%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU702^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:25:16 AM UTC 2026
% Result : Theorem 1.32s 0.52s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU702^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:12:30 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.20/0.28 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p
% 1.32/0.52 % Version: 3.5.1-ho
% 1.32/0.52 % Preprocessing class: HSLMSLSSLLLCHSA.
% 1.32/0.52 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.52 % Starting ho_unfolding_5 with 1200s (4) cores
% 1.32/0.52 % Starting pre_casc_3 with 300s (1) cores
% 1.32/0.52 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.32/0.52 % Starting full_lambda_10 with 300s (1) cores
% 1.32/0.52 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 1.32/0.52 % ho_unfolding_5 with pid 4063273 completed with status 0
% 1.32/0.52 % Result found by ho_unfolding_5
% 1.32/0.52 % Preprocessing class: HSLMSLSSLLLCHSA.
% 1.32/0.52 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.52 % Starting ho_unfolding_5 with 1200s (4) cores
% 1.32/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.32/0.52 % No SInE strategy applied
% 1.32/0.52 % Search class: HGHSM-FSLM32-MHSMMSBN
% 1.32/0.52 % Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 1.32/0.52 % Starting SubtermCWHack with 109s (1) cores
% 1.32/0.52 % Starting ho_unfolding_5 with 121s (1) cores
% 1.32/0.52 % Starting new_ho_6 with 99s (1) cores
% 1.32/0.52 % Starting pre_casc_4 with 99s (1) cores
% 1.32/0.52 % pre_casc_4 with pid 4063325 completed with status 0
% 1.32/0.52 % Result found by pre_casc_4
% 1.32/0.52 % Preprocessing class: HSLMSLSSLLLCHSA.
% 1.32/0.52 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.52 % Starting ho_unfolding_5 with 1200s (4) cores
% 1.32/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.32/0.52 % No SInE strategy applied
% 1.32/0.52 % Search class: HGHSM-FSLM32-MHSMMSBN
% 1.32/0.52 % Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 1.32/0.52 % Starting SubtermCWHack with 109s (1) cores
% 1.32/0.52 % Starting ho_unfolding_5 with 121s (1) cores
% 1.32/0.52 % Starting new_ho_6 with 99s (1) cores
% 1.32/0.52 % Starting pre_casc_4 with 99s (1) cores
% 1.32/0.52 % Preprocessing time : 0.009 s
% 1.32/0.52 % Presaturation interreduction done
% 1.32/0.52
% 1.32/0.52 % Proof found!
% 1.32/0.52 % SZS status Theorem
% 1.32/0.52 % SZS output start CNFRefutation
% 1.32/0.52 thf(decl_23, type, in: $i > $i > $o).
% 1.32/0.52 thf(decl_24, type, exu: ($i > $o) > $o).
% 1.32/0.52 thf(decl_25, type, setextAx: $o).
% 1.32/0.52 thf(decl_26, type, emptyset: $i).
% 1.32/0.52 thf(decl_27, type, emptysetAx: $o).
% 1.32/0.52 thf(decl_28, type, setadjoin: $i > $i > $i).
% 1.32/0.52 thf(decl_29, type, setadjoinAx: $o).
% 1.32/0.52 thf(decl_30, type, powerset: $i > $i).
% 1.32/0.52 thf(decl_31, type, powersetAx: $o).
% 1.32/0.52 thf(decl_32, type, setunion: $i > $i).
% 1.32/0.52 thf(decl_33, type, setunionAx: $o).
% 1.32/0.52 thf(decl_34, type, omega: $i).
% 1.32/0.52 thf(decl_35, type, omega0Ax: $o).
% 1.32/0.52 thf(decl_36, type, omegaSAx: $o).
% 1.32/0.52 thf(decl_37, type, omegaIndAx: $o).
% 1.32/0.52 thf(decl_38, type, replAx: $o).
% 1.32/0.52 thf(decl_39, type, foundationAx: $o).
% 1.32/0.52 thf(decl_40, type, wellorderingAx: $o).
% 1.32/0.52 thf(decl_41, type, descr: ($i > $o) > $i).
% 1.32/0.52 thf(decl_42, type, descrp: $o).
% 1.32/0.52 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_44, type, dsetconstrI: $o).
% 1.32/0.52 thf(decl_45, type, dsetconstrEL: $o).
% 1.32/0.52 thf(decl_46, type, dsetconstrER: $o).
% 1.32/0.52 thf(decl_47, type, exuE1: $o).
% 1.32/0.52 thf(decl_48, type, prop2set: $o > $i).
% 1.32/0.52 thf(decl_49, type, prop2setE: $o).
% 1.32/0.52 thf(decl_50, type, emptysetE: $o).
% 1.32/0.52 thf(decl_51, type, emptysetimpfalse: $o).
% 1.32/0.52 thf(decl_52, type, notinemptyset: $o).
% 1.32/0.52 thf(decl_53, type, exuE3e: $o).
% 1.32/0.52 thf(decl_54, type, setext: $o).
% 1.32/0.52 thf(decl_55, type, emptyI: $o).
% 1.32/0.52 thf(decl_56, type, noeltsimpempty: $o).
% 1.32/0.52 thf(decl_57, type, setbeta: $o).
% 1.32/0.52 thf(decl_58, type, nonempty: $i > $o).
% 1.32/0.52 thf(decl_59, type, nonemptyE1: $o).
% 1.32/0.52 thf(decl_60, type, nonemptyI: $o).
% 1.32/0.52 thf(decl_61, type, nonemptyI1: $o).
% 1.32/0.52 thf(decl_62, type, setadjoinIL: $o).
% 1.32/0.52 thf(decl_63, type, emptyinunitempty: $o).
% 1.32/0.52 thf(decl_64, type, setadjoinIR: $o).
% 1.32/0.52 thf(decl_65, type, setadjoinE: $o).
% 1.32/0.52 thf(decl_66, type, setadjoinOr: $o).
% 1.32/0.52 thf(decl_67, type, setoftrueEq: $o).
% 1.32/0.52 thf(decl_68, type, powersetI: $o).
% 1.32/0.52 thf(decl_69, type, emptyinPowerset: $o).
% 1.32/0.52 thf(decl_70, type, emptyInPowerset: $o).
% 1.32/0.52 thf(decl_71, type, powersetE: $o).
% 1.32/0.52 thf(decl_72, type, setunionI: $o).
% 1.32/0.52 thf(decl_73, type, setunionE: $o).
% 1.32/0.52 thf(decl_74, type, subPowSU: $o).
% 1.32/0.52 thf(decl_75, type, exuE2: $o).
% 1.32/0.52 thf(decl_76, type, nonemptyImpWitness: $o).
% 1.32/0.52 thf(decl_77, type, uniqinunit: $o).
% 1.32/0.52 thf(decl_78, type, notinsingleton: $o).
% 1.32/0.52 thf(decl_79, type, eqinunit: $o).
% 1.32/0.52 thf(decl_80, type, singletonsswitch: $o).
% 1.32/0.52 thf(decl_81, type, upairsetE: $o).
% 1.32/0.52 thf(decl_82, type, upairsetIL: $o).
% 1.32/0.52 thf(decl_83, type, upairsetIR: $o).
% 1.32/0.52 thf(decl_84, type, emptyE1: $o).
% 1.32/0.52 thf(decl_85, type, vacuousDall: $o).
% 1.32/0.52 thf(decl_86, type, quantDeMorgan1: $o).
% 1.32/0.52 thf(decl_87, type, quantDeMorgan2: $o).
% 1.32/0.52 thf(decl_88, type, quantDeMorgan3: $o).
% 1.32/0.52 thf(decl_89, type, quantDeMorgan4: $o).
% 1.32/0.52 thf(decl_90, type, prop2setI: $o).
% 1.32/0.52 thf(decl_91, type, set2prop: $i > $o).
% 1.32/0.52 thf(decl_92, type, prop2set2propI: $o).
% 1.32/0.52 thf(decl_93, type, notdexE: $o).
% 1.32/0.52 thf(decl_94, type, notdallE: $o).
% 1.32/0.52 thf(decl_95, type, exuI1: $o).
% 1.32/0.52 thf(decl_96, type, exuI3: $o).
% 1.32/0.52 thf(decl_97, type, exuI2: $o).
% 1.32/0.52 thf(decl_98, type, inCongP: $o).
% 1.32/0.52 thf(decl_99, type, in__Cong: $o).
% 1.32/0.52 thf(decl_100, type, exuE3u: $o).
% 1.32/0.52 thf(decl_101, type, exu__Cong: $o).
% 1.32/0.52 thf(decl_102, type, emptyset__Cong: $o).
% 1.32/0.52 thf(decl_103, type, setadjoin__Cong: $o).
% 1.32/0.52 thf(decl_104, type, powerset__Cong: $o).
% 1.32/0.52 thf(decl_105, type, setunion__Cong: $o).
% 1.32/0.52 thf(decl_106, type, omega__Cong: $o).
% 1.32/0.52 thf(decl_107, type, exuEu: $o).
% 1.32/0.52 thf(decl_108, type, descr__Cong: $o).
% 1.32/0.52 thf(decl_109, type, dsetconstr__Cong: $o).
% 1.32/0.52 thf(decl_110, type, subset: $i > $i > $o).
% 1.32/0.52 thf(decl_113, type, subsetI1: $o).
% 1.32/0.52 thf(decl_114, type, eqimpsubset2: $o).
% 1.32/0.52 thf(decl_115, type, eqimpsubset1: $o).
% 1.32/0.52 thf(decl_116, type, subsetI2: $o).
% 1.32/0.52 thf(decl_117, type, emptysetsubset: $o).
% 1.32/0.52 thf(decl_118, type, subsetE: $o).
% 1.32/0.52 thf(decl_119, type, subsetE2: $o).
% 1.32/0.52 thf(decl_120, type, notsubsetI: $o).
% 1.32/0.52 thf(decl_121, type, notequalI1: $o).
% 1.32/0.52 thf(decl_122, type, notequalI2: $o).
% 1.32/0.52 thf(decl_123, type, subsetRefl: $o).
% 1.32/0.52 thf(decl_124, type, subsetTrans: $o).
% 1.32/0.52 thf(decl_125, type, setadjoinSub: $o).
% 1.32/0.52 thf(decl_126, type, setadjoinSub2: $o).
% 1.32/0.52 thf(decl_127, type, subset2powerset: $o).
% 1.32/0.52 thf(decl_128, type, setextsub: $o).
% 1.32/0.52 thf(decl_129, type, subsetemptysetimpeq: $o).
% 1.32/0.52 thf(decl_130, type, powersetI1: $o).
% 1.32/0.52 thf(decl_131, type, powersetE1: $o).
% 1.32/0.52 thf(decl_132, type, inPowerset: $o).
% 1.32/0.52 thf(decl_133, type, powersetsubset: $o).
% 1.32/0.52 thf(decl_134, type, sepInPowerset: $o).
% 1.32/0.52 thf(decl_135, type, sepSubset: $o).
% 1.32/0.52 thf(decl_136, type, binunion: $i > $i > $i).
% 1.32/0.52 thf(decl_137, type, binunionIL: $o).
% 1.32/0.52 thf(decl_138, type, upairset2IR: $o).
% 1.32/0.52 thf(decl_139, type, binunionIR: $o).
% 1.32/0.52 thf(decl_140, type, binunionEcases: $o).
% 1.32/0.52 thf(decl_141, type, binunionE: $o).
% 1.32/0.52 thf(decl_142, type, binunionLsub: $o).
% 1.32/0.52 thf(decl_143, type, binunionRsub: $o).
% 1.32/0.52 thf(decl_144, type, binintersect: $i > $i > $i).
% 1.32/0.52 thf(decl_145, type, binintersectI: $o).
% 1.32/0.52 thf(decl_146, type, binintersectSubset5: $o).
% 1.32/0.52 thf(decl_147, type, binintersectEL: $o).
% 1.32/0.52 thf(decl_148, type, binintersectLsub: $o).
% 1.32/0.52 thf(decl_149, type, binintersectSubset2: $o).
% 1.32/0.52 thf(decl_150, type, binintersectSubset3: $o).
% 1.32/0.52 thf(decl_151, type, binintersectER: $o).
% 1.32/0.52 thf(decl_152, type, disjointsetsI1: $o).
% 1.32/0.52 thf(decl_153, type, binintersectRsub: $o).
% 1.32/0.52 thf(decl_154, type, binintersectSubset4: $o).
% 1.32/0.52 thf(decl_155, type, binintersectSubset1: $o).
% 1.32/0.52 thf(decl_156, type, bs114d: $o).
% 1.32/0.52 thf(decl_158, type, setminus: $i > $i > $i).
% 1.32/0.52 thf(decl_159, type, setminusI: $o).
% 1.32/0.52 thf(decl_160, type, setminusEL: $o).
% 1.32/0.52 thf(decl_161, type, setminusER: $o).
% 1.32/0.52 thf(decl_162, type, setminusSubset2: $o).
% 1.32/0.52 thf(decl_163, type, setminusERneg: $o).
% 1.32/0.52 thf(decl_164, type, setminusELneg: $o).
% 1.32/0.52 thf(decl_165, type, setminusILneg: $o).
% 1.32/0.52 thf(decl_166, type, setminusIRneg: $o).
% 1.32/0.52 thf(decl_167, type, setminusLsub: $o).
% 1.32/0.52 thf(decl_168, type, setminusSubset1: $o).
% 1.32/0.52 thf(decl_169, type, symdiff: $i > $i > $i).
% 1.32/0.52 thf(decl_170, type, symdiffE: $o).
% 1.32/0.52 thf(decl_171, type, symdiffI1: $o).
% 1.32/0.52 thf(decl_172, type, symdiffI2: $o).
% 1.32/0.52 thf(decl_173, type, symdiffIneg1: $o).
% 1.32/0.52 thf(decl_174, type, symdiffIneg2: $o).
% 1.32/0.52 thf(decl_175, type, iskpair: $i > $o).
% 1.32/0.52 thf(decl_176, type, secondinupair: $o).
% 1.32/0.52 thf(decl_177, type, setukpairIL: $o).
% 1.32/0.52 thf(decl_178, type, setukpairIR: $o).
% 1.32/0.52 thf(decl_179, type, kpairiskpair: $o).
% 1.32/0.52 thf(decl_180, type, kpair: $i > $i > $i).
% 1.32/0.52 thf(decl_181, type, kpairp: $o).
% 1.32/0.52 thf(decl_182, type, cartprod: $i > $i > $i).
% 1.32/0.52 thf(decl_183, type, singletonsubset: $o).
% 1.32/0.52 thf(decl_184, type, singletoninpowerset: $o).
% 1.32/0.52 thf(decl_185, type, singletoninpowunion: $o).
% 1.32/0.52 thf(decl_186, type, upairset2E: $o).
% 1.32/0.52 thf(decl_187, type, upairsubunion: $o).
% 1.32/0.52 thf(decl_188, type, upairinpowunion: $o).
% 1.32/0.52 thf(decl_189, type, ubforcartprodlem1: $o).
% 1.32/0.52 thf(decl_190, type, ubforcartprodlem2: $o).
% 1.32/0.52 thf(decl_191, type, ubforcartprodlem3: $o).
% 1.32/0.52 thf(decl_192, type, cartprodpairin: $o).
% 1.32/0.52 thf(decl_193, type, cartprodmempair1: $o).
% 1.32/0.52 thf(decl_194, type, cartprodmempair: $o).
% 1.32/0.52 thf(decl_195, type, setunionE2: $o).
% 1.32/0.52 thf(decl_196, type, setunionsingleton1: $o).
% 1.32/0.52 thf(decl_197, type, setunionsingleton2: $o).
% 1.32/0.52 thf(decl_198, type, setunionsingleton: $o).
% 1.32/0.52 thf(decl_199, type, singleton: $i > $o).
% 1.32/0.52 thf(decl_200, type, singletonprop: $o).
% 1.32/0.52 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 1.32/0.52 thf(decl_202, type, ex1E1: $o).
% 1.32/0.52 thf(decl_203, type, ex1I: $o).
% 1.32/0.52 thf(decl_204, type, ex1I2: $o).
% 1.32/0.52 thf(decl_205, type, singletonsuniq: $o).
% 1.32/0.52 thf(decl_210, type, setukpairinjL1: $o).
% 1.32/0.52 thf(decl_211, type, kfstsingleton: $o).
% 1.32/0.52 thf(decl_212, type, theprop: $o).
% 1.32/0.52 thf(decl_213, type, kfst: $i > $i).
% 1.32/0.52 thf(decl_214, type, kfstpairEq: $o).
% 1.32/0.52 thf(decl_215, type, cartprodfstin: $o).
% 1.32/0.52 thf(decl_216, type, setukpairinjL2: $o).
% 1.32/0.52 thf(decl_217, type, setukpairinjL: $o).
% 1.32/0.52 thf(decl_218, type, setukpairinjR11: $o).
% 1.32/0.52 thf(decl_219, type, setukpairinjR12: $o).
% 1.32/0.52 thf(decl_220, type, setukpairinjR1: $o).
% 1.32/0.52 thf(decl_221, type, upairequniteq: $o).
% 1.32/0.52 thf(decl_222, type, setukpairinjR2: $o).
% 1.32/0.52 thf(decl_223, type, setukpairinjR: $o).
% 1.32/0.52 thf(decl_224, type, ksndsingleton: $o).
% 1.32/0.52 thf(decl_225, type, ksnd: $i > $i).
% 1.32/0.52 thf(decl_226, type, ksndpairEq: $o).
% 1.32/0.52 thf(decl_227, type, kpairsurjEq: $o).
% 1.32/0.52 thf(decl_228, type, cartprodsndin: $o).
% 1.32/0.52 thf(decl_229, type, cartprodpairmemEL: $o).
% 1.32/0.52 thf(decl_230, type, cartprodpairmemER: $o).
% 1.32/0.52 thf(decl_231, type, cartprodmempaircEq: $o).
% 1.32/0.52 thf(decl_232, type, cartprodfstpairEq: $o).
% 1.32/0.52 thf(decl_233, type, cartprodsndpairEq: $o).
% 1.32/0.52 thf(decl_234, type, cartprodpairsurjEq: $o).
% 1.32/0.52 thf(decl_235, type, breln: $i > $i > $i > $o).
% 1.32/0.52 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.32/0.52 thf(decl_237, type, dpsetconstrI: $o).
% 1.32/0.52 thf(decl_238, type, dpsetconstrSub: $o).
% 1.32/0.52 thf(decl_239, type, setOfPairsIsBReln: $o).
% 1.32/0.52 thf(decl_240, type, dpsetconstrERa: $o).
% 1.32/0.52 thf(decl_241, type, dpsetconstrEL1: $o).
% 1.32/0.52 thf(decl_242, type, dpsetconstrEL2: $o).
% 1.32/0.52 thf(decl_243, type, dpsetconstrER: $o).
% 1.32/0.52 thf(decl_244, type, func: $i > $i > $i > $o).
% 1.32/0.52 thf(decl_245, type, funcSet: $i > $i > $i).
% 1.32/0.52 thf(decl_246, type, funcImageSingleton: $o).
% 1.32/0.52 thf(decl_247, type, apProp: $o).
% 1.32/0.52 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 1.32/0.52 thf(decl_249, type, app: $o).
% 1.32/0.52 thf(decl_250, type, infuncsetfunc: $o).
% 1.32/0.52 thf(decl_251, type, ap2p: $o).
% 1.32/0.52 thf(decl_252, type, funcinfuncset: $o).
% 1.32/0.52 thf(decl_253, type, lamProp: $o).
% 1.32/0.52 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 1.32/0.52 thf(decl_255, type, lamp: $o).
% 1.32/0.52 thf(decl_256, type, lam2p: $o).
% 1.32/0.52 thf(decl_257, type, brelnall1: $o).
% 1.32/0.52 thf(decl_258, type, brelnall2: $o).
% 1.32/0.52 thf(decl_259, type, ex1E2: $o).
% 1.32/0.52 thf(decl_260, type, funcGraphProp1: $o).
% 1.32/0.52 thf(decl_261, type, funcGraphProp3: $o).
% 1.32/0.52 thf(decl_262, type, funcGraphProp2: $o).
% 1.32/0.52 thf(decl_263, type, funcextLem: $o).
% 1.32/0.52 thf(decl_264, type, funcGraphProp4: $o).
% 1.32/0.52 thf(decl_265, type, subbreln: $o).
% 1.32/0.52 thf(decl_266, type, eqbreln: $o).
% 1.32/0.52 thf(decl_267, type, funcext: $o).
% 1.32/0.52 thf(decl_268, type, funcext2: $o).
% 1.32/0.52 thf(decl_269, type, ap2apEq1: $o).
% 1.32/0.52 thf(decl_270, type, ap2apEq2: $o).
% 1.32/0.52 thf(decl_271, type, beta1: $o).
% 1.32/0.52 thf(decl_272, type, eta1: $o).
% 1.32/0.52 thf(decl_273, type, lam2lamEq: $o).
% 1.32/0.52 thf(decl_274, type, beta2: $o).
% 1.32/0.52 thf(decl_275, type, eta2: $o).
% 1.32/0.52 thf(decl_276, type, iffalseProp1: $o).
% 1.32/0.52 thf(decl_277, type, iffalseProp2: $o).
% 1.32/0.52 thf(decl_278, type, epred1_0: $o).
% 1.32/0.52 thf(decl_279, type, esk1_2: $i > $i > $i).
% 1.32/0.52 thf(decl_280, type, esk2_2: $i > $i > $i).
% 1.32/0.52 thf(decl_281, type, esk3_2: $i > $i > $i).
% 1.32/0.52 thf(decl_282, type, esk4_1: $i > $i).
% 1.32/0.52 thf(decl_283, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.32/0.52 thf(decl_284, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 1.32/0.52 thf(decl_285, type, esk7_2: ($i > $i > $o) > $i > $i).
% 1.32/0.52 thf(decl_286, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 1.32/0.52 thf(decl_287, type, esk9_1: $i > $i).
% 1.32/0.52 thf(decl_288, type, esk10_2: ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_289, type, esk11_2: ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_290, type, esk12_1: ($i > $o) > $i).
% 1.32/0.52 thf(decl_291, type, esk13_2: ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_292, type, esk14_1: ($i > $o) > $i).
% 1.32/0.52 thf(decl_293, type, esk15_2: $i > $i > $i).
% 1.32/0.52 thf(decl_294, type, esk16_2: $i > $i > $i).
% 1.32/0.52 thf(decl_295, type, esk17_1: $i > $i).
% 1.32/0.52 thf(decl_296, type, esk18_1: $i > $i).
% 1.32/0.52 thf(decl_297, type, esk19_1: $i > $i).
% 1.32/0.52 thf(decl_298, type, esk20_2: $i > $i > $i).
% 1.32/0.52 thf(decl_299, type, esk21_3: $i > $i > $o > $i).
% 1.32/0.52 thf(decl_300, type, esk22_2: ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_301, type, esk23_1: ($i > $o) > $i).
% 1.32/0.52 thf(decl_302, type, esk24_1: $i > $i).
% 1.32/0.52 thf(decl_303, type, esk25_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_304, type, esk26_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_305, type, esk27_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_306, type, esk28_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_307, type, esk29_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_308, type, esk30_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_309, type, esk31_2: ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_310, type, esk32_1: ($i > $o) > $i).
% 1.32/0.52 thf(decl_311, type, esk33_1: ($i > $o) > $i).
% 1.32/0.52 thf(decl_312, type, esk34_1: ($i > $o) > $i).
% 1.32/0.52 thf(decl_313, type, esk35_1: ($i > $o) > $i).
% 1.32/0.52 thf(decl_314, type, esk36_2: ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_315, type, esk37_1: ($i > $o) > $i).
% 1.32/0.52 thf(decl_316, type, esk38_2: ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_317, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 1.32/0.52 thf(decl_318, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 1.32/0.52 thf(decl_319, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_320, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 1.32/0.52 thf(decl_321, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_322, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 1.32/0.52 thf(decl_323, type, esk45_2: ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_324, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 1.32/0.52 thf(decl_325, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 1.32/0.52 thf(decl_326, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_327, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_328, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.32/0.52 thf(decl_329, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.32/0.52 thf(decl_330, type, esk52_2: $i > $i > $i).
% 1.32/0.52 thf(decl_331, type, esk53_2: $i > $i > $i).
% 1.32/0.52 thf(decl_332, type, esk54_2: $i > $i > $i).
% 1.32/0.52 thf(decl_333, type, esk55_3: $i > $i > $i > $i).
% 1.32/0.52 thf(decl_334, type, esk56_3: $i > $i > $i > $i).
% 1.32/0.52 thf(decl_335, type, esk57_2: $i > $i > $i).
% 1.32/0.52 thf(decl_336, type, esk58_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_337, type, esk59_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_338, type, esk60_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_339, type, esk61_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_340, type, esk62_3: $i > ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_341, type, esk63_3: $i > ($i > $o) > $i > $i).
% 1.32/0.52 thf(decl_342, type, esk64_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_343, type, esk65_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_344, type, esk66_2: $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_345, type, esk67_1: $i > $i).
% 1.32/0.52 thf(decl_346, type, esk68_1: $i > $i).
% 1.32/0.52 thf(decl_347, type, esk69_4: $i > $i > $i > $i > $i).
% 1.32/0.52 thf(decl_348, type, esk70_3: $i > $i > ($i > $i) > $i).
% 1.32/0.52 thf(decl_349, type, esk71_3: $i > $i > ($i > $i) > $i).
% 1.32/0.52 thf(decl_350, type, esk72_3: $i > $i > ($i > $i) > $i).
% 1.32/0.52 thf(decl_351, type, esk73_4: $i > $i > $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_352, type, esk74_4: $i > $i > $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_353, type, esk75_4: $i > $i > $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_354, type, esk76_4: $i > $i > $i > ($i > $o) > $i).
% 1.32/0.52 thf(decl_355, type, esk77_4: $i > $i > $i > $i > $i).
% 1.32/0.52 thf(decl_356, type, esk78_4: $i > $i > $i > $i > $i).
% 1.32/0.52 thf(decl_357, type, esk79_4: $i > $i > $i > $i > $i).
% 1.32/0.52 thf(decl_358, type, esk80_4: $i > $i > $i > $i > $i).
% 1.32/0.52 thf(decl_359, type, esk81_4: $i > $i > $i > $i > $i).
% 1.32/0.52 thf(decl_360, type, esk82_4: $i > $i > $i > $i > $i).
% 1.32/0.52 thf(decl_361, type, esk83_4: $i > $i > $i > $i > $i).
% 1.32/0.52 thf(decl_362, type, esk84_4: $i > $i > $i > $i > $i).
% 1.32/0.52 thf(decl_363, type, esk85_4: $i > $i > $i > $i > $i).
% 1.32/0.52 thf(decl_364, type, esk86_3: $i > $i > ($i > $i) > $i).
% 1.32/0.52 thf(decl_365, type, esk87_3: $i > $i > ($i > $i) > $i).
% 1.32/0.52 thf(decl_366, type, esk88_3: $i > $i > ($i > $i) > $i).
% 1.32/0.52 thf(decl_367, type, esk89_0: $i).
% 1.32/0.52 thf(decl_368, type, epred2_0: $o).
% 1.32/0.52 thf(decl_369, type, esk90_0: $i).
% 1.32/0.52 thf(decl_370, type, esk91_0: $i).
% 1.32/0.52 thf(decl_376, type, epred3_0: $i > $o).
% 1.32/0.52 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ex1)).
% 1.32/0.52 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', singleton)).
% 1.32/0.52 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', replAx)).
% 1.32/0.52 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', exu)).
% 1.32/0.52 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', descrp)).
% 1.32/0.52 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', exuE1)).
% 1.32/0.52 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', exuE3e)).
% 1.32/0.52 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', nonempty)).
% 1.32/0.52 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', nonemptyI)).
% 1.32/0.52 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', exuE2)).
% 1.32/0.52 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', exuI1)).
% 1.32/0.52 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', exuI3)).
% 1.32/0.52 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', exuI2)).
% 1.32/0.52 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', exuE3u)).
% 1.32/0.52 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', exu__Cong)).
% 1.32/0.52 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', exuEu)).
% 1.32/0.52 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', descr__Cong)).
% 1.32/0.52 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', singletonprop)).
% 1.32/0.52 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ex1E1)).
% 1.32/0.52 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ex1I)).
% 1.32/0.52 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ex1I2)).
% 1.32/0.52 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', kfstsingleton)).
% 1.32/0.52 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ksndsingleton)).
% 1.32/0.52 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setOfPairsIsBReln)).
% 1.32/0.52 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', breln)).
% 1.32/0.52 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', funcImageSingleton)).
% 1.32/0.52 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ex1E2)).
% 1.32/0.52 thf(iftrueProp1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', iftrueProp1)).
% 1.32/0.52 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', dsetconstrI)).
% 1.32/0.52 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', dsetconstrEL)).
% 1.32/0.52 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', dsetconstrER)).
% 1.32/0.52 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setbeta)).
% 1.32/0.52 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', nonemptyE1)).
% 1.32/0.52 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', nonemptyI1)).
% 1.32/0.52 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setoftrueEq)).
% 1.32/0.52 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', nonemptyImpWitness)).
% 1.32/0.52 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', emptyE1)).
% 1.32/0.52 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', dsetconstr__Cong)).
% 1.32/0.52 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', sepInPowerset)).
% 1.32/0.52 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', sepSubset)).
% 1.32/0.52 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', theprop)).
% 1.32/0.52 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', dpsetconstrI)).
% 1.32/0.52 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', dpsetconstrSub)).
% 1.32/0.52 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', dpsetconstrERa)).
% 1.32/0.52 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', dpsetconstrEL1)).
% 1.32/0.52 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', dpsetconstrEL2)).
% 1.32/0.52 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', dpsetconstrER)).
% 1.32/0.52 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', apProp)).
% 1.32/0.52 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', lamProp)).
% 1.32/0.52 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', lamp)).
% 1.32/0.52 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', lam2p)).
% 1.32/0.52 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', brelnall1)).
% 1.32/0.52 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', brelnall2)).
% 1.32/0.52 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', subbreln)).
% 1.32/0.52 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', eqbreln)).
% 1.32/0.52 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', beta1)).
% 1.32/0.52 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', eta1)).
% 1.32/0.52 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', lam2lamEq)).
% 1.32/0.52 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', beta2)).
% 1.32/0.52 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', eta2)).
% 1.32/0.52 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', iffalseProp1)).
% 1.32/0.52 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', iffalseProp2)).
% 1.32/0.52 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setextAx)).
% 1.32/0.52 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', emptysetAx)).
% 1.32/0.52 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setadjoinAx)).
% 1.32/0.52 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', powersetAx)).
% 1.32/0.52 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setunionAx)).
% 1.32/0.52 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', omega0Ax)).
% 1.32/0.52 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', omegaSAx)).
% 1.32/0.52 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', omegaIndAx)).
% 1.32/0.52 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', foundationAx)).
% 1.32/0.52 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', wellorderingAx)).
% 1.32/0.52 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', prop2setE)).
% 1.32/0.52 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', emptysetE)).
% 1.32/0.52 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', emptysetimpfalse)).
% 1.32/0.52 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', notinemptyset)).
% 1.32/0.52 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setext)).
% 1.32/0.52 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', emptyI)).
% 1.32/0.52 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', noeltsimpempty)).
% 1.32/0.52 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setadjoinIL)).
% 1.32/0.52 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', emptyinunitempty)).
% 1.32/0.52 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setadjoinIR)).
% 1.32/0.52 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setadjoinE)).
% 1.32/0.52 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setadjoinOr)).
% 1.32/0.52 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', powersetI)).
% 1.32/0.52 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', emptyinPowerset)).
% 1.32/0.52 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', emptyInPowerset)).
% 1.32/0.52 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', powersetE)).
% 1.32/0.52 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setunionI)).
% 1.32/0.52 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setunionE)).
% 1.32/0.52 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', subPowSU)).
% 1.32/0.52 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', uniqinunit)).
% 1.32/0.52 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', notinsingleton)).
% 1.32/0.52 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', eqinunit)).
% 1.32/0.52 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', singletonsswitch)).
% 1.32/0.52 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', upairsetE)).
% 1.32/0.52 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', upairsetIL)).
% 1.32/0.52 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', upairsetIR)).
% 1.32/0.52 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', vacuousDall)).
% 1.32/0.52 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', quantDeMorgan1)).
% 1.32/0.52 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', quantDeMorgan2)).
% 1.32/0.52 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', quantDeMorgan3)).
% 1.32/0.52 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', quantDeMorgan4)).
% 1.32/0.52 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', prop2setI)).
% 1.32/0.52 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', prop2set2propI)).
% 1.32/0.52 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', notdexE)).
% 1.32/0.52 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', notdallE)).
% 1.32/0.52 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', inCongP)).
% 1.32/0.52 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', in__Cong)).
% 1.32/0.52 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', emptyset__Cong)).
% 1.32/0.52 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setadjoin__Cong)).
% 1.32/0.52 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', powerset__Cong)).
% 1.32/0.52 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setunion__Cong)).
% 1.32/0.52 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', omega__Cong)).
% 1.32/0.52 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', subsetI1)).
% 1.32/0.52 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', eqimpsubset2)).
% 1.32/0.52 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', eqimpsubset1)).
% 1.32/0.52 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', subsetI2)).
% 1.32/0.52 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', emptysetsubset)).
% 1.32/0.52 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', subsetE)).
% 1.32/0.52 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', subsetE2)).
% 1.32/0.52 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', notsubsetI)).
% 1.32/0.52 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', notequalI1)).
% 1.32/0.52 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', notequalI2)).
% 1.32/0.52 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', subsetRefl)).
% 1.32/0.52 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', subsetTrans)).
% 1.32/0.52 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setadjoinSub)).
% 1.32/0.52 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setadjoinSub2)).
% 1.32/0.52 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', subset2powerset)).
% 1.32/0.52 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setextsub)).
% 1.32/0.52 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', subsetemptysetimpeq)).
% 1.32/0.52 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', powersetI1)).
% 1.32/0.52 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', powersetE1)).
% 1.32/0.52 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', inPowerset)).
% 1.32/0.52 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', powersetsubset)).
% 1.32/0.52 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binunionIL)).
% 1.32/0.52 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', upairset2IR)).
% 1.32/0.52 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binunionIR)).
% 1.32/0.52 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binunionEcases)).
% 1.32/0.52 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binunionE)).
% 1.32/0.52 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binunionLsub)).
% 1.32/0.52 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binunionRsub)).
% 1.32/0.52 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binintersectI)).
% 1.32/0.52 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binintersectSubset5)).
% 1.32/0.52 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binintersectEL)).
% 1.32/0.52 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binintersectLsub)).
% 1.32/0.52 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binintersectSubset2)).
% 1.32/0.52 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binintersectSubset3)).
% 1.32/0.52 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binintersectER)).
% 1.32/0.52 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', disjointsetsI1)).
% 1.32/0.52 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binintersectRsub)).
% 1.32/0.52 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binintersectSubset4)).
% 1.32/0.52 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', binintersectSubset1)).
% 1.32/0.52 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', bs114d)).
% 1.32/0.52 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setminusI)).
% 1.32/0.52 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setminusEL)).
% 1.32/0.52 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setminusER)).
% 1.32/0.52 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setminusSubset2)).
% 1.32/0.52 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setminusERneg)).
% 1.32/0.52 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setminusELneg)).
% 1.32/0.52 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setminusILneg)).
% 1.32/0.52 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setminusIRneg)).
% 1.32/0.52 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setminusLsub)).
% 1.32/0.52 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setminusSubset1)).
% 1.32/0.52 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', symdiffE)).
% 1.32/0.52 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', symdiffI1)).
% 1.32/0.52 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', symdiffI2)).
% 1.32/0.52 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', symdiffIneg1)).
% 1.32/0.52 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', symdiffIneg2)).
% 1.32/0.52 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', secondinupair)).
% 1.32/0.52 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setukpairIL)).
% 1.32/0.52 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setukpairIR)).
% 1.32/0.52 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', kpairiskpair)).
% 1.32/0.52 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', kpairp)).
% 1.32/0.52 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', singletonsubset)).
% 1.32/0.52 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', singletoninpowerset)).
% 1.32/0.52 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', singletoninpowunion)).
% 1.32/0.52 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', upairset2E)).
% 1.32/0.52 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', upairsubunion)).
% 1.32/0.52 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', upairinpowunion)).
% 1.32/0.52 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ubforcartprodlem1)).
% 1.32/0.52 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ubforcartprodlem2)).
% 1.32/0.52 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ubforcartprodlem3)).
% 1.32/0.52 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', cartprodpairin)).
% 1.32/0.52 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', cartprodmempair1)).
% 1.32/0.52 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', cartprodmempair)).
% 1.32/0.52 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setunionE2)).
% 1.32/0.52 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setunionsingleton1)).
% 1.32/0.52 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setunionsingleton2)).
% 1.32/0.52 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setunionsingleton)).
% 1.32/0.52 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', singletonsuniq)).
% 1.32/0.52 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setukpairinjL1)).
% 1.32/0.52 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', kfstpairEq)).
% 1.32/0.52 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', cartprodfstin)).
% 1.32/0.52 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setukpairinjL2)).
% 1.32/0.52 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setukpairinjL)).
% 1.32/0.52 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setukpairinjR11)).
% 1.32/0.52 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setukpairinjR12)).
% 1.32/0.52 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setukpairinjR1)).
% 1.32/0.52 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', upairequniteq)).
% 1.32/0.52 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setukpairinjR2)).
% 1.32/0.52 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', setukpairinjR)).
% 1.32/0.52 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ksndpairEq)).
% 1.32/0.52 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', kpairsurjEq)).
% 1.32/0.52 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', cartprodsndin)).
% 1.32/0.52 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', cartprodpairmemEL)).
% 1.32/0.52 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', cartprodpairmemER)).
% 1.32/0.52 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', cartprodmempaircEq)).
% 1.32/0.52 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', cartprodfstpairEq)).
% 1.32/0.52 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', cartprodsndpairEq)).
% 1.32/0.52 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', cartprodpairsurjEq)).
% 1.32/0.52 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', app)).
% 1.32/0.52 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', infuncsetfunc)).
% 1.32/0.52 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ap2p)).
% 1.32/0.52 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', funcinfuncset)).
% 1.32/0.52 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', funcGraphProp1)).
% 1.32/0.52 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', funcGraphProp3)).
% 1.32/0.52 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', funcGraphProp2)).
% 1.32/0.52 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', funcextLem)).
% 1.32/0.52 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', funcGraphProp4)).
% 1.32/0.52 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', funcext)).
% 1.32/0.52 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', funcext2)).
% 1.32/0.52 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ap2apEq1)).
% 1.32/0.52 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3jjGGScXhA/E---3.1_4063247.p', ap2apEq2)).
% 1.32/0.52 thf(c_0_224, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X741:$i]:((((in @ X741 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X741 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 1.32/0.52 thf(c_0_225, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 1.32/0.52 thf(c_0_226, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 1.32/0.52 thf(c_0_227, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 1.32/0.52 thf(c_0_228, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.32/0.52 thf(c_0_229, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.32/0.52 thf(c_0_230, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.32/0.52 thf(c_0_231, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 1.32/0.52 thf(c_0_232, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.32/0.52 thf(c_0_233, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.32/0.52 thf(c_0_234, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 1.32/0.52 thf(c_0_235, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.32/0.52 thf(c_0_236, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.32/0.52 thf(c_0_237, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 1.32/0.52 thf(c_0_238, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.32/0.52 thf(c_0_239, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.32/0.52 thf(c_0_240, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.32/0.52 thf(c_0_241, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 1.32/0.52 thf(c_0_242, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 1.32/0.52 thf(c_0_243, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X741:$i]:((((in @ X741 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X741 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_224, c_0_225])).
% 1.32/0.52 thf(c_0_244, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 1.32/0.52 thf(c_0_245, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 1.32/0.52 thf(c_0_246, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 1.32/0.52 thf(c_0_247, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 1.32/0.52 thf(c_0_248, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 1.32/0.52 thf(c_0_249, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 1.32/0.52 thf(c_0_250, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 1.32/0.52 thf(c_0_251, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 1.32/0.52 thf(c_0_252, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[iftrueProp1])).
% 1.32/0.52 thf(c_0_253, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X712:$i]:(((((X6 @ X2 @ X712)))&(![X713:$i]:(((((X6 @ X2 @ X713)))=>(((X712)=(X713)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_227])).
% 1.32/0.52 thf(c_0_254, plain, ((descrp)=(![X1:$i > $o]:((((?[X714:$i]:(((((X1 @ X714)))&(![X715:$i]:(((((X1 @ X715)))=>(((X714)=(X715))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_227])).
% 1.32/0.52 thf(c_0_255, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.32/0.52 thf(c_0_256, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.32/0.52 thf(c_0_257, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.32/0.52 thf(c_0_258, plain, ((exuE1)=(![X1:$i > $o]:((((?[X716:$i]:(((((X1 @ X716)))&(![X717:$i]:(((((X1 @ X717)))=>(((X716)=(X717))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_229, c_0_227])).
% 1.32/0.52 thf(c_0_259, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X718:$i]:(((((X1 @ X718)))&(![X719:$i]:(((((X1 @ X719)))=>(((X718)=(X719))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_227])).
% 1.32/0.52 thf(c_0_260, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.32/0.52 thf(c_0_261, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_231])).
% 1.32/0.52 thf(c_0_262, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_231])).
% 1.32/0.52 thf(c_0_263, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_231])).
% 1.32/0.52 thf(c_0_264, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.32/0.52 thf(c_0_265, plain, ((exuE2)=(![X1:$i > $o]:((((?[X720:$i]:(((((X1 @ X720)))&(![X721:$i]:(((((X1 @ X721)))=>(((X720)=(X721))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_227])).
% 1.32/0.52 thf(c_0_266, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_231])).
% 1.32/0.52 thf(c_0_267, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 1.32/0.52 thf(c_0_268, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X722:$i]:(((((X1 @ X722)))&(![X723:$i]:(((((X1 @ X723)))=>(((X722)=(X723)))))))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_227])).
% 1.32/0.52 thf(c_0_269, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X724:$i]:(((((X1 @ X724)))&(![X725:$i]:(((((X1 @ X725)))=>(((X724)=(X725)))))))))))))))), inference(apply_def,[status(thm)],[c_0_235, c_0_227])).
% 1.32/0.52 thf(c_0_270, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X726:$i]:(((((X1 @ X726)))&(![X727:$i]:(((((X1 @ X727)))=>(((X726)=(X727)))))))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_227])).
% 1.32/0.52 thf(c_0_271, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X728:$i]:(((((X1 @ X728)))&(![X729:$i]:(((((X1 @ X729)))=>(((X728)=(X729))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_227])).
% 1.32/0.52 thf(c_0_272, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X730:$i]:(((((X1 @ X730)))&(![X731:$i]:(((((X1 @ X731)))=>(((X730)=(X731))))))))))<=>((?[X732:$i]:(((((X17 @ X732)))&(![X733:$i]:(((((X17 @ X733)))=>(((X732)=(X733)))))))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_227])).
% 1.32/0.52 thf(c_0_273, plain, ((exuEu)=(![X1:$i > $o]:((((?[X734:$i]:(((((X1 @ X734)))&(![X735:$i]:(((((X1 @ X735)))=>(((X734)=(X735))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_227])).
% 1.32/0.52 thf(c_0_274, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X736:$i]:(((((X1 @ X736)))&(![X737:$i]:(((((X1 @ X737)))=>(((X736)=(X737))))))))))=>((((?[X738:$i]:(((((X17 @ X738)))&(![X739:$i]:(((((X17 @ X739)))=>(((X738)=(X739))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_227])).
% 1.32/0.52 thf(c_0_275, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.32/0.52 thf(c_0_276, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 1.32/0.52 thf(c_0_277, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 1.32/0.52 thf(c_0_278, 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)))))=>((?[X740:$i]:((((in @ X740 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X740 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_225])).
% 1.32/0.52 thf(c_0_279, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X742:$i]:((((in @ X742 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X742 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_243])).
% 1.32/0.52 thf(c_0_280, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X743:$i]:((((in @ X743 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X743 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_243])).
% 1.32/0.52 thf(c_0_281, 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)))))=>((?[X744:$i]:((((in @ X744 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X744 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_243])).
% 1.32/0.52 thf(c_0_282, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X745:$i]:((((in @ X745 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X745 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_225])).
% 1.32/0.52 thf(c_0_283, axiom, ((theprop)=(![X21:$i]:((((?[X746:$i]:((((in @ X746 @ X21))&(((X21)=(setadjoin @ X746 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_225])).
% 1.32/0.52 thf(c_0_284, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X747:$i]:((((in @ X747 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X747 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_247, c_0_225])).
% 1.32/0.52 thf(c_0_285, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 1.32/0.52 thf(c_0_286, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 1.32/0.52 thf(c_0_287, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_248, c_0_249])).
% 1.32/0.52 thf(c_0_288, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 1.32/0.52 thf(c_0_289, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 1.32/0.52 thf(c_0_290, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 1.32/0.52 thf(c_0_291, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 1.32/0.52 thf(c_0_292, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:((((func @ X4 @ X5 @ X29))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X748:$i]:((((in @ X748 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X748 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[c_0_250, c_0_225])).
% 1.32/0.52 thf(c_0_293, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 1.32/0.52 thf(c_0_294, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 1.32/0.52 thf(c_0_295, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 1.32/0.52 thf(c_0_296, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 1.32/0.52 thf(c_0_297, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_249])).
% 1.32/0.52 thf(c_0_298, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_249])).
% 1.32/0.52 thf(c_0_299, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((?[X749:$i]:((((in @ X749 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X749 @ emptyset)))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_251, c_0_243])).
% 1.32/0.52 thf(c_0_300, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_249])).
% 1.32/0.52 thf(c_0_301, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_249])).
% 1.32/0.52 thf(c_0_302, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
% 1.32/0.52 thf(c_0_303, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
% 1.32/0.52 thf(c_0_304, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
% 1.32/0.52 thf(c_0_305, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
% 1.32/0.52 thf(c_0_306, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
% 1.32/0.52 thf(c_0_307, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 1.32/0.52 thf(c_0_308, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 1.32/0.52 thf(c_0_309, plain, ((epred1_0)<=>![X779:$i]:(?[X780:$i]:((((![X781:$i]:(((in @ X781 @ X780)=>![X782:$i]:(((in @ X782 @ X781)=>(in @ X782 @ X779)))))&![X783:$i, X784:$i]:((((in @ X783 @ X779)&(in @ X784 @ X779))=>(![X785:$i]:(((in @ X785 @ X780)=>((in @ X783 @ X785)<=>(in @ X784 @ X785))))=>((X783)=(X784))))))&![X786:$i, X787:$i]:((((in @ X786 @ X780)&(in @ X787 @ X780))=>(![X788:$i]:(((in @ X788 @ X786)=>(in @ X788 @ X787)))|![X789:$i]:(((in @ X789 @ X787)=>(in @ X789 @ X786)))))))&![X790:$i]:(((![X791:$i]:(((in @ X791 @ X790)=>(in @ X791 @ X779)))&?[X792:$i]:((in @ X792 @ X790)))=>?[X793:$i, X794:$i]:(((((in @ X793 @ X780)&(in @ X794 @ X790))&~(?[X795:$i]:(((in @ X795 @ X793)&(in @ X795 @ X790)))))&![X796:$i]:(((in @ X796 @ X780)=>(![X797:$i]:(((in @ X797 @ X796)=>(in @ X797 @ X793)))|(in @ X794 @ X796)))))))))))), introduced(definition)).
% 1.32/0.52 thf(c_0_310, negated_conjecture, ~((![X750:$i, X751:$i]:((![X752:$i]:(((in @ X752 @ X750)<=>(in @ X752 @ X751)))=>((X750)=(X751))))=>(![X753:$i]:(~(in @ X753 @ emptyset))=>(![X754:$i, X755:$i, X756:$i]:(((in @ X756 @ (setadjoin @ X754 @ X755))<=>(((X756)=(X754))|(in @ X756 @ X755))))=>(![X757:$i, X758:$i]:(((in @ X758 @ (powerset @ X757))<=>![X759:$i]:(((in @ X759 @ X758)=>(in @ X759 @ X757)))))=>(![X760:$i, X761:$i]:(((in @ X761 @ (setunion @ X760))<=>?[X762:$i]:(((in @ X761 @ X762)&(in @ X762 @ X760)))))=>((in @ emptyset @ omega)=>(![X763:$i]:(((in @ X763 @ omega)=>(in @ (setadjoin @ X763 @ X763) @ omega)))=>(![X764:$i]:((((in @ emptyset @ X764)&![X765:$i]:((((in @ X765 @ omega)&(in @ X765 @ X764))=>(in @ (setadjoin @ X765 @ X765) @ X764))))=>![X766:$i]:(((in @ X766 @ omega)=>(in @ X766 @ X764)))))=>(![X767:$i > $i > $o, X768:$i]:((![X769:$i]:(((in @ X769 @ X768)=>?[X770:$i]:(((X767 @ X769 @ X770)&![X771:$i]:(((X767 @ X769 @ X771)=>((X770)=(X771))))))))=>?[X772:$i]:(![X773:$i]:(((in @ X773 @ X772)<=>?[X774:$i]:(((in @ X774 @ X768)&(X767 @ X774 @ X773))))))))=>(![X775:$i]:((?[X776:$i]:((in @ X776 @ X775))=>?[X777:$i]:(((in @ X777 @ X775)&~(?[X778:$i]:(((in @ X778 @ X777)&(in @ X778 @ X775))))))))=>((epred1_0)=>(![X798:$i > $o]:((?[X799:$i]:(((X798 @ X799)&![X800:$i]:(((X798 @ X800)=>((X799)=(X800))))))=>(X798 @ (descr @ (^[Z0:$i]:(X798 @ Z0))))))=>(![X801:$i, X802:$i > $o, X803:$i]:(((in @ X803 @ X801)=>((X802 @ X803)=>(in @ X803 @ (dsetconstr @ X801 @ X802)))))=>(![X804:$i, X805:$i > $o, X806:$i]:(((in @ X806 @ (dsetconstr @ X804 @ X805))=>(in @ X806 @ X804)))=>(![X807:$i, X808:$i > $o, X809:$i]:(((in @ X809 @ (dsetconstr @ X807 @ X808))=>(X808 @ X809)))=>(![X810:$i > $o]:((?[X811:$i]:(((X810 @ X811)&![X812:$i]:(((X810 @ X812)=>((X811)=(X812))))))=>?[X813:$i]:(((X810 @ X813)&![X814:$i]:(((X810 @ X814)=>((X813)=(X814))))))))=>(![X815:$o, X816:$i]:(((in @ X816 @ (prop2set @ ((X815))))=>(X815)))=>(![X817:$i]:(((in @ X817 @ emptyset)=>![X818:$o]:((X818))))=>(![X819:$i]:(((in @ X819 @ emptyset)=>~($true)))=>(![X820:$i]:(~(in @ X820 @ emptyset))=>(![X821:$i > $o]:((?[X822:$i]:(((X821 @ X822)&![X823:$i]:(((X821 @ X823)=>((X822)=(X823))))))=>?[X824:$i]:((X821 @ X824))))=>(![X825:$i, X826:$i]:((![X827:$i]:(((in @ X827 @ X825)=>(in @ X827 @ X826)))=>(![X828:$i]:(((in @ X828 @ X826)=>(in @ X828 @ X825)))=>((X825)=(X826)))))=>(![X829:$i]:((![X830:$i]:(~(in @ X830 @ X829))=>((X829)=(emptyset))))=>(![X831:$i]:((![X832:$i]:(~(in @ X832 @ X831))=>((X831)=(emptyset))))=>(![X833:$i, X834:$i > $o, X835:$i]:(((in @ X835 @ X833)=>((in @ X835 @ (dsetconstr @ X833 @ X834))<=>(X834 @ X835))))=>(![X836:$i]:((((X836)!=(emptyset))=>?[X837:$i]:((in @ X837 @ X836))))=>(![X838:$i, X839:$i > $o, X840:$i]:(((in @ X840 @ X838)=>((X839 @ X840)=>((dsetconstr @ X838 @ X839)!=(emptyset)))))=>(![X841:$i]:((?[X842:$i]:((in @ X842 @ X841))=>((X841)!=(emptyset))))=>(![X843:$i, X844:$i]:((in @ X843 @ (setadjoin @ X843 @ X844)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X845:$i, X846:$i, X847:$i]:(((in @ X847 @ X846)=>(in @ X847 @ (setadjoin @ X845 @ X846))))=>(![X848:$i, X849:$i, X850:$i]:(((in @ X850 @ (setadjoin @ X848 @ X849))=>![X851:$o]:(((((X850)=(X848))=>(X851))=>(((in @ X850 @ X849)=>(X851))=>(X851))))))=>(![X852:$i, X853:$i, X854:$i]:(((in @ X854 @ (setadjoin @ X852 @ X853))=>(((X854)=(X852))|(in @ X854 @ X853))))=>(![X855:$i]:(((dsetconstr @ X855 @ (^[Z0:$i]:($true)))=(X855)))=>(![X856:$i, X857:$i]:((![X858:$i]:(((in @ X858 @ X857)=>(in @ X858 @ X856)))=>(in @ X857 @ (powerset @ X856))))=>(![X859:$i]:((in @ emptyset @ (powerset @ X859)))=>(![X860:$i]:((in @ emptyset @ (powerset @ X860)))=>(![X861:$i, X862:$i, X863:$i]:(((in @ X862 @ (powerset @ X861))=>((in @ X863 @ X862)=>(in @ X863 @ X861))))=>(![X864:$i, X865:$i, X866:$i]:(((in @ X865 @ X866)=>((in @ X866 @ X864)=>(in @ X865 @ (setunion @ X864)))))=>(![X867:$i, X868:$i]:(((in @ X868 @ (setunion @ X867))=>![X869:$o]:((![X870:$i]:(((in @ X868 @ X870)=>((in @ X870 @ X867)=>(X869))))=>(X869)))))=>(![X871:$i, X872:$i]:(((in @ X872 @ X871)=>(in @ X872 @ (powerset @ (setunion @ X871)))))=>(![X873:$i > $o]:((?[X874:$i]:(((X873 @ X874)&![X875:$i]:(((X873 @ X875)=>((X874)=(X875))))))=>?[X876:$i]:(![X877:$i]:(((X873 @ X877)<=>((X877)=(X876)))))))=>(![X878:$i]:((((X878)!=(emptyset))=>?[X879:$i]:(((in @ X879 @ X878)&$true))))=>(![X880:$i, X881:$i]:(((in @ X880 @ (setadjoin @ X881 @ emptyset))=>((X880)=(X881))))=>(![X882:$i, X883:$i]:((((X882)!=(X883))=>~(in @ X883 @ (setadjoin @ X882 @ emptyset))))=>(![X884:$i, X885:$i]:((((X884)=(X885))=>(in @ X884 @ (setadjoin @ X885 @ emptyset))))=>(![X886:$i, X887:$i]:(((in @ X886 @ (setadjoin @ X887 @ emptyset))=>(in @ X887 @ (setadjoin @ X886 @ emptyset))))=>(![X888:$i, X889:$i, X890:$i]:(((in @ X890 @ (setadjoin @ X888 @ (setadjoin @ X889 @ emptyset)))=>(((X890)=(X888))|((X890)=(X889)))))=>(![X891:$i, X892:$i]:((in @ X891 @ (setadjoin @ X891 @ (setadjoin @ X892 @ emptyset))))=>(![X893:$i, X894:$i]:((in @ X894 @ (setadjoin @ X893 @ (setadjoin @ X894 @ emptyset))))=>(![X895:$i, X896:$i > $o]:((?[X897:$i]:(((in @ X897 @ X895)&(X896 @ X897)))=>(((dsetconstr @ X895 @ X896)=(emptyset))=>~($true))))=>(![X898:$i > $o, X899:$i]:(((in @ X899 @ emptyset)=>(X898 @ X899)))=>(![X900:$i, X901:$i > $o]:((~(![X902:$i]:(((in @ X902 @ X900)=>(X901 @ X902))))=>?[X903:$i]:(((in @ X903 @ X900)&~((X901 @ X903))))))=>(![X904:$i, X905:$i > $o]:((![X906:$i]:(((in @ X906 @ X904)=>~((X905 @ X906))))=>~(?[X907:$i]:(((in @ X907 @ X904)&(X905 @ X907))))))=>(![X908:$i, X909:$i > $o]:((~(?[X910:$i]:(((in @ X910 @ X908)&(X909 @ X910))))=>![X911:$i]:(((in @ X911 @ X908)=>~((X909 @ X911))))))=>(![X912:$i, X913:$i > $o]:((?[X914:$i]:(((in @ X914 @ X912)&~((X913 @ X914))))=>~(![X915:$i]:(((in @ X915 @ X912)=>(X913 @ X915))))))=>(![X916:$o]:(((X916)=>(in @ emptyset @ (prop2set @ ((X916))))))=>(![X917:$o]:(((X917)=>(set2prop @ (prop2set @ ((X917))))))=>(![X918:$i, X919:$i > $o]:((~(?[X920:$i]:(((in @ X920 @ X918)&(X919 @ X920))))=>![X921:$i]:(((in @ X921 @ X918)=>~((X919 @ X921))))))=>(![X922:$i, X923:$i > $o]:((~(![X924:$i]:(((in @ X924 @ X922)=>(X923 @ X924))))=>?[X925:$i]:(((in @ X925 @ X922)&~((X923 @ X925))))))=>(![X926:$i > $o]:((?[X927:$i]:(((X926 @ X927)&![X928:$i]:(((X926 @ X928)=>((X927)=(X928))))))=>?[X929:$i]:(((X926 @ X929)&![X930:$i]:(((X926 @ X930)=>((X929)=(X930))))))))=>(![X931:$i > $o]:((?[X932:$i]:((X931 @ X932))=>(![X933:$i, X934:$i]:(((X931 @ X933)=>((X931 @ X934)=>((X933)=(X934)))))=>?[X935:$i]:(((X931 @ X935)&![X936:$i]:(((X931 @ X936)=>((X935)=(X936)))))))))=>(![X937:$i > $o]:((?[X938:$i]:(![X939:$i]:(((X937 @ X939)<=>((X939)=(X938)))))=>?[X940:$i]:(((X937 @ X940)&![X941:$i]:(((X937 @ X941)=>((X940)=(X941))))))))=>(![X942:$i, X943:$i]:((((X942)=(X943))=>![X944:$i, X945:$i]:((((X944)=(X945))=>((in @ X944 @ X942)=>(in @ X945 @ X943))))))=>(![X946:$i, X947:$i]:((((X946)=(X947))=>![X948:$i, X949:$i]:((((X948)=(X949))=>((in @ X948 @ X946)<=>(in @ X949 @ X947))))))=>(![X950:$i > $o]:((?[X951:$i]:(((X950 @ X951)&![X952:$i]:(((X950 @ X952)=>((X951)=(X952))))))=>![X953:$i, X954:$i]:(((X950 @ X953)=>((X950 @ X954)=>((X953)=(X954)))))))=>(![X955:$i > $o, X956:$i > $o]:((![X957:$i, X958:$i]:((((X957)=(X958))=>((X955 @ X957)<=>(X956 @ X958))))=>(?[X959:$i]:(((X955 @ X959)&![X960:$i]:(((X955 @ X960)=>((X959)=(X960))))))<=>?[X961:$i]:(((X956 @ X961)&![X962:$i]:(((X956 @ X962)=>((X961)=(X962)))))))))=>(((emptyset)=(emptyset))=>(![X963:$i, X964:$i]:((((X963)=(X964))=>![X965:$i, X966:$i]:((((X965)=(X966))=>((setadjoin @ X963 @ X965)=(setadjoin @ X964 @ X966))))))=>(![X967:$i, X968:$i]:((((X967)=(X968))=>((powerset @ X967)=(powerset @ X968))))=>(![X969:$i, X970:$i]:((((X969)=(X970))=>((setunion @ X969)=(setunion @ X970))))=>(((omega)=(omega))=>(![X971:$i > $o]:((?[X972:$i]:(((X971 @ X972)&![X973:$i]:(((X971 @ X973)=>((X972)=(X973))))))=>![X974:$i, X975:$i]:(((X971 @ X974)=>((X971 @ X975)=>((X974)=(X975)))))))=>(![X976:$i 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kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_278]), c_0_279]), c_0_280]), c_0_281]), singletonsuniq]), setukpairinjL1]), c_0_282]), c_0_283]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_284]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_294]), c_0_295]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_300]), c_0_301]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), c_0_306]), c_0_307]), c_0_308])])]), c_0_309])).
% 1.32/0.52 thf(c_0_311, negated_conjecture, ![X1453:$i, X1454:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1466:$i, X1467:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1475:$i, X1476:$i > $i > $o, X1477:$i, X1479:$i, X1482:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1489:$i, X1490:$i > $o, X1491:$i, X1493:$i, X1494:$i > $o, X1495:$i, X1496:$i, X1497:$i > $o, X1498:$i, X1499:$i, X1500:$i > $o, X1501:$i, X1502:$i > $o, X1503:$i, X1506:$i, X1507:$o, X1508:$i, X1509:$i, X1510:$o, X1511:$i, X1512:$i, X1513:$i > $o, X1514:$i, X1517:$i, X1518:$i, X1521:$i, X1523:$i, X1525:$i, X1526:$i > $o, X1527:$i, X1528:$i, X1530:$i, X1531:$i > $o, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$o, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$o, X1563:$i, X1564:$i, X1565:$i > $o, X1566:$i, X1569:$i, X1570:$i, X1571:$i, X1573:$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 > $o, X1590:$i, X1591:$i > $o, X1592:$i, X1593:$i, X1594:$i > $o, X1595:$i, X1597:$i, X1598:$i > $o, X1600:$i, X1601:$i, X1602:$i > $o, X1604:$i, X1605:$i, X1606:$i > $o, X1607:$i, X1609:$o, X1610:$o, X1611:$i, X1612:$i > $o, X1614:$i, X1615:$i, X1616:$i > $o, X1617:$i, X1619:$i > $o, X1620:$i, X1623:$i, X1624:$i > $o, X1625:$i, X1629:$i, X1630:$i > $o, X1631:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i > $o, X1644:$i, X1646:$i, X1647:$i, X1648:$i > $o, X1649:$i > $o, X1652:$i, X1655:$i, X1656:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i > $o, X1669:$i, X1671:$i, X1672:$i, X1673:$i > $o, X1674:$i > $o, X1677:$i, X1679:$i, X1681:$i, X1682:$i, X1683:$i > $o, X1684:$i > $o, X1687:$i, X1688:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i > $o, X1735:$i, X1736:$i > $o, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$o, X1749:$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, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, 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:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$o, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i > $o, X1891:$i, X1893:$i, X1894:$i > $o, X1895:$i, X1897:$i, X1898:$i > $o, X1899:$i, X1902:$i, X1903:$i > $o, X1906:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i > $i > $o, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i > $i > $o, X1988:$i, X1989:$i, X1990:$i > $i > $o, X1991:$i, X1992:$i, X1993:$i > $i > $o, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i > $i > $o, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i > $i > $o, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i > $i > $o, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i > $i, X2038:$i, X2039:$i, X2040:$i > $i, X2042:$i, X2043:$i, X2044:$i > $i, X2046:$i, X2047:$i, X2048:$i, X2049:$i > $o, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i > $o, X2059:$i, X2060:$i, X2061:$i > $o, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i > $i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i > $i, X2134:$i, X2135:$i, X2136:$i > $i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$o, X2144:$i, X2145:$i, X2146:$i, X2147:$o, X2148:$i, X2149:$i]:((((~(in @ (esk1_2 @ X1453 @ X1454) @ X1453)|~(in @ (esk1_2 @ X1453 @ X1454) @ X1454)|((X1453)=(X1454)))&((in @ (esk1_2 @ X1453 @ X1454) @ X1453)|(in @ (esk1_2 @ X1453 @ X1454) @ X1454)|((X1453)=(X1454))))&(~(in @ X1456 @ emptyset)&(((~(in @ X1459 @ (setadjoin @ X1457 @ X1458))|(((X1459)=(X1457))|(in @ X1459 @ X1458)))&((((X1459)!=(X1457))|(in @ X1459 @ (setadjoin @ X1457 @ X1458)))&(~(in @ X1459 @ X1458)|(in @ X1459 @ (setadjoin @ X1457 @ X1458)))))&(((~(in @ X1461 @ (powerset @ X1460))|(~(in @ X1462 @ X1461)|(in @ X1462 @ X1460)))&(((in @ (esk2_2 @ X1463 @ X1464) @ X1464)|(in @ X1464 @ (powerset @ X1463)))&(~(in @ (esk2_2 @ X1463 @ X1464) @ X1463)|(in @ X1464 @ (powerset @ X1463)))))&(((((in @ X1467 @ (esk3_2 @ X1466 @ X1467))|~(in @ X1467 @ (setunion @ X1466)))&((in @ (esk3_2 @ X1466 @ X1467) @ X1466)|~(in @ X1467 @ (setunion @ X1466))))&(~(in @ X1470 @ X1471)|~(in @ X1471 @ X1469)|(in @ X1470 @ (setunion @ X1469))))&((in @ emptyset @ omega)&((~(in @ X1472 @ omega)|(in @ (setadjoin @ X1472 @ X1472) @ omega))&(((((in @ (esk4_1 @ X1473) @ omega)|~(in @ emptyset @ X1473)|(~(in @ X1475 @ omega)|(in @ X1475 @ X1473)))&((in @ (esk4_1 @ X1473) @ X1473)|~(in @ emptyset @ X1473)|(~(in @ X1475 @ omega)|(in @ X1475 @ X1473))))&(~(in @ (setadjoin @ (esk4_1 @ X1473) @ (esk4_1 @ X1473)) @ X1473)|~(in @ emptyset @ X1473)|(~(in @ X1475 @ omega)|(in @ X1475 @ X1473))))&((((((in @ (esk8_3 @ X1476 @ X1477 @ X1482) @ X1477)|~(in @ X1482 @ (esk7_2 @ X1476 @ X1477))|(in @ (esk5_2 @ X1476 @ X1477) @ X1477))&((X1476 @ (esk8_3 @ X1476 @ X1477 @ X1482) @ X1482)|~(in @ X1482 @ (esk7_2 @ X1476 @ X1477))|(in @ (esk5_2 @ X1476 @ X1477) @ X1477)))&(~(in @ X1485 @ X1477)|~(X1476 @ X1485 @ X1484)|(in @ X1484 @ (esk7_2 @ X1476 @ X1477))|(in @ (esk5_2 @ X1476 @ X1477) @ X1477)))&(((((in @ (esk8_3 @ X1476 @ X1477 @ X1482) @ X1477)|~(in @ X1482 @ (esk7_2 @ X1476 @ X1477))|((X1476 @ (esk5_2 @ X1476 @ X1477) @ (esk6_3 @ X1476 @ X1477 @ X1479))|~(X1476 @ (esk5_2 @ X1476 @ X1477) @ X1479)))&((X1476 @ (esk8_3 @ X1476 @ X1477 @ X1482) @ X1482)|~(in @ X1482 @ (esk7_2 @ X1476 @ X1477))|((X1476 @ (esk5_2 @ X1476 @ X1477) @ (esk6_3 @ X1476 @ X1477 @ X1479))|~(X1476 @ (esk5_2 @ X1476 @ X1477) @ X1479))))&(~(in @ X1485 @ X1477)|~(X1476 @ X1485 @ X1484)|(in @ X1484 @ (esk7_2 @ X1476 @ X1477))|((X1476 @ (esk5_2 @ X1476 @ X1477) @ (esk6_3 @ X1476 @ X1477 @ X1479))|~(X1476 @ (esk5_2 @ X1476 @ X1477) @ X1479))))&((((in @ (esk8_3 @ X1476 @ X1477 @ X1482) @ X1477)|~(in @ X1482 @ (esk7_2 @ X1476 @ X1477))|(((X1479)!=(esk6_3 @ X1476 @ X1477 @ X1479))|~(X1476 @ (esk5_2 @ X1476 @ X1477) @ X1479)))&((X1476 @ (esk8_3 @ X1476 @ X1477 @ X1482) @ X1482)|~(in @ X1482 @ (esk7_2 @ X1476 @ X1477))|(((X1479)!=(esk6_3 @ X1476 @ X1477 @ X1479))|~(X1476 @ (esk5_2 @ X1476 @ X1477) @ X1479))))&(~(in @ X1485 @ X1477)|~(X1476 @ X1485 @ X1484)|(in @ X1484 @ (esk7_2 @ X1476 @ X1477))|(((X1479)!=(esk6_3 @ X1476 @ X1477 @ X1479))|~(X1476 @ (esk5_2 @ X1476 @ X1477) @ X1479))))))&((((in @ (esk9_1 @ X1486) @ X1486)|~(in @ X1487 @ X1486))&(~(in @ X1489 @ (esk9_1 @ X1486))|~(in @ X1489 @ X1486)|~(in @ X1487 @ X1486)))&((epred1_0)&((((X1490 @ (esk10_2 @ X1490 @ X1491))|~(X1490 @ X1491)|(X1490 @ (descr @ X1490)))&(((X1491)!=(esk10_2 @ X1490 @ X1491))|~(X1490 @ X1491)|(X1490 @ (descr @ X1490))))&((~(in @ X1495 @ X1493)|(~(X1494 @ X1495)|(in @ X1495 @ (dsetconstr @ X1493 @ X1494))))&((~(in @ X1498 @ (dsetconstr @ X1496 @ X1497))|(in @ X1498 @ X1496))&((~(in @ X1501 @ (dsetconstr @ X1499 @ X1500))|(X1500 @ X1501))&(((((X1502 @ (esk12_1 @ X1502))|((X1502 @ (esk11_2 @ X1502 @ X1503))|~(X1502 @ X1503)))&(~(X1502 @ X1506)|((esk12_1 @ X1502)=(X1506))|((X1502 @ (esk11_2 @ X1502 @ X1503))|~(X1502 @ X1503))))&(((X1502 @ (esk12_1 @ X1502))|(((X1503)!=(esk11_2 @ X1502 @ X1503))|~(X1502 @ X1503)))&(~(X1502 @ X1506)|((esk12_1 @ X1502)=(X1506))|(((X1503)!=(esk11_2 @ X1502 @ X1503))|~(X1502 @ X1503)))))&((~(in @ X1508 @ (prop2set @ ((X1507))))|(X1507))&((~(in @ X1509 @ emptyset)|(X1510))&((~(in @ X1511 @ emptyset)|~($true))&(~(in @ X1512 @ emptyset)&((((X1513 @ (esk13_2 @ X1513 @ X1514))|~(X1513 @ X1514)|(X1513 @ (esk14_1 @ X1513)))&(((X1514)!=(esk13_2 @ X1513 @ X1514))|~(X1513 @ X1514)|(X1513 @ (esk14_1 @ X1513))))&(((((in @ (esk16_2 @ X1517 @ X1518) @ X1518)|((X1517)=(X1518))|(in @ (esk15_2 @ X1517 @ X1518) @ X1517))&(~(in @ (esk16_2 @ X1517 @ X1518) @ X1517)|((X1517)=(X1518))|(in @ (esk15_2 @ X1517 @ X1518) @ X1517)))&(((in @ (esk16_2 @ X1517 @ X1518) @ X1518)|((X1517)=(X1518))|~(in @ (esk15_2 @ X1517 @ X1518) @ X1518))&(~(in @ (esk16_2 @ X1517 @ X1518) @ X1517)|((X1517)=(X1518))|~(in @ (esk15_2 @ X1517 @ X1518) @ X1518))))&(((in @ (esk17_1 @ X1521) @ X1521)|((X1521)=(emptyset)))&(((in @ (esk18_1 @ X1523) @ X1523)|((X1523)=(emptyset)))&(((~(in @ X1527 @ (dsetconstr @ X1525 @ X1526))|(X1526 @ X1527)|~(in @ X1527 @ X1525))&(~(X1526 @ X1527)|(in @ X1527 @ (dsetconstr @ X1525 @ X1526))|~(in @ X1527 @ X1525)))&((((X1528)=(emptyset))|(in @ (esk19_1 @ X1528) @ X1528))&((~(in @ X1532 @ X1530)|(~(X1531 @ X1532)|((dsetconstr @ X1530 @ X1531)!=(emptyset))))&((~(in @ X1534 @ X1533)|((X1533)!=(emptyset)))&((in @ X1535 @ (setadjoin @ X1535 @ X1536))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1539 @ X1538)|(in @ X1539 @ (setadjoin @ X1537 @ X1538)))&(((((in @ X1542 @ X1541)|(X1543)|((X1542)=(X1540))|~(in @ X1542 @ (setadjoin @ X1540 @ X1541)))&(~(X1543)|(X1543)|((X1542)=(X1540))|~(in @ X1542 @ (setadjoin @ X1540 @ X1541))))&(((in @ X1542 @ X1541)|(X1543)|~(X1543)|~(in @ X1542 @ (setadjoin @ X1540 @ 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(kpair @ X1971 @ X1972))=(X1971))))&((~(in @ X1975 @ X1973)|(~(in @ X1976 @ X1974)|((ksnd @ (kpair @ X1975 @ X1976))=(X1976))))&((~(in @ X1979 @ (cartprod @ X1977 @ X1978))|((kpair @ (kfst @ X1979) @ (ksnd @ X1979))=(X1979)))&((~(in @ X1983 @ X1980)|(~(in @ X1984 @ X1981)|(~(X1982 @ X1983 @ X1984)|(in @ (kpair @ X1983 @ X1984) @ (dpsetconstr @ X1980 @ X1981 @ X1982)))))&((subset @ (dpsetconstr @ X1985 @ X1986 @ X1987) @ (cartprod @ X1985 @ X1986))&((subset @ (dpsetconstr @ X1988 @ X1989 @ X1990) @ (cartprod @ X1988 @ X1989))&((~(in @ X1994 @ X1991)|(~(in @ X1995 @ X1992)|(~(in @ (kpair @ X1994 @ X1995) @ (dpsetconstr @ X1991 @ X1992 @ X1993))|(X1993 @ X1994 @ X1995))))&((~(in @ (kpair @ X1999 @ X2000) @ (dpsetconstr @ X1996 @ X1997 @ X1998))|(in @ X1999 @ X1996))&((~(in @ (kpair @ X2004 @ X2005) @ (dpsetconstr @ X2001 @ X2002 @ X2003))|(in @ X2005 @ X2002))&((~(in @ (kpair @ X2009 @ X2010) @ (dpsetconstr @ X2006 @ X2007 @ X2008))|(X2008 @ X2009 @ X2010))&((((in @ (esk69_4 @ X2011 @ X2012 @ X2013 @ X2014) @ (dsetconstr @ X2012 @ (^[Z0:$i]:((in @ (kpair @ X2014 @ Z0) @ X2013)))))|~(in @ X2014 @ X2011)|~(func @ X2011 @ X2012 @ X2013))&(((dsetconstr @ X2012 @ (^[Z0:$i]:((in @ (kpair @ X2014 @ Z0) @ X2013))))=(setadjoin @ (esk69_4 @ X2011 @ X2012 @ X2013 @ X2014) @ emptyset))|~(in @ X2014 @ X2011)|~(func @ X2011 @ X2012 @ X2013)))&((~(func @ X2016 @ X2017 @ X2018)|(~(in @ X2019 @ X2016)|(in @ (setunion @ (dsetconstr @ X2017 @ (^[Z0:$i]:((in @ (kpair @ X2019 @ Z0) @ X2018))))) @ X2017)))&((~(func @ X2020 @ X2021 @ X2022)|(~(in @ X2023 @ X2020)|(in @ (ap @ X2020 @ X2021 @ X2022 @ X2023) @ X2021)))&((~(in @ X2026 @ (funcSet @ X2024 @ X2025))|(func @ X2024 @ X2025 @ X2026))&((~(in @ X2029 @ (funcSet @ X2027 @ X2028))|(~(in @ X2030 @ X2027)|(in @ (ap @ X2027 @ X2028 @ X2029 @ X2030) @ X2028)))&((~(func @ X2031 @ X2032 @ X2033)|(in @ X2033 @ (funcSet @ X2031 @ X2032)))&((((in @ (esk70_3 @ X2034 @ X2035 @ X2036) @ X2034)|(func @ X2034 @ X2035 @ (dpsetconstr @ X2034 @ X2035 @ (^[Z0:$i]:($eq @ (X2036 @ Z0))))))&(~(in @ (X2036 @ (esk70_3 @ X2034 @ X2035 @ X2036)) @ X2035)|(func @ X2034 @ X2035 @ (dpsetconstr @ X2034 @ X2035 @ (^[Z0:$i]:($eq @ (X2036 @ Z0)))))))&((((in @ (esk71_3 @ X2038 @ X2039 @ X2040) @ X2038)|(func @ X2038 @ X2039 @ (lam @ X2038 @ X2039 @ X2040)))&(~(in @ (X2040 @ (esk71_3 @ X2038 @ X2039 @ X2040)) @ X2039)|(func @ X2038 @ X2039 @ (lam @ X2038 @ X2039 @ X2040))))&((((in @ (esk72_3 @ X2042 @ X2043 @ X2044) @ X2042)|(in @ (lam @ X2042 @ X2043 @ X2044) @ (funcSet @ X2042 @ X2043)))&(~(in @ (X2044 @ (esk72_3 @ X2042 @ X2043 @ X2044)) @ X2043)|(in @ (lam @ X2042 @ X2043 @ X2044) @ (funcSet @ X2042 @ X2043))))&((((in @ (esk73_4 @ X2046 @ X2047 @ X2048 @ X2049) @ X2046)|(~(in @ X2052 @ X2048)|(X2049 @ X2052))|~(subset @ X2048 @ (cartprod @ X2046 @ X2047)))&(((in @ (esk74_4 @ X2046 @ X2047 @ X2048 @ X2049) @ X2047)|(~(in @ X2052 @ X2048)|(X2049 @ X2052))|~(subset @ X2048 @ (cartprod @ X2046 @ X2047)))&(((in @ (kpair @ (esk73_4 @ X2046 @ X2047 @ X2048 @ X2049) @ (esk74_4 @ X2046 @ X2047 @ X2048 @ X2049)) @ X2048)|(~(in @ X2052 @ X2048)|(X2049 @ X2052))|~(subset @ X2048 @ (cartprod @ X2046 @ X2047)))&(~(X2049 @ (kpair @ (esk73_4 @ X2046 @ X2047 @ X2048 @ X2049) @ (esk74_4 @ X2046 @ X2047 @ X2048 @ X2049)))|(~(in @ X2052 @ X2048)|(X2049 @ X2052))|~(subset @ X2048 @ (cartprod @ X2046 @ X2047))))))&((((in @ (esk75_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2053)|(~(in @ X2059 @ X2055)|(X2056 @ X2059))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (esk76_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2054)|(~(in @ X2059 @ X2055)|(X2056 @ X2059))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (kpair @ (esk75_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk76_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2055)|(~(in @ X2059 @ X2055)|(X2056 @ X2059))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(~(X2056 @ (kpair @ (esk75_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk76_4 @ X2053 @ X2054 @ X2055 @ X2056)))|(~(in @ X2059 @ X2055)|(X2056 @ X2059))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054))))))&((~(in @ X2062 @ (dsetconstr @ X2060 @ X2061))|((dsetconstr @ X2060 @ X2061)!=(setadjoin @ X2062 @ emptyset))|(~(in @ X2063 @ X2060)|(~(in @ X2064 @ X2060)|(~(X2061 @ X2063)|(~(X2061 @ X2064)|((X2063)=(X2064)))))))&((~(func @ X2065 @ X2066 @ X2067)|(~(in @ X2068 @ X2065)|(in @ (kpair @ X2068 @ (ap @ X2065 @ X2066 @ X2067 @ X2068)) @ X2067)))&((~(in @ X2071 @ (funcSet @ X2069 @ X2070))|(~(in @ X2072 @ X2069)|(in @ (kpair @ X2072 @ (ap @ X2069 @ X2070 @ X2071 @ X2072)) @ X2071)))&((~(func @ X2073 @ X2074 @ X2075)|(~(in @ X2076 @ X2073)|(~(in @ X2077 @ X2074)|(~(in @ (kpair @ X2076 @ X2077) @ X2075)|((ap @ X2073 @ X2074 @ X2075 @ X2076)=(X2077))))))&((((in @ (esk77_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|(~(in @ X2083 @ X2078)|(~(in @ X2084 @ X2079)|(~(in @ (kpair @ X2083 @ X2084) @ X2081)|(in @ (kpair @ X2083 @ X2084) @ X2080))))|~(func @ X2078 @ X2079 @ X2081)|~(func @ X2078 @ X2079 @ X2080))&(((ap @ X2078 @ X2079 @ X2080 @ (esk77_4 @ X2078 @ X2079 @ X2080 @ X2081))!=(ap @ X2078 @ X2079 @ X2081 @ (esk77_4 @ X2078 @ X2079 @ X2080 @ X2081)))|(~(in @ X2083 @ X2078)|(~(in @ X2084 @ X2079)|(~(in @ (kpair @ X2083 @ X2084) @ X2081)|(in @ (kpair @ X2083 @ X2084) @ X2080))))|~(func @ X2078 @ X2079 @ X2081)|~(func @ X2078 @ X2079 @ X2080)))&((~(in @ X2087 @ (funcSet @ X2085 @ X2086))|(~(in @ X2088 @ X2085)|(~(in @ X2089 @ X2086)|(~(in @ (kpair @ X2088 @ X2089) @ X2087)|((ap @ X2085 @ X2086 @ X2087 @ X2088)=(X2089))))))&((((in @ (esk78_4 @ X2090 @ X2091 @ X2092 @ X2093) @ X2090)|(subset @ X2092 @ X2093)|~(subset @ X2093 @ (cartprod @ X2090 @ X2091))|~(subset @ X2092 @ (cartprod @ X2090 @ X2091)))&(((in @ (esk79_4 @ X2090 @ X2091 @ X2092 @ X2093) @ X2091)|(subset @ X2092 @ X2093)|~(subset @ X2093 @ (cartprod @ X2090 @ X2091))|~(subset @ X2092 @ (cartprod @ X2090 @ X2091)))&(((in @ (kpair @ (esk78_4 @ X2090 @ X2091 @ X2092 @ X2093) @ (esk79_4 @ X2090 @ X2091 @ X2092 @ X2093)) @ X2092)|(subset @ X2092 @ X2093)|~(subset @ X2093 @ (cartprod @ X2090 @ X2091))|~(subset @ X2092 @ (cartprod @ X2090 @ X2091)))&(~(in @ (kpair @ (esk78_4 @ X2090 @ X2091 @ X2092 @ X2093) @ (esk79_4 @ X2090 @ X2091 @ X2092 @ X2093)) @ X2093)|(subset @ X2092 @ X2093)|~(subset @ X2093 @ (cartprod @ X2090 @ X2091))|~(subset @ X2092 @ (cartprod @ X2090 @ X2091))))))&(((((in @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|((X2098)=(X2099))|(in @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|((X2098)=(X2099))|(in @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|((X2098)=(X2099))|(in @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(~(in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|((X2098)=(X2099))|(in @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097))))))&((((in @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|((X2098)=(X2099))|(in @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|((X2098)=(X2099))|(in @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|((X2098)=(X2099))|(in @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(~(in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|((X2098)=(X2099))|(in @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097))))))&((((in @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|((X2098)=(X2099))|(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|((X2098)=(X2099))|(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|((X2098)=(X2099))|(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(~(in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|((X2098)=(X2099))|(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097))))))&(((in @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|((X2098)=(X2099))|~(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|((X2098)=(X2099))|~(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|((X2098)=(X2099))|~(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(~(in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|((X2098)=(X2099))|~(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))))))))&((((in @ (esk84_4 @ X2104 @ X2105 @ X2106 @ X2107) @ X2104)|((X2106)=(X2107))|~(func @ X2104 @ X2105 @ X2107)|~(func @ X2104 @ X2105 @ X2106))&(((ap @ X2104 @ X2105 @ X2106 @ (esk84_4 @ X2104 @ X2105 @ X2106 @ X2107))!=(ap @ X2104 @ X2105 @ X2107 @ (esk84_4 @ X2104 @ X2105 @ X2106 @ X2107)))|((X2106)=(X2107))|~(func @ X2104 @ X2105 @ X2107)|~(func @ X2104 @ X2105 @ X2106)))&((((in @ (esk85_4 @ X2109 @ X2110 @ X2111 @ X2112) @ X2109)|((X2111)=(X2112))|~(in @ X2112 @ (funcSet @ X2109 @ X2110))|~(in @ X2111 @ (funcSet @ X2109 @ X2110)))&(((ap @ X2109 @ X2110 @ X2111 @ (esk85_4 @ X2109 @ X2110 @ X2111 @ X2112))!=(ap @ X2109 @ X2110 @ X2112 @ (esk85_4 @ X2109 @ X2110 @ X2111 @ X2112)))|((X2111)=(X2112))|~(in @ X2112 @ (funcSet @ X2109 @ X2110))|~(in @ X2111 @ (funcSet @ X2109 @ X2110))))&((~(in @ X2116 @ (funcSet @ X2114 @ X2115))|(~(in @ X2117 @ X2114)|((ap @ X2114 @ X2115 @ X2116 @ X2117)=(ap @ X2114 @ X2115 @ X2116 @ X2117))))&((~(func @ X2118 @ X2119 @ X2120)|(~(in @ X2121 @ X2118)|((ap @ X2118 @ X2119 @ X2120 @ X2121)=(ap @ X2118 @ X2119 @ X2120 @ X2121))))&((((in @ (esk86_3 @ X2122 @ X2123 @ X2124) @ X2122)|(~(in @ X2126 @ X2122)|((ap @ X2122 @ X2123 @ (lam @ X2122 @ X2123 @ X2124) @ X2126)=(X2124 @ X2126))))&(~(in @ (X2124 @ (esk86_3 @ X2122 @ X2123 @ X2124)) @ X2123)|(~(in @ X2126 @ X2122)|((ap @ X2122 @ X2123 @ (lam @ X2122 @ X2123 @ X2124) @ X2126)=(X2124 @ X2126)))))&((~(func @ X2127 @ X2128 @ X2129)|((lam @ X2127 @ X2128 @ (ap @ X2127 @ X2128 @ X2129))=(X2129)))&((((in @ (esk87_3 @ X2130 @ X2131 @ X2132) @ X2130)|((lam @ X2130 @ X2131 @ X2132)=(lam @ X2130 @ X2131 @ X2132)))&(~(in @ (X2132 @ (esk87_3 @ X2130 @ X2131 @ X2132)) @ X2131)|((lam @ X2130 @ X2131 @ X2132)=(lam @ X2130 @ X2131 @ X2132))))&((((in @ (esk88_3 @ X2134 @ X2135 @ X2136) @ X2134)|(~(in @ X2138 @ X2134)|((ap @ X2134 @ X2135 @ (lam @ X2134 @ X2135 @ X2136) @ X2138)=(X2136 @ X2138))))&(~(in @ (X2136 @ (esk88_3 @ X2134 @ X2135 @ X2136)) @ X2135)|(~(in @ X2138 @ X2134)|((ap @ X2134 @ X2135 @ (lam @ X2134 @ X2135 @ X2136) @ X2138)=(X2136 @ X2138)))))&((~(in @ X2141 @ (funcSet @ X2139 @ X2140))|((lam @ X2139 @ X2140 @ (ap @ X2139 @ X2140 @ X2141))=(X2141)))&((~(in @ X2144 @ X2142)|(~(in @ X2145 @ X2142)|((X2143)|(in @ X2145 @ (dsetconstr @ X2142 @ (^[Z0:$i]:((((((X2143))&(((Z0)=(X2144)))))|(((~((X2143)))&(((Z0)=(X2145)))))))))))))&((~(in @ X2148 @ X2146)|(~(in @ X2149 @ X2146)|((X2147)|((dsetconstr @ X2146 @ (^[Z0:$i]:((((((X2147))&(((Z0)=(X2148)))))|(((~((X2147)))&(((Z0)=(X2149)))))))))=(setadjoin @ X2149 @ emptyset)))))&((in @ esk90_0 @ esk89_0)&((in @ esk91_0 @ esk89_0)&((epred2_0)&~(in @ esk90_0 @ (dsetconstr @ esk89_0 @ (^[Z0:$i]:((((((epred2_0))&(((Z0)=(esk90_0)))))|(((~((epred2_0)))&(((Z0)=(esk91_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_310])])])])])])])).
% 1.32/0.53 thf(c_0_312, plain, ![X2173:$i]:(((epred3_0 @ X2173)<=>(((epred2_0)&((X2173)=(esk90_0)))|(~((epred2_0))&((X2173)=(esk91_0)))))), introduced(definition)).
% 1.32/0.53 thf(c_0_313, plain, ![X2186:$i]:(((((~(epred2_0)|(epred2_0)|~(epred3_0 @ X2186))&(((X2186)=(esk91_0))|(epred2_0)|~(epred3_0 @ X2186)))&((~(epred2_0)|((X2186)=(esk90_0))|~(epred3_0 @ X2186))&(((X2186)=(esk91_0))|((X2186)=(esk90_0))|~(epred3_0 @ X2186))))&((~(epred2_0)|((X2186)!=(esk90_0))|(epred3_0 @ X2186))&((epred2_0)|((X2186)!=(esk91_0))|(epred3_0 @ X2186))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])])).
% 1.32/0.53 thf(c_0_314, negated_conjecture, ~((((in @ esk90_0 @ (dsetconstr @ esk89_0 @ epred3_0)))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_311]), c_0_312])).
% 1.32/0.53 thf(c_0_315, plain, ![X2:$i]:(((epred3_0 @ X2)|~((epred2_0))|((X2)!=(esk90_0)))), inference(split_conjunct,[status(thm)],[c_0_313])).
% 1.32/0.53 thf(c_0_316, negated_conjecture, (epred2_0), inference(split_conjunct,[status(thm)],[c_0_311])).
% 1.32/0.53 thf(c_0_317, negated_conjecture, ~((in @ esk90_0 @ (dsetconstr @ esk89_0 @ epred3_0))), inference(cn,[status(thm)],[c_0_314])).
% 1.32/0.53 thf(c_0_318, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_311])).
% 1.32/0.53 thf(c_0_319, negated_conjecture, (in @ esk90_0 @ esk89_0), inference(split_conjunct,[status(thm)],[c_0_311])).
% 1.32/0.53 thf(c_0_320, plain, (epred3_0 @ esk90_0), inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_315, c_0_316])])])).
% 1.32/0.53 thf(c_0_321, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_317, c_0_318]), c_0_319]), c_0_320])]), ['proof']).
% 1.32/0.53 % SZS output end CNFRefutation
% 1.32/0.53 % Parsed axioms : 479
% 1.32/0.53 % Removed by relevancy pruning/SinE : 0
% 1.32/0.53 % Initial clauses : 683
% 1.32/0.53 % Removed in clause preprocessing : 291
% 1.32/0.53 % Initial clauses in saturation : 392
% 1.32/0.53 % Processed clauses : 647
% 1.32/0.53 % ...of these trivial : 14
% 1.32/0.53 % ...subsumed : 66
% 1.32/0.53 % ...remaining for further processing : 567
% 1.32/0.53 % Other redundant clauses eliminated : 27
% 1.32/0.53 % Clauses deleted for lack of memory : 0
% 1.32/0.53 % Backward-subsumed : 0
% 1.32/0.53 % Backward-rewritten : 5
% 1.32/0.53 % Generated clauses : 1377
% 1.32/0.53 % ...of the previous two non-redundant : 1243
% 1.32/0.53 % ...aggressively subsumed : 0
% 1.32/0.53 % Contextual simplify-reflections : 1
% 1.32/0.53 % Paramodulations : 1324
% 1.32/0.53 % Factorizations : 0
% 1.32/0.53 % NegExts : 10
% 1.32/0.53 % Equation resolutions : 30
% 1.32/0.53 % Disequality decompositions : 0
% 1.32/0.53 % Total rewrite steps : 161
% 1.32/0.53 % ...of those cached : 103
% 1.32/0.53 % Propositional unsat checks : 0
% 1.32/0.53 % Propositional check models : 0
% 1.32/0.53 % Propositional check unsatisfiable : 0
% 1.32/0.53 % Propositional clauses : 0
% 1.32/0.53 % Propositional clauses after purity: 0
% 1.32/0.53 % Propositional unsat core size : 0
% 1.32/0.53 % Propositional preprocessing time : 0.000
% 1.32/0.53 % Propositional encoding time : 0.000
% 1.32/0.53 % Propositional solver time : 0.000
% 1.32/0.53 % Success case prop preproc time : 0.000
% 1.32/0.53 % Success case prop encoding time : 0.000
% 1.32/0.53 % Success case prop solver time : 0.000
% 1.32/0.53 % Current number of processed clauses : 200
% 1.32/0.53 % Positive orientable unit clauses : 52
% 1.32/0.53 % Positive unorientable unit clauses: 0
% 1.32/0.53 % Negative unit clauses : 4
% 1.32/0.53 % Non-unit-clauses : 144
% 1.32/0.53 % Current number of unprocessed clauses: 1325
% 1.32/0.53 % ...number of literals in the above : 3603
% 1.32/0.53 % Current number of archived formulas : 0
% 1.32/0.53 % Current number of archived clauses : 351
% 1.32/0.53 % Clause-clause subsumption calls (NU) : 20233
% 1.32/0.53 % Rec. Clause-clause subsumption calls : 7788
% 1.32/0.53 % Non-unit clause-clause subsumptions : 42
% 1.32/0.53 % Unit Clause-clause subsumption calls : 182
% 1.32/0.53 % Rewrite failures with RHS unbound : 0
% 1.32/0.53 % BW rewrite match attempts : 27
% 1.32/0.53 % BW rewrite match successes : 3
% 1.32/0.53 % Condensation attempts : 0
% 1.32/0.53 % Condensation successes : 0
% 1.32/0.53 % Termbank termtop insertions : 88638
% 1.32/0.53 % Search garbage collected termcells : 23168
% 1.32/0.53
% 1.32/0.53 % -------------------------------------------------
% 1.32/0.53 % User time : 0.173 s
% 1.32/0.53 % System time : 0.024 s
% 1.32/0.53 % Total time : 0.197 s
% 1.32/0.53 % Maximum resident set size: 9524 pages
% 1.32/0.53
% 1.32/0.53 % -------------------------------------------------
% 1.32/0.53 % User time : 0.473 s
% 1.32/0.53 % System time : 0.057 s
% 1.32/0.53 % Total time : 0.530 s
% 1.32/0.53 % Maximum resident set size: 5632 pages
% 1.32/0.53 % E exiting
%------------------------------------------------------------------------------