%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU734^1 : 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 : n006.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 08:27:35 AM UTC 2026
% Result : Theorem 2.16s 0.59s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU734^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n006.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:18:24 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.22/0.26 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.dHbjzuzRAL/E---3.1_790403.p
% 2.16/0.59 % Version: 3.5.1-ho
% 2.16/0.59 % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.16/0.59 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.16/0.59 % Starting ehoh_best5 with 300s (1) cores
% 2.16/0.59 % Starting almost_fo_3_lam with 300s (1) cores
% 2.16/0.59 % Starting new_bool_5 with 300s (1) cores
% 2.16/0.59 % Starting pre_casc_3 with 300s (1) cores
% 2.16/0.59 % Starting ho_unfolding_8 with 300s (1) cores
% 2.16/0.59 % Starting new_ho_10_cnf2 with 300s (1) cores
% 2.16/0.59 % Starting new_bool_3 with 300s (1) cores
% 2.16/0.59 % Starting new_ho_5 with 300s (1) cores
% 2.16/0.59 % new_ho_5 with pid 790423 completed with status 9
% 2.16/0.59 % ehoh_best5 with pid 790416 completed with status 0
% 2.16/0.59 % Result found by ehoh_best5
% 2.16/0.59 % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.16/0.59 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.16/0.59 % Starting ehoh_best5 with 300s (1) cores
% 2.16/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.16/0.59 % No SInE strategy applied
% 2.16/0.59 % Search class: HGHSM-FSLM32-MHFMMSBN
% 2.16/0.59 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 2.16/0.59 % Starting SubtermCWHack with 28s (1) cores
% 2.16/0.59 % SubtermCWHack with pid 790431 completed with status 0
% 2.16/0.59 % Result found by SubtermCWHack
% 2.16/0.59 % Preprocessing class: HSLMSLSSLLLCHFA.
% 2.16/0.59 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.16/0.59 % Starting ehoh_best5 with 300s (1) cores
% 2.16/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.16/0.59 % No SInE strategy applied
% 2.16/0.59 % Search class: HGHSM-FSLM32-MHFMMSBN
% 2.16/0.59 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 2.16/0.59 % Starting SubtermCWHack with 28s (1) cores
% 2.16/0.59 % Preprocessing time : 0.004 s
% 2.16/0.59
% 2.16/0.59 % Proof found!
% 2.16/0.59 % SZS status Theorem
% 2.16/0.59 % SZS output start CNFRefutation
% 2.16/0.59 thf(decl_23, type, in: $i > $i > $o).
% 2.16/0.59 thf(decl_24, type, exu: ($i > $o) > $o).
% 2.16/0.59 thf(decl_25, type, setextAx: $o).
% 2.16/0.59 thf(decl_26, type, emptyset: $i).
% 2.16/0.59 thf(decl_27, type, emptysetAx: $o).
% 2.16/0.59 thf(decl_28, type, setadjoin: $i > $i > $i).
% 2.16/0.59 thf(decl_29, type, setadjoinAx: $o).
% 2.16/0.59 thf(decl_30, type, powerset: $i > $i).
% 2.16/0.59 thf(decl_31, type, powersetAx: $o).
% 2.16/0.59 thf(decl_32, type, setunion: $i > $i).
% 2.16/0.59 thf(decl_33, type, setunionAx: $o).
% 2.16/0.59 thf(decl_34, type, omega: $i).
% 2.16/0.59 thf(decl_35, type, omega0Ax: $o).
% 2.16/0.59 thf(decl_36, type, omegaSAx: $o).
% 2.16/0.59 thf(decl_37, type, omegaIndAx: $o).
% 2.16/0.59 thf(decl_38, type, replAx: $o).
% 2.16/0.59 thf(decl_39, type, foundationAx: $o).
% 2.16/0.59 thf(decl_40, type, wellorderingAx: $o).
% 2.16/0.59 thf(decl_41, type, descr: ($i > $o) > $i).
% 2.16/0.59 thf(decl_42, type, descrp: $o).
% 2.16/0.59 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_44, type, dsetconstrI: $o).
% 2.16/0.59 thf(decl_45, type, dsetconstrEL: $o).
% 2.16/0.59 thf(decl_46, type, dsetconstrER: $o).
% 2.16/0.59 thf(decl_47, type, exuE1: $o).
% 2.16/0.59 thf(decl_48, type, prop2set: $o > $i).
% 2.16/0.59 thf(decl_49, type, prop2setE: $o).
% 2.16/0.59 thf(decl_50, type, emptysetE: $o).
% 2.16/0.59 thf(decl_51, type, emptysetimpfalse: $o).
% 2.16/0.59 thf(decl_52, type, notinemptyset: $o).
% 2.16/0.59 thf(decl_53, type, exuE3e: $o).
% 2.16/0.59 thf(decl_54, type, setext: $o).
% 2.16/0.59 thf(decl_55, type, emptyI: $o).
% 2.16/0.59 thf(decl_56, type, noeltsimpempty: $o).
% 2.16/0.59 thf(decl_57, type, setbeta: $o).
% 2.16/0.59 thf(decl_58, type, nonempty: $i > $o).
% 2.16/0.59 thf(decl_59, type, nonemptyE1: $o).
% 2.16/0.59 thf(decl_60, type, nonemptyI: $o).
% 2.16/0.59 thf(decl_61, type, nonemptyI1: $o).
% 2.16/0.59 thf(decl_62, type, setadjoinIL: $o).
% 2.16/0.59 thf(decl_63, type, emptyinunitempty: $o).
% 2.16/0.59 thf(decl_64, type, setadjoinIR: $o).
% 2.16/0.59 thf(decl_65, type, setadjoinE: $o).
% 2.16/0.59 thf(decl_66, type, setadjoinOr: $o).
% 2.16/0.59 thf(decl_67, type, setoftrueEq: $o).
% 2.16/0.59 thf(decl_68, type, powersetI: $o).
% 2.16/0.59 thf(decl_69, type, emptyinPowerset: $o).
% 2.16/0.59 thf(decl_70, type, emptyInPowerset: $o).
% 2.16/0.59 thf(decl_71, type, powersetE: $o).
% 2.16/0.59 thf(decl_72, type, setunionI: $o).
% 2.16/0.59 thf(decl_73, type, setunionE: $o).
% 2.16/0.59 thf(decl_74, type, subPowSU: $o).
% 2.16/0.59 thf(decl_75, type, exuE2: $o).
% 2.16/0.59 thf(decl_76, type, nonemptyImpWitness: $o).
% 2.16/0.59 thf(decl_77, type, uniqinunit: $o).
% 2.16/0.59 thf(decl_78, type, notinsingleton: $o).
% 2.16/0.59 thf(decl_79, type, eqinunit: $o).
% 2.16/0.59 thf(decl_80, type, singletonsswitch: $o).
% 2.16/0.59 thf(decl_81, type, upairsetE: $o).
% 2.16/0.59 thf(decl_82, type, upairsetIL: $o).
% 2.16/0.59 thf(decl_83, type, upairsetIR: $o).
% 2.16/0.59 thf(decl_84, type, emptyE1: $o).
% 2.16/0.59 thf(decl_85, type, vacuousDall: $o).
% 2.16/0.59 thf(decl_86, type, quantDeMorgan1: $o).
% 2.16/0.59 thf(decl_87, type, quantDeMorgan2: $o).
% 2.16/0.59 thf(decl_88, type, quantDeMorgan3: $o).
% 2.16/0.59 thf(decl_89, type, quantDeMorgan4: $o).
% 2.16/0.59 thf(decl_90, type, prop2setI: $o).
% 2.16/0.59 thf(decl_91, type, set2prop: $i > $o).
% 2.16/0.59 thf(decl_92, type, prop2set2propI: $o).
% 2.16/0.59 thf(decl_93, type, notdexE: $o).
% 2.16/0.59 thf(decl_94, type, notdallE: $o).
% 2.16/0.59 thf(decl_95, type, exuI1: $o).
% 2.16/0.59 thf(decl_96, type, exuI3: $o).
% 2.16/0.59 thf(decl_97, type, exuI2: $o).
% 2.16/0.59 thf(decl_98, type, inCongP: $o).
% 2.16/0.59 thf(decl_99, type, in__Cong: $o).
% 2.16/0.59 thf(decl_100, type, exuE3u: $o).
% 2.16/0.59 thf(decl_101, type, exu__Cong: $o).
% 2.16/0.59 thf(decl_102, type, emptyset__Cong: $o).
% 2.16/0.59 thf(decl_103, type, setadjoin__Cong: $o).
% 2.16/0.59 thf(decl_104, type, powerset__Cong: $o).
% 2.16/0.59 thf(decl_105, type, setunion__Cong: $o).
% 2.16/0.59 thf(decl_106, type, omega__Cong: $o).
% 2.16/0.59 thf(decl_107, type, exuEu: $o).
% 2.16/0.59 thf(decl_108, type, descr__Cong: $o).
% 2.16/0.59 thf(decl_109, type, dsetconstr__Cong: $o).
% 2.16/0.59 thf(decl_110, type, subset: $i > $i > $o).
% 2.16/0.59 thf(decl_113, type, subsetI1: $o).
% 2.16/0.59 thf(decl_114, type, eqimpsubset2: $o).
% 2.16/0.59 thf(decl_115, type, eqimpsubset1: $o).
% 2.16/0.59 thf(decl_116, type, subsetI2: $o).
% 2.16/0.59 thf(decl_117, type, emptysetsubset: $o).
% 2.16/0.59 thf(decl_118, type, subsetE: $o).
% 2.16/0.59 thf(decl_119, type, subsetE2: $o).
% 2.16/0.59 thf(decl_120, type, notsubsetI: $o).
% 2.16/0.59 thf(decl_121, type, notequalI1: $o).
% 2.16/0.59 thf(decl_122, type, notequalI2: $o).
% 2.16/0.59 thf(decl_123, type, subsetRefl: $o).
% 2.16/0.59 thf(decl_124, type, subsetTrans: $o).
% 2.16/0.59 thf(decl_125, type, setadjoinSub: $o).
% 2.16/0.59 thf(decl_126, type, setadjoinSub2: $o).
% 2.16/0.59 thf(decl_127, type, subset2powerset: $o).
% 2.16/0.59 thf(decl_128, type, setextsub: $o).
% 2.16/0.59 thf(decl_129, type, subsetemptysetimpeq: $o).
% 2.16/0.59 thf(decl_130, type, powersetI1: $o).
% 2.16/0.59 thf(decl_131, type, powersetE1: $o).
% 2.16/0.59 thf(decl_132, type, inPowerset: $o).
% 2.16/0.59 thf(decl_133, type, powersetsubset: $o).
% 2.16/0.59 thf(decl_134, type, sepInPowerset: $o).
% 2.16/0.59 thf(decl_135, type, sepSubset: $o).
% 2.16/0.59 thf(decl_136, type, binunion: $i > $i > $i).
% 2.16/0.59 thf(decl_137, type, binunionIL: $o).
% 2.16/0.59 thf(decl_138, type, upairset2IR: $o).
% 2.16/0.59 thf(decl_139, type, binunionIR: $o).
% 2.16/0.59 thf(decl_140, type, binunionEcases: $o).
% 2.16/0.59 thf(decl_141, type, binunionE: $o).
% 2.16/0.59 thf(decl_142, type, binunionLsub: $o).
% 2.16/0.59 thf(decl_143, type, binunionRsub: $o).
% 2.16/0.59 thf(decl_144, type, binintersect: $i > $i > $i).
% 2.16/0.59 thf(decl_145, type, binintersectI: $o).
% 2.16/0.59 thf(decl_146, type, binintersectSubset5: $o).
% 2.16/0.59 thf(decl_147, type, binintersectEL: $o).
% 2.16/0.59 thf(decl_148, type, binintersectLsub: $o).
% 2.16/0.59 thf(decl_149, type, binintersectSubset2: $o).
% 2.16/0.59 thf(decl_150, type, binintersectSubset3: $o).
% 2.16/0.59 thf(decl_151, type, binintersectER: $o).
% 2.16/0.59 thf(decl_152, type, disjointsetsI1: $o).
% 2.16/0.59 thf(decl_153, type, binintersectRsub: $o).
% 2.16/0.59 thf(decl_154, type, binintersectSubset4: $o).
% 2.16/0.59 thf(decl_155, type, binintersectSubset1: $o).
% 2.16/0.59 thf(decl_156, type, bs114d: $o).
% 2.16/0.59 thf(decl_158, type, setminus: $i > $i > $i).
% 2.16/0.59 thf(decl_159, type, setminusI: $o).
% 2.16/0.59 thf(decl_160, type, setminusEL: $o).
% 2.16/0.59 thf(decl_161, type, setminusER: $o).
% 2.16/0.59 thf(decl_162, type, setminusSubset2: $o).
% 2.16/0.59 thf(decl_163, type, setminusERneg: $o).
% 2.16/0.59 thf(decl_164, type, setminusELneg: $o).
% 2.16/0.59 thf(decl_165, type, setminusILneg: $o).
% 2.16/0.59 thf(decl_166, type, setminusIRneg: $o).
% 2.16/0.59 thf(decl_167, type, setminusLsub: $o).
% 2.16/0.59 thf(decl_168, type, setminusSubset1: $o).
% 2.16/0.59 thf(decl_169, type, symdiff: $i > $i > $i).
% 2.16/0.59 thf(decl_170, type, symdiffE: $o).
% 2.16/0.59 thf(decl_171, type, symdiffI1: $o).
% 2.16/0.59 thf(decl_172, type, symdiffI2: $o).
% 2.16/0.59 thf(decl_173, type, symdiffIneg1: $o).
% 2.16/0.59 thf(decl_174, type, symdiffIneg2: $o).
% 2.16/0.59 thf(decl_175, type, iskpair: $i > $o).
% 2.16/0.59 thf(decl_176, type, secondinupair: $o).
% 2.16/0.59 thf(decl_177, type, setukpairIL: $o).
% 2.16/0.59 thf(decl_178, type, setukpairIR: $o).
% 2.16/0.59 thf(decl_179, type, kpairiskpair: $o).
% 2.16/0.59 thf(decl_180, type, kpair: $i > $i > $i).
% 2.16/0.59 thf(decl_181, type, kpairp: $o).
% 2.16/0.59 thf(decl_182, type, cartprod: $i > $i > $i).
% 2.16/0.59 thf(decl_183, type, singletonsubset: $o).
% 2.16/0.59 thf(decl_184, type, singletoninpowerset: $o).
% 2.16/0.59 thf(decl_185, type, singletoninpowunion: $o).
% 2.16/0.59 thf(decl_186, type, upairset2E: $o).
% 2.16/0.59 thf(decl_187, type, upairsubunion: $o).
% 2.16/0.59 thf(decl_188, type, upairinpowunion: $o).
% 2.16/0.59 thf(decl_189, type, ubforcartprodlem1: $o).
% 2.16/0.59 thf(decl_190, type, ubforcartprodlem2: $o).
% 2.16/0.59 thf(decl_191, type, ubforcartprodlem3: $o).
% 2.16/0.59 thf(decl_192, type, cartprodpairin: $o).
% 2.16/0.59 thf(decl_193, type, cartprodmempair1: $o).
% 2.16/0.59 thf(decl_194, type, cartprodmempair: $o).
% 2.16/0.59 thf(decl_195, type, setunionE2: $o).
% 2.16/0.59 thf(decl_196, type, setunionsingleton1: $o).
% 2.16/0.59 thf(decl_197, type, setunionsingleton2: $o).
% 2.16/0.59 thf(decl_198, type, setunionsingleton: $o).
% 2.16/0.59 thf(decl_199, type, singleton: $i > $o).
% 2.16/0.59 thf(decl_200, type, singletonprop: $o).
% 2.16/0.59 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 2.16/0.59 thf(decl_202, type, ex1E1: $o).
% 2.16/0.59 thf(decl_203, type, ex1I: $o).
% 2.16/0.59 thf(decl_204, type, ex1I2: $o).
% 2.16/0.59 thf(decl_205, type, singletonsuniq: $o).
% 2.16/0.59 thf(decl_210, type, setukpairinjL1: $o).
% 2.16/0.59 thf(decl_211, type, kfstsingleton: $o).
% 2.16/0.59 thf(decl_212, type, theprop: $o).
% 2.16/0.59 thf(decl_213, type, kfst: $i > $i).
% 2.16/0.59 thf(decl_214, type, kfstpairEq: $o).
% 2.16/0.59 thf(decl_215, type, cartprodfstin: $o).
% 2.16/0.59 thf(decl_216, type, setukpairinjL2: $o).
% 2.16/0.59 thf(decl_217, type, setukpairinjL: $o).
% 2.16/0.59 thf(decl_218, type, setukpairinjR11: $o).
% 2.16/0.59 thf(decl_219, type, setukpairinjR12: $o).
% 2.16/0.59 thf(decl_220, type, setukpairinjR1: $o).
% 2.16/0.59 thf(decl_221, type, upairequniteq: $o).
% 2.16/0.59 thf(decl_222, type, setukpairinjR2: $o).
% 2.16/0.59 thf(decl_223, type, setukpairinjR: $o).
% 2.16/0.59 thf(decl_224, type, ksndsingleton: $o).
% 2.16/0.59 thf(decl_225, type, ksnd: $i > $i).
% 2.16/0.59 thf(decl_226, type, ksndpairEq: $o).
% 2.16/0.59 thf(decl_227, type, kpairsurjEq: $o).
% 2.16/0.59 thf(decl_228, type, cartprodsndin: $o).
% 2.16/0.59 thf(decl_229, type, cartprodpairmemEL: $o).
% 2.16/0.59 thf(decl_230, type, cartprodpairmemER: $o).
% 2.16/0.59 thf(decl_231, type, cartprodmempaircEq: $o).
% 2.16/0.59 thf(decl_232, type, cartprodfstpairEq: $o).
% 2.16/0.59 thf(decl_233, type, cartprodsndpairEq: $o).
% 2.16/0.59 thf(decl_234, type, cartprodpairsurjEq: $o).
% 2.16/0.59 thf(decl_235, type, breln: $i > $i > $i > $o).
% 2.16/0.59 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 2.16/0.59 thf(decl_237, type, dpsetconstrI: $o).
% 2.16/0.59 thf(decl_238, type, dpsetconstrSub: $o).
% 2.16/0.59 thf(decl_239, type, setOfPairsIsBReln: $o).
% 2.16/0.59 thf(decl_240, type, dpsetconstrERa: $o).
% 2.16/0.59 thf(decl_241, type, dpsetconstrEL1: $o).
% 2.16/0.59 thf(decl_242, type, dpsetconstrEL2: $o).
% 2.16/0.59 thf(decl_243, type, dpsetconstrER: $o).
% 2.16/0.59 thf(decl_244, type, func: $i > $i > $i > $o).
% 2.16/0.59 thf(decl_245, type, funcSet: $i > $i > $i).
% 2.16/0.59 thf(decl_246, type, funcImageSingleton: $o).
% 2.16/0.59 thf(decl_247, type, apProp: $o).
% 2.16/0.59 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 2.16/0.59 thf(decl_249, type, app: $o).
% 2.16/0.59 thf(decl_250, type, infuncsetfunc: $o).
% 2.16/0.59 thf(decl_251, type, ap2p: $o).
% 2.16/0.59 thf(decl_252, type, funcinfuncset: $o).
% 2.16/0.59 thf(decl_253, type, lamProp: $o).
% 2.16/0.59 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 2.16/0.59 thf(decl_255, type, lamp: $o).
% 2.16/0.59 thf(decl_256, type, lam2p: $o).
% 2.16/0.59 thf(decl_257, type, brelnall1: $o).
% 2.16/0.59 thf(decl_258, type, brelnall2: $o).
% 2.16/0.59 thf(decl_259, type, ex1E2: $o).
% 2.16/0.59 thf(decl_260, type, funcGraphProp1: $o).
% 2.16/0.59 thf(decl_261, type, funcGraphProp3: $o).
% 2.16/0.59 thf(decl_262, type, funcGraphProp2: $o).
% 2.16/0.59 thf(decl_263, type, funcextLem: $o).
% 2.16/0.59 thf(decl_264, type, funcGraphProp4: $o).
% 2.16/0.59 thf(decl_265, type, subbreln: $o).
% 2.16/0.59 thf(decl_266, type, eqbreln: $o).
% 2.16/0.59 thf(decl_267, type, funcext: $o).
% 2.16/0.59 thf(decl_268, type, funcext2: $o).
% 2.16/0.59 thf(decl_269, type, ap2apEq1: $o).
% 2.16/0.59 thf(decl_270, type, ap2apEq2: $o).
% 2.16/0.59 thf(decl_271, type, beta1: $o).
% 2.16/0.59 thf(decl_272, type, eta1: $o).
% 2.16/0.59 thf(decl_273, type, lam2lamEq: $o).
% 2.16/0.59 thf(decl_274, type, beta2: $o).
% 2.16/0.59 thf(decl_275, type, eta2: $o).
% 2.16/0.59 thf(decl_276, type, iffalseProp1: $o).
% 2.16/0.59 thf(decl_277, type, iffalseProp2: $o).
% 2.16/0.59 thf(decl_278, type, iftrueProp1: $o).
% 2.16/0.59 thf(decl_279, type, iftrueProp2: $o).
% 2.16/0.59 thf(decl_280, type, ifSingleton: $o).
% 2.16/0.59 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 2.16/0.59 thf(decl_282, type, ifp: $o).
% 2.16/0.59 thf(decl_283, type, theeq: $o).
% 2.16/0.59 thf(decl_284, type, iftrue: $o).
% 2.16/0.59 thf(decl_285, type, iffalse: $o).
% 2.16/0.59 thf(decl_286, type, iftrueorfalse: $o).
% 2.16/0.59 thf(decl_287, type, binintersectT_lem: $o).
% 2.16/0.59 thf(decl_288, type, binunionT_lem: $o).
% 2.16/0.59 thf(decl_289, type, powersetT_lem: $o).
% 2.16/0.59 thf(decl_290, type, setminusT_lem: $o).
% 2.16/0.59 thf(decl_291, type, complementT_lem: $o).
% 2.16/0.59 thf(decl_292, type, setextT: $o).
% 2.16/0.59 thf(decl_293, type, subsetTI: $o).
% 2.16/0.59 thf(decl_294, type, powersetTI1: $o).
% 2.16/0.59 thf(decl_295, type, powersetTE1: $o).
% 2.16/0.59 thf(decl_296, type, complementTI1: $o).
% 2.16/0.59 thf(decl_297, type, complementTE1: $o).
% 2.16/0.59 thf(decl_298, type, binintersectTELcontra: $o).
% 2.16/0.59 thf(decl_299, type, binintersectTERcontra: $o).
% 2.16/0.59 thf(decl_300, type, contrasubsetT: $o).
% 2.16/0.59 thf(decl_301, type, contrasubsetT1: $o).
% 2.16/0.59 thf(decl_302, type, contrasubsetT2: $o).
% 2.16/0.59 thf(decl_303, type, contrasubsetT3: $o).
% 2.16/0.59 thf(decl_304, type, doubleComplementI1: $o).
% 2.16/0.59 thf(decl_305, type, doubleComplementE1: $o).
% 2.16/0.59 thf(decl_306, type, doubleComplementSub1: $o).
% 2.16/0.59 thf(decl_307, type, doubleComplementSub2: $o).
% 2.16/0.59 thf(decl_308, type, doubleComplementEq: $o).
% 2.16/0.59 thf(decl_309, type, complementTnotintersectT: $o).
% 2.16/0.59 thf(decl_310, type, complementImpComplementIntersect: $o).
% 2.16/0.59 thf(decl_311, type, epred1_0: $o).
% 2.16/0.59 thf(decl_312, type, esk1_2: $i > $i > $i).
% 2.16/0.59 thf(decl_313, type, esk2_2: $i > $i > $i).
% 2.16/0.59 thf(decl_314, type, esk3_2: $i > $i > $i).
% 2.16/0.59 thf(decl_315, type, esk4_1: $i > $i).
% 2.16/0.59 thf(decl_316, type, esk5_2: ($i > $i > $o) > $i > $i).
% 2.16/0.59 thf(decl_317, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 2.16/0.59 thf(decl_318, type, esk7_2: ($i > $i > $o) > $i > $i).
% 2.16/0.59 thf(decl_319, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 2.16/0.59 thf(decl_320, type, esk9_1: $i > $i).
% 2.16/0.59 thf(decl_321, type, esk10_2: ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_322, type, esk11_2: ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_323, type, esk12_1: ($i > $o) > $i).
% 2.16/0.59 thf(decl_324, type, esk13_2: ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_325, type, esk14_1: ($i > $o) > $i).
% 2.16/0.59 thf(decl_326, type, esk15_2: $i > $i > $i).
% 2.16/0.59 thf(decl_327, type, esk16_2: $i > $i > $i).
% 2.16/0.59 thf(decl_328, type, esk17_1: $i > $i).
% 2.16/0.59 thf(decl_329, type, esk18_1: $i > $i).
% 2.16/0.59 thf(decl_330, type, esk19_1: $i > $i).
% 2.16/0.59 thf(decl_331, type, esk20_2: $i > $i > $i).
% 2.16/0.59 thf(decl_332, type, esk21_3: $i > $i > $o > $i).
% 2.16/0.59 thf(decl_333, type, esk22_2: ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_334, type, esk23_1: ($i > $o) > $i).
% 2.16/0.59 thf(decl_335, type, esk24_1: $i > $i).
% 2.16/0.59 thf(decl_336, type, esk25_2: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_337, type, esk26_2: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_338, type, esk27_2: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_339, type, esk28_2: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_340, type, esk29_2: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_341, type, esk30_2: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_342, type, esk31_2: ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_343, type, esk32_1: ($i > $o) > $i).
% 2.16/0.59 thf(decl_344, type, esk33_1: ($i > $o) > $i).
% 2.16/0.59 thf(decl_345, type, esk34_1: ($i > $o) > $i).
% 2.16/0.59 thf(decl_346, type, esk35_1: ($i > $o) > $i).
% 2.16/0.59 thf(decl_347, type, esk36_2: ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_348, type, esk37_1: ($i > $o) > $i).
% 2.16/0.59 thf(decl_349, type, esk38_2: ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_350, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 2.16/0.59 thf(decl_351, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 2.16/0.59 thf(decl_352, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_353, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 2.16/0.59 thf(decl_354, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_355, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 2.16/0.59 thf(decl_356, type, esk45_2: ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_357, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 2.16/0.59 thf(decl_358, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 2.16/0.59 thf(decl_359, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_360, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_361, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.16/0.59 thf(decl_362, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.16/0.59 thf(decl_363, type, esk52_2: $i > $i > $i).
% 2.16/0.59 thf(decl_364, type, esk53_2: $i > $i > $i).
% 2.16/0.59 thf(decl_365, type, esk54_2: $i > $i > $i).
% 2.16/0.59 thf(decl_366, type, esk55_3: $i > $i > $i > $i).
% 2.16/0.59 thf(decl_367, type, esk56_3: $i > $i > $i > $i).
% 2.16/0.59 thf(decl_368, type, esk57_2: $i > $i > $i).
% 2.16/0.59 thf(decl_369, type, esk58_2: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_370, type, esk59_2: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_371, type, esk60_2: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_372, type, esk61_3: $i > ($i > $o) > $i > $i).
% 2.16/0.59 thf(decl_373, type, esk62_2: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_374, type, esk63_2: $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_375, type, esk64_3: $i > $i > ($i > $i) > $i).
% 2.16/0.59 thf(decl_376, type, esk65_3: $i > $i > ($i > $i) > $i).
% 2.16/0.59 thf(decl_377, type, esk66_3: $i > $i > ($i > $i) > $i).
% 2.16/0.59 thf(decl_378, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_379, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_380, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_381, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
% 2.16/0.59 thf(decl_382, type, esk71_4: $i > $i > $i > $i > $i).
% 2.16/0.59 thf(decl_383, type, esk72_4: $i > $i > $i > $i > $i).
% 2.16/0.59 thf(decl_384, type, esk73_4: $i > $i > $i > $i > $i).
% 2.16/0.59 thf(decl_385, type, esk74_4: $i > $i > $i > $i > $i).
% 2.16/0.59 thf(decl_386, type, esk75_4: $i > $i > $i > $i > $i).
% 2.16/0.59 thf(decl_387, type, esk76_4: $i > $i > $i > $i > $i).
% 2.16/0.59 thf(decl_388, type, esk77_4: $i > $i > $i > $i > $i).
% 2.16/0.59 thf(decl_389, type, esk78_4: $i > $i > $i > $i > $i).
% 2.16/0.59 thf(decl_390, type, esk79_4: $i > $i > $i > $i > $i).
% 2.16/0.59 thf(decl_391, type, esk80_3: $i > $i > ($i > $i) > $i).
% 2.16/0.59 thf(decl_392, type, esk81_3: $i > $i > ($i > $i) > $i).
% 2.16/0.59 thf(decl_393, type, esk82_3: $i > $i > ($i > $i) > $i).
% 2.16/0.59 thf(decl_394, type, esk83_3: $i > $i > $i > $i).
% 2.16/0.59 thf(decl_395, type, esk84_3: $i > $i > $i > $i).
% 2.16/0.59 thf(decl_396, type, esk85_3: $i > $i > $i > $i).
% 2.16/0.59 thf(decl_397, type, esk86_3: $i > $i > $i > $i).
% 2.16/0.59 thf(decl_398, type, esk87_0: $i).
% 2.16/0.59 thf(decl_399, type, esk88_0: $i).
% 2.16/0.59 thf(decl_400, type, esk89_0: $i).
% 2.16/0.59 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', replAx)).
% 2.16/0.59 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', exu)).
% 2.16/0.59 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', descrp)).
% 2.16/0.59 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', exuE1)).
% 2.16/0.59 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', exuE3e)).
% 2.16/0.59 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', nonempty)).
% 2.16/0.59 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', nonemptyI)).
% 2.16/0.59 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', exuE2)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', exuI1)).
% 2.16/0.59 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', exuI3)).
% 2.16/0.59 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', exuI2)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', exuE3u)).
% 2.16/0.59 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', exu__Cong)).
% 2.16/0.59 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', exuEu)).
% 2.16/0.59 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', descr__Cong)).
% 2.16/0.59 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ex1E1)).
% 2.16/0.59 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ex1)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', ex1I)).
% 2.16/0.59 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ex1I2)).
% 2.16/0.59 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setOfPairsIsBReln)).
% 2.16/0.59 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', breln)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', ex1E2)).
% 2.16/0.59 thf(complementSubsetComplementIntersect, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', complementSubsetComplementIntersect)).
% 2.16/0.59 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', dsetconstrI)).
% 2.16/0.59 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', dsetconstrEL)).
% 2.16/0.59 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', dsetconstrER)).
% 2.16/0.59 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setbeta)).
% 2.16/0.59 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', nonemptyE1)).
% 2.16/0.59 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', nonemptyI1)).
% 2.16/0.59 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setoftrueEq)).
% 2.16/0.59 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', nonemptyImpWitness)).
% 2.16/0.59 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.dHbjzuzRAL/E---3.1_790403.p', emptyE1)).
% 2.16/0.59 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', dsetconstr__Cong)).
% 2.16/0.59 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', sepInPowerset)).
% 2.16/0.59 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', sepSubset)).
% 2.16/0.59 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', singletonprop)).
% 2.16/0.59 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', kfstsingleton)).
% 2.16/0.59 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ksndsingleton)).
% 2.16/0.59 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', dpsetconstrI)).
% 2.16/0.59 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', dpsetconstrSub)).
% 2.16/0.59 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', dpsetconstrERa)).
% 2.16/0.59 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', dpsetconstrEL1)).
% 2.16/0.59 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', dpsetconstrEL2)).
% 2.16/0.59 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', dpsetconstrER)).
% 2.16/0.59 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.dHbjzuzRAL/E---3.1_790403.p', funcImageSingleton)).
% 2.16/0.59 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', apProp)).
% 2.16/0.59 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.dHbjzuzRAL/E---3.1_790403.p', lamProp)).
% 2.16/0.59 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', lamp)).
% 2.16/0.59 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', lam2p)).
% 2.16/0.59 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.dHbjzuzRAL/E---3.1_790403.p', brelnall1)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', brelnall2)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', subbreln)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', eqbreln)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', beta1)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', eta1)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', lam2lamEq)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', beta2)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', eta2)).
% 2.16/0.59 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', iffalseProp1)).
% 2.16/0.59 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', iffalseProp2)).
% 2.16/0.59 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', iftrueProp1)).
% 2.16/0.59 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', iftrueProp2)).
% 2.16/0.59 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ifSingleton)).
% 2.16/0.59 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setextAx)).
% 2.16/0.59 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', emptysetAx)).
% 2.16/0.59 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setadjoinAx)).
% 2.16/0.59 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', powersetAx)).
% 2.16/0.59 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setunionAx)).
% 2.16/0.59 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', omega0Ax)).
% 2.16/0.59 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', omegaSAx)).
% 2.16/0.59 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.dHbjzuzRAL/E---3.1_790403.p', omegaIndAx)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', foundationAx)).
% 2.16/0.59 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', wellorderingAx)).
% 2.16/0.59 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', prop2setE)).
% 2.16/0.59 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', emptysetE)).
% 2.16/0.59 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', emptysetimpfalse)).
% 2.16/0.59 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', notinemptyset)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', setext)).
% 2.16/0.59 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', emptyI)).
% 2.16/0.59 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', noeltsimpempty)).
% 2.16/0.59 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setadjoinIL)).
% 2.16/0.59 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', emptyinunitempty)).
% 2.16/0.59 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setadjoinIR)).
% 2.16/0.59 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setadjoinE)).
% 2.16/0.59 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setadjoinOr)).
% 2.16/0.59 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', powersetI)).
% 2.16/0.59 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', emptyinPowerset)).
% 2.16/0.59 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', emptyInPowerset)).
% 2.16/0.59 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', powersetE)).
% 2.16/0.59 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setunionI)).
% 2.16/0.59 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setunionE)).
% 2.16/0.59 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', subPowSU)).
% 2.16/0.59 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', uniqinunit)).
% 2.16/0.59 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', notinsingleton)).
% 2.16/0.59 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', eqinunit)).
% 2.16/0.59 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', singletonsswitch)).
% 2.16/0.59 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', upairsetE)).
% 2.16/0.59 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', upairsetIL)).
% 2.16/0.59 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', upairsetIR)).
% 2.16/0.59 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', vacuousDall)).
% 2.16/0.59 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', quantDeMorgan1)).
% 2.16/0.59 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', quantDeMorgan2)).
% 2.16/0.59 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', quantDeMorgan3)).
% 2.16/0.59 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', quantDeMorgan4)).
% 2.16/0.59 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', prop2setI)).
% 2.16/0.59 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', prop2set2propI)).
% 2.16/0.59 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', notdexE)).
% 2.16/0.59 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', notdallE)).
% 2.16/0.59 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', inCongP)).
% 2.16/0.59 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', in__Cong)).
% 2.16/0.59 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', emptyset__Cong)).
% 2.16/0.59 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setadjoin__Cong)).
% 2.16/0.59 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', powerset__Cong)).
% 2.16/0.59 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setunion__Cong)).
% 2.16/0.59 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', omega__Cong)).
% 2.16/0.59 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', subsetI1)).
% 2.16/0.59 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', eqimpsubset2)).
% 2.16/0.59 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', eqimpsubset1)).
% 2.16/0.59 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', subsetI2)).
% 2.16/0.59 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', emptysetsubset)).
% 2.16/0.59 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', subsetE)).
% 2.16/0.59 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', subsetE2)).
% 2.16/0.59 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', notsubsetI)).
% 2.16/0.59 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', notequalI1)).
% 2.16/0.59 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', notequalI2)).
% 2.16/0.59 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', subsetRefl)).
% 2.16/0.59 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', subsetTrans)).
% 2.16/0.59 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setadjoinSub)).
% 2.16/0.59 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setadjoinSub2)).
% 2.16/0.59 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', subset2powerset)).
% 2.16/0.59 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setextsub)).
% 2.16/0.59 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', subsetemptysetimpeq)).
% 2.16/0.59 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', powersetI1)).
% 2.16/0.59 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', powersetE1)).
% 2.16/0.59 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', inPowerset)).
% 2.16/0.59 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', powersetsubset)).
% 2.16/0.59 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binunionIL)).
% 2.16/0.59 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', upairset2IR)).
% 2.16/0.59 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binunionIR)).
% 2.16/0.59 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binunionEcases)).
% 2.16/0.59 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binunionE)).
% 2.16/0.59 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binunionLsub)).
% 2.16/0.59 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binunionRsub)).
% 2.16/0.59 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectI)).
% 2.16/0.59 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectSubset5)).
% 2.16/0.59 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectEL)).
% 2.16/0.59 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectLsub)).
% 2.16/0.59 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectSubset2)).
% 2.16/0.59 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectSubset3)).
% 2.16/0.59 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectER)).
% 2.16/0.59 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', disjointsetsI1)).
% 2.16/0.59 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectRsub)).
% 2.16/0.59 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectSubset4)).
% 2.16/0.59 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectSubset1)).
% 2.16/0.59 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', bs114d)).
% 2.16/0.59 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setminusI)).
% 2.16/0.59 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setminusEL)).
% 2.16/0.59 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setminusER)).
% 2.16/0.59 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setminusSubset2)).
% 2.16/0.59 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setminusERneg)).
% 2.16/0.59 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setminusELneg)).
% 2.16/0.59 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setminusILneg)).
% 2.16/0.59 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setminusIRneg)).
% 2.16/0.59 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setminusLsub)).
% 2.16/0.59 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setminusSubset1)).
% 2.16/0.59 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', symdiffE)).
% 2.16/0.59 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', symdiffI1)).
% 2.16/0.59 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', symdiffI2)).
% 2.16/0.59 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', symdiffIneg1)).
% 2.16/0.59 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', symdiffIneg2)).
% 2.16/0.59 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', secondinupair)).
% 2.16/0.59 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setukpairIL)).
% 2.16/0.59 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setukpairIR)).
% 2.16/0.59 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', kpairiskpair)).
% 2.16/0.59 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', kpairp)).
% 2.16/0.59 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', singletonsubset)).
% 2.16/0.59 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', singletoninpowerset)).
% 2.16/0.59 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', singletoninpowunion)).
% 2.16/0.59 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', upairset2E)).
% 2.16/0.59 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', upairsubunion)).
% 2.16/0.59 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', upairinpowunion)).
% 2.16/0.59 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ubforcartprodlem1)).
% 2.16/0.59 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ubforcartprodlem2)).
% 2.16/0.59 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ubforcartprodlem3)).
% 2.16/0.59 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', cartprodpairin)).
% 2.16/0.59 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.dHbjzuzRAL/E---3.1_790403.p', cartprodmempair1)).
% 2.16/0.59 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', cartprodmempair)).
% 2.16/0.59 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setunionE2)).
% 2.16/0.59 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setunionsingleton1)).
% 2.16/0.59 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setunionsingleton2)).
% 2.16/0.59 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setunionsingleton)).
% 2.16/0.59 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', singletonsuniq)).
% 2.16/0.59 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.dHbjzuzRAL/E---3.1_790403.p', setukpairinjL1)).
% 2.16/0.59 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', theprop)).
% 2.16/0.59 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', kfstpairEq)).
% 2.16/0.59 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', cartprodfstin)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', setukpairinjL2)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', setukpairinjL)).
% 2.16/0.59 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setukpairinjR11)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', setukpairinjR12)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', setukpairinjR1)).
% 2.16/0.59 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', upairequniteq)).
% 2.16/0.59 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setukpairinjR2)).
% 2.16/0.59 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setukpairinjR)).
% 2.16/0.59 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ksndpairEq)).
% 2.16/0.59 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', kpairsurjEq)).
% 2.16/0.59 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', cartprodsndin)).
% 2.16/0.59 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', cartprodpairmemEL)).
% 2.16/0.59 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', cartprodpairmemER)).
% 2.16/0.59 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', cartprodmempaircEq)).
% 2.16/0.59 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', cartprodfstpairEq)).
% 2.16/0.59 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', cartprodsndpairEq)).
% 2.16/0.59 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', cartprodpairsurjEq)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', app)).
% 2.16/0.59 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', infuncsetfunc)).
% 2.16/0.59 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ap2p)).
% 2.16/0.59 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', funcinfuncset)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', funcGraphProp1)).
% 2.16/0.59 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.dHbjzuzRAL/E---3.1_790403.p', funcGraphProp3)).
% 2.16/0.59 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', funcGraphProp2)).
% 2.16/0.59 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.dHbjzuzRAL/E---3.1_790403.p', funcextLem)).
% 2.16/0.59 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', funcGraphProp4)).
% 2.16/0.59 thf(funcext, axiom, ((funcext)<=>![X4:$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.dHbjzuzRAL/E---3.1_790403.p', funcext)).
% 2.16/0.59 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', funcext2)).
% 2.16/0.59 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ap2apEq1)).
% 2.16/0.59 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ap2apEq2)).
% 2.16/0.59 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', ifp)).
% 2.16/0.59 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', theeq)).
% 2.16/0.59 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', iftrue)).
% 2.16/0.59 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', iffalse)).
% 2.16/0.59 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', iftrueorfalse)).
% 2.16/0.59 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectT_lem)).
% 2.16/0.59 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binunionT_lem)).
% 2.16/0.59 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', powersetT_lem)).
% 2.16/0.59 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setminusT_lem)).
% 2.16/0.59 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', complementT_lem)).
% 2.16/0.59 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', setextT)).
% 2.16/0.59 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', subsetTI)).
% 2.16/0.59 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', powersetTI1)).
% 2.16/0.59 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', powersetTE1)).
% 2.16/0.59 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', complementTI1)).
% 2.16/0.59 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', complementTE1)).
% 2.16/0.59 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectTELcontra)).
% 2.16/0.59 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', binintersectTERcontra)).
% 2.16/0.59 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', contrasubsetT)).
% 2.16/0.59 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', contrasubsetT1)).
% 2.16/0.59 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', contrasubsetT2)).
% 2.16/0.59 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', contrasubsetT3)).
% 2.16/0.59 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', doubleComplementI1)).
% 2.16/0.59 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', doubleComplementE1)).
% 2.16/0.59 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', doubleComplementSub1)).
% 2.16/0.59 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', doubleComplementSub2)).
% 2.16/0.59 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', doubleComplementEq)).
% 2.16/0.59 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', complementTnotintersectT)).
% 2.16/0.59 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.dHbjzuzRAL/E---3.1_790403.p', complementImpComplementIntersect)).
% 2.16/0.59 thf(c_0_255, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 2.16/0.59 thf(c_0_256, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 2.16/0.59 thf(c_0_257, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 2.16/0.59 thf(c_0_258, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 2.16/0.59 thf(c_0_259, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 2.16/0.59 thf(c_0_260, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 2.16/0.59 thf(c_0_261, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 2.16/0.59 thf(c_0_262, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 2.16/0.59 thf(c_0_263, 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])).
% 2.16/0.59 thf(c_0_264, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 2.16/0.59 thf(c_0_265, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 2.16/0.59 thf(c_0_266, 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])).
% 2.16/0.59 thf(c_0_267, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 2.16/0.59 thf(c_0_268, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 2.16/0.59 thf(c_0_269, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 2.16/0.59 thf(c_0_270, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 2.16/0.59 thf(c_0_271, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 2.16/0.59 thf(c_0_272, 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])).
% 2.16/0.59 thf(c_0_273, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 2.16/0.59 thf(c_0_274, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 2.16/0.59 thf(c_0_275, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 2.16/0.59 thf(c_0_276, 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])).
% 2.16/0.59 thf(c_0_277, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[complementSubsetComplementIntersect])).
% 2.16/0.59 thf(c_0_278, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X826:$i]:(((((X6 @ X2 @ X826)))&(![X827:$i]:(((((X6 @ X2 @ X827)))=>(((X826)=(X827)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_255, c_0_256])).
% 2.16/0.59 thf(c_0_279, plain, ((descrp)=(![X1:$i > $o]:((((?[X828:$i]:(((((X1 @ X828)))&(![X829:$i]:(((((X1 @ X829)))=>(((X828)=(X829))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_257, c_0_256])).
% 2.16/0.59 thf(c_0_280, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 2.16/0.59 thf(c_0_281, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 2.16/0.59 thf(c_0_282, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 2.16/0.59 thf(c_0_283, plain, ((exuE1)=(![X1:$i > $o]:((((?[X830:$i]:(((((X1 @ X830)))&(![X831:$i]:(((((X1 @ X831)))=>(((X830)=(X831))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_258, c_0_256])).
% 2.16/0.59 thf(c_0_284, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X832:$i]:(((((X1 @ X832)))&(![X833:$i]:(((((X1 @ X833)))=>(((X832)=(X833))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_259, c_0_256])).
% 2.16/0.59 thf(c_0_285, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 2.16/0.59 thf(c_0_286, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_260])).
% 2.16/0.59 thf(c_0_287, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_261, c_0_260])).
% 2.16/0.59 thf(c_0_288, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_260])).
% 2.16/0.59 thf(c_0_289, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 2.16/0.59 thf(c_0_290, plain, ((exuE2)=(![X1:$i > $o]:((((?[X834:$i]:(((((X1 @ X834)))&(![X835:$i]:(((((X1 @ X835)))=>(((X834)=(X835))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_262, c_0_256])).
% 2.16/0.59 thf(c_0_291, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_260])).
% 2.16/0.59 thf(c_0_292, 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])).
% 2.16/0.59 thf(c_0_293, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X836:$i]:(((((X1 @ X836)))&(![X837:$i]:(((((X1 @ X837)))=>(((X836)=(X837)))))))))))))), inference(apply_def,[status(thm)],[c_0_263, c_0_256])).
% 2.16/0.59 thf(c_0_294, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X838:$i]:(((((X1 @ X838)))&(![X839:$i]:(((((X1 @ X839)))=>(((X838)=(X839)))))))))))))))), inference(apply_def,[status(thm)],[c_0_264, c_0_256])).
% 2.16/0.59 thf(c_0_295, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X840:$i]:(((((X1 @ X840)))&(![X841:$i]:(((((X1 @ X841)))=>(((X840)=(X841)))))))))))))), inference(apply_def,[status(thm)],[c_0_265, c_0_256])).
% 2.16/0.59 thf(c_0_296, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X842:$i]:(((((X1 @ X842)))&(![X843:$i]:(((((X1 @ X843)))=>(((X842)=(X843))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_266, c_0_256])).
% 2.16/0.59 thf(c_0_297, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X844:$i]:(((((X1 @ X844)))&(![X845:$i]:(((((X1 @ X845)))=>(((X844)=(X845))))))))))<=>((?[X846:$i]:(((((X17 @ X846)))&(![X847:$i]:(((((X17 @ X847)))=>(((X846)=(X847)))))))))))))))), inference(apply_def,[status(thm)],[c_0_267, c_0_256])).
% 2.16/0.59 thf(c_0_298, plain, ((exuEu)=(![X1:$i > $o]:((((?[X848:$i]:(((((X1 @ X848)))&(![X849:$i]:(((((X1 @ X849)))=>(((X848)=(X849))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_268, c_0_256])).
% 2.16/0.59 thf(c_0_299, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X850:$i]:(((((X1 @ X850)))&(![X851:$i]:(((((X1 @ X851)))=>(((X850)=(X851))))))))))=>((((?[X852:$i]:(((((X17 @ X852)))&(![X853:$i]:(((((X17 @ X853)))=>(((X852)=(X853))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_269, c_0_256])).
% 2.16/0.59 thf(c_0_300, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 2.16/0.59 thf(c_0_301, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 2.16/0.59 thf(c_0_302, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 2.16/0.59 thf(c_0_303, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 2.16/0.59 thf(c_0_304, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_270, c_0_271])).
% 2.16/0.59 thf(c_0_305, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))))), inference(apply_def,[status(thm)],[c_0_272, c_0_271])).
% 2.16/0.59 thf(c_0_306, 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)))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_273, c_0_271])).
% 2.16/0.59 thf(c_0_307, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 2.16/0.59 thf(c_0_308, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 2.16/0.59 thf(c_0_309, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 2.16/0.59 thf(c_0_310, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 2.16/0.59 thf(c_0_311, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_274, c_0_275])).
% 2.16/0.59 thf(c_0_312, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 2.16/0.59 thf(c_0_313, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 2.16/0.59 thf(c_0_314, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 2.16/0.59 thf(c_0_315, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 2.16/0.59 thf(c_0_316, plain, ((funcImageSingleton)<=>![X4:$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])).
% 2.16/0.59 thf(c_0_317, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 2.16/0.59 thf(c_0_318, plain, ((lamProp)<=>![X4:$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])).
% 2.16/0.59 thf(c_0_319, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 2.16/0.59 thf(c_0_320, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 2.16/0.59 thf(c_0_321, axiom, ((brelnall1)=(![X4:$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_275])).
% 2.16/0.59 thf(c_0_322, 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_275])).
% 2.16/0.59 thf(c_0_323, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_276, c_0_271])).
% 2.16/0.59 thf(c_0_324, 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_275])).
% 2.16/0.59 thf(c_0_325, 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_275])).
% 2.16/0.59 thf(c_0_326, 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])).
% 2.16/0.59 thf(c_0_327, 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])).
% 2.16/0.59 thf(c_0_328, 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])).
% 2.16/0.59 thf(c_0_329, 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])).
% 2.16/0.59 thf(c_0_330, 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])).
% 2.16/0.59 thf(c_0_331, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 2.16/0.59 thf(c_0_332, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 2.16/0.59 thf(c_0_333, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 2.16/0.59 thf(c_0_334, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 2.16/0.59 thf(c_0_335, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 2.16/0.59 thf(c_0_336, plain, ((epred1_0)<=>![X883:$i]:(?[X884:$i]:((((![X885:$i]:(((in @ X885 @ X884)=>![X886:$i]:(((in @ X886 @ X885)=>(in @ X886 @ X883)))))&![X887:$i, X888:$i]:((((in @ X887 @ X883)&(in @ X888 @ X883))=>(![X889:$i]:(((in @ X889 @ X884)=>((in @ X887 @ X889)<=>(in @ X888 @ X889))))=>((X887)=(X888))))))&![X890:$i, X891:$i]:((((in @ X890 @ X884)&(in @ X891 @ X884))=>(![X892:$i]:(((in @ X892 @ X890)=>(in @ X892 @ X891)))|![X893:$i]:(((in @ X893 @ X891)=>(in @ X893 @ X890)))))))&![X894:$i]:(((![X895:$i]:(((in @ X895 @ X894)=>(in @ X895 @ X883)))&?[X896:$i]:((in @ X896 @ X894)))=>?[X897:$i, X898:$i]:(((((in @ X897 @ X884)&(in @ X898 @ X894))&~(?[X899:$i]:(((in @ X899 @ X897)&(in @ X899 @ X894)))))&![X900:$i]:(((in @ X900 @ X884)=>(![X901:$i]:(((in @ X901 @ X900)=>(in @ X901 @ X897)))|(in @ X898 @ X900)))))))))))), introduced(definition)).
% 2.16/0.59 thf(c_0_337, negated_conjecture, ~((![X854:$i, X855:$i]:((![X856:$i]:(((in @ X856 @ X854)<=>(in @ X856 @ X855)))=>((X854)=(X855))))=>(![X857:$i]:(~(in @ X857 @ emptyset))=>(![X858:$i, X859:$i, X860:$i]:(((in @ X860 @ (setadjoin @ X858 @ X859))<=>(((X860)=(X858))|(in @ X860 @ X859))))=>(![X861:$i, X862:$i]:(((in @ X862 @ (powerset @ X861))<=>![X863:$i]:(((in @ X863 @ X862)=>(in @ X863 @ X861)))))=>(![X864:$i, X865:$i]:(((in @ X865 @ (setunion @ X864))<=>?[X866:$i]:(((in @ X865 @ X866)&(in @ X866 @ X864)))))=>((in @ emptyset @ omega)=>(![X867:$i]:(((in @ X867 @ omega)=>(in @ (setadjoin @ X867 @ X867) @ omega)))=>(![X868:$i]:((((in @ emptyset @ X868)&![X869:$i]:((((in @ X869 @ omega)&(in @ X869 @ X868))=>(in @ (setadjoin @ X869 @ X869) @ X868))))=>![X870:$i]:(((in @ X870 @ omega)=>(in @ X870 @ X868)))))=>(![X871:$i > $i > $o, X872:$i]:((![X873:$i]:(((in @ X873 @ X872)=>?[X874:$i]:(((X871 @ X873 @ X874)&![X875:$i]:(((X871 @ X873 @ X875)=>((X874)=(X875))))))))=>?[X876:$i]:(![X877:$i]:(((in @ X877 @ X876)<=>?[X878:$i]:(((in @ X878 @ X872)&(X871 @ X878 @ X877))))))))=>(![X879:$i]:((?[X880:$i]:((in @ X880 @ X879))=>?[X881:$i]:(((in @ X881 @ X879)&~(?[X882:$i]:(((in @ X882 @ X881)&(in @ X882 @ X879))))))))=>((epred1_0)=>(![X902:$i > $o]:((?[X903:$i]:(((X902 @ X903)&![X904:$i]:(((X902 @ X904)=>((X903)=(X904))))))=>(X902 @ (descr @ (^[Z0:$i]:(X902 @ Z0))))))=>(![X905:$i, X906:$i > $o, X907:$i]:(((in @ X907 @ X905)=>((X906 @ X907)=>(in @ X907 @ (dsetconstr @ X905 @ X906)))))=>(![X908:$i, X909:$i > $o, X910:$i]:(((in @ X910 @ (dsetconstr @ X908 @ X909))=>(in @ X910 @ X908)))=>(![X911:$i, X912:$i > $o, X913:$i]:(((in @ X913 @ (dsetconstr @ X911 @ X912))=>(X912 @ X913)))=>(![X914:$i > $o]:((?[X915:$i]:(((X914 @ X915)&![X916:$i]:(((X914 @ X916)=>((X915)=(X916))))))=>?[X917:$i]:(((X914 @ X917)&![X918:$i]:(((X914 @ X918)=>((X917)=(X918))))))))=>(![X919:$o, X920:$i]:(((in @ X920 @ (prop2set @ ((X919))))=>(X919)))=>(![X921:$i]:(((in @ X921 @ emptyset)=>![X922:$o]:((X922))))=>(![X923:$i]:(((in @ X923 @ emptyset)=>~($true)))=>(![X924:$i]:(~(in @ X924 @ emptyset))=>(![X925:$i > $o]:((?[X926:$i]:(((X925 @ X926)&![X927:$i]:(((X925 @ X927)=>((X926)=(X927))))))=>?[X928:$i]:((X925 @ X928))))=>(![X929:$i, X930:$i]:((![X931:$i]:(((in @ X931 @ X929)=>(in @ X931 @ X930)))=>(![X932:$i]:(((in @ X932 @ X930)=>(in @ X932 @ X929)))=>((X929)=(X930)))))=>(![X933:$i]:((![X934:$i]:(~(in @ X934 @ X933))=>((X933)=(emptyset))))=>(![X935:$i]:((![X936:$i]:(~(in @ X936 @ X935))=>((X935)=(emptyset))))=>(![X937:$i, X938:$i > $o, X939:$i]:(((in @ X939 @ X937)=>((in @ X939 @ (dsetconstr @ X937 @ X938))<=>(X938 @ X939))))=>(![X940:$i]:((((X940)!=(emptyset))=>?[X941:$i]:((in @ X941 @ X940))))=>(![X942:$i, X943:$i > $o, X944:$i]:(((in @ X944 @ X942)=>((X943 @ X944)=>((dsetconstr @ X942 @ X943)!=(emptyset)))))=>(![X945:$i]:((?[X946:$i]:((in @ X946 @ X945))=>((X945)!=(emptyset))))=>(![X947:$i, X948:$i]:((in @ 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kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_303]), c_0_304]), c_0_305]), c_0_306]), singletonsuniq]), setukpairinjL1]), c_0_307]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_308]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_309]), c_0_310]), c_0_311]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_318]), c_0_319]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_324]), c_0_325]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_326]), c_0_327]), c_0_328]), c_0_329]), c_0_330]), c_0_331]), c_0_332]), c_0_333]), c_0_334]), c_0_335]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect])])]), c_0_336])).
% 2.16/0.59 thf(c_0_338, negated_conjecture, ![X1656:$i, X1657:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1669:$i, X1670:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1678:$i, X1679:$i > $i > $o, X1680:$i, X1682:$i, X1685:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1692:$i, X1693:$i > $o, X1694:$i, X1696:$i, X1697:$i > $o, X1698:$i, X1699:$i, X1700:$i > $o, X1701:$i, X1702:$i, X1703:$i > $o, X1704:$i, X1705:$i > $o, X1706:$i, X1709:$i, X1710:$o, X1711:$i, X1712:$i, X1713:$o, X1714:$i, X1715:$i, X1716:$i > $o, X1717:$i, X1720:$i, X1721:$i, X1724:$i, X1726:$i, X1728:$i, X1729:$i > $o, X1730:$i, X1731:$i, X1733:$i, X1734:$i > $o, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$o, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$o, X1766:$i, X1767:$i, X1768:$i > $o, X1769:$i, X1772:$i, X1773:$i, X1774:$i, X1776:$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 > $o, X1793:$i, X1794:$i > $o, X1795:$i, X1796:$i, X1797:$i > $o, X1798:$i, X1800:$i, X1801:$i > $o, X1803:$i, X1804:$i, X1805:$i > $o, X1807:$i, X1808:$i, X1809:$i > $o, X1810:$i, X1812:$o, X1813:$o, X1814:$i, X1815:$i > $o, X1817:$i, X1818:$i, X1819:$i > $o, X1820:$i, X1822:$i > $o, X1823:$i, X1826:$i, X1827:$i > $o, X1828:$i, X1832:$i, X1833:$i > $o, X1834:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i > $o, X1847:$i, X1849:$i, X1850:$i, X1851:$i > $o, X1852:$i > $o, X1855:$i, X1858:$i, X1859:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i > $o, X1872:$i, X1874:$i, X1875:$i, X1876:$i > $o, X1877:$i > $o, X1880:$i, X1882:$i, X1884:$i, X1885:$i, X1886:$i > $o, X1887:$i > $o, X1890:$i, X1891:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1900:$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:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i > $o, X1938:$i, X1939:$i > $o, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$o, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$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:$i, X2019:$o, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, 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, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i > $o, X2094:$i, X2095:$i, X2096:$i > $o, X2098:$i, X2099:$i > $o, X2100:$i, X2102:$i, X2103:$i > $o, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i > $i > $o, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i > $i > $o, X2184:$i, X2185:$i, X2186:$i > $i > $o, X2187:$i, X2188:$i, X2189:$i > $i > $o, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i > $i > $o, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i > $i > $o, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i > $i > $o, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i > $i, X2233:$i, X2234:$i, X2235:$i > $i, X2237:$i, X2238:$i, X2239:$i > $i, X2241:$i, X2242:$i, X2243:$i, X2244:$i > $o, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i > $o, X2254:$i, X2255:$i, X2256:$i > $o, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i > $i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i > $i, X2328:$i, X2329:$i, X2330:$i > $i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$o, X2338:$i, X2339:$i, X2340:$i, X2341:$o, X2342:$i, X2343:$i, X2344:$i, X2345:$o, X2346:$i, X2347:$i, X2348:$i, X2349:$o, X2350:$i, X2351:$i, X2352:$i, X2353:$o, X2354:$i, X2355:$i, X2356:$i, X2357:$o, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$o, X2364:$i, X2365:$i, X2366:$i, X2367:$o, X2368:$i, X2369:$i, X2370:$i, X2371:$o, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2392:$i, X2393:$i, X2394:$i, X2396:$i, X2397:$i, X2398:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i]:((((~(in @ (esk1_2 @ X1656 @ X1657) @ X1656)|~(in @ (esk1_2 @ X1656 @ X1657) @ X1657)|((X1656)=(X1657)))&((in @ (esk1_2 @ X1656 @ X1657) @ X1656)|(in @ (esk1_2 @ X1656 @ X1657) @ X1657)|((X1656)=(X1657))))&(~(in @ X1659 @ emptyset)&(((~(in @ X1662 @ (setadjoin @ X1660 @ X1661))|(((X1662)=(X1660))|(in @ X1662 @ X1661)))&((((X1662)!=(X1660))|(in @ X1662 @ (setadjoin @ X1660 @ X1661)))&(~(in @ X1662 @ X1661)|(in @ X1662 @ (setadjoin @ X1660 @ X1661)))))&(((~(in @ X1664 @ (powerset @ X1663))|(~(in @ X1665 @ X1664)|(in @ X1665 @ X1663)))&(((in @ (esk2_2 @ X1666 @ X1667) @ X1667)|(in @ X1667 @ (powerset @ X1666)))&(~(in @ (esk2_2 @ X1666 @ X1667) @ X1666)|(in @ X1667 @ (powerset @ X1666)))))&(((((in @ X1670 @ (esk3_2 @ X1669 @ X1670))|~(in @ X1670 @ (setunion @ X1669)))&((in @ (esk3_2 @ X1669 @ X1670) @ X1669)|~(in @ X1670 @ (setunion @ X1669))))&(~(in @ X1673 @ X1674)|~(in @ X1674 @ X1672)|(in @ X1673 @ (setunion @ X1672))))&((in @ emptyset @ omega)&((~(in @ X1675 @ omega)|(in @ (setadjoin @ X1675 @ X1675) @ omega))&(((((in @ (esk4_1 @ X1676) @ omega)|~(in @ emptyset @ X1676)|(~(in @ X1678 @ omega)|(in @ X1678 @ X1676)))&((in @ (esk4_1 @ X1676) @ X1676)|~(in @ emptyset @ X1676)|(~(in @ X1678 @ omega)|(in @ X1678 @ X1676))))&(~(in @ (setadjoin @ (esk4_1 @ X1676) @ (esk4_1 @ X1676)) @ X1676)|~(in @ emptyset @ X1676)|(~(in @ X1678 @ omega)|(in @ X1678 @ X1676))))&((((((in @ (esk8_3 @ X1679 @ X1680 @ X1685) @ X1680)|~(in @ X1685 @ (esk7_2 @ X1679 @ X1680))|(in @ (esk5_2 @ X1679 @ X1680) @ X1680))&((X1679 @ (esk8_3 @ X1679 @ X1680 @ X1685) @ X1685)|~(in @ X1685 @ (esk7_2 @ X1679 @ X1680))|(in @ (esk5_2 @ X1679 @ X1680) @ X1680)))&(~(in @ X1688 @ X1680)|~(X1679 @ X1688 @ X1687)|(in @ X1687 @ (esk7_2 @ X1679 @ X1680))|(in @ (esk5_2 @ X1679 @ X1680) @ X1680)))&(((((in @ (esk8_3 @ X1679 @ X1680 @ X1685) @ X1680)|~(in @ X1685 @ (esk7_2 @ X1679 @ X1680))|((X1679 @ (esk5_2 @ X1679 @ X1680) @ (esk6_3 @ X1679 @ X1680 @ X1682))|~(X1679 @ (esk5_2 @ X1679 @ X1680) @ X1682)))&((X1679 @ (esk8_3 @ X1679 @ X1680 @ X1685) @ X1685)|~(in @ X1685 @ (esk7_2 @ X1679 @ X1680))|((X1679 @ (esk5_2 @ X1679 @ X1680) @ (esk6_3 @ X1679 @ X1680 @ X1682))|~(X1679 @ (esk5_2 @ X1679 @ X1680) @ X1682))))&(~(in @ X1688 @ X1680)|~(X1679 @ X1688 @ X1687)|(in @ X1687 @ (esk7_2 @ X1679 @ X1680))|((X1679 @ (esk5_2 @ X1679 @ X1680) @ (esk6_3 @ X1679 @ X1680 @ X1682))|~(X1679 @ (esk5_2 @ X1679 @ X1680) @ X1682))))&((((in @ (esk8_3 @ X1679 @ X1680 @ X1685) @ X1680)|~(in @ X1685 @ (esk7_2 @ X1679 @ X1680))|(((X1682)!=(esk6_3 @ X1679 @ X1680 @ X1682))|~(X1679 @ (esk5_2 @ X1679 @ X1680) @ X1682)))&((X1679 @ (esk8_3 @ X1679 @ X1680 @ X1685) @ X1685)|~(in @ X1685 @ (esk7_2 @ X1679 @ X1680))|(((X1682)!=(esk6_3 @ X1679 @ X1680 @ X1682))|~(X1679 @ (esk5_2 @ X1679 @ X1680) @ X1682))))&(~(in @ X1688 @ X1680)|~(X1679 @ X1688 @ X1687)|(in @ X1687 @ (esk7_2 @ X1679 @ X1680))|(((X1682)!=(esk6_3 @ X1679 @ X1680 @ X1682))|~(X1679 @ (esk5_2 @ X1679 @ X1680) @ X1682))))))&((((in @ (esk9_1 @ X1689) @ X1689)|~(in @ X1690 @ X1689))&(~(in @ X1692 @ (esk9_1 @ X1689))|~(in @ X1692 @ X1689)|~(in @ X1690 @ X1689)))&((epred1_0)&((((X1693 @ (esk10_2 @ X1693 @ X1694))|~(X1693 @ X1694)|(X1693 @ (descr @ X1693)))&(((X1694)!=(esk10_2 @ X1693 @ X1694))|~(X1693 @ X1694)|(X1693 @ (descr @ X1693))))&((~(in @ X1698 @ X1696)|(~(X1697 @ X1698)|(in @ X1698 @ (dsetconstr @ X1696 @ X1697))))&((~(in @ X1701 @ (dsetconstr @ X1699 @ X1700))|(in @ X1701 @ X1699))&((~(in @ X1704 @ (dsetconstr @ X1702 @ X1703))|(X1703 @ X1704))&(((((X1705 @ (esk12_1 @ X1705))|((X1705 @ 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@ X2387)|((X2388)=(X2389))|~(in @ (esk83_3 @ X2387 @ X2388 @ X2389) @ X2389)|~(in @ X2389 @ (powerset @ X2387))|~(in @ X2388 @ (powerset @ X2387)))&(((in @ (esk84_3 @ X2387 @ X2388 @ X2389) @ X2389)|((X2388)=(X2389))|~(in @ (esk83_3 @ X2387 @ X2388 @ X2389) @ X2389)|~(in @ X2389 @ (powerset @ X2387))|~(in @ X2388 @ (powerset @ X2387)))&(~(in @ (esk84_3 @ X2387 @ X2388 @ X2389) @ X2388)|((X2388)=(X2389))|~(in @ (esk83_3 @ X2387 @ X2388 @ X2389) @ X2389)|~(in @ X2389 @ (powerset @ X2387))|~(in @ X2388 @ (powerset @ X2387)))))))&((((in @ (esk85_3 @ X2392 @ X2393 @ X2394) @ X2392)|(subset @ X2393 @ X2394)|~(in @ X2394 @ (powerset @ X2392))|~(in @ X2393 @ (powerset @ X2392)))&(((in @ (esk85_3 @ X2392 @ X2393 @ X2394) @ X2393)|(subset @ X2393 @ X2394)|~(in @ X2394 @ (powerset @ X2392))|~(in @ X2393 @ (powerset @ X2392)))&(~(in @ (esk85_3 @ X2392 @ X2393 @ X2394) @ X2394)|(subset @ X2393 @ X2394)|~(in @ X2394 @ (powerset @ X2392))|~(in @ X2393 @ (powerset @ X2392)))))&((((in @ (esk86_3 @ X2396 @ X2397 @ X2398) @ X2396)|(in @ X2397 @ (powerset @ X2398))|~(in @ X2398 @ (powerset @ X2396))|~(in @ X2397 @ (powerset @ X2396)))&(((in @ (esk86_3 @ X2396 @ X2397 @ X2398) @ X2397)|(in @ X2397 @ (powerset @ X2398))|~(in @ X2398 @ (powerset @ X2396))|~(in @ X2397 @ (powerset @ X2396)))&(~(in @ (esk86_3 @ X2396 @ X2397 @ X2398) @ X2398)|(in @ X2397 @ (powerset @ X2398))|~(in @ X2398 @ (powerset @ X2396))|~(in @ X2397 @ (powerset @ X2396)))))&((~(in @ X2401 @ (powerset @ X2400))|(~(in @ X2402 @ (powerset @ X2400))|(~(in @ X2403 @ X2400)|(~(in @ X2401 @ (powerset @ X2402))|(~(in @ X2403 @ X2401)|(in @ X2403 @ X2402))))))&((~(in @ X2405 @ (powerset @ X2404))|(~(in @ X2406 @ X2404)|(~(in @ X2406 @ X2405)|~(in @ X2406 @ (setminus @ X2404 @ X2405)))))&((~(in @ X2408 @ (powerset @ X2407))|(~(in @ X2409 @ X2407)|((in @ X2409 @ (setminus @ X2407 @ X2408))|(in @ X2409 @ X2408))))&((~(in @ X2411 @ (powerset @ X2410))|(~(in @ X2412 @ (powerset @ X2410))|(~(in @ X2413 @ X2410)|((in @ X2413 @ X2411)|~(in @ X2413 @ (binintersect @ X2411 @ X2412))))))&((~(in @ X2415 @ (powerset @ X2414))|(~(in @ X2416 @ (powerset @ X2414))|(~(in @ X2417 @ X2414)|((in @ X2417 @ X2416)|~(in @ X2417 @ (binintersect @ X2415 @ X2416))))))&((~(in @ X2419 @ (powerset @ X2418))|(~(in @ X2420 @ (powerset @ X2418))|(~(in @ X2421 @ X2418)|(~(subset @ X2419 @ (setminus @ X2418 @ X2420))|(~(in @ X2421 @ X2420)|~(in @ X2421 @ X2419))))))&((~(in @ X2423 @ (powerset @ X2422))|(~(in @ X2424 @ (powerset @ X2422))|(~(in @ X2425 @ X2422)|(~(subset @ X2423 @ X2424)|((in @ X2425 @ X2424)|~(in @ X2425 @ X2423))))))&((~(in @ X2427 @ (powerset @ X2426))|(~(in @ X2428 @ (powerset @ X2426))|(~(subset @ X2427 @ X2428)|(subset @ (setminus @ X2426 @ X2428) @ (setminus @ X2426 @ X2427)))))&((~(in @ X2430 @ (powerset @ X2429))|(~(in @ X2431 @ (powerset @ X2429))|(~(subset @ (setminus @ X2429 @ X2431) @ (setminus @ X2429 @ X2430))|(subset @ X2430 @ X2431))))&((~(in @ X2433 @ (powerset @ X2432))|(~(in @ X2434 @ X2432)|(~(in @ X2434 @ X2433)|(in @ X2434 @ (setminus @ X2432 @ (setminus @ X2432 @ X2433))))))&((~(in @ X2436 @ (powerset @ X2435))|(~(in @ X2437 @ X2435)|(~(in @ X2437 @ (setminus @ X2435 @ (setminus @ X2435 @ X2436)))|(in @ X2437 @ X2436))))&((~(in @ X2439 @ (powerset @ X2438))|(subset @ X2439 @ (setminus @ X2438 @ (setminus @ X2438 @ X2439))))&((~(in @ X2441 @ (powerset @ X2440))|(subset @ (setminus @ X2440 @ (setminus @ X2440 @ X2441)) @ X2441))&((~(in @ X2443 @ (powerset @ X2442))|((X2443)=(setminus @ X2442 @ (setminus @ X2442 @ X2443))))&((~(in @ X2445 @ (powerset @ X2444))|(~(in @ X2446 @ (powerset @ X2444))|(~(in @ X2447 @ X2444)|(~(in @ X2447 @ (setminus @ X2444 @ X2445))|~(in @ X2447 @ (binintersect @ X2445 @ X2446))))))&((~(in @ X2449 @ (powerset @ X2448))|(~(in @ X2450 @ (powerset @ X2448))|(~(in @ X2451 @ X2448)|(~(in @ X2451 @ (setminus @ X2448 @ X2449))|(in @ X2451 @ (setminus @ X2448 @ (binintersect @ X2449 @ X2450)))))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&~(subset @ (setminus @ esk87_0 @ esk88_0) @ (setminus @ esk87_0 @ (binintersect @ esk88_0 @ esk89_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_337])])])])])])])).
% 2.16/0.59 thf(c_0_339, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_338])).
% 2.16/0.59 thf(c_0_340, negated_conjecture, (in @ esk89_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_338])).
% 2.16/0.59 thf(c_0_341, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X2 @ X4)|~((subset @ X2 @ X3))|~((subset @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_338])).
% 2.16/0.59 thf(c_0_342, negated_conjecture, (subset @ esk89_0 @ esk87_0), inference(spm,[status(thm)],[c_0_339, c_0_340])).
% 2.16/0.59 thf(c_0_343, negated_conjecture, ~((subset @ (setminus @ esk87_0 @ esk88_0) @ (setminus @ esk87_0 @ (binintersect @ esk88_0 @ esk89_0)))), inference(split_conjunct,[status(thm)],[c_0_338])).
% 2.16/0.59 thf(c_0_344, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ (setminus @ X3 @ X4) @ (setminus @ X3 @ X2))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((subset @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_338])).
% 2.16/0.59 thf(c_0_345, negated_conjecture, (in @ esk88_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_338])).
% 2.16/0.59 thf(c_0_346, negated_conjecture, ![X3:$i, X2:$i]:((subset @ (binintersect @ X2 @ X3) @ X2)), inference(split_conjunct,[status(thm)],[c_0_338])).
% 2.16/0.59 thf(c_0_347, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk87_0)|~((subset @ X2 @ esk89_0)))), inference(spm,[status(thm)],[c_0_341, c_0_342])).
% 2.16/0.59 thf(c_0_348, negated_conjecture, ![X2:$i, X3:$i]:((subset @ (binintersect @ X2 @ X3) @ X3)), inference(split_conjunct,[status(thm)],[c_0_338])).
% 2.16/0.59 thf(c_0_349, negated_conjecture, ~((in @ (binintersect @ esk88_0 @ esk89_0) @ (powerset @ esk87_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_343, c_0_344]), c_0_345]), c_0_346])])).
% 2.16/0.59 thf(c_0_350, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_338])).
% 2.16/0.59 thf(c_0_351, negated_conjecture, ![X2:$i]:((subset @ (binintersect @ X2 @ esk89_0) @ esk87_0)), inference(spm,[status(thm)],[c_0_347, c_0_348])).
% 2.16/0.59 thf(c_0_352, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_349, c_0_350]), c_0_351])]), ['proof']).
% 2.16/0.59 % SZS output end CNFRefutation
% 2.16/0.59 % Parsed axioms : 543
% 2.16/0.59 % Removed by relevancy pruning/SinE : 0
% 2.16/0.59 % Initial clauses : 743
% 2.16/0.59 % Removed in clause preprocessing : 322
% 2.16/0.59 % Initial clauses in saturation : 421
% 2.16/0.59 % Processed clauses : 1673
% 2.16/0.59 % ...of these trivial : 16
% 2.16/0.59 % ...subsumed : 886
% 2.16/0.59 % ...remaining for further processing : 771
% 2.16/0.59 % Other redundant clauses eliminated : 36
% 2.16/0.59 % Clauses deleted for lack of memory : 0
% 2.16/0.59 % Backward-subsumed : 17
% 2.16/0.59 % Backward-rewritten : 8
% 2.16/0.59 % Generated clauses : 21310
% 2.16/0.59 % ...of the previous two non-redundant : 17613
% 2.16/0.59 % ...aggressively subsumed : 0
% 2.16/0.59 % Contextual simplify-reflections : 0
% 2.16/0.59 % Paramodulations : 21266
% 2.16/0.59 % Factorizations : 2
% 2.16/0.59 % NegExts : 0
% 2.16/0.59 % Equation resolutions : 39
% 2.16/0.59 % Disequality decompositions : 0
% 2.16/0.59 % Total rewrite steps : 7656
% 2.16/0.59 % ...of those cached : 7316
% 2.16/0.59 % Propositional unsat checks : 0
% 2.16/0.59 % Propositional check models : 0
% 2.16/0.59 % Propositional check unsatisfiable : 0
% 2.16/0.59 % Propositional clauses : 0
% 2.16/0.59 % Propositional clauses after purity: 0
% 2.16/0.59 % Propositional unsat core size : 0
% 2.16/0.59 % Propositional preprocessing time : 0.000
% 2.16/0.59 % Propositional encoding time : 0.000
% 2.16/0.59 % Propositional solver time : 0.000
% 2.16/0.59 % Success case prop preproc time : 0.000
% 2.16/0.59 % Success case prop encoding time : 0.000
% 2.16/0.59 % Success case prop solver time : 0.000
% 2.16/0.59 % Current number of processed clauses : 733
% 2.16/0.59 % Positive orientable unit clauses : 283
% 2.16/0.59 % Positive unorientable unit clauses: 0
% 2.16/0.59 % Negative unit clauses : 13
% 2.16/0.59 % Non-unit-clauses : 437
% 2.16/0.59 % Current number of unprocessed clauses: 16312
% 2.16/0.59 % ...number of literals in the above : 47251
% 2.16/0.59 % Current number of archived formulas : 0
% 2.16/0.59 % Current number of archived clauses : 26
% 2.16/0.59 % Clause-clause subsumption calls (NU) : 29775
% 2.16/0.59 % Rec. Clause-clause subsumption calls : 24576
% 2.16/0.59 % Non-unit clause-clause subsumptions : 652
% 2.16/0.59 % Unit Clause-clause subsumption calls : 2183
% 2.16/0.59 % Rewrite failures with RHS unbound : 0
% 2.16/0.59 % BW rewrite match attempts : 1798
% 2.16/0.59 % BW rewrite match successes : 6
% 2.16/0.59 % Condensation attempts : 0
% 2.16/0.59 % Condensation successes : 0
% 2.16/0.59 % Termbank termtop insertions : 361884
% 2.16/0.59 % Search garbage collected termcells : 26179
% 2.16/0.59
% 2.16/0.59 % -------------------------------------------------
% 2.16/0.59 % User time : 0.265 s
% 2.16/0.59 % System time : 0.013 s
% 2.16/0.59 % Total time : 0.279 s
% 2.16/0.59 % Maximum resident set size: 9864 pages
% 2.16/0.59
% 2.16/0.59 % -------------------------------------------------
% 2.16/0.59 % User time : 0.400 s
% 2.16/0.59 % System time : 0.078 s
% 2.16/0.59 % Total time : 0.478 s
% 2.16/0.59 % Maximum resident set size: 5120 pages
% 2.16/0.59 % E exiting
%------------------------------------------------------------------------------