%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU700^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:27:27 AM UTC 2026
% Result : Theorem 0.58s 0.47s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU700^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:17:50 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.21/0.28 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p
% 0.58/0.47 % Version: 3.5.1-ho
% 0.58/0.47 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.58/0.47 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.47 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.58/0.47 % Starting pre_casc_3 with 300s (1) cores
% 0.58/0.47 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.58/0.47 % Starting full_lambda_10 with 300s (1) cores
% 0.58/0.47 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.58/0.47 % ho_unfolding_5 with pid 1308647 completed with status 0
% 0.58/0.47 % Result found by ho_unfolding_5
% 0.58/0.47 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.58/0.47 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.47 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.58/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.58/0.47 % No SInE strategy applied
% 0.58/0.47 % Search class: HGHSM-FSLM32-MHSMMSBN
% 0.58/0.47 % Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 0.58/0.47 % Starting SubtermCWHack with 109s (1) cores
% 0.58/0.47 % Starting ho_unfolding_5 with 121s (1) cores
% 0.58/0.47 % Starting new_ho_6 with 99s (1) cores
% 0.58/0.47 % Starting pre_casc_4 with 99s (1) cores
% 0.58/0.47 % SubtermCWHack with pid 1308656 completed with status 0
% 0.58/0.47 % Result found by SubtermCWHack
% 0.58/0.47 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.58/0.47 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.47 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.58/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.58/0.47 % No SInE strategy applied
% 0.58/0.47 % Search class: HGHSM-FSLM32-MHSMMSBN
% 0.58/0.47 % Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 0.58/0.47 % Starting SubtermCWHack with 109s (1) cores
% 0.58/0.47 % Preprocessing time : 0.004 s
% 0.58/0.47
% 0.58/0.47 % Proof found!
% 0.58/0.47 % SZS status Theorem
% 0.58/0.47 % SZS output start CNFRefutation
% 0.58/0.47 thf(decl_23, type, in: $i > $i > $o).
% 0.58/0.47 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.58/0.47 thf(decl_25, type, setextAx: $o).
% 0.58/0.47 thf(decl_26, type, emptyset: $i).
% 0.58/0.47 thf(decl_27, type, emptysetAx: $o).
% 0.58/0.47 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.58/0.47 thf(decl_29, type, setadjoinAx: $o).
% 0.58/0.47 thf(decl_30, type, powerset: $i > $i).
% 0.58/0.47 thf(decl_31, type, powersetAx: $o).
% 0.58/0.47 thf(decl_32, type, setunion: $i > $i).
% 0.58/0.47 thf(decl_33, type, setunionAx: $o).
% 0.58/0.47 thf(decl_34, type, omega: $i).
% 0.58/0.47 thf(decl_35, type, omega0Ax: $o).
% 0.58/0.47 thf(decl_36, type, omegaSAx: $o).
% 0.58/0.47 thf(decl_37, type, omegaIndAx: $o).
% 0.58/0.47 thf(decl_38, type, replAx: $o).
% 0.58/0.47 thf(decl_39, type, foundationAx: $o).
% 0.58/0.47 thf(decl_40, type, wellorderingAx: $o).
% 0.58/0.47 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.58/0.47 thf(decl_42, type, descrp: $o).
% 0.58/0.47 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_44, type, dsetconstrI: $o).
% 0.58/0.47 thf(decl_45, type, dsetconstrEL: $o).
% 0.58/0.47 thf(decl_46, type, dsetconstrER: $o).
% 0.58/0.47 thf(decl_47, type, exuE1: $o).
% 0.58/0.47 thf(decl_48, type, prop2set: $o > $i).
% 0.58/0.47 thf(decl_49, type, prop2setE: $o).
% 0.58/0.47 thf(decl_50, type, emptysetE: $o).
% 0.58/0.47 thf(decl_51, type, emptysetimpfalse: $o).
% 0.58/0.47 thf(decl_52, type, notinemptyset: $o).
% 0.58/0.47 thf(decl_53, type, exuE3e: $o).
% 0.58/0.47 thf(decl_54, type, setext: $o).
% 0.58/0.47 thf(decl_55, type, emptyI: $o).
% 0.58/0.47 thf(decl_56, type, noeltsimpempty: $o).
% 0.58/0.47 thf(decl_57, type, setbeta: $o).
% 0.58/0.47 thf(decl_58, type, nonempty: $i > $o).
% 0.58/0.47 thf(decl_59, type, nonemptyE1: $o).
% 0.58/0.47 thf(decl_60, type, nonemptyI: $o).
% 0.58/0.47 thf(decl_61, type, nonemptyI1: $o).
% 0.58/0.47 thf(decl_62, type, setadjoinIL: $o).
% 0.58/0.47 thf(decl_63, type, emptyinunitempty: $o).
% 0.58/0.47 thf(decl_64, type, setadjoinIR: $o).
% 0.58/0.47 thf(decl_65, type, setadjoinE: $o).
% 0.58/0.47 thf(decl_66, type, setadjoinOr: $o).
% 0.58/0.47 thf(decl_67, type, setoftrueEq: $o).
% 0.58/0.47 thf(decl_68, type, powersetI: $o).
% 0.58/0.47 thf(decl_69, type, emptyinPowerset: $o).
% 0.58/0.47 thf(decl_70, type, emptyInPowerset: $o).
% 0.58/0.47 thf(decl_71, type, powersetE: $o).
% 0.58/0.47 thf(decl_72, type, setunionI: $o).
% 0.58/0.47 thf(decl_73, type, setunionE: $o).
% 0.58/0.47 thf(decl_74, type, subPowSU: $o).
% 0.58/0.47 thf(decl_75, type, exuE2: $o).
% 0.58/0.47 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.58/0.47 thf(decl_77, type, uniqinunit: $o).
% 0.58/0.47 thf(decl_78, type, notinsingleton: $o).
% 0.58/0.47 thf(decl_79, type, eqinunit: $o).
% 0.58/0.47 thf(decl_80, type, singletonsswitch: $o).
% 0.58/0.47 thf(decl_81, type, upairsetE: $o).
% 0.58/0.47 thf(decl_82, type, upairsetIL: $o).
% 0.58/0.47 thf(decl_83, type, upairsetIR: $o).
% 0.58/0.47 thf(decl_84, type, emptyE1: $o).
% 0.58/0.47 thf(decl_85, type, vacuousDall: $o).
% 0.58/0.47 thf(decl_86, type, quantDeMorgan1: $o).
% 0.58/0.47 thf(decl_87, type, quantDeMorgan2: $o).
% 0.58/0.47 thf(decl_88, type, quantDeMorgan3: $o).
% 0.58/0.47 thf(decl_89, type, quantDeMorgan4: $o).
% 0.58/0.47 thf(decl_90, type, prop2setI: $o).
% 0.58/0.47 thf(decl_91, type, set2prop: $i > $o).
% 0.58/0.47 thf(decl_92, type, prop2set2propI: $o).
% 0.58/0.47 thf(decl_93, type, notdexE: $o).
% 0.58/0.47 thf(decl_94, type, notdallE: $o).
% 0.58/0.47 thf(decl_95, type, exuI1: $o).
% 0.58/0.47 thf(decl_96, type, exuI3: $o).
% 0.58/0.47 thf(decl_97, type, exuI2: $o).
% 0.58/0.47 thf(decl_98, type, inCongP: $o).
% 0.58/0.47 thf(decl_99, type, in__Cong: $o).
% 0.58/0.47 thf(decl_100, type, exuE3u: $o).
% 0.58/0.47 thf(decl_101, type, exu__Cong: $o).
% 0.58/0.47 thf(decl_102, type, emptyset__Cong: $o).
% 0.58/0.47 thf(decl_103, type, setadjoin__Cong: $o).
% 0.58/0.47 thf(decl_104, type, powerset__Cong: $o).
% 0.58/0.47 thf(decl_105, type, setunion__Cong: $o).
% 0.58/0.47 thf(decl_106, type, omega__Cong: $o).
% 0.58/0.47 thf(decl_107, type, exuEu: $o).
% 0.58/0.47 thf(decl_108, type, descr__Cong: $o).
% 0.58/0.47 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.58/0.47 thf(decl_110, type, subset: $i > $i > $o).
% 0.58/0.47 thf(decl_113, type, subsetI1: $o).
% 0.58/0.47 thf(decl_114, type, eqimpsubset2: $o).
% 0.58/0.47 thf(decl_115, type, eqimpsubset1: $o).
% 0.58/0.47 thf(decl_116, type, subsetI2: $o).
% 0.58/0.47 thf(decl_117, type, emptysetsubset: $o).
% 0.58/0.47 thf(decl_118, type, subsetE: $o).
% 0.58/0.47 thf(decl_119, type, subsetE2: $o).
% 0.58/0.47 thf(decl_120, type, notsubsetI: $o).
% 0.58/0.47 thf(decl_121, type, notequalI1: $o).
% 0.58/0.47 thf(decl_122, type, notequalI2: $o).
% 0.58/0.47 thf(decl_123, type, subsetRefl: $o).
% 0.58/0.47 thf(decl_124, type, subsetTrans: $o).
% 0.58/0.47 thf(decl_125, type, setadjoinSub: $o).
% 0.58/0.47 thf(decl_126, type, setadjoinSub2: $o).
% 0.58/0.47 thf(decl_127, type, subset2powerset: $o).
% 0.58/0.47 thf(decl_128, type, setextsub: $o).
% 0.58/0.47 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.58/0.47 thf(decl_130, type, powersetI1: $o).
% 0.58/0.47 thf(decl_131, type, powersetE1: $o).
% 0.58/0.47 thf(decl_132, type, inPowerset: $o).
% 0.58/0.47 thf(decl_133, type, powersetsubset: $o).
% 0.58/0.47 thf(decl_134, type, sepInPowerset: $o).
% 0.58/0.47 thf(decl_135, type, sepSubset: $o).
% 0.58/0.47 thf(decl_136, type, binunion: $i > $i > $i).
% 0.58/0.47 thf(decl_137, type, binunionIL: $o).
% 0.58/0.47 thf(decl_138, type, upairset2IR: $o).
% 0.58/0.47 thf(decl_139, type, binunionIR: $o).
% 0.58/0.47 thf(decl_140, type, binunionEcases: $o).
% 0.58/0.47 thf(decl_141, type, binunionE: $o).
% 0.58/0.47 thf(decl_142, type, binunionLsub: $o).
% 0.58/0.47 thf(decl_143, type, binunionRsub: $o).
% 0.58/0.47 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.58/0.47 thf(decl_145, type, binintersectI: $o).
% 0.58/0.47 thf(decl_146, type, binintersectSubset5: $o).
% 0.58/0.47 thf(decl_147, type, binintersectEL: $o).
% 0.58/0.47 thf(decl_148, type, binintersectLsub: $o).
% 0.58/0.47 thf(decl_149, type, binintersectSubset2: $o).
% 0.58/0.47 thf(decl_150, type, binintersectSubset3: $o).
% 0.58/0.47 thf(decl_151, type, binintersectER: $o).
% 0.58/0.47 thf(decl_152, type, disjointsetsI1: $o).
% 0.58/0.47 thf(decl_153, type, binintersectRsub: $o).
% 0.58/0.47 thf(decl_154, type, binintersectSubset4: $o).
% 0.58/0.47 thf(decl_155, type, binintersectSubset1: $o).
% 0.58/0.47 thf(decl_156, type, bs114d: $o).
% 0.58/0.47 thf(decl_158, type, setminus: $i > $i > $i).
% 0.58/0.47 thf(decl_159, type, setminusI: $o).
% 0.58/0.47 thf(decl_160, type, setminusEL: $o).
% 0.58/0.47 thf(decl_161, type, setminusER: $o).
% 0.58/0.47 thf(decl_162, type, setminusSubset2: $o).
% 0.58/0.47 thf(decl_163, type, setminusERneg: $o).
% 0.58/0.47 thf(decl_164, type, setminusELneg: $o).
% 0.58/0.47 thf(decl_165, type, setminusILneg: $o).
% 0.58/0.47 thf(decl_166, type, setminusIRneg: $o).
% 0.58/0.47 thf(decl_167, type, setminusLsub: $o).
% 0.58/0.47 thf(decl_168, type, setminusSubset1: $o).
% 0.58/0.47 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.58/0.47 thf(decl_170, type, symdiffE: $o).
% 0.58/0.47 thf(decl_171, type, symdiffI1: $o).
% 0.58/0.47 thf(decl_172, type, symdiffI2: $o).
% 0.58/0.47 thf(decl_173, type, symdiffIneg1: $o).
% 0.58/0.47 thf(decl_174, type, symdiffIneg2: $o).
% 0.58/0.47 thf(decl_175, type, iskpair: $i > $o).
% 0.58/0.47 thf(decl_176, type, secondinupair: $o).
% 0.58/0.47 thf(decl_177, type, setukpairIL: $o).
% 0.58/0.47 thf(decl_178, type, setukpairIR: $o).
% 0.58/0.47 thf(decl_179, type, kpairiskpair: $o).
% 0.58/0.47 thf(decl_180, type, kpair: $i > $i > $i).
% 0.58/0.47 thf(decl_181, type, kpairp: $o).
% 0.58/0.47 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.58/0.47 thf(decl_183, type, singletonsubset: $o).
% 0.58/0.47 thf(decl_184, type, singletoninpowerset: $o).
% 0.58/0.47 thf(decl_185, type, singletoninpowunion: $o).
% 0.58/0.47 thf(decl_186, type, upairset2E: $o).
% 0.58/0.47 thf(decl_187, type, upairsubunion: $o).
% 0.58/0.47 thf(decl_188, type, upairinpowunion: $o).
% 0.58/0.47 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.58/0.47 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.58/0.47 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.58/0.47 thf(decl_192, type, cartprodpairin: $o).
% 0.58/0.47 thf(decl_193, type, cartprodmempair1: $o).
% 0.58/0.47 thf(decl_194, type, cartprodmempair: $o).
% 0.58/0.47 thf(decl_195, type, setunionE2: $o).
% 0.58/0.47 thf(decl_196, type, setunionsingleton1: $o).
% 0.58/0.47 thf(decl_197, type, setunionsingleton2: $o).
% 0.58/0.47 thf(decl_198, type, setunionsingleton: $o).
% 0.58/0.47 thf(decl_199, type, singleton: $i > $o).
% 0.58/0.47 thf(decl_200, type, singletonprop: $o).
% 0.58/0.47 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 0.58/0.47 thf(decl_202, type, ex1E1: $o).
% 0.58/0.47 thf(decl_203, type, ex1I: $o).
% 0.58/0.47 thf(decl_204, type, ex1I2: $o).
% 0.58/0.47 thf(decl_205, type, singletonsuniq: $o).
% 0.58/0.47 thf(decl_210, type, setukpairinjL1: $o).
% 0.58/0.47 thf(decl_211, type, kfstsingleton: $o).
% 0.58/0.47 thf(decl_212, type, theprop: $o).
% 0.58/0.47 thf(decl_213, type, kfst: $i > $i).
% 0.58/0.47 thf(decl_214, type, kfstpairEq: $o).
% 0.58/0.47 thf(decl_215, type, cartprodfstin: $o).
% 0.58/0.47 thf(decl_216, type, setukpairinjL2: $o).
% 0.58/0.47 thf(decl_217, type, setukpairinjL: $o).
% 0.58/0.47 thf(decl_218, type, setukpairinjR11: $o).
% 0.58/0.47 thf(decl_219, type, setukpairinjR12: $o).
% 0.58/0.47 thf(decl_220, type, setukpairinjR1: $o).
% 0.58/0.47 thf(decl_221, type, upairequniteq: $o).
% 0.58/0.47 thf(decl_222, type, setukpairinjR2: $o).
% 0.58/0.47 thf(decl_223, type, setukpairinjR: $o).
% 0.58/0.47 thf(decl_224, type, ksndsingleton: $o).
% 0.58/0.47 thf(decl_225, type, ksnd: $i > $i).
% 0.58/0.47 thf(decl_226, type, ksndpairEq: $o).
% 0.58/0.47 thf(decl_227, type, kpairsurjEq: $o).
% 0.58/0.47 thf(decl_228, type, cartprodsndin: $o).
% 0.58/0.47 thf(decl_229, type, cartprodpairmemEL: $o).
% 0.58/0.47 thf(decl_230, type, cartprodpairmemER: $o).
% 0.58/0.47 thf(decl_231, type, cartprodmempaircEq: $o).
% 0.58/0.47 thf(decl_232, type, cartprodfstpairEq: $o).
% 0.58/0.47 thf(decl_233, type, cartprodsndpairEq: $o).
% 0.58/0.47 thf(decl_234, type, cartprodpairsurjEq: $o).
% 0.58/0.47 thf(decl_235, type, breln: $i > $i > $i > $o).
% 0.58/0.47 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.58/0.47 thf(decl_237, type, dpsetconstrI: $o).
% 0.58/0.47 thf(decl_238, type, dpsetconstrSub: $o).
% 0.58/0.47 thf(decl_239, type, setOfPairsIsBReln: $o).
% 0.58/0.47 thf(decl_240, type, dpsetconstrERa: $o).
% 0.58/0.47 thf(decl_241, type, dpsetconstrEL1: $o).
% 0.58/0.47 thf(decl_242, type, dpsetconstrEL2: $o).
% 0.58/0.47 thf(decl_243, type, dpsetconstrER: $o).
% 0.58/0.47 thf(decl_244, type, func: $i > $i > $i > $o).
% 0.58/0.47 thf(decl_245, type, funcSet: $i > $i > $i).
% 0.58/0.47 thf(decl_246, type, funcImageSingleton: $o).
% 0.58/0.47 thf(decl_247, type, apProp: $o).
% 0.58/0.47 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 0.58/0.47 thf(decl_249, type, app: $o).
% 0.58/0.47 thf(decl_250, type, infuncsetfunc: $o).
% 0.58/0.47 thf(decl_251, type, ap2p: $o).
% 0.58/0.47 thf(decl_252, type, funcinfuncset: $o).
% 0.58/0.47 thf(decl_253, type, lamProp: $o).
% 0.58/0.47 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 0.58/0.47 thf(decl_255, type, lamp: $o).
% 0.58/0.47 thf(decl_256, type, lam2p: $o).
% 0.58/0.47 thf(decl_257, type, brelnall1: $o).
% 0.58/0.47 thf(decl_258, type, brelnall2: $o).
% 0.58/0.47 thf(decl_259, type, ex1E2: $o).
% 0.58/0.47 thf(decl_260, type, funcGraphProp1: $o).
% 0.58/0.47 thf(decl_261, type, funcGraphProp3: $o).
% 0.58/0.47 thf(decl_262, type, funcGraphProp2: $o).
% 0.58/0.47 thf(decl_263, type, funcextLem: $o).
% 0.58/0.47 thf(decl_264, type, funcGraphProp4: $o).
% 0.58/0.47 thf(decl_265, type, subbreln: $o).
% 0.58/0.47 thf(decl_266, type, eqbreln: $o).
% 0.58/0.47 thf(decl_267, type, funcext: $o).
% 0.58/0.47 thf(decl_268, type, funcext2: $o).
% 0.58/0.47 thf(decl_269, type, ap2apEq1: $o).
% 0.58/0.47 thf(decl_270, type, ap2apEq2: $o).
% 0.58/0.47 thf(decl_271, type, beta1: $o).
% 0.58/0.47 thf(decl_272, type, eta1: $o).
% 0.58/0.47 thf(decl_273, type, lam2lamEq: $o).
% 0.58/0.47 thf(decl_274, type, beta2: $o).
% 0.58/0.47 thf(decl_275, type, eta2: $o).
% 0.58/0.47 thf(decl_276, type, epred1_0: $o).
% 0.58/0.47 thf(decl_277, type, esk1_2: $i > $i > $i).
% 0.58/0.47 thf(decl_278, type, esk2_2: $i > $i > $i).
% 0.58/0.47 thf(decl_279, type, esk3_2: $i > $i > $i).
% 0.58/0.47 thf(decl_280, type, esk4_1: $i > $i).
% 0.58/0.47 thf(decl_281, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.58/0.47 thf(decl_282, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.58/0.47 thf(decl_283, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.58/0.47 thf(decl_284, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.58/0.47 thf(decl_285, type, esk9_1: $i > $i).
% 0.58/0.47 thf(decl_286, type, esk10_2: ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_287, type, esk11_2: ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_288, type, esk12_1: ($i > $o) > $i).
% 0.58/0.47 thf(decl_289, type, esk13_2: ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_290, type, esk14_1: ($i > $o) > $i).
% 0.58/0.47 thf(decl_291, type, esk15_2: $i > $i > $i).
% 0.58/0.47 thf(decl_292, type, esk16_2: $i > $i > $i).
% 0.58/0.47 thf(decl_293, type, esk17_1: $i > $i).
% 0.58/0.47 thf(decl_294, type, esk18_1: $i > $i).
% 0.58/0.47 thf(decl_295, type, esk19_1: $i > $i).
% 0.58/0.47 thf(decl_296, type, esk20_2: $i > $i > $i).
% 0.58/0.47 thf(decl_297, type, esk21_3: $i > $i > $o > $i).
% 0.58/0.47 thf(decl_298, type, esk22_2: ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_299, type, esk23_1: ($i > $o) > $i).
% 0.58/0.47 thf(decl_300, type, esk24_1: $i > $i).
% 0.58/0.47 thf(decl_301, type, esk25_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_302, type, esk26_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_303, type, esk27_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_304, type, esk28_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_305, type, esk29_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_306, type, esk30_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_307, type, esk31_2: ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_308, type, esk32_1: ($i > $o) > $i).
% 0.58/0.47 thf(decl_309, type, esk33_1: ($i > $o) > $i).
% 0.58/0.47 thf(decl_310, type, esk34_1: ($i > $o) > $i).
% 0.58/0.47 thf(decl_311, type, esk35_1: ($i > $o) > $i).
% 0.58/0.47 thf(decl_312, type, esk36_2: ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_313, type, esk37_1: ($i > $o) > $i).
% 0.58/0.47 thf(decl_314, type, esk38_2: ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_315, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.58/0.47 thf(decl_316, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.58/0.47 thf(decl_317, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_318, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.58/0.47 thf(decl_319, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_320, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.58/0.47 thf(decl_321, type, esk45_2: ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_322, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.58/0.47 thf(decl_323, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.58/0.47 thf(decl_324, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_325, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_326, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.58/0.47 thf(decl_327, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.58/0.47 thf(decl_328, type, esk52_2: $i > $i > $i).
% 0.58/0.47 thf(decl_329, type, esk53_2: $i > $i > $i).
% 0.58/0.47 thf(decl_330, type, esk54_2: $i > $i > $i).
% 0.58/0.47 thf(decl_331, type, esk55_3: $i > $i > $i > $i).
% 0.58/0.47 thf(decl_332, type, esk56_3: $i > $i > $i > $i).
% 0.58/0.47 thf(decl_333, type, esk57_2: $i > $i > $i).
% 0.58/0.47 thf(decl_334, type, esk58_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_335, type, esk59_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_336, type, esk60_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_337, type, esk61_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_338, type, esk62_3: $i > ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_339, type, esk63_3: $i > ($i > $o) > $i > $i).
% 0.58/0.47 thf(decl_340, type, esk64_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_341, type, esk65_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_342, type, esk66_2: $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_343, type, esk67_1: $i > $i).
% 0.58/0.47 thf(decl_344, type, esk68_1: $i > $i).
% 0.58/0.47 thf(decl_345, type, esk69_4: $i > $i > $i > $i > $i).
% 0.58/0.47 thf(decl_346, type, esk70_3: $i > $i > ($i > $i) > $i).
% 0.58/0.47 thf(decl_347, type, esk71_3: $i > $i > ($i > $i) > $i).
% 0.58/0.47 thf(decl_348, type, esk72_3: $i > $i > ($i > $i) > $i).
% 0.58/0.47 thf(decl_349, type, esk73_4: $i > $i > $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_350, type, esk74_4: $i > $i > $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_351, type, esk75_4: $i > $i > $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_352, type, esk76_4: $i > $i > $i > ($i > $o) > $i).
% 0.58/0.47 thf(decl_353, type, esk77_4: $i > $i > $i > $i > $i).
% 0.58/0.47 thf(decl_354, type, esk78_4: $i > $i > $i > $i > $i).
% 0.58/0.47 thf(decl_355, type, esk79_4: $i > $i > $i > $i > $i).
% 0.58/0.47 thf(decl_356, type, esk80_4: $i > $i > $i > $i > $i).
% 0.58/0.47 thf(decl_357, type, esk81_4: $i > $i > $i > $i > $i).
% 0.58/0.47 thf(decl_358, type, esk82_4: $i > $i > $i > $i > $i).
% 0.58/0.47 thf(decl_359, type, esk83_4: $i > $i > $i > $i > $i).
% 0.58/0.47 thf(decl_360, type, esk84_4: $i > $i > $i > $i > $i).
% 0.58/0.47 thf(decl_361, type, esk85_4: $i > $i > $i > $i > $i).
% 0.58/0.47 thf(decl_362, type, esk86_3: $i > $i > ($i > $i) > $i).
% 0.58/0.47 thf(decl_363, type, esk87_3: $i > $i > ($i > $i) > $i).
% 0.58/0.47 thf(decl_364, type, esk88_3: $i > $i > ($i > $i) > $i).
% 0.58/0.47 thf(decl_365, type, esk89_0: $i).
% 0.58/0.47 thf(decl_366, type, epred2_0: $o).
% 0.58/0.47 thf(decl_367, type, esk90_0: $i).
% 0.58/0.47 thf(decl_368, type, esk91_0: $i).
% 0.58/0.47 thf(decl_374, type, epred3_0: $i > $o).
% 0.58/0.47 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ex1)).
% 0.58/0.47 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', singleton)).
% 0.58/0.47 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', replAx)).
% 0.58/0.47 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', exu)).
% 0.58/0.47 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', descrp)).
% 0.58/0.47 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', exuE1)).
% 0.58/0.47 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', exuE3e)).
% 0.58/0.47 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', nonempty)).
% 0.58/0.47 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', nonemptyI)).
% 0.58/0.47 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', exuE2)).
% 0.58/0.47 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', exuI1)).
% 0.58/0.47 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', exuI3)).
% 0.58/0.47 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', exuI2)).
% 0.58/0.47 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', exuE3u)).
% 0.58/0.47 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', exu__Cong)).
% 0.58/0.47 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', exuEu)).
% 0.58/0.47 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', descr__Cong)).
% 0.58/0.47 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', singletonprop)).
% 0.58/0.47 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ex1E1)).
% 0.58/0.47 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ex1I)).
% 0.58/0.47 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ex1I2)).
% 0.58/0.47 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', kfstsingleton)).
% 0.58/0.47 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ksndsingleton)).
% 0.58/0.47 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setOfPairsIsBReln)).
% 0.58/0.47 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', breln)).
% 0.58/0.47 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', funcImageSingleton)).
% 0.58/0.47 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ex1E2)).
% 0.58/0.47 thf(iffalseProp1, 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)=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', iffalseProp1)).
% 0.58/0.47 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', dsetconstrI)).
% 0.58/0.47 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', dsetconstrEL)).
% 0.58/0.47 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', dsetconstrER)).
% 0.58/0.47 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setbeta)).
% 0.58/0.47 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', nonemptyE1)).
% 0.58/0.47 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', nonemptyI1)).
% 0.58/0.47 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setoftrueEq)).
% 0.58/0.47 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', nonemptyImpWitness)).
% 0.58/0.47 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', emptyE1)).
% 0.58/0.47 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', dsetconstr__Cong)).
% 0.58/0.47 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', sepInPowerset)).
% 0.58/0.47 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', sepSubset)).
% 0.58/0.47 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', theprop)).
% 0.58/0.47 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', dpsetconstrI)).
% 0.58/0.47 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', dpsetconstrSub)).
% 0.58/0.47 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', dpsetconstrERa)).
% 0.58/0.47 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', dpsetconstrEL1)).
% 0.58/0.47 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', dpsetconstrEL2)).
% 0.58/0.47 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', dpsetconstrER)).
% 0.58/0.47 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', apProp)).
% 0.58/0.47 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', lamProp)).
% 0.58/0.47 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', lamp)).
% 0.58/0.47 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', lam2p)).
% 0.58/0.47 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', brelnall1)).
% 0.58/0.47 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', brelnall2)).
% 0.58/0.47 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', subbreln)).
% 0.58/0.47 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', eqbreln)).
% 0.58/0.47 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', beta1)).
% 0.58/0.47 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', eta1)).
% 0.58/0.47 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', lam2lamEq)).
% 0.58/0.47 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', beta2)).
% 0.58/0.47 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', eta2)).
% 0.58/0.47 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setextAx)).
% 0.58/0.47 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', emptysetAx)).
% 0.58/0.47 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setadjoinAx)).
% 0.58/0.47 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', powersetAx)).
% 0.58/0.47 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setunionAx)).
% 0.58/0.47 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', omega0Ax)).
% 0.58/0.47 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', omegaSAx)).
% 0.58/0.47 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', omegaIndAx)).
% 0.58/0.47 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', foundationAx)).
% 0.58/0.47 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', wellorderingAx)).
% 0.58/0.47 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', prop2setE)).
% 0.58/0.47 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', emptysetE)).
% 0.58/0.47 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', emptysetimpfalse)).
% 0.58/0.47 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', notinemptyset)).
% 0.58/0.47 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setext)).
% 0.58/0.47 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', emptyI)).
% 0.58/0.47 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', noeltsimpempty)).
% 0.58/0.47 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setadjoinIL)).
% 0.58/0.47 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', emptyinunitempty)).
% 0.58/0.47 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setadjoinIR)).
% 0.58/0.47 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setadjoinE)).
% 0.58/0.47 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setadjoinOr)).
% 0.58/0.47 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', powersetI)).
% 0.58/0.47 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', emptyinPowerset)).
% 0.58/0.47 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', emptyInPowerset)).
% 0.58/0.47 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', powersetE)).
% 0.58/0.47 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setunionI)).
% 0.58/0.47 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setunionE)).
% 0.58/0.47 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', subPowSU)).
% 0.58/0.47 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', uniqinunit)).
% 0.58/0.47 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', notinsingleton)).
% 0.58/0.47 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', eqinunit)).
% 0.58/0.47 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', singletonsswitch)).
% 0.58/0.47 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', upairsetE)).
% 0.58/0.47 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', upairsetIL)).
% 0.58/0.47 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', upairsetIR)).
% 0.58/0.47 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', vacuousDall)).
% 0.58/0.47 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', quantDeMorgan1)).
% 0.58/0.47 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', quantDeMorgan2)).
% 0.58/0.47 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', quantDeMorgan3)).
% 0.58/0.47 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', quantDeMorgan4)).
% 0.58/0.47 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', prop2setI)).
% 0.58/0.47 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', prop2set2propI)).
% 0.58/0.47 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', notdexE)).
% 0.58/0.47 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', notdallE)).
% 0.58/0.47 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', inCongP)).
% 0.58/0.47 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', in__Cong)).
% 0.58/0.47 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', emptyset__Cong)).
% 0.58/0.47 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setadjoin__Cong)).
% 0.58/0.47 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', powerset__Cong)).
% 0.58/0.47 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setunion__Cong)).
% 0.58/0.47 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', omega__Cong)).
% 0.58/0.47 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', subsetI1)).
% 0.58/0.47 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', eqimpsubset2)).
% 0.58/0.47 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', eqimpsubset1)).
% 0.58/0.47 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', subsetI2)).
% 0.58/0.47 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', emptysetsubset)).
% 0.58/0.47 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', subsetE)).
% 0.58/0.47 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', subsetE2)).
% 0.58/0.47 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', notsubsetI)).
% 0.58/0.47 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', notequalI1)).
% 0.58/0.47 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', notequalI2)).
% 0.58/0.47 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', subsetRefl)).
% 0.58/0.47 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', subsetTrans)).
% 0.58/0.47 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setadjoinSub)).
% 0.58/0.47 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setadjoinSub2)).
% 0.58/0.47 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', subset2powerset)).
% 0.58/0.47 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setextsub)).
% 0.58/0.47 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', subsetemptysetimpeq)).
% 0.58/0.47 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', powersetI1)).
% 0.58/0.47 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', powersetE1)).
% 0.58/0.47 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', inPowerset)).
% 0.58/0.47 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', powersetsubset)).
% 0.58/0.47 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binunionIL)).
% 0.58/0.47 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', upairset2IR)).
% 0.58/0.47 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binunionIR)).
% 0.58/0.47 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binunionEcases)).
% 0.58/0.47 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binunionE)).
% 0.58/0.47 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binunionLsub)).
% 0.58/0.47 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binunionRsub)).
% 0.58/0.47 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binintersectI)).
% 0.58/0.47 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binintersectSubset5)).
% 0.58/0.47 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binintersectEL)).
% 0.58/0.47 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binintersectLsub)).
% 0.58/0.47 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binintersectSubset2)).
% 0.58/0.47 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binintersectSubset3)).
% 0.58/0.47 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binintersectER)).
% 0.58/0.47 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', disjointsetsI1)).
% 0.58/0.47 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binintersectRsub)).
% 0.58/0.47 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binintersectSubset4)).
% 0.58/0.47 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', binintersectSubset1)).
% 0.58/0.47 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', bs114d)).
% 0.58/0.47 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setminusI)).
% 0.58/0.47 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setminusEL)).
% 0.58/0.47 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setminusER)).
% 0.58/0.47 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setminusSubset2)).
% 0.58/0.47 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setminusERneg)).
% 0.58/0.47 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setminusELneg)).
% 0.58/0.47 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setminusILneg)).
% 0.58/0.47 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setminusIRneg)).
% 0.58/0.47 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setminusLsub)).
% 0.58/0.47 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setminusSubset1)).
% 0.58/0.47 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', symdiffE)).
% 0.58/0.47 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', symdiffI1)).
% 0.58/0.47 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', symdiffI2)).
% 0.58/0.47 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', symdiffIneg1)).
% 0.58/0.47 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', symdiffIneg2)).
% 0.58/0.47 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', secondinupair)).
% 0.58/0.47 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setukpairIL)).
% 0.58/0.47 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setukpairIR)).
% 0.58/0.47 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', kpairiskpair)).
% 0.58/0.47 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', kpairp)).
% 0.58/0.47 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', singletonsubset)).
% 0.58/0.47 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', singletoninpowerset)).
% 0.58/0.47 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', singletoninpowunion)).
% 0.58/0.47 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', upairset2E)).
% 0.58/0.47 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', upairsubunion)).
% 0.58/0.47 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', upairinpowunion)).
% 0.58/0.47 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ubforcartprodlem1)).
% 0.58/0.47 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ubforcartprodlem2)).
% 0.58/0.47 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ubforcartprodlem3)).
% 0.58/0.47 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', cartprodpairin)).
% 0.58/0.47 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', cartprodmempair1)).
% 0.58/0.47 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', cartprodmempair)).
% 0.58/0.47 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setunionE2)).
% 0.58/0.47 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setunionsingleton1)).
% 0.58/0.47 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setunionsingleton2)).
% 0.58/0.47 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setunionsingleton)).
% 0.58/0.47 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', singletonsuniq)).
% 0.58/0.47 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setukpairinjL1)).
% 0.58/0.47 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', kfstpairEq)).
% 0.58/0.47 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', cartprodfstin)).
% 0.58/0.47 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setukpairinjL2)).
% 0.58/0.47 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setukpairinjL)).
% 0.58/0.47 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setukpairinjR11)).
% 0.58/0.47 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setukpairinjR12)).
% 0.58/0.47 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setukpairinjR1)).
% 0.58/0.47 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', upairequniteq)).
% 0.58/0.47 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setukpairinjR2)).
% 0.58/0.47 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', setukpairinjR)).
% 0.58/0.47 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ksndpairEq)).
% 0.58/0.47 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', kpairsurjEq)).
% 0.58/0.47 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', cartprodsndin)).
% 0.58/0.47 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', cartprodpairmemEL)).
% 0.58/0.47 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', cartprodpairmemER)).
% 0.58/0.47 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', cartprodmempaircEq)).
% 0.58/0.47 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', cartprodfstpairEq)).
% 0.58/0.47 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', cartprodsndpairEq)).
% 0.58/0.47 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', cartprodpairsurjEq)).
% 0.58/0.47 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', app)).
% 0.58/0.47 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', infuncsetfunc)).
% 0.58/0.47 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ap2p)).
% 0.58/0.47 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', funcinfuncset)).
% 0.58/0.47 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', funcGraphProp1)).
% 0.58/0.47 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', funcGraphProp3)).
% 0.58/0.47 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', funcGraphProp2)).
% 0.58/0.47 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', funcextLem)).
% 0.58/0.47 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', funcGraphProp4)).
% 0.58/0.47 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', funcext)).
% 0.58/0.47 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', funcext2)).
% 0.58/0.47 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ap2apEq1)).
% 0.58/0.47 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.1FLtMS16RB/E---3.1_1308634.p', ap2apEq2)).
% 0.58/0.47 thf(c_0_222, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X731:$i]:((((in @ X731 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X731 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 0.58/0.47 thf(c_0_223, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 0.58/0.47 thf(c_0_224, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.58/0.47 thf(c_0_225, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.58/0.47 thf(c_0_226, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.58/0.47 thf(c_0_227, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.58/0.47 thf(c_0_228, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.58/0.47 thf(c_0_229, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.58/0.47 thf(c_0_230, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.58/0.47 thf(c_0_231, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.58/0.47 thf(c_0_232, 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])).
% 0.58/0.47 thf(c_0_233, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.58/0.47 thf(c_0_234, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.58/0.47 thf(c_0_235, 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])).
% 0.58/0.47 thf(c_0_236, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.58/0.47 thf(c_0_237, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.58/0.47 thf(c_0_238, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.58/0.47 thf(c_0_239, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 0.58/0.47 thf(c_0_240, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 0.58/0.47 thf(c_0_241, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X731:$i]:((((in @ X731 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X731 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_222, c_0_223])).
% 0.58/0.47 thf(c_0_242, 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])).
% 0.58/0.47 thf(c_0_243, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 0.58/0.47 thf(c_0_244, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 0.58/0.47 thf(c_0_245, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 0.58/0.47 thf(c_0_246, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 0.58/0.47 thf(c_0_247, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 0.58/0.47 thf(c_0_248, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 0.58/0.47 thf(c_0_249, plain, ((ex1E2)<=>![X4:$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])).
% 0.58/0.47 thf(c_0_250, 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)=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[iffalseProp1])).
% 0.58/0.47 thf(c_0_251, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X702:$i]:(((((X6 @ X2 @ X702)))&(![X703:$i]:(((((X6 @ X2 @ X703)))=>(((X702)=(X703)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_224, c_0_225])).
% 0.58/0.47 thf(c_0_252, plain, ((descrp)=(![X1:$i > $o]:((((?[X704:$i]:(((((X1 @ X704)))&(![X705:$i]:(((((X1 @ X705)))=>(((X704)=(X705))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_225])).
% 0.58/0.47 thf(c_0_253, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.58/0.47 thf(c_0_254, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.58/0.47 thf(c_0_255, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.58/0.47 thf(c_0_256, plain, ((exuE1)=(![X1:$i > $o]:((((?[X706:$i]:(((((X1 @ X706)))&(![X707:$i]:(((((X1 @ X707)))=>(((X706)=(X707))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_227, c_0_225])).
% 0.58/0.47 thf(c_0_257, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X708:$i]:(((((X1 @ X708)))&(![X709:$i]:(((((X1 @ X709)))=>(((X708)=(X709))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_225])).
% 0.58/0.47 thf(c_0_258, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.58/0.47 thf(c_0_259, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_229])).
% 0.58/0.47 thf(c_0_260, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_229])).
% 0.58/0.47 thf(c_0_261, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_229])).
% 0.58/0.47 thf(c_0_262, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.58/0.47 thf(c_0_263, plain, ((exuE2)=(![X1:$i > $o]:((((?[X710:$i]:(((((X1 @ X710)))&(![X711:$i]:(((((X1 @ X711)))=>(((X710)=(X711))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_231, c_0_225])).
% 0.58/0.47 thf(c_0_264, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_229])).
% 0.58/0.47 thf(c_0_265, 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])).
% 0.58/0.47 thf(c_0_266, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X712:$i]:(((((X1 @ X712)))&(![X713:$i]:(((((X1 @ X713)))=>(((X712)=(X713)))))))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_225])).
% 0.58/0.47 thf(c_0_267, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X714:$i]:(((((X1 @ X714)))&(![X715:$i]:(((((X1 @ X715)))=>(((X714)=(X715)))))))))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_225])).
% 0.58/0.47 thf(c_0_268, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X716:$i]:(((((X1 @ X716)))&(![X717:$i]:(((((X1 @ X717)))=>(((X716)=(X717)))))))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_225])).
% 0.58/0.47 thf(c_0_269, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X718:$i]:(((((X1 @ X718)))&(![X719:$i]:(((((X1 @ X719)))=>(((X718)=(X719))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_235, c_0_225])).
% 0.58/0.47 thf(c_0_270, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X720:$i]:(((((X1 @ X720)))&(![X721:$i]:(((((X1 @ X721)))=>(((X720)=(X721))))))))))<=>((?[X722:$i]:(((((X17 @ X722)))&(![X723:$i]:(((((X17 @ X723)))=>(((X722)=(X723)))))))))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_225])).
% 0.58/0.47 thf(c_0_271, plain, ((exuEu)=(![X1:$i > $o]:((((?[X724:$i]:(((((X1 @ X724)))&(![X725:$i]:(((((X1 @ X725)))=>(((X724)=(X725))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_225])).
% 0.58/0.47 thf(c_0_272, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X726:$i]:(((((X1 @ X726)))&(![X727:$i]:(((((X1 @ X727)))=>(((X726)=(X727))))))))))=>((((?[X728:$i]:(((((X17 @ X728)))&(![X729:$i]:(((((X17 @ X729)))=>(((X728)=(X729))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_225])).
% 0.58/0.47 thf(c_0_273, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.58/0.47 thf(c_0_274, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.58/0.47 thf(c_0_275, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.58/0.47 thf(c_0_276, 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)))))=>((?[X730:$i]:((((in @ X730 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X730 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_223])).
% 0.58/0.47 thf(c_0_277, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X732:$i]:((((in @ X732 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X732 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_241])).
% 0.58/0.47 thf(c_0_278, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X733:$i]:((((in @ X733 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X733 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_241])).
% 0.58/0.47 thf(c_0_279, 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)))))=>((?[X734:$i]:((((in @ X734 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X734 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_241])).
% 0.58/0.47 thf(c_0_280, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X735:$i]:((((in @ X735 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X735 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_223])).
% 0.58/0.47 thf(c_0_281, axiom, ((theprop)=(![X21:$i]:((((?[X736:$i]:((((in @ X736 @ X21))&(((X21)=(setadjoin @ X736 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_223])).
% 0.58/0.47 thf(c_0_282, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X737:$i]:((((in @ X737 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X737 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_223])).
% 0.58/0.47 thf(c_0_283, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 0.58/0.47 thf(c_0_284, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 0.58/0.47 thf(c_0_285, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_246, c_0_247])).
% 0.58/0.47 thf(c_0_286, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 0.58/0.47 thf(c_0_287, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 0.58/0.47 thf(c_0_288, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 0.58/0.47 thf(c_0_289, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 0.58/0.47 thf(c_0_290, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:((((func @ X4 @ X5 @ X29))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X738:$i]:((((in @ X738 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X738 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[c_0_248, c_0_223])).
% 0.58/0.47 thf(c_0_291, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 0.58/0.47 thf(c_0_292, plain, ((lamProp)<=>![X4:$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])).
% 0.58/0.47 thf(c_0_293, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 0.58/0.47 thf(c_0_294, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 0.58/0.47 thf(c_0_295, axiom, ((brelnall1)=(![X4:$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_247])).
% 0.58/0.47 thf(c_0_296, 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_247])).
% 0.58/0.47 thf(c_0_297, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((?[X739:$i]:((((in @ X739 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X739 @ emptyset)))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_249, c_0_241])).
% 0.58/0.47 thf(c_0_298, 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_247])).
% 0.58/0.47 thf(c_0_299, 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_247])).
% 0.58/0.47 thf(c_0_300, 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])).
% 0.58/0.47 thf(c_0_301, 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])).
% 0.58/0.47 thf(c_0_302, 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])).
% 0.58/0.47 thf(c_0_303, 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])).
% 0.58/0.47 thf(c_0_304, 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])).
% 0.58/0.47 thf(c_0_305, plain, ((epred1_0)<=>![X769:$i]:(?[X770:$i]:((((![X771:$i]:(((in @ X771 @ X770)=>![X772:$i]:(((in @ X772 @ X771)=>(in @ X772 @ X769)))))&![X773:$i, X774:$i]:((((in @ X773 @ X769)&(in @ X774 @ X769))=>(![X775:$i]:(((in @ X775 @ X770)=>((in @ X773 @ X775)<=>(in @ X774 @ X775))))=>((X773)=(X774))))))&![X776:$i, X777:$i]:((((in @ X776 @ X770)&(in @ X777 @ X770))=>(![X778:$i]:(((in @ X778 @ X776)=>(in @ X778 @ X777)))|![X779:$i]:(((in @ X779 @ X777)=>(in @ X779 @ X776)))))))&![X780:$i]:(((![X781:$i]:(((in @ X781 @ X780)=>(in @ X781 @ X769)))&?[X782:$i]:((in @ X782 @ X780)))=>?[X783:$i, X784:$i]:(((((in @ X783 @ X770)&(in @ X784 @ X780))&~(?[X785:$i]:(((in @ X785 @ X783)&(in @ X785 @ X780)))))&![X786:$i]:(((in @ X786 @ X770)=>(![X787:$i]:(((in @ X787 @ X786)=>(in @ X787 @ X783)))|(in @ X784 @ X786)))))))))))), introduced(definition)).
% 0.58/0.47 thf(c_0_306, negated_conjecture, ~((![X740:$i, X741:$i]:((![X742:$i]:(((in @ X742 @ X740)<=>(in @ X742 @ X741)))=>((X740)=(X741))))=>(![X743:$i]:(~(in @ X743 @ emptyset))=>(![X744:$i, X745:$i, X746:$i]:(((in @ X746 @ (setadjoin @ X744 @ X745))<=>(((X746)=(X744))|(in @ X746 @ X745))))=>(![X747:$i, X748:$i]:(((in @ X748 @ (powerset @ X747))<=>![X749:$i]:(((in @ X749 @ X748)=>(in @ X749 @ X747)))))=>(![X750:$i, X751:$i]:(((in @ X751 @ (setunion @ X750))<=>?[X752:$i]:(((in @ X751 @ X752)&(in @ X752 @ X750)))))=>((in @ emptyset @ omega)=>(![X753:$i]:(((in @ X753 @ omega)=>(in @ (setadjoin @ X753 @ X753) @ omega)))=>(![X754:$i]:((((in @ emptyset @ X754)&![X755:$i]:((((in @ X755 @ omega)&(in @ X755 @ X754))=>(in @ (setadjoin @ X755 @ X755) @ X754))))=>![X756:$i]:(((in @ X756 @ omega)=>(in @ X756 @ X754)))))=>(![X757:$i > $i > $o, X758:$i]:((![X759:$i]:(((in @ X759 @ X758)=>?[X760:$i]:(((X757 @ X759 @ X760)&![X761:$i]:(((X757 @ X759 @ X761)=>((X760)=(X761))))))))=>?[X762:$i]:(![X763:$i]:(((in @ X763 @ X762)<=>?[X764:$i]:(((in @ X764 @ X758)&(X757 @ X764 @ X763))))))))=>(![X765:$i]:((?[X766:$i]:((in @ X766 @ X765))=>?[X767:$i]:(((in @ X767 @ X765)&~(?[X768:$i]:(((in @ X768 @ X767)&(in @ X768 @ X765))))))))=>((epred1_0)=>(![X788:$i > $o]:((?[X789:$i]:(((X788 @ X789)&![X790:$i]:(((X788 @ X790)=>((X789)=(X790))))))=>(X788 @ (descr @ (^[Z0:$i]:(X788 @ Z0))))))=>(![X791:$i, X792:$i > $o, X793:$i]:(((in @ X793 @ X791)=>((X792 @ X793)=>(in @ X793 @ (dsetconstr @ X791 @ X792)))))=>(![X794:$i, X795:$i > $o, X796:$i]:(((in @ X796 @ (dsetconstr @ X794 @ X795))=>(in @ X796 @ X794)))=>(![X797:$i, X798:$i > $o, X799:$i]:(((in @ X799 @ (dsetconstr @ X797 @ X798))=>(X798 @ X799)))=>(![X800:$i > $o]:((?[X801:$i]:(((X800 @ X801)&![X802:$i]:(((X800 @ X802)=>((X801)=(X802))))))=>?[X803:$i]:(((X800 @ X803)&![X804:$i]:(((X800 @ X804)=>((X803)=(X804))))))))=>(![X805:$o, X806:$i]:(((in @ X806 @ (prop2set @ ((X805))))=>(X805)))=>(![X807:$i]:(((in @ X807 @ emptyset)=>![X808:$o]:((X808))))=>(![X809:$i]:(((in @ X809 @ emptyset)=>~($true)))=>(![X810:$i]:(~(in @ X810 @ emptyset))=>(![X811:$i > $o]:((?[X812:$i]:(((X811 @ X812)&![X813:$i]:(((X811 @ X813)=>((X812)=(X813))))))=>?[X814:$i]:((X811 @ X814))))=>(![X815:$i, X816:$i]:((![X817:$i]:(((in @ X817 @ X815)=>(in @ X817 @ X816)))=>(![X818:$i]:(((in @ X818 @ X816)=>(in @ X818 @ X815)))=>((X815)=(X816)))))=>(![X819:$i]:((![X820:$i]:(~(in @ X820 @ X819))=>((X819)=(emptyset))))=>(![X821:$i]:((![X822:$i]:(~(in @ X822 @ X821))=>((X821)=(emptyset))))=>(![X823:$i, X824:$i > $o, X825:$i]:(((in @ X825 @ X823)=>((in @ X825 @ (dsetconstr @ X823 @ X824))<=>(X824 @ X825))))=>(![X826:$i]:((((X826)!=(emptyset))=>?[X827:$i]:((in @ X827 @ X826))))=>(![X828:$i, X829:$i > $o, X830:$i]:(((in @ X830 @ X828)=>((X829 @ X830)=>((dsetconstr @ X828 @ X829)!=(emptyset)))))=>(![X831:$i]:((?[X832:$i]:((in @ X832 @ X831))=>((X831)!=(emptyset))))=>(![X833:$i, X834:$i]:((in @ X833 @ (setadjoin @ X833 @ X834)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X835:$i, X836:$i, X837:$i]:(((in @ X837 @ X836)=>(in @ X837 @ (setadjoin @ X835 @ X836))))=>(![X838:$i, X839:$i, X840:$i]:(((in @ X840 @ (setadjoin @ X838 @ X839))=>![X841:$o]:(((((X840)=(X838))=>(X841))=>(((in @ X840 @ X839)=>(X841))=>(X841))))))=>(![X842:$i, X843:$i, X844:$i]:(((in @ X844 @ (setadjoin @ X842 @ X843))=>(((X844)=(X842))|(in @ X844 @ X843))))=>(![X845:$i]:(((dsetconstr @ X845 @ (^[Z0:$i]:($true)))=(X845)))=>(![X846:$i, X847:$i]:((![X848:$i]:(((in @ X848 @ X847)=>(in @ X848 @ X846)))=>(in @ X847 @ (powerset @ X846))))=>(![X849:$i]:((in @ emptyset @ (powerset @ X849)))=>(![X850:$i]:((in @ emptyset @ (powerset @ X850)))=>(![X851:$i, X852:$i, X853:$i]:(((in @ X852 @ (powerset @ X851))=>((in @ X853 @ X852)=>(in @ X853 @ X851))))=>(![X854:$i, X855:$i, X856:$i]:(((in @ X855 @ X856)=>((in @ X856 @ X854)=>(in @ X855 @ (setunion @ X854)))))=>(![X857:$i, X858:$i]:(((in @ X858 @ (setunion @ X857))=>![X859:$o]:((![X860:$i]:(((in @ X858 @ X860)=>((in @ X860 @ X857)=>(X859))))=>(X859)))))=>(![X861:$i, X862:$i]:(((in @ X862 @ X861)=>(in @ X862 @ (powerset @ (setunion @ X861)))))=>(![X863:$i > $o]:((?[X864:$i]:(((X863 @ X864)&![X865:$i]:(((X863 @ X865)=>((X864)=(X865))))))=>?[X866:$i]:(![X867:$i]:(((X863 @ X867)<=>((X867)=(X866)))))))=>(![X868:$i]:((((X868)!=(emptyset))=>?[X869:$i]:(((in @ X869 @ X868)&$true))))=>(![X870:$i, X871:$i]:(((in @ X870 @ (setadjoin @ X871 @ emptyset))=>((X870)=(X871))))=>(![X872:$i, X873:$i]:((((X872)!=(X873))=>~(in @ X873 @ (setadjoin @ X872 @ emptyset))))=>(![X874:$i, X875:$i]:((((X874)=(X875))=>(in @ X874 @ (setadjoin @ X875 @ emptyset))))=>(![X876:$i, X877:$i]:(((in @ X876 @ (setadjoin @ X877 @ emptyset))=>(in @ X877 @ (setadjoin @ X876 @ emptyset))))=>(![X878:$i, X879:$i, X880:$i]:(((in @ X880 @ (setadjoin @ X878 @ (setadjoin @ X879 @ emptyset)))=>(((X880)=(X878))|((X880)=(X879)))))=>(![X881:$i, X882:$i]:((in @ X881 @ (setadjoin @ X881 @ (setadjoin @ X882 @ emptyset))))=>(![X883:$i, X884:$i]:((in @ X884 @ (setadjoin @ X883 @ (setadjoin @ X884 @ emptyset))))=>(![X885:$i, X886:$i > $o]:((?[X887:$i]:(((in @ X887 @ X885)&(X886 @ X887)))=>(((dsetconstr @ X885 @ X886)=(emptyset))=>~($true))))=>(![X888:$i > $o, X889:$i]:(((in @ X889 @ emptyset)=>(X888 @ X889)))=>(![X890:$i, X891:$i > $o]:((~(![X892:$i]:(((in @ X892 @ X890)=>(X891 @ X892))))=>?[X893:$i]:(((in @ X893 @ X890)&~((X891 @ X893))))))=>(![X894:$i, X895:$i > $o]:((![X896:$i]:(((in @ X896 @ X894)=>~((X895 @ X896))))=>~(?[X897:$i]:(((in @ X897 @ X894)&(X895 @ X897))))))=>(![X898:$i, X899:$i > $o]:((~(?[X900:$i]:(((in @ X900 @ X898)&(X899 @ X900))))=>![X901:$i]:(((in @ X901 @ X898)=>~((X899 @ X901))))))=>(![X902:$i, X903:$i > $o]:((?[X904:$i]:(((in @ X904 @ X902)&~((X903 @ X904))))=>~(![X905:$i]:(((in @ X905 @ X902)=>(X903 @ X905))))))=>(![X906:$o]:(((X906)=>(in @ emptyset @ (prop2set @ ((X906))))))=>(![X907:$o]:(((X907)=>(set2prop @ (prop2set @ ((X907))))))=>(![X908:$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:$i]:(((in @ X915 @ X912)&~((X913 @ X915))))))=>(![X916:$i > $o]:((?[X917:$i]:(((X916 @ X917)&![X918:$i]:(((X916 @ X918)=>((X917)=(X918))))))=>?[X919:$i]:(((X916 @ X919)&![X920:$i]:(((X916 @ X920)=>((X919)=(X920))))))))=>(![X921:$i > $o]:((?[X922:$i]:((X921 @ X922))=>(![X923:$i, X924:$i]:(((X921 @ X923)=>((X921 @ X924)=>((X923)=(X924)))))=>?[X925:$i]:(((X921 @ X925)&![X926:$i]:(((X921 @ X926)=>((X925)=(X926)))))))))=>(![X927:$i > $o]:((?[X928:$i]:(![X929:$i]:(((X927 @ X929)<=>((X929)=(X928)))))=>?[X930:$i]:(((X927 @ X930)&![X931:$i]:(((X927 @ X931)=>((X930)=(X931))))))))=>(![X932:$i, X933:$i]:((((X932)=(X933))=>![X934:$i, X935:$i]:((((X934)=(X935))=>((in @ X934 @ X932)=>(in @ X935 @ X933))))))=>(![X936:$i, X937:$i]:((((X936)=(X937))=>![X938:$i, X939:$i]:((((X938)=(X939))=>((in @ X938 @ X936)<=>(in @ X939 @ X937))))))=>(![X940:$i > $o]:((?[X941:$i]:(((X940 @ X941)&![X942:$i]:(((X940 @ X942)=>((X941)=(X942))))))=>![X943:$i, X944:$i]:(((X940 @ X943)=>((X940 @ X944)=>((X943)=(X944)))))))=>(![X945:$i > $o, X946:$i > $o]:((![X947:$i, X948:$i]:((((X947)=(X948))=>((X945 @ X947)<=>(X946 @ X948))))=>(?[X949:$i]:(((X945 @ X949)&![X950:$i]:(((X945 @ X950)=>((X949)=(X950))))))<=>?[X951:$i]:(((X946 @ X951)&![X952:$i]:(((X946 @ X952)=>((X951)=(X952)))))))))=>(((emptyset)=(emptyset))=>(![X953:$i, X954:$i]:((((X953)=(X954))=>![X955:$i, X956:$i]:((((X955)=(X956))=>((setadjoin @ X953 @ X955)=(setadjoin @ X954 @ X956))))))=>(![X957:$i, X958:$i]:((((X957)=(X958))=>((powerset @ X957)=(powerset @ X958))))=>(![X959:$i, X960:$i]:((((X959)=(X960))=>((setunion @ X959)=(setunion @ X960))))=>(((omega)=(omega))=>(![X961:$i > $o]:((?[X962:$i]:(((X961 @ X962)&![X963:$i]:(((X961 @ X963)=>((X962)=(X963))))))=>![X964:$i, X965:$i]:(((X961 @ X964)=>((X961 @ X965)=>((X964)=(X965)))))))=>(![X966:$i > $o, X967:$i > $o]:((![X968:$i, X969:$i]:((((X968)=(X969))=>((X966 @ X968)<=>(X967 @ X969))))=>(?[X970:$i]:(((X966 @ X970)&![X971:$i]:(((X966 @ X971)=>((X970)=(X971))))))=>(?[X972:$i]:(((X967 @ X972)&![X973:$i]:(((X967 @ X973)=>((X972)=(X973))))))=>((descr @ X966)=(descr @ X967))))))=>(![X974:$i, X975:$i]:((((X974)=(X975))=>![X976:$i > $o, X977:$i > $o]:((![X978:$i]:(((in @ X978 @ X974)=>![X979:$i]:(((in @ X979 @ X975)=>(((X978)=(X979))=>((X976 @ X978)<=>(X977 @ X979)))))))=>((dsetconstr @ X974 @ X976)=(dsetconstr @ X975 @ X977))))))=>(![X980:$i, X981:$i]:((![X982:$i]:(((in @ X982 @ X980)=>(in @ X982 @ X981)))=>(subset @ X980 @ X981)))=>(![X983:$i, X984:$i]:((((X983)=(X984))=>(subset @ X984 @ X983)))=>(![X985:$i, X986:$i]:((((X985)=(X986))=>(subset @ X985 @ X986)))=>(![X987:$i, X988:$i]:((![X989:$i]:(((in @ X989 @ X987)=>(in @ X989 @ X988)))=>(subset @ X987 @ X988)))=>(![X990:$i]:((subset @ emptyset @ X990))=>(![X991:$i, X992:$i, X993:$i]:(((subset @ X991 @ X992)=>((in @ X993 @ 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X1347))=>![X1349:$i > $o]:((![X1350:$i]:(((in @ X1350 @ X1346)=>![X1351:$i]:(((in @ X1351 @ X1347)=>((in @ (kpair @ X1350 @ X1351) @ X1348)=>(X1349 @ (kpair @ X1350 @ X1351)))))))=>![X1352:$i]:(((in @ X1352 @ X1348)=>(X1349 @ X1352)))))))=>(![X1353:$i, X1354:$i > $o]:((?[X1355:$i]:(((in @ X1355 @ (dsetconstr @ X1353 @ X1354))&((dsetconstr @ X1353 @ X1354)=(setadjoin @ X1355 @ emptyset))))=>![X1356:$i]:(((in @ X1356 @ X1353)=>![X1357:$i]:(((in @ X1357 @ X1353)=>((X1354 @ X1356)=>((X1354 @ X1357)=>((X1356)=(X1357))))))))))=>(![X1358:$i, X1359:$i, X1360:$i]:(((func @ X1358 @ X1359 @ X1360)=>![X1361:$i]:(((in @ X1361 @ X1358)=>(in @ (kpair @ X1361 @ (ap @ X1358 @ X1359 @ X1360 @ X1361)) @ X1360)))))=>(![X1362:$i, X1363:$i, X1364:$i]:(((in @ X1364 @ (funcSet @ X1362 @ X1363))=>![X1365:$i]:(((in @ X1365 @ X1362)=>(in @ (kpair @ X1365 @ (ap @ X1362 @ X1363 @ X1364 @ X1365)) @ X1364)))))=>(![X1366:$i, X1367:$i, X1368:$i]:(((func @ X1366 @ X1367 @ X1368)=>![X1369:$i]:(((in @ X1369 @ X1366)=>![X1370:$i]:(((in @ X1370 @ X1367)=>((in @ (kpair @ X1369 @ X1370) @ X1368)=>((ap @ X1366 @ X1367 @ X1368 @ X1369)=(X1370)))))))))=>(![X1371:$i, X1372:$i, X1373:$i]:(((func @ X1371 @ X1372 @ X1373)=>![X1374:$i]:(((func @ X1371 @ X1372 @ X1374)=>(![X1375:$i]:(((in @ X1375 @ X1371)=>((ap @ X1371 @ X1372 @ X1373 @ X1375)=(ap @ X1371 @ X1372 @ X1374 @ X1375))))=>![X1376:$i]:(((in @ X1376 @ X1371)=>![X1377:$i]:(((in @ X1377 @ X1372)=>((in @ (kpair @ X1376 @ X1377) @ X1374)=>(in @ (kpair @ X1376 @ X1377) @ X1373)))))))))))=>(![X1378:$i, X1379:$i, X1380:$i]:(((in @ X1380 @ (funcSet @ X1378 @ X1379))=>![X1381:$i]:(((in @ X1381 @ X1378)=>![X1382:$i]:(((in @ X1382 @ X1379)=>((in @ (kpair @ X1381 @ X1382) @ X1380)=>((ap @ X1378 @ X1379 @ X1380 @ X1381)=(X1382)))))))))=>(![X1383:$i, X1384:$i, X1385:$i]:(((subset @ X1385 @ (cartprod @ X1383 @ X1384))=>![X1386:$i]:(((subset @ X1386 @ (cartprod @ X1383 @ X1384))=>(![X1387:$i]:(((in @ X1387 @ X1383)=>![X1388:$i]:(((in @ X1388 @ X1384)=>((in @ (kpair @ X1387 @ X1388) @ X1385)=>(in @ (kpair @ X1387 @ X1388) @ X1386))))))=>(subset @ X1385 @ X1386))))))=>(![X1389:$i, X1390:$i, X1391:$i]:(((subset @ X1391 @ (cartprod @ X1389 @ X1390))=>![X1392:$i]:(((subset @ X1392 @ (cartprod @ X1389 @ X1390))=>(![X1393:$i]:(((in @ X1393 @ X1389)=>![X1394:$i]:(((in @ X1394 @ X1390)=>((in @ (kpair @ X1393 @ X1394) @ X1391)=>(in @ (kpair @ X1393 @ X1394) @ X1392))))))=>(![X1395:$i]:(((in @ X1395 @ X1389)=>![X1396:$i]:(((in @ X1396 @ X1390)=>((in @ (kpair @ X1395 @ X1396) @ X1392)=>(in @ (kpair @ X1395 @ X1396) @ X1391))))))=>((X1391)=(X1392))))))))=>(![X1397:$i, X1398:$i, X1399:$i]:(((func @ X1397 @ X1398 @ X1399)=>![X1400:$i]:(((func @ X1397 @ X1398 @ X1400)=>(![X1401:$i]:(((in @ X1401 @ X1397)=>((ap @ X1397 @ X1398 @ X1399 @ X1401)=(ap @ X1397 @ X1398 @ X1400 @ X1401))))=>((X1399)=(X1400)))))))=>(![X1402:$i, X1403:$i, X1404:$i]:(((in @ X1404 @ (funcSet @ X1402 @ X1403))=>![X1405:$i]:(((in @ X1405 @ (funcSet @ X1402 @ X1403))=>(![X1406:$i]:(((in @ X1406 @ X1402)=>((ap @ X1402 @ X1403 @ X1404 @ X1406)=(ap @ X1402 @ X1403 @ X1405 @ X1406))))=>((X1404)=(X1405)))))))=>(![X1407:$i, X1408:$i, X1409:$i]:(((in @ X1409 @ (funcSet @ X1407 @ X1408))=>![X1410:$i]:(((in @ X1410 @ X1407)=>((ap @ X1407 @ X1408 @ X1409 @ X1410)=(ap @ X1407 @ X1408 @ X1409 @ X1410))))))=>(![X1411:$i, X1412:$i, X1413:$i]:(((func @ X1411 @ X1412 @ X1413)=>![X1414:$i]:(((in @ X1414 @ X1411)=>((ap @ X1411 @ X1412 @ X1413 @ X1414)=(ap @ X1411 @ X1412 @ X1413 @ X1414))))))=>(![X1415:$i, X1416:$i, X1417:$i > $i]:((![X1418:$i]:(((in @ X1418 @ X1415)=>(in @ (X1417 @ X1418) @ X1416)))=>![X1419:$i]:(((in @ X1419 @ X1415)=>((ap @ X1415 @ X1416 @ (lam @ X1415 @ X1416 @ X1417) @ X1419)=(X1417 @ X1419))))))=>(![X1420:$i, X1421:$i, X1422:$i]:(((func @ X1420 @ X1421 @ X1422)=>((lam @ X1420 @ X1421 @ (ap @ X1420 @ X1421 @ X1422))=(X1422))))=>(![X1423:$i, X1424:$i, X1425:$i > $i]:((![X1426:$i]:(((in @ X1426 @ X1423)=>(in @ (X1425 @ X1426) @ X1424)))=>((lam @ X1423 @ X1424 @ X1425)=(lam @ X1423 @ X1424 @ X1425))))=>(![X1427:$i, X1428:$i, X1429:$i > $i]:((![X1430:$i]:(((in @ X1430 @ X1427)=>(in @ (X1429 @ X1430) @ X1428)))=>![X1431:$i]:(((in @ X1431 @ X1427)=>((ap @ X1427 @ X1428 @ (lam @ X1427 @ X1428 @ X1429) @ X1431)=(X1429 @ X1431))))))=>(![X1432:$i, X1433:$i, X1434:$i]:(((in @ X1434 @ (funcSet @ X1432 @ X1433))=>((lam @ X1432 @ X1433 @ (ap @ X1432 @ X1433 @ X1434))=(X1434))))=>![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(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_250]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_251]), foundationAx]), wellorderingAx]), c_0_252]), c_0_253]), c_0_254]), c_0_255]), c_0_256]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_257]), setext]), emptyI]), noeltsimpempty]), c_0_258]), c_0_259]), c_0_260]), c_0_261]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_262]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_263]), c_0_264]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_265]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_266]), c_0_267]), c_0_268]), inCongP]), in__Cong]), c_0_269]), c_0_270]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_271]), c_0_272]), c_0_273]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_274]), c_0_275]), 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]), c_0_276]), c_0_277]), c_0_278]), c_0_279]), singletonsuniq]), setukpairinjL1]), c_0_280]), c_0_281]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_282]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), c_0_297]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_298]), c_0_299]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304])])]), c_0_305])).
% 0.58/0.47 thf(c_0_307, negated_conjecture, ![X1435:$i, X1436:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1448:$i, X1449:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1457:$i, X1458:$i > $i > $o, X1459:$i, X1461:$i, X1464:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1471:$i, X1472:$i > $o, X1473:$i, X1475:$i, X1476:$i > $o, X1477:$i, X1478:$i, X1479:$i > $o, X1480:$i, X1481:$i, X1482:$i > $o, X1483:$i, X1484:$i > $o, X1485:$i, X1488:$i, X1489:$o, X1490:$i, X1491:$i, X1492:$o, X1493:$i, X1494:$i, X1495:$i > $o, X1496:$i, X1499:$i, X1500:$i, X1503:$i, X1505:$i, X1507:$i, X1508:$i > $o, X1509:$i, X1510:$i, X1512:$i, X1513:$i > $o, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$o, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$o, X1545:$i, X1546:$i, X1547:$i > $o, X1548:$i, X1551:$i, X1552:$i, X1553:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i > $o, X1572:$i, X1573:$i > $o, X1574:$i, X1575:$i, X1576:$i > $o, X1577:$i, X1579:$i, X1580:$i > $o, X1582:$i, X1583:$i, X1584:$i > $o, X1586:$i, X1587:$i, X1588:$i > $o, X1589:$i, X1591:$o, X1592:$o, X1593:$i, X1594:$i > $o, X1596:$i, X1597:$i, X1598:$i > $o, X1599:$i, X1601:$i > $o, X1602:$i, X1605:$i, X1606:$i > $o, X1607:$i, X1611:$i, X1612:$i > $o, X1613:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i > $o, X1626:$i, X1628:$i, X1629:$i, X1630:$i > $o, X1631:$i > $o, X1634:$i, X1637:$i, X1638:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i > $o, X1651:$i, X1653:$i, X1654:$i, X1655:$i > $o, X1656:$i > $o, X1659:$i, X1661:$i, X1663:$i, X1664:$i, X1665:$i > $o, X1666:$i > $o, X1669:$i, X1670:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i > $o, X1717:$i, X1718:$i > $o, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$o, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, 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:$i, X1776:$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:$i, X1798:$o, 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:$i, X1816:$i, 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:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i > $o, X1873:$i, X1875:$i, X1876:$i > $o, X1877:$i, X1879:$i, X1880:$i > $o, X1881:$i, X1884:$i, X1885:$i > $o, X1888:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$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:$i, X1933:$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, X1950:$i, X1951:$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 > $i > $o, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i > $i > $o, X1970:$i, X1971:$i, X1972:$i > $i > $o, X1973:$i, X1974:$i, X1975:$i > $i > $o, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i > $i > $o, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i > $i > $o, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i > $i > $o, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i > $i, X2020:$i, X2021:$i, X2022:$i > $i, X2024:$i, X2025:$i, X2026:$i > $i, X2028:$i, X2029:$i, X2030:$i, X2031:$i > $o, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i > $o, X2041:$i, X2042:$i, X2043:$i > $o, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i > $i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i > $i, X2116:$i, X2117:$i, X2118:$i > $i, X2120:$i, X2121:$i, X2122:$i, X2123:$i]:((((~(in @ (esk1_2 @ X1435 @ X1436) @ X1435)|~(in @ (esk1_2 @ X1435 @ X1436) @ X1436)|((X1435)=(X1436)))&((in @ (esk1_2 @ X1435 @ X1436) @ X1435)|(in @ (esk1_2 @ X1435 @ X1436) @ X1436)|((X1435)=(X1436))))&(~(in @ X1438 @ emptyset)&(((~(in @ X1441 @ (setadjoin @ X1439 @ X1440))|(((X1441)=(X1439))|(in @ X1441 @ X1440)))&((((X1441)!=(X1439))|(in @ X1441 @ (setadjoin @ X1439 @ X1440)))&(~(in @ X1441 @ X1440)|(in @ X1441 @ (setadjoin @ X1439 @ X1440)))))&(((~(in @ X1443 @ (powerset @ X1442))|(~(in @ X1444 @ X1443)|(in @ X1444 @ X1442)))&(((in @ (esk2_2 @ X1445 @ X1446) @ X1446)|(in @ X1446 @ (powerset @ X1445)))&(~(in @ (esk2_2 @ X1445 @ X1446) @ X1445)|(in @ X1446 @ (powerset @ X1445)))))&(((((in @ X1449 @ (esk3_2 @ X1448 @ X1449))|~(in @ X1449 @ (setunion @ X1448)))&((in @ (esk3_2 @ X1448 @ X1449) @ X1448)|~(in @ X1449 @ (setunion @ X1448))))&(~(in @ X1452 @ X1453)|~(in @ X1453 @ X1451)|(in @ X1452 @ (setunion @ X1451))))&((in @ emptyset @ omega)&((~(in @ X1454 @ omega)|(in @ (setadjoin @ X1454 @ X1454) @ omega))&(((((in @ (esk4_1 @ X1455) @ omega)|~(in @ emptyset @ X1455)|(~(in @ X1457 @ omega)|(in @ X1457 @ X1455)))&((in @ (esk4_1 @ X1455) @ X1455)|~(in @ emptyset @ X1455)|(~(in @ X1457 @ omega)|(in @ X1457 @ X1455))))&(~(in @ (setadjoin @ (esk4_1 @ X1455) @ (esk4_1 @ X1455)) @ X1455)|~(in @ emptyset @ X1455)|(~(in @ X1457 @ omega)|(in @ X1457 @ X1455))))&((((((in @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1459)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|(in @ (esk5_2 @ X1458 @ X1459) @ X1459))&((X1458 @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1464)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|(in @ (esk5_2 @ X1458 @ X1459) @ X1459)))&(~(in @ X1467 @ X1459)|~(X1458 @ X1467 @ X1466)|(in @ X1466 @ (esk7_2 @ X1458 @ X1459))|(in @ (esk5_2 @ X1458 @ X1459) @ X1459)))&(((((in @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1459)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|((X1458 @ (esk5_2 @ X1458 @ X1459) @ (esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461)))&((X1458 @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1464)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|((X1458 @ (esk5_2 @ X1458 @ X1459) @ (esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461))))&(~(in @ X1467 @ X1459)|~(X1458 @ X1467 @ X1466)|(in @ X1466 @ (esk7_2 @ X1458 @ X1459))|((X1458 @ (esk5_2 @ X1458 @ X1459) @ (esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461))))&((((in @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1459)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|(((X1461)!=(esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461)))&((X1458 @ (esk8_3 @ X1458 @ X1459 @ X1464) @ X1464)|~(in @ X1464 @ (esk7_2 @ X1458 @ X1459))|(((X1461)!=(esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461))))&(~(in @ X1467 @ X1459)|~(X1458 @ X1467 @ X1466)|(in @ X1466 @ (esk7_2 @ X1458 @ X1459))|(((X1461)!=(esk6_3 @ X1458 @ X1459 @ X1461))|~(X1458 @ (esk5_2 @ X1458 @ X1459) @ X1461))))))&((((in @ (esk9_1 @ X1468) @ X1468)|~(in @ X1469 @ X1468))&(~(in @ X1471 @ (esk9_1 @ X1468))|~(in @ X1471 @ X1468)|~(in @ X1469 @ X1468)))&((epred1_0)&((((X1472 @ (esk10_2 @ X1472 @ X1473))|~(X1472 @ X1473)|(X1472 @ (descr @ X1472)))&(((X1473)!=(esk10_2 @ X1472 @ X1473))|~(X1472 @ X1473)|(X1472 @ (descr @ X1472))))&((~(in @ X1477 @ X1475)|(~(X1476 @ X1477)|(in @ X1477 @ (dsetconstr @ X1475 @ X1476))))&((~(in @ X1480 @ (dsetconstr @ X1478 @ X1479))|(in @ X1480 @ X1478))&((~(in @ X1483 @ (dsetconstr @ X1481 @ X1482))|(X1482 @ X1483))&(((((X1484 @ (esk12_1 @ X1484))|((X1484 @ (esk11_2 @ X1484 @ X1485))|~(X1484 @ X1485)))&(~(X1484 @ X1488)|((esk12_1 @ X1484)=(X1488))|((X1484 @ (esk11_2 @ X1484 @ X1485))|~(X1484 @ X1485))))&(((X1484 @ (esk12_1 @ X1484))|(((X1485)!=(esk11_2 @ X1484 @ X1485))|~(X1484 @ X1485)))&(~(X1484 @ X1488)|((esk12_1 @ X1484)=(X1488))|(((X1485)!=(esk11_2 @ X1484 @ X1485))|~(X1484 @ X1485)))))&((~(in @ X1490 @ (prop2set @ ((X1489))))|(X1489))&((~(in @ X1491 @ emptyset)|(X1492))&((~(in @ X1493 @ emptyset)|~($true))&(~(in @ X1494 @ emptyset)&((((X1495 @ (esk13_2 @ X1495 @ X1496))|~(X1495 @ X1496)|(X1495 @ (esk14_1 @ X1495)))&(((X1496)!=(esk13_2 @ X1495 @ X1496))|~(X1495 @ X1496)|(X1495 @ (esk14_1 @ X1495))))&(((((in @ (esk16_2 @ X1499 @ X1500) @ X1500)|((X1499)=(X1500))|(in @ (esk15_2 @ X1499 @ X1500) @ X1499))&(~(in @ (esk16_2 @ X1499 @ X1500) @ X1499)|((X1499)=(X1500))|(in @ (esk15_2 @ X1499 @ X1500) @ X1499)))&(((in @ (esk16_2 @ X1499 @ X1500) @ X1500)|((X1499)=(X1500))|~(in @ (esk15_2 @ X1499 @ X1500) @ X1500))&(~(in @ (esk16_2 @ X1499 @ X1500) @ X1499)|((X1499)=(X1500))|~(in @ (esk15_2 @ X1499 @ X1500) @ X1500))))&(((in @ (esk17_1 @ X1503) @ X1503)|((X1503)=(emptyset)))&(((in @ (esk18_1 @ X1505) @ X1505)|((X1505)=(emptyset)))&(((~(in @ X1509 @ (dsetconstr @ X1507 @ X1508))|(X1508 @ X1509)|~(in @ X1509 @ X1507))&(~(X1508 @ X1509)|(in @ X1509 @ (dsetconstr @ X1507 @ X1508))|~(in @ X1509 @ X1507)))&((((X1510)=(emptyset))|(in @ (esk19_1 @ X1510) @ X1510))&((~(in @ X1514 @ X1512)|(~(X1513 @ X1514)|((dsetconstr @ X1512 @ X1513)!=(emptyset))))&((~(in @ X1516 @ X1515)|((X1515)!=(emptyset)))&((in @ X1517 @ (setadjoin @ X1517 @ X1518))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1521 @ X1520)|(in @ X1521 @ (setadjoin @ X1519 @ X1520)))&(((((in @ X1524 @ X1523)|(X1525)|((X1524)=(X1522))|~(in @ X1524 @ (setadjoin @ X1522 @ X1523)))&(~(X1525)|(X1525)|((X1524)=(X1522))|~(in @ X1524 @ (setadjoin @ X1522 @ X1523))))&(((in @ X1524 @ X1523)|(X1525)|~(X1525)|~(in @ X1524 @ (setadjoin @ X1522 @ X1523)))&(~(X1525)|(X1525)|~(X1525)|~(in @ X1524 @ (setadjoin @ X1522 @ X1523)))))&((~(in @ X1528 @ (setadjoin @ X1526 @ X1527))|(((X1528)=(X1526))|(in @ X1528 @ X1527)))&(((dsetconstr @ X1529 @ (^[Z0:$i]:($true)))=(X1529))&((((in @ (esk20_2 @ X1530 @ X1531) @ X1531)|(in @ X1531 @ (powerset @ X1530)))&(~(in @ (esk20_2 @ X1530 @ X1531) @ X1530)|(in @ X1531 @ (powerset @ X1530))))&((in @ emptyset @ (powerset @ X1533))&((in @ emptyset @ (powerset @ X1534))&((~(in @ X1536 @ (powerset @ X1535))|(~(in @ X1537 @ X1536)|(in @ X1537 @ X1535)))&((~(in @ X1539 @ X1540)|(~(in @ X1540 @ X1538)|(in @ X1539 @ (setunion @ X1538))))&((((in @ X1542 @ (esk21_3 @ X1541 @ X1542 @ X1543))|(X1543)|~(in @ X1542 @ (setunion @ X1541)))&(((in @ (esk21_3 @ X1541 @ X1542 @ X1543) @ X1541)|(X1543)|~(in @ X1542 @ (setunion @ X1541)))&(~(X1543)|(X1543)|~(in @ X1542 @ (setunion @ X1541)))))&((~(in @ X1546 @ X1545)|(in @ X1546 @ (powerset @ (setunion @ X1545))))&((((~(X1547 @ X1551)|((X1551)=(esk23_1 @ X1547))|((X1547 @ (esk22_2 @ X1547 @ X1548))|~(X1547 @ X1548)))&(((X1552)!=(esk23_1 @ X1547))|(X1547 @ X1552)|((X1547 @ (esk22_2 @ X1547 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emptyset)|(X1573 @ X1574))&((((in @ (esk25_2 @ X1575 @ X1576) @ X1575)|(~(in @ X1577 @ X1575)|(X1576 @ X1577)))&(~(X1576 @ (esk25_2 @ X1575 @ X1576))|(~(in @ X1577 @ X1575)|(X1576 @ X1577))))&((((in @ (esk26_2 @ X1579 @ X1580) @ X1579)|(~(in @ X1582 @ X1579)|~(X1580 @ X1582)))&((X1580 @ (esk26_2 @ X1579 @ X1580))|(~(in @ X1582 @ X1579)|~(X1580 @ X1582))))&((((in @ (esk27_2 @ X1583 @ X1584) @ X1583)|(~(in @ X1586 @ X1583)|~(X1584 @ X1586)))&((X1584 @ (esk27_2 @ X1583 @ X1584))|(~(in @ X1586 @ X1583)|~(X1584 @ X1586))))&((((in @ (esk28_2 @ X1587 @ X1588) @ X1587)|(~(in @ X1589 @ X1587)|(X1588 @ X1589)))&(~(X1588 @ (esk28_2 @ X1587 @ X1588))|(~(in @ X1589 @ X1587)|(X1588 @ X1589))))&((~(X1591)|(in @ emptyset @ (prop2set @ ((X1591)))))&((~(X1592)|(set2prop @ (prop2set @ ((X1592)))))&((((in @ (esk29_2 @ X1593 @ X1594) @ X1593)|(~(in @ X1596 @ X1593)|~(X1594 @ X1596)))&((X1594 @ (esk29_2 @ X1593 @ X1594))|(~(in @ X1596 @ X1593)|~(X1594 @ X1596))))&((((in @ (esk30_2 @ X1597 @ X1598) @ 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@ Z0) @ X1995)))))|~(in @ X1996 @ X1993)|~(func @ X1993 @ X1994 @ X1995))&(((dsetconstr @ X1994 @ (^[Z0:$i]:((in @ (kpair @ X1996 @ Z0) @ X1995))))=(setadjoin @ (esk69_4 @ X1993 @ X1994 @ X1995 @ X1996) @ emptyset))|~(in @ X1996 @ X1993)|~(func @ X1993 @ X1994 @ X1995)))&((~(func @ X1998 @ X1999 @ X2000)|(~(in @ X2001 @ X1998)|(in @ (setunion @ (dsetconstr @ X1999 @ (^[Z0:$i]:((in @ (kpair @ X2001 @ Z0) @ X2000))))) @ X1999)))&((~(func @ X2002 @ X2003 @ X2004)|(~(in @ X2005 @ X2002)|(in @ (ap @ X2002 @ X2003 @ X2004 @ X2005) @ X2003)))&((~(in @ X2008 @ (funcSet @ X2006 @ X2007))|(func @ X2006 @ X2007 @ X2008))&((~(in @ X2011 @ (funcSet @ X2009 @ X2010))|(~(in @ X2012 @ X2009)|(in @ (ap @ X2009 @ X2010 @ X2011 @ X2012) @ X2010)))&((~(func @ X2013 @ X2014 @ X2015)|(in @ X2015 @ (funcSet @ X2013 @ X2014)))&((((in @ (esk70_3 @ X2016 @ X2017 @ X2018) @ X2016)|(func @ X2016 @ X2017 @ (dpsetconstr @ X2016 @ X2017 @ (^[Z0:$i]:($eq @ (X2018 @ Z0))))))&(~(in @ (X2018 @ (esk70_3 @ X2016 @ X2017 @ X2018)) @ X2017)|(func @ X2016 @ X2017 @ (dpsetconstr @ X2016 @ X2017 @ (^[Z0:$i]:($eq @ (X2018 @ Z0)))))))&((((in @ (esk71_3 @ X2020 @ X2021 @ X2022) @ X2020)|(func @ X2020 @ X2021 @ (lam @ X2020 @ X2021 @ X2022)))&(~(in @ (X2022 @ (esk71_3 @ X2020 @ X2021 @ X2022)) @ X2021)|(func @ X2020 @ X2021 @ (lam @ X2020 @ X2021 @ X2022))))&((((in @ (esk72_3 @ X2024 @ X2025 @ X2026) @ X2024)|(in @ (lam @ X2024 @ X2025 @ X2026) @ (funcSet @ X2024 @ X2025)))&(~(in @ (X2026 @ (esk72_3 @ X2024 @ X2025 @ X2026)) @ X2025)|(in @ (lam @ X2024 @ X2025 @ X2026) @ (funcSet @ X2024 @ X2025))))&((((in @ (esk73_4 @ X2028 @ X2029 @ X2030 @ X2031) @ X2028)|(~(in @ X2034 @ X2030)|(X2031 @ X2034))|~(subset @ X2030 @ (cartprod @ X2028 @ X2029)))&(((in @ (esk74_4 @ X2028 @ X2029 @ X2030 @ X2031) @ X2029)|(~(in @ X2034 @ X2030)|(X2031 @ X2034))|~(subset @ X2030 @ (cartprod @ X2028 @ X2029)))&(((in @ (kpair @ (esk73_4 @ X2028 @ X2029 @ X2030 @ X2031) @ (esk74_4 @ X2028 @ X2029 @ X2030 @ X2031)) @ X2030)|(~(in @ X2034 @ X2030)|(X2031 @ X2034))|~(subset @ X2030 @ (cartprod @ X2028 @ X2029)))&(~(X2031 @ (kpair @ (esk73_4 @ X2028 @ X2029 @ X2030 @ X2031) @ (esk74_4 @ X2028 @ X2029 @ X2030 @ X2031)))|(~(in @ X2034 @ X2030)|(X2031 @ X2034))|~(subset @ X2030 @ (cartprod @ X2028 @ X2029))))))&((((in @ (esk75_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2035)|(~(in @ X2041 @ X2037)|(X2038 @ X2041))|~(subset @ X2037 @ (cartprod @ X2035 @ X2036)))&(((in @ (esk76_4 @ X2035 @ X2036 @ X2037 @ X2038) @ X2036)|(~(in @ X2041 @ X2037)|(X2038 @ X2041))|~(subset @ X2037 @ (cartprod @ X2035 @ X2036)))&(((in @ (kpair @ (esk75_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk76_4 @ X2035 @ X2036 @ X2037 @ X2038)) @ X2037)|(~(in @ X2041 @ X2037)|(X2038 @ X2041))|~(subset @ X2037 @ (cartprod @ X2035 @ X2036)))&(~(X2038 @ (kpair @ (esk75_4 @ X2035 @ X2036 @ X2037 @ X2038) @ (esk76_4 @ X2035 @ X2036 @ X2037 @ X2038)))|(~(in @ X2041 @ X2037)|(X2038 @ X2041))|~(subset @ X2037 @ (cartprod @ X2035 @ X2036))))))&((~(in @ X2044 @ (dsetconstr @ X2042 @ X2043))|((dsetconstr @ X2042 @ X2043)!=(setadjoin @ X2044 @ emptyset))|(~(in @ X2045 @ X2042)|(~(in @ X2046 @ X2042)|(~(X2043 @ X2045)|(~(X2043 @ X2046)|((X2045)=(X2046)))))))&((~(func @ X2047 @ X2048 @ X2049)|(~(in @ X2050 @ X2047)|(in @ (kpair @ X2050 @ (ap @ X2047 @ X2048 @ X2049 @ X2050)) @ X2049)))&((~(in @ X2053 @ (funcSet @ X2051 @ X2052))|(~(in @ X2054 @ X2051)|(in @ (kpair @ X2054 @ (ap @ X2051 @ X2052 @ X2053 @ X2054)) @ X2053)))&((~(func @ X2055 @ X2056 @ X2057)|(~(in @ X2058 @ X2055)|(~(in @ X2059 @ X2056)|(~(in @ (kpair @ X2058 @ X2059) @ X2057)|((ap @ X2055 @ X2056 @ X2057 @ X2058)=(X2059))))))&((((in @ (esk77_4 @ X2060 @ X2061 @ X2062 @ X2063) @ X2060)|(~(in @ X2065 @ X2060)|(~(in @ X2066 @ X2061)|(~(in @ (kpair @ X2065 @ X2066) @ X2063)|(in @ (kpair @ X2065 @ X2066) @ X2062))))|~(func @ X2060 @ X2061 @ X2063)|~(func @ X2060 @ X2061 @ X2062))&(((ap @ X2060 @ X2061 @ X2062 @ (esk77_4 @ X2060 @ X2061 @ X2062 @ X2063))!=(ap @ X2060 @ X2061 @ X2063 @ (esk77_4 @ X2060 @ X2061 @ X2062 @ X2063)))|(~(in @ X2065 @ X2060)|(~(in @ X2066 @ X2061)|(~(in @ (kpair @ X2065 @ X2066) @ X2063)|(in @ (kpair @ X2065 @ X2066) @ X2062))))|~(func @ X2060 @ X2061 @ X2063)|~(func @ X2060 @ X2061 @ X2062)))&((~(in @ X2069 @ (funcSet @ X2067 @ X2068))|(~(in @ X2070 @ X2067)|(~(in @ X2071 @ X2068)|(~(in @ (kpair @ X2070 @ X2071) @ X2069)|((ap @ X2067 @ X2068 @ X2069 @ X2070)=(X2071))))))&((((in @ (esk78_4 @ X2072 @ X2073 @ X2074 @ X2075) @ X2072)|(subset @ X2074 @ X2075)|~(subset @ X2075 @ (cartprod @ X2072 @ X2073))|~(subset @ X2074 @ (cartprod @ X2072 @ X2073)))&(((in @ (esk79_4 @ X2072 @ X2073 @ X2074 @ X2075) @ X2073)|(subset @ X2074 @ X2075)|~(subset @ X2075 @ (cartprod @ X2072 @ X2073))|~(subset @ X2074 @ (cartprod @ X2072 @ X2073)))&(((in @ (kpair @ (esk78_4 @ X2072 @ X2073 @ X2074 @ X2075) @ (esk79_4 @ X2072 @ X2073 @ X2074 @ X2075)) @ X2074)|(subset @ X2074 @ X2075)|~(subset @ X2075 @ (cartprod @ X2072 @ X2073))|~(subset @ X2074 @ (cartprod @ X2072 @ X2073)))&(~(in @ (kpair @ (esk78_4 @ X2072 @ X2073 @ X2074 @ X2075) @ (esk79_4 @ X2072 @ X2073 @ X2074 @ X2075)) @ X2075)|(subset @ X2074 @ X2075)|~(subset @ X2075 @ (cartprod @ X2072 @ X2073))|~(subset @ X2074 @ (cartprod @ X2072 @ X2073))))))&(((((in @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|((X2080)=(X2081))|(in @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|((X2080)=(X2081))|(in @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|((X2080)=(X2081))|(in @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(~(in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|((X2080)=(X2081))|(in @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079))))))&((((in @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|((X2080)=(X2081))|(in @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|((X2080)=(X2081))|(in @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|((X2080)=(X2081))|(in @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(~(in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|((X2080)=(X2081))|(in @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079))))))&((((in @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|((X2080)=(X2081))|(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|((X2080)=(X2081))|(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|((X2080)=(X2081))|(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(~(in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|((X2080)=(X2081))|(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079))))))&(((in @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|((X2080)=(X2081))|~(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2079)|((X2080)=(X2081))|~(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(((in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|((X2080)=(X2081))|~(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))&(~(in @ (kpair @ (esk82_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk83_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2080)|((X2080)=(X2081))|~(in @ (kpair @ (esk80_4 @ X2078 @ X2079 @ X2080 @ X2081) @ (esk81_4 @ X2078 @ X2079 @ X2080 @ X2081)) @ X2081)|~(subset @ X2081 @ (cartprod @ X2078 @ X2079))|~(subset @ X2080 @ (cartprod @ X2078 @ X2079)))))))))&((((in @ (esk84_4 @ X2086 @ X2087 @ X2088 @ X2089) @ X2086)|((X2088)=(X2089))|~(func @ X2086 @ X2087 @ X2089)|~(func @ X2086 @ X2087 @ X2088))&(((ap @ X2086 @ X2087 @ X2088 @ (esk84_4 @ X2086 @ X2087 @ X2088 @ X2089))!=(ap @ X2086 @ X2087 @ X2089 @ (esk84_4 @ X2086 @ X2087 @ X2088 @ X2089)))|((X2088)=(X2089))|~(func @ X2086 @ X2087 @ X2089)|~(func @ X2086 @ X2087 @ X2088)))&((((in @ (esk85_4 @ X2091 @ X2092 @ X2093 @ X2094) @ X2091)|((X2093)=(X2094))|~(in @ X2094 @ (funcSet @ X2091 @ X2092))|~(in @ X2093 @ (funcSet @ X2091 @ X2092)))&(((ap @ X2091 @ X2092 @ X2093 @ (esk85_4 @ X2091 @ X2092 @ X2093 @ X2094))!=(ap @ X2091 @ X2092 @ X2094 @ (esk85_4 @ X2091 @ X2092 @ X2093 @ X2094)))|((X2093)=(X2094))|~(in @ X2094 @ (funcSet @ X2091 @ X2092))|~(in @ X2093 @ (funcSet @ X2091 @ X2092))))&((~(in @ X2098 @ (funcSet @ X2096 @ X2097))|(~(in @ X2099 @ X2096)|((ap @ X2096 @ X2097 @ X2098 @ X2099)=(ap @ X2096 @ X2097 @ X2098 @ X2099))))&((~(func @ X2100 @ X2101 @ X2102)|(~(in @ X2103 @ X2100)|((ap @ X2100 @ X2101 @ X2102 @ X2103)=(ap @ X2100 @ X2101 @ X2102 @ X2103))))&((((in @ (esk86_3 @ X2104 @ X2105 @ X2106) @ X2104)|(~(in @ X2108 @ X2104)|((ap @ X2104 @ X2105 @ (lam @ X2104 @ X2105 @ X2106) @ X2108)=(X2106 @ X2108))))&(~(in @ (X2106 @ (esk86_3 @ X2104 @ X2105 @ X2106)) @ X2105)|(~(in @ X2108 @ X2104)|((ap @ X2104 @ X2105 @ (lam @ X2104 @ X2105 @ X2106) @ X2108)=(X2106 @ X2108)))))&((~(func @ X2109 @ X2110 @ X2111)|((lam @ X2109 @ X2110 @ (ap @ X2109 @ X2110 @ X2111))=(X2111)))&((((in @ (esk87_3 @ X2112 @ X2113 @ X2114) @ X2112)|((lam @ X2112 @ X2113 @ X2114)=(lam @ X2112 @ X2113 @ X2114)))&(~(in @ (X2114 @ (esk87_3 @ X2112 @ X2113 @ X2114)) @ X2113)|((lam @ X2112 @ X2113 @ X2114)=(lam @ X2112 @ X2113 @ X2114))))&((((in @ (esk88_3 @ X2116 @ X2117 @ X2118) @ X2116)|(~(in @ X2120 @ X2116)|((ap @ X2116 @ X2117 @ (lam @ X2116 @ X2117 @ X2118) @ X2120)=(X2118 @ X2120))))&(~(in @ (X2118 @ (esk88_3 @ X2116 @ X2117 @ X2118)) @ X2117)|(~(in @ X2120 @ X2116)|((ap @ X2116 @ X2117 @ (lam @ X2116 @ X2117 @ X2118) @ X2120)=(X2118 @ X2120)))))&((~(in @ X2123 @ (funcSet @ X2121 @ X2122))|((lam @ X2121 @ X2122 @ (ap @ X2121 @ X2122 @ X2123))=(X2123)))&((in @ esk90_0 @ esk89_0)&((in @ esk91_0 @ esk89_0)&(~(epred2_0)&~(in @ esk91_0 @ (dsetconstr @ esk89_0 @ (^[Z0:$i]:((((((epred2_0))&(((Z0)=(esk90_0)))))|(((~((epred2_0)))&(((Z0)=(esk91_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_306])])])])])])])).
% 0.58/0.47 thf(c_0_308, plain, ![X2147:$i]:(((epred3_0 @ X2147)<=>(((epred2_0)&((X2147)=(esk90_0)))|(~((epred2_0))&((X2147)=(esk91_0)))))), introduced(definition)).
% 0.58/0.47 thf(c_0_309, plain, ![X2158:$i]:(((((~(epred2_0)|(epred2_0)|~(epred3_0 @ X2158))&(((X2158)=(esk91_0))|(epred2_0)|~(epred3_0 @ X2158)))&((~(epred2_0)|((X2158)=(esk90_0))|~(epred3_0 @ X2158))&(((X2158)=(esk91_0))|((X2158)=(esk90_0))|~(epred3_0 @ X2158))))&((~(epred2_0)|((X2158)!=(esk90_0))|(epred3_0 @ X2158))&((epred2_0)|((X2158)!=(esk91_0))|(epred3_0 @ X2158))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])])).
% 0.58/0.47 thf(c_0_310, negated_conjecture, ~((((in @ esk91_0 @ (dsetconstr @ esk89_0 @ epred3_0)))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_307]), c_0_308])).
% 0.58/0.47 thf(c_0_311, plain, ![X2:$i]:(((epred2_0)|(epred3_0 @ X2)|((X2)!=(esk91_0)))), inference(split_conjunct,[status(thm)],[c_0_309])).
% 0.58/0.47 thf(c_0_312, negated_conjecture, ~((epred2_0)), inference(split_conjunct,[status(thm)],[c_0_307])).
% 0.58/0.47 thf(c_0_313, negated_conjecture, ~((in @ esk91_0 @ (dsetconstr @ esk89_0 @ epred3_0))), inference(cn,[status(thm)],[c_0_310])).
% 0.58/0.47 thf(c_0_314, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_307])).
% 0.58/0.47 thf(c_0_315, negated_conjecture, (in @ esk91_0 @ esk89_0), inference(split_conjunct,[status(thm)],[c_0_307])).
% 0.58/0.47 thf(c_0_316, plain, (epred3_0 @ esk91_0), inference(er,[status(thm)],[inference(sr,[status(thm)],[c_0_311, c_0_312])])).
% 0.58/0.47 thf(c_0_317, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313, c_0_314]), c_0_315]), c_0_316])]), ['proof']).
% 0.58/0.47 % SZS output end CNFRefutation
% 0.58/0.47 % Parsed axioms : 475
% 0.58/0.47 % Removed by relevancy pruning/SinE : 0
% 0.58/0.47 % Initial clauses : 673
% 0.58/0.47 % Removed in clause preprocessing : 286
% 0.58/0.47 % Initial clauses in saturation : 387
% 0.58/0.47 % Processed clauses : 704
% 0.58/0.47 % ...of these trivial : 14
% 0.58/0.47 % ...subsumed : 329
% 0.58/0.47 % ...remaining for further processing : 361
% 0.58/0.47 % Other redundant clauses eliminated : 29
% 0.58/0.47 % Clauses deleted for lack of memory : 0
% 0.58/0.47 % Backward-subsumed : 1
% 0.58/0.47 % Backward-rewritten : 4
% 0.58/0.47 % Generated clauses : 5101
% 0.58/0.47 % ...of the previous two non-redundant : 4053
% 0.58/0.47 % ...aggressively subsumed : 0
% 0.58/0.47 % Contextual simplify-reflections : 0
% 0.58/0.47 % Paramodulations : 5067
% 0.58/0.47 % Factorizations : 2
% 0.58/0.47 % NegExts : 0
% 0.58/0.47 % Equation resolutions : 32
% 0.58/0.47 % Disequality decompositions : 0
% 0.58/0.47 % Total rewrite steps : 1979
% 0.58/0.47 % ...of those cached : 1870
% 0.58/0.47 % Propositional unsat checks : 0
% 0.58/0.47 % Propositional check models : 0
% 0.58/0.47 % Propositional check unsatisfiable : 0
% 0.58/0.47 % Propositional clauses : 0
% 0.58/0.47 % Propositional clauses after purity: 0
% 0.58/0.47 % Propositional unsat core size : 0
% 0.58/0.47 % Propositional preprocessing time : 0.000
% 0.58/0.47 % Propositional encoding time : 0.000
% 0.58/0.47 % Propositional solver time : 0.000
% 0.58/0.47 % Success case prop preproc time : 0.000
% 0.58/0.47 % Success case prop encoding time : 0.000
% 0.58/0.47 % Success case prop solver time : 0.000
% 0.58/0.47 % Current number of processed clauses : 346
% 0.58/0.47 % Positive orientable unit clauses : 114
% 0.58/0.47 % Positive unorientable unit clauses: 0
% 0.58/0.47 % Negative unit clauses : 4
% 0.58/0.47 % Non-unit-clauses : 228
% 0.58/0.47 % Current number of unprocessed clauses: 3712
% 0.58/0.47 % ...number of literals in the above : 10315
% 0.58/0.47 % Current number of archived formulas : 0
% 0.58/0.47 % Current number of archived clauses : 7
% 0.58/0.47 % Clause-clause subsumption calls (NU) : 6598
% 0.58/0.47 % Rec. Clause-clause subsumption calls : 5640
% 0.58/0.47 % Non-unit clause-clause subsumptions : 220
% 0.58/0.47 % Unit Clause-clause subsumption calls : 260
% 0.58/0.47 % Rewrite failures with RHS unbound : 0
% 0.58/0.47 % BW rewrite match attempts : 203
% 0.58/0.47 % BW rewrite match successes : 3
% 0.58/0.47 % Condensation attempts : 0
% 0.58/0.47 % Condensation successes : 0
% 0.58/0.47 % Termbank termtop insertions : 121987
% 0.58/0.47 % Search garbage collected termcells : 22837
% 0.58/0.47
% 0.58/0.47 % -------------------------------------------------
% 0.58/0.47 % User time : 0.148 s
% 0.58/0.47 % System time : 0.010 s
% 0.58/0.47 % Total time : 0.158 s
% 0.58/0.47 % Maximum resident set size: 9004 pages
% 0.58/0.47
% 0.58/0.47 % -------------------------------------------------
% 0.58/0.47 % User time : 0.285 s
% 0.58/0.47 % System time : 0.036 s
% 0.58/0.47 % Total time : 0.321 s
% 0.58/0.47 % Maximum resident set size: 5120 pages
% 0.58/0.47 % E exiting
%------------------------------------------------------------------------------