2.20 thf(decl_417, type, esk24_1: $i > $i).
% 14.84/2.20 thf(decl_418, type, esk25_2: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_419, type, esk26_2: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_420, type, esk27_2: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_421, type, esk28_2: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_422, type, esk29_2: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_423, type, esk30_2: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_424, type, esk31_2: ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_425, type, esk32_1: ($i > $o) > $i).
% 14.84/2.20 thf(decl_426, type, esk33_1: ($i > $o) > $i).
% 14.84/2.20 thf(decl_427, type, esk34_1: ($i > $o) > $i).
% 14.84/2.20 thf(decl_428, type, esk35_1: ($i > $o) > $i).
% 14.84/2.20 thf(decl_429, type, esk36_2: ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_430, type, esk37_1: ($i > $o) > $i).
% 14.84/2.20 thf(decl_431, type, esk38_2: ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_432, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 14.84/2.20 thf(decl_433, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 14.84/2.20 thf(decl_434, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_435, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 14.84/2.20 thf(decl_436, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_437, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 14.84/2.20 thf(decl_438, type, esk45_2: ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_439, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 14.84/2.20 thf(decl_440, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 14.84/2.20 thf(decl_441, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_442, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_443, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 14.84/2.20 thf(decl_444, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 14.84/2.20 thf(decl_445, type, esk52_2: $i > $i > $i).
% 14.84/2.20 thf(decl_446, type, esk53_2: $i > $i > $i).
% 14.84/2.20 thf(decl_447, type, esk54_2: $i > $i > $i).
% 14.84/2.20 thf(decl_448, type, esk55_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_449, type, esk56_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_450, type, esk57_2: $i > $i > $i).
% 14.84/2.20 thf(decl_451, type, esk58_2: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_452, type, esk59_2: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_453, type, esk60_2: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_454, type, esk61_3: $i > ($i > $o) > $i > $i).
% 14.84/2.20 thf(decl_455, type, esk62_2: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_456, type, esk63_2: $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_457, type, esk64_3: $i > $i > ($i > $i) > $i).
% 14.84/2.20 thf(decl_458, type, esk65_3: $i > $i > ($i > $i) > $i).
% 14.84/2.20 thf(decl_459, type, esk66_3: $i > $i > ($i > $i) > $i).
% 14.84/2.20 thf(decl_460, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_461, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_462, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_463, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_464, type, esk71_4: $i > $i > $i > $i > $i).
% 14.84/2.20 thf(decl_465, type, esk72_4: $i > $i > $i > $i > $i).
% 14.84/2.20 thf(decl_466, type, esk73_4: $i > $i > $i > $i > $i).
% 14.84/2.20 thf(decl_467, type, esk74_4: $i > $i > $i > $i > $i).
% 14.84/2.20 thf(decl_468, type, esk75_4: $i > $i > $i > $i > $i).
% 14.84/2.20 thf(decl_469, type, esk76_4: $i > $i > $i > $i > $i).
% 14.84/2.20 thf(decl_470, type, esk77_4: $i > $i > $i > $i > $i).
% 14.84/2.20 thf(decl_471, type, esk78_4: $i > $i > $i > $i > $i).
% 14.84/2.20 thf(decl_472, type, esk79_4: $i > $i > $i > $i > $i).
% 14.84/2.20 thf(decl_473, type, esk80_3: $i > $i > ($i > $i) > $i).
% 14.84/2.20 thf(decl_474, type, esk81_3: $i > $i > ($i > $i) > $i).
% 14.84/2.20 thf(decl_475, type, esk82_3: $i > $i > ($i > $i) > $i).
% 14.84/2.20 thf(decl_476, type, esk83_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_477, type, esk84_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_478, type, esk85_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_479, type, esk86_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_480, type, esk87_3: $i > $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_481, type, esk88_3: $i > $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_482, type, esk89_3: $i > $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_483, type, esk90_3: $i > $i > ($i > $o) > $i).
% 14.84/2.20 thf(decl_484, type, esk91_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_485, type, esk92_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_486, type, esk93_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_487, type, esk94_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_488, type, esk95_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_489, type, esk96_3: $i > $i > $i > $i).
% 14.84/2.20 thf(decl_490, type, esk97_5: $i > $i > $i > $i > $i > $i).
% 14.84/2.20 thf(decl_491, type, esk98_6: $i > $i > $i > $i > $i > $o > $i).
% 14.84/2.20 thf(decl_492, type, esk99_2: $i > ($i > $i) > $i).
% 14.84/2.20 thf(decl_493, type, esk100_3: $i > ($i > $i) > $i > $i).
% 14.84/2.20 thf(decl_494, type, esk101_2: $i > ($i > $i) > $i).
% 14.84/2.20 thf(decl_495, type, esk102_3: $i > ($i > $i) > $i > $i).
% 14.84/2.20 thf(decl_496, type, esk103_3: $i > ($i > $i) > $i > $i).
% 14.84/2.20 thf(decl_497, type, esk104_3: $i > ($i > $i) > $i > $i).
% 14.84/2.20 thf(decl_498, type, esk105_3: $i > ($i > $i) > $i > $i).
% 14.84/2.20 thf(decl_499, type, esk106_3: $i > ($i > $i) > $i > $i).
% 14.84/2.20 thf(decl_500, type, esk107_0: $i).
% 14.84/2.20 thf(decl_501, type, esk108_0: $i).
% 14.84/2.20 thf(decl_502, type, esk109_0: $i).
% 14.84/2.20 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', descr__Cong)).
% 14.84/2.20 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', exu)).
% 14.84/2.20 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', exu__Cong)).
% 14.84/2.20 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', exuEu)).
% 14.84/2.20 thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', image1Ex1)).
% 14.84/2.20 thf(surjFuncSet, axiom, ((surjFuncSet)=(^[X4:$i, X5:$i]:(dsetconstr @ (funcSet @ X4 @ X5) @ (^[X29:$i]:((surjective @ X4 @ X5 @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', surjFuncSet)).
% 14.84/2.20 thf(surjective, axiom, ((surjective)=(^[X4:$i, X5:$i, X29:$i]:(![X2:$i]:((((in @ X2 @ X5))=>(?[X3:$i]:((((in @ X3 @ X4))&(((ap @ X4 @ X5 @ X29 @ X3)=(X2))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', surjective)).
% 14.84/2.20 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', exuE3u)).
% 14.84/2.20 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', exuI2)).
% 14.84/2.20 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', exuI3)).
% 14.84/2.20 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', exuI1)).
% 14.84/2.20 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', nonempty)).
% 14.84/2.20 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', exuE2)).
% 14.84/2.20 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', nonemptyI)).
% 14.84/2.20 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', exuE3e)).
% 14.84/2.20 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', exuE1)).
% 14.84/2.20 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', descrp)).
% 14.84/2.20 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', replAx)).
% 14.84/2.20 thf(surjFuncSetFuncIn, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>((breln1compprop)=>((breln1compI)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>((breln1unionIR)=>((breln1unionI)=>((breln1unionE)=>((breln1unionEcases)=>((breln1unionCommutes)=>((woz2Ex)=>((woz2W)=>((woz2A)=>((woz2B)=>((image1Ex)=>((image1Ex1)=>((image1Equiv)=>((image1E)=>((image1I)=>((injFuncInInjFuncSet)=>((injFuncSetFuncIn)=>((injFuncSetFuncInj)=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', surjFuncSetFuncIn)).
% 14.84/2.20 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', dsetconstr__Cong)).
% 14.84/2.20 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setOfPairsIsBReln1)).
% 14.84/2.20 thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', image1Equiv)).
% 14.84/2.20 thf(image1E, axiom, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', image1E)).
% 14.84/2.20 thf(image1I, axiom, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X61 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', image1I)).
% 14.84/2.20 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', sepSubset)).
% 14.84/2.20 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', sepInPowerset)).
% 14.84/2.20 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', dpsetconstrER)).
% 14.84/2.20 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', lamProp)).
% 14.84/2.20 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', apProp)).
% 14.84/2.20 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ex1E1)).
% 14.84/2.20 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', singletonprop)).
% 14.84/2.20 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ex1I)).
% 14.84/2.20 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', kfstsingleton)).
% 14.84/2.20 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ex1I2)).
% 14.84/2.20 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ksndsingleton)).
% 14.84/2.20 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', dpsetconstrEL2)).
% 14.84/2.20 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', dpsetconstrEL1)).
% 14.84/2.20 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', dpsetconstrERa)).
% 14.84/2.20 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setOfPairsIsBReln)).
% 14.84/2.20 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', dpsetconstrSub)).
% 14.84/2.20 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', dpsetconstrI)).
% 14.84/2.20 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', funcImageSingleton)).
% 14.84/2.20 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', lamp)).
% 14.84/2.20 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ex1E2)).
% 14.84/2.20 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', lam2p)).
% 14.84/2.20 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', beta1)).
% 14.84/2.20 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', iftrueProp1)).
% 14.84/2.20 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', iffalseProp2)).
% 14.84/2.20 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', iffalseProp1)).
% 14.84/2.20 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', eta2)).
% 14.84/2.20 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', beta2)).
% 14.84/2.20 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', lam2lamEq)).
% 14.84/2.20 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', eta1)).
% 14.84/2.20 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', iftrueProp2)).
% 14.84/2.20 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ifSingleton)).
% 14.84/2.20 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', emptyE1)).
% 14.84/2.20 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', nonemptyImpWitness)).
% 14.84/2.20 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setoftrueEq)).
% 14.84/2.20 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', nonemptyI1)).
% 14.84/2.20 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', nonemptyE1)).
% 14.84/2.20 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setbeta)).
% 14.84/2.20 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', dsetconstrER)).
% 14.84/2.20 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', dsetconstrEL)).
% 14.84/2.20 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', dsetconstrI)).
% 14.84/2.20 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setadjoin__Cong)).
% 14.84/2.20 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', demorgan2a1)).
% 14.84/2.20 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', complementUnionInPowersetComplement)).
% 14.84/2.20 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', demorgan2a2)).
% 14.84/2.20 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', demorgan1a)).
% 14.84/2.20 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', demorgan1b)).
% 14.84/2.20 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', demorgan1)).
% 14.84/2.20 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', demorgan2a)).
% 14.84/2.20 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', demorgan2b2)).
% 14.84/2.20 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', demorgan2b)).
% 14.84/2.20 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', demorgan2)).
% 14.84/2.20 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz13rule0)).
% 14.84/2.20 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz13rule1)).
% 14.84/2.20 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz13rule2)).
% 14.84/2.20 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz13rule3)).
% 14.84/2.20 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz13rule4)).
% 14.84/2.20 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz1_1)).
% 14.84/2.20 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', omega__Cong)).
% 14.84/2.20 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz1_2)).
% 14.84/2.20 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setunion__Cong)).
% 14.84/2.20 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz1_3)).
% 14.84/2.20 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', powerset__Cong)).
% 14.84/2.20 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz1_4)).
% 14.84/2.20 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subsetRefl)).
% 14.84/2.20 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', notequalI2)).
% 14.84/2.20 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz1_5)).
% 14.84/2.20 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subsetI1)).
% 14.84/2.20 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1all2)).
% 14.84/2.20 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1SetBreln1)).
% 14.84/2.20 thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1all1)).
% 14.84/2.20 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subbreln1)).
% 14.84/2.20 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', eqbreln1)).
% 14.84/2.20 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1invprop)).
% 14.84/2.20 thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1invI)).
% 14.84/2.20 thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1invE)).
% 14.84/2.20 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1compprop)).
% 14.84/2.20 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1compI)).
% 14.84/2.20 thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1compE)).
% 14.84/2.20 thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1compEex)).
% 14.84/2.20 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', notsubsetI)).
% 14.84/2.20 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1unionprop)).
% 14.84/2.20 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subsetE2)).
% 14.84/2.20 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1unionIL)).
% 14.84/2.20 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subsetE)).
% 14.84/2.20 thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1unionIR)).
% 14.84/2.20 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', emptysetsubset)).
% 14.84/2.20 thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1unionI)).
% 14.84/2.20 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subsetI2)).
% 14.84/2.20 thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1unionE)).
% 14.84/2.20 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', eqimpsubset1)).
% 14.84/2.20 thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1unionEcases)).
% 14.84/2.20 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', eqimpsubset2)).
% 14.84/2.20 thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', breln1unionCommutes)).
% 14.84/2.20 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', notequalI1)).
% 14.84/2.20 thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz2Ex)).
% 14.84/2.20 thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz2W)).
% 14.84/2.20 thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz2A)).
% 14.84/2.20 thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', woz2B)).
% 14.84/2.20 thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', image1Ex)).
% 14.84/2.20 thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', injFuncInInjFuncSet)).
% 14.84/2.20 thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', injFuncSetFuncIn)).
% 14.84/2.20 thf(injFuncSetFuncInj, axiom, ((injFuncSetFuncInj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', injFuncSetFuncInj)).
% 14.84/2.20 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setextsub)).
% 14.84/2.20 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subset2powerset)).
% 14.84/2.20 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setadjoinSub2)).
% 14.84/2.20 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setadjoinSub)).
% 14.84/2.20 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subsetTrans)).
% 14.84/2.20 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setminusEL)).
% 14.84/2.20 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setminusI)).
% 14.84/2.20 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', bs114d)).
% 14.84/2.20 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setminusILneg)).
% 14.84/2.20 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subsetemptysetimpeq)).
% 14.84/2.20 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binunionIL)).
% 14.84/2.20 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', powersetsubset)).
% 14.84/2.20 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', inPowerset)).
% 14.84/2.20 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', powersetE1)).
% 14.84/2.20 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', powersetI1)).
% 14.84/2.20 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', upairset2IR)).
% 14.84/2.20 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', emptyset__Cong)).
% 14.84/2.20 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectSubset5)).
% 14.84/2.20 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectI)).
% 14.84/2.20 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binunionRsub)).
% 14.84/2.20 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binunionLsub)).
% 14.84/2.20 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binunionE)).
% 14.84/2.20 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binunionEcases)).
% 14.84/2.20 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binunionIR)).
% 14.84/2.20 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectEL)).
% 14.84/2.20 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectSubset4)).
% 14.84/2.20 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectRsub)).
% 14.84/2.20 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', disjointsetsI1)).
% 14.84/2.20 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectER)).
% 14.84/2.20 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectSubset3)).
% 14.84/2.20 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectSubset2)).
% 14.84/2.20 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectLsub)).
% 14.84/2.20 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectSubset1)).
% 14.84/2.20 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setminusELneg)).
% 14.84/2.20 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setminusERneg)).
% 14.84/2.20 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setminusSubset2)).
% 14.84/2.20 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setminusER)).
% 14.84/2.20 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', cartprodpairsurjEq)).
% 14.84/2.20 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', funcinfuncset)).
% 14.84/2.20 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ap2p)).
% 14.84/2.20 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', infuncsetfunc)).
% 14.84/2.20 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', app)).
% 14.84/2.20 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', symdiffIneg1)).
% 14.84/2.20 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', symdiffI2)).
% 14.84/2.20 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', symdiffI1)).
% 14.84/2.20 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', symdiffE)).
% 14.84/2.20 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setminusSubset1)).
% 14.84/2.20 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setminusLsub)).
% 14.84/2.20 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setminusIRneg)).
% 14.84/2.20 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', symdiffIneg2)).
% 14.84/2.20 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', singletoninpowerset)).
% 14.84/2.20 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', singletonsubset)).
% 14.84/2.20 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', kpairp)).
% 14.84/2.20 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', kpairiskpair)).
% 14.84/2.20 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setukpairIR)).
% 14.84/2.20 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setukpairIL)).
% 14.84/2.20 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', secondinupair)).
% 14.84/2.20 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', singletoninpowunion)).
% 14.84/2.20 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', cartprodpairin)).
% 14.84/2.20 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ubforcartprodlem3)).
% 14.84/2.20 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ubforcartprodlem2)).
% 14.84/2.20 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ubforcartprodlem1)).
% 14.84/2.20 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', upairinpowunion)).
% 14.84/2.20 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', upairsubunion)).
% 14.84/2.20 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', upairset2E)).
% 14.84/2.20 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', cartprodmempair1)).
% 14.84/2.20 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setunionsingleton)).
% 14.84/2.20 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setunionsingleton2)).
% 14.84/2.20 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setunionsingleton1)).
% 14.84/2.20 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setunionE2)).
% 14.84/2.20 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', cartprodmempair)).
% 14.84/2.20 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', cartprodfstin)).
% 14.84/2.20 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', kfstpairEq)).
% 14.84/2.20 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', theprop)).
% 14.84/2.20 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setukpairinjL1)).
% 14.84/2.20 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', singletonsuniq)).
% 14.84/2.20 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setukpairinjL2)).
% 14.84/2.20 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setukpairinjR)).
% 14.84/2.20 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setukpairinjR2)).
% 14.84/2.20 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', upairequniteq)).
% 14.84/2.20 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setukpairinjR1)).
% 14.84/2.20 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setukpairinjR12)).
% 14.84/2.20 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setukpairinjR11)).
% 14.84/2.20 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setukpairinjL)).
% 14.84/2.20 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', cartprodfstpairEq)).
% 14.84/2.20 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', cartprodmempaircEq)).
% 14.84/2.20 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', cartprodpairmemER)).
% 14.84/2.20 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', cartprodpairmemEL)).
% 14.84/2.20 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', cartprodsndin)).
% 14.84/2.20 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', kpairsurjEq)).
% 14.84/2.20 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ksndpairEq)).
% 14.84/2.20 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', cartprodsndpairEq)).
% 14.84/2.20 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', funcGraphProp2)).
% 14.84/2.20 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', funcGraphProp3)).
% 14.84/2.20 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', funcGraphProp1)).
% 14.84/2.20 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', brelnall2)).
% 14.84/2.20 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', brelnall1)).
% 14.84/2.20 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', funcextLem)).
% 14.84/2.20 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ap2apEq2)).
% 14.84/2.20 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ap2apEq1)).
% 14.84/2.20 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', funcext2)).
% 14.84/2.20 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', funcext)).
% 14.84/2.20 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', eqbreln)).
% 14.84/2.20 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subbreln)).
% 14.84/2.20 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', funcGraphProp4)).
% 14.84/2.20 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectT_lem)).
% 14.84/2.20 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', iftrueorfalse)).
% 14.84/2.20 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', iffalse)).
% 14.84/2.20 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', iftrue)).
% 14.84/2.20 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', theeq)).
% 14.84/2.20 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', ifp)).
% 14.84/2.20 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binunionT_lem)).
% 14.84/2.20 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', powersetTE1)).
% 14.84/2.20 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', powersetTI1)).
% 14.84/2.20 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subsetTI)).
% 14.84/2.20 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setextT)).
% 14.84/2.20 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', complementT_lem)).
% 14.84/2.20 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setminusT_lem)).
% 14.84/2.20 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', powersetT_lem)).
% 14.84/2.20 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', complementTI1)).
% 14.84/2.20 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', contrasubsetT3)).
% 14.84/2.20 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', contrasubsetT2)).
% 14.84/2.20 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', contrasubsetT1)).
% 14.84/2.20 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', contrasubsetT)).
% 14.84/2.20 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectTERcontra)).
% 14.84/2.20 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binintersectTELcontra)).
% 14.84/2.20 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', complementTE1)).
% 14.84/2.20 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', doubleComplementI1)).
% 14.84/2.20 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', complementSubsetComplementIntersect)).
% 14.84/2.20 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', complementImpComplementIntersect)).
% 14.84/2.20 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', complementTnotintersectT)).
% 14.84/2.20 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', doubleComplementEq)).
% 14.84/2.20 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', doubleComplementSub2)).
% 14.84/2.20 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', doubleComplementSub1)).
% 14.84/2.20 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', doubleComplementE1)).
% 14.84/2.20 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', complementInPowersetComplementIntersect)).
% 14.84/2.20 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', inIntersectImpInIntersectUnions)).
% 14.84/2.20 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', inIntersectImpInUnion2)).
% 14.84/2.20 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', inIntersectImpInUnion)).
% 14.84/2.20 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binunionTIRcontra)).
% 14.84/2.20 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binunionTILcontra)).
% 14.84/2.20 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', complementTcontraSubset)).
% 14.84/2.20 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', contraSubsetComplement)).
% 14.84/2.20 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', inComplementUnionImpNotIn1)).
% 14.84/2.20 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', inComplementUnionImpInComplement1)).
% 14.84/2.20 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binunionTE)).
% 14.84/2.20 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', binunionTEcontra)).
% 14.84/2.20 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', intersectInPowersetIntersectUnions)).
% 14.84/2.20 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', in__Cong)).
% 14.84/2.20 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', inCongP)).
% 14.84/2.20 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', notdallE)).
% 14.84/2.20 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', notdexE)).
% 14.84/2.20 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', prop2setI)).
% 14.84/2.20 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', quantDeMorgan4)).
% 14.84/2.20 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', quantDeMorgan3)).
% 14.84/2.20 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', quantDeMorgan2)).
% 14.84/2.20 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', quantDeMorgan1)).
% 14.84/2.20 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', vacuousDall)).
% 14.84/2.20 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', upairsetIR)).
% 14.84/2.20 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', upairsetIL)).
% 14.84/2.20 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', upairsetE)).
% 14.84/2.20 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', singletonsswitch)).
% 14.84/2.20 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', eqinunit)).
% 14.84/2.20 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', notinsingleton)).
% 14.84/2.20 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', uniqinunit)).
% 14.84/2.20 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', subPowSU)).
% 14.84/2.20 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setunionE)).
% 14.84/2.20 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setunionI)).
% 14.84/2.20 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', powersetE)).
% 14.84/2.20 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', emptyInPowerset)).
% 14.84/2.20 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', emptyinPowerset)).
% 14.84/2.20 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', powersetI)).
% 14.84/2.20 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setadjoinOr)).
% 14.84/2.20 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setadjoinE)).
% 14.84/2.20 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setadjoinIR)).
% 14.84/2.20 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', emptyinunitempty)).
% 14.84/2.20 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setadjoinIL)).
% 14.84/2.20 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', noeltsimpempty)).
% 14.84/2.20 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', emptyI)).
% 14.84/2.20 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setext)).
% 14.84/2.20 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', notinemptyset)).
% 14.84/2.20 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', emptysetimpfalse)).
% 14.84/2.20 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', emptysetE)).
% 14.84/2.20 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', prop2setE)).
% 14.84/2.20 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', wellorderingAx)).
% 14.84/2.20 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', foundationAx)).
% 14.84/2.20 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', omegaIndAx)).
% 14.84/2.20 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', omegaSAx)).
% 14.84/2.20 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', omega0Ax)).
% 14.84/2.20 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setunionAx)).
% 14.84/2.20 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', powersetAx)).
% 14.84/2.20 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setadjoinAx)).
% 14.84/2.20 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', emptysetAx)).
% 14.84/2.20 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.gxI164ziiz/E---3.1_1748346.p', setextAx)).
% 14.84/2.20 thf(c_0_320, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 14.84/2.20 thf(c_0_321, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 14.84/2.20 thf(c_0_322, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 14.84/2.20 thf(c_0_323, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 14.84/2.20 thf(c_0_324, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0:$i]:(![X2:$i]:((((in @ X2 @ Z0))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])).
% 14.84/2.20 thf(c_0_325, plain, ((surjFuncSet)=(^[Z0:$i, Z1:$i]:(dsetconstr @ (funcSet @ Z0 @ Z1) @ (^[Z2:$i]:((![X1134:$i]:((((in @ X1134 @ Z1))=>(?[X1135:$i]:((((in @ X1135 @ Z0))&(((ap @ Z0 @ Z1 @ Z2 @ X1135)=(X1134)))))))))))))), inference(fof_simplification,[status(thm)],[surjFuncSet])).
% 14.84/2.20 thf(c_0_326, plain, ((surjective)=(^[Z0:$i, Z1:$i, Z2:$i]:(![X2:$i]:((((in @ X2 @ Z1))=>(?[X3:$i]:((((in @ X3 @ Z0))&(((ap @ Z0 @ Z1 @ Z2 @ X3)=(X2))))))))))), inference(fof_simplification,[status(thm)],[surjective])).
% 14.84/2.20 thf(c_0_327, 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])).
% 14.84/2.20 thf(c_0_328, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 14.84/2.20 thf(c_0_329, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 14.84/2.20 thf(c_0_330, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 14.84/2.20 thf(c_0_331, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 14.84/2.20 thf(c_0_332, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 14.84/2.20 thf(c_0_333, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 14.84/2.20 thf(c_0_334, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 14.84/2.20 thf(c_0_335, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 14.84/2.20 thf(c_0_336, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 14.84/2.20 thf(c_0_337, plain, ((replAx)<=>![X6:$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])).
% 14.84/2.20 thf(c_0_338, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>((breln1compprop)=>((breln1compI)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>((breln1unionIR)=>((breln1unionI)=>((breln1unionE)=>((breln1unionEcases)=>((breln1unionCommutes)=>((woz2Ex)=>((woz2W)=>((woz2A)=>((woz2B)=>((image1Ex)=>((image1Ex1)=>((image1Equiv)=>((image1E)=>((image1I)=>((injFuncInInjFuncSet)=>((injFuncSetFuncIn)=>((injFuncSetFuncInj)=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[surjFuncSetFuncIn])).
% 14.84/2.20 thf(c_0_339, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 14.84/2.20 thf(c_0_340, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1128:$i]:(((((X1 @ X1128)))&(![X1129:$i]:(((((X1 @ X1129)))=>(((X1128)=(X1129))))))))))=>((((?[X1130:$i]:(((((X17 @ X1130)))&(![X1131:$i]:(((((X17 @ X1131)))=>(((X1130)=(X1131))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_320, c_0_321])).
% 14.84/2.20 thf(c_0_341, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1122:$i]:(((((X1 @ X1122)))&(![X1123:$i]:(((((X1 @ X1123)))=>(((X1122)=(X1123))))))))))<=>((?[X1124:$i]:(((((X17 @ X1124)))&(![X1125:$i]:(((((X17 @ X1125)))=>(((X1124)=(X1125)))))))))))))))), inference(apply_def,[status(thm)],[c_0_322, c_0_321])).
% 14.84/2.20 thf(c_0_342, plain, ((exuEu)=(![X1:$i > $o]:((((?[X1126:$i]:(((((X1 @ X1126)))&(![X1127:$i]:(((((X1 @ X1127)))=>(((X1126)=(X1127))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_323, c_0_321])).
% 14.84/2.20 thf(c_0_343, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
% 14.84/2.20 thf(c_0_344, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1132:$i]:((((![X2:$i]:((((in @ X2 @ X1132))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))&(![X1133:$i]:((((![X2:$i]:((((in @ X2 @ X1133))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))=>(((X1132)=(X1133)))))))))))), inference(apply_def,[status(thm)],[c_0_324, c_0_321])).
% 14.84/2.20 thf(c_0_345, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])).
% 14.84/2.20 thf(c_0_346, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])).
% 14.84/2.20 thf(c_0_347, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])).
% 14.84/2.20 thf(c_0_348, plain, ((surjFuncSet)=(^[Z0:$i, Z1:$i]:(dsetconstr @ (funcSet @ Z0 @ Z1) @ (^[Z2:$i]:((![X1134:$i]:((((in @ X1134 @ Z1))=>(?[X1135:$i]:((((in @ X1135 @ Z0))&(((ap @ Z0 @ Z1 @ Z2 @ X1135)=(X1134)))))))))))))), inference(apply_def,[status(thm)],[c_0_325, c_0_326])).
% 14.84/2.20 thf(c_0_349, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 14.84/2.20 thf(c_0_350, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 14.84/2.20 thf(c_0_351, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 14.84/2.20 thf(c_0_352, plain, ((lamProp)<=>![X4:$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])).
% 14.84/2.20 thf(c_0_353, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 14.84/2.20 thf(c_0_354, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 14.84/2.20 thf(c_0_355, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 14.84/2.20 thf(c_0_356, plain, ((ex1I)<=>![X4:$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])).
% 14.84/2.20 thf(c_0_357, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 14.84/2.20 thf(c_0_358, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 14.84/2.20 thf(c_0_359, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 14.84/2.20 thf(c_0_360, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 14.84/2.20 thf(c_0_361, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 14.84/2.20 thf(c_0_362, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 14.84/2.20 thf(c_0_363, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 14.84/2.20 thf(c_0_364, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 14.84/2.20 thf(c_0_365, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 14.84/2.20 thf(c_0_366, plain, ((funcImageSingleton)<=>![X4:$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])).
% 14.84/2.20 thf(c_0_367, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 14.84/2.20 thf(c_0_368, plain, ((ex1E2)<=>![X4:$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])).
% 14.84/2.20 thf(c_0_369, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 14.84/2.20 thf(c_0_370, plain, ((beta1)<=>![X4:$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])).
% 14.84/2.20 thf(c_0_371, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 14.84/2.20 thf(c_0_372, plain, ((iffalseProp2)<=>![X4:$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])).
% 14.84/2.20 thf(c_0_373, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 14.84/2.20 thf(c_0_374, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
% 14.84/2.20 thf(c_0_375, plain, ((beta2)<=>![X4:$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])).
% 14.84/2.20 thf(c_0_376, 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])).
% 14.84/2.20 thf(c_0_377, 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])).
% 14.84/2.20 thf(c_0_378, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 14.84/2.20 thf(c_0_379, plain, ((ifSingleton)<=>![X4:$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])).
% 14.84/2.20 thf(c_0_380, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X1120:$i]:(((((X1 @ X1120)))&(![X1121:$i]:(((((X1 @ X1121)))=>(((X1120)=(X1121))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_327, c_0_321])).
% 14.84/2.20 thf(c_0_381, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X1118:$i]:(((((X1 @ X1118)))&(![X1119:$i]:(((((X1 @ X1119)))=>(((X1118)=(X1119)))))))))))))), inference(apply_def,[status(thm)],[c_0_328, c_0_321])).
% 14.84/2.20 thf(c_0_382, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X1116:$i]:(((((X1 @ X1116)))&(![X1117:$i]:(((((X1 @ X1117)))=>(((X1116)=(X1117)))))))))))))))), inference(apply_def,[status(thm)],[c_0_329, c_0_321])).
% 14.84/2.20 thf(c_0_383, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X1114:$i]:(((((X1 @ X1114)))&(![X1115:$i]:(((((X1 @ X1115)))=>(((X1114)=(X1115)))))))))))))), inference(apply_def,[status(thm)],[c_0_330, c_0_321])).
% 14.84/2.20 thf(c_0_384, plain, ((emptyE1)<=>![X4:$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])).
% 14.84/2.20 thf(c_0_385, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_331])).
% 14.84/2.20 thf(c_0_386, plain, ((exuE2)=(![X1:$i > $o]:((((?[X1112:$i]:(((((X1 @ X1112)))&(![X1113:$i]:(((((X1 @ X1113)))=>(((X1112)=(X1113))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_332, c_0_321])).
% 14.84/2.20 thf(c_0_387, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 14.84/2.20 thf(c_0_388, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_331])).
% 14.84/2.20 thf(c_0_389, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_333, c_0_331])).
% 14.84/2.20 thf(c_0_390, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_331])).
% 14.84/2.20 thf(c_0_391, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 14.84/2.20 thf(c_0_392, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X1110:$i]:(((((X1 @ X1110)))&(![X1111:$i]:(((((X1 @ X1111)))=>(((X1110)=(X1111))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_334, c_0_321])).
% 14.84/2.20 thf(c_0_393, plain, ((exuE1)=(![X1:$i > $o]:((((?[X1108:$i]:(((((X1 @ X1108)))&(![X1109:$i]:(((((X1 @ X1109)))=>(((X1108)=(X1109))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_335, c_0_321])).
% 14.84/2.20 thf(c_0_394, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 14.84/2.20 thf(c_0_395, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 14.84/2.20 thf(c_0_396, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 14.84/2.20 thf(c_0_397, plain, ((descrp)=(![X1:$i > $o]:((((?[X1106:$i]:(((((X1 @ X1106)))&(![X1107:$i]:(((((X1 @ X1107)))=>(((X1106)=(X1107))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_336, c_0_321])).
% 14.84/2.20 thf(c_0_398, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X1104:$i]:(((((X6 @ X2 @ X1104)))&(![X1105:$i]:(((((X6 @ X2 @ X1105)))=>(((X1104)=(X1105)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_337, c_0_321])).
% 14.84/2.20 thf(c_0_399, plain, ((epred1_0)<=>![X1165:$i]:(?[X1166:$i]:((((![X1167:$i]:(((in @ X1167 @ X1166)=>![X1168:$i]:(((in @ X1168 @ X1167)=>(in @ X1168 @ X1165)))))&![X1169:$i, X1170:$i]:((((in @ X1169 @ X1165)&(in @ X1170 @ X1165))=>(![X1171:$i]:(((in @ X1171 @ X1166)=>((in @ X1169 @ X1171)<=>(in @ X1170 @ X1171))))=>((X1169)=(X1170))))))&![X1172:$i, X1173:$i]:((((in @ X1172 @ X1166)&(in @ X1173 @ X1166))=>(![X1174:$i]:(((in @ X1174 @ X1172)=>(in @ X1174 @ X1173)))|![X1175:$i]:(((in @ X1175 @ X1173)=>(in @ X1175 @ X1172)))))))&![X1176:$i]:(((![X1177:$i]:(((in @ X1177 @ X1176)=>(in @ X1177 @ X1165)))&?[X1178:$i]:((in @ X1178 @ X1176)))=>?[X1179:$i, X1180:$i]:(((((in @ X1179 @ X1166)&(in @ X1180 @ X1176))&~(?[X1181:$i]:(((in @ X1181 @ X1179)&(in @ X1181 @ X1176)))))&![X1182:$i]:(((in @ X1182 @ X1166)=>(![X1183:$i]:(((in @ X1183 @ X1182)=>(in @ X1183 @ X1179)))|(in @ X1180 @ X1182)))))))))))), introduced(definition)).
% 14.84/2.20 thf(c_0_400, negated_conjecture, ~((![X1136:$i, X1137:$i]:((![X1138:$i]:(((in @ X1138 @ X1136)<=>(in @ X1138 @ X1137)))=>((X1136)=(X1137))))=>(![X1139:$i]:(~(in @ X1139 @ emptyset))=>(![X1140:$i, X1141:$i, X1142:$i]:(((in @ X1142 @ (setadjoin @ X1140 @ X1141))<=>(((X1142)=(X1140))|(in @ X1142 @ X1141))))=>(![X1143:$i, X1144:$i]:(((in @ X1144 @ (powerset @ X1143))<=>![X1145:$i]:(((in @ X1145 @ X1144)=>(in @ X1145 @ X1143)))))=>(![X1146:$i, X1147:$i]:(((in @ X1147 @ (setunion @ X1146))<=>?[X1148:$i]:(((in @ X1147 @ X1148)&(in @ X1148 @ X1146)))))=>((in @ emptyset @ omega)=>(![X1149:$i]:(((in @ X1149 @ omega)=>(in @ (setadjoin @ X1149 @ X1149) @ omega)))=>(![X1150:$i]:((((in @ emptyset @ X1150)&![X1151:$i]:((((in @ X1151 @ omega)&(in @ X1151 @ X1150))=>(in @ (setadjoin @ X1151 @ X1151) @ X1150))))=>![X1152:$i]:(((in @ X1152 @ omega)=>(in @ X1152 @ X1150)))))=>(![X1153:$i > $i > $o, X1154:$i]:((![X1155:$i]:(((in @ X1155 @ X1154)=>?[X1156:$i]:(((X1153 @ X1155 @ X1156)&![X1157:$i]:(((X1153 @ X1155 @ X1157)=>((X1156)=(X1157))))))))=>?[X1158:$i]:(![X1159:$i]:(((in @ X1159 @ X1158)<=>?[X1160:$i]:(((in @ X1160 @ X1154)&(X1153 @ X1160 @ X1159))))))))=>(![X1161:$i]:((?[X1162:$i]:((in @ X1162 @ X1161))=>?[X1163:$i]:(((in @ X1163 @ X1161)&~(?[X1164:$i]:(((in @ X1164 @ X1163)&(in @ X1164 @ X1161))))))))=>((epred1_0)=>(![X1184:$i > $o]:((?[X1185:$i]:(((X1184 @ X1185)&![X1186:$i]:(((X1184 @ X1186)=>((X1185)=(X1186))))))=>(X1184 @ (descr @ (^[Z0:$i]:(X1184 @ Z0))))))=>(![X1187:$i, X1188:$i > $o, X1189:$i]:(((in @ X1189 @ X1187)=>((X1188 @ X1189)=>(in @ X1189 @ (dsetconstr @ X1187 @ X1188)))))=>(![X1190:$i, X1191:$i > $o, X1192:$i]:(((in @ X1192 @ (dsetconstr @ X1190 @ X1191))=>(in @ X1192 @ X1190)))=>(![X1193:$i, X1194:$i > $o, X1195:$i]:(((in @ X1195 @ (dsetconstr @ X1193 @ X1194))=>(X1194 @ X1195)))=>(![X1196:$i > $o]:((?[X1197:$i]:(((X1196 @ X1197)&![X1198:$i]:(((X1196 @ X1198)=>((X1197)=(X1198))))))=>?[X1199:$i]:(((X1196 @ X1199)&![X1200:$i]:(((X1196 @ X1200)=>((X1199)=(X1200))))))))=>(![X1201:$o, X1202:$i]:(((in @ X1202 @ (prop2set @ ((X1201))))=>(X1201)))=>(![X1203:$i]:(((in @ X1203 @ emptyset)=>![X1204:$o]:((X1204))))=>(![X1205:$i]:(((in @ X1205 @ emptyset)=>~($true)))=>(![X1206:$i]:(~(in @ X1206 @ emptyset))=>(![X1207:$i > $o]:((?[X1208:$i]:(((X1207 @ X1208)&![X1209:$i]:(((X1207 @ X1209)=>((X1208)=(X1209))))))=>?[X1210:$i]:((X1207 @ X1210))))=>(![X1211:$i, X1212:$i]:((![X1213:$i]:(((in @ X1213 @ X1211)=>(in @ X1213 @ X1212)))=>(![X1214:$i]:(((in @ X1214 @ X1212)=>(in @ X1214 @ X1211)))=>((X1211)=(X1212)))))=>(![X1215:$i]:((![X1216:$i]:(~(in @ X1216 @ X1215))=>((X1215)=(emptyset))))=>(![X1217:$i]:((![X1218:$i]:(~(in @ X1218 @ X1217))=>((X1217)=(emptyset))))=>(![X1219:$i, X1220:$i > $o, X1221:$i]:(((in @ X1221 @ X1219)=>((in @ X1221 @ (dsetconstr @ X1219 @ X1220))<=>(X1220 @ X1221))))=>(![X1222:$i]:((((X1222)!=(emptyset))=>?[X1223:$i]:((in @ X1223 @ X1222))))=>(![X1224:$i, X1225:$i > $o, X1226:$i]:(((in @ X1226 @ X1224)=>((X1225 @ X1226)=>((dsetconstr @ X1224 @ X1225)!=(emptyset)))))=>(![X1227:$i]:((?[X1228:$i]:((in @ X1228 @ X1227))=>((X1227)!=(emptyset))))=>(![X1229:$i, X1230:$i]:((in @ X1229 @ (setadjoin @ X1229 @ X1230)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1231:$i, X1232:$i, X1233:$i]:(((in @ X1233 @ X1232)=>(in @ X1233 @ (setadjoin @ X1231 @ X1232))))=>(![X1234:$i, X1235:$i, X1236:$i]:(((in @ X1236 @ (setadjoin @ X1234 @ X1235))=>![X1237:$o]:(((((X1236)=(X1234))=>(X1237))=>(((in @ X1236 @ X1235)=>(X1237))=>(X1237))))))=>(![X1238:$i, X1239:$i, X1240:$i]:(((in @ X1240 @ (setadjoin @ X1238 @ X1239))=>(((X1240)=(X1238))|(in @ X1240 @ X1239))))=>(![X1241:$i]:(((dsetconstr @ X1241 @ (^[Z0:$i]:($true)))=(X1241)))=>(![X1242:$i, X1243:$i]:((![X1244:$i]:(((in @ X1244 @ X1243)=>(in @ X1244 @ X1242)))=>(in @ X1243 @ (powerset @ X1242))))=>(![X1245:$i]:((in @ emptyset @ (powerset @ X1245)))=>(![X1246:$i]:((in @ emptyset @ (powerset @ X1246)))=>(![X1247:$i, X1248:$i, X1249:$i]:(((in @ X1248 @ 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(kpair @ X2129 @ X2127) @ X2125)=>(X2128)))))=>(X2128))))))))))))=>(![X2130:$i, X2131:$i]:(((breln1 @ X2130 @ X2131)=>![X2132:$i]:(((breln1 @ X2130 @ X2132)=>(breln1 @ X2130 @ (binunion @ X2131 @ X2132))))))=>(![X2133:$i, X2134:$i]:(((breln1 @ X2133 @ X2134)=>![X2135:$i]:(((breln1 @ X2133 @ X2135)=>![X2136:$i]:(((in @ X2136 @ X2133)=>![X2137:$i]:(((in @ X2137 @ X2133)=>((in @ (kpair @ X2136 @ X2137) @ X2134)=>(in @ (kpair @ X2136 @ X2137) @ (binunion @ X2134 @ X2135)))))))))))=>(![X2138:$i, X2139:$i]:(((breln1 @ X2138 @ X2139)=>![X2140:$i]:(((breln1 @ X2138 @ X2140)=>![X2141:$i]:(((in @ X2141 @ X2138)=>![X2142:$i]:(((in @ X2142 @ X2138)=>((in @ (kpair @ X2141 @ X2142) @ X2140)=>(in @ (kpair @ X2141 @ X2142) @ (binunion @ X2139 @ X2140)))))))))))=>(![X2143:$i, X2144:$i]:(((breln1 @ X2143 @ X2144)=>![X2145:$i]:(((breln1 @ X2143 @ X2145)=>![X2146:$i]:(((in @ X2146 @ X2143)=>![X2147:$i]:(((in @ X2147 @ X2143)=>(((in @ (kpair @ X2146 @ X2147) @ X2144)|(in @ (kpair @ X2146 @ X2147) @ X2145))=>(in @ (kpair @ X2146 @ X2147) @ (binunion @ X2144 @ X2145)))))))))))=>(![X2148:$i, X2149:$i]:(((breln1 @ X2148 @ X2149)=>![X2150:$i]:(((breln1 @ X2148 @ X2150)=>![X2151:$i]:(((in @ X2151 @ X2148)=>![X2152:$i]:(((in @ X2152 @ X2148)=>((in @ (kpair @ X2151 @ X2152) @ (binunion @ X2149 @ X2150))=>((in @ (kpair @ X2151 @ X2152) @ X2149)|(in @ (kpair @ X2151 @ X2152) @ X2150)))))))))))=>(![X2153:$i, X2154:$i]:(((breln1 @ X2153 @ X2154)=>![X2155:$i]:(((breln1 @ X2153 @ X2155)=>![X2156:$i]:(((in @ X2156 @ X2153)=>![X2157:$i]:(((in @ X2157 @ X2153)=>((in @ (kpair @ X2156 @ X2157) @ (binunion @ X2154 @ X2155))=>![X2158:$o]:((((in @ (kpair @ X2156 @ X2157) @ X2154)=>(X2158))=>(((in @ (kpair @ X2156 @ X2157) @ X2155)=>(X2158))=>(X2158)))))))))))))=>(![X2159:$i, X2160:$i]:(((breln1 @ X2159 @ X2160)=>![X2161:$i]:(((breln1 @ X2159 @ X2161)=>((binunion @ X2160 @ X2161)=(binunion @ X2161 @ X2160))))))=>(![X2162:$i, X2163:$i]:(((breln1 @ X2162 @ X2163)=>((X2163)=(breln1invset @ X2162 @ 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y_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_338, setadjoin__Cong]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), c_0_339]), woz13rule2]), c_0_340]), woz13rule3]), c_0_341]), woz13rule4]), c_0_342]), woz1_1]), omega__Cong]), woz1_2]), setunion__Cong]), woz1_3]), powerset__Cong]), woz1_4]), subsetRefl]), notequalI2]), woz1_5]), subsetI1]), breln1all2]), breln1SetBreln1]), c_0_343]), breln1all1]), subbreln1]), eqbreln1]), breln1invprop]), breln1invI]), breln1invE]), breln1compprop]), breln1compI]), breln1compE]), breln1compEex]), notsubsetI]), breln1unionprop]), subsetE2]), breln1unionIL]), subsetE]), breln1unionIR]), emptysetsubset]), breln1unionI]), subsetI2]), breln1unionE]), eqimpsubset1]), breln1unionEcases]), eqimpsubset2]), breln1unionCommutes]), notequalI1]), woz2Ex]), woz2W]), woz2A]), woz2B]), image1Ex]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), injFuncInInjFuncSet]), injFuncSetFuncIn]), injFuncSetFuncInj]), c_0_348]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), setminusEL]), setminusI]), bs114d]), setminusILneg]), subsetemptysetimpeq]), binunionIL]), c_0_349]), c_0_350]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), upairset2IR]), emptyset__Cong]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), binintersectEL]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectSubset1]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), cartprodpairsurjEq]), c_0_351]), c_0_352]), funcinfuncset]), ap2p]), infuncsetfunc]), app]), c_0_353]), symdiffIneg1]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), symdiffIneg2]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), singletoninpowunion]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), upairset2E]), cartprodmempair1]), c_0_354]), c_0_355]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair]), c_0_356]), cartprodfstin]), kfstpairEq]), theprop]), c_0_357]), setukpairinjL1]), singletonsuniq]), c_0_358]), setukpairinjL2]), setukpairinjR]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), c_0_359]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), cartprodsndpairEq]), c_0_360]), c_0_361]), c_0_362]), c_0_363]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), c_0_368]), brelnall2]), brelnall1]), c_0_369]), funcextLem]), ap2apEq2]), ap2apEq1]), funcext2]), funcext]), eqbreln]), subbreln]), funcGraphProp4]), c_0_370]), c_0_371]), c_0_372]), c_0_373]), c_0_374]), c_0_375]), c_0_376]), c_0_377]), c_0_378]), binintersectT_lem]), iftrueorfalse]), iffalse]), iftrue]), theeq]), ifp]), c_0_379]), binunionT_lem]), powersetTE1]), powersetTI1]), subsetTI]), setextT]), complementT_lem]), setminusT_lem]), powersetT_lem]), complementTI1]), contrasubsetT3]), contrasubsetT2]), contrasubsetT1]), contrasubsetT]), binintersectTERcontra]), binintersectTELcontra]), complementTE1]), doubleComplementI1]), complementSubsetComplementIntersect]), complementImpComplementIntersect]), complementTnotintersectT]), doubleComplementEq]), doubleComplementSub2]), doubleComplementSub1]), doubleComplementE1]), complementInPowersetComplementIntersect]), inIntersectImpInIntersectUnions]), inIntersectImpInUnion2]), inIntersectImpInUnion]), binunionTIRcontra]), binunionTILcontra]), complementTcontraSubset]), contraSubsetComplement]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), intersectInPowersetIntersectUnions]), c_0_380]), in__Cong]), inCongP]), c_0_381]), c_0_382]), c_0_383]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_384]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_385]), c_0_386]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_387]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_388]), c_0_389]), c_0_390]), c_0_391]), noeltsimpempty]), emptyI]), setext]), c_0_392]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_393]), c_0_394]), c_0_395]), c_0_396]), c_0_397]), wellorderingAx]), foundationAx]), c_0_398]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_399])).
% 14.84/2.20 thf(c_0_401, negated_conjecture, ![X2211:$i, X2212:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2224:$i, X2225:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2233:$i, X2234:$i > $i > $o, X2235:$i, X2237:$i, X2240:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2247:$i, X2248:$i > $o, X2249:$i, X2251:$i, X2252:$i > $o, X2253:$i, X2254:$i, X2255:$i > $o, X2256:$i, X2257:$i, X2258:$i > $o, X2259:$i, X2260:$i > $o, X2261:$i, X2264:$i, X2265:$o, X2266:$i, X2267:$i, X2268:$o, X2269:$i, X2270:$i, X2271:$i > $o, X2272:$i, X2275:$i, X2276:$i, X2279:$i, X2281:$i, X2283:$i, X2284:$i > $o, X2285:$i, X2286:$i, X2288:$i, X2289:$i > $o, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$o, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$o, X2321:$i, X2322:$i, X2323:$i > $o, X2324:$i, X2327:$i, X2328:$i, X2329:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i > $o, X2348:$i, X2349:$i > $o, X2350:$i, X2351:$i, X2352:$i > $o, X2353:$i, X2355:$i, X2356:$i > $o, X2358:$i, X2359:$i, X2360:$i > $o, X2362:$i, X2363:$i, X2364:$i > $o, X2365:$i, X2367:$o, X2368:$i, X2369:$i > $o, X2371:$i, X2372:$i, X2373:$i > $o, X2374:$i, X2376:$i > $o, X2377:$i, X2380:$i, X2381:$i > $o, X2382:$i, X2386:$i, X2387:$i > $o, X2388:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i > $o, X2401:$i, X2403:$i, X2404:$i, X2405:$i > $o, X2406:$i > $o, X2409:$i, X2412:$i, X2413:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i > $o, X2426:$i, X2428:$i, X2429:$i, X2430:$i > $o, X2431:$i > $o, X2434:$i, X2436:$i, X2438:$i, X2439:$i, X2440:$i > $o, X2441:$i > $o, X2444:$i, X2445:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i > $o, X2492:$i, X2493:$i > $o, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$o, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$o, 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:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i > $o, X2648:$i, X2649:$i, X2650:$i > $o, X2652:$i, X2653:$i > $o, X2654:$i, X2656:$i, X2657:$i > $o, X2660:$i, X2661:$i, X2662:$i, 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 > $i > $o, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i > $i > $o, X2738:$i, X2739:$i, X2740:$i > $i > $o, X2741:$i, X2742:$i, X2743:$i > $i > $o, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i > $i > $o, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i > $i > $o, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i > $i > $o, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i > $i, X2787:$i, X2788:$i, X2789:$i > $i, X2791:$i, X2792:$i, X2793:$i > $i, X2795:$i, X2796:$i, X2797:$i, X2798:$i > $o, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i > $o, X2808:$i, X2809:$i, X2810:$i > $o, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i, X2871:$i, X2872:$i > $i, X2874:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i > $i, X2882:$i, X2883:$i, X2884:$i > $i, X2886:$i, X2887:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$o, X2892:$i, X2893:$i, X2894:$i, X2895:$o, X2896:$i, X2897:$i, X2898:$i, X2899:$o, X2900:$i, X2901:$i, X2902:$i, X2903:$o, X2904:$i, X2905:$i, X2906:$i, X2907:$o, X2908:$i, X2909:$i, X2910:$i, X2911:$o, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$o, X2918:$i, X2919:$i, X2920:$i, X2921:$o, X2922:$i, X2923:$i, X2924:$i, X2925:$o, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i, X2946:$i, X2947:$i, X2948:$i, X2950:$i, X2951:$i, X2952:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i, X2976:$i, X2977:$i, X2978:$i, X2979:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3002:$i, X3003:$i, X3004:$i, X3005:$i, X3006:$i, X3007:$i, X3008:$i, X3009:$i, X3010:$i, X3011:$i, X3012:$i, X3013:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i, X3023:$i, X3024:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i, X3037:$i, X3038:$i, X3039:$i, X3040:$i, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3047:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$o, X3058:$i, X3059:$i, X3060:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i, X3068:$i, X3069:$i, X3070:$i, X3071:$i, X3072:$i, X3073:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i, X3079:$i, X3080:$i, X3081:$i, X3082:$i, X3083:$i, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i, X3090:$i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$i, X3115:$i, X3116:$i, X3117:$i, X3118:$i, X3119:$i, X3120:$i, X3121:$i, X3122:$i, X3123:$i, X3124:$i, X3125:$i, X3126:$i, X3127:$i, X3128:$i, X3129:$i, X3130:$i, X3131:$i, X3132:$i, X3133:$i, X3134:$i, X3135:$i, X3136:$i, X3137:$i, X3138:$i, X3139:$i, X3140:$i, X3141:$i > $o, X3144:$i, X3145:$i, X3146:$i, X3147:$i, X3148:$i > $i > $o, X3149:$i, X3150:$i, X3151:$i > $o, X3154:$i, X3155:$i, X3156:$i, X3157:$i, X3160:$i, X3161:$i, X3162:$i, X3167:$i, X3168:$i, 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@ X3209)))))))&(((~(in @ (kpair @ X3215 @ X3216) @ X3213)|(in @ (kpair @ X3215 @ X3216) @ (binunion @ X3213 @ X3214))|~(in @ X3216 @ X3212)|~(in @ X3215 @ X3212)|~(breln1 @ X3212 @ X3214)|~(breln1 @ X3212 @ X3213))&(~(in @ (kpair @ X3215 @ X3216) @ X3214)|(in @ (kpair @ X3215 @ X3216) @ (binunion @ X3213 @ X3214))|~(in @ X3216 @ X3212)|~(in @ X3215 @ X3212)|~(breln1 @ X3212 @ X3214)|~(breln1 @ X3212 @ X3213)))&((~(breln1 @ X3217 @ X3218)|(~(breln1 @ X3217 @ X3219)|(~(in @ X3220 @ X3217)|(~(in @ X3221 @ X3217)|(~(in @ (kpair @ X3220 @ X3221) @ (binunion @ X3218 @ X3219))|((in @ (kpair @ X3220 @ X3221) @ X3218)|(in @ (kpair @ X3220 @ X3221) @ X3219)))))))&(((((in @ (kpair @ X3225 @ X3226) @ X3224)|(X3227)|(in @ (kpair @ X3225 @ X3226) @ X3223)|~(in @ (kpair @ X3225 @ X3226) @ (binunion @ X3223 @ X3224))|~(in @ X3226 @ X3222)|~(in @ X3225 @ X3222)|~(breln1 @ X3222 @ X3224)|~(breln1 @ X3222 @ X3223))&(~(X3227)|(X3227)|(in @ (kpair @ X3225 @ X3226) @ X3223)|~(in @ (kpair @ X3225 @ X3226) @ (binunion @ X3223 @ X3224))|~(in @ X3226 @ X3222)|~(in @ X3225 @ X3222)|~(breln1 @ X3222 @ X3224)|~(breln1 @ X3222 @ X3223)))&(((in @ (kpair @ X3225 @ X3226) @ X3224)|(X3227)|~(X3227)|~(in @ (kpair @ X3225 @ X3226) @ (binunion @ X3223 @ X3224))|~(in @ X3226 @ X3222)|~(in @ X3225 @ X3222)|~(breln1 @ X3222 @ X3224)|~(breln1 @ X3222 @ X3223))&(~(X3227)|(X3227)|~(X3227)|~(in @ (kpair @ X3225 @ X3226) @ (binunion @ X3223 @ X3224))|~(in @ X3226 @ X3222)|~(in @ X3225 @ X3222)|~(breln1 @ X3222 @ X3224)|~(breln1 @ X3222 @ X3223))))&((~(breln1 @ X3228 @ X3229)|(~(breln1 @ X3228 @ X3230)|((binunion @ X3229 @ X3230)=(binunion @ X3230 @ X3229))))&((~(breln1 @ X3231 @ X3232)|((X3232)=(breln1invset @ X3231 @ (breln1invset @ X3231 @ X3232))))&((~(breln1 @ X3233 @ X3234)|(~(breln1 @ X3233 @ X3235)|((breln1invset @ X3233 @ (breln1compset @ X3233 @ X3234 @ X3235))=(breln1compset @ X3233 @ (breln1invset @ X3233 @ X3235) @ (breln1invset @ X3233 @ X3234)))))&((~(breln1 @ X3236 @ X3237)|(~(breln1 @ X3236 @ X3238)|(~(breln1 @ X3236 @ X3239)|((breln1compset @ X3236 @ (binunion @ X3237 @ X3238) @ X3239)=(binunion @ (breln1compset @ X3236 @ X3237 @ X3239) @ (breln1compset @ X3236 @ X3238 @ X3239))))))&((~(breln1 @ X3240 @ X3241)|(~(breln1 @ X3240 @ X3242)|(~(breln1 @ X3240 @ X3243)|((breln1compset @ X3240 @ (binunion @ X3241 @ X3242) @ X3243)=(binunion @ (breln1invset @ X3240 @ (breln1compset @ X3240 @ (breln1invset @ X3240 @ X3243) @ (breln1invset @ X3240 @ X3242))) @ (breln1invset @ X3240 @ (breln1compset @ X3240 @ (breln1invset @ X3240 @ X3243) @ (breln1invset @ X3240 @ X3241))))))))&(((((in @ (esk100_3 @ X3244 @ X3245 @ X3247) @ X3244)|~(in @ X3247 @ (esk99_2 @ X3244 @ X3245)))&(((X3247)=(X3245 @ (esk100_3 @ X3244 @ X3245 @ X3247)))|~(in @ X3247 @ (esk99_2 @ X3244 @ X3245))))&(~(in @ X3250 @ X3244)|((X3249)!=(X3245 @ X3250))|(in @ X3249 @ (esk99_2 @ X3244 @ X3245))))&((((((in @ (esk102_3 @ X3251 @ X3252 @ X3254) @ X3251)|~(in @ X3254 @ (esk101_2 @ X3251 @ X3252)))&(((X3254)=(X3252 @ (esk102_3 @ X3251 @ X3252 @ X3254)))|~(in @ X3254 @ (esk101_2 @ X3251 @ X3252))))&(~(in @ X3257 @ X3251)|((X3256)!=(X3252 @ X3257))|(in @ X3256 @ (esk101_2 @ X3251 @ X3252))))&((~(in @ (esk103_3 @ X3251 @ X3252 @ X3258) @ X3258)|(~(in @ X3260 @ X3251)|((esk103_3 @ X3251 @ X3252 @ X3258)!=(X3252 @ X3260)))|((esk101_2 @ X3251 @ X3252)=(X3258)))&(((in @ (esk104_3 @ X3251 @ X3252 @ X3258) @ X3251)|(in @ (esk103_3 @ X3251 @ X3252 @ X3258) @ X3258)|((esk101_2 @ X3251 @ X3252)=(X3258)))&(((esk103_3 @ X3251 @ X3252 @ X3258)=(X3252 @ (esk104_3 @ X3251 @ X3252 @ X3258)))|(in @ (esk103_3 @ X3251 @ X3252 @ X3258) @ X3258)|((esk101_2 @ X3251 @ X3252)=(X3258))))))&(((((in @ (esk105_3 @ X3262 @ X3263 @ X3264) @ X3262)|~(in @ X3264 @ (image1 @ X3262 @ X3263)))&(((X3264)=(X3263 @ (esk105_3 @ X3262 @ X3263 @ X3264)))|~(in @ X3264 @ (image1 @ X3262 @ X3263))))&(~(in @ X3269 @ X3266)|((X3268)!=(X3267 @ X3269))|(in @ X3268 @ (image1 @ X3266 @ X3267))))&((((in @ (esk106_3 @ X3270 @ X3271 @ X3272) @ X3270)|~(in @ X3272 @ (image1 @ X3270 @ X3271)))&(((X3272)=(X3271 @ (esk106_3 @ X3270 @ X3271 @ X3272)))|~(in @ X3272 @ (image1 @ X3270 @ X3271))))&((~(in @ X3277 @ X3274)|((X3276)!=(X3275 @ X3277))|(in @ X3276 @ (image1 @ X3274 @ X3275)))&((~(in @ X3280 @ (funcSet @ X3278 @ X3279))|(~(injective @ X3278 @ X3279 @ X3280)|(in @ X3280 @ (injFuncSet @ X3278 @ X3279))))&((~(in @ X3283 @ (injFuncSet @ X3281 @ X3282))|(in @ X3283 @ (funcSet @ X3281 @ X3282)))&((~(in @ X3286 @ (injFuncSet @ X3284 @ X3285))|(injective @ X3284 @ X3285 @ X3286))&((in @ esk109_0 @ (dsetconstr @ (funcSet @ esk107_0 @ esk108_0) @ (^[Z0:$i]:(![X2209:$i]:((((in @ X2209 @ esk108_0))=>(?[X2210:$i]:((((in @ X2210 @ esk107_0))&(((ap @ esk107_0 @ esk108_0 @ Z0 @ X2210)=(X2209))))))))))))&~(in @ esk109_0 @ (funcSet @ esk107_0 @ esk108_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_400])])])])])])])).
% 14.84/2.20 thf(c_0_402, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ X2 @ X3)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_401])).
% 14.84/2.20 thf(c_0_403, negated_conjecture, (in @ esk109_0 @ (dsetconstr @ (funcSet @ esk107_0 @ esk108_0) @ (^[Z0:$i]:(![X3309:$i]:((((in @ X3309 @ esk108_0))=>(?[X3310:$i]:((((in @ X3310 @ esk107_0))&(((ap @ esk107_0 @ esk108_0 @ Z0 @ X3310)=(X3309)))))))))))), inference(split_conjunct,[status(thm)],[c_0_401])).
% 14.84/2.20 thf(c_0_404, negated_conjecture, ~((in @ esk109_0 @ (funcSet @ esk107_0 @ esk108_0))), inference(split_conjunct,[status(thm)],[c_0_401])).
% 14.84/2.20 thf(c_0_405, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_402, c_0_403]), c_0_404]), ['proof']).
% 14.84/2.20 % SZS output end CNFRefutation
% 14.84/2.20 % Parsed axioms : 692
% 14.84/2.20 % Removed by relevancy pruning/SinE : 372
% 14.84/2.20 % Initial clauses : 546
% 14.84/2.20 % Removed in clause preprocessing : 36
% 14.84/2.20 % Initial clauses in saturation : 510
% 14.84/2.20 % Processed clauses : 4389
% 14.84/2.20 % ...of these trivial : 284
% 14.84/2.20 % ...subsumed : 2909
% 14.84/2.20 % ...remaining for further processing : 1196
% 14.84/2.20 % Other redundant clauses eliminated : 261
% 14.84/2.20 % Clauses deleted for lack of memory : 0
% 14.84/2.20 % Backward-subsumed : 21
% 14.84/2.20 % Backward-rewritten : 34
% 14.84/2.20 % Generated clauses : 72748
% 14.84/2.20 % ...of the previous two non-redundant : 67059
% 14.84/2.20 % ...aggressively subsumed : 0
% 14.84/2.20 % Contextual simplify-reflections : 18
% 14.84/2.20 % Paramodulations : 72474
% 14.84/2.20 % Factorizations : 6
% 14.84/2.20 % NegExts : 0
% 14.84/2.20 % Equation resolutions : 268
% 14.84/2.20 % Disequality decompositions : 0
% 14.84/2.20 % Total rewrite steps : 13415
% 14.84/2.20 % ...of those cached : 12610
% 14.84/2.20 % Propositional unsat checks : 0
% 14.84/2.20 % Propositional check models : 0
% 14.84/2.20 % Propositional check unsatisfiable : 0
% 14.84/2.20 % Propositional clauses : 0
% 14.84/2.20 % Propositional clauses after purity: 0
% 14.84/2.20 % Propositional unsat core size : 0
% 14.84/2.20 % Propositional preprocessing time : 0.000
% 14.84/2.20 % Propositional encoding time : 0.000
% 14.84/2.20 % Propositional solver time : 0.000
% 14.84/2.20 % Success case prop preproc time : 0.000
% 14.84/2.20 % Success case prop encoding time : 0.000
% 14.84/2.20 % Success case prop solver time : 0.000
% 14.84/2.20 % Current number of processed clauses : 1122
% 14.84/2.20 % Positive orientable unit clauses : 289
% 14.84/2.20 % Positive unorientable unit clauses: 0
% 14.84/2.20 % Negative unit clauses : 14
% 14.84/2.20 % Non-unit-clauses : 819
% 14.84/2.20 % Current number of unprocessed clauses: 60006
% 14.84/2.20 % ...number of literals in the above : 221197
% 14.84/2.20 % Current number of archived formulas : 0
% 14.84/2.20 % Current number of archived clauses : 55
% 14.84/2.20 % Clause-clause subsumption calls (NU) : 131479
% 14.84/2.20 % Rec. Clause-clause subsumption calls : 65194
% 14.84/2.20 % Non-unit clause-clause subsumptions : 1886
% 14.84/2.20 % Unit Clause-clause subsumption calls : 1929
% 14.84/2.20 % Rewrite failures with RHS unbound : 0
% 14.84/2.20 % BW rewrite match attempts : 998
% 14.84/2.20 % BW rewrite match successes : 24
% 14.84/2.20 % Condensation attempts : 0
% 14.84/2.20 % Condensation successes : 0
% 14.84/2.20 % Termbank termtop insertions : 1211153
% 14.84/2.20 % Search garbage collected termcells : 35428
% 14.84/2.20
% 14.84/2.20 % -------------------------------------------------
% 14.84/2.20 % User time : 1.545 s
% 14.84/2.20 % System time : 0.068 s
% 14.84/2.20 % Total time : 1.613 s
% 14.84/2.20 % Maximum resident set size: 12624 pages
% 14.84/2.20
% 14.84/2.20 % -------------------------------------------------
% 14.84/2.20 % User time : 1.565 s
% 14.84/2.20 % System time : 0.078 s
% 14.84/2.20 % Total time : 1.642 s
% 14.84/2.20 % Maximum resident set size: 5888 pages
% 14.84/2.20 % E exiting
%------------------------------------------------------------------------------