0.00/0.03	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.09/0.35	% Computer : n031.cluster.edu
0.09/0.35	% Model    : x86_64 x86_64
0.09/0.35	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.35	% Memory   : 8046.5625MB
0.09/0.35	% OS       : Linux 6.8.0-71-generic
0.09/0.35	% CPULimit : 1440
0.09/0.35	% WCLimit  : 180
0.09/0.35	% DateTime : Mon Jul 27 12:36:40 UTC 2026
0.09/0.35	% CPUTime  : 
0.09/0.35	Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.09/0.40	Running higher-order theorem proving
0.09/0.47	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=180 /export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p
124.91/18.52	% Version: 3.5.1-ho
124.91/18.52	% Preprocessing class: HSLMSLSSLLLCHFA.
124.91/18.52	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
124.91/18.52	% Starting ehoh_best5 with 180s (1) cores
124.91/18.52	% Starting almost_fo_3_lam with 180s (1) cores
124.91/18.52	% Starting new_bool_5 with 180s (1) cores
124.91/18.52	% Starting pre_casc_3 with 180s (1) cores
124.91/18.52	% Starting ho_unfolding_8 with 180s (1) cores
124.91/18.52	% Starting new_ho_10_cnf2 with 180s (1) cores
124.91/18.52	% Starting new_bool_3 with 180s (1) cores
124.91/18.52	% Starting new_ho_5 with 180s (1) cores
124.91/18.52	% new_bool_5 with pid 4030 completed with status 0
124.91/18.52	% Result found by new_bool_5
124.91/18.52	% Preprocessing class: HSLMSLSSLLLCHFA.
124.91/18.52	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
124.91/18.52	% Starting ehoh_best5 with 180s (1) cores
124.91/18.52	% Starting almost_fo_3_lam with 180s (1) cores
124.91/18.52	% Starting new_bool_5 with 180s (1) cores
124.91/18.52	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
124.91/18.52	% SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
124.91/18.52	% Search class: HGHSM-FSLM31-MHFMMSBN
124.91/18.52	% Scheduled 7 strats onto 1 cores with 180 seconds (180 total)
124.91/18.52	% Starting SubtermCWHack with 17s (1) cores
124.91/18.52	% SubtermCWHack with pid 4037 completed with status 8
124.91/18.52	% Starting new_bool_5 with 19s (1) cores
124.91/18.52	% new_bool_5 with pid 4044 completed with status 0
124.91/18.52	% Result found by new_bool_5
124.91/18.52	% Preprocessing class: HSLMSLSSLLLCHFA.
124.91/18.52	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
124.91/18.52	% Starting ehoh_best5 with 180s (1) cores
124.91/18.52	% Starting almost_fo_3_lam with 180s (1) cores
124.91/18.52	% Starting new_bool_5 with 180s (1) cores
124.91/18.52	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
124.91/18.52	% SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
124.91/18.52	% Search class: HGHSM-FSLM31-MHFMMSBN
124.91/18.52	% Scheduled 7 strats onto 1 cores with 180 seconds (180 total)
124.91/18.52	% Starting SubtermCWHack with 17s (1) cores
124.91/18.52	% SubtermCWHack with pid 4037 completed with status 8
124.91/18.52	% Starting new_bool_5 with 19s (1) cores
124.91/18.52	% Preprocessing time       : 0.006 s
124.91/18.52	% Presaturation interreduction done
124.91/18.52	
124.91/18.52	% Proof found!
124.91/18.52	% SZS status Theorem
124.91/18.52	% SZS output start CNFRefutation
124.91/18.52	thf(decl_23, type, in: $i > $i > $o).
124.91/18.52	thf(decl_24, type, exu: ($i > $o) > $o).
124.91/18.52	thf(decl_25, type, setextAx: $o).
124.91/18.52	thf(decl_26, type, emptyset: $i).
124.91/18.52	thf(decl_27, type, emptysetAx: $o).
124.91/18.52	thf(decl_28, type, setadjoin: $i > $i > $i).
124.91/18.52	thf(decl_29, type, setadjoinAx: $o).
124.91/18.52	thf(decl_30, type, powerset: $i > $i).
124.91/18.52	thf(decl_31, type, powersetAx: $o).
124.91/18.52	thf(decl_32, type, setunion: $i > $i).
124.91/18.52	thf(decl_33, type, setunionAx: $o).
124.91/18.52	thf(decl_34, type, omega: $i).
124.91/18.52	thf(decl_35, type, omega0Ax: $o).
124.91/18.52	thf(decl_36, type, omegaSAx: $o).
124.91/18.52	thf(decl_37, type, omegaIndAx: $o).
124.91/18.52	thf(decl_38, type, replAx: $o).
124.91/18.52	thf(decl_39, type, foundationAx: $o).
124.91/18.52	thf(decl_40, type, wellorderingAx: $o).
124.91/18.52	thf(decl_41, type, descr: ($i > $o) > $i).
124.91/18.52	thf(decl_42, type, descrp: $o).
124.91/18.52	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
124.91/18.52	thf(decl_44, type, dsetconstrI: $o).
124.91/18.52	thf(decl_45, type, dsetconstrEL: $o).
124.91/18.52	thf(decl_46, type, dsetconstrER: $o).
124.91/18.52	thf(decl_47, type, exuE1: $o).
124.91/18.52	thf(decl_48, type, prop2set: $o > $i).
124.91/18.52	thf(decl_49, type, prop2setE: $o).
124.91/18.52	thf(decl_50, type, emptysetE: $o).
124.91/18.52	thf(decl_51, type, emptysetimpfalse: $o).
124.91/18.52	thf(decl_52, type, notinemptyset: $o).
124.91/18.52	thf(decl_53, type, exuE3e: $o).
124.91/18.52	thf(decl_54, type, setext: $o).
124.91/18.52	thf(decl_55, type, emptyI: $o).
124.91/18.52	thf(decl_56, type, noeltsimpempty: $o).
124.91/18.52	thf(decl_57, type, setbeta: $o).
124.91/18.52	thf(decl_58, type, nonempty: $i > $o).
124.91/18.52	thf(decl_59, type, nonemptyE1: $o).
124.91/18.52	thf(decl_60, type, nonemptyI: $o).
124.91/18.52	thf(decl_61, type, nonemptyI1: $o).
124.91/18.52	thf(decl_62, type, setadjoinIL: $o).
124.91/18.52	thf(decl_63, type, emptyinunitempty: $o).
124.91/18.52	thf(decl_64, type, setadjoinIR: $o).
124.91/18.52	thf(decl_65, type, setadjoinE: $o).
124.91/18.52	thf(decl_66, type, setadjoinOr: $o).
124.91/18.52	thf(decl_67, type, setoftrueEq: $o).
124.91/18.52	thf(decl_68, type, powersetI: $o).
124.91/18.52	thf(decl_69, type, emptyinPowerset: $o).
124.91/18.52	thf(decl_70, type, emptyInPowerset: $o).
124.91/18.52	thf(decl_71, type, powersetE: $o).
124.91/18.52	thf(decl_72, type, setunionI: $o).
124.91/18.52	thf(decl_73, type, setunionE: $o).
124.91/18.52	thf(decl_74, type, subPowSU: $o).
124.91/18.52	thf(decl_75, type, exuE2: $o).
124.91/18.52	thf(decl_76, type, nonemptyImpWitness: $o).
124.91/18.52	thf(decl_77, type, uniqinunit: $o).
124.91/18.52	thf(decl_78, type, notinsingleton: $o).
124.91/18.52	thf(decl_79, type, eqinunit: $o).
124.91/18.52	thf(decl_80, type, singletonsswitch: $o).
124.91/18.52	thf(decl_81, type, upairsetE: $o).
124.91/18.52	thf(decl_82, type, upairsetIL: $o).
124.91/18.52	thf(decl_83, type, upairsetIR: $o).
124.91/18.52	thf(decl_84, type, emptyE1: $o).
124.91/18.52	thf(decl_85, type, vacuousDall: $o).
124.91/18.52	thf(decl_86, type, quantDeMorgan1: $o).
124.91/18.52	thf(decl_87, type, quantDeMorgan2: $o).
124.91/18.52	thf(decl_88, type, quantDeMorgan3: $o).
124.91/18.52	thf(decl_89, type, quantDeMorgan4: $o).
124.91/18.52	thf(decl_90, type, prop2setI: $o).
124.91/18.52	thf(decl_92, type, prop2set2propI: $o).
124.91/18.52	thf(decl_93, type, notdexE: $o).
124.91/18.52	thf(decl_94, type, notdallE: $o).
124.91/18.52	thf(decl_95, type, exuI1: $o).
124.91/18.52	thf(decl_96, type, exuI3: $o).
124.91/18.52	thf(decl_97, type, exuI2: $o).
124.91/18.52	thf(decl_98, type, inCongP: $o).
124.91/18.52	thf(decl_99, type, in__Cong: $o).
124.91/18.52	thf(decl_100, type, exuE3u: $o).
124.91/18.52	thf(decl_101, type, exu__Cong: $o).
124.91/18.52	thf(decl_102, type, emptyset__Cong: $o).
124.91/18.52	thf(decl_103, type, setadjoin__Cong: $o).
124.91/18.52	thf(decl_104, type, powerset__Cong: $o).
124.91/18.52	thf(decl_105, type, setunion__Cong: $o).
124.91/18.52	thf(decl_106, type, omega__Cong: $o).
124.91/18.52	thf(decl_107, type, exuEu: $o).
124.91/18.52	thf(decl_108, type, descr__Cong: $o).
124.91/18.52	thf(decl_109, type, dsetconstr__Cong: $o).
124.91/18.52	thf(decl_110, type, subset: $i > $i > $o).
124.91/18.52	thf(decl_113, type, subsetI1: $o).
124.91/18.52	thf(decl_114, type, eqimpsubset2: $o).
124.91/18.52	thf(decl_115, type, eqimpsubset1: $o).
124.91/18.52	thf(decl_116, type, subsetI2: $o).
124.91/18.52	thf(decl_117, type, emptysetsubset: $o).
124.91/18.52	thf(decl_118, type, subsetE: $o).
124.91/18.52	thf(decl_119, type, subsetE2: $o).
124.91/18.52	thf(decl_120, type, notsubsetI: $o).
124.91/18.52	thf(decl_121, type, notequalI1: $o).
124.91/18.52	thf(decl_122, type, notequalI2: $o).
124.91/18.52	thf(decl_123, type, subsetRefl: $o).
124.91/18.52	thf(decl_124, type, subsetTrans: $o).
124.91/18.52	thf(decl_125, type, setadjoinSub: $o).
124.91/18.52	thf(decl_126, type, setadjoinSub2: $o).
124.91/18.52	thf(decl_127, type, subset2powerset: $o).
124.91/18.52	thf(decl_128, type, setextsub: $o).
124.91/18.52	thf(decl_129, type, subsetemptysetimpeq: $o).
124.91/18.52	thf(decl_130, type, powersetI1: $o).
124.91/18.52	thf(decl_131, type, powersetE1: $o).
124.91/18.52	thf(decl_132, type, inPowerset: $o).
124.91/18.52	thf(decl_133, type, powersetsubset: $o).
124.91/18.52	thf(decl_134, type, sepInPowerset: $o).
124.91/18.52	thf(decl_135, type, sepSubset: $o).
124.91/18.52	thf(decl_136, type, binunion: $i > $i > $i).
124.91/18.52	thf(decl_137, type, binunionIL: $o).
124.91/18.52	thf(decl_138, type, upairset2IR: $o).
124.91/18.52	thf(decl_139, type, binunionIR: $o).
124.91/18.52	thf(decl_140, type, binunionEcases: $o).
124.91/18.52	thf(decl_141, type, binunionE: $o).
124.91/18.52	thf(decl_142, type, binunionLsub: $o).
124.91/18.52	thf(decl_143, type, binunionRsub: $o).
124.91/18.52	thf(decl_144, type, binintersect: $i > $i > $i).
124.91/18.52	thf(decl_145, type, binintersectI: $o).
124.91/18.52	thf(decl_146, type, binintersectSubset5: $o).
124.91/18.52	thf(decl_147, type, binintersectEL: $o).
124.91/18.52	thf(decl_148, type, binintersectLsub: $o).
124.91/18.52	thf(decl_149, type, binintersectSubset2: $o).
124.91/18.52	thf(decl_150, type, binintersectSubset3: $o).
124.91/18.52	thf(decl_151, type, binintersectER: $o).
124.91/18.52	thf(decl_152, type, disjointsetsI1: $o).
124.91/18.52	thf(decl_153, type, binintersectRsub: $o).
124.91/18.52	thf(decl_154, type, binintersectSubset4: $o).
124.91/18.52	thf(decl_155, type, binintersectSubset1: $o).
124.91/18.52	thf(decl_156, type, bs114d: $o).
124.91/18.52	thf(decl_158, type, setminus: $i > $i > $i).
124.91/18.52	thf(decl_159, type, setminusI: $o).
124.91/18.52	thf(decl_160, type, setminusEL: $o).
124.91/18.53	thf(decl_161, type, setminusER: $o).
124.91/18.53	thf(decl_162, type, setminusSubset2: $o).
124.91/18.53	thf(decl_163, type, setminusERneg: $o).
124.91/18.53	thf(decl_164, type, setminusELneg: $o).
124.91/18.53	thf(decl_165, type, setminusILneg: $o).
124.91/18.53	thf(decl_166, type, setminusIRneg: $o).
124.91/18.53	thf(decl_167, type, setminusLsub: $o).
124.91/18.53	thf(decl_168, type, setminusSubset1: $o).
124.91/18.53	thf(decl_169, type, symdiff: $i > $i > $i).
124.91/18.53	thf(decl_170, type, symdiffE: $o).
124.91/18.53	thf(decl_171, type, symdiffI1: $o).
124.91/18.53	thf(decl_172, type, symdiffI2: $o).
124.91/18.53	thf(decl_173, type, symdiffIneg1: $o).
124.91/18.53	thf(decl_174, type, symdiffIneg2: $o).
124.91/18.53	thf(decl_175, type, iskpair: $i > $o).
124.91/18.53	thf(decl_176, type, secondinupair: $o).
124.91/18.53	thf(decl_177, type, setukpairIL: $o).
124.91/18.53	thf(decl_178, type, setukpairIR: $o).
124.91/18.53	thf(decl_179, type, kpairiskpair: $o).
124.91/18.53	thf(decl_180, type, kpair: $i > $i > $i).
124.91/18.53	thf(decl_181, type, kpairp: $o).
124.91/18.53	thf(decl_182, type, cartprod: $i > $i > $i).
124.91/18.53	thf(decl_183, type, singletonsubset: $o).
124.91/18.53	thf(decl_184, type, singletoninpowerset: $o).
124.91/18.53	thf(decl_185, type, singletoninpowunion: $o).
124.91/18.53	thf(decl_186, type, upairset2E: $o).
124.91/18.53	thf(decl_187, type, upairsubunion: $o).
124.91/18.53	thf(decl_188, type, upairinpowunion: $o).
124.91/18.53	thf(decl_189, type, ubforcartprodlem1: $o).
124.91/18.53	thf(decl_190, type, ubforcartprodlem2: $o).
124.91/18.53	thf(decl_191, type, ubforcartprodlem3: $o).
124.91/18.53	thf(decl_192, type, cartprodpairin: $o).
124.91/18.53	thf(decl_193, type, cartprodmempair1: $o).
124.91/18.53	thf(decl_194, type, cartprodmempair: $o).
124.91/18.53	thf(decl_195, type, setunionE2: $o).
124.91/18.53	thf(decl_196, type, setunionsingleton1: $o).
124.91/18.53	thf(decl_197, type, setunionsingleton2: $o).
124.91/18.53	thf(decl_198, type, setunionsingleton: $o).
124.91/18.53	thf(decl_199, type, singleton: $i > $o).
124.91/18.53	thf(decl_200, type, singletonprop: $o).
124.91/18.53	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
124.91/18.53	thf(decl_202, type, ex1E1: $o).
124.91/18.53	thf(decl_203, type, ex1I: $o).
124.91/18.53	thf(decl_204, type, ex1I2: $o).
124.91/18.53	thf(decl_205, type, singletonsuniq: $o).
124.91/18.53	thf(decl_210, type, setukpairinjL1: $o).
124.91/18.53	thf(decl_211, type, kfstsingleton: $o).
124.91/18.53	thf(decl_212, type, theprop: $o).
124.91/18.53	thf(decl_213, type, kfst: $i > $i).
124.91/18.53	thf(decl_214, type, kfstpairEq: $o).
124.91/18.53	thf(decl_215, type, cartprodfstin: $o).
124.91/18.53	thf(decl_216, type, setukpairinjL2: $o).
124.91/18.53	thf(decl_217, type, setukpairinjL: $o).
124.91/18.53	thf(decl_218, type, setukpairinjR11: $o).
124.91/18.53	thf(decl_219, type, setukpairinjR12: $o).
124.91/18.53	thf(decl_220, type, setukpairinjR1: $o).
124.91/18.53	thf(decl_221, type, upairequniteq: $o).
124.91/18.53	thf(decl_222, type, setukpairinjR2: $o).
124.91/18.53	thf(decl_223, type, setukpairinjR: $o).
124.91/18.53	thf(decl_224, type, ksndsingleton: $o).
124.91/18.53	thf(decl_225, type, ksnd: $i > $i).
124.91/18.53	thf(decl_226, type, ksndpairEq: $o).
124.91/18.53	thf(decl_227, type, kpairsurjEq: $o).
124.91/18.53	thf(decl_228, type, cartprodsndin: $o).
124.91/18.53	thf(decl_229, type, cartprodpairmemEL: $o).
124.91/18.53	thf(decl_230, type, cartprodpairmemER: $o).
124.91/18.53	thf(decl_231, type, cartprodmempaircEq: $o).
124.91/18.53	thf(decl_232, type, cartprodfstpairEq: $o).
124.91/18.53	thf(decl_233, type, cartprodsndpairEq: $o).
124.91/18.53	thf(decl_234, type, cartprodpairsurjEq: $o).
124.91/18.53	thf(decl_235, type, breln: $i > $i > $i > $o).
124.91/18.53	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
124.91/18.53	thf(decl_237, type, dpsetconstrI: $o).
124.91/18.53	thf(decl_238, type, dpsetconstrSub: $o).
124.91/18.53	thf(decl_239, type, setOfPairsIsBReln: $o).
124.91/18.53	thf(decl_240, type, dpsetconstrERa: $o).
124.91/18.53	thf(decl_241, type, dpsetconstrEL1: $o).
124.91/18.53	thf(decl_242, type, dpsetconstrEL2: $o).
124.91/18.53	thf(decl_243, type, dpsetconstrER: $o).
124.91/18.53	thf(decl_244, type, func: $i > $i > $i > $o).
124.91/18.53	thf(decl_245, type, funcSet: $i > $i > $i).
124.91/18.53	thf(decl_246, type, funcImageSingleton: $o).
124.91/18.53	thf(decl_247, type, apProp: $o).
124.91/18.53	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
124.91/18.53	thf(decl_249, type, app: $o).
124.91/18.53	thf(decl_250, type, epred1_0: $o).
124.91/18.53	thf(decl_251, type, esk1_2: $i > $i > $i).
124.91/18.53	thf(decl_252, type, esk2_2: $i > $i > $i).
124.91/18.53	thf(decl_253, type, esk3_2: $i > $i > $i).
124.91/18.53	thf(decl_254, type, esk4_1: $i > $i).
124.91/18.53	thf(decl_255, type, esk5_2: ($i > $i > $o) > $i > $i).
124.91/18.53	thf(decl_256, type, esk6_2: ($i > $i > $o) > $i > $i).
124.91/18.53	thf(decl_257, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
124.91/18.53	thf(decl_258, type, esk8_1: $i > $i).
124.91/18.53	thf(decl_259, type, esk9_1: ($i > $o) > $i).
124.91/18.53	thf(decl_260, type, esk10_1: ($i > $o) > $i).
124.91/18.53	thf(decl_261, type, esk11_2: $i > $i > $i).
124.91/18.53	thf(decl_262, type, esk12_2: $i > $i > $i).
124.91/18.53	thf(decl_263, type, esk13_1: $i > $i).
124.91/18.53	thf(decl_264, type, esk14_1: $i > $i).
124.91/18.53	thf(decl_265, type, esk15_1: $i > $i).
124.91/18.53	thf(decl_266, type, esk16_2: $i > $i > $i).
124.91/18.53	thf(decl_267, type, esk17_3: $i > $i > $o > $i).
124.91/18.53	thf(decl_268, type, esk18_1: ($i > $o) > $i).
124.91/18.53	thf(decl_269, type, esk19_1: $i > $i).
124.91/18.53	thf(decl_270, type, esk20_2: $i > ($i > $o) > $i).
124.91/18.53	thf(decl_271, type, esk21_2: $i > ($i > $o) > $i).
124.91/18.53	thf(decl_272, type, esk22_2: $i > ($i > $o) > $i).
124.91/18.53	thf(decl_273, type, esk23_2: $i > ($i > $o) > $i).
124.91/18.53	thf(decl_274, type, esk24_2: $i > ($i > $o) > $i).
124.91/18.53	thf(decl_275, type, esk25_2: $i > ($i > $o) > $i).
124.91/18.53	thf(decl_276, type, esk26_2: ($i > $o) > $i > $i).
124.91/18.53	thf(decl_277, type, esk27_1: ($i > $o) > $i).
124.91/18.53	thf(decl_278, type, esk28_1: ($i > $o) > $i).
124.91/18.53	thf(decl_279, type, esk29_2: ($i > $o) > $i > $i).
124.91/18.53	thf(decl_280, type, esk30_2: ($i > $o) > ($i > $o) > $i).
124.91/18.53	thf(decl_281, type, esk31_2: ($i > $o) > ($i > $o) > $i).
124.91/18.53	thf(decl_282, type, esk32_2: ($i > $o) > ($i > $o) > $i).
124.91/18.53	thf(decl_283, type, esk33_2: ($i > $o) > ($i > $o) > $i).
124.91/18.53	thf(decl_284, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
124.91/18.53	thf(decl_285, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
124.91/18.53	thf(decl_286, type, esk36_2: $i > $i > $i).
124.91/18.53	thf(decl_287, type, esk37_2: $i > $i > $i).
124.91/18.53	thf(decl_288, type, esk38_2: $i > $i > $i).
124.91/18.53	thf(decl_289, type, esk39_3: $i > $i > $i > $i).
124.91/18.53	thf(decl_290, type, esk40_3: $i > $i > $i > $i).
124.91/18.53	thf(decl_291, type, esk41_2: $i > $i > $i).
124.91/18.53	thf(decl_292, type, esk42_2: $i > ($i > $o) > $i).
124.91/18.53	thf(decl_293, type, esk43_2: $i > ($i > $o) > $i).
124.91/18.53	thf(decl_294, type, esk44_2: $i > ($i > $o) > $i).
124.91/18.53	thf(decl_295, type, esk45_3: $i > ($i > $o) > $i > $i).
124.91/18.53	thf(decl_296, type, esk46_2: $i > ($i > $o) > $i).
124.91/18.53	thf(decl_297, type, esk47_2: $i > ($i > $o) > $i).
124.91/18.53	thf(decl_298, type, esk48_0: $i).
124.91/18.53	thf(decl_299, type, esk49_0: $i).
124.91/18.53	thf(decl_300, type, esk50_0: $i).
124.91/18.53	thf(infuncsetfunc, conjecture, ((setextAx)=>(((setadjoinAx)=>(((((omegaSAx)=>(((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>(((dsetconstrEL)=>((((prop2setE)=>((emptysetE)=>(((notinemptyset)=>(((setext)=>((emptyI)=>(((setbeta)=>((nonemptyE1)=>((((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>(((emptyinPowerset)=>(((powersetE)=>((setunionI)=>((setunionE)=>(((exuE2)=>(((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((((((emptyE1)=>(((quantDeMorgan1)=>(((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((((notdallE)=>((exuI1)=>((exuI3)=>((((((exu__Cong)=>((((powerset__Cong)=>((setunion__Cong)=>(((((dsetconstr__Cong)=>((((eqimpsubset1)=>(((emptysetsubset)=>(((((((((setadjoinSub)=>((setadjoinSub2)=>(((((powersetI1)=>((((powersetsubset)=>((sepInPowerset)=>(((binunionIL)=>((upairset2IR)=>((((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>(((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>(((binintersectRsub)=>((binintersectSubset4)=>(((bs114d)=>((setminusI)=>((((setminusSubset2)=>((((setminusILneg)=>(((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((((symdiffIneg2)=>(((setukpairIL)=>((setukpairIR)=>(((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>(((cartprodpairin)=>(((cartprodmempair)=>(((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(((ex1E1)=>((ex1I)=>(((((kfstsingleton)=>((((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>(((((((((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>(((((((app)=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)<=(in @ X30 @ (funcSet @ X4 @ X5)))))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER))<=(dpsetconstrEL2))<=(dpsetconstrEL1))))))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin)))))))<=(upairequniteq))<=(setukpairinjR1)))))))<=(kfstpairEq))<=(theprop)))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2))))<=(singletonprop)))))<=(setunionE2)))<=(cartprodmempair1)))<=(ubforcartprodlem3)))))))))))<=(kpairiskpair))))<=(secondinupair)))<=(symdiffIneg1))<=(symdiffI2))))))<=(setminusIRneg)))<=(setminusELneg))<=(setminusERneg)))<=(setminusER))<=(setminusEL))))<=(binintersectSubset1))))<=(disjointsetsI1))))))<=(binintersectEL)))))))<=(binunionEcases))<=(binunionIR))))<=(sepSubset))))<=(inPowerset))<=(powersetE1)))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset))))<=(subsetTrans))<=(subsetRefl))<=(notequalI2))<=(notequalI1))<=(notsubsetI))<=(subsetE2))<=(subsetE)))<=(subsetI2)))<=(eqimpsubset2))<=(subsetI1)))<=(descr__Cong))<=(exuEu))<=(omega__Cong))))<=(setadjoin__Cong))<=(emptyset__Cong)))<=(exuE3u))<=(in__Cong))<=(inCongP))<=(exuI2)))))<=(notdexE))<=(prop2set2propI)))))<=(quantDeMorgan2)))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch)))))<=(nonemptyImpWitness)))<=(subPowSU)))))<=(emptyInPowerset)))<=(powersetI))))))))<=(nonemptyI1))<=(nonemptyI))))<=(noeltsimpempty))))<=(exuE3e)))<=(emptysetimpfalse))))<=(exuE1))<=(dsetconstrER)))<=(dsetconstrI))))))<=(omegaIndAx)))<=(omega0Ax))<=(setunionAx))<=(powersetAx)))<=(emptysetAx))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', infuncsetfunc)).
124.91/18.53	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', sepSubset)).
124.91/18.53	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', descr__Cong)).
124.91/18.53	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', exuEu)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', exuE2)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', exuE3u)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', exuI1)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', exuI2)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', emptyE1)).
124.91/18.53	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', exuI3)).
124.91/18.53	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', nonemptyI)).
124.91/18.53	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', exuE3e)).
124.91/18.53	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', exuE1)).
124.91/18.53	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', dsetconstrER)).
124.91/18.53	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', dsetconstrI)).
124.91/18.53	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', dsetconstr__Cong)).
124.91/18.53	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', exu__Cong)).
124.91/18.53	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', sepInPowerset)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', kfstsingleton)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', ex1I)).
124.91/18.53	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', ex1E1)).
124.91/18.53	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', dpsetconstrI)).
124.91/18.53	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', ksndsingleton)).
124.91/18.53	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', dpsetconstrSub)).
124.91/18.53	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', dpsetconstrEL2)).
124.91/18.53	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', dpsetconstrER)).
124.91/18.53	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', funcImageSingleton)).
124.91/18.53	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', apProp)).
124.91/18.53	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', dpsetconstrERa)).
124.91/18.53	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setOfPairsIsBReln)).
124.91/18.53	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', dpsetconstrEL1)).
124.91/18.53	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', singletonprop)).
124.91/18.53	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', ex1I2)).
124.91/18.53	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setoftrueEq)).
124.91/18.53	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setbeta)).
124.91/18.53	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', dsetconstrEL)).
124.91/18.53	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', descrp)).
124.91/18.53	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', replAx)).
124.91/18.53	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', notdallE)).
124.91/18.53	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', subset2powerset)).
124.91/18.53	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', subsetemptysetimpeq)).
124.91/18.53	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', inPowerset)).
124.91/18.53	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', powersetE1)).
124.91/18.53	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setextsub)).
124.91/18.53	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', subsetTrans)).
124.91/18.53	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', subsetRefl)).
124.91/18.53	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', notinsingleton)).
124.91/18.53	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', notequalI2)).
124.91/18.53	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', uniqinunit)).
124.91/18.53	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', notequalI1)).
124.91/18.53	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', eqinunit)).
124.91/18.53	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', notsubsetI)).
124.91/18.53	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', subsetE2)).
124.91/18.53	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', subsetE)).
124.91/18.53	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', subsetI2)).
124.91/18.53	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', eqimpsubset2)).
124.91/18.53	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', subsetI1)).
124.91/18.53	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', omega__Cong)).
124.91/18.53	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setadjoin__Cong)).
124.91/18.53	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', emptyset__Cong)).
124.91/18.53	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', in__Cong)).
124.91/18.53	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', inCongP)).
124.91/18.53	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binunionE)).
124.91/18.53	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', upairset2IR)).
124.91/18.53	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', notdexE)).
124.91/18.53	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', prop2setI)).
124.91/18.53	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', quantDeMorgan2)).
124.91/18.53	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', quantDeMorgan4)).
124.91/18.53	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', vacuousDall)).
124.91/18.53	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', quantDeMorgan3)).
124.91/18.53	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', upairsetIR)).
124.91/18.53	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', quantDeMorgan1)).
124.91/18.53	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', upairsetIL)).
124.91/18.53	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', upairsetE)).
124.91/18.53	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', singletonsswitch)).
124.91/18.53	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', nonemptyImpWitness)).
124.91/18.53	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', subPowSU)).
124.91/18.53	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', emptyInPowerset)).
124.91/18.53	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', powersetI)).
124.91/18.53	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', nonemptyI1)).
124.91/18.53	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', noeltsimpempty)).
124.91/18.53	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', emptysetimpfalse)).
124.91/18.53	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setadjoinSub)).
124.91/18.53	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.laYLe1vXiE/E---3.1_3989.p', omegaIndAx)).
124.91/18.53	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', emptysetsubset)).
124.91/18.53	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', omega0Ax)).
124.91/18.53	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', eqimpsubset1)).
124.91/18.53	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setunionAx)).
124.91/18.53	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', powersetAx)).
124.91/18.53	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setunion__Cong)).
124.91/18.53	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', emptysetAx)).
124.91/18.53	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', powerset__Cong)).
124.91/18.53	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setadjoinSub2)).
124.91/18.53	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binunionLsub)).
124.91/18.53	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setunionsingleton1)).
124.91/18.53	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', cartprodmempair)).
124.91/18.53	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', cartprodpairin)).
124.91/18.53	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', ubforcartprodlem2)).
124.91/18.53	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', ubforcartprodlem1)).
124.91/18.53	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', upairinpowunion)).
124.91/18.53	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binunionIL)).
124.91/18.53	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', powersetsubset)).
124.91/18.53	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', powersetI1)).
124.91/18.53	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binunionRsub)).
124.91/18.53	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binintersectRsub)).
124.91/18.53	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binintersectER)).
124.91/18.53	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binintersectSubset3)).
124.91/18.53	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binintersectSubset2)).
124.91/18.53	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binintersectLsub)).
124.91/18.53	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binintersectSubset5)).
124.91/18.53	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binintersectI)).
124.91/18.53	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binintersectSubset4)).
124.91/18.53	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', symdiffE)).
124.91/18.53	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setminusSubset1)).
124.91/18.53	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setminusLsub)).
124.91/18.53	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setminusILneg)).
124.91/18.53	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setminusSubset2)).
124.91/18.53	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setminusI)).
124.91/18.53	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', bs114d)).
124.91/18.53	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', symdiffI1)).
124.91/18.53	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', singletoninpowunion)).
124.91/18.53	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', singletoninpowerset)).
124.91/18.53	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', singletonsubset)).
124.91/18.53	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', kpairp)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', setukpairIR)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', setukpairIL)).
124.91/18.53	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', symdiffIneg2)).
124.91/18.53	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', upairset2E)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', upairsubunion)).
124.91/18.53	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setunionsingleton2)).
124.91/18.53	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setukpairinjL)).
124.91/18.53	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setukpairinjL2)).
124.91/18.53	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', cartprodfstin)).
124.91/18.53	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setunionsingleton)).
124.91/18.53	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setukpairinjR11)).
124.91/18.53	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', kpairsurjEq)).
124.91/18.53	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', ksndpairEq)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', setukpairinjR)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', setukpairinjR2)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', setukpairinjR12)).
124.91/18.53	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', app)).
124.91/18.53	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', cartprodsndin)).
124.91/18.53	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', cartprodpairmemEL)).
124.91/18.53	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', cartprodpairmemER)).
124.91/18.53	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', cartprodmempaircEq)).
124.91/18.53	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', cartprodfstpairEq)).
124.91/18.53	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', cartprodsndpairEq)).
124.91/18.53	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', cartprodpairsurjEq)).
124.91/18.53	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', upairequniteq)).
124.91/18.53	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', singletonsuniq)).
124.91/18.53	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.laYLe1vXiE/E---3.1_3989.p', setukpairinjL1)).
124.91/18.53	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', theprop)).
124.91/18.53	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', kfstpairEq)).
124.91/18.53	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setukpairinjR1)).
124.91/18.53	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setunionE2)).
124.91/18.53	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setminusIRneg)).
124.91/18.53	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', symdiffI2)).
124.91/18.53	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', symdiffIneg1)).
124.91/18.53	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', secondinupair)).
124.91/18.53	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', kpairiskpair)).
124.91/18.53	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', ubforcartprodlem3)).
124.91/18.53	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.laYLe1vXiE/E---3.1_3989.p', cartprodmempair1)).
124.91/18.53	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setminusELneg)).
124.91/18.53	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binunionEcases)).
124.91/18.53	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binintersectEL)).
124.91/18.53	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', disjointsetsI1)).
124.91/18.53	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binintersectSubset1)).
124.91/18.53	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setminusEL)).
124.91/18.53	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setminusER)).
124.91/18.53	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setminusERneg)).
124.91/18.53	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', binunionIR)).
124.91/18.53	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setunionE)).
124.91/18.53	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setunionI)).
124.91/18.53	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', powersetE)).
124.91/18.53	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', emptyinPowerset)).
124.91/18.53	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setadjoinOr)).
124.91/18.53	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setadjoinE)).
124.91/18.53	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setadjoinIR)).
124.91/18.53	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', emptyinunitempty)).
124.91/18.53	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setadjoinIL)).
124.91/18.53	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', nonemptyE1)).
124.91/18.53	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', emptyI)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', setext)).
124.91/18.53	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', notinemptyset)).
124.91/18.53	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', emptysetE)).
124.91/18.53	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', prop2setE)).
124.91/18.53	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.laYLe1vXiE/E---3.1_3989.p', wellorderingAx)).
124.91/18.53	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.laYLe1vXiE/E---3.1_3989.p', foundationAx)).
124.91/18.53	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', omegaSAx)).
124.91/18.53	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setadjoinAx)).
124.91/18.53	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', setextAx)).
124.91/18.53	thf(funcSet, axiom, ((funcSet)=(^[X4:$i, X5:$i]:(dsetconstr @ (powerset @ (cartprod @ X4 @ X5)) @ (^[X30:$i]:((func @ X4 @ X5 @ X30)))))), file('/export/starexec/sandbox2/tmp/tmp.laYLe1vXiE/E---3.1_3989.p', funcSet)).
124.91/18.53	thf(c_0_192, negated_conjecture, ~(((setextAx)=>(((setadjoinAx)=>(((((omegaSAx)=>(((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>(((dsetconstrEL)=>((((prop2setE)=>((emptysetE)=>(((notinemptyset)=>(((setext)=>((emptyI)=>(((setbeta)=>((nonemptyE1)=>((((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>(((emptyinPowerset)=>(((powersetE)=>((setunionI)=>((setunionE)=>(((exuE2)=>(((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((((((emptyE1)=>(((quantDeMorgan1)=>(((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((((notdallE)=>((exuI1)=>((exuI3)=>((((((exu__Cong)=>((((powerset__Cong)=>((setunion__Cong)=>(((((dsetconstr__Cong)=>((((eqimpsubset1)=>(((emptysetsubset)=>(((((((((setadjoinSub)=>((setadjoinSub2)=>(((((powersetI1)=>((((powersetsubset)=>((sepInPowerset)=>(((binunionIL)=>((upairset2IR)=>((((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>(((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>(((binintersectRsub)=>((binintersectSubset4)=>(((bs114d)=>((setminusI)=>((((setminusSubset2)=>((((setminusILneg)=>(((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((((symdiffIneg2)=>(((setukpairIL)=>((setukpairIR)=>(((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>(((cartprodpairin)=>(((cartprodmempair)=>(((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(((ex1E1)=>((ex1I)=>(((((kfstsingleton)=>((((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>(((((((((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>(((((((app)=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)<=(in @ X30 @ (funcSet @ X4 @ X5)))))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER))<=(dpsetconstrEL2))<=(dpsetconstrEL1))))))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin)))))))<=(upairequniteq))<=(setukpairinjR1)))))))<=(kfstpairEq))<=(theprop)))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2))))<=(singletonprop)))))<=(setunionE2)))<=(cartprodmempair1)))<=(ubforcartprodlem3)))))))))))<=(kpairiskpair))))<=(secondinupair)))<=(symdiffIneg1))<=(symdiffI2))))))<=(setminusIRneg)))<=(setminusELneg))<=(setminusERneg)))<=(setminusER))<=(setminusEL))))<=(binintersectSubset1))))<=(disjointsetsI1))))))<=(binintersectEL)))))))<=(binunionEcases))<=(binunionIR))))<=(sepSubset))))<=(inPowerset))<=(powersetE1)))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset))))<=(subsetTrans))<=(subsetRefl))<=(notequalI2))<=(notequalI1))<=(notsubsetI))<=(subsetE2))<=(subsetE)))<=(subsetI2)))<=(eqimpsubset2))<=(subsetI1)))<=(descr__Cong))<=(exuEu))<=(omega__Cong))))<=(setadjoin__Cong))<=(emptyset__Cong)))<=(exuE3u))<=(in__Cong))<=(inCongP))<=(exuI2)))))<=(notdexE))<=(prop2set2propI)))))<=(quantDeMorgan2)))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch)))))<=(nonemptyImpWitness)))<=(subPowSU)))))<=(emptyInPowerset)))<=(powersetI))))))))<=(nonemptyI1))<=(nonemptyI))))<=(noeltsimpempty))))<=(exuE3e)))<=(emptysetimpfalse))))<=(exuE1))<=(dsetconstrER)))<=(dsetconstrI))))))<=(omegaIndAx)))<=(omega0Ax))<=(setunionAx))<=(powersetAx)))<=(emptysetAx)))), inference(assume_negation,[status(cth)],[infuncsetfunc])).
124.91/18.53	thf(c_0_193, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
124.91/18.53	thf(c_0_194, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
124.91/18.53	thf(c_0_195, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
124.91/18.53	thf(c_0_196, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
124.91/18.53	thf(c_0_197, 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])).
124.91/18.53	thf(c_0_198, 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])).
124.91/18.53	thf(c_0_199, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
124.91/18.53	thf(c_0_200, 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])).
124.91/18.53	thf(c_0_201, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
124.91/18.53	thf(c_0_202, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
124.91/18.53	thf(c_0_203, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
124.91/18.53	thf(c_0_204, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
124.91/18.53	thf(c_0_205, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
124.91/18.53	thf(c_0_206, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
124.91/18.53	thf(c_0_207, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
124.91/18.53	thf(c_0_208, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
124.91/18.53	thf(c_0_209, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
124.91/18.53	thf(c_0_210, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
124.91/18.53	thf(c_0_211, 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])).
124.91/18.53	thf(c_0_212, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
124.91/18.53	thf(c_0_213, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
124.91/18.53	thf(c_0_214, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
124.91/18.53	thf(c_0_215, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
124.91/18.53	thf(c_0_216, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
124.91/18.53	thf(c_0_217, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
124.91/18.53	thf(c_0_218, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
124.91/18.53	thf(c_0_219, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
124.91/18.53	thf(c_0_220, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
124.91/18.53	thf(c_0_221, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
124.91/18.53	thf(c_0_222, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
124.91/18.53	thf(c_0_223, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
124.91/18.53	thf(c_0_224, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
124.91/18.53	thf(c_0_225, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
124.91/18.53	thf(c_0_226, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
124.91/18.53	thf(c_0_227, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
124.91/18.53	thf(c_0_228, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
124.91/18.53	thf(c_0_229, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
124.91/18.53	thf(c_0_230, plain, ((epred1_0)<=>![X591:$i]:(?[X592:$i]:((((![X593:$i]:(((in @ X593 @ X592)=>![X594:$i]:(((in @ X594 @ X593)=>(in @ X594 @ X591)))))&![X595:$i, X596:$i]:((((in @ X595 @ X591)&(in @ X596 @ X591))=>(![X597:$i]:(((in @ X597 @ X592)=>((in @ X595 @ X597)<=>(in @ X596 @ X597))))=>((X595)=(X596))))))&![X598:$i, X599:$i]:((((in @ X598 @ X592)&(in @ X599 @ X592))=>(![X600:$i]:(((in @ X600 @ X598)=>(in @ X600 @ X599)))|![X601:$i]:(((in @ X601 @ X599)=>(in @ X601 @ X598)))))))&![X602:$i]:(((![X603:$i]:(((in @ X603 @ X602)=>(in @ X603 @ X591)))&?[X604:$i]:((in @ X604 @ X602)))=>?[X605:$i, X606:$i]:(((((in @ X605 @ X592)&(in @ X606 @ X602))&~(?[X607:$i]:(((in @ X607 @ X605)&(in @ X607 @ X602)))))&![X608:$i]:(((in @ X608 @ X592)=>(![X609:$i]:(((in @ X609 @ X608)=>(in @ X609 @ X605)))|(in @ X606 @ X608)))))))))))), introduced(definition)).
124.91/18.53	thf(c_0_231, negated_conjecture, ~((![X574:$i, X575:$i]:((![X576:$i]:(((in @ X576 @ X574)<=>(in @ X576 @ X575)))=>((X574)=(X575))))=>(![X1113:$i]:(~(in @ X1113 @ emptyset))=>(![X577:$i, X578:$i, X579:$i]:(((in @ X579 @ (setadjoin @ X577 @ X578))<=>(((X579)=(X577))|(in @ X579 @ X578))))=>(![X1110:$i, X1111:$i]:(((in @ X1111 @ (powerset @ X1110))<=>![X1112:$i]:(((in @ X1112 @ X1111)=>(in @ X1112 @ X1110)))))=>(![X1107:$i, X1108:$i]:(((in @ X1108 @ (setunion @ X1107))<=>?[X1109:$i]:(((in @ X1108 @ X1109)&(in @ X1109 @ X1107)))))=>((in @ emptyset @ omega)=>(![X580:$i]:(((in @ X580 @ omega)=>(in @ (setadjoin @ X580 @ X580) @ omega)))=>(![X1104:$i]:((((in @ emptyset @ X1104)&![X1105:$i]:((((in @ X1105 @ omega)&(in @ X1105 @ X1104))=>(in @ (setadjoin @ X1105 @ X1105) @ X1104))))=>![X1106:$i]:(((in @ X1106 @ omega)=>(in @ X1106 @ X1104)))))=>(![X581:$i > $i > $o, X582:$i]:((![X583:$i]:(((in @ X583 @ X582)=>(exu @ (X581 @ X583))))=>?[X584:$i]:(![X585:$i]:(((in @ X585 @ X584)<=>?[X586:$i]:(((in @ X586 @ X582)&(X581 @ X586 @ X585))))))))=>(![X587:$i]:((?[X588:$i]:((in @ X588 @ X587))=>?[X589:$i]:(((in @ X589 @ X587)&~(?[X590:$i]:(((in @ X590 @ X589)&(in @ X590 @ X587))))))))=>((epred1_0)=>(![X610:$i > $o]:(((exu @ X610)=>(X610 @ (descr @ (^[Z0:$i]:(X610 @ Z0))))))=>(![X1101:$i, X1102:$i > $o, X1103:$i]:(((in @ X1103 @ X1101)=>((X1102 @ X1103)=>(in @ X1103 @ (dsetconstr @ X1101 @ X1102)))))=>(![X611:$i, X612:$i > $o, X613:$i]:(((in @ X613 @ (dsetconstr @ X611 @ X612))=>(in @ X613 @ X611)))=>(![X1098:$i, X1099:$i > $o, X1100:$i]:(((in @ X1100 @ (dsetconstr @ X1098 @ X1099))=>(X1099 @ X1100)))=>(![X1095:$i > $o]:(((exu @ X1095)=>?[X1096:$i]:(((X1095 @ X1096)&![X1097:$i]:(((X1095 @ X1097)=>((X1096)=(X1097))))))))=>(![X614:$o, X615:$i]:(((in @ X615 @ (prop2set @ ((X614))))=>(X614)))=>(![X616:$i]:(((in @ X616 @ emptyset)=>![X617:$o]:((X617))))=>(![X1094:$i]:(((in @ X1094 @ emptyset)=>~($true)))=>(![X618:$i]:(~(in @ X618 @ emptyset))=>(![X1092:$i > $o]:(((exu @ X1092)=>?[X1093:$i]:((X1092 @ X1093))))=>(![X619:$i, X620:$i]:((![X621:$i]:(((in @ X621 @ X619)=>(in @ X621 @ X620)))=>(![X622:$i]:(((in @ X622 @ X620)=>(in @ X622 @ X619)))=>((X619)=(X620)))))=>(![X623:$i]:((![X624:$i]:(~(in @ X624 @ X623))=>((X623)=(emptyset))))=>(![X1090:$i]:((![X1091:$i]:(~(in @ X1091 @ X1090))=>((X1090)=(emptyset))))=>(![X625:$i, X626:$i > $o, X627:$i]:(((in @ X627 @ X625)=>((in @ X627 @ (dsetconstr @ X625 @ X626))<=>(X626 @ X627))))=>(![X628:$i]:(((nonempty @ X628)=>?[X629:$i]:((in @ X629 @ X628))))=>(![X1087:$i, X1088:$i > $o, X1089:$i]:(((in @ X1089 @ X1087)=>((X1088 @ X1089)=>(nonempty @ (dsetconstr @ X1087 @ X1088)))))=>(![X1085:$i]:((?[X1086:$i]:((in @ X1086 @ X1085))=>(nonempty @ X1085)))=>(![X630:$i, X631:$i]:((in @ X630 @ (setadjoin @ X630 @ X631)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X632:$i, X633:$i, X634:$i]:(((in @ X634 @ X633)=>(in @ X634 @ (setadjoin @ X632 @ X633))))=>(![X635:$i, X636:$i, X637:$i]:(((in @ X637 @ (setadjoin @ X635 @ X636))=>![X638:$o]:(((((X637)=(X635))=>(X638))=>(((in @ X637 @ X636)=>(X638))=>(X638))))))=>(![X639:$i, X640:$i, X641:$i]:(((in @ X641 @ (setadjoin @ X639 @ X640))=>(((X641)=(X639))|(in @ X641 @ X640))))=>(![X642:$i]:(((dsetconstr @ X642 @ (^[Z0:$i]:($true)))=(X642)))=>(![X1082:$i, X1083:$i]:((![X1084:$i]:(((in @ X1084 @ X1083)=>(in @ X1084 @ X1082)))=>(in @ X1083 @ (powerset @ X1082))))=>(![X643:$i]:((in @ emptyset @ (powerset @ X643)))=>(![X1081:$i]:((in @ emptyset @ (powerset @ X1081)))=>(![X644:$i, X645:$i, X646:$i]:(((in @ X645 @ (powerset @ X644))=>((in @ X646 @ X645)=>(in @ X646 @ X644))))=>(![X647:$i, X648:$i, X649:$i]:(((in @ X648 @ X649)=>((in @ X649 @ X647)=>(in @ X648 @ (setunion @ X647)))))=>(![X650:$i, X651:$i]:(((in @ X651 @ (setunion @ X650))=>![X652:$o]:((![X653:$i]:(((in @ X651 @ X653)=>((in @ X653 @ X650)=>(X652))))=>(X652)))))=>(![X1079:$i, X1080:$i]:(((in @ X1080 @ X1079)=>(in @ X1080 @ (powerset @ (setunion @ X1079)))))=>(![X654:$i > $o]:(((exu @ X654)=>?[X655:$i]:(![X656:$i]:(((X654 @ X656)<=>((X656)=(X655)))))))=>(![X1077:$i]:(((nonempty @ X1077)=>?[X1078:$i]:(((in @ X1078 @ X1077)&$true))))=>(![X657:$i, X658:$i]:(((in @ X657 @ (setadjoin @ X658 @ emptyset))=>((X657)=(X658))))=>(![X659:$i, X660:$i]:((((X659)!=(X660))=>~(in @ X660 @ (setadjoin @ X659 @ emptyset))))=>(![X661:$i, X662:$i]:((((X661)=(X662))=>(in @ X661 @ (setadjoin @ X662 @ emptyset))))=>(![X1075:$i, X1076:$i]:(((in @ X1075 @ (setadjoin @ X1076 @ emptyset))=>(in @ X1076 @ (setadjoin @ X1075 @ emptyset))))=>(![X1072:$i, X1073:$i, X1074:$i]:(((in @ X1074 @ (setadjoin @ X1072 @ (setadjoin @ X1073 @ emptyset)))=>(((X1074)=(X1072))|((X1074)=(X1073)))))=>(![X1070:$i, X1071:$i]:((in @ X1070 @ (setadjoin @ X1070 @ (setadjoin @ X1071 @ emptyset))))=>(![X1068:$i, X1069:$i]:((in @ X1069 @ (setadjoin @ X1068 @ (setadjoin @ X1069 @ emptyset))))=>(![X663:$i, X664:$i > $o]:((?[X665:$i]:(((in @ X665 @ X663)&(X664 @ X665)))=>(((dsetconstr @ X663 @ X664)=(emptyset))=>~($true))))=>(![X1066:$i > $o, X1067:$i]:(((in @ X1067 @ emptyset)=>(X1066 @ X1067)))=>(![X666:$i, X667:$i > $o]:((~(![X668:$i]:(((in @ X668 @ X666)=>(X667 @ X668))))=>?[X669:$i]:(((in @ X669 @ X666)&~((X667 @ X669))))))=>(![X1062:$i, X1063:$i > $o]:((![X1064:$i]:(((in @ X1064 @ X1062)=>~((X1063 @ X1064))))=>~(?[X1065:$i]:(((in @ X1065 @ X1062)&(X1063 @ X1065))))))=>(![X670:$i, X671:$i > $o]:((~(?[X672:$i]:(((in @ X672 @ X670)&(X671 @ X672))))=>![X673:$i]:(((in @ X673 @ X670)=>~((X671 @ X673))))))=>(![X674:$i, X675:$i > $o]:((?[X676:$i]:(((in @ X676 @ X674)&~((X675 @ X676))))=>~(![X677:$i]:(((in @ X677 @ X674)=>(X675 @ X677))))))=>(![X678:$o]:(((X678)=>(in @ emptyset @ (prop2set @ ((X678))))))=>((prop2set2propI)=>(![X1058:$i, X1059:$i > $o]:((~(?[X1060:$i]:(((in @ X1060 @ X1058)&(X1059 @ X1060))))=>![X1061:$i]:(((in @ X1061 @ X1058)=>~((X1059 @ X1061))))))=>(![X679:$i, X680:$i > $o]:((~(![X681:$i]:(((in @ X681 @ X679)=>(X680 @ X681))))=>?[X682:$i]:(((in @ X682 @ X679)&~((X680 @ X682))))))=>(![X683:$i > $o]:((?[X684:$i]:(((X683 @ X684)&![X685:$i]:(((X683 @ X685)=>((X684)=(X685))))))=>(exu @ X683)))=>(![X686:$i > $o]:((?[X687:$i]:((X686 @ X687))=>(![X688:$i, X689:$i]:(((X686 @ X688)=>((X686 @ X689)=>((X688)=(X689)))))=>(exu @ X686))))=>(![X1055:$i > $o]:((?[X1056:$i]:(![X1057:$i]:(((X1055 @ X1057)<=>((X1057)=(X1056)))))=>(exu @ X1055)))=>(![X1051:$i, X1052:$i]:((((X1051)=(X1052))=>![X1053:$i, X1054:$i]:((((X1053)=(X1054))=>((in @ X1053 @ X1051)=>(in @ X1054 @ X1052))))))=>(![X1047:$i, X1048:$i]:((((X1047)=(X1048))=>![X1049:$i, X1050:$i]:((((X1049)=(X1050))=>((in @ X1049 @ X1047)<=>(in @ X1050 @ X1048))))))=>(![X1044:$i > $o]:(((exu @ X1044)=>![X1045:$i, X1046:$i]:(((X1044 @ X1045)=>((X1044 @ X1046)=>((X1045)=(X1046)))))))=>(![X690:$i > $o, X691:$i > $o]:((![X692:$i, X693:$i]:((((X692)=(X693))=>((X690 @ X692)<=>(X691 @ X693))))=>((exu @ X690)<=>(exu @ X691))))=>(((emptyset)=(emptyset))=>(![X1040:$i, X1041:$i]:((((X1040)=(X1041))=>![X1042:$i, X1043:$i]:((((X1042)=(X1043))=>((setadjoin @ X1040 @ X1042)=(setadjoin @ X1041 @ X1043))))))=>(![X694:$i, X695:$i]:((((X694)=(X695))=>((powerset @ X694)=(powerset @ X695))))=>(![X696:$i, X697:$i]:((((X696)=(X697))=>((setunion @ X696)=(setunion @ X697))))=>(((omega)=(omega))=>(![X1037:$i > $o]:(((exu @ X1037)=>![X1038:$i, X1039:$i]:(((X1037 @ X1038)=>((X1037 @ X1039)=>((X1038)=(X1039)))))))=>(![X1033:$i > $o, X1034:$i > $o]:((![X1035:$i, X1036:$i]:((((X1035)=(X1036))=>((X1033 @ X1035)<=>(X1034 @ X1036))))=>((exu @ X1033)=>((exu @ X1034)=>((descr @ X1033)=(descr @ X1034))))))=>(![X698:$i, X699:$i]:((((X698)=(X699))=>![X700:$i > $o, X701:$i > $o]:((![X702:$i]:(((in @ X702 @ X698)=>![X703:$i]:(((in @ X703 @ X699)=>(((X702)=(X703))=>((X700 @ X702)<=>(X701 @ X703)))))))=>((dsetconstr @ X698 @ X700)=(dsetconstr @ X699 @ X701))))))=>(![X1030:$i, X1031:$i]:((![X1032:$i]:(((in @ X1032 @ X1030)=>(in @ X1032 @ X1031)))=>(subset @ X1030 @ X1031)))=>(![X1028:$i, X1029:$i]:((((X1028)=(X1029))=>(subset @ X1029 @ X1028)))=>(![X704:$i, X705:$i]:((((X704)=(X705))=>(subset @ X704 @ X705)))=>(![X1025:$i, X1026:$i]:((![X1027:$i]:(((in @ X1027 @ X1025)=>(in @ X1027 @ X1026)))=>(subset @ X1025 @ X1026)))=>(![X706:$i]:((subset @ emptyset @ X706))=>(![X1022:$i, X1023:$i, X1024:$i]:(((subset @ X1022 @ X1023)=>((in @ X1024 @ X1022)=>(in @ X1024 @ X1023))))=>(![X1019:$i, X1020:$i, X1021:$i]:(((subset @ X1019 @ X1020)=>(~(in @ X1021 @ X1020)=>~(in @ X1021 @ X1019))))=>(![X1016:$i, X1017:$i, X1018:$i]:(((in @ X1018 @ X1016)=>(~(in @ X1018 @ X1017)=>~(subset @ X1016 @ X1017))))=>(![X1014:$i, X1015:$i]:((~(subset @ X1014 @ X1015)=>((X1014)!=(X1015))))=>(![X1011:$i, X1012:$i, X1013:$i]:(((in @ X1013 @ X1011)=>(~(in @ X1013 @ X1012)=>((X1011)!=(X1012)))))=>(![X1010:$i]:((subset @ X1010 @ X1010))=>(![X1007:$i, X1008:$i, X1009:$i]:(((subset @ X1007 @ X1008)=>((subset @ X1008 @ X1009)=>(subset @ X1007 @ X1009))))=>(![X707:$i, X708:$i]:((subset @ X708 @ (setadjoin @ X707 @ X708)))=>(![X709:$i, X710:$i, X711:$i]:(((subset @ X709 @ X711)=>(subset @ X709 @ (setadjoin @ X710 @ X711))))=>(![X1005:$i, X1006:$i]:(((subset @ X1005 @ X1006)=>(in @ X1005 @ (powerset @ X1006))))=>(![X1003:$i, X1004:$i]:(((subset @ X1003 @ X1004)=>((subset @ X1004 @ X1003)=>((X1003)=(X1004)))))=>(![X1002:$i]:(((subset @ X1002 @ emptyset)=>((X1002)=(emptyset))))=>(![X712:$i, X713:$i]:(((subset @ X713 @ X712)=>(in @ X713 @ (powerset @ X712))))=>(![X1000:$i, X1001:$i]:(((in @ X1001 @ (powerset @ X1000))=>(subset @ X1001 @ X1000)))=>(![X999:$i]:((in @ X999 @ (powerset @ X999)))=>(![X714:$i, X715:$i]:(((subset @ X714 @ X715)=>(subset @ (powerset @ X714) @ (powerset @ X715))))=>(![X716:$i, X717:$i > $o]:((in @ (dsetconstr @ X716 @ X717) @ (powerset @ X716)))=>(![X997:$i, X998:$i > $o]:((subset @ (dsetconstr @ X997 @ X998) @ X997))=>(![X718:$i, X719:$i, X720:$i]:(((in @ X720 @ X718)=>(in @ X720 @ (binunion @ X718 @ X719))))=>(![X721:$i, X722:$i]:((in @ X722 @ (setadjoin @ X721 @ (setadjoin @ X722 @ emptyset))))=>(![X994:$i, X995:$i, X996:$i]:(((in @ X996 @ X995)=>(in @ X996 @ (binunion @ X994 @ X995))))=>(![X990:$i, X991:$i, X992:$i, X993:$o]:(((in @ X992 @ (binunion @ X990 @ X991))=>(((in @ X992 @ X990)=>(X993))=>(((in @ X992 @ X991)=>(X993))=>(X993)))))=>(![X723:$i, X724:$i, X725:$i]:(((in @ X725 @ (binunion @ X723 @ X724))=>((in @ X725 @ X723)|(in @ X725 @ X724))))=>(![X726:$i, X727:$i]:((subset @ X726 @ (binunion @ X726 @ X727)))=>(![X728:$i, X729:$i]:((subset @ X729 @ (binunion @ X728 @ X729)))=>(![X730:$i, X731:$i, X732:$i]:(((in @ X732 @ X730)=>((in @ X732 @ X731)=>(in @ X732 @ (binintersect @ X730 @ X731)))))=>(![X733:$i, X734:$i, X735:$i]:(((subset @ X735 @ X733)=>((subset @ X735 @ X734)=>(subset @ X735 @ (binintersect @ X733 @ X734)))))=>(![X987:$i, X988:$i, X989:$i]:(((in @ X989 @ (binintersect @ X987 @ X988))=>(in @ X989 @ X987)))=>(![X736:$i, X737:$i]:((subset @ (binintersect @ X736 @ X737) @ X736))=>(![X738:$i, X739:$i]:(((subset @ X738 @ X739)=>((binintersect @ X738 @ X739)=(X738))))=>(![X740:$i, X741:$i]:((((binintersect @ X740 @ X741)=(X741))=>(subset @ X741 @ X740)))=>(![X742:$i, X743:$i, X744:$i]:(((in @ X744 @ (binintersect @ X742 @ X743))=>(in @ X744 @ X743)))=>(![X984:$i, X985:$i]:((~(?[X986:$i]:(((in @ X986 @ X984)&(in @ X986 @ X985))))=>((binintersect @ X984 @ X985)=(emptyset))))=>(![X745:$i, X746:$i]:((subset @ (binintersect @ X745 @ X746) @ X746))=>(![X747:$i, X748:$i]:(((subset @ X748 @ X747)=>((binintersect @ X747 @ X748)=(X748))))=>(![X982:$i, X983:$i]:((((binintersect @ X982 @ X983)=(X982))=>(subset @ X982 @ X983)))=>(![X749:$i, X750:$i, X751:$i]:(((binintersect @ X749 @ (binunion @ X750 @ X751))=(binunion @ (binintersect @ X749 @ X750) @ (binintersect @ X749 @ X751))))=>(![X752:$i, X753:$i, X754:$i]:(((in @ X754 @ X752)=>(~(in @ X754 @ X753)=>(in @ X754 @ (setminus @ X752 @ X753)))))=>(![X979:$i, X980:$i, X981:$i]:(((in @ X981 @ (setminus @ X979 @ X980))=>(in @ X981 @ X979)))=>(![X976:$i, X977:$i, X978:$i]:(((in @ X978 @ (setminus @ X976 @ X977))=>~(in @ X978 @ X977)))=>(![X755:$i, X756:$i]:(((subset @ X755 @ X756)=>((setminus @ X755 @ X756)=(emptyset))))=>(![X973:$i, X974:$i, X975:$i]:((~(in @ X975 @ (setminus @ X973 @ X974))=>((in @ X975 @ X973)=>(in @ X975 @ X974))))=>(![X970:$i, X971:$i, X972:$i]:((~(in @ X972 @ (setminus @ X970 @ X971))=>(~(in @ X972 @ X971)=>~(in @ X972 @ X970))))=>(![X757:$i, X758:$i, X759:$i]:((~(in @ X759 @ X757)=>~(in @ X759 @ (setminus @ X757 @ X758))))=>(![X967:$i, X968:$i, X969:$i]:(((in @ X969 @ X968)=>~(in @ X969 @ (setminus @ X967 @ X968))))=>(![X760:$i, X761:$i]:((subset @ (setminus @ X760 @ X761) @ X760))=>(![X762:$i, X763:$i]:((((setminus @ X762 @ X763)=(emptyset))=>(subset @ X762 @ X763)))=>(![X764:$i, X765:$i, X766:$i]:(((in @ X766 @ (symdiff @ X764 @ X765))=>![X767:$o]:((((in @ X766 @ X764)=>(~(in @ X766 @ X765)=>(X767)))=>((~(in @ X766 @ X764)=>((in @ X766 @ X765)=>(X767)))=>(X767))))))=>(![X768:$i, X769:$i, X770:$i]:(((in @ X770 @ 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,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_192, notdallE]), subset2powerset]), subsetemptysetimpeq]), inPowerset]), powersetE1]), setextsub]), c_0_193]), subsetTrans]), subsetRefl]), notinsingleton]), notequalI2]), uniqinunit]), notequalI1]), eqinunit]), notsubsetI]), subsetE2]), subsetE]), subsetI2]), eqimpsubset2]), subsetI1]), c_0_194]), c_0_195]), omega__Cong]), setadjoin__Cong]), c_0_196]), emptyset__Cong]), c_0_197]), in__Cong]), inCongP]), c_0_198]), c_0_199]), binunionE]), upairset2IR]), notdexE]), prop2setI]), quantDeMorgan2]), quantDeMorgan4]), vacuousDall]), quantDeMorgan3]), upairsetIR]), quantDeMorgan1]), upairsetIL]), c_0_200]), upairsetE]), c_0_201]), singletonsswitch]), nonemptyImpWitness]), subPowSU]), emptyInPowerset]), powersetI]), nonemptyI1]), c_0_202]), noeltsimpempty]), c_0_203]), emptysetimpfalse]), c_0_204]), c_0_205]), c_0_206]), setadjoinSub]), omegaIndAx]), emptysetsubset]), omega0Ax]), eqimpsubset1]), setunionAx]), c_0_207]), powersetAx]), setunion__Cong]), emptysetAx]), powerset__Cong]), c_0_208]), setadjoinSub2]), binunionLsub]), setunionsingleton1]), cartprodmempair]), cartprodpairin]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), binunionIL]), c_0_209]), powersetsubset]), powersetI1]), binunionRsub]), binintersectRsub]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectSubset5]), binintersectI]), binintersectSubset4]), symdiffE]), setminusSubset1]), setminusLsub]), setminusILneg]), setminusSubset2]), setminusI]), bs114d]), symdiffI1]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), setukpairIR]), setukpairIL]), symdiffIneg2]), upairset2E]), upairsubunion]), setunionsingleton2]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), c_0_210]), c_0_211]), c_0_212]), setunionsingleton]), setukpairinjR11]), c_0_213]), kpairsurjEq]), ksndpairEq]), c_0_214]), setukpairinjR]), setukpairinjR2]), setukpairinjR12]), c_0_215]), c_0_216]), c_0_217]), c_0_218]), c_0_219]), app]), c_0_220]), c_0_221]), c_0_222]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), upairequniteq]), c_0_223]), c_0_224]), singletonsuniq]), setukpairinjL1]), theprop]), kfstpairEq]), setukpairinjR1]), setunionE2]), setminusIRneg]), symdiffI2]), symdiffIneg1]), secondinupair]), kpairiskpair]), ubforcartprodlem3]), cartprodmempair1]), setminusELneg]), binunionEcases]), binintersectEL]), disjointsetsI1]), binintersectSubset1]), setminusEL]), setminusER]), setminusERneg]), binunionIR]), setunionE]), setunionI]), powersetE]), emptyinPowerset]), c_0_225]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyE1]), c_0_226]), emptyI]), setext]), notinemptyset]), emptysetE]), prop2setE]), c_0_227]), c_0_228]), wellorderingAx]), foundationAx]), c_0_229]), omegaSAx]), setadjoinAx]), setextAx])])]), c_0_230])).
124.91/18.53	thf(c_0_232, plain, ![X1114:$i, X1115:$i]:(((funcSet @ X1114 @ X1115)=(dsetconstr @ (powerset @ (cartprod @ X1114 @ X1115)) @ (^[Z0:$i]:((func @ X1114 @ X1115 @ Z0)))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[funcSet])])).
124.91/18.53	thf(c_0_233, negated_conjecture, ![X1116:$i, X1117:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1129:$i, X1130:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1138:$i, X1139:$i > $i > $o, X1140:$i, X1143:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1150:$i, X1151:$i > $o, X1152:$i, X1153:$i > $o, X1154:$i, X1155:$i, X1156:$i > $o, X1157:$i, X1158:$i, X1159:$i > $o, X1160:$i, X1161:$i > $o, X1163:$i, X1164:$o, X1165:$i, X1166:$i, X1167:$o, X1168:$i, X1169:$i, X1170:$i > $o, X1172:$i, X1173:$i, X1176:$i, X1178:$i, X1180:$i, X1181:$i > $o, X1182:$i, X1183:$i, X1185:$i, X1186:$i > $o, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$o, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$o, X1218:$i, X1219:$i, X1220:$i > $o, X1222:$i, X1223:$i, X1224:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i > $o, X1243:$i, X1244:$i > $o, X1245:$i, X1246:$i, X1247:$i > $o, X1248:$i, X1250:$i, X1251:$i > $o, X1253:$i, X1254:$i, X1255:$i > $o, X1257:$i, X1258:$i, X1259:$i > $o, X1260:$i, X1262:$o, X1263:$i, X1264:$i > $o, X1266:$i, X1267:$i, X1268:$i > $o, X1269:$i, X1271:$i > $o, X1272:$i, X1274:$i > $o, X1275:$i, X1278:$i > $o, X1279:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i > $o, X1290:$i, X1291:$i, X1292:$i > $o, X1293:$i > $o, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i > $o, X1305:$i, X1306:$i, X1307:$i > $o, X1308:$i > $o, X1311:$i, X1312:$i, X1313:$i > $o, X1314:$i > $o, X1317:$i, X1318:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i > $o, X1365:$i, X1366:$i > $o, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$o, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$o, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i > $o, X1521:$i, X1522:$i, X1523:$i > $o, X1525:$i, X1526:$i > $o, X1527:$i, X1529:$i, X1530:$i > $o, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i > $i > $o, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i > $i > $o, X1611:$i, X1612:$i, X1613:$i > $i > $o, X1614:$i, X1615:$i, X1616:$i > $i > $o, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i > $i > $o, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i > $i > $o, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i > $i > $o, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i]:((((~(in @ (esk1_2 @ X1116 @ X1117) @ X1116)|~(in @ (esk1_2 @ X1116 @ X1117) @ X1117)|((X1116)=(X1117)))&((in @ (esk1_2 @ X1116 @ X1117) @ X1116)|(in @ (esk1_2 @ X1116 @ X1117) @ X1117)|((X1116)=(X1117))))&(~(in @ X1119 @ emptyset)&(((~(in @ X1122 @ (setadjoin @ X1120 @ X1121))|(((X1122)=(X1120))|(in @ X1122 @ X1121)))&((((X1122)!=(X1120))|(in @ X1122 @ (setadjoin @ X1120 @ X1121)))&(~(in @ X1122 @ X1121)|(in @ X1122 @ (setadjoin @ X1120 @ X1121)))))&(((~(in @ X1124 @ (powerset @ X1123))|(~(in @ X1125 @ X1124)|(in @ X1125 @ X1123)))&(((in @ (esk2_2 @ X1126 @ X1127) @ X1127)|(in @ X1127 @ (powerset @ X1126)))&(~(in @ (esk2_2 @ X1126 @ X1127) @ X1126)|(in @ X1127 @ (powerset @ X1126)))))&(((((in @ X1130 @ (esk3_2 @ X1129 @ X1130))|~(in @ X1130 @ (setunion @ X1129)))&((in @ (esk3_2 @ X1129 @ X1130) @ X1129)|~(in @ X1130 @ (setunion @ X1129))))&(~(in @ X1133 @ X1134)|~(in @ X1134 @ X1132)|(in @ X1133 @ (setunion @ X1132))))&((in @ emptyset @ omega)&((~(in @ X1135 @ omega)|(in @ (setadjoin @ X1135 @ X1135) @ omega))&(((((in @ (esk4_1 @ X1136) @ omega)|~(in @ emptyset @ X1136)|(~(in @ X1138 @ omega)|(in @ X1138 @ X1136)))&((in @ (esk4_1 @ X1136) @ X1136)|~(in @ emptyset @ X1136)|(~(in @ X1138 @ omega)|(in @ X1138 @ X1136))))&(~(in @ (setadjoin @ (esk4_1 @ X1136) @ (esk4_1 @ X1136)) @ X1136)|~(in @ emptyset @ X1136)|(~(in @ X1138 @ omega)|(in @ X1138 @ X1136))))&((((((in @ (esk7_3 @ X1139 @ X1140 @ X1143) @ X1140)|~(in @ X1143 @ (esk6_2 @ X1139 @ X1140))|(in @ (esk5_2 @ X1139 @ X1140) @ X1140))&((X1139 @ (esk7_3 @ X1139 @ X1140 @ X1143) @ X1143)|~(in @ X1143 @ (esk6_2 @ X1139 @ X1140))|(in @ (esk5_2 @ X1139 @ X1140) @ X1140)))&(~(in @ X1146 @ X1140)|~(X1139 @ X1146 @ X1145)|(in @ X1145 @ (esk6_2 @ X1139 @ X1140))|(in @ (esk5_2 @ X1139 @ X1140) @ X1140)))&((((in @ (esk7_3 @ X1139 @ X1140 @ X1143) @ X1140)|~(in @ X1143 @ (esk6_2 @ X1139 @ X1140))|~(exu @ (X1139 @ (esk5_2 @ X1139 @ X1140))))&((X1139 @ (esk7_3 @ X1139 @ X1140 @ X1143) @ X1143)|~(in @ X1143 @ (esk6_2 @ X1139 @ X1140))|~(exu @ (X1139 @ (esk5_2 @ X1139 @ X1140)))))&(~(in @ X1146 @ X1140)|~(X1139 @ X1146 @ X1145)|(in @ X1145 @ (esk6_2 @ X1139 @ X1140))|~(exu @ (X1139 @ (esk5_2 @ X1139 @ X1140))))))&((((in @ (esk8_1 @ X1147) @ X1147)|~(in @ X1148 @ X1147))&(~(in @ X1150 @ (esk8_1 @ X1147))|~(in @ X1150 @ X1147)|~(in @ X1148 @ X1147)))&((epred1_0)&((~(exu @ X1151)|(X1151 @ (descr @ X1151)))&((~(in @ X1154 @ X1152)|(~(X1153 @ X1154)|(in @ X1154 @ (dsetconstr @ X1152 @ X1153))))&((~(in @ X1157 @ (dsetconstr @ X1155 @ X1156))|(in @ X1157 @ X1155))&((~(in @ X1160 @ (dsetconstr @ X1158 @ X1159))|(X1159 @ X1160))&((((X1161 @ (esk9_1 @ X1161))|~(exu @ X1161))&(~(X1161 @ X1163)|((esk9_1 @ X1161)=(X1163))|~(exu @ X1161)))&((~(in @ X1165 @ (prop2set @ ((X1164))))|(X1164))&((~(in @ X1166 @ emptyset)|(X1167))&((~(in @ X1168 @ emptyset)|~($true))&(~(in @ X1169 @ emptyset)&((~(exu @ X1170)|(X1170 @ (esk10_1 @ X1170)))&(((((in @ (esk12_2 @ X1172 @ X1173) @ X1173)|((X1172)=(X1173))|(in @ (esk11_2 @ X1172 @ X1173) @ X1172))&(~(in @ (esk12_2 @ X1172 @ X1173) @ X1172)|((X1172)=(X1173))|(in @ (esk11_2 @ X1172 @ X1173) @ X1172)))&(((in @ (esk12_2 @ X1172 @ X1173) @ X1173)|((X1172)=(X1173))|~(in @ (esk11_2 @ X1172 @ X1173) @ X1173))&(~(in @ (esk12_2 @ X1172 @ X1173) @ X1172)|((X1172)=(X1173))|~(in @ (esk11_2 @ X1172 @ X1173) @ X1173))))&(((in @ (esk13_1 @ X1176) @ X1176)|((X1176)=(emptyset)))&(((in @ (esk14_1 @ X1178) @ X1178)|((X1178)=(emptyset)))&(((~(in @ X1182 @ (dsetconstr @ X1180 @ X1181))|(X1181 @ X1182)|~(in @ X1182 @ X1180))&(~(X1181 @ X1182)|(in @ X1182 @ (dsetconstr @ X1180 @ X1181))|~(in @ X1182 @ X1180)))&((~(nonempty @ X1183)|(in @ (esk15_1 @ X1183) @ X1183))&((~(in @ X1187 @ X1185)|(~(X1186 @ X1187)|(nonempty @ (dsetconstr @ X1185 @ X1186))))&((~(in @ X1189 @ X1188)|(nonempty @ X1188))&((in @ X1190 @ (setadjoin @ X1190 @ X1191))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1194 @ X1193)|(in @ X1194 @ (setadjoin @ X1192 @ X1193)))&(((((in @ X1197 @ X1196)|(X1198)|((X1197)=(X1195))|~(in @ X1197 @ (setadjoin @ X1195 @ X1196)))&(~(X1198)|(X1198)|((X1197)=(X1195))|~(in @ X1197 @ (setadjoin @ X1195 @ X1196))))&(((in @ X1197 @ X1196)|(X1198)|~(X1198)|~(in @ X1197 @ (setadjoin @ X1195 @ X1196)))&(~(X1198)|(X1198)|~(X1198)|~(in @ X1197 @ (setadjoin @ X1195 @ X1196)))))&((~(in @ X1201 @ (setadjoin @ X1199 @ X1200))|(((X1201)=(X1199))|(in @ X1201 @ X1200)))&(((dsetconstr @ X1202 @ (^[Z0:$i]:($true)))=(X1202))&((((in @ (esk16_2 @ X1203 @ X1204) @ X1204)|(in @ X1204 @ (powerset @ X1203)))&(~(in @ (esk16_2 @ X1203 @ X1204) @ X1203)|(in @ X1204 @ (powerset @ X1203))))&((in @ emptyset @ (powerset @ X1206))&((in @ emptyset @ (powerset @ X1207))&((~(in @ X1209 @ (powerset @ X1208))|(~(in @ X1210 @ X1209)|(in @ X1210 @ X1208)))&((~(in @ X1212 @ X1213)|(~(in @ X1213 @ X1211)|(in @ X1212 @ (setunion @ X1211))))&((((in @ X1215 @ (esk17_3 @ X1214 @ X1215 @ X1216))|(X1216)|~(in @ X1215 @ (setunion @ X1214)))&(((in @ (esk17_3 @ X1214 @ X1215 @ X1216) @ X1214)|(X1216)|~(in @ X1215 @ (setunion @ X1214)))&(~(X1216)|(X1216)|~(in @ X1215 @ (setunion @ X1214)))))&((~(in @ X1219 @ X1218)|(in @ X1219 @ (powerset @ (setunion @ X1218))))&(((~(X1220 @ X1222)|((X1222)=(esk18_1 @ X1220))|~(exu @ X1220))&(((X1223)!=(esk18_1 @ X1220))|(X1220 @ X1223)|~(exu @ X1220)))&((((in @ (esk19_1 @ X1224) @ X1224)|~(nonempty @ X1224))&(($true)|~(nonempty @ X1224)))&((~(in @ X1226 @ (setadjoin @ X1227 @ emptyset))|((X1226)=(X1227)))&((((X1228)=(X1229))|~(in @ X1229 @ (setadjoin @ X1228 @ emptyset)))&((((X1230)!=(X1231))|(in @ X1230 @ (setadjoin @ X1231 @ emptyset)))&((~(in @ X1232 @ (setadjoin @ X1233 @ emptyset))|(in @ X1233 @ (setadjoin @ X1232 @ emptyset)))&((~(in @ X1236 @ (setadjoin @ X1234 @ (setadjoin @ X1235 @ emptyset)))|(((X1236)=(X1234))|((X1236)=(X1235))))&((in @ X1237 @ (setadjoin @ X1237 @ (setadjoin @ X1238 @ 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X1523)))&((((in @ (esk45_3 @ X1525 @ X1526 @ X1527) @ X1525)|(ex1 @ X1525 @ X1526)|~(X1526 @ X1527)|~(in @ X1527 @ X1525))&(((X1526 @ (esk45_3 @ X1525 @ X1526 @ X1527))|(ex1 @ X1525 @ X1526)|~(X1526 @ X1527)|~(in @ X1527 @ X1525))&(((esk45_3 @ X1525 @ X1526 @ X1527)!=(X1527))|(ex1 @ X1525 @ X1526)|~(X1526 @ X1527)|~(in @ X1527 @ X1525))))&((((in @ (esk46_2 @ X1529 @ X1530) @ X1529)|(~(in @ X1533 @ X1529)|~(X1530 @ X1533)|(ex1 @ X1529 @ X1530)))&(((in @ (esk47_2 @ X1529 @ X1530) @ X1529)|(~(in @ X1533 @ X1529)|~(X1530 @ X1533)|(ex1 @ X1529 @ X1530)))&(((X1530 @ (esk46_2 @ X1529 @ X1530))|(~(in @ X1533 @ X1529)|~(X1530 @ X1533)|(ex1 @ X1529 @ X1530)))&(((X1530 @ (esk47_2 @ X1529 @ X1530))|(~(in @ X1533 @ X1529)|~(X1530 @ X1533)|(ex1 @ X1529 @ X1530)))&(((esk46_2 @ X1529 @ X1530)!=(esk47_2 @ X1529 @ X1530))|(~(in @ X1533 @ X1529)|~(X1530 @ X1533)|(ex1 @ X1529 @ X1530)))))))&((((setadjoin @ X1534 @ emptyset)!=(setadjoin @ X1535 @ emptyset))|((X1534)=(X1535)))&((~(in @ (setadjoin @ X1538 @ emptyset) @ (setadjoin @ (setadjoin @ X1536 @ emptyset) @ (setadjoin @ (setadjoin @ X1536 @ (setadjoin @ X1537 @ emptyset)) @ emptyset)))|((X1536)=(X1538)))&((~(iskpair @ X1539)|(singleton @ (dsetconstr @ (setunion @ X1539) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1539))))))&((~(singleton @ X1540)|(in @ (setunion @ X1540) @ X1540))&(((kfst @ (kpair @ X1541 @ X1542))=(X1541))&((~(in @ X1545 @ (cartprod @ X1543 @ X1544))|(in @ (kfst @ X1545) @ X1543))&((((setadjoin @ (setadjoin @ X1546 @ emptyset) @ (setadjoin @ (setadjoin @ X1546 @ (setadjoin @ X1547 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1548 @ emptyset) @ (setadjoin @ (setadjoin @ X1548 @ (setadjoin @ X1549 @ emptyset)) @ emptyset)))|((X1546)=(X1548)))&((((kpair @ X1550 @ X1551)!=(kpair @ X1552 @ X1553))|((X1550)=(X1552)))&((((X1554)!=(X1555))|((setadjoin @ X1554 @ (setadjoin @ X1555 @ emptyset))=(setadjoin @ X1554 @ emptyset)))&((((X1556)!=(X1557))|((setadjoin @ (setadjoin @ X1556 @ emptyset) @ (setadjoin @ (setadjoin @ X1556 @ (setadjoin @ X1557 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1556 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1558 @ emptyset) @ (setadjoin @ (setadjoin @ X1558 @ (setadjoin @ X1559 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1560 @ emptyset) @ (setadjoin @ (setadjoin @ X1560 @ (setadjoin @ X1561 @ emptyset)) @ emptyset)))|(((X1560)!=(X1561))|((X1559)=(X1561))))&((((setadjoin @ X1562 @ (setadjoin @ X1563 @ emptyset))!=(setadjoin @ X1564 @ emptyset))|((X1562)=(X1563)))&((((setadjoin @ (setadjoin @ X1565 @ emptyset) @ (setadjoin @ (setadjoin @ X1565 @ (setadjoin @ X1566 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1567 @ emptyset) @ (setadjoin @ (setadjoin @ X1567 @ (setadjoin @ X1568 @ emptyset)) @ emptyset)))|((X1566)=(X1568)))&((((kpair @ X1569 @ X1570)!=(kpair @ X1571 @ X1572))|((X1570)=(X1572)))&((~(iskpair @ X1573)|(singleton @ (dsetconstr @ (setunion @ X1573) @ (^[Z0:$i]:(((X1573)=(kpair @ (kfst @ X1573) @ Z0)))))))&(((ksnd @ (kpair @ X1574 @ X1575))=(X1575))&((~(iskpair @ X1576)|((kpair @ (kfst @ X1576) @ (ksnd @ X1576))=(X1576)))&((~(in @ X1579 @ (cartprod @ X1577 @ X1578))|(in @ (ksnd @ X1579) @ X1578))&((~(in @ (kpair @ X1582 @ X1583) @ (cartprod @ X1580 @ X1581))|(in @ X1582 @ X1580))&((~(in @ (kpair @ X1586 @ X1587) @ (cartprod @ X1584 @ X1585))|(in @ X1587 @ X1585))&((~(in @ X1590 @ X1588)|(~(in @ X1591 @ X1589)|((kpair @ X1590 @ X1591)=(kpair @ X1590 @ X1591))))&((~(in @ X1594 @ X1592)|(~(in @ X1595 @ X1593)|((kfst @ (kpair @ X1594 @ X1595))=(X1594))))&((~(in @ X1598 @ X1596)|(~(in @ X1599 @ X1597)|((ksnd @ (kpair @ X1598 @ X1599))=(X1599))))&((~(in @ X1602 @ (cartprod @ X1600 @ X1601))|((kpair @ (kfst @ X1602) @ (ksnd @ X1602))=(X1602)))&((~(in @ X1606 @ X1603)|(~(in @ X1607 @ X1604)|(~(X1605 @ X1606 @ X1607)|(in @ (kpair @ X1606 @ X1607) @ (dpsetconstr @ X1603 @ X1604 @ X1605)))))&((subset @ (dpsetconstr @ X1608 @ X1609 @ X1610) @ (cartprod @ X1608 @ X1609))&((breln @ X1611 @ X1612 @ (dpsetconstr @ X1611 @ X1612 @ X1613))&((~(in @ X1617 @ X1614)|(~(in @ X1618 @ X1615)|(~(in @ (kpair @ X1617 @ X1618) @ (dpsetconstr @ X1614 @ X1615 @ X1616))|(X1616 @ X1617 @ X1618))))&((~(in @ (kpair @ X1622 @ X1623) @ (dpsetconstr @ X1619 @ X1620 @ X1621))|(in @ X1622 @ X1619))&((~(in @ (kpair @ X1627 @ X1628) @ (dpsetconstr @ X1624 @ X1625 @ X1626))|(in @ X1628 @ X1625))&((~(in @ (kpair @ X1632 @ X1633) @ (dpsetconstr @ X1629 @ X1630 @ X1631))|(X1631 @ X1632 @ X1633))&((~(func @ X1634 @ X1635 @ X1636)|(~(in @ X1637 @ X1634)|(singleton @ (dsetconstr @ X1635 @ (^[Z0:$i]:((in @ (kpair @ X1637 @ Z0) @ X1636)))))))&((~(func @ X1638 @ X1639 @ X1640)|(~(in @ X1641 @ X1638)|(in @ (setunion @ (dsetconstr @ X1639 @ (^[Z0:$i]:((in @ (kpair @ X1641 @ Z0) @ X1640))))) @ X1639)))&((~(func @ X1642 @ X1643 @ X1644)|(~(in @ X1645 @ X1642)|(in @ (ap @ X1642 @ X1643 @ X1644 @ X1645) @ X1643)))&((in @ esk50_0 @ (funcSet @ esk48_0 @ esk49_0))&~(func @ esk48_0 @ esk49_0 @ esk50_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_231])])])])])])])).
124.91/18.53	thf(c_0_234, plain, ![X1649:$i, X1650:$i]:(((funcSet @ X1649 @ X1650)=(dsetconstr @ (powerset @ (cartprod @ X1649 @ X1650)) @ (^[Z0:$i]:((func @ X1649 @ X1650 @ Z0)))))), inference(variable_rename,[status(thm)],[c_0_232])).
124.91/18.53	thf(c_0_235, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_233])).
124.91/18.53	thf(c_0_236, plain, ![X2:$i, X3:$i]:(((funcSet @ X2 @ X3)=(dsetconstr @ (powerset @ (cartprod @ X2 @ X3)) @ (func @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_234])).
124.91/18.53	thf(c_0_237, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((func @ X2 @ X3 @ X4)|~((in @ X4 @ (funcSet @ X2 @ X3))))), inference(spm,[status(thm)],[c_0_235, c_0_236])).
124.91/18.53	thf(c_0_238, negated_conjecture, (in @ esk50_0 @ (funcSet @ esk48_0 @ esk49_0)), inference(split_conjunct,[status(thm)],[c_0_233])).
124.91/18.53	thf(c_0_239, negated_conjecture, ~((func @ esk48_0 @ esk49_0 @ esk50_0)), inference(split_conjunct,[status(thm)],[c_0_233])).
124.91/18.53	thf(c_0_240, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_237, c_0_238]), c_0_239]), ['proof']).
124.91/18.53	% SZS output end CNFRefutation
124.91/18.53	% Parsed axioms                        : 427
124.91/18.53	% Removed by relevancy pruning/SinE    : 235
124.91/18.53	% Initial clauses                      : 293
124.91/18.53	% Removed in clause preprocessing      : 26
124.91/18.53	% Initial clauses in saturation        : 267
124.91/18.53	% Processed clauses                    : 1639
124.91/18.53	% ...of these trivial                  : 27
124.91/18.53	% ...subsumed                          : 517
124.91/18.53	% ...remaining for further processing  : 1095
124.91/18.53	% Other redundant clauses eliminated   : 69
124.91/18.53	% Clauses deleted for lack of memory   : 0
124.91/18.53	% Backward-subsumed                    : 21
124.91/18.53	% Backward-rewritten                   : 16
124.91/18.53	% Generated clauses                    : 26977
124.91/18.53	% ...of the previous two non-redundant : 26034
124.91/18.53	% ...aggressively subsumed             : 0
124.91/18.53	% Contextual simplify-reflections      : 0
124.91/18.53	% Paramodulations                      : 26889
124.91/18.53	% Factorizations                       : 2
124.91/18.53	% NegExts                              : 2
124.91/18.53	% Equation resolutions                 : 74
124.91/18.53	% Disequality decompositions           : 0
124.91/18.53	% Total rewrite steps                  : 1206
124.91/18.53	% ...of those cached                   : 1025
124.91/18.53	% Propositional unsat checks           : 0
124.91/18.53	%    Propositional check models        : 0
124.91/18.53	%    Propositional check unsatisfiable : 0
124.91/18.53	%    Propositional clauses             : 0
124.91/18.53	%    Propositional clauses after purity: 0
124.91/18.53	%    Propositional unsat core size     : 0
124.91/18.53	%    Propositional preprocessing time  : 0.000
124.91/18.53	%    Propositional encoding time       : 0.000
124.91/18.53	%    Propositional solver time         : 0.000
124.91/18.53	%    Success case prop preproc time    : 0.000
124.91/18.53	%    Success case prop encoding time   : 0.000
124.91/18.53	%    Success case prop solver time     : 0.000
124.91/18.53	% Current number of processed clauses  : 819
124.91/18.53	%    Positive orientable unit clauses  : 82
124.91/18.53	%    Positive unorientable unit clauses: 0
124.91/18.53	%    Negative unit clauses             : 21
124.91/18.53	%    Non-unit-clauses                  : 716
124.91/18.53	% Current number of unprocessed clauses: 24656
124.91/18.53	% ...number of literals in the above   : 78710
124.91/18.53	% Current number of archived formulas  : 0
124.91/18.53	% Current number of archived clauses   : 263
124.91/18.53	% Clause-clause subsumption calls (NU) : 50188
124.91/18.53	% Rec. Clause-clause subsumption calls : 39051
124.91/18.53	% Non-unit clause-clause subsumptions  : 291
124.91/18.53	% Unit Clause-clause subsumption calls : 1953
124.91/18.53	% Rewrite failures with RHS unbound    : 0
124.91/18.53	% BW rewrite match attempts            : 32
124.91/18.53	% BW rewrite match successes           : 13
124.91/18.53	% Condensation attempts                : 1639
124.91/18.53	% Condensation successes               : 15
124.91/18.53	% Termbank termtop insertions          : 443541
124.91/18.53	% Search garbage collected termcells   : 17070
124.91/18.53	
124.91/18.53	% -------------------------------------------------
124.91/18.53	% User time                : 17.202 s
124.91/18.53	% System time              : 0.583 s
124.91/18.53	% Total time               : 17.785 s
124.91/18.53	% Maximum resident set size: 7652 pages
124.91/18.53	
124.91/18.53	% -------------------------------------------------
124.91/18.53	% User time                : 17.218 s
124.91/18.53	% System time              : 0.596 s
124.91/18.53	% Total time               : 17.814 s
124.91/18.53	% Maximum resident set size: 5376 pages
124.91/18.53	% E exiting
124.91/18.53	EOF