0.06/0.21	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.21	% Command    : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM
0.10/0.42	% Computer : n010.cluster.edu
0.10/0.42	% Model    : x86_64 x86_64
0.10/0.42	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.42	% Memory   : 8042.1875MB
0.10/0.42	% OS       : Linux 3.10.0-693.el7.x86_64
0.10/0.42	% CPULimit   : 1920
0.10/0.42	% WCLimit    : 240
0.10/0.42	% DateTime   : Wed Jul 30 08:30:34 EDT 2025
0.10/0.43	% CPUTime    : 
0.26/0.65	Running higher-order theorem proving
0.26/0.69	Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p
69.60/16.34	# Version: 3.0.0-ho
69.60/16.34	# Preprocessing class: HSLMSLSSLLLCHFA.
69.60/16.34	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
69.60/16.34	# Starting ehoh_best5 with 240s (1) cores
69.60/16.34	# Starting almost_fo_3_lam with 240s (1) cores
69.60/16.34	# Starting new_bool_5 with 240s (1) cores
69.60/16.34	# Starting pre_casc_3 with 240s (1) cores
69.60/16.34	# Starting ho_unfolding_8 with 240s (1) cores
69.60/16.34	# Starting new_ho_10_cnf2 with 240s (1) cores
69.60/16.34	# Starting new_bool_3 with 240s (1) cores
69.60/16.34	# Starting new_ho_5 with 240s (1) cores
69.60/16.34	# new_bool_5 with pid 11716 completed with status 0
69.60/16.34	# Result found by new_bool_5
69.60/16.34	# Preprocessing class: HSLMSLSSLLLCHFA.
69.60/16.34	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
69.60/16.34	# Starting ehoh_best5 with 240s (1) cores
69.60/16.34	# Starting almost_fo_3_lam with 240s (1) cores
69.60/16.34	# Starting new_bool_5 with 240s (1) cores
69.60/16.34	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
69.60/16.34	# Search class: HGHSM-FSLM32-MHFMMSBN
69.60/16.34	# Scheduled 10 strats onto 1 cores with 240 seconds (240 total)
69.60/16.34	# Starting ho_unfolding_8 with 44s (1) cores
69.60/16.34	# ho_unfolding_8 with pid 11728 completed with status 0
69.60/16.34	# Result found by ho_unfolding_8
69.60/16.34	# Preprocessing class: HSLMSLSSLLLCHFA.
69.60/16.34	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
69.60/16.34	# Starting ehoh_best5 with 240s (1) cores
69.60/16.34	# Starting almost_fo_3_lam with 240s (1) cores
69.60/16.34	# Starting new_bool_5 with 240s (1) cores
69.60/16.34	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
69.60/16.34	# Search class: HGHSM-FSLM32-MHFMMSBN
69.60/16.34	# Scheduled 10 strats onto 1 cores with 240 seconds (240 total)
69.60/16.34	# Starting ho_unfolding_8 with 44s (1) cores
69.60/16.34	# Preprocessing time       : 0.042 s
69.60/16.34	# Presaturation interreduction done
69.60/16.34	
69.60/16.34	# Proof found!
69.60/16.34	# SZS status Theorem
69.60/16.34	# SZS output start CNFRefutation
69.60/16.34	thf(decl_23, type, in: $i > $i > $o).
69.60/16.34	thf(decl_24, type, exu: ($i > $o) > $o).
69.60/16.34	thf(decl_25, type, setextAx: $o).
69.60/16.34	thf(decl_26, type, emptyset: $i).
69.60/16.34	thf(decl_27, type, emptysetAx: $o).
69.60/16.34	thf(decl_28, type, setadjoin: $i > $i > $i).
69.60/16.34	thf(decl_29, type, setadjoinAx: $o).
69.60/16.34	thf(decl_30, type, powerset: $i > $i).
69.60/16.34	thf(decl_31, type, powersetAx: $o).
69.60/16.34	thf(decl_32, type, setunion: $i > $i).
69.60/16.34	thf(decl_33, type, setunionAx: $o).
69.60/16.34	thf(decl_34, type, omega: $i).
69.60/16.34	thf(decl_35, type, omega0Ax: $o).
69.60/16.34	thf(decl_36, type, omegaSAx: $o).
69.60/16.34	thf(decl_37, type, omegaIndAx: $o).
69.60/16.34	thf(decl_38, type, replAx: $o).
69.60/16.34	thf(decl_39, type, foundationAx: $o).
69.60/16.34	thf(decl_40, type, wellorderingAx: $o).
69.60/16.34	thf(decl_41, type, descr: ($i > $o) > $i).
69.60/16.34	thf(decl_42, type, descrp: $o).
69.60/16.34	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_44, type, dsetconstrI: $o).
69.60/16.34	thf(decl_45, type, dsetconstrEL: $o).
69.60/16.34	thf(decl_46, type, dsetconstrER: $o).
69.60/16.34	thf(decl_47, type, exuE1: $o).
69.60/16.34	thf(decl_48, type, prop2set: $o > $i).
69.60/16.34	thf(decl_49, type, prop2setE: $o).
69.60/16.34	thf(decl_50, type, emptysetE: $o).
69.60/16.34	thf(decl_51, type, emptysetimpfalse: $o).
69.60/16.34	thf(decl_52, type, notinemptyset: $o).
69.60/16.34	thf(decl_53, type, exuE3e: $o).
69.60/16.34	thf(decl_54, type, setext: $o).
69.60/16.34	thf(decl_55, type, emptyI: $o).
69.60/16.34	thf(decl_56, type, noeltsimpempty: $o).
69.60/16.34	thf(decl_57, type, setbeta: $o).
69.60/16.34	thf(decl_58, type, nonempty: $i > $o).
69.60/16.34	thf(decl_59, type, nonemptyE1: $o).
69.60/16.34	thf(decl_60, type, nonemptyI: $o).
69.60/16.34	thf(decl_61, type, nonemptyI1: $o).
69.60/16.34	thf(decl_62, type, setadjoinIL: $o).
69.60/16.34	thf(decl_63, type, emptyinunitempty: $o).
69.60/16.34	thf(decl_64, type, setadjoinIR: $o).
69.60/16.34	thf(decl_65, type, setadjoinE: $o).
69.60/16.34	thf(decl_66, type, setadjoinOr: $o).
69.60/16.34	thf(decl_67, type, setoftrueEq: $o).
69.60/16.34	thf(decl_68, type, powersetI: $o).
69.60/16.34	thf(decl_69, type, emptyinPowerset: $o).
69.60/16.34	thf(decl_70, type, emptyInPowerset: $o).
69.60/16.34	thf(decl_71, type, powersetE: $o).
69.60/16.34	thf(decl_72, type, setunionI: $o).
69.60/16.34	thf(decl_73, type, setunionE: $o).
69.60/16.34	thf(decl_74, type, subPowSU: $o).
69.60/16.34	thf(decl_75, type, exuE2: $o).
69.60/16.34	thf(decl_76, type, nonemptyImpWitness: $o).
69.60/16.34	thf(decl_77, type, uniqinunit: $o).
69.60/16.34	thf(decl_78, type, notinsingleton: $o).
69.60/16.34	thf(decl_79, type, eqinunit: $o).
69.60/16.34	thf(decl_80, type, singletonsswitch: $o).
69.60/16.34	thf(decl_81, type, upairsetE: $o).
69.60/16.34	thf(decl_82, type, upairsetIL: $o).
69.60/16.34	thf(decl_83, type, upairsetIR: $o).
69.60/16.34	thf(decl_84, type, emptyE1: $o).
69.60/16.34	thf(decl_85, type, vacuousDall: $o).
69.60/16.34	thf(decl_86, type, quantDeMorgan1: $o).
69.60/16.34	thf(decl_87, type, quantDeMorgan2: $o).
69.60/16.34	thf(decl_88, type, quantDeMorgan3: $o).
69.60/16.34	thf(decl_89, type, quantDeMorgan4: $o).
69.60/16.34	thf(decl_90, type, prop2setI: $o).
69.60/16.34	thf(decl_92, type, prop2set2propI: $o).
69.60/16.34	thf(decl_93, type, notdexE: $o).
69.60/16.34	thf(decl_94, type, notdallE: $o).
69.60/16.34	thf(decl_95, type, exuI1: $o).
69.60/16.34	thf(decl_96, type, exuI3: $o).
69.60/16.34	thf(decl_97, type, exuI2: $o).
69.60/16.34	thf(decl_98, type, inCongP: $o).
69.60/16.34	thf(decl_99, type, in__Cong: $o).
69.60/16.34	thf(decl_100, type, exuE3u: $o).
69.60/16.34	thf(decl_101, type, exu__Cong: $o).
69.60/16.34	thf(decl_102, type, emptyset__Cong: $o).
69.60/16.34	thf(decl_103, type, setadjoin__Cong: $o).
69.60/16.34	thf(decl_104, type, powerset__Cong: $o).
69.60/16.34	thf(decl_105, type, setunion__Cong: $o).
69.60/16.34	thf(decl_106, type, omega__Cong: $o).
69.60/16.34	thf(decl_107, type, exuEu: $o).
69.60/16.34	thf(decl_108, type, descr__Cong: $o).
69.60/16.34	thf(decl_109, type, dsetconstr__Cong: $o).
69.60/16.34	thf(decl_110, type, subset: $i > $i > $o).
69.60/16.34	thf(decl_113, type, subsetI1: $o).
69.60/16.34	thf(decl_114, type, eqimpsubset2: $o).
69.60/16.34	thf(decl_115, type, eqimpsubset1: $o).
69.60/16.34	thf(decl_116, type, subsetI2: $o).
69.60/16.34	thf(decl_117, type, emptysetsubset: $o).
69.60/16.34	thf(decl_118, type, subsetE: $o).
69.60/16.34	thf(decl_119, type, subsetE2: $o).
69.60/16.34	thf(decl_120, type, notsubsetI: $o).
69.60/16.34	thf(decl_121, type, notequalI1: $o).
69.60/16.34	thf(decl_122, type, notequalI2: $o).
69.60/16.34	thf(decl_123, type, subsetRefl: $o).
69.60/16.34	thf(decl_124, type, subsetTrans: $o).
69.60/16.34	thf(decl_125, type, setadjoinSub: $o).
69.60/16.34	thf(decl_126, type, setadjoinSub2: $o).
69.60/16.34	thf(decl_127, type, subset2powerset: $o).
69.60/16.34	thf(decl_128, type, setextsub: $o).
69.60/16.34	thf(decl_129, type, subsetemptysetimpeq: $o).
69.60/16.34	thf(decl_130, type, powersetI1: $o).
69.60/16.34	thf(decl_131, type, powersetE1: $o).
69.60/16.34	thf(decl_132, type, inPowerset: $o).
69.60/16.34	thf(decl_133, type, powersetsubset: $o).
69.60/16.34	thf(decl_134, type, sepInPowerset: $o).
69.60/16.34	thf(decl_135, type, sepSubset: $o).
69.60/16.34	thf(decl_136, type, binunion: $i > $i > $i).
69.60/16.34	thf(decl_137, type, binunionIL: $o).
69.60/16.34	thf(decl_138, type, upairset2IR: $o).
69.60/16.34	thf(decl_139, type, binunionIR: $o).
69.60/16.34	thf(decl_140, type, binunionEcases: $o).
69.60/16.34	thf(decl_141, type, binunionE: $o).
69.60/16.34	thf(decl_142, type, binunionLsub: $o).
69.60/16.34	thf(decl_143, type, binunionRsub: $o).
69.60/16.34	thf(decl_144, type, binintersect: $i > $i > $i).
69.60/16.34	thf(decl_145, type, binintersectI: $o).
69.60/16.34	thf(decl_146, type, binintersectSubset5: $o).
69.60/16.34	thf(decl_147, type, binintersectEL: $o).
69.60/16.34	thf(decl_148, type, binintersectLsub: $o).
69.60/16.34	thf(decl_149, type, binintersectSubset2: $o).
69.60/16.34	thf(decl_150, type, binintersectSubset3: $o).
69.60/16.34	thf(decl_151, type, binintersectER: $o).
69.60/16.34	thf(decl_152, type, disjointsetsI1: $o).
69.60/16.34	thf(decl_153, type, binintersectRsub: $o).
69.60/16.34	thf(decl_154, type, binintersectSubset4: $o).
69.60/16.34	thf(decl_155, type, binintersectSubset1: $o).
69.60/16.34	thf(decl_156, type, bs114d: $o).
69.60/16.34	thf(decl_158, type, setminus: $i > $i > $i).
69.60/16.34	thf(decl_159, type, setminusI: $o).
69.60/16.34	thf(decl_160, type, setminusEL: $o).
69.60/16.34	thf(decl_161, type, setminusER: $o).
69.60/16.34	thf(decl_162, type, setminusSubset2: $o).
69.60/16.34	thf(decl_163, type, setminusERneg: $o).
69.60/16.34	thf(decl_164, type, setminusELneg: $o).
69.60/16.34	thf(decl_165, type, setminusILneg: $o).
69.60/16.34	thf(decl_166, type, setminusIRneg: $o).
69.60/16.34	thf(decl_167, type, setminusLsub: $o).
69.60/16.34	thf(decl_168, type, setminusSubset1: $o).
69.60/16.34	thf(decl_169, type, symdiff: $i > $i > $i).
69.60/16.34	thf(decl_170, type, symdiffE: $o).
69.60/16.34	thf(decl_171, type, symdiffI1: $o).
69.60/16.34	thf(decl_172, type, symdiffI2: $o).
69.60/16.34	thf(decl_173, type, symdiffIneg1: $o).
69.60/16.34	thf(decl_174, type, symdiffIneg2: $o).
69.60/16.34	thf(decl_175, type, iskpair: $i > $o).
69.60/16.34	thf(decl_176, type, secondinupair: $o).
69.60/16.34	thf(decl_177, type, setukpairIL: $o).
69.60/16.34	thf(decl_178, type, setukpairIR: $o).
69.60/16.34	thf(decl_179, type, kpairiskpair: $o).
69.60/16.34	thf(decl_180, type, kpair: $i > $i > $i).
69.60/16.34	thf(decl_181, type, kpairp: $o).
69.60/16.34	thf(decl_182, type, cartprod: $i > $i > $i).
69.60/16.34	thf(decl_183, type, singletonsubset: $o).
69.60/16.34	thf(decl_184, type, singletoninpowerset: $o).
69.60/16.34	thf(decl_185, type, singletoninpowunion: $o).
69.60/16.34	thf(decl_186, type, upairset2E: $o).
69.60/16.34	thf(decl_187, type, upairsubunion: $o).
69.60/16.34	thf(decl_188, type, upairinpowunion: $o).
69.60/16.34	thf(decl_189, type, ubforcartprodlem1: $o).
69.60/16.34	thf(decl_190, type, ubforcartprodlem2: $o).
69.60/16.34	thf(decl_191, type, ubforcartprodlem3: $o).
69.60/16.34	thf(decl_192, type, cartprodpairin: $o).
69.60/16.34	thf(decl_193, type, cartprodmempair1: $o).
69.60/16.34	thf(decl_194, type, cartprodmempair: $o).
69.60/16.34	thf(decl_195, type, setunionE2: $o).
69.60/16.34	thf(decl_196, type, setunionsingleton1: $o).
69.60/16.34	thf(decl_197, type, setunionsingleton2: $o).
69.60/16.34	thf(decl_198, type, setunionsingleton: $o).
69.60/16.34	thf(decl_199, type, singleton: $i > $o).
69.60/16.34	thf(decl_200, type, singletonprop: $o).
69.60/16.34	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
69.60/16.34	thf(decl_202, type, ex1E1: $o).
69.60/16.34	thf(decl_203, type, ex1I: $o).
69.60/16.34	thf(decl_204, type, ex1I2: $o).
69.60/16.34	thf(decl_205, type, singletonsuniq: $o).
69.60/16.34	thf(decl_210, type, setukpairinjL1: $o).
69.60/16.34	thf(decl_211, type, kfstsingleton: $o).
69.60/16.34	thf(decl_212, type, theprop: $o).
69.60/16.34	thf(decl_213, type, kfst: $i > $i).
69.60/16.34	thf(decl_214, type, kfstpairEq: $o).
69.60/16.34	thf(decl_215, type, cartprodfstin: $o).
69.60/16.34	thf(decl_216, type, setukpairinjL2: $o).
69.60/16.34	thf(decl_217, type, setukpairinjL: $o).
69.60/16.34	thf(decl_218, type, setukpairinjR11: $o).
69.60/16.34	thf(decl_219, type, setukpairinjR12: $o).
69.60/16.34	thf(decl_220, type, setukpairinjR1: $o).
69.60/16.34	thf(decl_221, type, upairequniteq: $o).
69.60/16.34	thf(decl_222, type, setukpairinjR2: $o).
69.60/16.34	thf(decl_223, type, setukpairinjR: $o).
69.60/16.34	thf(decl_224, type, ksndsingleton: $o).
69.60/16.34	thf(decl_225, type, ksnd: $i > $i).
69.60/16.34	thf(decl_226, type, ksndpairEq: $o).
69.60/16.34	thf(decl_227, type, kpairsurjEq: $o).
69.60/16.34	thf(decl_228, type, cartprodsndin: $o).
69.60/16.34	thf(decl_229, type, cartprodpairmemEL: $o).
69.60/16.34	thf(decl_230, type, cartprodpairmemER: $o).
69.60/16.34	thf(decl_231, type, cartprodmempaircEq: $o).
69.60/16.34	thf(decl_232, type, cartprodfstpairEq: $o).
69.60/16.34	thf(decl_233, type, cartprodsndpairEq: $o).
69.60/16.34	thf(decl_234, type, cartprodpairsurjEq: $o).
69.60/16.34	thf(decl_235, type, breln: $i > $i > $i > $o).
69.60/16.34	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
69.60/16.34	thf(decl_237, type, dpsetconstrI: $o).
69.60/16.34	thf(decl_238, type, dpsetconstrSub: $o).
69.60/16.34	thf(decl_239, type, setOfPairsIsBReln: $o).
69.60/16.34	thf(decl_240, type, dpsetconstrERa: $o).
69.60/16.34	thf(decl_241, type, dpsetconstrEL1: $o).
69.60/16.34	thf(decl_242, type, dpsetconstrEL2: $o).
69.60/16.34	thf(decl_243, type, dpsetconstrER: $o).
69.60/16.34	thf(decl_244, type, func: $i > $i > $i > $o).
69.60/16.34	thf(decl_245, type, funcSet: $i > $i > $i).
69.60/16.34	thf(decl_246, type, funcImageSingleton: $o).
69.60/16.34	thf(decl_247, type, apProp: $o).
69.60/16.34	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
69.60/16.34	thf(decl_249, type, app: $o).
69.60/16.34	thf(decl_250, type, infuncsetfunc: $o).
69.60/16.34	thf(decl_251, type, ap2p: $o).
69.60/16.34	thf(decl_252, type, funcinfuncset: $o).
69.60/16.34	thf(decl_253, type, lamProp: $o).
69.60/16.34	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
69.60/16.34	thf(decl_255, type, lamp: $o).
69.60/16.34	thf(decl_256, type, lam2p: $o).
69.60/16.34	thf(decl_257, type, brelnall1: $o).
69.60/16.34	thf(decl_258, type, brelnall2: $o).
69.60/16.34	thf(decl_259, type, ex1E2: $o).
69.60/16.34	thf(decl_260, type, funcGraphProp1: $o).
69.60/16.34	thf(decl_261, type, funcGraphProp3: $o).
69.60/16.34	thf(decl_262, type, funcGraphProp2: $o).
69.60/16.34	thf(decl_263, type, funcextLem: $o).
69.60/16.34	thf(decl_264, type, funcGraphProp4: $o).
69.60/16.34	thf(decl_265, type, subbreln: $o).
69.60/16.34	thf(decl_266, type, eqbreln: $o).
69.60/16.34	thf(decl_267, type, funcext: $o).
69.60/16.34	thf(decl_268, type, funcext2: $o).
69.60/16.34	thf(decl_269, type, ap2apEq1: $o).
69.60/16.34	thf(decl_270, type, ap2apEq2: $o).
69.60/16.34	thf(decl_271, type, beta1: $o).
69.60/16.34	thf(decl_272, type, eta1: $o).
69.60/16.34	thf(decl_273, type, lam2lamEq: $o).
69.60/16.34	thf(decl_274, type, beta2: $o).
69.60/16.34	thf(decl_275, type, eta2: $o).
69.60/16.34	thf(decl_276, type, iffalseProp1: $o).
69.60/16.34	thf(decl_277, type, iffalseProp2: $o).
69.60/16.34	thf(decl_278, type, iftrueProp1: $o).
69.60/16.34	thf(decl_279, type, iftrueProp2: $o).
69.60/16.34	thf(decl_280, type, ifSingleton: $o).
69.60/16.34	thf(decl_281, type, if: $i > $o > $i > $i > $i).
69.60/16.34	thf(decl_282, type, ifp: $o).
69.60/16.34	thf(decl_283, type, theeq: $o).
69.60/16.34	thf(decl_284, type, iftrue: $o).
69.60/16.34	thf(decl_285, type, iffalse: $o).
69.60/16.34	thf(decl_286, type, iftrueorfalse: $o).
69.60/16.34	thf(decl_287, type, binintersectT_lem: $o).
69.60/16.34	thf(decl_288, type, binunionT_lem: $o).
69.60/16.34	thf(decl_289, type, powersetT_lem: $o).
69.60/16.34	thf(decl_290, type, setminusT_lem: $o).
69.60/16.34	thf(decl_291, type, complementT_lem: $o).
69.60/16.34	thf(decl_292, type, epred1_0: $o).
69.60/16.34	thf(decl_293, type, esk1_2: $i > $i > $i).
69.60/16.34	thf(decl_294, type, esk2_2: $i > $i > $i).
69.60/16.34	thf(decl_295, type, esk3_2: $i > $i > $i).
69.60/16.34	thf(decl_296, type, esk4_1: $i > $i).
69.60/16.34	thf(decl_297, type, esk5_2: ($i > $i > $o) > $i > $i).
69.60/16.34	thf(decl_298, type, esk6_2: ($i > $i > $o) > $i > $i).
69.60/16.34	thf(decl_299, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
69.60/16.34	thf(decl_300, type, esk8_1: $i > $i).
69.60/16.34	thf(decl_301, type, esk9_1: ($i > $o) > $i).
69.60/16.34	thf(decl_302, type, esk10_1: ($i > $o) > $i).
69.60/16.34	thf(decl_303, type, esk11_2: $i > $i > $i).
69.60/16.34	thf(decl_304, type, esk12_2: $i > $i > $i).
69.60/16.34	thf(decl_305, type, esk13_1: $i > $i).
69.60/16.34	thf(decl_306, type, esk14_1: $i > $i).
69.60/16.34	thf(decl_307, type, esk15_1: $i > $i).
69.60/16.34	thf(decl_308, type, esk16_2: $i > $i > $i).
69.60/16.34	thf(decl_309, type, esk17_3: $i > $i > $o > $i).
69.60/16.34	thf(decl_310, type, esk18_1: ($i > $o) > $i).
69.60/16.34	thf(decl_311, type, esk19_1: $i > $i).
69.60/16.34	thf(decl_312, type, esk20_2: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_313, type, esk21_2: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_314, type, esk22_2: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_315, type, esk23_2: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_316, type, esk24_2: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_317, type, esk25_2: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_318, type, esk26_2: ($i > $o) > $i > $i).
69.60/16.34	thf(decl_319, type, esk27_1: ($i > $o) > $i).
69.60/16.34	thf(decl_320, type, esk28_1: ($i > $o) > $i).
69.60/16.34	thf(decl_321, type, esk29_2: ($i > $o) > $i > $i).
69.60/16.34	thf(decl_322, type, esk30_2: ($i > $o) > ($i > $o) > $i).
69.60/16.34	thf(decl_323, type, esk31_2: ($i > $o) > ($i > $o) > $i).
69.60/16.34	thf(decl_324, type, esk32_2: ($i > $o) > ($i > $o) > $i).
69.60/16.34	thf(decl_325, type, esk33_2: ($i > $o) > ($i > $o) > $i).
69.60/16.34	thf(decl_326, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
69.60/16.34	thf(decl_327, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
69.60/16.34	thf(decl_328, type, esk36_2: $i > $i > $i).
69.60/16.34	thf(decl_329, type, esk37_2: $i > $i > $i).
69.60/16.34	thf(decl_330, type, esk38_2: $i > $i > $i).
69.60/16.34	thf(decl_331, type, esk39_3: $i > $i > $i > $i).
69.60/16.34	thf(decl_332, type, esk40_3: $i > $i > $i > $i).
69.60/16.34	thf(decl_333, type, esk41_2: $i > $i > $i).
69.60/16.34	thf(decl_334, type, esk42_2: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_335, type, esk43_2: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_336, type, esk44_2: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_337, type, esk45_3: $i > ($i > $o) > $i > $i).
69.60/16.34	thf(decl_338, type, esk46_2: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_339, type, esk47_2: $i > ($i > $o) > $i).
69.60/16.34	thf(decl_340, type, esk48_3: $i > $i > ($i > $i) > $i).
69.60/16.34	thf(decl_341, type, esk49_3: $i > $i > ($i > $i) > $i).
69.60/16.34	thf(decl_342, type, esk50_3: $i > $i > ($i > $i) > $i).
69.60/16.34	thf(decl_343, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
69.60/16.34	thf(decl_344, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
69.60/16.34	thf(decl_345, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
69.60/16.34	thf(decl_346, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
69.60/16.34	thf(decl_347, type, esk55_4: $i > $i > $i > $i > $i).
69.60/16.34	thf(decl_348, type, esk56_4: $i > $i > $i > $i > $i).
69.60/16.34	thf(decl_349, type, esk57_4: $i > $i > $i > $i > $i).
69.60/16.34	thf(decl_350, type, esk58_4: $i > $i > $i > $i > $i).
69.60/16.34	thf(decl_351, type, esk59_4: $i > $i > $i > $i > $i).
69.60/16.34	thf(decl_352, type, esk60_4: $i > $i > $i > $i > $i).
69.60/16.34	thf(decl_353, type, esk61_4: $i > $i > $i > $i > $i).
69.60/16.34	thf(decl_354, type, esk62_4: $i > $i > $i > $i > $i).
69.60/16.34	thf(decl_355, type, esk63_4: $i > $i > $i > $i > $i).
69.60/16.34	thf(decl_356, type, esk64_3: $i > $i > ($i > $i) > $i).
69.60/16.34	thf(decl_357, type, esk65_3: $i > $i > ($i > $i) > $i).
69.60/16.34	thf(decl_358, type, esk66_3: $i > $i > ($i > $i) > $i).
69.60/16.34	thf(decl_359, type, esk67_0: $i).
69.60/16.34	thf(decl_360, type, esk68_0: $i).
69.60/16.34	thf(decl_361, type, esk69_0: $i).
69.60/16.34	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', sepSubset)).
69.60/16.34	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', sepInPowerset)).
69.60/16.34	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', dsetconstr__Cong)).
69.60/16.34	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', descr__Cong)).
69.60/16.34	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', exuE3u)).
69.60/16.34	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', exuE2)).
69.60/16.34	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', nonemptyI)).
69.60/16.34	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setbeta)).
69.60/16.34	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', dsetconstrEL)).
69.60/16.34	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ex1I)).
69.60/16.34	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setOfPairsIsBReln)).
69.60/16.34	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', dpsetconstrEL2)).
69.60/16.34	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', dpsetconstrER)).
69.60/16.34	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', funcImageSingleton)).
69.60/16.34	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', lamProp)).
69.60/16.34	thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', beta1)).
69.60/16.34	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', iftrueProp1)).
69.60/16.34	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ifSingleton)).
69.60/16.34	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', iftrueProp2)).
69.60/16.34	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', iffalseProp2)).
69.60/16.34	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', iffalseProp1)).
69.60/16.34	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', eta2)).
69.60/16.34	thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', beta2)).
69.60/16.34	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', lam2lamEq)).
69.60/16.34	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', eta1)).
69.60/16.34	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ex1E2)).
69.60/16.34	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', lam2p)).
69.60/16.34	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', lamp)).
69.60/16.34	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', apProp)).
69.60/16.34	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', dpsetconstrEL1)).
69.60/16.34	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', dpsetconstrERa)).
69.60/16.34	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', dpsetconstrSub)).
69.60/16.34	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', dpsetconstrI)).
69.60/16.34	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ksndsingleton)).
69.60/16.34	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', kfstsingleton)).
69.60/16.34	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ex1I2)).
69.60/16.34	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ex1E1)).
69.60/16.34	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', singletonprop)).
69.60/16.34	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', exuEu)).
69.60/16.34	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', exu__Cong)).
69.60/16.34	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', exuI2)).
69.60/16.34	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', exuI3)).
69.60/16.34	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', exuI1)).
69.60/16.34	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', emptyE1)).
69.60/16.34	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setoftrueEq)).
69.60/16.34	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', exuE3e)).
69.60/16.34	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', exuE1)).
69.60/16.34	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', dsetconstrER)).
69.60/16.34	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', dsetconstrI)).
69.60/16.34	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', descrp)).
69.60/16.34	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', replAx)).
69.60/16.34	thf(setextT, conjecture, ((setextAx)=>(((setadjoinAx)=>((((omega0Ax)=>((omegaSAx)=>(((replAx)=>(((wellorderingAx)=>((descrp)=>((dsetconstrI)=>(((dsetconstrER)=>((exuE1)=>(((emptysetE)=>((((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>(((nonemptyE1)=>(((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>(((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>(((emptyInPowerset)=>((((setunionE)=>((((nonemptyImpWitness)=>((uniqinunit)=>(((((upairsetE)=>((upairsetIL)=>(((emptyE1)=>((vacuousDall)=>(((quantDeMorgan2)=>((((prop2setI)=>((prop2set2propI)=>((((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>(((((exuEu)=>((((((eqimpsubset1)=>((subsetI2)=>(((subsetE)=>((subsetE2)=>(((notequalI1)=>(((subsetRefl)=>((((setadjoinSub2)=>(((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>(((binunionIL)=>((((binunionEcases)=>((binunionE)=>((((((binintersectEL)=>((binintersectLsub)=>(((binintersectSubset3)=>((binintersectER)=>((((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>(((setminusER)=>((setminusSubset2)=>(((setminusELneg)=>((setminusILneg)=>(((((((symdiffI2)=>(((symdiffIneg2)=>((((setukpairIR)=>(((((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>(((((ubforcartprodlem2)=>((ubforcartprodlem3)=>(((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((((ex1I)=>(((((((kfstpairEq)=>((cartprodfstin)=>(((setukpairinjL)=>((setukpairinjR11)=>((((((setukpairinjR)=>(((ksndpairEq)=>(((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>(((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((((setOfPairsIsBReln)=>((((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>(((app)=>(((ap2p)=>((funcinfuncset)=>((lamProp)=>((((brelnall1)=>((brelnall2)=>(((funcGraphProp1)=>((((funcextLem)=>(((((funcext)=>(((((beta1)=>((((((((iftrueProp1)=>(((ifSingleton)=>((ifp)=>((((iffalse)=>(((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>(((complementT_lem)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)<=(in @ X2 @ X21))))=>(((X21)=(X48))<=![X2:$i]:((((in @ X2 @ X48)=>(in @ X2 @ X21))<=(in @ X2 @ X4)))))<=(in @ X48 @ (powerset @ X4)))))))<=(setminusT_lem)))))<=(iftrueorfalse)))<=(iftrue))<=(theeq))))<=(iftrueProp2)))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))<=(beta2))<=(lam2lamEq))<=(eta1)))<=(ap2apEq2))<=(ap2apEq1))<=(funcext2)))<=(eqbreln))<=(subbreln))<=(funcGraphProp4)))<=(funcGraphProp2))<=(funcGraphProp3)))<=(ex1E2))))<=(lam2p))<=(lamp)))))<=(infuncsetfunc)))<=(apProp)))))<=(dpsetconstrEL1))<=(dpsetconstrERa)))<=(dpsetconstrSub))<=(dpsetconstrI)))))<=(cartprodmempaircEq)))))<=(kpairsurjEq)))<=(ksndsingleton)))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1))<=(setukpairinjR12))))<=(setukpairinjL2))))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2)))<=(ex1E1))<=(singletonprop))))))))<=(cartprodpairin))))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion)))))<=(singletonsubset))<=(kpairp))<=(kpairiskpair)))<=(setukpairIL))<=(secondinupair)))<=(symdiffIneg1)))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1))<=(setminusLsub))<=(setminusIRneg))))<=(setminusERneg))))<=(setminusEL))))))<=(binintersectRsub))<=(disjointsetsI1))))<=(binintersectSubset2))))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))<=(binunionLsub))))<=(binunionIR))<=(upairset2IR)))<=(sepSubset)))))<=(powersetE1)))))<=(subset2powerset)))<=(setadjoinSub))<=(subsetTrans)))<=(notequalI2)))<=(notsubsetI))))<=(emptysetsubset))))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong))<=(powerset__Cong)))))<=(exuE3u)))))))<=(notdallE))<=(notdexE))))<=(quantDeMorgan4))<=(quantDeMorgan3)))<=(quantDeMorgan1))))<=(upairsetIR))))<=(singletonsswitch))<=(eqinunit))<=(notinsingleton))))<=(exuE2))<=(subPowSU)))<=(setunionI))<=(powersetE)))<=(emptyinPowerset)))))<=(setadjoinE))))))<=(nonemptyI)))<=(setbeta))))))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))))<=(dsetconstrEL)))))<=(foundationAx)))<=(omegaIndAx))))<=(setunionAx))<=(powersetAx)))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setextT)).
69.60/16.34	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binintersectEL)).
69.60/16.34	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', emptysetAx)).
69.60/16.34	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binunionLsub)).
69.60/16.34	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', subsetRefl)).
69.60/16.34	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binunionIR)).
69.60/16.34	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', powersetI1)).
69.60/16.34	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', upairset2IR)).
69.60/16.34	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', inPowerset)).
69.60/16.34	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', powersetE1)).
69.60/16.34	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', subset2powerset)).
69.60/16.34	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setadjoinSub)).
69.60/16.34	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', powersetsubset)).
69.60/16.34	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', subsetTrans)).
69.60/16.34	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', notequalI2)).
69.60/16.34	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', notsubsetI)).
69.60/16.34	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', emptysetsubset)).
69.60/16.34	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', eqimpsubset2)).
69.60/16.34	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binunionIL)).
69.60/16.34	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', subsetI1)).
69.60/16.34	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binunionEcases)).
69.60/16.34	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', omega__Cong)).
69.60/16.34	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setunion__Cong)).
69.60/16.34	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', powerset__Cong)).
69.60/16.34	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binunionE)).
69.60/16.34	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', notdallE)).
69.60/16.34	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', singletoninpowerset)).
69.60/16.34	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', notdexE)).
69.60/16.34	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', quantDeMorgan4)).
69.60/16.34	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setadjoinSub2)).
69.60/16.34	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', quantDeMorgan3)).
69.60/16.34	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', quantDeMorgan1)).
69.60/16.34	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binintersectLsub)).
69.60/16.34	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', upairsetIR)).
69.60/16.34	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', singletonsswitch)).
69.60/16.34	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setextsub)).
69.60/16.34	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', eqinunit)).
69.60/16.34	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binintersectSubset3)).
69.60/16.34	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', notinsingleton)).
69.60/16.34	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', subPowSU)).
69.60/16.34	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binintersectER)).
69.60/16.34	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setunionI)).
69.60/16.34	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', powersetE)).
69.60/16.34	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binintersectSubset4)).
69.60/16.34	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', emptyinPowerset)).
69.60/16.34	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setadjoinE)).
69.60/16.34	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binintersectSubset1)).
69.60/16.34	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', notinemptyset)).
69.60/16.34	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', bs114d)).
69.60/16.34	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', emptysetimpfalse)).
69.60/16.34	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', prop2setE)).
69.60/16.34	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setminusI)).
69.60/16.34	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', foundationAx)).
69.60/16.34	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', omegaIndAx)).
69.60/16.34	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setminusER)).
69.60/16.34	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setunionAx)).
69.60/16.34	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', powersetAx)).
69.60/16.34	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setminusSubset2)).
69.60/16.34	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setminusELneg)).
69.60/16.34	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setminusILneg)).
69.60/16.34	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', symdiffI2)).
69.60/16.34	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', symdiffIneg2)).
69.60/16.34	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setukpairIR)).
69.60/16.34	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', brelnall1)).
69.60/16.34	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', brelnall2)).
69.60/16.34	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', singletoninpowunion)).
69.60/16.34	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', upairset2E)).
69.60/16.34	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ubforcartprodlem2)).
69.60/16.34	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ubforcartprodlem3)).
69.60/16.34	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', cartprodmempair1)).
69.60/16.34	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', cartprodmempair)).
69.60/16.34	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setunionE2)).
69.60/16.34	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setunionsingleton1)).
69.60/16.34	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setunionsingleton2)).
69.60/16.34	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', subsetemptysetimpeq)).
69.60/16.34	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setunionsingleton)).
69.60/16.34	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', kfstpairEq)).
69.60/16.34	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', cartprodfstin)).
69.60/16.34	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setukpairinjL)).
69.60/16.34	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setukpairinjR11)).
69.60/16.34	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setukpairinjR)).
69.60/16.34	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ksndpairEq)).
69.60/16.34	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', cartprodsndin)).
69.60/16.34	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', cartprodpairmemEL)).
69.60/16.34	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', cartprodpairmemER)).
69.60/16.34	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', cartprodfstpairEq)).
69.60/16.34	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', cartprodsndpairEq)).
69.60/16.34	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', cartprodpairsurjEq)).
69.60/16.35	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', app)).
69.60/16.35	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ap2p)).
69.60/16.35	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', funcinfuncset)).
69.60/16.35	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', funcGraphProp1)).
69.60/16.35	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', funcextLem)).
69.60/16.35	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', funcext)).
69.60/16.35	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ifp)).
69.60/16.35	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', iffalse)).
69.60/16.35	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binintersectT_lem)).
69.60/16.35	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binunionT_lem)).
69.60/16.35	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', powersetT_lem)).
69.60/16.35	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', complementT_lem)).
69.60/16.35	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setminusT_lem)).
69.60/16.35	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', iftrueorfalse)).
69.60/16.35	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', iftrue)).
69.60/16.35	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', theeq)).
69.60/16.35	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ap2apEq2)).
69.60/16.35	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ap2apEq1)).
69.60/16.35	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', funcext2)).
69.60/16.35	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', eqbreln)).
69.60/16.35	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', subbreln)).
69.60/16.35	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', funcGraphProp4)).
69.60/16.35	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', funcGraphProp2)).
69.60/16.35	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', funcGraphProp3)).
69.60/16.35	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', infuncsetfunc)).
69.60/16.35	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', cartprodmempaircEq)).
69.60/16.35	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', kpairsurjEq)).
69.60/16.35	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setukpairinjR2)).
69.60/16.35	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', upairequniteq)).
69.60/16.35	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setukpairinjR1)).
69.60/16.35	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setukpairinjR12)).
69.60/16.35	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setukpairinjL2)).
69.60/16.35	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', theprop)).
69.60/16.35	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setukpairinjL1)).
69.60/16.35	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', singletonsuniq)).
69.60/16.35	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', cartprodpairin)).
69.60/16.35	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', ubforcartprodlem1)).
69.60/16.35	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', upairinpowunion)).
69.60/16.35	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', upairsubunion)).
69.60/16.35	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', singletonsubset)).
69.60/16.35	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', kpairp)).
69.60/16.35	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', kpairiskpair)).
69.60/16.35	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setukpairIL)).
69.60/16.35	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', secondinupair)).
69.60/16.35	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', symdiffIneg1)).
69.60/16.35	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', symdiffI1)).
69.60/16.35	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', symdiffE)).
69.60/16.35	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setminusSubset1)).
69.60/16.35	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setminusLsub)).
69.60/16.35	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setminusIRneg)).
69.60/16.35	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setminusERneg)).
69.60/16.35	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setminusEL)).
69.60/16.35	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binintersectRsub)).
69.60/16.35	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', disjointsetsI1)).
69.60/16.35	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binintersectSubset2)).
69.60/16.35	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binintersectSubset5)).
69.60/16.35	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binintersectI)).
69.60/16.35	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', binunionRsub)).
69.60/16.35	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', notequalI1)).
69.60/16.35	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', subsetE2)).
69.60/16.35	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', subsetE)).
69.60/16.35	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', subsetI2)).
69.60/16.35	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', eqimpsubset1)).
69.60/16.35	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setadjoin__Cong)).
69.60/16.35	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', emptyset__Cong)).
69.60/16.35	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', in__Cong)).
69.60/16.35	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', inCongP)).
69.60/16.35	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', prop2setI)).
69.60/16.35	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', quantDeMorgan2)).
69.60/16.35	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', vacuousDall)).
69.60/16.35	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', upairsetIL)).
69.60/16.35	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', upairsetE)).
69.60/16.35	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', uniqinunit)).
69.60/16.35	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', nonemptyImpWitness)).
69.60/16.35	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setunionE)).
69.60/16.35	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', emptyInPowerset)).
69.60/16.35	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', powersetI)).
69.60/16.35	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setadjoinOr)).
69.60/16.35	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setadjoinIR)).
69.60/16.35	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', emptyinunitempty)).
69.60/16.35	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setadjoinIL)).
69.60/16.35	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', nonemptyI1)).
69.60/16.35	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', nonemptyE1)).
69.60/16.35	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', noeltsimpempty)).
69.60/16.35	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', emptyI)).
69.60/16.35	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setext)).
69.60/16.35	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', emptysetE)).
69.60/16.35	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', wellorderingAx)).
69.60/16.35	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', omegaSAx)).
69.60/16.35	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', omega0Ax)).
69.60/16.35	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setadjoinAx)).
69.60/16.35	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.4TMUXKxHr2/E---3.1_11636.p', setextAx)).
69.60/16.35	thf(c_0_231, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
69.60/16.35	thf(c_0_232, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
69.60/16.35	thf(c_0_233, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
69.60/16.35	thf(c_0_234, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
69.60/16.35	thf(c_0_235, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
69.60/16.35	thf(c_0_236, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
69.60/16.35	thf(c_0_237, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
69.60/16.35	thf(c_0_238, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
69.60/16.35	thf(c_0_239, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
69.60/16.35	thf(c_0_240, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
69.60/16.35	thf(c_0_241, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
69.60/16.35	thf(c_0_242, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
69.60/16.35	thf(c_0_243, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
69.60/16.35	thf(c_0_244, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
69.60/16.35	thf(c_0_245, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
69.60/16.35	thf(c_0_246, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
69.60/16.35	thf(c_0_247, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
69.60/16.35	thf(c_0_248, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
69.60/16.35	thf(c_0_249, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
69.60/16.35	thf(c_0_250, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
69.60/16.35	thf(c_0_251, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
69.60/16.35	thf(c_0_252, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
69.60/16.35	thf(c_0_253, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
69.60/16.35	thf(c_0_254, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
69.60/16.35	thf(c_0_255, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
69.60/16.35	thf(c_0_256, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
69.60/16.35	thf(c_0_257, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
69.60/16.35	thf(c_0_258, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
69.60/16.35	thf(c_0_259, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
69.60/16.35	thf(c_0_260, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
69.60/16.35	thf(c_0_261, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
69.60/16.35	thf(c_0_262, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
69.60/16.35	thf(c_0_263, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
69.60/16.35	thf(c_0_264, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
69.60/16.35	thf(c_0_265, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
69.60/16.35	thf(c_0_266, plain, ((ex1I2)<=>![X4:$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/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
69.60/16.35	thf(c_0_267, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
69.60/16.35	thf(c_0_268, plain, ((singletonprop)<=>![X4:$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/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
69.60/16.35	thf(c_0_269, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
69.60/16.35	thf(c_0_270, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
69.60/16.35	thf(c_0_271, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
69.60/16.35	thf(c_0_272, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
69.60/16.35	thf(c_0_273, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
69.60/16.35	thf(c_0_274, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
69.60/16.35	thf(c_0_275, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
69.60/16.35	thf(c_0_276, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
69.60/16.35	thf(c_0_277, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
69.60/16.35	thf(c_0_278, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
69.60/16.35	thf(c_0_279, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
69.60/16.35	thf(c_0_280, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
69.60/16.35	thf(c_0_281, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
69.60/16.35	thf(c_0_282, plain, ((epred1_0)<=>![X775:$i]:(?[X776:$i]:((((![X777:$i]:(((in @ X777 @ X776)=>![X778:$i]:(((in @ X778 @ X777)=>(in @ X778 @ X775)))))&![X779:$i, X780:$i]:((((in @ X779 @ X775)&(in @ X780 @ X775))=>(![X781:$i]:(((in @ X781 @ X776)=>((in @ X779 @ X781)<=>(in @ X780 @ X781))))=>((X779)=(X780))))))&![X782:$i, X783:$i]:((((in @ X782 @ X776)&(in @ X783 @ X776))=>(![X784:$i]:(((in @ X784 @ X782)=>(in @ X784 @ X783)))|![X785:$i]:(((in @ X785 @ X783)=>(in @ X785 @ X782)))))))&![X786:$i]:(((![X787:$i]:(((in @ X787 @ X786)=>(in @ X787 @ X775)))&?[X788:$i]:((in @ X788 @ X786)))=>?[X789:$i, X790:$i]:(((((in @ X789 @ X776)&(in @ X790 @ X786))&~(?[X791:$i]:(((in @ X791 @ X789)&(in @ X791 @ X786)))))&![X792:$i]:(((in @ X792 @ X776)=>(![X793:$i]:(((in @ X793 @ X792)=>(in @ X793 @ X789)))|(in @ X790 @ X792)))))))))))), introduced(definition)).
69.60/16.35	thf(c_0_283, negated_conjecture, ~((![X762:$i, X763:$i]:((![X764:$i]:(((in @ X764 @ X762)<=>(in @ X764 @ X763)))=>((X762)=(X763))))=>(![X1469:$i]:(~(in @ X1469 @ emptyset))=>(![X765:$i, X766:$i, X767:$i]:(((in @ X767 @ (setadjoin @ X765 @ X766))<=>(((X767)=(X765))|(in @ X767 @ X766))))=>(![X1466:$i, X1467:$i]:(((in @ X1467 @ (powerset @ X1466))<=>![X1468:$i]:(((in @ X1468 @ X1467)=>(in @ X1468 @ X1466)))))=>(![X1463:$i, X1464:$i]:(((in @ X1464 @ (setunion @ X1463))<=>?[X1465:$i]:(((in @ X1464 @ X1465)&(in @ X1465 @ X1463)))))=>((in @ emptyset @ omega)=>(![X768:$i]:(((in @ X768 @ omega)=>(in @ (setadjoin @ X768 @ X768) @ omega)))=>(![X1460:$i]:((((in @ emptyset @ X1460)&![X1461:$i]:((((in @ X1461 @ omega)&(in @ X1461 @ X1460))=>(in @ (setadjoin @ X1461 @ X1461) @ X1460))))=>![X1462:$i]:(((in @ X1462 @ omega)=>(in @ X1462 @ X1460)))))=>(![X769:$i > $i > $o, X770:$i]:((![X771:$i]:(((in @ X771 @ X770)=>(exu @ (X769 @ X771))))=>?[X772:$i]:(![X773:$i]:(((in @ X773 @ X772)<=>?[X774:$i]:(((in @ X774 @ X770)&(X769 @ X774 @ X773))))))))=>(![X1456:$i]:((?[X1457:$i]:((in @ X1457 @ X1456))=>?[X1458:$i]:(((in @ X1458 @ X1456)&~(?[X1459:$i]:(((in @ X1459 @ X1458)&(in @ X1459 @ X1456))))))))=>((epred1_0)=>(![X794:$i > $o]:(((exu @ X794)=>(X794 @ (descr @ (^[Z0/* 17 */:$i]:(X794 @ Z0))))))=>(![X795:$i, X796:$i > $o, X797:$i]:(((in @ X797 @ X795)=>((X796 @ X797)=>(in @ X797 @ (dsetconstr @ X795 @ X796)))))=>(![X1453:$i, X1454:$i > $o, X1455:$i]:(((in @ X1455 @ (dsetconstr @ X1453 @ X1454))=>(in @ X1455 @ X1453)))=>(![X798:$i, X799:$i > $o, X800:$i]:(((in @ X800 @ (dsetconstr @ X798 @ X799))=>(X799 @ X800)))=>(![X801:$i > $o]:(((exu @ X801)=>?[X802:$i]:(((X801 @ X802)&![X803:$i]:(((X801 @ X803)=>((X802)=(X803))))))))=>(![X1451:$o, X1452:$i]:(((in @ X1452 @ (prop2set @ ((X1451))))=>(X1451)))=>(![X804:$i]:(((in @ X804 @ emptyset)=>![X805:$o]:((X805))))=>(![X1450:$i]:(((in @ X1450 @ emptyset)=>~($true)))=>(![X1449:$i]:(~(in @ X1449 @ emptyset))=>(![X806:$i > $o]:(((exu @ X806)=>?[X807:$i]:((X806 @ X807))))=>(![X808:$i, X809:$i]:((![X810:$i]:(((in @ X810 @ X808)=>(in @ X810 @ X809)))=>(![X811:$i]:(((in @ X811 @ X809)=>(in @ X811 @ X808)))=>((X808)=(X809)))))=>(![X812:$i]:((![X813:$i]:(~(in @ X813 @ X812))=>((X812)=(emptyset))))=>(![X814:$i]:((![X815:$i]:(~(in @ X815 @ X814))=>((X814)=(emptyset))))=>(![X1446:$i, X1447:$i > $o, X1448:$i]:(((in @ X1448 @ X1446)=>((in @ X1448 @ (dsetconstr @ X1446 @ X1447))<=>(X1447 @ X1448))))=>(![X816:$i]:(((nonempty @ X816)=>?[X817:$i]:((in @ X817 @ X816))))=>(![X1443:$i, X1444:$i > $o, X1445:$i]:(((in @ X1445 @ X1443)=>((X1444 @ X1445)=>(nonempty @ (dsetconstr @ X1443 @ X1444)))))=>(![X818:$i]:((?[X819:$i]:((in @ X819 @ X818))=>(nonempty @ X818)))=>(![X820:$i, X821:$i]:((in @ X820 @ (setadjoin @ X820 @ X821)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X822:$i, X823:$i, X824:$i]:(((in @ X824 @ X823)=>(in @ X824 @ (setadjoin @ X822 @ X823))))=>(![X1439:$i, X1440:$i, X1441:$i]:(((in @ X1441 @ (setadjoin @ X1439 @ X1440))=>![X1442:$o]:(((((X1441)=(X1439))=>(X1442))=>(((in @ X1441 @ X1440)=>(X1442))=>(X1442))))))=>(![X825:$i, X826:$i, X827:$i]:(((in @ X827 @ (setadjoin @ X825 @ X826))=>(((X827)=(X825))|(in @ X827 @ X826))))=>(![X828:$i]:(((dsetconstr @ X828 @ (^[Z0/* 1 */:$i]:($true)))=(X828)))=>(![X829:$i, X830:$i]:((![X831:$i]:(((in @ X831 @ X830)=>(in @ X831 @ X829)))=>(in @ X830 @ (powerset @ X829))))=>(![X1438:$i]:((in @ emptyset @ (powerset @ X1438)))=>(![X832:$i]:((in @ emptyset @ (powerset @ X832)))=>(![X1435:$i, X1436:$i, X1437:$i]:(((in @ X1436 @ (powerset @ X1435))=>((in @ X1437 @ X1436)=>(in @ X1437 @ X1435))))=>(![X1432:$i, X1433:$i, X1434:$i]:(((in @ X1433 @ X1434)=>((in @ X1434 @ X1432)=>(in @ X1433 @ (setunion @ X1432)))))=>(![X833:$i, X834:$i]:(((in @ X834 @ (setunion @ X833))=>![X835:$o]:((![X836:$i]:(((in @ X834 @ X836)=>((in @ X836 @ X833)=>(X835))))=>(X835)))))=>(![X1430:$i, X1431:$i]:(((in @ X1431 @ X1430)=>(in @ X1431 @ (powerset @ (setunion @ X1430)))))=>(![X1427:$i > $o]:(((exu @ X1427)=>?[X1428:$i]:(![X1429:$i]:(((X1427 @ X1429)<=>((X1429)=(X1428)))))))=>(![X837:$i]:(((nonempty @ X837)=>?[X838:$i]:(((in @ X838 @ X837)&$true))))=>(![X839:$i, X840:$i]:(((in @ X839 @ (setadjoin @ X840 @ emptyset))=>((X839)=(X840))))=>(![X1425:$i, X1426:$i]:((((X1425)!=(X1426))=>~(in @ X1426 @ (setadjoin @ X1425 @ emptyset))))=>(![X1423:$i, X1424:$i]:((((X1423)=(X1424))=>(in @ X1423 @ (setadjoin @ X1424 @ emptyset))))=>(![X1421:$i, X1422:$i]:(((in @ X1421 @ (setadjoin @ X1422 @ emptyset))=>(in @ X1422 @ (setadjoin @ X1421 @ emptyset))))=>(![X841:$i, X842:$i, X843:$i]:(((in @ X843 @ (setadjoin @ X841 @ (setadjoin @ X842 @ emptyset)))=>(((X843)=(X841))|((X843)=(X842)))))=>(![X844:$i, X845:$i]:((in @ X844 @ (setadjoin @ X844 @ (setadjoin @ X845 @ emptyset))))=>(![X1419:$i, X1420:$i]:((in @ X1420 @ (setadjoin @ X1419 @ (setadjoin @ X1420 @ emptyset))))=>(![X846:$i, X847:$i > $o]:((?[X848:$i]:(((in @ X848 @ X846)&(X847 @ X848)))=>(((dsetconstr @ X846 @ X847)=(emptyset))=>~($true))))=>(![X849:$i > $o, X850:$i]:(((in @ X850 @ emptyset)=>(X849 @ X850)))=>(![X1415:$i, X1416:$i > $o]:((~(![X1417:$i]:(((in @ X1417 @ X1415)=>(X1416 @ X1417))))=>?[X1418:$i]:(((in @ X1418 @ X1415)&~((X1416 @ X1418))))))=>(![X851:$i, X852:$i > $o]:((![X853:$i]:(((in @ X853 @ X851)=>~((X852 @ X853))))=>~(?[X854:$i]:(((in @ X854 @ X851)&(X852 @ X854))))))=>(![X1411:$i, X1412:$i > $o]:((~(?[X1413:$i]:(((in @ X1413 @ X1411)&(X1412 @ X1413))))=>![X1414:$i]:(((in @ X1414 @ X1411)=>~((X1412 @ X1414))))))=>(![X1407:$i, X1408:$i > $o]:((?[X1409:$i]:(((in @ X1409 @ X1407)&~((X1408 @ X1409))))=>~(![X1410:$i]:(((in @ X1410 @ X1407)=>(X1408 @ X1410))))))=>(![X855:$o]:(((X855)=>(in @ emptyset @ (prop2set @ ((X855))))))=>((prop2set2propI)=>(![X1403:$i, X1404:$i > $o]:((~(?[X1405:$i]:(((in @ X1405 @ X1403)&(X1404 @ X1405))))=>![X1406:$i]:(((in @ X1406 @ X1403)=>~((X1404 @ X1406))))))=>(![X1399:$i, X1400:$i > $o]:((~(![X1401:$i]:(((in @ X1401 @ X1399)=>(X1400 @ X1401))))=>?[X1402:$i]:(((in @ X1402 @ X1399)&~((X1400 @ X1402))))))=>(![X856:$i > $o]:((?[X857:$i]:(((X856 @ X857)&![X858:$i]:(((X856 @ X858)=>((X857)=(X858))))))=>(exu @ X856)))=>(![X859:$i > $o]:((?[X860:$i]:((X859 @ X860))=>(![X861:$i, X862:$i]:(((X859 @ X861)=>((X859 @ X862)=>((X861)=(X862)))))=>(exu @ X859))))=>(![X863:$i > $o]:((?[X864:$i]:(![X865:$i]:(((X863 @ X865)<=>((X865)=(X864)))))=>(exu @ X863)))=>(![X866:$i, X867:$i]:((((X866)=(X867))=>![X868:$i, X869:$i]:((((X868)=(X869))=>((in @ X868 @ X866)=>(in @ X869 @ X867))))))=>(![X870:$i, X871:$i]:((((X870)=(X871))=>![X872:$i, X873:$i]:((((X872)=(X873))=>((in @ X872 @ X870)<=>(in @ X873 @ X871))))))=>(![X1396:$i > $o]:(((exu @ X1396)=>![X1397:$i, X1398:$i]:(((X1396 @ X1397)=>((X1396 @ X1398)=>((X1397)=(X1398)))))))=>(![X874:$i > $o, X875:$i > $o]:((![X876:$i, X877:$i]:((((X876)=(X877))=>((X874 @ X876)<=>(X875 @ X877))))=>((exu @ X874)<=>(exu @ X875))))=>(((emptyset)=(emptyset))=>(![X878:$i, X879:$i]:((((X878)=(X879))=>![X880:$i, X881:$i]:((((X880)=(X881))=>((setadjoin @ X878 @ X880)=(setadjoin @ X879 @ X881))))))=>(![X1394:$i, X1395:$i]:((((X1394)=(X1395))=>((powerset @ X1394)=(powerset @ X1395))))=>(![X1392:$i, X1393:$i]:((((X1392)=(X1393))=>((setunion @ X1392)=(setunion @ X1393))))=>(((omega)=(omega))=>(![X882:$i > $o]:(((exu @ X882)=>![X883:$i, X884:$i]:(((X882 @ X883)=>((X882 @ X884)=>((X883)=(X884)))))))=>(![X1388:$i > $o, X1389:$i > $o]:((![X1390:$i, X1391:$i]:((((X1390)=(X1391))=>((X1388 @ X1390)<=>(X1389 @ X1391))))=>((exu @ X1388)=>((exu @ X1389)=>((descr @ X1388)=(descr @ X1389))))))=>(![X1382:$i, X1383:$i]:((((X1382)=(X1383))=>![X1384:$i > $o, X1385:$i > $o]:((![X1386:$i]:(((in @ X1386 @ X1382)=>![X1387:$i]:(((in @ X1387 @ X1383)=>(((X1386)=(X1387))=>((X1384 @ X1386)<=>(X1385 @ X1387)))))))=>((dsetconstr @ X1382 @ X1384)=(dsetconstr @ X1383 @ X1385))))))=>(![X1379:$i, X1380:$i]:((![X1381:$i]:(((in @ X1381 @ X1379)=>(in @ X1381 @ X1380)))=>(subset @ X1379 @ X1380)))=>(![X1377:$i, X1378:$i]:((((X1377)=(X1378))=>(subset @ X1378 @ X1377)))=>(![X885:$i, X886:$i]:((((X885)=(X886))=>(subset @ X885 @ X886)))=>(![X887:$i, X888:$i]:((![X889:$i]:(((in @ X889 @ X887)=>(in @ X889 @ X888)))=>(subset @ X887 @ X888)))=>(![X1376:$i]:((subset @ emptyset @ X1376))=>(![X890:$i, X891:$i, X892:$i]:(((subset @ X890 @ X891)=>((in @ X892 @ X890)=>(in @ X892 @ X891))))=>(![X893:$i, X894:$i, X895:$i]:(((subset @ X893 @ X894)=>(~(in @ X895 @ X894)=>~(in @ X895 @ X893))))=>(![X1373:$i, X1374:$i, X1375:$i]:(((in @ X1375 @ X1373)=>(~(in @ X1375 @ X1374)=>~(subset @ X1373 @ X1374))))=>(![X896:$i, X897:$i]:((~(subset @ X896 @ X897)=>((X896)!=(X897))))=>(![X1370:$i, X1371:$i, X1372:$i]:(((in @ X1372 @ X1370)=>(~(in @ X1372 @ X1371)=>((X1370)!=(X1371)))))=>(![X898:$i]:((subset @ X898 @ X898))=>(![X1367:$i, X1368:$i, X1369:$i]:(((subset @ X1367 @ X1368)=>((subset @ X1368 @ X1369)=>(subset @ X1367 @ X1369))))=>(![X1365:$i, X1366:$i]:((subset @ X1366 @ (setadjoin @ X1365 @ X1366)))=>(![X899:$i, X900:$i, X901:$i]:(((subset @ X899 @ X901)=>(subset @ X899 @ (setadjoin @ X900 @ X901))))=>(![X1363:$i, X1364:$i]:(((subset @ X1363 @ X1364)=>(in @ X1363 @ (powerset @ X1364))))=>(![X902:$i, X903:$i]:(((subset @ X902 @ X903)=>((subset @ X903 @ X902)=>((X902)=(X903)))))=>(![X904:$i]:(((subset @ X904 @ emptyset)=>((X904)=(emptyset))))=>(![X905:$i, X906:$i]:(((subset @ X906 @ X905)=>(in @ X906 @ (powerset @ X905))))=>(![X1361:$i, X1362:$i]:(((in @ X1362 @ (powerset @ X1361))=>(subset @ X1362 @ X1361)))=>(![X907:$i]:((in @ X907 @ (powerset @ X907)))=>(![X908:$i, X909:$i]:(((subset @ X908 @ X909)=>(subset @ (powerset @ X908) @ (powerset @ X909))))=>(![X910:$i, X911:$i > $o]:((in @ (dsetconstr @ X910 @ X911) @ (powerset @ X910)))=>(![X1359:$i, X1360:$i > $o]:((subset @ (dsetconstr @ X1359 @ X1360) @ X1359))=>(![X912:$i, X913:$i, X914:$i]:(((in @ X914 @ X912)=>(in @ X914 @ (binunion @ X912 @ X913))))=>(![X1357:$i, X1358:$i]:((in @ X1358 @ (setadjoin @ X1357 @ (setadjoin @ X1358 @ 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setminusSubset2]), setminusELneg]), setminusILneg]), symdiffI2]), symdiffIneg2]), setukpairIR]), brelnall1]), brelnall2]), singletoninpowunion]), upairset2E]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), subsetemptysetimpeq]), setunionsingleton]), c_0_240]), kfstpairEq]), cartprodfstin]), setukpairinjL]), setukpairinjR11]), setukpairinjR]), ksndpairEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_241]), c_0_242]), c_0_243]), c_0_244]), app]), ap2p]), funcinfuncset]), c_0_245]), funcGraphProp1]), funcextLem]), funcext]), c_0_246]), c_0_247]), c_0_248]), ifp]), iffalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), complementT_lem]), setminusT_lem]), iftrueorfalse]), iftrue]), theeq]), c_0_249]), c_0_250]), c_0_251]), c_0_252]), c_0_253]), c_0_254]), c_0_255]), ap2apEq2]), ap2apEq1]), funcext2]), eqbreln]), subbreln]), funcGraphProp4]), funcGraphProp2]), funcGraphProp3]), c_0_256]), c_0_257]), c_0_258]), infuncsetfunc]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), c_0_263]), cartprodmempaircEq]), kpairsurjEq]), c_0_264]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjL2]), theprop]), c_0_265]), setukpairinjL1]), singletonsuniq]), c_0_266]), c_0_267]), c_0_268]), cartprodpairin]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIL]), secondinupair]), symdiffIneg1]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusERneg]), setminusEL]), binintersectRsub]), disjointsetsI1]), binintersectSubset2]), binintersectSubset5]), binintersectI]), binunionRsub]), notequalI1]), subsetE2]), subsetE]), subsetI2]), eqimpsubset1]), c_0_269]), setadjoin__Cong]), emptyset__Cong]), c_0_270]), in__Cong]), inCongP]), c_0_271]), c_0_272]), c_0_273]), prop2setI]), quantDeMorgan2]), vacuousDall]), c_0_274]), upairsetIL]), upairsetE]), uniqinunit]), nonemptyImpWitness]), setunionE]), emptyInPowerset]), powersetI]), c_0_275]), setadjoinOr]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), nonemptyE1]), noeltsimpempty]), emptyI]), setext]), c_0_276]), emptysetE]), c_0_277]), c_0_278]), c_0_279]), c_0_280]), wellorderingAx]), c_0_281]), omegaSAx]), omega0Ax]), setadjoinAx]), setextAx])])]), c_0_282])).
69.60/16.35	thf(c_0_284, negated_conjecture, ![X1470:$i, X1471:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1483:$i, X1484:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1492:$i, X1493:$i > $i > $o, X1494:$i, X1497:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1504:$i, X1505:$i > $o, X1506:$i, X1507:$i > $o, X1508:$i, X1509:$i, X1510:$i > $o, X1511:$i, X1512:$i, X1513:$i > $o, X1514:$i, X1515:$i > $o, X1517:$i, X1518:$o, X1519:$i, X1520:$i, X1521:$o, X1522:$i, X1523:$i, X1524:$i > $o, X1526:$i, X1527:$i, X1530:$i, X1532:$i, X1534:$i, X1535:$i > $o, X1536:$i, X1537:$i, X1539:$i, X1540:$i > $o, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$o, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$o, X1572:$i, X1573:$i, X1574:$i > $o, X1576:$i, X1577:$i, X1578:$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 > $o, X1597:$i, X1598:$i > $o, X1599:$i, X1600:$i, X1601:$i > $o, X1602:$i, X1604:$i, X1605:$i > $o, X1607:$i, X1608:$i, X1609:$i > $o, X1611:$i, X1612:$i, X1613:$i > $o, X1614:$i, X1616:$o, X1617:$i, X1618:$i > $o, X1620:$i, X1621:$i, X1622:$i > $o, X1623:$i, X1625:$i > $o, X1626:$i, X1628:$i > $o, X1629:$i, X1632:$i > $o, X1633:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i > $o, X1644:$i, X1645:$i, X1646:$i > $o, X1647:$i > $o, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i > $o, X1659:$i, X1660:$i, X1661:$i > $o, X1662:$i > $o, X1665:$i, X1666:$i, X1667:$i > $o, X1668:$i > $o, X1671:$i, X1672:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i > $o, X1719:$i, X1720:$i > $o, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$o, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$o, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i > $o, X1875:$i, X1876:$i, X1877:$i > $o, X1879:$i, X1880:$i > $o, X1881:$i, X1883:$i, X1884:$i > $o, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i > $i > $o, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i > $i > $o, X1965:$i, X1966:$i, X1967:$i > $i > $o, X1968:$i, X1969:$i, X1970:$i > $i > $o, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i > $i > $o, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i > $i > $o, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i > $i > $o, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i > $i, X2014:$i, X2015:$i, X2016:$i > $i, X2018:$i, X2019:$i, X2020:$i > $i, X2022:$i, X2023:$i, X2024:$i, X2025:$i > $o, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i > $o, X2035:$i, X2036:$i, X2037:$i > $o, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i > $i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i > $i, X2109:$i, X2110:$i, X2111:$i > $i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$o, X2119:$i, X2120:$i, X2121:$i, X2122:$o, X2123:$i, X2124:$i, X2125:$i, X2126:$o, X2127:$i, X2128:$i, X2129:$i, X2130:$o, X2131:$i, X2132:$i, X2133:$i, X2134:$o, X2135:$i, X2136:$i, X2137:$i, X2138:$o, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$o, X2145:$i, X2146:$i, X2147:$i, X2148:$o, X2149:$i, X2150:$i, X2151:$i, X2152:$o, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2171:$i, X2172:$i]:((((~(in @ (esk1_2 @ X1470 @ X1471) @ X1470)|~(in @ (esk1_2 @ X1470 @ X1471) @ X1471)|((X1470)=(X1471)))&((in @ (esk1_2 @ X1470 @ X1471) @ X1470)|(in @ (esk1_2 @ X1470 @ X1471) @ X1471)|((X1470)=(X1471))))&(~(in @ X1473 @ emptyset)&(((~(in @ X1476 @ (setadjoin @ X1474 @ X1475))|(((X1476)=(X1474))|(in @ X1476 @ X1475)))&((((X1476)!=(X1474))|(in @ X1476 @ (setadjoin @ X1474 @ X1475)))&(~(in @ X1476 @ X1475)|(in @ X1476 @ (setadjoin @ X1474 @ X1475)))))&(((~(in @ X1478 @ (powerset @ X1477))|(~(in @ X1479 @ X1478)|(in @ X1479 @ X1477)))&(((in @ (esk2_2 @ X1480 @ X1481) @ X1481)|(in @ X1481 @ (powerset @ X1480)))&(~(in @ (esk2_2 @ X1480 @ X1481) @ X1480)|(in @ X1481 @ (powerset @ X1480)))))&(((((in @ X1484 @ (esk3_2 @ X1483 @ X1484))|~(in @ X1484 @ (setunion @ X1483)))&((in @ (esk3_2 @ X1483 @ X1484) @ X1483)|~(in @ X1484 @ (setunion @ X1483))))&(~(in @ X1487 @ X1488)|~(in @ X1488 @ X1486)|(in @ X1487 @ (setunion @ X1486))))&((in @ emptyset @ omega)&((~(in @ X1489 @ omega)|(in @ (setadjoin @ X1489 @ X1489) @ omega))&(((((in @ (esk4_1 @ X1490) @ omega)|~(in @ emptyset @ X1490)|(~(in @ X1492 @ omega)|(in @ X1492 @ X1490)))&((in @ (esk4_1 @ X1490) @ X1490)|~(in @ emptyset @ X1490)|(~(in @ X1492 @ omega)|(in @ X1492 @ X1490))))&(~(in @ (setadjoin @ (esk4_1 @ X1490) @ (esk4_1 @ X1490)) @ X1490)|~(in @ emptyset @ X1490)|(~(in @ X1492 @ omega)|(in @ X1492 @ X1490))))&((((((in @ (esk7_3 @ X1493 @ X1494 @ X1497) @ X1494)|~(in @ X1497 @ (esk6_2 @ X1493 @ X1494))|(in @ (esk5_2 @ X1493 @ X1494) @ X1494))&((X1493 @ (esk7_3 @ X1493 @ X1494 @ X1497) @ X1497)|~(in @ X1497 @ (esk6_2 @ X1493 @ X1494))|(in @ (esk5_2 @ X1493 @ X1494) @ X1494)))&(~(in @ X1500 @ X1494)|~(X1493 @ X1500 @ X1499)|(in @ X1499 @ (esk6_2 @ X1493 @ X1494))|(in @ (esk5_2 @ X1493 @ X1494) @ X1494)))&((((in @ (esk7_3 @ X1493 @ X1494 @ X1497) @ X1494)|~(in @ X1497 @ (esk6_2 @ X1493 @ X1494))|~(exu @ (X1493 @ (esk5_2 @ X1493 @ X1494))))&((X1493 @ (esk7_3 @ X1493 @ X1494 @ X1497) @ X1497)|~(in @ X1497 @ (esk6_2 @ X1493 @ X1494))|~(exu @ (X1493 @ (esk5_2 @ X1493 @ X1494)))))&(~(in @ X1500 @ X1494)|~(X1493 @ X1500 @ X1499)|(in @ X1499 @ (esk6_2 @ X1493 @ X1494))|~(exu @ (X1493 @ (esk5_2 @ X1493 @ X1494))))))&((((in @ (esk8_1 @ X1501) @ X1501)|~(in @ X1502 @ X1501))&(~(in @ X1504 @ (esk8_1 @ X1501))|~(in @ X1504 @ X1501)|~(in @ X1502 @ X1501)))&((epred1_0)&((~(exu @ X1505)|(X1505 @ (descr @ X1505)))&((~(in @ X1508 @ X1506)|(~(X1507 @ X1508)|(in @ X1508 @ (dsetconstr @ X1506 @ X1507))))&((~(in @ X1511 @ (dsetconstr @ X1509 @ X1510))|(in @ X1511 @ X1509))&((~(in @ X1514 @ (dsetconstr @ X1512 @ X1513))|(X1513 @ X1514))&((((X1515 @ (esk9_1 @ X1515))|~(exu @ X1515))&(~(X1515 @ X1517)|((esk9_1 @ X1515)=(X1517))|~(exu @ X1515)))&((~(in @ X1519 @ (prop2set @ ((X1518))))|(X1518))&((~(in @ X1520 @ emptyset)|(X1521))&((~(in @ X1522 @ emptyset)|~($true))&(~(in @ X1523 @ emptyset)&((~(exu @ X1524)|(X1524 @ (esk10_1 @ X1524)))&(((((in @ (esk12_2 @ X1526 @ X1527) @ X1527)|((X1526)=(X1527))|(in @ (esk11_2 @ X1526 @ X1527) @ X1526))&(~(in @ (esk12_2 @ X1526 @ X1527) @ X1526)|((X1526)=(X1527))|(in @ (esk11_2 @ X1526 @ X1527) @ X1526)))&(((in @ (esk12_2 @ X1526 @ X1527) @ X1527)|((X1526)=(X1527))|~(in @ (esk11_2 @ X1526 @ X1527) @ X1527))&(~(in @ (esk12_2 @ X1526 @ X1527) @ X1526)|((X1526)=(X1527))|~(in @ (esk11_2 @ X1526 @ X1527) @ X1527))))&(((in @ (esk13_1 @ X1530) @ X1530)|((X1530)=(emptyset)))&(((in @ (esk14_1 @ X1532) @ X1532)|((X1532)=(emptyset)))&(((~(in @ X1536 @ (dsetconstr @ X1534 @ X1535))|(X1535 @ X1536)|~(in @ X1536 @ X1534))&(~(X1535 @ X1536)|(in @ X1536 @ (dsetconstr @ X1534 @ X1535))|~(in @ X1536 @ X1534)))&((~(nonempty @ X1537)|(in @ (esk15_1 @ X1537) @ X1537))&((~(in @ X1541 @ X1539)|(~(X1540 @ X1541)|(nonempty @ (dsetconstr @ X1539 @ X1540))))&((~(in @ X1543 @ X1542)|(nonempty @ X1542))&((in @ X1544 @ (setadjoin @ X1544 @ X1545))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1548 @ X1547)|(in @ X1548 @ (setadjoin @ X1546 @ X1547)))&(((((in @ X1551 @ X1550)|(X1552)|((X1551)=(X1549))|~(in @ X1551 @ (setadjoin @ X1549 @ X1550)))&(~(X1552)|(X1552)|((X1551)=(X1549))|~(in @ X1551 @ (setadjoin @ X1549 @ X1550))))&(((in @ X1551 @ X1550)|(X1552)|~(X1552)|~(in @ X1551 @ (setadjoin @ X1549 @ X1550)))&(~(X1552)|(X1552)|~(X1552)|~(in @ X1551 @ (setadjoin @ X1549 @ X1550)))))&((~(in @ X1555 @ (setadjoin @ X1553 @ X1554))|(((X1555)=(X1553))|(in @ X1555 @ X1554)))&(((dsetconstr @ X1556 @ (^[Z0/* 1 */:$i]:($true)))=(X1556))&((((in @ (esk16_2 @ X1557 @ X1558) @ X1558)|(in @ X1558 @ (powerset @ X1557)))&(~(in @ (esk16_2 @ X1557 @ X1558) @ X1557)|(in @ X1558 @ (powerset @ X1557))))&((in @ emptyset @ (powerset @ X1560))&((in @ emptyset @ (powerset @ X1561))&((~(in @ X1563 @ (powerset @ X1562))|(~(in @ X1564 @ X1563)|(in @ X1564 @ X1562)))&((~(in @ X1566 @ X1567)|(~(in @ X1567 @ X1565)|(in @ X1566 @ (setunion @ X1565))))&((((in @ X1569 @ (esk17_3 @ X1568 @ X1569 @ X1570))|(X1570)|~(in @ X1569 @ (setunion @ X1568)))&(((in @ (esk17_3 @ X1568 @ X1569 @ X1570) @ X1568)|(X1570)|~(in @ X1569 @ (setunion @ X1568)))&(~(X1570)|(X1570)|~(in @ X1569 @ (setunion @ X1568)))))&((~(in @ X1573 @ X1572)|(in @ X1573 @ (powerset @ (setunion @ X1572))))&(((~(X1574 @ X1576)|((X1576)=(esk18_1 @ X1574))|~(exu @ X1574))&(((X1577)!=(esk18_1 @ X1574))|(X1574 @ X1577)|~(exu @ X1574)))&((((in @ (esk19_1 @ X1578) @ X1578)|~(nonempty @ X1578))&(($true)|~(nonempty @ X1578)))&((~(in @ X1580 @ (setadjoin @ X1581 @ emptyset))|((X1580)=(X1581)))&((((X1582)=(X1583))|~(in @ X1583 @ (setadjoin @ X1582 @ emptyset)))&((((X1584)!=(X1585))|(in @ X1584 @ (setadjoin @ X1585 @ emptyset)))&((~(in @ X1586 @ (setadjoin @ X1587 @ emptyset))|(in @ X1587 @ (setadjoin @ X1586 @ emptyset)))&((~(in @ X1590 @ (setadjoin @ X1588 @ (setadjoin @ X1589 @ emptyset)))|(((X1590)=(X1588))|((X1590)=(X1589))))&((in @ X1591 @ (setadjoin @ X1591 @ (setadjoin @ X1592 @ emptyset)))&((in @ X1594 @ (setadjoin @ X1593 @ (setadjoin @ X1594 @ emptyset)))&((~(in @ X1597 @ X1595)|~(X1596 @ X1597)|(((dsetconstr @ X1595 @ X1596)!=(emptyset))|~($true)))&((~(in @ X1599 @ emptyset)|(X1598 @ X1599))&((((in @ (esk20_2 @ X1600 @ X1601) @ X1600)|(~(in @ X1602 @ X1600)|(X1601 @ X1602)))&(~(X1601 @ (esk20_2 @ X1600 @ X1601))|(~(in @ X1602 @ X1600)|(X1601 @ X1602))))&((((in @ (esk21_2 @ X1604 @ X1605) @ X1604)|(~(in 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@ X2090 @ X2091 @ X2092))))&((~(func @ X2093 @ X2094 @ X2095)|(~(in @ X2096 @ X2093)|((ap @ X2093 @ X2094 @ X2095 @ X2096)=(ap @ X2093 @ X2094 @ X2095 @ X2096))))&((((in @ (esk64_3 @ X2097 @ X2098 @ X2099) @ X2097)|(~(in @ X2101 @ X2097)|((ap @ X2097 @ X2098 @ (lam @ X2097 @ X2098 @ X2099) @ X2101)=(X2099 @ X2101))))&(~(in @ (X2099 @ (esk64_3 @ X2097 @ X2098 @ X2099)) @ X2098)|(~(in @ X2101 @ X2097)|((ap @ X2097 @ X2098 @ (lam @ X2097 @ X2098 @ X2099) @ X2101)=(X2099 @ X2101)))))&((~(func @ X2102 @ X2103 @ X2104)|((lam @ X2102 @ X2103 @ (ap @ X2102 @ X2103 @ X2104))=(X2104)))&((((in @ (esk65_3 @ X2105 @ X2106 @ X2107) @ X2105)|((lam @ X2105 @ X2106 @ X2107)=(lam @ X2105 @ X2106 @ X2107)))&(~(in @ (X2107 @ (esk65_3 @ X2105 @ X2106 @ X2107)) @ X2106)|((lam @ X2105 @ X2106 @ X2107)=(lam @ X2105 @ X2106 @ X2107))))&((((in @ (esk66_3 @ X2109 @ X2110 @ X2111) @ X2109)|(~(in @ X2113 @ X2109)|((ap @ X2109 @ X2110 @ (lam @ X2109 @ X2110 @ X2111) @ X2113)=(X2111 @ X2113))))&(~(in @ (X2111 @ (esk66_3 @ X2109 @ X2110 @ X2111)) @ X2110)|(~(in @ X2113 @ X2109)|((ap @ X2109 @ X2110 @ (lam @ X2109 @ X2110 @ X2111) @ X2113)=(X2111 @ X2113)))))&((~(in @ X2116 @ (funcSet @ X2114 @ X2115))|((lam @ X2114 @ X2115 @ (ap @ X2114 @ X2115 @ X2116))=(X2116)))&((~(in @ X2119 @ X2117)|(~(in @ X2120 @ X2117)|((X2118)|(in @ X2120 @ (dsetconstr @ X2117 @ (^[Z0/* 9 */:$i]:((((X2118)&((Z0)=(X2119)))|(~((X2118))&((Z0)=(X2120)))))))))))&((~(in @ X2123 @ X2121)|(~(in @ X2124 @ X2121)|((X2122)|((dsetconstr @ X2121 @ (^[Z0/* 9 */:$i]:((((X2122)&((Z0)=(X2123)))|(~((X2122))&((Z0)=(X2124)))))))=(setadjoin @ X2124 @ emptyset)))))&((~(in @ X2127 @ X2125)|(~(in @ X2128 @ X2125)|(~(X2126)|(in @ X2127 @ (dsetconstr @ X2125 @ (^[Z0/* 9 */:$i]:((((X2126)&((Z0)=(X2127)))|(~((X2126))&((Z0)=(X2128)))))))))))&((~(in @ X2131 @ X2129)|(~(in @ X2132 @ X2129)|(~(X2130)|((dsetconstr @ X2129 @ (^[Z0/* 9 */:$i]:((((X2130)&((Z0)=(X2131)))|(~((X2130))&((Z0)=(X2132)))))))=(setadjoin @ X2131 @ emptyset)))))&((~(in @ X2135 @ X2133)|(~(in @ X2136 @ X2133)|(singleton @ (dsetconstr @ X2133 @ (^[Z0/* 9 */:$i]:((((X2134)&((Z0)=(X2135)))|(~((X2134))&((Z0)=(X2136))))))))))&((~(in @ X2139 @ X2137)|(~(in @ X2140 @ X2137)|(in @ (if @ X2137 @ ((X2138)) @ X2139 @ X2140) @ X2137)))&((~(singleton @ X2141)|(~(in @ X2142 @ X2141)|((setunion @ X2141)=(X2142))))&((~(in @ X2145 @ X2143)|(~(in @ X2146 @ X2143)|(~(X2144)|((if @ X2143 @ ((X2144)) @ X2145 @ X2146)=(X2145)))))&((~(in @ X2149 @ X2147)|(~(in @ X2150 @ X2147)|((X2148)|((if @ X2147 @ ((X2148)) @ X2149 @ X2150)=(X2150)))))&((~(in @ X2153 @ X2151)|(~(in @ X2154 @ X2151)|(in @ (if @ X2151 @ ((X2152)) @ X2153 @ X2154) @ (setadjoin @ X2153 @ (setadjoin @ X2154 @ emptyset)))))&((~(in @ X2156 @ (powerset @ X2155))|(~(in @ X2157 @ (powerset @ X2155))|(in @ (binintersect @ X2156 @ X2157) @ (powerset @ X2155))))&((~(in @ X2159 @ (powerset @ X2158))|(~(in @ X2160 @ (powerset @ X2158))|(in @ (binunion @ X2159 @ X2160) @ (powerset @ X2158))))&((~(in @ X2162 @ (powerset @ X2161))|(in @ (powerset @ X2162) @ (powerset @ (powerset @ X2161))))&((~(in @ X2164 @ (powerset @ X2163))|(~(in @ X2165 @ (powerset @ X2163))|(in @ (setminus @ X2164 @ X2165) @ (powerset @ X2163))))&((~(in @ X2167 @ (powerset @ X2166))|(in @ (setminus @ X2166 @ X2167) @ (powerset @ X2166)))&((in @ esk68_0 @ (powerset @ esk67_0))&((in @ esk69_0 @ (powerset @ esk67_0))&((~(in @ X2171 @ esk67_0)|(~(in @ X2171 @ esk68_0)|(in @ X2171 @ esk69_0)))&((~(in @ X2172 @ esk67_0)|(~(in @ X2172 @ esk69_0)|(in @ X2172 @ esk68_0)))&((esk68_0)!=(esk69_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_283])])])])])])])).
69.60/16.35	thf(c_0_285, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_286, negated_conjecture, (in @ esk68_0 @ (powerset @ esk67_0)), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_287, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|(in @ (esk11_2 @ X2 @ X3) @ X2)|~((in @ (esk12_2 @ X2 @ X3) @ X2)))), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_288, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk69_0)|~((in @ X2 @ esk67_0))|~((in @ X2 @ esk68_0)))), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_289, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk67_0)|~((in @ X2 @ esk68_0)))), inference(spm,[status(thm)],[c_0_285, c_0_286])).
69.60/16.35	thf(c_0_290, negated_conjecture, (in @ esk69_0 @ (powerset @ esk67_0)), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_291, negated_conjecture, ![X2:$i]:((((esk69_0)=(X2))|(in @ (esk11_2 @ esk69_0 @ X2) @ esk69_0)|~((in @ (esk12_2 @ esk69_0 @ X2) @ esk68_0)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_287, c_0_288]), c_0_289])).
69.60/16.35	thf(c_0_292, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk12_2 @ X2 @ X3) @ X3)|((X2)=(X3))|(in @ (esk11_2 @ X2 @ X3) @ X2))), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_293, negated_conjecture, ((esk68_0)!=(esk69_0)), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_294, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk67_0)|~((in @ X2 @ esk69_0)))), inference(spm,[status(thm)],[c_0_285, c_0_290])).
69.60/16.35	thf(c_0_295, negated_conjecture, (in @ (esk11_2 @ esk69_0 @ esk68_0) @ esk69_0), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_291, c_0_292]), c_0_293])).
69.60/16.35	thf(c_0_296, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk36_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_297, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk68_0)|~((in @ X2 @ esk67_0))|~((in @ X2 @ esk69_0)))), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_298, negated_conjecture, (in @ (esk11_2 @ esk69_0 @ esk68_0) @ esk67_0), inference(spm,[status(thm)],[c_0_294, c_0_295])).
69.60/16.35	thf(c_0_299, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk69_0)|~((in @ (esk36_2 @ X2 @ esk69_0) @ esk68_0)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_296, c_0_288]), c_0_289])).
69.60/16.35	thf(c_0_300, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk36_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_301, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(X3))|~((in @ (esk12_2 @ X2 @ X3) @ X2))|~((in @ (esk11_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_302, negated_conjecture, (in @ (esk11_2 @ esk69_0 @ esk68_0) @ esk68_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297, c_0_295]), c_0_298])])).
69.60/16.35	thf(c_0_303, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_304, negated_conjecture, (subset @ esk68_0 @ esk69_0), inference(spm,[status(thm)],[c_0_299, c_0_300])).
69.60/16.35	thf(c_0_305, negated_conjecture, ~((in @ (esk12_2 @ esk69_0 @ esk68_0) @ esk69_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_301, c_0_302]), c_0_293])).
69.60/16.35	thf(c_0_306, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk69_0)|~((in @ X2 @ esk68_0)))), inference(spm,[status(thm)],[c_0_303, c_0_304])).
69.60/16.35	thf(c_0_307, negated_conjecture, ~((in @ (esk12_2 @ esk69_0 @ esk68_0) @ esk68_0)), inference(spm,[status(thm)],[c_0_305, c_0_306])).
69.60/16.35	thf(c_0_308, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk12_2 @ X2 @ X3) @ X3)|((X2)=(X3))|~((in @ (esk11_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_284])).
69.60/16.35	thf(c_0_309, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_307, c_0_308]), c_0_302])]), c_0_293]), ['proof']).
69.60/16.35	# SZS output end CNFRefutation
69.60/16.35	# Parsed axioms                        : 505
69.60/16.35	# Removed by relevancy pruning/SinE    : 274
69.60/16.35	# Initial clauses                      : 381
69.60/16.35	# Removed in clause preprocessing      : 34
69.60/16.35	# Initial clauses in saturation        : 347
69.60/16.35	# Processed clauses                    : 8510
69.60/16.35	# ...of these trivial                  : 59
69.60/16.35	# ...subsumed                          : 4557
69.60/16.35	# ...remaining for further processing  : 3894
69.60/16.35	# Other redundant clauses eliminated   : 131
69.60/16.35	# Clauses deleted for lack of memory   : 0
69.60/16.35	# Backward-subsumed                    : 756
69.60/16.35	# Backward-rewritten                   : 205
69.60/16.35	# Generated clauses                    : 351738
69.60/16.35	# ...of the previous two non-redundant : 349139
69.60/16.35	# ...aggressively subsumed             : 0
69.60/16.35	# Contextual simplify-reflections      : 86
69.60/16.35	# Paramodulations                      : 351463
69.60/16.35	# Factorizations                       : 68
69.60/16.35	# NegExts                              : 40
69.60/16.35	# Equation resolutions                 : 139
69.60/16.35	# Disequality decompositions           : 0
69.60/16.35	# Total rewrite steps                  : 9393
69.60/16.35	# ...of those cached                   : 8842
69.60/16.35	# Propositional unsat checks           : 0
69.60/16.35	#    Propositional check models        : 0
69.60/16.35	#    Propositional check unsatisfiable : 0
69.60/16.35	#    Propositional clauses             : 0
69.60/16.35	#    Propositional clauses after purity: 0
69.60/16.35	#    Propositional unsat core size     : 0
69.60/16.35	#    Propositional preprocessing time  : 0.000
69.60/16.35	#    Propositional encoding time       : 0.000
69.60/16.35	#    Propositional solver time         : 0.000
69.60/16.35	#    Success case prop preproc time    : 0.000
69.60/16.35	#    Success case prop encoding time   : 0.000
69.60/16.35	#    Success case prop solver time     : 0.000
69.60/16.35	# Current number of processed clauses  : 2609
69.60/16.35	#    Positive orientable unit clauses  : 90
69.60/16.35	#    Positive unorientable unit clauses: 0
69.60/16.35	#    Negative unit clauses             : 242
69.60/16.35	#    Non-unit-clauses                  : 2277
69.60/16.35	# Current number of unprocessed clauses: 340410
69.60/16.35	# ...number of literals in the above   : 1315244
69.60/16.35	# Current number of archived formulas  : 0
69.60/16.35	# Current number of archived clauses   : 1269
69.60/16.35	# Clause-clause subsumption calls (NU) : 944795
69.60/16.35	# Rec. Clause-clause subsumption calls : 505285
69.60/16.35	# Non-unit clause-clause subsumptions  : 3682
69.60/16.35	# Unit Clause-clause subsumption calls : 46052
69.60/16.35	# Rewrite failures with RHS unbound    : 0
69.60/16.35	# BW rewrite match attempts            : 50
69.60/16.35	# BW rewrite match successes           : 18
69.60/16.35	# Condensation attempts                : 0
69.60/16.35	# Condensation successes               : 0
69.60/16.35	# Termbank termtop insertions          : 6852840
69.60/16.35	# Search garbage collected termcells   : 22498
69.60/16.35	
69.60/16.35	# -------------------------------------------------
69.60/16.35	# User time                : 7.665 s
69.60/16.35	# System time              : 0.233 s
69.60/16.35	# Total time               : 7.898 s
69.60/16.35	# Maximum resident set size: 7500 pages
69.60/16.35	
69.60/16.35	# -------------------------------------------------
69.60/16.35	# User time                : 7.673 s
69.60/16.35	# System time              : 0.236 s
69.60/16.35	# Total time               : 7.908 s
69.60/16.35	# Maximum resident set size: 2612 pages
69.60/16.35	% E exiting
69.60/16.35	% E exiting
69.60/16.35	EOF