%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU687^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:27:13 AM UTC 2026
% Result : Theorem 205.32s 30.31s
% Output : CNFRefutation 205.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU687^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:11:37 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.20/0.28 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p
% 205.32/30.31 % Version: 3.5.1-ho
% 205.32/30.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 205.32/30.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 205.32/30.31 % Starting ehoh_best5 with 300s (1) cores
% 205.32/30.31 % Starting almost_fo_3_lam with 300s (1) cores
% 205.32/30.31 % Starting new_bool_5 with 300s (1) cores
% 205.32/30.31 % Starting pre_casc_3 with 300s (1) cores
% 205.32/30.31 % Starting ho_unfolding_8 with 300s (1) cores
% 205.32/30.31 % Starting new_ho_10_cnf2 with 300s (1) cores
% 205.32/30.31 % Starting new_bool_3 with 300s (1) cores
% 205.32/30.31 % Starting new_ho_5 with 300s (1) cores
% 205.32/30.31 % new_bool_5 with pid 1345831 completed with status 0
% 205.32/30.31 % Result found by new_bool_5
% 205.32/30.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 205.32/30.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 205.32/30.31 % Starting ehoh_best5 with 300s (1) cores
% 205.32/30.31 % Starting almost_fo_3_lam with 300s (1) cores
% 205.32/30.31 % Starting new_bool_5 with 300s (1) cores
% 205.32/30.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 205.32/30.31 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 205.32/30.31 % Search class: HGHSM-FSLM32-MHFMMSBN
% 205.32/30.31 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 205.32/30.31 % Starting SubtermCWHack with 28s (1) cores
% 205.32/30.31 % SubtermCWHack with pid 1345862 completed with status 8
% 205.32/30.31 % Starting new_bool_5 with 31s (1) cores
% 205.32/30.31 % new_bool_5 with pid 1346391 completed with status 0
% 205.32/30.31 % Result found by new_bool_5
% 205.32/30.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 205.32/30.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 205.32/30.31 % Starting ehoh_best5 with 300s (1) cores
% 205.32/30.31 % Starting almost_fo_3_lam with 300s (1) cores
% 205.32/30.31 % Starting new_bool_5 with 300s (1) cores
% 205.32/30.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 205.32/30.31 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 205.32/30.31 % Search class: HGHSM-FSLM32-MHFMMSBN
% 205.32/30.31 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 205.32/30.31 % Starting SubtermCWHack with 28s (1) cores
% 205.32/30.31 % SubtermCWHack with pid 1345862 completed with status 8
% 205.32/30.31 % Starting new_bool_5 with 31s (1) cores
% 205.32/30.31 % Preprocessing time : 0.007 s
% 205.32/30.31 % Presaturation interreduction done
% 205.32/30.31
% 205.32/30.31 % Proof found!
% 205.32/30.31 % SZS status Theorem
% 205.32/30.31 % SZS output start CNFRefutation
% 205.32/30.31 thf(decl_23, type, in: $i > $i > $o).
% 205.32/30.31 thf(decl_24, type, exu: ($i > $o) > $o).
% 205.32/30.31 thf(decl_25, type, setextAx: $o).
% 205.32/30.31 thf(decl_26, type, emptyset: $i).
% 205.32/30.31 thf(decl_27, type, emptysetAx: $o).
% 205.32/30.31 thf(decl_28, type, setadjoin: $i > $i > $i).
% 205.32/30.31 thf(decl_29, type, setadjoinAx: $o).
% 205.32/30.31 thf(decl_30, type, powerset: $i > $i).
% 205.32/30.31 thf(decl_31, type, powersetAx: $o).
% 205.32/30.31 thf(decl_32, type, setunion: $i > $i).
% 205.32/30.31 thf(decl_33, type, setunionAx: $o).
% 205.32/30.31 thf(decl_34, type, omega: $i).
% 205.32/30.31 thf(decl_35, type, omega0Ax: $o).
% 205.32/30.31 thf(decl_36, type, omegaSAx: $o).
% 205.32/30.31 thf(decl_37, type, omegaIndAx: $o).
% 205.32/30.31 thf(decl_38, type, replAx: $o).
% 205.32/30.31 thf(decl_39, type, foundationAx: $o).
% 205.32/30.31 thf(decl_40, type, wellorderingAx: $o).
% 205.32/30.31 thf(decl_41, type, descr: ($i > $o) > $i).
% 205.32/30.31 thf(decl_42, type, descrp: $o).
% 205.32/30.31 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 205.32/30.31 thf(decl_44, type, dsetconstrI: $o).
% 205.32/30.31 thf(decl_45, type, dsetconstrEL: $o).
% 205.32/30.31 thf(decl_46, type, dsetconstrER: $o).
% 205.32/30.31 thf(decl_47, type, exuE1: $o).
% 205.32/30.31 thf(decl_48, type, prop2set: $o > $i).
% 205.32/30.31 thf(decl_49, type, prop2setE: $o).
% 205.32/30.31 thf(decl_50, type, emptysetE: $o).
% 205.32/30.31 thf(decl_51, type, emptysetimpfalse: $o).
% 205.32/30.31 thf(decl_52, type, notinemptyset: $o).
% 205.32/30.31 thf(decl_53, type, exuE3e: $o).
% 205.32/30.31 thf(decl_54, type, setext: $o).
% 205.32/30.31 thf(decl_55, type, emptyI: $o).
% 205.32/30.31 thf(decl_56, type, noeltsimpempty: $o).
% 205.32/30.31 thf(decl_57, type, setbeta: $o).
% 205.32/30.31 thf(decl_58, type, nonempty: $i > $o).
% 205.32/30.31 thf(decl_59, type, nonemptyE1: $o).
% 205.32/30.31 thf(decl_60, type, nonemptyI: $o).
% 205.32/30.31 thf(decl_61, type, nonemptyI1: $o).
% 205.32/30.31 thf(decl_62, type, setadjoinIL: $o).
% 205.32/30.31 thf(decl_63, type, emptyinunitempty: $o).
% 205.32/30.31 thf(decl_64, type, setadjoinIR: $o).
% 205.32/30.31 thf(decl_65, type, setadjoinE: $o).
% 205.32/30.31 thf(decl_66, type, setadjoinOr: $o).
% 205.32/30.31 thf(decl_67, type, setoftrueEq: $o).
% 205.32/30.31 thf(decl_68, type, powersetI: $o).
% 205.32/30.31 thf(decl_69, type, emptyinPowerset: $o).
% 205.32/30.31 thf(decl_70, type, emptyInPowerset: $o).
% 205.32/30.31 thf(decl_71, type, powersetE: $o).
% 205.32/30.31 thf(decl_72, type, setunionI: $o).
% 205.32/30.31 thf(decl_73, type, setunionE: $o).
% 205.32/30.31 thf(decl_74, type, subPowSU: $o).
% 205.32/30.31 thf(decl_75, type, exuE2: $o).
% 205.32/30.31 thf(decl_76, type, nonemptyImpWitness: $o).
% 205.32/30.31 thf(decl_77, type, uniqinunit: $o).
% 205.32/30.31 thf(decl_78, type, notinsingleton: $o).
% 205.32/30.31 thf(decl_79, type, eqinunit: $o).
% 205.32/30.31 thf(decl_80, type, singletonsswitch: $o).
% 205.32/30.31 thf(decl_81, type, upairsetE: $o).
% 205.32/30.31 thf(decl_82, type, upairsetIL: $o).
% 205.32/30.31 thf(decl_83, type, upairsetIR: $o).
% 205.32/30.31 thf(decl_84, type, emptyE1: $o).
% 205.32/30.31 thf(decl_85, type, vacuousDall: $o).
% 205.32/30.31 thf(decl_86, type, quantDeMorgan1: $o).
% 205.32/30.31 thf(decl_87, type, quantDeMorgan2: $o).
% 205.32/30.31 thf(decl_88, type, quantDeMorgan3: $o).
% 205.32/30.31 thf(decl_89, type, quantDeMorgan4: $o).
% 205.32/30.31 thf(decl_90, type, prop2setI: $o).
% 205.32/30.31 thf(decl_92, type, prop2set2propI: $o).
% 205.32/30.31 thf(decl_93, type, notdexE: $o).
% 205.32/30.31 thf(decl_94, type, notdallE: $o).
% 205.32/30.31 thf(decl_95, type, exuI1: $o).
% 205.32/30.31 thf(decl_96, type, exuI3: $o).
% 205.32/30.31 thf(decl_97, type, exuI2: $o).
% 205.32/30.31 thf(decl_98, type, inCongP: $o).
% 205.32/30.31 thf(decl_99, type, in__Cong: $o).
% 205.32/30.31 thf(decl_100, type, exuE3u: $o).
% 205.32/30.31 thf(decl_101, type, exu__Cong: $o).
% 205.32/30.31 thf(decl_102, type, emptyset__Cong: $o).
% 205.32/30.31 thf(decl_103, type, setadjoin__Cong: $o).
% 205.32/30.31 thf(decl_104, type, powerset__Cong: $o).
% 205.32/30.31 thf(decl_105, type, setunion__Cong: $o).
% 205.32/30.31 thf(decl_106, type, omega__Cong: $o).
% 205.32/30.31 thf(decl_107, type, exuEu: $o).
% 205.32/30.31 thf(decl_108, type, descr__Cong: $o).
% 205.32/30.31 thf(decl_109, type, dsetconstr__Cong: $o).
% 205.32/30.31 thf(decl_110, type, subset: $i > $i > $o).
% 205.32/30.31 thf(decl_113, type, subsetI1: $o).
% 205.32/30.31 thf(decl_114, type, eqimpsubset2: $o).
% 205.32/30.31 thf(decl_115, type, eqimpsubset1: $o).
% 205.32/30.31 thf(decl_116, type, subsetI2: $o).
% 205.32/30.31 thf(decl_117, type, emptysetsubset: $o).
% 205.32/30.31 thf(decl_118, type, subsetE: $o).
% 205.32/30.31 thf(decl_119, type, subsetE2: $o).
% 205.32/30.31 thf(decl_120, type, notsubsetI: $o).
% 205.32/30.31 thf(decl_121, type, notequalI1: $o).
% 205.32/30.31 thf(decl_122, type, notequalI2: $o).
% 205.32/30.31 thf(decl_123, type, subsetRefl: $o).
% 205.32/30.31 thf(decl_124, type, subsetTrans: $o).
% 205.32/30.31 thf(decl_125, type, setadjoinSub: $o).
% 205.32/30.31 thf(decl_126, type, setadjoinSub2: $o).
% 205.32/30.31 thf(decl_127, type, subset2powerset: $o).
% 205.32/30.31 thf(decl_128, type, setextsub: $o).
% 205.32/30.31 thf(decl_129, type, subsetemptysetimpeq: $o).
% 205.32/30.31 thf(decl_130, type, powersetI1: $o).
% 205.32/30.31 thf(decl_131, type, powersetE1: $o).
% 205.32/30.31 thf(decl_132, type, inPowerset: $o).
% 205.32/30.31 thf(decl_133, type, powersetsubset: $o).
% 205.32/30.31 thf(decl_134, type, sepInPowerset: $o).
% 205.32/30.31 thf(decl_135, type, sepSubset: $o).
% 205.32/30.31 thf(decl_136, type, binunion: $i > $i > $i).
% 205.32/30.31 thf(decl_137, type, binunionIL: $o).
% 205.32/30.31 thf(decl_138, type, upairset2IR: $o).
% 205.32/30.31 thf(decl_139, type, binunionIR: $o).
% 205.32/30.31 thf(decl_140, type, binunionEcases: $o).
% 205.32/30.31 thf(decl_141, type, binunionE: $o).
% 205.32/30.31 thf(decl_142, type, binunionLsub: $o).
% 205.32/30.31 thf(decl_143, type, binunionRsub: $o).
% 205.32/30.31 thf(decl_144, type, binintersect: $i > $i > $i).
% 205.32/30.31 thf(decl_145, type, binintersectI: $o).
% 205.32/30.31 thf(decl_146, type, binintersectSubset5: $o).
% 205.32/30.31 thf(decl_147, type, binintersectEL: $o).
% 205.32/30.31 thf(decl_148, type, binintersectLsub: $o).
% 205.32/30.31 thf(decl_149, type, binintersectSubset2: $o).
% 205.32/30.31 thf(decl_150, type, binintersectSubset3: $o).
% 205.32/30.31 thf(decl_151, type, binintersectER: $o).
% 205.32/30.31 thf(decl_152, type, disjointsetsI1: $o).
% 205.32/30.31 thf(decl_153, type, binintersectRsub: $o).
% 205.32/30.31 thf(decl_154, type, binintersectSubset4: $o).
% 205.32/30.31 thf(decl_155, type, binintersectSubset1: $o).
% 205.32/30.31 thf(decl_156, type, bs114d: $o).
% 205.32/30.31 thf(decl_158, type, setminus: $i > $i > $i).
% 205.32/30.31 thf(decl_159, type, setminusI: $o).
% 205.32/30.31 thf(decl_160, type, setminusEL: $o).
% 205.32/30.31 thf(decl_161, type, setminusER: $o).
% 205.32/30.31 thf(decl_162, type, setminusSubset2: $o).
% 205.32/30.31 thf(decl_163, type, setminusERneg: $o).
% 205.32/30.31 thf(decl_164, type, setminusELneg: $o).
% 205.32/30.31 thf(decl_165, type, setminusILneg: $o).
% 205.32/30.31 thf(decl_166, type, setminusIRneg: $o).
% 205.32/30.31 thf(decl_167, type, setminusLsub: $o).
% 205.32/30.31 thf(decl_168, type, setminusSubset1: $o).
% 205.32/30.31 thf(decl_169, type, symdiff: $i > $i > $i).
% 205.32/30.31 thf(decl_170, type, symdiffE: $o).
% 205.32/30.31 thf(decl_171, type, symdiffI1: $o).
% 205.32/30.31 thf(decl_172, type, symdiffI2: $o).
% 205.32/30.31 thf(decl_173, type, symdiffIneg1: $o).
% 205.32/30.31 thf(decl_174, type, symdiffIneg2: $o).
% 205.32/30.31 thf(decl_175, type, iskpair: $i > $o).
% 205.32/30.31 thf(decl_176, type, secondinupair: $o).
% 205.32/30.31 thf(decl_177, type, setukpairIL: $o).
% 205.32/30.31 thf(decl_178, type, setukpairIR: $o).
% 205.32/30.31 thf(decl_179, type, kpairiskpair: $o).
% 205.32/30.31 thf(decl_180, type, kpair: $i > $i > $i).
% 205.32/30.31 thf(decl_181, type, kpairp: $o).
% 205.32/30.31 thf(decl_182, type, cartprod: $i > $i > $i).
% 205.32/30.31 thf(decl_183, type, singletonsubset: $o).
% 205.32/30.31 thf(decl_184, type, singletoninpowerset: $o).
% 205.32/30.31 thf(decl_185, type, singletoninpowunion: $o).
% 205.32/30.31 thf(decl_186, type, upairset2E: $o).
% 205.32/30.31 thf(decl_187, type, upairsubunion: $o).
% 205.32/30.31 thf(decl_188, type, upairinpowunion: $o).
% 205.32/30.31 thf(decl_189, type, ubforcartprodlem1: $o).
% 205.32/30.31 thf(decl_190, type, ubforcartprodlem2: $o).
% 205.32/30.31 thf(decl_191, type, ubforcartprodlem3: $o).
% 205.32/30.31 thf(decl_192, type, cartprodpairin: $o).
% 205.32/30.31 thf(decl_193, type, cartprodmempair1: $o).
% 205.32/30.31 thf(decl_194, type, cartprodmempair: $o).
% 205.32/30.31 thf(decl_195, type, setunionE2: $o).
% 205.32/30.31 thf(decl_196, type, setunionsingleton1: $o).
% 205.32/30.31 thf(decl_197, type, setunionsingleton2: $o).
% 205.32/30.31 thf(decl_198, type, setunionsingleton: $o).
% 205.32/30.31 thf(decl_199, type, singleton: $i > $o).
% 205.32/30.31 thf(decl_200, type, singletonprop: $o).
% 205.32/30.31 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 205.32/30.31 thf(decl_202, type, ex1E1: $o).
% 205.32/30.31 thf(decl_203, type, ex1I: $o).
% 205.32/30.31 thf(decl_204, type, ex1I2: $o).
% 205.32/30.31 thf(decl_205, type, singletonsuniq: $o).
% 205.32/30.31 thf(decl_210, type, setukpairinjL1: $o).
% 205.32/30.31 thf(decl_211, type, kfstsingleton: $o).
% 205.32/30.31 thf(decl_212, type, theprop: $o).
% 205.32/30.31 thf(decl_213, type, kfst: $i > $i).
% 205.32/30.31 thf(decl_214, type, kfstpairEq: $o).
% 205.32/30.31 thf(decl_215, type, cartprodfstin: $o).
% 205.32/30.32 thf(decl_216, type, setukpairinjL2: $o).
% 205.32/30.32 thf(decl_217, type, setukpairinjL: $o).
% 205.32/30.32 thf(decl_218, type, setukpairinjR11: $o).
% 205.32/30.32 thf(decl_219, type, setukpairinjR12: $o).
% 205.32/30.32 thf(decl_220, type, setukpairinjR1: $o).
% 205.32/30.32 thf(decl_221, type, upairequniteq: $o).
% 205.32/30.32 thf(decl_222, type, setukpairinjR2: $o).
% 205.32/30.32 thf(decl_223, type, setukpairinjR: $o).
% 205.32/30.32 thf(decl_224, type, ksndsingleton: $o).
% 205.32/30.32 thf(decl_225, type, ksnd: $i > $i).
% 205.32/30.32 thf(decl_226, type, ksndpairEq: $o).
% 205.32/30.32 thf(decl_227, type, kpairsurjEq: $o).
% 205.32/30.32 thf(decl_228, type, cartprodsndin: $o).
% 205.32/30.32 thf(decl_229, type, cartprodpairmemEL: $o).
% 205.32/30.32 thf(decl_230, type, cartprodpairmemER: $o).
% 205.32/30.32 thf(decl_231, type, cartprodmempaircEq: $o).
% 205.32/30.32 thf(decl_232, type, cartprodfstpairEq: $o).
% 205.32/30.32 thf(decl_233, type, cartprodsndpairEq: $o).
% 205.32/30.32 thf(decl_234, type, cartprodpairsurjEq: $o).
% 205.32/30.32 thf(decl_235, type, breln: $i > $i > $i > $o).
% 205.32/30.32 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 205.32/30.32 thf(decl_237, type, dpsetconstrI: $o).
% 205.32/30.32 thf(decl_238, type, dpsetconstrSub: $o).
% 205.32/30.32 thf(decl_239, type, setOfPairsIsBReln: $o).
% 205.32/30.32 thf(decl_240, type, dpsetconstrERa: $o).
% 205.32/30.32 thf(decl_241, type, dpsetconstrEL1: $o).
% 205.32/30.32 thf(decl_242, type, dpsetconstrEL2: $o).
% 205.32/30.32 thf(decl_243, type, dpsetconstrER: $o).
% 205.32/30.32 thf(decl_244, type, func: $i > $i > $i > $o).
% 205.32/30.32 thf(decl_245, type, funcSet: $i > $i > $i).
% 205.32/30.32 thf(decl_246, type, funcImageSingleton: $o).
% 205.32/30.32 thf(decl_247, type, apProp: $o).
% 205.32/30.32 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 205.32/30.32 thf(decl_249, type, app: $o).
% 205.32/30.32 thf(decl_250, type, infuncsetfunc: $o).
% 205.32/30.32 thf(decl_251, type, ap2p: $o).
% 205.32/30.32 thf(decl_252, type, funcinfuncset: $o).
% 205.32/30.32 thf(decl_253, type, lamProp: $o).
% 205.32/30.32 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 205.32/30.32 thf(decl_255, type, lamp: $o).
% 205.32/30.32 thf(decl_256, type, lam2p: $o).
% 205.32/30.32 thf(decl_257, type, brelnall1: $o).
% 205.32/30.32 thf(decl_258, type, brelnall2: $o).
% 205.32/30.32 thf(decl_259, type, ex1E2: $o).
% 205.32/30.32 thf(decl_260, type, funcGraphProp1: $o).
% 205.32/30.32 thf(decl_261, type, funcGraphProp3: $o).
% 205.32/30.32 thf(decl_262, type, funcGraphProp2: $o).
% 205.32/30.32 thf(decl_263, type, epred1_0: $o).
% 205.32/30.32 thf(decl_264, type, esk1_2: $i > $i > $i).
% 205.32/30.32 thf(decl_265, type, esk2_2: $i > $i > $i).
% 205.32/30.32 thf(decl_266, type, esk3_2: $i > $i > $i).
% 205.32/30.32 thf(decl_267, type, esk4_1: $i > $i).
% 205.32/30.32 thf(decl_268, type, esk5_2: ($i > $i > $o) > $i > $i).
% 205.32/30.32 thf(decl_269, type, esk6_2: ($i > $i > $o) > $i > $i).
% 205.32/30.32 thf(decl_270, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 205.32/30.32 thf(decl_271, type, esk8_1: $i > $i).
% 205.32/30.32 thf(decl_272, type, esk9_1: ($i > $o) > $i).
% 205.32/30.32 thf(decl_273, type, esk10_1: ($i > $o) > $i).
% 205.32/30.32 thf(decl_274, type, esk11_2: $i > $i > $i).
% 205.32/30.32 thf(decl_275, type, esk12_2: $i > $i > $i).
% 205.32/30.32 thf(decl_276, type, esk13_1: $i > $i).
% 205.32/30.32 thf(decl_277, type, esk14_1: $i > $i).
% 205.32/30.32 thf(decl_278, type, esk15_1: $i > $i).
% 205.32/30.32 thf(decl_279, type, esk16_2: $i > $i > $i).
% 205.32/30.32 thf(decl_280, type, esk17_3: $i > $i > $o > $i).
% 205.32/30.32 thf(decl_281, type, esk18_1: ($i > $o) > $i).
% 205.32/30.32 thf(decl_282, type, esk19_1: $i > $i).
% 205.32/30.32 thf(decl_283, type, esk20_2: $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_284, type, esk21_2: $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_285, type, esk22_2: $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_286, type, esk23_2: $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_287, type, esk24_2: $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_288, type, esk25_2: $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_289, type, esk26_2: ($i > $o) > $i > $i).
% 205.32/30.32 thf(decl_290, type, esk27_1: ($i > $o) > $i).
% 205.32/30.32 thf(decl_291, type, esk28_1: ($i > $o) > $i).
% 205.32/30.32 thf(decl_292, type, esk29_2: ($i > $o) > $i > $i).
% 205.32/30.32 thf(decl_293, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 205.32/30.32 thf(decl_294, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 205.32/30.32 thf(decl_295, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 205.32/30.32 thf(decl_296, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 205.32/30.32 thf(decl_297, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 205.32/30.32 thf(decl_298, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 205.32/30.32 thf(decl_299, type, esk36_2: $i > $i > $i).
% 205.32/30.32 thf(decl_300, type, esk37_2: $i > $i > $i).
% 205.32/30.32 thf(decl_301, type, esk38_2: $i > $i > $i).
% 205.32/30.32 thf(decl_302, type, esk39_3: $i > $i > $i > $i).
% 205.32/30.32 thf(decl_303, type, esk40_3: $i > $i > $i > $i).
% 205.32/30.32 thf(decl_304, type, esk41_2: $i > $i > $i).
% 205.32/30.32 thf(decl_305, type, esk42_2: $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_306, type, esk43_2: $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_307, type, esk44_2: $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_308, type, esk45_3: $i > ($i > $o) > $i > $i).
% 205.32/30.32 thf(decl_309, type, esk46_2: $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_310, type, esk47_2: $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_311, type, esk48_3: $i > $i > ($i > $i) > $i).
% 205.32/30.32 thf(decl_312, type, esk49_3: $i > $i > ($i > $i) > $i).
% 205.32/30.32 thf(decl_313, type, esk50_3: $i > $i > ($i > $i) > $i).
% 205.32/30.32 thf(decl_314, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_315, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_316, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_317, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 205.32/30.32 thf(decl_318, type, esk55_0: $i).
% 205.32/30.32 thf(decl_319, type, esk56_0: $i).
% 205.32/30.32 thf(decl_320, type, esk57_0: $i).
% 205.32/30.32 thf(decl_321, type, esk58_0: $i).
% 205.32/30.32 thf(decl_322, type, esk59_0: $i).
% 205.32/30.32 thf(decl_323, type, esk60_0: $i).
% 205.32/30.32 thf(funcextLem, 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)=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X35:$i]:(((func @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X30 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X30)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', funcextLem)).
% 205.32/30.32 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', ex1I2)).
% 205.32/30.32 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', kfstsingleton)).
% 205.32/30.32 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', ksndsingleton)).
% 205.32/30.32 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', emptyE1)).
% 205.32/30.32 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setoftrueEq)).
% 205.32/30.32 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', dpsetconstrI)).
% 205.32/30.32 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', dpsetconstrSub)).
% 205.32/30.32 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setOfPairsIsBReln)).
% 205.32/30.32 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', dpsetconstrERa)).
% 205.32/30.32 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', dpsetconstrEL1)).
% 205.32/30.32 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', dpsetconstrEL2)).
% 205.32/30.32 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', dpsetconstrER)).
% 205.32/30.32 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', funcImageSingleton)).
% 205.32/30.32 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', apProp)).
% 205.32/30.32 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X31 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', lamProp)).
% 205.32/30.32 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X33 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', lamp)).
% 205.32/30.32 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X34 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', lam2p)).
% 205.32/30.32 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', exuE2)).
% 205.32/30.32 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', ex1E2)).
% 205.32/30.32 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', exuI2)).
% 205.32/30.32 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', exuI3)).
% 205.32/30.32 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', exuI1)).
% 205.32/30.32 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', exu__Cong)).
% 205.32/30.32 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', exuE3u)).
% 205.32/30.32 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', dsetconstr__Cong)).
% 205.32/30.32 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', descr__Cong)).
% 205.32/30.32 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', exuEu)).
% 205.32/30.32 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', sepSubset)).
% 205.32/30.32 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', sepInPowerset)).
% 205.32/30.32 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', singletonprop)).
% 205.32/30.32 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', ex1E1)).
% 205.32/30.32 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', ex1I)).
% 205.32/30.32 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', nonemptyI)).
% 205.32/30.32 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setbeta)).
% 205.32/30.32 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', exuE3e)).
% 205.32/30.32 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', exuE1)).
% 205.32/30.32 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', dsetconstrER)).
% 205.32/30.32 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', dsetconstrEL)).
% 205.32/30.32 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', dsetconstrI)).
% 205.32/30.32 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', descrp)).
% 205.32/30.32 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', replAx)).
% 205.32/30.32 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', powersetI)).
% 205.32/30.32 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', singletonsuniq)).
% 205.32/30.32 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setukpairinjL1)).
% 205.32/30.32 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setadjoinIR)).
% 205.32/30.32 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', theprop)).
% 205.32/30.32 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', kfstpairEq)).
% 205.32/30.32 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', cartprodfstin)).
% 205.32/30.32 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setukpairinjL2)).
% 205.32/30.32 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setukpairinjL)).
% 205.32/30.32 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setukpairinjR11)).
% 205.32/30.32 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setukpairinjR12)).
% 205.32/30.32 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setukpairinjR1)).
% 205.32/30.32 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', upairequniteq)).
% 205.32/30.32 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setukpairinjR2)).
% 205.32/30.32 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setukpairinjR)).
% 205.32/30.32 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', ksndpairEq)).
% 205.32/30.32 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', kpairsurjEq)).
% 205.32/30.32 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', powersetE)).
% 205.32/30.32 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', cartprodsndin)).
% 205.32/30.32 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', emptyInPowerset)).
% 205.32/30.32 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', cartprodpairmemEL)).
% 205.32/30.32 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', emptyinPowerset)).
% 205.32/30.32 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', cartprodpairmemER)).
% 205.32/30.32 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', upairsetIR)).
% 205.32/30.32 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', cartprodmempaircEq)).
% 205.32/30.32 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', cartprodfstpairEq)).
% 205.32/30.32 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setadjoinOr)).
% 205.32/30.32 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', cartprodsndpairEq)).
% 205.32/30.32 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setadjoinE)).
% 205.32/30.32 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', cartprodpairsurjEq)).
% 205.32/30.32 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setunionI)).
% 205.32/30.32 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', app)).
% 205.32/30.32 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', infuncsetfunc)).
% 205.32/30.32 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', ap2p)).
% 205.32/30.32 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>(in @ X30 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', funcinfuncset)).
% 205.32/30.32 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', eqinunit)).
% 205.32/30.32 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', notinsingleton)).
% 205.32/30.32 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', uniqinunit)).
% 205.32/30.32 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', nonemptyImpWitness)).
% 205.32/30.32 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', brelnall1)).
% 205.32/30.32 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', brelnall2)).
% 205.32/30.32 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', subPowSU)).
% 205.32/30.32 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setunionE)).
% 205.32/30.32 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', funcGraphProp1)).
% 205.32/30.32 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setadjoinIL)).
% 205.32/30.32 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', funcGraphProp3)).
% 205.32/30.32 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', singletonsswitch)).
% 205.32/30.32 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X30)=>((ap @ X4 @ X5 @ X30 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', funcGraphProp2)).
% 205.32/30.32 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', quantDeMorgan2)).
% 205.32/30.32 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', quantDeMorgan1)).
% 205.32/30.32 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', vacuousDall)).
% 205.32/30.32 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', notequalI2)).
% 205.32/30.32 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', notequalI1)).
% 205.32/30.32 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', notsubsetI)).
% 205.32/30.32 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', subsetE2)).
% 205.32/30.32 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', subsetE)).
% 205.32/30.32 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setadjoinSub)).
% 205.32/30.32 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', upairsetIL)).
% 205.32/30.32 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', upairsetE)).
% 205.32/30.32 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', quantDeMorgan3)).
% 205.32/30.32 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', notdallE)).
% 205.32/30.32 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', notdexE)).
% 205.32/30.32 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', prop2setI)).
% 205.32/30.32 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', emptyinunitempty)).
% 205.32/30.32 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', quantDeMorgan4)).
% 205.32/30.32 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', inCongP)).
% 205.32/30.32 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setunion__Cong)).
% 205.32/30.32 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', powerset__Cong)).
% 205.32/30.32 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setadjoin__Cong)).
% 205.32/30.32 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', emptyset__Cong)).
% 205.32/30.32 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', in__Cong)).
% 205.32/30.32 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', omega__Cong)).
% 205.32/30.32 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', subsetI2)).
% 205.32/30.32 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', eqimpsubset1)).
% 205.32/30.32 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', eqimpsubset2)).
% 205.32/30.32 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', subsetI1)).
% 205.32/30.32 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', emptysetsubset)).
% 205.32/30.32 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', subsetTrans)).
% 205.32/30.32 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', subsetRefl)).
% 205.32/30.32 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', inPowerset)).
% 205.32/30.32 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', powersetE1)).
% 205.32/30.32 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', powersetI1)).
% 205.32/30.32 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', subsetemptysetimpeq)).
% 205.32/30.32 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setextsub)).
% 205.32/30.32 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', subset2powerset)).
% 205.32/30.32 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setadjoinSub2)).
% 205.32/30.32 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', powersetsubset)).
% 205.32/30.32 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binunionE)).
% 205.32/30.32 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binunionEcases)).
% 205.32/30.32 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binunionIR)).
% 205.32/30.32 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', upairset2IR)).
% 205.32/30.32 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binunionIL)).
% 205.32/30.32 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binunionLsub)).
% 205.32/30.32 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binintersectSubset3)).
% 205.32/30.32 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binintersectSubset2)).
% 205.32/30.32 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binintersectLsub)).
% 205.32/30.32 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binintersectEL)).
% 205.32/30.32 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binintersectSubset5)).
% 205.32/30.32 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binintersectI)).
% 205.32/30.32 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binunionRsub)).
% 205.32/30.32 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binintersectER)).
% 205.32/30.32 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setminusEL)).
% 205.32/30.32 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setminusI)).
% 205.32/30.32 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', bs114d)).
% 205.32/30.32 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binintersectSubset1)).
% 205.32/30.32 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binintersectSubset4)).
% 205.32/30.32 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', binintersectRsub)).
% 205.32/30.32 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', disjointsetsI1)).
% 205.32/30.32 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setminusER)).
% 205.32/30.32 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setminusSubset1)).
% 205.32/30.32 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setminusLsub)).
% 205.32/30.32 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setminusIRneg)).
% 205.32/30.32 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setminusILneg)).
% 205.32/30.32 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setminusELneg)).
% 205.32/30.32 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setminusERneg)).
% 205.32/30.32 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setminusSubset2)).
% 205.32/30.32 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', symdiffE)).
% 205.32/30.32 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setukpairIR)).
% 205.32/30.32 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setukpairIL)).
% 205.32/30.32 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', secondinupair)).
% 205.32/30.32 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', symdiffIneg2)).
% 205.32/30.32 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', symdiffIneg1)).
% 205.32/30.32 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', symdiffI2)).
% 205.32/30.32 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', symdiffI1)).
% 205.32/30.32 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', kpairiskpair)).
% 205.32/30.32 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', upairinpowunion)).
% 205.32/30.32 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', upairsubunion)).
% 205.32/30.32 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', upairset2E)).
% 205.32/30.32 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', singletoninpowunion)).
% 205.32/30.32 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', singletoninpowerset)).
% 205.32/30.32 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', singletonsubset)).
% 205.32/30.32 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', kpairp)).
% 205.32/30.32 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', ubforcartprodlem1)).
% 205.32/30.32 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setunionsingleton1)).
% 205.32/30.32 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setunionE2)).
% 205.32/30.32 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', cartprodmempair)).
% 205.32/30.32 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', cartprodmempair1)).
% 205.32/30.32 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', cartprodpairin)).
% 205.32/30.32 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', ubforcartprodlem3)).
% 205.32/30.32 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setunionsingleton)).
% 205.32/30.32 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', ubforcartprodlem2)).
% 205.32/30.32 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setunionsingleton2)).
% 205.32/30.32 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', nonemptyI1)).
% 205.32/30.32 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', nonemptyE1)).
% 205.32/30.32 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', noeltsimpempty)).
% 205.32/30.32 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', emptyI)).
% 205.32/30.32 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setext)).
% 205.32/30.32 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', notinemptyset)).
% 205.32/30.32 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', emptysetimpfalse)).
% 205.32/30.32 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', emptysetE)).
% 205.32/30.32 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', prop2setE)).
% 205.32/30.32 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', wellorderingAx)).
% 205.32/30.32 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', foundationAx)).
% 205.32/30.32 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', omegaIndAx)).
% 205.32/30.32 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', omegaSAx)).
% 205.32/30.32 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', omega0Ax)).
% 205.32/30.32 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setunionAx)).
% 205.32/30.32 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', powersetAx)).
% 205.32/30.32 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setadjoinAx)).
% 205.32/30.32 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', emptysetAx)).
% 205.32/30.32 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Da7Uz4eOXQ/E---3.1_1345788.p', setextAx)).
% 205.32/30.32 thf(c_0_203, 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)=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X35:$i]:(((func @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X30 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X30))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[funcextLem])).
% 205.32/30.32 thf(c_0_204, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 205.32/30.32 thf(c_0_205, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 205.32/30.32 thf(c_0_206, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 205.32/30.32 thf(c_0_207, plain, ((emptyE1)<=>![X4:$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])).
% 205.32/30.32 thf(c_0_208, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 205.32/30.32 thf(c_0_209, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 205.32/30.32 thf(c_0_210, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 205.32/30.32 thf(c_0_211, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 205.32/30.32 thf(c_0_212, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 205.32/30.32 thf(c_0_213, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 205.32/30.32 thf(c_0_214, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 205.32/30.32 thf(c_0_215, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 205.32/30.32 thf(c_0_216, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 205.32/30.32 thf(c_0_217, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 205.32/30.32 thf(c_0_218, plain, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 205.32/30.32 thf(c_0_219, plain, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X33 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 205.32/30.32 thf(c_0_220, plain, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X34 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 205.32/30.32 thf(c_0_221, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 205.32/30.32 thf(c_0_222, 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])).
% 205.32/30.32 thf(c_0_223, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 205.32/30.32 thf(c_0_224, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 205.32/30.32 thf(c_0_225, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 205.32/30.32 thf(c_0_226, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 205.32/30.32 thf(c_0_227, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 205.32/30.32 thf(c_0_228, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 205.32/30.32 thf(c_0_229, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 205.32/30.32 thf(c_0_230, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 205.32/30.32 thf(c_0_231, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 205.32/30.32 thf(c_0_232, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 205.32/30.32 thf(c_0_233, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 205.32/30.32 thf(c_0_234, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 205.32/30.32 thf(c_0_235, plain, ((ex1I)<=>![X4:$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])).
% 205.32/30.32 thf(c_0_236, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 205.32/30.32 thf(c_0_237, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 205.32/30.32 thf(c_0_238, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 205.32/30.32 thf(c_0_239, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 205.32/30.32 thf(c_0_240, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 205.32/30.32 thf(c_0_241, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 205.32/30.32 thf(c_0_242, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 205.32/30.32 thf(c_0_243, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 205.32/30.32 thf(c_0_244, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 205.32/30.32 thf(c_0_245, plain, ((epred1_0)<=>![X663:$i]:(?[X664:$i]:((((![X665:$i]:(((in @ X665 @ X664)=>![X666:$i]:(((in @ X666 @ X665)=>(in @ X666 @ X663)))))&![X667:$i, X668:$i]:((((in @ X667 @ X663)&(in @ X668 @ X663))=>(![X669:$i]:(((in @ X669 @ X664)=>((in @ X667 @ X669)<=>(in @ X668 @ X669))))=>((X667)=(X668))))))&![X670:$i, X671:$i]:((((in @ X670 @ X664)&(in @ X671 @ X664))=>(![X672:$i]:(((in @ X672 @ X670)=>(in @ X672 @ X671)))|![X673:$i]:(((in @ X673 @ X671)=>(in @ X673 @ X670)))))))&![X674:$i]:(((![X675:$i]:(((in @ X675 @ X674)=>(in @ X675 @ X663)))&?[X676:$i]:((in @ X676 @ X674)))=>?[X677:$i, X678:$i]:(((((in @ X677 @ X664)&(in @ X678 @ X674))&~(?[X679:$i]:(((in @ X679 @ X677)&(in @ X679 @ X674)))))&![X680:$i]:(((in @ X680 @ X664)=>(![X681:$i]:(((in @ X681 @ X680)=>(in @ X681 @ X677)))|(in @ X678 @ X680)))))))))))), introduced(definition)).
% 205.32/30.32 thf(c_0_246, negated_conjecture, ~((![X636:$i, X637:$i]:((![X638:$i]:(((in @ X638 @ X636)<=>(in @ X638 @ X637)))=>((X636)=(X637))))=>(![X639:$i]:(~(in @ X639 @ emptyset))=>(![X640:$i, X641:$i, X642:$i]:(((in @ X642 @ (setadjoin @ X640 @ X641))<=>(((X642)=(X640))|(in @ X642 @ X641))))=>(![X643:$i, X644:$i]:(((in @ X644 @ (powerset @ X643))<=>![X645:$i]:(((in @ X645 @ X644)=>(in @ X645 @ X643)))))=>(![X646:$i, X647:$i]:(((in @ X647 @ (setunion @ X646))<=>?[X648:$i]:(((in @ X647 @ X648)&(in @ X648 @ X646)))))=>((in @ emptyset @ omega)=>(![X649:$i]:(((in @ X649 @ omega)=>(in @ (setadjoin @ X649 @ X649) @ omega)))=>(![X650:$i]:((((in @ emptyset @ X650)&![X651:$i]:((((in @ X651 @ omega)&(in @ X651 @ X650))=>(in @ (setadjoin @ X651 @ X651) @ X650))))=>![X652:$i]:(((in @ X652 @ omega)=>(in @ X652 @ X650)))))=>(![X653:$i > $i > $o, X654:$i]:((![X655:$i]:(((in @ X655 @ X654)=>(exu @ (X653 @ X655))))=>?[X656:$i]:(![X657:$i]:(((in @ X657 @ X656)<=>?[X658:$i]:(((in @ X658 @ X654)&(X653 @ X658 @ X657))))))))=>(![X659:$i]:((?[X660:$i]:((in @ X660 @ X659))=>?[X661:$i]:(((in @ X661 @ X659)&~(?[X662:$i]:(((in @ X662 @ X661)&(in @ X662 @ X659))))))))=>((epred1_0)=>(![X682:$i > $o]:(((exu @ X682)=>(X682 @ (descr @ (^[Z0:$i]:(X682 @ Z0))))))=>(![X683:$i, X684:$i > $o, X685:$i]:(((in @ X685 @ X683)=>((X684 @ X685)=>(in @ X685 @ (dsetconstr @ X683 @ X684)))))=>(![X686:$i, X687:$i > $o, X688:$i]:(((in @ X688 @ (dsetconstr @ X686 @ X687))=>(in @ X688 @ X686)))=>(![X689:$i, X690:$i > $o, X691:$i]:(((in @ X691 @ (dsetconstr @ X689 @ X690))=>(X690 @ X691)))=>(![X692:$i > $o]:(((exu @ X692)=>?[X693:$i]:(((X692 @ X693)&![X694:$i]:(((X692 @ X694)=>((X693)=(X694))))))))=>(![X695:$o, X696:$i]:(((in @ X696 @ (prop2set @ ((X695))))=>(X695)))=>(![X697:$i]:(((in @ X697 @ emptyset)=>![X698:$o]:((X698))))=>(![X699:$i]:(((in @ X699 @ emptyset)=>~($true)))=>(![X700:$i]:(~(in @ X700 @ emptyset))=>(![X701:$i > $o]:(((exu @ X701)=>?[X702:$i]:((X701 @ X702))))=>(![X703:$i, X704:$i]:((![X705:$i]:(((in @ X705 @ X703)=>(in @ X705 @ X704)))=>(![X706:$i]:(((in @ X706 @ X704)=>(in @ X706 @ X703)))=>((X703)=(X704)))))=>(![X707:$i]:((![X708:$i]:(~(in @ X708 @ X707))=>((X707)=(emptyset))))=>(![X709:$i]:((![X710:$i]:(~(in @ X710 @ X709))=>((X709)=(emptyset))))=>(![X711:$i, X712:$i > $o, X713:$i]:(((in @ X713 @ X711)=>((in @ X713 @ (dsetconstr @ X711 @ X712))<=>(X712 @ X713))))=>(![X714:$i]:(((nonempty @ X714)=>?[X715:$i]:((in @ X715 @ X714))))=>(![X716:$i, X717:$i > $o, X718:$i]:(((in @ X718 @ X716)=>((X717 @ X718)=>(nonempty @ (dsetconstr @ X716 @ X717)))))=>(![X719:$i]:((?[X720:$i]:((in @ X720 @ X719))=>(nonempty @ X719)))=>(![X721:$i, X722:$i]:((in @ X721 @ (setadjoin @ X721 @ X722)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X723:$i, X724:$i, X725:$i]:(((in @ X725 @ X724)=>(in @ X725 @ (setadjoin @ X723 @ X724))))=>(![X726:$i, X727:$i, X728:$i]:(((in @ X728 @ (setadjoin @ X726 @ X727))=>![X729:$o]:(((((X728)=(X726))=>(X729))=>(((in @ X728 @ X727)=>(X729))=>(X729))))))=>(![X730:$i, X731:$i, X732:$i]:(((in @ X732 @ (setadjoin @ X730 @ X731))=>(((X732)=(X730))|(in @ X732 @ X731))))=>(![X733:$i]:(((dsetconstr @ X733 @ (^[Z0:$i]:($true)))=(X733)))=>(![X734:$i, X735:$i]:((![X736:$i]:(((in @ X736 @ X735)=>(in @ X736 @ X734)))=>(in @ X735 @ (powerset @ X734))))=>(![X737:$i]:((in @ emptyset @ (powerset @ X737)))=>(![X738:$i]:((in @ emptyset @ (powerset @ X738)))=>(![X739:$i, X740:$i, X741:$i]:(((in @ X740 @ (powerset @ X739))=>((in @ X741 @ X740)=>(in @ X741 @ X739))))=>(![X742:$i, X743:$i, X744:$i]:(((in @ X743 @ X744)=>((in @ X744 @ X742)=>(in @ X743 @ (setunion @ X742)))))=>(![X745:$i, X746:$i]:(((in @ X746 @ (setunion @ X745))=>![X747:$o]:((![X748:$i]:(((in @ X746 @ X748)=>((in @ X748 @ X745)=>(X747))))=>(X747)))))=>(![X749:$i, X750:$i]:(((in @ X750 @ X749)=>(in @ X750 @ (powerset @ (setunion @ X749)))))=>(![X751:$i > $o]:(((exu @ X751)=>?[X752:$i]:(![X753:$i]:(((X751 @ X753)<=>((X753)=(X752)))))))=>(![X754:$i]:(((nonempty @ X754)=>?[X755:$i]:(((in @ X755 @ X754)&$true))))=>(![X756:$i, X757:$i]:(((in @ X756 @ (setadjoin @ X757 @ emptyset))=>((X756)=(X757))))=>(![X758:$i, X759:$i]:((((X758)!=(X759))=>~(in @ X759 @ (setadjoin @ X758 @ emptyset))))=>(![X760:$i, X761:$i]:((((X760)=(X761))=>(in @ X760 @ (setadjoin @ X761 @ emptyset))))=>(![X762:$i, X763:$i]:(((in @ X762 @ (setadjoin @ X763 @ emptyset))=>(in @ X763 @ (setadjoin @ X762 @ emptyset))))=>(![X764:$i, X765:$i, X766:$i]:(((in @ X766 @ (setadjoin @ X764 @ (setadjoin @ X765 @ emptyset)))=>(((X766)=(X764))|((X766)=(X765)))))=>(![X767:$i, X768:$i]:((in @ X767 @ (setadjoin @ X767 @ (setadjoin @ X768 @ emptyset))))=>(![X769:$i, X770:$i]:((in @ X770 @ (setadjoin @ X769 @ (setadjoin @ X770 @ emptyset))))=>(![X771:$i, X772:$i > $o]:((?[X773:$i]:(((in @ X773 @ X771)&(X772 @ X773)))=>(((dsetconstr @ X771 @ X772)=(emptyset))=>~($true))))=>(![X774:$i > $o, X775:$i]:(((in @ X775 @ emptyset)=>(X774 @ X775)))=>(![X776:$i, X777:$i > $o]:((~(![X778:$i]:(((in @ X778 @ X776)=>(X777 @ X778))))=>?[X779:$i]:(((in @ X779 @ X776)&~((X777 @ X779))))))=>(![X780:$i, X781:$i > $o]:((![X782:$i]:(((in @ X782 @ X780)=>~((X781 @ X782))))=>~(?[X783:$i]:(((in @ X783 @ X780)&(X781 @ X783))))))=>(![X784:$i, X785:$i > $o]:((~(?[X786:$i]:(((in @ X786 @ X784)&(X785 @ X786))))=>![X787:$i]:(((in @ X787 @ X784)=>~((X785 @ X787))))))=>(![X788:$i, X789:$i > $o]:((?[X790:$i]:(((in @ X790 @ X788)&~((X789 @ X790))))=>~(![X791:$i]:(((in @ X791 @ X788)=>(X789 @ X791))))))=>(![X792:$o]:(((X792)=>(in @ emptyset @ (prop2set @ ((X792))))))=>((prop2set2propI)=>(![X793:$i, X794:$i > $o]:((~(?[X795:$i]:(((in @ X795 @ X793)&(X794 @ X795))))=>![X796:$i]:(((in @ X796 @ X793)=>~((X794 @ X796))))))=>(![X797:$i, X798:$i > $o]:((~(![X799:$i]:(((in @ X799 @ X797)=>(X798 @ X799))))=>?[X800:$i]:(((in @ X800 @ X797)&~((X798 @ X800))))))=>(![X801:$i > $o]:((?[X802:$i]:(((X801 @ X802)&![X803:$i]:(((X801 @ X803)=>((X802)=(X803))))))=>(exu @ X801)))=>(![X804:$i > $o]:((?[X805:$i]:((X804 @ X805))=>(![X806:$i, X807:$i]:(((X804 @ X806)=>((X804 @ X807)=>((X806)=(X807)))))=>(exu @ X804))))=>(![X808:$i > $o]:((?[X809:$i]:(![X810:$i]:(((X808 @ X810)<=>((X810)=(X809)))))=>(exu @ X808)))=>(![X811:$i, X812:$i]:((((X811)=(X812))=>![X813:$i, X814:$i]:((((X813)=(X814))=>((in @ X813 @ X811)=>(in @ X814 @ X812))))))=>(![X815:$i, X816:$i]:((((X815)=(X816))=>![X817:$i, X818:$i]:((((X817)=(X818))=>((in @ X817 @ X815)<=>(in @ X818 @ X816))))))=>(![X819:$i > $o]:(((exu @ X819)=>![X820:$i, X821:$i]:(((X819 @ X820)=>((X819 @ X821)=>((X820)=(X821)))))))=>(![X822:$i > $o, X823:$i > $o]:((![X824:$i, X825:$i]:((((X824)=(X825))=>((X822 @ X824)<=>(X823 @ X825))))=>((exu @ X822)<=>(exu @ X823))))=>(((emptyset)=(emptyset))=>(![X826:$i, X827:$i]:((((X826)=(X827))=>![X828:$i, X829:$i]:((((X828)=(X829))=>((setadjoin @ X826 @ X828)=(setadjoin @ X827 @ X829))))))=>(![X830:$i, X831:$i]:((((X830)=(X831))=>((powerset @ X830)=(powerset @ X831))))=>(![X832:$i, X833:$i]:((((X832)=(X833))=>((setunion @ X832)=(setunion @ X833))))=>(((omega)=(omega))=>(![X834:$i > $o]:(((exu @ X834)=>![X835:$i, X836:$i]:(((X834 @ X835)=>((X834 @ X836)=>((X835)=(X836)))))))=>(![X837:$i > $o, X838:$i > $o]:((![X839:$i, X840:$i]:((((X839)=(X840))=>((X837 @ X839)<=>(X838 @ X840))))=>((exu @ X837)=>((exu @ X838)=>((descr @ X837)=(descr @ X838))))))=>(![X841:$i, X842:$i]:((((X841)=(X842))=>![X843:$i > $o, X844:$i > $o]:((![X845:$i]:(((in @ X845 @ X841)=>![X846:$i]:(((in @ X846 @ X842)=>(((X845)=(X846))=>((X843 @ X845)<=>(X844 @ X846)))))))=>((dsetconstr @ X841 @ X843)=(dsetconstr @ X842 @ X844))))))=>(![X847:$i, X848:$i]:((![X849:$i]:(((in @ X849 @ X847)=>(in @ X849 @ X848)))=>(subset @ X847 @ X848)))=>(![X850:$i, X851:$i]:((((X850)=(X851))=>(subset @ X851 @ X850)))=>(![X852:$i, X853:$i]:((((X852)=(X853))=>(subset @ X852 @ X853)))=>(![X854:$i, X855:$i]:((![X856:$i]:(((in @ X856 @ X854)=>(in @ X856 @ X855)))=>(subset @ X854 @ X855)))=>(![X857:$i]:((subset @ emptyset @ X857))=>(![X858:$i, X859:$i, X860:$i]:(((subset @ X858 @ X859)=>((in @ X860 @ X858)=>(in @ X860 @ X859))))=>(![X861:$i, X862:$i, X863:$i]:(((subset @ X861 @ X862)=>(~(in @ X863 @ X862)=>~(in @ X863 @ X861))))=>(![X864:$i, X865:$i, X866:$i]:(((in @ X866 @ X864)=>(~(in @ X866 @ X865)=>~(subset @ X864 @ X865))))=>(![X867:$i, X868:$i]:((~(subset @ X867 @ X868)=>((X867)!=(X868))))=>(![X869:$i, X870:$i, X871:$i]:(((in @ X871 @ X869)=>(~(in @ X871 @ X870)=>((X869)!=(X870)))))=>(![X872:$i]:((subset @ X872 @ X872))=>(![X873:$i, X874:$i, X875:$i]:(((subset @ X873 @ X874)=>((subset @ X874 @ X875)=>(subset @ X873 @ X875))))=>(![X876:$i, X877:$i]:((subset @ X877 @ (setadjoin @ X876 @ X877)))=>(![X878:$i, X879:$i, X880:$i]:(((subset @ X878 @ X880)=>(subset @ X878 @ (setadjoin @ X879 @ X880))))=>(![X881:$i, X882:$i]:(((subset @ X881 @ X882)=>(in @ X881 @ (powerset @ X882))))=>(![X883:$i, X884:$i]:(((subset @ X883 @ X884)=>((subset @ X884 @ X883)=>((X883)=(X884)))))=>(![X885:$i]:(((subset @ X885 @ emptyset)=>((X885)=(emptyset))))=>(![X886:$i, X887:$i]:(((subset @ X887 @ X886)=>(in @ X887 @ (powerset @ X886))))=>(![X888:$i, X889:$i]:(((in @ X889 @ (powerset @ X888))=>(subset @ X889 @ X888)))=>(![X890:$i]:((in @ X890 @ (powerset @ X890)))=>(![X891:$i, X892:$i]:(((subset @ X891 @ X892)=>(subset @ (powerset @ X891) @ (powerset @ X892))))=>(![X893:$i, X894:$i > $o]:((in @ (dsetconstr @ X893 @ X894) @ (powerset @ X893)))=>(![X895:$i, X896:$i > $o]:((subset @ (dsetconstr @ X895 @ X896) @ X895))=>(![X897:$i, X898:$i, X899:$i]:(((in @ X899 @ X897)=>(in @ X899 @ (binunion @ X897 @ X898))))=>(![X900:$i, X901:$i]:((in @ X901 @ (setadjoin @ X900 @ (setadjoin @ X901 @ emptyset))))=>(![X902:$i, X903:$i, X904:$i]:(((in @ X904 @ X903)=>(in @ X904 @ (binunion @ X902 @ X903))))=>(![X905:$i, X906:$i, X907:$i, X908:$o]:(((in @ X907 @ (binunion @ X905 @ X906))=>(((in @ X907 @ X905)=>(X908))=>(((in @ X907 @ X906)=>(X908))=>(X908)))))=>(![X909:$i, X910:$i, X911:$i]:(((in @ X911 @ (binunion @ X909 @ X910))=>((in @ X911 @ X909)|(in @ X911 @ X910))))=>(![X912:$i, X913:$i]:((subset @ X912 @ (binunion @ X912 @ X913)))=>(![X914:$i, X915:$i]:((subset @ X915 @ (binunion @ X914 @ X915)))=>(![X916:$i, X917:$i, X918:$i]:(((in @ X918 @ X916)=>((in @ X918 @ X917)=>(in @ X918 @ (binintersect @ X916 @ X917)))))=>(![X919:$i, X920:$i, X921:$i]:(((subset @ X921 @ X919)=>((subset @ X921 @ X920)=>(subset @ X921 @ (binintersect @ X919 @ X920)))))=>(![X922:$i, X923:$i, X924:$i]:(((in @ X924 @ (binintersect @ X922 @ X923))=>(in @ X924 @ X922)))=>(![X925:$i, X926:$i]:((subset @ (binintersect @ X925 @ X926) @ X925))=>(![X927:$i, X928:$i]:(((subset @ X927 @ X928)=>((binintersect @ X927 @ X928)=(X927))))=>(![X929:$i, X930:$i]:((((binintersect @ X929 @ X930)=(X930))=>(subset @ X930 @ X929)))=>(![X931:$i, X932:$i, X933:$i]:(((in @ X933 @ (binintersect @ X931 @ X932))=>(in @ X933 @ X932)))=>(![X934:$i, X935:$i]:((~(?[X936:$i]:(((in @ X936 @ X934)&(in @ X936 @ X935))))=>((binintersect @ X934 @ X935)=(emptyset))))=>(![X937:$i, X938:$i]:((subset @ (binintersect @ X937 @ X938) @ X938))=>(![X939:$i, X940:$i]:(((subset @ X940 @ X939)=>((binintersect @ X939 @ X940)=(X940))))=>(![X941:$i, X942:$i]:((((binintersect @ X941 @ X942)=(X941))=>(subset @ X941 @ X942)))=>(![X943:$i, X944:$i, X945:$i]:(((binintersect @ X943 @ (binunion @ X944 @ X945))=(binunion @ (binintersect @ X943 @ X944) @ (binintersect @ X943 @ X945))))=>(![X946:$i, X947:$i, X948:$i]:(((in @ X948 @ X946)=>(~(in @ X948 @ X947)=>(in @ X948 @ (setminus @ X946 @ X947)))))=>(![X949:$i, X950:$i, X951:$i]:(((in @ X951 @ (setminus @ X949 @ X950))=>(in @ X951 @ X949)))=>(![X952:$i, X953:$i, X954:$i]:(((in @ X954 @ (setminus @ X952 @ X953))=>~(in @ X954 @ X953)))=>(![X955:$i, X956:$i]:(((subset @ X955 @ X956)=>((setminus @ X955 @ X956)=(emptyset))))=>(![X957:$i, X958:$i, X959:$i]:((~(in @ X959 @ (setminus @ X957 @ X958))=>((in @ X959 @ X957)=>(in @ X959 @ X958))))=>(![X960:$i, X961:$i, X962:$i]:((~(in @ X962 @ (setminus @ X960 @ X961))=>(~(in @ X962 @ X961)=>~(in @ X962 @ X960))))=>(![X963:$i, X964:$i, X965:$i]:((~(in @ X965 @ X963)=>~(in @ X965 @ (setminus @ X963 @ X964))))=>(![X966:$i, X967:$i, X968:$i]:(((in @ X968 @ X967)=>~(in @ X968 @ (setminus @ X966 @ X967))))=>(![X969:$i, X970:$i]:((subset @ (setminus @ X969 @ X970) @ X969))=>(![X971:$i, X972:$i]:((((setminus @ X971 @ X972)=(emptyset))=>(subset @ X971 @ X972)))=>(![X973:$i, X974:$i, X975:$i]:(((in @ X975 @ (symdiff @ X973 @ X974))=>![X976:$o]:((((in @ X975 @ X973)=>(~(in @ X975 @ X974)=>(X976)))=>((~(in @ X975 @ X973)=>((in @ X975 @ X974)=>(X976)))=>(X976))))))=>(![X977:$i, X978:$i, X979:$i]:(((in @ X979 @ X977)=>(~(in @ X979 @ X978)=>(in @ X979 @ (symdiff @ X977 @ X978)))))=>(![X980:$i, X981:$i, X982:$i]:((~(in @ X982 @ X980)=>((in @ X982 @ X981)=>(in @ X982 @ (symdiff @ X980 @ X981)))))=>(![X983:$i, X984:$i, X985:$i]:(((in @ X985 @ X983)=>((in @ X985 @ X984)=>~(in @ X985 @ (symdiff @ X983 @ X984)))))=>(![X986:$i, X987:$i, X988:$i]:((~(in @ X988 @ 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powersetI]), singletonsuniq]), c_0_204]), setukpairinjL1]), c_0_205]), setadjoinIR]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_206]), ksndpairEq]), kpairsurjEq]), powersetE]), cartprodsndin]), emptyInPowerset]), cartprodpairmemEL]), emptyinPowerset]), cartprodpairmemER]), c_0_207]), upairsetIR]), cartprodmempaircEq]), c_0_208]), cartprodfstpairEq]), setadjoinOr]), cartprodsndpairEq]), setadjoinE]), cartprodpairsurjEq]), setunionI]), c_0_209]), c_0_210]), c_0_211]), c_0_212]), c_0_213]), c_0_214]), c_0_215]), c_0_216]), c_0_217]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), eqinunit]), c_0_218]), notinsingleton]), c_0_219]), uniqinunit]), c_0_220]), nonemptyImpWitness]), brelnall1]), c_0_221]), brelnall2]), subPowSU]), c_0_222]), setunionE]), funcGraphProp1]), setadjoinIL]), funcGraphProp3]), singletonsswitch]), funcGraphProp2]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), setadjoinSub]), upairsetIL]), upairsetE]), quantDeMorgan3]), c_0_223]), c_0_224]), c_0_225]), notdallE]), notdexE]), prop2setI]), emptyinunitempty]), quantDeMorgan4]), inCongP]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_226]), c_0_227]), in__Cong]), omega__Cong]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_228]), c_0_229]), c_0_230]), emptysetsubset]), subsetTrans]), subsetRefl]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), powersetsubset]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_231]), c_0_232]), binunionLsub]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), binintersectER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), setminusER]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), symdiffE]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), kpairiskpair]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), ubforcartprodlem1]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), setunionsingleton]), c_0_233]), c_0_234]), c_0_235]), ubforcartprodlem2]), setunionsingleton2]), nonemptyI1]), c_0_236]), nonemptyE1]), c_0_237]), noeltsimpempty]), emptyI]), setext]), c_0_238]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_239]), c_0_240]), c_0_241]), c_0_242]), c_0_243]), wellorderingAx]), foundationAx]), c_0_244]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_245])).
% 205.32/30.32 thf(c_0_247, negated_conjecture, ![X1229:$i, X1230:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1242:$i, X1243:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1251:$i, X1252:$i > $i > $o, X1253:$i, X1256:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1263:$i, X1264:$i > $o, X1265:$i, X1266:$i > $o, X1267:$i, X1268:$i, X1269:$i > $o, X1270:$i, X1271:$i, X1272:$i > $o, X1273:$i, X1274:$i > $o, X1276:$i, X1277:$o, X1278:$i, X1279:$i, X1280:$o, X1281:$i, X1282:$i, X1283:$i > $o, X1285:$i, X1286:$i, X1289:$i, X1291:$i, X1293:$i, X1294:$i > $o, X1295:$i, X1296:$i, X1298:$i, X1299:$i > $o, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$o, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$o, X1331:$i, X1332:$i, X1333:$i > $o, X1335:$i, X1336:$i, X1337:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i > $o, X1356:$i, X1357:$i > $o, X1358:$i, X1359:$i, X1360:$i > $o, X1361:$i, X1363:$i, X1364:$i > $o, X1366:$i, X1367:$i, X1368:$i > $o, X1370:$i, X1371:$i, X1372:$i > $o, X1373:$i, X1375:$o, X1376:$i, X1377:$i > $o, X1379:$i, X1380:$i, X1381:$i > $o, X1382:$i, X1384:$i > $o, X1385:$i, X1387:$i > $o, X1388:$i, X1391:$i > $o, X1392:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i > $o, X1403:$i, X1404:$i, X1405:$i > $o, X1406:$i > $o, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i > $o, X1418:$i, X1419:$i, X1420:$i > $o, X1421:$i > $o, X1424:$i, X1425:$i, X1426:$i > $o, X1427:$i > $o, X1430:$i, X1431:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i > $o, X1478:$i, X1479:$i > $o, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$o, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$o, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i > $o, X1634:$i, X1635:$i, X1636:$i > $o, X1638:$i, X1639:$i > $o, X1640:$i, X1642:$i, X1643:$i > $o, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i > $i > $o, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i > $i > $o, X1724:$i, X1725:$i, X1726:$i > $i > $o, X1727:$i, X1728:$i, X1729:$i > $i > $o, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i > $i > $o, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i > $i > $o, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i > $i > $o, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i > $i, X1773:$i, X1774:$i, X1775:$i > $i, X1777:$i, X1778:$i, X1779:$i > $i, X1781:$i, X1782:$i, X1783:$i, X1784:$i > $o, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i > $o, X1794:$i, X1795:$i, X1796:$i > $o, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1816:$i]:((((~(in @ (esk1_2 @ X1229 @ X1230) @ X1229)|~(in @ (esk1_2 @ X1229 @ X1230) @ X1230)|((X1229)=(X1230)))&((in @ (esk1_2 @ X1229 @ X1230) @ X1229)|(in @ (esk1_2 @ X1229 @ X1230) @ X1230)|((X1229)=(X1230))))&(~(in @ X1232 @ emptyset)&(((~(in @ X1235 @ (setadjoin @ X1233 @ X1234))|(((X1235)=(X1233))|(in @ X1235 @ X1234)))&((((X1235)!=(X1233))|(in @ X1235 @ (setadjoin @ X1233 @ X1234)))&(~(in @ X1235 @ X1234)|(in @ X1235 @ (setadjoin @ X1233 @ X1234)))))&(((~(in @ X1237 @ (powerset @ X1236))|(~(in @ X1238 @ X1237)|(in @ X1238 @ X1236)))&(((in @ (esk2_2 @ X1239 @ X1240) @ X1240)|(in @ X1240 @ (powerset @ X1239)))&(~(in @ (esk2_2 @ X1239 @ X1240) @ X1239)|(in @ X1240 @ (powerset @ X1239)))))&(((((in @ X1243 @ (esk3_2 @ X1242 @ X1243))|~(in @ X1243 @ (setunion @ X1242)))&((in @ (esk3_2 @ X1242 @ X1243) @ X1242)|~(in @ X1243 @ (setunion @ X1242))))&(~(in @ X1246 @ X1247)|~(in @ X1247 @ X1245)|(in @ X1246 @ (setunion @ X1245))))&((in @ emptyset @ omega)&((~(in @ X1248 @ omega)|(in @ (setadjoin @ X1248 @ X1248) @ omega))&(((((in @ (esk4_1 @ X1249) @ omega)|~(in @ emptyset @ X1249)|(~(in @ X1251 @ omega)|(in @ X1251 @ X1249)))&((in @ (esk4_1 @ X1249) @ X1249)|~(in @ emptyset @ X1249)|(~(in @ X1251 @ omega)|(in @ X1251 @ X1249))))&(~(in @ (setadjoin @ (esk4_1 @ X1249) @ (esk4_1 @ X1249)) @ X1249)|~(in @ emptyset @ X1249)|(~(in @ X1251 @ omega)|(in @ X1251 @ X1249))))&((((((in @ (esk7_3 @ X1252 @ X1253 @ X1256) @ X1253)|~(in @ X1256 @ (esk6_2 @ X1252 @ X1253))|(in @ (esk5_2 @ X1252 @ X1253) @ X1253))&((X1252 @ (esk7_3 @ X1252 @ X1253 @ X1256) @ X1256)|~(in @ X1256 @ (esk6_2 @ X1252 @ X1253))|(in @ (esk5_2 @ X1252 @ X1253) @ X1253)))&(~(in @ X1259 @ X1253)|~(X1252 @ X1259 @ X1258)|(in @ X1258 @ (esk6_2 @ X1252 @ X1253))|(in @ (esk5_2 @ X1252 @ X1253) @ X1253)))&((((in @ (esk7_3 @ X1252 @ X1253 @ X1256) @ X1253)|~(in @ X1256 @ (esk6_2 @ X1252 @ X1253))|~(exu @ (X1252 @ (esk5_2 @ X1252 @ X1253))))&((X1252 @ (esk7_3 @ X1252 @ X1253 @ X1256) @ X1256)|~(in @ X1256 @ (esk6_2 @ X1252 @ X1253))|~(exu @ (X1252 @ (esk5_2 @ X1252 @ X1253)))))&(~(in @ X1259 @ X1253)|~(X1252 @ X1259 @ X1258)|(in @ X1258 @ (esk6_2 @ X1252 @ X1253))|~(exu @ (X1252 @ (esk5_2 @ X1252 @ X1253))))))&((((in @ (esk8_1 @ X1260) @ X1260)|~(in @ X1261 @ X1260))&(~(in @ X1263 @ (esk8_1 @ X1260))|~(in @ X1263 @ X1260)|~(in @ X1261 @ X1260)))&((epred1_0)&((~(exu 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X1558 @ X1556)|~(in @ X1558 @ (symdiff @ X1556 @ X1557)))&(~(X1559)|(X1559)|(in @ X1558 @ X1556)|~(in @ X1558 @ (symdiff @ X1556 @ X1557)))))&(((~(in @ X1558 @ X1556)|(X1559)|~(in @ X1558 @ X1557)|~(in @ X1558 @ (symdiff @ X1556 @ X1557)))&(((in @ X1558 @ X1557)|(X1559)|~(in @ X1558 @ X1557)|~(in @ X1558 @ (symdiff @ X1556 @ X1557)))&(~(X1559)|(X1559)|~(in @ X1558 @ X1557)|~(in @ X1558 @ (symdiff @ X1556 @ X1557)))))&((~(in @ X1558 @ X1556)|(X1559)|~(X1559)|~(in @ X1558 @ (symdiff @ X1556 @ X1557)))&(((in @ X1558 @ X1557)|(X1559)|~(X1559)|~(in @ X1558 @ (symdiff @ X1556 @ X1557)))&(~(X1559)|(X1559)|~(X1559)|~(in @ X1558 @ (symdiff @ X1556 @ X1557)))))))&((~(in @ X1562 @ X1560)|((in @ X1562 @ X1561)|(in @ X1562 @ (symdiff @ X1560 @ X1561))))&(((in @ X1565 @ X1563)|(~(in @ X1565 @ X1564)|(in @ X1565 @ (symdiff @ X1563 @ X1564))))&((~(in @ X1568 @ X1566)|(~(in @ X1568 @ X1567)|~(in @ X1568 @ (symdiff @ X1566 @ X1567))))&(((in @ X1571 @ X1569)|((in @ X1571 @ X1570)|~(in @ X1571 @ (symdiff @ X1569 @ X1570))))&((in @ X1573 @ (setadjoin @ X1572 @ (setadjoin @ X1573 @ emptyset)))&((in @ X1574 @ (setunion @ (setadjoin @ (setadjoin @ X1574 @ emptyset) @ (setadjoin @ (setadjoin @ X1574 @ (setadjoin @ X1575 @ emptyset)) @ emptyset))))&((in @ X1577 @ (setunion @ (setadjoin @ (setadjoin @ X1576 @ emptyset) @ (setadjoin @ (setadjoin @ X1576 @ (setadjoin @ X1577 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1578 @ emptyset) @ (setadjoin @ (setadjoin @ X1578 @ (setadjoin @ X1579 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1580 @ X1581))&((~(in @ X1583 @ X1582)|(subset @ (setadjoin @ X1583 @ emptyset) @ X1582))&((~(in @ X1585 @ X1584)|(in @ (setadjoin @ X1585 @ emptyset) @ (powerset @ X1584)))&((~(in @ X1588 @ X1586)|(in @ (setadjoin @ X1588 @ emptyset) @ (powerset @ (binunion @ X1586 @ X1587))))&((~(in @ X1591 @ (setadjoin @ X1589 @ (setadjoin @ X1590 @ emptyset)))|(((X1591)=(X1589))|((X1591)=(X1590))))&((~(in @ X1594 @ X1592)|(~(in @ X1595 @ X1593)|(subset @ (setadjoin @ X1594 @ (setadjoin @ X1595 @ emptyset)) @ (binunion @ X1592 @ X1593))))&((~(in @ X1598 @ X1596)|(~(in @ X1599 @ X1597)|(in @ (setadjoin @ X1598 @ (setadjoin @ X1599 @ emptyset)) @ (powerset @ (binunion @ X1596 @ X1597)))))&((~(in @ X1602 @ X1600)|(~(in @ X1603 @ X1601)|(subset @ (setadjoin @ (setadjoin @ X1602 @ emptyset) @ (setadjoin @ (setadjoin @ X1602 @ (setadjoin @ X1603 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1600 @ X1601)))))&((~(in @ X1606 @ X1604)|(~(in @ X1607 @ X1605)|(in @ (setadjoin @ (setadjoin @ X1606 @ emptyset) @ (setadjoin @ (setadjoin @ X1606 @ (setadjoin @ X1607 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1604 @ X1605))))))&((~(in @ X1610 @ X1608)|(~(in @ X1611 @ X1609)|(in @ (kpair @ X1610 @ X1611) @ (powerset @ (powerset @ (binunion @ X1608 @ X1609))))))&((~(in @ X1614 @ X1612)|(~(in @ X1615 @ X1613)|(in @ (kpair @ X1614 @ X1615) @ (cartprod @ X1612 @ X1613))))&((((in @ (esk39_3 @ X1616 @ X1617 @ X1618) @ X1616)|~(in @ X1618 @ (cartprod @ X1616 @ X1617)))&(((in @ (esk40_3 @ X1616 @ X1617 @ X1618) @ X1617)|~(in @ X1618 @ (cartprod @ X1616 @ X1617)))&(((X1618)=(kpair @ (esk39_3 @ X1616 @ X1617 @ X1618) @ (esk40_3 @ X1616 @ X1617 @ X1618)))|~(in @ X1618 @ (cartprod @ X1616 @ X1617)))))&((~(in @ X1623 @ (cartprod @ X1621 @ X1622))|(iskpair @ X1623))&((((in @ (esk41_2 @ X1624 @ X1625) @ X1624)|~(in @ X1625 @ (setunion @ X1624)))&((in @ X1625 @ (esk41_2 @ X1624 @ X1625))|~(in @ X1625 @ (setunion @ X1624))))&((subset @ (setunion @ (setadjoin @ X1627 @ emptyset)) @ X1627)&((subset @ X1628 @ (setunion @ (setadjoin @ X1628 @ emptyset)))&(((setunion @ (setadjoin @ X1629 @ emptyset))=(X1629))&((((in @ (esk42_2 @ X1630 @ X1631) @ X1630)|(~(in @ X1634 @ X1630)|~(X1631 @ X1634)|(singleton @ (dsetconstr @ X1630 @ X1631))))&(((in @ (esk43_2 @ X1630 @ X1631) @ X1630)|(~(in @ X1634 @ X1630)|~(X1631 @ X1634)|(singleton @ (dsetconstr @ X1630 @ X1631))))&(((X1631 @ (esk42_2 @ X1630 @ X1631))|(~(in @ X1634 @ X1630)|~(X1631 @ X1634)|(singleton @ (dsetconstr @ X1630 @ X1631))))&(((X1631 @ (esk43_2 @ X1630 @ X1631))|(~(in @ X1634 @ X1630)|~(X1631 @ X1634)|(singleton @ (dsetconstr @ X1630 @ X1631))))&(((esk42_2 @ X1630 @ X1631)!=(esk43_2 @ X1630 @ X1631))|(~(in @ X1634 @ X1630)|~(X1631 @ X1634)|(singleton @ (dsetconstr @ X1630 @ X1631))))))))&((((in @ (esk44_2 @ X1635 @ X1636) @ X1635)|~(ex1 @ X1635 @ X1636))&((X1636 @ (esk44_2 @ X1635 @ X1636))|~(ex1 @ X1635 @ X1636)))&((((in @ (esk45_3 @ X1638 @ X1639 @ X1640) @ X1638)|(ex1 @ X1638 @ X1639)|~(X1639 @ X1640)|~(in @ X1640 @ X1638))&(((X1639 @ (esk45_3 @ X1638 @ X1639 @ X1640))|(ex1 @ X1638 @ X1639)|~(X1639 @ X1640)|~(in @ X1640 @ X1638))&(((esk45_3 @ X1638 @ X1639 @ X1640)!=(X1640))|(ex1 @ X1638 @ X1639)|~(X1639 @ X1640)|~(in @ X1640 @ X1638))))&((((in @ (esk46_2 @ X1642 @ X1643) @ X1642)|(~(in @ X1646 @ X1642)|~(X1643 @ X1646)|(ex1 @ X1642 @ X1643)))&(((in @ (esk47_2 @ X1642 @ X1643) @ X1642)|(~(in @ X1646 @ X1642)|~(X1643 @ X1646)|(ex1 @ X1642 @ X1643)))&(((X1643 @ (esk46_2 @ X1642 @ X1643))|(~(in @ X1646 @ X1642)|~(X1643 @ X1646)|(ex1 @ X1642 @ X1643)))&(((X1643 @ (esk47_2 @ X1642 @ X1643))|(~(in @ X1646 @ X1642)|~(X1643 @ X1646)|(ex1 @ X1642 @ X1643)))&(((esk46_2 @ X1642 @ X1643)!=(esk47_2 @ X1642 @ X1643))|(~(in @ X1646 @ X1642)|~(X1643 @ X1646)|(ex1 @ X1642 @ X1643)))))))&((((setadjoin @ X1647 @ emptyset)!=(setadjoin @ X1648 @ emptyset))|((X1647)=(X1648)))&((~(in @ (setadjoin @ X1651 @ emptyset) @ (setadjoin @ (setadjoin @ X1649 @ emptyset) @ (setadjoin @ (setadjoin @ X1649 @ (setadjoin @ X1650 @ emptyset)) @ emptyset)))|((X1649)=(X1651)))&((~(iskpair @ X1652)|(singleton @ (dsetconstr @ (setunion @ X1652) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1652))))))&((~(singleton @ X1653)|(in @ (setunion @ X1653) @ X1653))&(((kfst @ (kpair @ X1654 @ X1655))=(X1654))&((~(in @ X1658 @ (cartprod @ X1656 @ X1657))|(in @ (kfst @ X1658) @ X1656))&((((setadjoin @ (setadjoin @ X1659 @ emptyset) @ (setadjoin @ (setadjoin @ X1659 @ (setadjoin @ X1660 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1661 @ emptyset) @ (setadjoin @ (setadjoin @ X1661 @ (setadjoin @ X1662 @ emptyset)) @ emptyset)))|((X1659)=(X1661)))&((((kpair @ X1663 @ X1664)!=(kpair @ X1665 @ X1666))|((X1663)=(X1665)))&((((X1667)!=(X1668))|((setadjoin @ X1667 @ (setadjoin @ X1668 @ emptyset))=(setadjoin @ X1667 @ emptyset)))&((((X1669)!=(X1670))|((setadjoin @ (setadjoin @ X1669 @ emptyset) @ (setadjoin @ (setadjoin @ X1669 @ (setadjoin @ X1670 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1669 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1671 @ emptyset) @ (setadjoin @ (setadjoin @ X1671 @ (setadjoin @ X1672 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1673 @ emptyset) @ (setadjoin @ (setadjoin @ X1673 @ (setadjoin @ X1674 @ emptyset)) @ emptyset)))|(((X1673)!=(X1674))|((X1672)=(X1674))))&((((setadjoin @ X1675 @ (setadjoin @ X1676 @ emptyset))!=(setadjoin @ X1677 @ emptyset))|((X1675)=(X1676)))&((((setadjoin @ (setadjoin @ X1678 @ emptyset) @ (setadjoin @ (setadjoin @ X1678 @ (setadjoin @ X1679 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1680 @ emptyset) @ (setadjoin @ (setadjoin @ X1680 @ (setadjoin @ X1681 @ emptyset)) @ emptyset)))|((X1679)=(X1681)))&((((kpair @ X1682 @ X1683)!=(kpair @ X1684 @ X1685))|((X1683)=(X1685)))&((~(iskpair @ X1686)|(singleton @ (dsetconstr @ (setunion @ X1686) @ (^[Z0:$i]:(((X1686)=(kpair @ (kfst @ X1686) @ Z0)))))))&(((ksnd @ (kpair @ X1687 @ X1688))=(X1688))&((~(iskpair @ X1689)|((kpair @ (kfst @ X1689) @ (ksnd @ X1689))=(X1689)))&((~(in @ X1692 @ (cartprod @ X1690 @ X1691))|(in @ (ksnd @ X1692) @ X1691))&((~(in @ (kpair @ X1695 @ X1696) @ (cartprod @ X1693 @ X1694))|(in @ X1695 @ X1693))&((~(in @ (kpair @ X1699 @ X1700) @ (cartprod @ X1697 @ X1698))|(in @ X1700 @ X1698))&((~(in @ X1703 @ X1701)|(~(in @ X1704 @ X1702)|((kpair @ X1703 @ X1704)=(kpair @ X1703 @ X1704))))&((~(in @ X1707 @ X1705)|(~(in @ X1708 @ X1706)|((kfst @ (kpair @ X1707 @ X1708))=(X1707))))&((~(in @ X1711 @ X1709)|(~(in @ X1712 @ X1710)|((ksnd @ (kpair @ X1711 @ X1712))=(X1712))))&((~(in @ X1715 @ (cartprod @ X1713 @ X1714))|((kpair @ (kfst @ X1715) @ (ksnd @ X1715))=(X1715)))&((~(in @ X1719 @ X1716)|(~(in @ X1720 @ X1717)|(~(X1718 @ X1719 @ X1720)|(in @ (kpair @ X1719 @ X1720) @ (dpsetconstr @ X1716 @ X1717 @ X1718)))))&((subset @ (dpsetconstr @ X1721 @ X1722 @ X1723) @ (cartprod @ X1721 @ X1722))&((breln @ X1724 @ X1725 @ (dpsetconstr @ X1724 @ X1725 @ X1726))&((~(in @ X1730 @ X1727)|(~(in @ X1731 @ X1728)|(~(in @ (kpair @ X1730 @ X1731) @ (dpsetconstr @ X1727 @ X1728 @ X1729))|(X1729 @ X1730 @ X1731))))&((~(in @ (kpair @ X1735 @ X1736) @ (dpsetconstr @ X1732 @ X1733 @ X1734))|(in @ X1735 @ X1732))&((~(in @ (kpair @ X1740 @ X1741) @ (dpsetconstr @ X1737 @ X1738 @ X1739))|(in @ X1741 @ X1738))&((~(in @ (kpair @ X1745 @ X1746) @ (dpsetconstr @ X1742 @ X1743 @ X1744))|(X1744 @ X1745 @ X1746))&((~(func @ X1747 @ X1748 @ X1749)|(~(in @ X1750 @ X1747)|(singleton @ (dsetconstr @ X1748 @ (^[Z0:$i]:((in @ (kpair @ X1750 @ Z0) @ X1749)))))))&((~(func @ X1751 @ X1752 @ X1753)|(~(in @ X1754 @ X1751)|(in @ (setunion @ (dsetconstr @ X1752 @ (^[Z0:$i]:((in @ (kpair @ X1754 @ Z0) @ X1753))))) @ X1752)))&((~(func @ X1755 @ X1756 @ X1757)|(~(in @ X1758 @ X1755)|(in @ (ap @ X1755 @ X1756 @ X1757 @ X1758) @ X1756)))&((~(in @ X1761 @ (funcSet @ X1759 @ X1760))|(func @ X1759 @ X1760 @ X1761))&((~(in @ X1764 @ (funcSet @ X1762 @ X1763))|(~(in @ X1765 @ X1762)|(in @ (ap @ X1762 @ X1763 @ X1764 @ X1765) @ X1763)))&((~(func @ X1766 @ X1767 @ X1768)|(in @ X1768 @ (funcSet @ X1766 @ X1767)))&((((in @ (esk48_3 @ X1769 @ X1770 @ X1771) @ X1769)|(func @ X1769 @ X1770 @ (dpsetconstr @ X1769 @ X1770 @ (^[Z0:$i]:($eq @ (X1771 @ Z0))))))&(~(in @ (X1771 @ (esk48_3 @ X1769 @ X1770 @ X1771)) @ X1770)|(func @ X1769 @ X1770 @ (dpsetconstr @ X1769 @ X1770 @ (^[Z0:$i]:($eq @ (X1771 @ Z0)))))))&((((in @ (esk49_3 @ X1773 @ X1774 @ X1775) @ X1773)|(func @ X1773 @ X1774 @ (lam @ X1773 @ X1774 @ X1775)))&(~(in @ (X1775 @ (esk49_3 @ X1773 @ X1774 @ X1775)) @ X1774)|(func @ X1773 @ X1774 @ (lam @ X1773 @ X1774 @ X1775))))&((((in @ (esk50_3 @ X1777 @ X1778 @ X1779) @ X1777)|(in @ (lam @ X1777 @ X1778 @ X1779) @ (funcSet @ X1777 @ X1778)))&(~(in @ (X1779 @ (esk50_3 @ X1777 @ X1778 @ X1779)) @ X1778)|(in @ (lam @ X1777 @ X1778 @ X1779) @ (funcSet @ X1777 @ X1778))))&((((in @ (esk51_4 @ X1781 @ X1782 @ X1783 @ X1784) @ X1781)|(~(in @ X1787 @ X1783)|(X1784 @ X1787))|~(breln @ X1781 @ X1782 @ X1783))&(((in @ (esk52_4 @ X1781 @ X1782 @ X1783 @ X1784) @ X1782)|(~(in @ X1787 @ X1783)|(X1784 @ X1787))|~(breln @ X1781 @ X1782 @ X1783))&(((in @ (kpair @ (esk51_4 @ X1781 @ X1782 @ X1783 @ X1784) @ (esk52_4 @ X1781 @ X1782 @ X1783 @ X1784)) @ X1783)|(~(in @ X1787 @ X1783)|(X1784 @ X1787))|~(breln @ X1781 @ X1782 @ X1783))&(~(X1784 @ (kpair @ (esk51_4 @ X1781 @ X1782 @ X1783 @ X1784) @ (esk52_4 @ X1781 @ X1782 @ X1783 @ X1784)))|(~(in @ X1787 @ X1783)|(X1784 @ X1787))|~(breln @ X1781 @ X1782 @ X1783)))))&((((in @ (esk53_4 @ X1788 @ X1789 @ X1790 @ X1791) @ X1788)|(~(in @ X1794 @ X1790)|(X1791 @ X1794))|~(breln @ X1788 @ X1789 @ X1790))&(((in @ (esk54_4 @ X1788 @ X1789 @ X1790 @ X1791) @ X1789)|(~(in @ X1794 @ X1790)|(X1791 @ X1794))|~(breln @ X1788 @ X1789 @ X1790))&(((in @ (kpair @ (esk53_4 @ X1788 @ X1789 @ X1790 @ X1791) @ (esk54_4 @ X1788 @ X1789 @ X1790 @ X1791)) @ X1790)|(~(in @ X1794 @ X1790)|(X1791 @ X1794))|~(breln @ X1788 @ X1789 @ X1790))&(~(X1791 @ (kpair @ (esk53_4 @ X1788 @ X1789 @ X1790 @ X1791) @ (esk54_4 @ X1788 @ X1789 @ X1790 @ X1791)))|(~(in @ X1794 @ X1790)|(X1791 @ X1794))|~(breln @ X1788 @ X1789 @ X1790)))))&((~(ex1 @ X1795 @ X1796)|(~(in @ X1797 @ X1795)|(~(in @ X1798 @ X1795)|(~(X1796 @ X1797)|(~(X1796 @ X1798)|((X1797)=(X1798)))))))&((~(func @ X1799 @ X1800 @ X1801)|(~(in @ X1802 @ X1799)|(in @ (kpair @ X1802 @ (ap @ X1799 @ X1800 @ X1801 @ X1802)) @ X1801)))&((~(in @ X1805 @ (funcSet @ X1803 @ X1804))|(~(in @ X1806 @ X1803)|(in @ (kpair @ X1806 @ (ap @ X1803 @ X1804 @ X1805 @ X1806)) @ X1805)))&((~(func @ X1807 @ X1808 @ X1809)|(~(in @ X1810 @ X1807)|(~(in @ X1811 @ X1808)|(~(in @ (kpair @ X1810 @ X1811) @ X1809)|((ap @ X1807 @ X1808 @ X1809 @ X1810)=(X1811))))))&((func @ esk55_0 @ esk56_0 @ esk57_0)&((func @ esk55_0 @ esk56_0 @ esk58_0)&((~(in @ X1816 @ esk55_0)|((ap @ esk55_0 @ esk56_0 @ esk57_0 @ X1816)=(ap @ esk55_0 @ esk56_0 @ esk58_0 @ X1816)))&((in @ esk59_0 @ esk55_0)&((in @ esk60_0 @ esk56_0)&((in @ (kpair @ esk59_0 @ esk60_0) @ esk58_0)&~(in @ (kpair @ esk59_0 @ esk60_0) @ esk57_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_246])])])])])])])).
% 205.32/30.32 thf(c_0_248, negated_conjecture, ![X3:$i, X2:$i, X7:$i, X5:$i, X4:$i]:((((ap @ X2 @ X3 @ X4 @ X5)=(X7))|~((func @ X2 @ X3 @ X4))|~((in @ X5 @ X2))|~((in @ X7 @ X3))|~((in @ (kpair @ X5 @ X7) @ X4)))), inference(split_conjunct,[status(thm)],[c_0_247])).
% 205.32/30.32 thf(c_0_249, negated_conjecture, (in @ (kpair @ esk59_0 @ esk60_0) @ esk58_0), inference(split_conjunct,[status(thm)],[c_0_247])).
% 205.32/30.32 thf(c_0_250, negated_conjecture, ![X2:$i]:((((ap @ esk55_0 @ esk56_0 @ esk57_0 @ X2)=(ap @ esk55_0 @ esk56_0 @ esk58_0 @ X2))|~((in @ X2 @ esk55_0)))), inference(split_conjunct,[status(thm)],[c_0_247])).
% 205.32/30.32 thf(c_0_251, negated_conjecture, ![X3:$i, X2:$i]:((((ap @ X2 @ X3 @ esk58_0 @ esk59_0)=(esk60_0))|~((func @ X2 @ X3 @ esk58_0))|~((in @ esk60_0 @ X3))|~((in @ esk59_0 @ X2)))), inference(spm,[status(thm)],[c_0_248, c_0_249])).
% 205.32/30.32 thf(c_0_252, negated_conjecture, (in @ esk59_0 @ esk55_0), inference(split_conjunct,[status(thm)],[c_0_247])).
% 205.32/30.32 thf(c_0_253, negated_conjecture, (func @ esk55_0 @ esk56_0 @ esk58_0), inference(split_conjunct,[status(thm)],[c_0_247])).
% 205.32/30.32 thf(c_0_254, negated_conjecture, (in @ esk60_0 @ esk56_0), inference(split_conjunct,[status(thm)],[c_0_247])).
% 205.32/30.32 thf(c_0_255, negated_conjecture, ![X3:$i, X5:$i, X4:$i, X2:$i]:(((in @ (kpair @ X5 @ (ap @ X2 @ X3 @ X4 @ X5)) @ X4)|~((func @ X2 @ X3 @ X4))|~((in @ X5 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_247])).
% 205.32/30.32 thf(c_0_256, negated_conjecture, ((ap @ esk55_0 @ esk56_0 @ esk57_0 @ esk59_0)=(esk60_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250, c_0_251]), c_0_252]), c_0_253]), c_0_254])])).
% 205.32/30.32 thf(c_0_257, negated_conjecture, (func @ esk55_0 @ esk56_0 @ esk57_0), inference(split_conjunct,[status(thm)],[c_0_247])).
% 205.32/30.32 thf(c_0_258, negated_conjecture, ~((in @ (kpair @ esk59_0 @ esk60_0) @ esk57_0)), inference(split_conjunct,[status(thm)],[c_0_247])).
% 205.32/30.32 thf(c_0_259, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255, c_0_256]), c_0_257]), c_0_252])]), c_0_258]), ['proof']).
% 205.32/30.32 % SZS output end CNFRefutation
% 205.32/30.32 % Parsed axioms : 451
% 205.32/30.32 % Removed by relevancy pruning/SinE : 248
% 205.32/30.32 % Initial clauses : 319
% 205.32/30.32 % Removed in clause preprocessing : 26
% 205.32/30.32 % Initial clauses in saturation : 293
% 205.32/30.32 % Processed clauses : 2102
% 205.32/30.32 % ...of these trivial : 34
% 205.32/30.32 % ...subsumed : 653
% 205.32/30.32 % ...remaining for further processing : 1415
% 205.32/30.32 % Other redundant clauses eliminated : 127
% 205.32/30.32 % Clauses deleted for lack of memory : 0
% 205.32/30.32 % Backward-subsumed : 19
% 205.32/30.32 % Backward-rewritten : 21
% 205.32/30.32 % Generated clauses : 48533
% 205.32/30.32 % ...of the previous two non-redundant : 47385
% 205.32/30.32 % ...aggressively subsumed : 0
% 205.32/30.32 % Contextual simplify-reflections : 1
% 205.32/30.32 % Paramodulations : 48385
% 205.32/30.32 % Factorizations : 6
% 205.32/30.32 % NegExts : 2
% 205.32/30.32 % Equation resolutions : 132
% 205.32/30.32 % Disequality decompositions : 0
% 205.32/30.32 % Total rewrite steps : 1687
% 205.32/30.32 % ...of those cached : 1466
% 205.32/30.32 % Propositional unsat checks : 0
% 205.32/30.32 % Propositional check models : 0
% 205.32/30.32 % Propositional check unsatisfiable : 0
% 205.32/30.32 % Propositional clauses : 0
% 205.32/30.32 % Propositional clauses after purity: 0
% 205.32/30.32 % Propositional unsat core size : 0
% 205.32/30.32 % Propositional preprocessing time : 0.000
% 205.32/30.32 % Propositional encoding time : 0.000
% 205.32/30.32 % Propositional solver time : 0.000
% 205.32/30.32 % Success case prop preproc time : 0.000
% 205.32/30.32 % Success case prop encoding time : 0.000
% 205.32/30.32 % Success case prop solver time : 0.000
% 205.32/30.32 % Current number of processed clauses : 1109
% 205.32/30.32 % Positive orientable unit clauses : 98
% 205.32/30.32 % Positive unorientable unit clauses: 0
% 205.32/30.32 % Negative unit clauses : 14
% 205.32/30.32 % Non-unit-clauses : 997
% 205.32/30.32 % Current number of unprocessed clauses: 45651
% 205.32/30.32 % ...number of literals in the above : 151483
% 205.32/30.32 % Current number of archived formulas : 0
% 205.32/30.32 % Current number of archived clauses : 293
% 205.32/30.32 % Clause-clause subsumption calls (NU) : 92473
% 205.32/30.32 % Rec. Clause-clause subsumption calls : 69167
% 205.32/30.32 % Non-unit clause-clause subsumptions : 398
% 205.32/30.32 % Unit Clause-clause subsumption calls : 2197
% 205.32/30.32 % Rewrite failures with RHS unbound : 0
% 205.32/30.32 % BW rewrite match attempts : 40
% 205.32/30.32 % BW rewrite match successes : 15
% 205.32/30.32 % Condensation attempts : 2102
% 205.32/30.32 % Condensation successes : 12
% 205.32/30.32 % Termbank termtop insertions : 774524
% 205.32/30.32 % Search garbage collected termcells : 18640
% 205.32/30.32
% 205.32/30.32 % -------------------------------------------------
% 205.32/30.32 % User time : 28.356 s
% 205.32/30.32 % System time : 0.995 s
% 205.32/30.32 % Total time : 29.351 s
% 205.32/30.32 % Maximum resident set size: 8456 pages
% 205.32/30.32
% 205.32/30.32 % -------------------------------------------------
% 205.32/30.32 % User time : 28.371 s
% 205.32/30.32 % System time : 1.002 s
% 205.32/30.32 % Total time : 29.373 s
% 205.32/30.32 % Maximum resident set size: 5376 pages
% 205.32/30.32 % E exiting
%------------------------------------------------------------------------------