0.00/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.12	% Command    : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.12/0.34	% Computer : n017.cluster.edu
0.12/0.34	% Model    : x86_64 x86_64
0.12/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory   : 8042.1875MB
0.12/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 1920
0.12/0.34	% WCLimit    : 240
0.12/0.34	% DateTime   : Wed Jul 30 05:36:35 EDT 2025
0.12/0.34	% CPUTime    : 
0.20/0.48	Running higher-order theorem proving
0.20/0.53	Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p
114.24/15.04	# Version: 3.0.0-ho
114.24/15.04	# Preprocessing class: HSLMSLSSLLLCHFA.
114.24/15.04	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
114.24/15.04	# Starting ehoh_best5 with 240s (1) cores
114.24/15.04	# Starting almost_fo_3_lam with 240s (1) cores
114.24/15.04	# Starting new_bool_5 with 240s (1) cores
114.24/15.04	# Starting pre_casc_3 with 240s (1) cores
114.24/15.04	# Starting ho_unfolding_8 with 240s (1) cores
114.24/15.04	# Starting new_ho_10_cnf2 with 240s (1) cores
114.24/15.04	# Starting new_bool_3 with 240s (1) cores
114.24/15.04	# Starting new_ho_5 with 240s (1) cores
114.24/15.04	# ho_unfolding_8 with pid 15101 completed with status 0
114.24/15.04	# Result found by ho_unfolding_8
114.24/15.04	# Preprocessing class: HSLMSLSSLLLCHFA.
114.24/15.04	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
114.24/15.04	# Starting ehoh_best5 with 240s (1) cores
114.24/15.04	# Starting almost_fo_3_lam with 240s (1) cores
114.24/15.04	# Starting new_bool_5 with 240s (1) cores
114.24/15.04	# Starting pre_casc_3 with 240s (1) cores
114.24/15.04	# Starting ho_unfolding_8 with 240s (1) cores
114.24/15.04	# No SInE strategy applied
114.24/15.04	# Search class: HGHSM-FSLM32-DHFMMSBN
114.24/15.04	# partial match(1): HGHSM-FSLM32-MHFMMSBN
114.24/15.04	# Scheduled 9 strats onto 1 cores with 240 seconds (240 total)
114.24/15.04	# Starting ho_unfolding_8 with 49s (1) cores
114.24/15.04	# ho_unfolding_8 with pid 15110 completed with status 0
114.24/15.04	# Result found by ho_unfolding_8
114.24/15.04	# Preprocessing class: HSLMSLSSLLLCHFA.
114.24/15.04	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
114.24/15.04	# Starting ehoh_best5 with 240s (1) cores
114.24/15.04	# Starting almost_fo_3_lam with 240s (1) cores
114.24/15.04	# Starting new_bool_5 with 240s (1) cores
114.24/15.04	# Starting pre_casc_3 with 240s (1) cores
114.24/15.04	# Starting ho_unfolding_8 with 240s (1) cores
114.24/15.04	# No SInE strategy applied
114.24/15.04	# Search class: HGHSM-FSLM32-DHFMMSBN
114.24/15.04	# partial match(1): HGHSM-FSLM32-MHFMMSBN
114.24/15.04	# Scheduled 9 strats onto 1 cores with 240 seconds (240 total)
114.24/15.04	# Starting ho_unfolding_8 with 49s (1) cores
114.24/15.04	# Preprocessing time       : 0.169 s
114.24/15.04	# Presaturation interreduction done
114.24/15.04	
114.24/15.04	# Proof found!
114.24/15.04	# SZS status Theorem
114.24/15.04	# SZS output start CNFRefutation
114.24/15.04	thf(decl_23, type, in: $i > $i > $o).
114.24/15.04	thf(decl_24, type, exu: ($i > $o) > $o).
114.24/15.04	thf(decl_25, type, setextAx: $o).
114.24/15.04	thf(decl_26, type, emptyset: $i).
114.24/15.04	thf(decl_27, type, emptysetAx: $o).
114.24/15.04	thf(decl_28, type, setadjoin: $i > $i > $i).
114.24/15.04	thf(decl_29, type, setadjoinAx: $o).
114.24/15.04	thf(decl_30, type, powerset: $i > $i).
114.24/15.04	thf(decl_31, type, powersetAx: $o).
114.24/15.04	thf(decl_32, type, setunion: $i > $i).
114.24/15.04	thf(decl_33, type, setunionAx: $o).
114.24/15.04	thf(decl_34, type, omega: $i).
114.24/15.04	thf(decl_35, type, omega0Ax: $o).
114.24/15.04	thf(decl_36, type, omegaSAx: $o).
114.24/15.04	thf(decl_37, type, omegaIndAx: $o).
114.24/15.04	thf(decl_38, type, replAx: $o).
114.24/15.04	thf(decl_39, type, foundationAx: $o).
114.24/15.04	thf(decl_40, type, wellorderingAx: $o).
114.24/15.04	thf(decl_41, type, descr: ($i > $o) > $i).
114.24/15.04	thf(decl_42, type, descrp: $o).
114.24/15.04	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_44, type, dsetconstrI: $o).
114.24/15.04	thf(decl_45, type, dsetconstrEL: $o).
114.24/15.04	thf(decl_46, type, dsetconstrER: $o).
114.24/15.04	thf(decl_47, type, exuE1: $o).
114.24/15.04	thf(decl_48, type, prop2set: $o > $i).
114.24/15.04	thf(decl_49, type, prop2setE: $o).
114.24/15.04	thf(decl_50, type, emptysetE: $o).
114.24/15.04	thf(decl_51, type, emptysetimpfalse: $o).
114.24/15.04	thf(decl_52, type, notinemptyset: $o).
114.24/15.04	thf(decl_53, type, exuE3e: $o).
114.24/15.04	thf(decl_54, type, setext: $o).
114.24/15.04	thf(decl_55, type, emptyI: $o).
114.24/15.04	thf(decl_56, type, noeltsimpempty: $o).
114.24/15.04	thf(decl_57, type, setbeta: $o).
114.24/15.04	thf(decl_58, type, nonempty: $i > $o).
114.24/15.04	thf(decl_59, type, nonemptyE1: $o).
114.24/15.04	thf(decl_60, type, nonemptyI: $o).
114.24/15.04	thf(decl_61, type, nonemptyI1: $o).
114.24/15.04	thf(decl_62, type, setadjoinIL: $o).
114.24/15.04	thf(decl_63, type, emptyinunitempty: $o).
114.24/15.04	thf(decl_64, type, setadjoinIR: $o).
114.24/15.04	thf(decl_65, type, setadjoinE: $o).
114.24/15.04	thf(decl_66, type, setadjoinOr: $o).
114.24/15.04	thf(decl_67, type, setoftrueEq: $o).
114.24/15.04	thf(decl_68, type, powersetI: $o).
114.24/15.04	thf(decl_69, type, emptyinPowerset: $o).
114.24/15.04	thf(decl_70, type, emptyInPowerset: $o).
114.24/15.04	thf(decl_71, type, powersetE: $o).
114.24/15.04	thf(decl_72, type, setunionI: $o).
114.24/15.04	thf(decl_73, type, setunionE: $o).
114.24/15.04	thf(decl_74, type, subPowSU: $o).
114.24/15.04	thf(decl_75, type, exuE2: $o).
114.24/15.04	thf(decl_76, type, nonemptyImpWitness: $o).
114.24/15.04	thf(decl_77, type, uniqinunit: $o).
114.24/15.04	thf(decl_78, type, notinsingleton: $o).
114.24/15.04	thf(decl_79, type, eqinunit: $o).
114.24/15.04	thf(decl_80, type, singletonsswitch: $o).
114.24/15.04	thf(decl_81, type, upairsetE: $o).
114.24/15.04	thf(decl_82, type, upairsetIL: $o).
114.24/15.04	thf(decl_83, type, upairsetIR: $o).
114.24/15.04	thf(decl_84, type, emptyE1: $o).
114.24/15.04	thf(decl_85, type, vacuousDall: $o).
114.24/15.04	thf(decl_86, type, quantDeMorgan1: $o).
114.24/15.04	thf(decl_87, type, quantDeMorgan2: $o).
114.24/15.04	thf(decl_88, type, quantDeMorgan3: $o).
114.24/15.04	thf(decl_89, type, quantDeMorgan4: $o).
114.24/15.04	thf(decl_90, type, prop2setI: $o).
114.24/15.04	thf(decl_91, type, set2prop: $i > $o).
114.24/15.04	thf(decl_92, type, prop2set2propI: $o).
114.24/15.04	thf(decl_93, type, notdexE: $o).
114.24/15.04	thf(decl_94, type, notdallE: $o).
114.24/15.04	thf(decl_95, type, exuI1: $o).
114.24/15.04	thf(decl_96, type, exuI3: $o).
114.24/15.04	thf(decl_97, type, exuI2: $o).
114.24/15.04	thf(decl_98, type, inCongP: $o).
114.24/15.04	thf(decl_99, type, in__Cong: $o).
114.24/15.04	thf(decl_100, type, exuE3u: $o).
114.24/15.04	thf(decl_101, type, exu__Cong: $o).
114.24/15.04	thf(decl_102, type, emptyset__Cong: $o).
114.24/15.04	thf(decl_103, type, setadjoin__Cong: $o).
114.24/15.04	thf(decl_104, type, powerset__Cong: $o).
114.24/15.04	thf(decl_105, type, setunion__Cong: $o).
114.24/15.04	thf(decl_106, type, omega__Cong: $o).
114.24/15.04	thf(decl_107, type, exuEu: $o).
114.24/15.04	thf(decl_108, type, descr__Cong: $o).
114.24/15.04	thf(decl_109, type, dsetconstr__Cong: $o).
114.24/15.04	thf(decl_110, type, subset: $i > $i > $o).
114.24/15.04	thf(decl_113, type, subsetI1: $o).
114.24/15.04	thf(decl_114, type, eqimpsubset2: $o).
114.24/15.04	thf(decl_115, type, eqimpsubset1: $o).
114.24/15.04	thf(decl_116, type, subsetI2: $o).
114.24/15.04	thf(decl_117, type, emptysetsubset: $o).
114.24/15.04	thf(decl_118, type, subsetE: $o).
114.24/15.04	thf(decl_119, type, subsetE2: $o).
114.24/15.04	thf(decl_120, type, notsubsetI: $o).
114.24/15.04	thf(decl_121, type, notequalI1: $o).
114.24/15.04	thf(decl_122, type, notequalI2: $o).
114.24/15.04	thf(decl_123, type, subsetRefl: $o).
114.24/15.04	thf(decl_124, type, subsetTrans: $o).
114.24/15.04	thf(decl_125, type, setadjoinSub: $o).
114.24/15.04	thf(decl_126, type, setadjoinSub2: $o).
114.24/15.04	thf(decl_127, type, subset2powerset: $o).
114.24/15.04	thf(decl_128, type, setextsub: $o).
114.24/15.04	thf(decl_129, type, subsetemptysetimpeq: $o).
114.24/15.04	thf(decl_130, type, powersetI1: $o).
114.24/15.04	thf(decl_131, type, powersetE1: $o).
114.24/15.04	thf(decl_132, type, inPowerset: $o).
114.24/15.04	thf(decl_133, type, powersetsubset: $o).
114.24/15.04	thf(decl_134, type, sepInPowerset: $o).
114.24/15.04	thf(decl_135, type, sepSubset: $o).
114.24/15.04	thf(decl_136, type, binunion: $i > $i > $i).
114.24/15.04	thf(decl_137, type, binunionIL: $o).
114.24/15.04	thf(decl_138, type, upairset2IR: $o).
114.24/15.04	thf(decl_139, type, binunionIR: $o).
114.24/15.04	thf(decl_140, type, binunionEcases: $o).
114.24/15.04	thf(decl_141, type, binunionE: $o).
114.24/15.04	thf(decl_142, type, binunionLsub: $o).
114.24/15.04	thf(decl_143, type, binunionRsub: $o).
114.24/15.04	thf(decl_144, type, binintersect: $i > $i > $i).
114.24/15.04	thf(decl_145, type, binintersectI: $o).
114.24/15.04	thf(decl_146, type, binintersectSubset5: $o).
114.24/15.04	thf(decl_147, type, binintersectEL: $o).
114.24/15.04	thf(decl_148, type, binintersectLsub: $o).
114.24/15.04	thf(decl_149, type, binintersectSubset2: $o).
114.24/15.04	thf(decl_150, type, binintersectSubset3: $o).
114.24/15.04	thf(decl_151, type, binintersectER: $o).
114.24/15.04	thf(decl_152, type, disjointsetsI1: $o).
114.24/15.04	thf(decl_153, type, binintersectRsub: $o).
114.24/15.04	thf(decl_154, type, binintersectSubset4: $o).
114.24/15.04	thf(decl_155, type, binintersectSubset1: $o).
114.24/15.04	thf(decl_156, type, bs114d: $o).
114.24/15.04	thf(decl_158, type, setminus: $i > $i > $i).
114.24/15.04	thf(decl_159, type, setminusI: $o).
114.24/15.04	thf(decl_160, type, setminusEL: $o).
114.24/15.04	thf(decl_161, type, setminusER: $o).
114.24/15.04	thf(decl_162, type, setminusSubset2: $o).
114.24/15.04	thf(decl_163, type, setminusERneg: $o).
114.24/15.04	thf(decl_164, type, setminusELneg: $o).
114.24/15.04	thf(decl_165, type, setminusILneg: $o).
114.24/15.04	thf(decl_166, type, setminusIRneg: $o).
114.24/15.04	thf(decl_167, type, setminusLsub: $o).
114.24/15.04	thf(decl_168, type, setminusSubset1: $o).
114.24/15.04	thf(decl_169, type, symdiff: $i > $i > $i).
114.24/15.04	thf(decl_170, type, symdiffE: $o).
114.24/15.04	thf(decl_171, type, symdiffI1: $o).
114.24/15.04	thf(decl_172, type, symdiffI2: $o).
114.24/15.04	thf(decl_173, type, symdiffIneg1: $o).
114.24/15.04	thf(decl_174, type, symdiffIneg2: $o).
114.24/15.04	thf(decl_175, type, iskpair: $i > $o).
114.24/15.04	thf(decl_176, type, secondinupair: $o).
114.24/15.04	thf(decl_177, type, setukpairIL: $o).
114.24/15.04	thf(decl_178, type, setukpairIR: $o).
114.24/15.04	thf(decl_179, type, kpairiskpair: $o).
114.24/15.04	thf(decl_180, type, kpair: $i > $i > $i).
114.24/15.04	thf(decl_181, type, kpairp: $o).
114.24/15.04	thf(decl_182, type, cartprod: $i > $i > $i).
114.24/15.04	thf(decl_183, type, singletonsubset: $o).
114.24/15.04	thf(decl_184, type, singletoninpowerset: $o).
114.24/15.04	thf(decl_185, type, singletoninpowunion: $o).
114.24/15.04	thf(decl_186, type, upairset2E: $o).
114.24/15.04	thf(decl_187, type, upairsubunion: $o).
114.24/15.04	thf(decl_188, type, upairinpowunion: $o).
114.24/15.04	thf(decl_189, type, ubforcartprodlem1: $o).
114.24/15.04	thf(decl_190, type, ubforcartprodlem2: $o).
114.24/15.04	thf(decl_191, type, ubforcartprodlem3: $o).
114.24/15.04	thf(decl_192, type, cartprodpairin: $o).
114.24/15.04	thf(decl_193, type, cartprodmempair1: $o).
114.24/15.04	thf(decl_194, type, cartprodmempair: $o).
114.24/15.04	thf(decl_195, type, setunionE2: $o).
114.24/15.04	thf(decl_196, type, setunionsingleton1: $o).
114.24/15.04	thf(decl_197, type, setunionsingleton2: $o).
114.24/15.04	thf(decl_198, type, setunionsingleton: $o).
114.24/15.04	thf(decl_199, type, singleton: $i > $o).
114.24/15.04	thf(decl_200, type, singletonprop: $o).
114.24/15.04	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
114.24/15.04	thf(decl_202, type, ex1E1: $o).
114.24/15.04	thf(decl_203, type, ex1I: $o).
114.24/15.04	thf(decl_204, type, ex1I2: $o).
114.24/15.04	thf(decl_205, type, singletonsuniq: $o).
114.24/15.04	thf(decl_210, type, setukpairinjL1: $o).
114.24/15.04	thf(decl_211, type, kfstsingleton: $o).
114.24/15.04	thf(decl_212, type, theprop: $o).
114.24/15.04	thf(decl_213, type, kfst: $i > $i).
114.24/15.04	thf(decl_214, type, kfstpairEq: $o).
114.24/15.04	thf(decl_215, type, cartprodfstin: $o).
114.24/15.04	thf(decl_216, type, setukpairinjL2: $o).
114.24/15.04	thf(decl_217, type, setukpairinjL: $o).
114.24/15.04	thf(decl_218, type, setukpairinjR11: $o).
114.24/15.04	thf(decl_219, type, setukpairinjR12: $o).
114.24/15.04	thf(decl_220, type, setukpairinjR1: $o).
114.24/15.04	thf(decl_221, type, upairequniteq: $o).
114.24/15.04	thf(decl_222, type, setukpairinjR2: $o).
114.24/15.04	thf(decl_223, type, setukpairinjR: $o).
114.24/15.04	thf(decl_224, type, ksndsingleton: $o).
114.24/15.04	thf(decl_225, type, ksnd: $i > $i).
114.24/15.04	thf(decl_226, type, ksndpairEq: $o).
114.24/15.04	thf(decl_227, type, kpairsurjEq: $o).
114.24/15.04	thf(decl_228, type, cartprodsndin: $o).
114.24/15.04	thf(decl_229, type, cartprodpairmemEL: $o).
114.24/15.04	thf(decl_230, type, cartprodpairmemER: $o).
114.24/15.04	thf(decl_231, type, cartprodmempaircEq: $o).
114.24/15.04	thf(decl_232, type, cartprodfstpairEq: $o).
114.24/15.04	thf(decl_233, type, cartprodsndpairEq: $o).
114.24/15.04	thf(decl_234, type, cartprodpairsurjEq: $o).
114.24/15.04	thf(decl_235, type, breln: $i > $i > $i > $o).
114.24/15.04	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
114.24/15.04	thf(decl_237, type, dpsetconstrI: $o).
114.24/15.04	thf(decl_238, type, dpsetconstrSub: $o).
114.24/15.04	thf(decl_239, type, setOfPairsIsBReln: $o).
114.24/15.04	thf(decl_240, type, dpsetconstrERa: $o).
114.24/15.04	thf(decl_241, type, dpsetconstrEL1: $o).
114.24/15.04	thf(decl_242, type, dpsetconstrEL2: $o).
114.24/15.04	thf(decl_243, type, dpsetconstrER: $o).
114.24/15.04	thf(decl_244, type, func: $i > $i > $i > $o).
114.24/15.04	thf(decl_245, type, funcSet: $i > $i > $i).
114.24/15.04	thf(decl_246, type, funcImageSingleton: $o).
114.24/15.04	thf(decl_247, type, apProp: $o).
114.24/15.04	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
114.24/15.04	thf(decl_249, type, app: $o).
114.24/15.04	thf(decl_250, type, infuncsetfunc: $o).
114.24/15.04	thf(decl_251, type, ap2p: $o).
114.24/15.04	thf(decl_252, type, funcinfuncset: $o).
114.24/15.04	thf(decl_253, type, lamProp: $o).
114.24/15.04	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
114.24/15.04	thf(decl_255, type, lamp: $o).
114.24/15.04	thf(decl_256, type, lam2p: $o).
114.24/15.04	thf(decl_257, type, brelnall1: $o).
114.24/15.04	thf(decl_258, type, brelnall2: $o).
114.24/15.04	thf(decl_259, type, ex1E2: $o).
114.24/15.04	thf(decl_260, type, funcGraphProp1: $o).
114.24/15.04	thf(decl_261, type, funcGraphProp3: $o).
114.24/15.04	thf(decl_262, type, funcGraphProp2: $o).
114.24/15.04	thf(decl_263, type, funcextLem: $o).
114.24/15.04	thf(decl_264, type, funcGraphProp4: $o).
114.24/15.04	thf(decl_265, type, subbreln: $o).
114.24/15.04	thf(decl_266, type, eqbreln: $o).
114.24/15.04	thf(decl_267, type, funcext: $o).
114.24/15.04	thf(decl_268, type, funcext2: $o).
114.24/15.04	thf(decl_269, type, ap2apEq1: $o).
114.24/15.04	thf(decl_270, type, ap2apEq2: $o).
114.24/15.04	thf(decl_271, type, beta1: $o).
114.24/15.04	thf(decl_272, type, eta1: $o).
114.24/15.04	thf(decl_273, type, lam2lamEq: $o).
114.24/15.04	thf(decl_274, type, beta2: $o).
114.24/15.04	thf(decl_275, type, eta2: $o).
114.24/15.04	thf(decl_276, type, iffalseProp1: $o).
114.24/15.04	thf(decl_277, type, iffalseProp2: $o).
114.24/15.04	thf(decl_278, type, iftrueProp1: $o).
114.24/15.04	thf(decl_279, type, iftrueProp2: $o).
114.24/15.04	thf(decl_280, type, ifSingleton: $o).
114.24/15.04	thf(decl_281, type, if: $i > $o > $i > $i > $i).
114.24/15.04	thf(decl_282, type, epred1_0: $o).
114.24/15.04	thf(decl_283, type, esk1_2: $i > $i > $i).
114.24/15.04	thf(decl_284, type, esk2_2: $i > $i > $i).
114.24/15.04	thf(decl_285, type, esk3_2: $i > $i > $i).
114.24/15.04	thf(decl_286, type, esk4_1: $i > $i).
114.24/15.04	thf(decl_287, type, esk5_2: ($i > $i > $o) > $i > $i).
114.24/15.04	thf(decl_288, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
114.24/15.04	thf(decl_289, type, esk7_2: ($i > $i > $o) > $i > $i).
114.24/15.04	thf(decl_290, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
114.24/15.04	thf(decl_291, type, esk9_1: $i > $i).
114.24/15.04	thf(decl_292, type, esk10_2: ($i > $o) > $i > $i).
114.24/15.04	thf(decl_293, type, esk11_2: ($i > $o) > $i > $i).
114.24/15.04	thf(decl_294, type, esk12_1: ($i > $o) > $i).
114.24/15.04	thf(decl_295, type, esk13_2: ($i > $o) > $i > $i).
114.24/15.04	thf(decl_296, type, esk14_1: ($i > $o) > $i).
114.24/15.04	thf(decl_297, type, esk15_2: $i > $i > $i).
114.24/15.04	thf(decl_298, type, esk16_2: $i > $i > $i).
114.24/15.04	thf(decl_299, type, esk17_1: $i > $i).
114.24/15.04	thf(decl_300, type, esk18_1: $i > $i).
114.24/15.04	thf(decl_301, type, esk19_1: $i > $i).
114.24/15.04	thf(decl_302, type, esk20_2: $i > $i > $i).
114.24/15.04	thf(decl_303, type, esk21_3: $i > $i > $o > $i).
114.24/15.04	thf(decl_304, type, esk22_2: ($i > $o) > $i > $i).
114.24/15.04	thf(decl_305, type, esk23_1: ($i > $o) > $i).
114.24/15.04	thf(decl_306, type, esk24_1: $i > $i).
114.24/15.04	thf(decl_307, type, esk25_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_308, type, esk26_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_309, type, esk27_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_310, type, esk28_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_311, type, esk29_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_312, type, esk30_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_313, type, esk31_2: ($i > $o) > $i > $i).
114.24/15.04	thf(decl_314, type, esk32_1: ($i > $o) > $i).
114.24/15.04	thf(decl_315, type, esk33_1: ($i > $o) > $i).
114.24/15.04	thf(decl_316, type, esk34_1: ($i > $o) > $i).
114.24/15.04	thf(decl_317, type, esk35_1: ($i > $o) > $i).
114.24/15.04	thf(decl_318, type, esk36_2: ($i > $o) > $i > $i).
114.24/15.04	thf(decl_319, type, esk37_1: ($i > $o) > $i).
114.24/15.04	thf(decl_320, type, esk38_2: ($i > $o) > $i > $i).
114.24/15.04	thf(decl_321, type, esk39_2: ($i > $o) > ($i > $o) > $i).
114.24/15.04	thf(decl_322, type, esk40_2: ($i > $o) > ($i > $o) > $i).
114.24/15.04	thf(decl_323, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
114.24/15.04	thf(decl_324, type, esk42_2: ($i > $o) > ($i > $o) > $i).
114.24/15.04	thf(decl_325, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
114.24/15.04	thf(decl_326, type, esk44_2: ($i > $o) > ($i > $o) > $i).
114.24/15.04	thf(decl_327, type, esk45_2: ($i > $o) > $i > $i).
114.24/15.04	thf(decl_328, type, esk46_2: ($i > $o) > ($i > $o) > $i).
114.24/15.04	thf(decl_329, type, esk47_2: ($i > $o) > ($i > $o) > $i).
114.24/15.04	thf(decl_330, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
114.24/15.04	thf(decl_331, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
114.24/15.04	thf(decl_332, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
114.24/15.04	thf(decl_333, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
114.24/15.04	thf(decl_334, type, esk52_2: $i > $i > $i).
114.24/15.04	thf(decl_335, type, esk53_2: $i > $i > $i).
114.24/15.04	thf(decl_336, type, esk54_2: $i > $i > $i).
114.24/15.04	thf(decl_337, type, esk55_3: $i > $i > $i > $i).
114.24/15.04	thf(decl_338, type, esk56_3: $i > $i > $i > $i).
114.24/15.04	thf(decl_339, type, esk57_2: $i > $i > $i).
114.24/15.04	thf(decl_340, type, esk58_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_341, type, esk59_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_342, type, esk60_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_343, type, esk61_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_344, type, esk62_3: $i > ($i > $o) > $i > $i).
114.24/15.04	thf(decl_345, type, esk63_3: $i > ($i > $o) > $i > $i).
114.24/15.04	thf(decl_346, type, esk64_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_347, type, esk65_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_348, type, esk66_2: $i > ($i > $o) > $i).
114.24/15.04	thf(decl_349, type, esk67_1: $i > $i).
114.24/15.04	thf(decl_350, type, esk68_1: $i > $i).
114.24/15.04	thf(decl_351, type, esk69_4: $i > $i > $i > $i > $i).
114.24/15.04	thf(decl_352, type, esk70_3: $i > $i > ($i > $i) > $i).
114.24/15.04	thf(decl_353, type, esk71_3: $i > $i > ($i > $i) > $i).
114.24/15.04	thf(decl_354, type, esk72_3: $i > $i > ($i > $i) > $i).
114.24/15.04	thf(decl_355, type, esk73_4: $i > $i > $i > ($i > $o) > $i).
114.24/15.04	thf(decl_356, type, esk74_4: $i > $i > $i > ($i > $o) > $i).
114.24/15.04	thf(decl_357, type, esk75_4: $i > $i > $i > ($i > $o) > $i).
114.24/15.04	thf(decl_358, type, esk76_4: $i > $i > $i > ($i > $o) > $i).
114.24/15.04	thf(decl_359, type, esk77_4: $i > $i > $i > $i > $i).
114.24/15.04	thf(decl_360, type, esk78_4: $i > $i > $i > $i > $i).
114.24/15.04	thf(decl_361, type, esk79_4: $i > $i > $i > $i > $i).
114.24/15.04	thf(decl_362, type, esk80_4: $i > $i > $i > $i > $i).
114.24/15.04	thf(decl_363, type, esk81_4: $i > $i > $i > $i > $i).
114.24/15.04	thf(decl_364, type, esk82_4: $i > $i > $i > $i > $i).
114.24/15.04	thf(decl_365, type, esk83_4: $i > $i > $i > $i > $i).
114.24/15.04	thf(decl_366, type, esk84_4: $i > $i > $i > $i > $i).
114.24/15.04	thf(decl_367, type, esk85_4: $i > $i > $i > $i > $i).
114.24/15.04	thf(decl_368, type, esk86_3: $i > $i > ($i > $i) > $i).
114.24/15.04	thf(decl_369, type, esk87_3: $i > $i > ($i > $i) > $i).
114.24/15.04	thf(decl_370, type, esk88_3: $i > $i > ($i > $i) > $i).
114.24/15.04	thf(decl_371, type, esk89_4: $i > $o > $i > $i > $i).
114.24/15.04	thf(decl_372, type, esk90_0: $i).
114.24/15.04	thf(decl_373, type, epred2_0: $o).
114.24/15.04	thf(decl_374, type, esk91_0: $i).
114.24/15.04	thf(decl_375, type, esk92_0: $i).
114.24/15.04	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ex1)).
114.24/15.04	thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', singleton)).
114.24/15.04	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', replAx)).
114.24/15.04	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', exu)).
114.24/15.04	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', descrp)).
114.24/15.04	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', exuE1)).
114.24/15.04	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', exuE3e)).
114.24/15.04	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', nonempty)).
114.24/15.04	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', nonemptyI)).
114.24/15.04	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', exuE2)).
114.24/15.04	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', exuI1)).
114.24/15.04	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', exuI3)).
114.24/15.04	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', exuI2)).
114.24/15.04	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', exuE3u)).
114.24/15.04	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', exu__Cong)).
114.24/15.04	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', exuEu)).
114.24/15.04	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', descr__Cong)).
114.24/15.04	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', singletonprop)).
114.24/15.04	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ex1E1)).
114.24/15.04	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ex1I)).
114.24/15.04	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ex1I2)).
114.24/15.04	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', kfstsingleton)).
114.24/15.04	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ksndsingleton)).
114.24/15.04	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setOfPairsIsBReln)).
114.24/15.04	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', breln)).
114.24/15.04	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', funcImageSingleton)).
114.24/15.04	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ex1E2)).
114.24/15.04	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ifSingleton)).
114.24/15.04	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', dsetconstrI)).
114.24/15.04	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', dsetconstrEL)).
114.24/15.04	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', dsetconstrER)).
114.24/15.04	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setbeta)).
114.24/15.04	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', nonemptyE1)).
114.24/15.04	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', nonemptyI1)).
114.24/15.04	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setoftrueEq)).
114.24/15.04	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', nonemptyImpWitness)).
114.24/15.04	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', emptyE1)).
114.24/15.04	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', dsetconstr__Cong)).
114.24/15.04	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', sepInPowerset)).
114.24/15.04	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', sepSubset)).
114.24/15.04	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', theprop)).
114.24/15.04	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', dpsetconstrI)).
114.24/15.04	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', dpsetconstrSub)).
114.24/15.04	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', dpsetconstrERa)).
114.24/15.04	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', dpsetconstrEL1)).
114.24/15.04	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', dpsetconstrEL2)).
114.24/15.04	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', dpsetconstrER)).
114.24/15.04	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', apProp)).
114.24/15.04	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', lamProp)).
114.24/15.04	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', lamp)).
114.24/15.04	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', lam2p)).
114.24/15.04	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', brelnall1)).
114.24/15.04	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', brelnall2)).
114.24/15.04	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', subbreln)).
114.24/15.04	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', eqbreln)).
114.24/15.04	thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', beta1)).
114.24/15.04	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', eta1)).
114.24/15.04	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', lam2lamEq)).
114.24/15.04	thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', beta2)).
114.24/15.04	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', eta2)).
114.24/15.04	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', iffalseProp1)).
114.24/15.04	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', iffalseProp2)).
114.24/15.04	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', iftrueProp1)).
114.24/15.04	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', iftrueProp2)).
114.24/15.04	thf(ifp, conjecture, ((setextAx)=>(((((((omegaSAx)=>((omegaIndAx)=>((((((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>(((emptyI)=>((noeltsimpempty)=>(((nonemptyE1)=>(((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>(((setadjoinOr)=>((setoftrueEq)=>((((emptyInPowerset)=>(((((((((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((((prop2setI)=>(((notdexE)=>(((exuI1)=>(((exuI2)=>(((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>(((exuEu)=>((((((eqimpsubset1)=>((subsetI2)=>(((subsetE)=>((subsetE2)=>((((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((((((((powersetE1)=>(((powersetsubset)=>(((sepSubset)=>((binunionIL)=>(((((binunionE)=>(((binunionRsub)=>((((((binintersectSubset2)=>((binintersectSubset3)=>(((disjointsetsI1)=>(((binintersectSubset4)=>(((((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((((((symdiffE)=>((symdiffI1)=>(((symdiffIneg1)=>((symdiffIneg2)=>((((setukpairIR)=>((kpairiskpair)=>(((((singletoninpowunion)=>((((((ubforcartprodlem2)=>(((((((setunionsingleton1)=>(((((((ex1I2)=>((singletonsuniq)=>(((kfstsingleton)=>((theprop)=>(((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((((((((ksndsingleton)=>(((kpairsurjEq)=>((cartprodsndin)=>((((((cartprodsndpairEq)=>((cartprodpairsurjEq)=>(((((dpsetconstrERa)=>(((dpsetconstrEL2)=>((dpsetconstrER)=>(((apProp)=>(((infuncsetfunc)=>(((((lamp)=>(((brelnall1)=>((brelnall2)=>(((funcGraphProp1)=>((((funcextLem)=>((funcGraphProp4)=>(((eqbreln)=>((((ap2apEq1)=>((((eta1)=>((lam2lamEq)=>(((eta2)=>((iffalseProp1)=>((((![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ (if @ X4 @ ((X45)) @ X2 @ X3) @ X4)<=(in @ X3 @ X4)))))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2))))<=(beta2))))<=(beta1))<=(ap2apEq2)))<=(funcext2))<=(funcext)))<=(subbreln))))<=(funcGraphProp2))<=(funcGraphProp3)))<=(ex1E2))))<=(lam2p)))<=(lamProp))<=(funcinfuncset))<=(ap2p)))<=(app)))<=(funcImageSingleton))))<=(dpsetconstrEL1)))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI))))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL))))<=(ksndpairEq)))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1))<=(setukpairinjR12))<=(setukpairinjR11)))))<=(kfstpairEq))))<=(setukpairinjL1))))<=(ex1I))<=(ex1E1))<=(singletonprop))<=(setunionsingleton))<=(setunionsingleton2)))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3)))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E)))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp))))<=(setukpairIL))<=(secondinupair))))<=(symdiffI2))))<=(setminusSubset1))<=(setminusLsub))<=(setminusIRneg))<=(setminusILneg)))))))<=(setminusI))<=(bs114d))<=(binintersectSubset1)))<=(binintersectRsub)))<=(binintersectER))))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR))<=(upairset2IR))))<=(sepInPowerset)))<=(inPowerset)))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset))<=(setadjoinSub2))<=(setadjoinSub)))))<=(notequalI1))<=(notsubsetI))))<=(emptysetsubset))))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong)))))))<=(exuE3u)))<=(inCongP)))<=(exuI3)))<=(notdallE)))<=(prop2set2propI)))<=(quantDeMorgan4))<=(quantDeMorgan3)))))))<=(upairsetIL))<=(upairsetE)))))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU))<=(setunionE))<=(setunionI))<=(powersetE)))<=(emptyinPowerset))<=(powersetI))))<=(setadjoinE))))))<=(nonemptyI)))<=(setbeta))))<=(setext)))))<=(emptysetE))<=(prop2setE))))))<=(descrp))<=(wellorderingAx))<=(foundationAx))<=(replAx))))<=(omega0Ax))<=(setunionAx))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ifp)).
114.24/15.04	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setextAx)).
114.24/15.04	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', emptysetAx)).
114.24/15.04	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setadjoinAx)).
114.24/15.04	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', powersetAx)).
114.24/15.04	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setunionAx)).
114.24/15.04	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', omega0Ax)).
114.24/15.04	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', omegaSAx)).
114.24/15.04	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', omegaIndAx)).
114.24/15.04	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', foundationAx)).
114.24/15.04	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', wellorderingAx)).
114.24/15.04	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', prop2setE)).
114.24/15.04	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', emptysetE)).
114.24/15.04	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', emptysetimpfalse)).
114.24/15.04	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', notinemptyset)).
114.24/15.04	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setext)).
114.24/15.04	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', emptyI)).
114.24/15.04	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', noeltsimpempty)).
114.24/15.04	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setadjoinIL)).
114.24/15.04	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', emptyinunitempty)).
114.24/15.04	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setadjoinIR)).
114.24/15.04	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setadjoinE)).
114.24/15.04	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setadjoinOr)).
114.24/15.04	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', powersetI)).
114.24/15.04	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', emptyinPowerset)).
114.24/15.04	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', emptyInPowerset)).
114.24/15.04	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', powersetE)).
114.24/15.04	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setunionI)).
114.24/15.04	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setunionE)).
114.24/15.04	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', subPowSU)).
114.24/15.04	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', uniqinunit)).
114.24/15.04	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', notinsingleton)).
114.24/15.04	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', eqinunit)).
114.24/15.04	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', singletonsswitch)).
114.24/15.04	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', upairsetE)).
114.24/15.04	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', upairsetIL)).
114.24/15.04	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', upairsetIR)).
114.24/15.04	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', vacuousDall)).
114.24/15.04	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', quantDeMorgan1)).
114.24/15.04	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', quantDeMorgan2)).
114.24/15.04	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', quantDeMorgan3)).
114.24/15.04	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', quantDeMorgan4)).
114.24/15.04	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', prop2setI)).
114.24/15.04	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', prop2set2propI)).
114.24/15.04	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', notdexE)).
114.24/15.04	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', notdallE)).
114.24/15.04	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', inCongP)).
114.24/15.04	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', in__Cong)).
114.24/15.04	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', emptyset__Cong)).
114.24/15.04	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setadjoin__Cong)).
114.24/15.04	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', powerset__Cong)).
114.24/15.04	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setunion__Cong)).
114.24/15.04	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', omega__Cong)).
114.24/15.04	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', subsetI1)).
114.24/15.04	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', eqimpsubset2)).
114.24/15.04	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', eqimpsubset1)).
114.24/15.04	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', subsetI2)).
114.24/15.04	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', emptysetsubset)).
114.24/15.04	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', subsetE)).
114.24/15.04	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', subsetE2)).
114.24/15.04	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', notsubsetI)).
114.24/15.04	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', notequalI1)).
114.24/15.04	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', notequalI2)).
114.24/15.04	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', subsetRefl)).
114.24/15.04	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', subsetTrans)).
114.24/15.04	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setadjoinSub)).
114.24/15.04	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setadjoinSub2)).
114.24/15.04	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', subset2powerset)).
114.24/15.04	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setextsub)).
114.24/15.04	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', subsetemptysetimpeq)).
114.24/15.04	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', powersetI1)).
114.24/15.04	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', powersetE1)).
114.24/15.04	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', inPowerset)).
114.24/15.04	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', powersetsubset)).
114.24/15.04	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binunionIL)).
114.24/15.04	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', upairset2IR)).
114.24/15.04	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binunionIR)).
114.24/15.04	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binunionEcases)).
114.24/15.04	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binunionE)).
114.24/15.04	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binunionLsub)).
114.24/15.04	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binunionRsub)).
114.24/15.04	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binintersectI)).
114.24/15.04	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binintersectSubset5)).
114.24/15.04	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binintersectEL)).
114.24/15.04	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binintersectLsub)).
114.24/15.04	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binintersectSubset2)).
114.24/15.04	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binintersectSubset3)).
114.24/15.04	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binintersectER)).
114.24/15.04	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', disjointsetsI1)).
114.24/15.04	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binintersectRsub)).
114.24/15.04	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binintersectSubset4)).
114.24/15.04	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', binintersectSubset1)).
114.24/15.04	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', bs114d)).
114.24/15.04	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setminusI)).
114.24/15.04	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setminusEL)).
114.24/15.04	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setminusER)).
114.24/15.04	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setminusSubset2)).
114.24/15.04	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setminusERneg)).
114.24/15.04	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setminusELneg)).
114.24/15.04	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setminusILneg)).
114.24/15.04	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setminusIRneg)).
114.24/15.04	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setminusLsub)).
114.24/15.04	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setminusSubset1)).
114.24/15.04	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', symdiffE)).
114.24/15.04	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', symdiffI1)).
114.24/15.04	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', symdiffI2)).
114.24/15.04	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', symdiffIneg1)).
114.24/15.04	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', symdiffIneg2)).
114.24/15.04	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', secondinupair)).
114.24/15.04	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setukpairIL)).
114.24/15.04	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setukpairIR)).
114.24/15.04	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', kpairiskpair)).
114.24/15.04	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', kpairp)).
114.24/15.04	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', singletonsubset)).
114.24/15.04	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', singletoninpowerset)).
114.24/15.04	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', singletoninpowunion)).
114.24/15.04	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', upairset2E)).
114.24/15.04	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', upairsubunion)).
114.24/15.04	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', upairinpowunion)).
114.24/15.04	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ubforcartprodlem1)).
114.24/15.04	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ubforcartprodlem2)).
114.24/15.04	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ubforcartprodlem3)).
114.24/15.04	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', cartprodpairin)).
114.24/15.04	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', cartprodmempair1)).
114.24/15.04	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', cartprodmempair)).
114.24/15.04	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setunionE2)).
114.24/15.04	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setunionsingleton1)).
114.24/15.04	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setunionsingleton2)).
114.24/15.04	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setunionsingleton)).
114.24/15.04	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', singletonsuniq)).
114.24/15.04	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setukpairinjL1)).
114.24/15.04	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', kfstpairEq)).
114.24/15.04	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', cartprodfstin)).
114.24/15.04	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setukpairinjL2)).
114.24/15.04	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setukpairinjL)).
114.24/15.04	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setukpairinjR11)).
114.24/15.04	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setukpairinjR12)).
114.24/15.04	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setukpairinjR1)).
114.24/15.04	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', upairequniteq)).
114.24/15.04	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setukpairinjR2)).
114.24/15.04	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', setukpairinjR)).
114.24/15.04	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ksndpairEq)).
114.24/15.04	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', kpairsurjEq)).
114.24/15.04	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', cartprodsndin)).
114.24/15.04	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', cartprodpairmemEL)).
114.24/15.04	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', cartprodpairmemER)).
114.24/15.04	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', cartprodmempaircEq)).
114.24/15.04	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', cartprodfstpairEq)).
114.24/15.04	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', cartprodsndpairEq)).
114.24/15.04	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', cartprodpairsurjEq)).
114.24/15.04	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', app)).
114.24/15.04	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', infuncsetfunc)).
114.24/15.04	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ap2p)).
114.24/15.04	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', funcinfuncset)).
114.24/15.04	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', funcGraphProp1)).
114.24/15.04	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', funcGraphProp3)).
114.24/15.04	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', funcGraphProp2)).
114.24/15.04	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', funcextLem)).
114.24/15.04	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', funcGraphProp4)).
114.24/15.04	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', funcext)).
114.24/15.04	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', funcext2)).
114.24/15.04	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ap2apEq1)).
114.24/15.04	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', ap2apEq2)).
114.24/15.04	thf(if, axiom, ((if)=(^[X4:$i, X44:$o, X2:$i, X3:$i]:(setunion @ (dsetconstr @ X4 @ (^[X14:$i]:((((X44)&((X14)=(X2)))|(~((X44))&((X14)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ccYajnxPJb/E---3.1_15019.p', if)).
114.24/15.04	thf(c_0_228, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X757:$i]:(((in @ X757 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X757 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
114.24/15.04	thf(c_0_229, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
114.24/15.04	thf(c_0_230, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
114.24/15.04	thf(c_0_231, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
114.24/15.04	thf(c_0_232, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
114.24/15.04	thf(c_0_233, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
114.24/15.04	thf(c_0_234, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
114.24/15.04	thf(c_0_235, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
114.24/15.04	thf(c_0_236, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
114.24/15.04	thf(c_0_237, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
114.24/15.04	thf(c_0_238, 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])).
114.24/15.04	thf(c_0_239, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
114.24/15.04	thf(c_0_240, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
114.24/15.04	thf(c_0_241, 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])).
114.24/15.04	thf(c_0_242, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
114.24/15.04	thf(c_0_243, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
114.24/15.04	thf(c_0_244, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
114.24/15.04	thf(c_0_245, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
114.24/15.04	thf(c_0_246, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
114.24/15.04	thf(c_0_247, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X757:$i]:(((in @ X757 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X757 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_229])).
114.24/15.04	thf(c_0_248, 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])).
114.24/15.04	thf(c_0_249, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
114.24/15.04	thf(c_0_250, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
114.24/15.04	thf(c_0_251, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
114.24/15.04	thf(c_0_252, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
114.24/15.04	thf(c_0_253, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
114.24/15.04	thf(c_0_254, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
114.24/15.04	thf(c_0_255, plain, ((ex1E2)<=>![X4:$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])).
114.24/15.04	thf(c_0_256, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
114.24/15.04	thf(c_0_257, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X728:$i]:((((X6 @ X2 @ X728))&![X729:$i]:((((X6 @ X2 @ X729))=>((X728)=(X729)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_231])).
114.24/15.04	thf(c_0_258, plain, ((descrp)=(![X1:$i > $o]:(((?[X730:$i]:((((X1 @ X730))&![X731:$i]:((((X1 @ X731))=>((X730)=(X731)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_231])).
114.24/15.04	thf(c_0_259, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
114.24/15.04	thf(c_0_260, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
114.24/15.04	thf(c_0_261, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
114.24/15.04	thf(c_0_262, plain, ((exuE1)=(![X1:$i > $o]:(((?[X732:$i]:((((X1 @ X732))&![X733:$i]:((((X1 @ X733))=>((X732)=(X733)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_231])).
114.24/15.04	thf(c_0_263, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X734:$i]:((((X1 @ X734))&![X735:$i]:((((X1 @ X735))=>((X734)=(X735)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_234, c_0_231])).
114.24/15.04	thf(c_0_264, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
114.24/15.04	thf(c_0_265, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_235])).
114.24/15.04	thf(c_0_266, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_235])).
114.24/15.04	thf(c_0_267, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_235])).
114.24/15.04	thf(c_0_268, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
114.24/15.04	thf(c_0_269, plain, ((exuE2)=(![X1:$i > $o]:(((?[X736:$i]:((((X1 @ X736))&![X737:$i]:((((X1 @ X737))=>((X736)=(X737)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_231])).
114.24/15.04	thf(c_0_270, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_235])).
114.24/15.04	thf(c_0_271, 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])).
114.24/15.04	thf(c_0_272, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X738:$i]:((((X1 @ X738))&![X739:$i]:((((X1 @ X739))=>((X738)=(X739))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_231])).
114.24/15.04	thf(c_0_273, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X740:$i]:((((X1 @ X740))&![X741:$i]:((((X1 @ X741))=>((X740)=(X741)))))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_231])).
114.24/15.04	thf(c_0_274, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X742:$i]:((((X1 @ X742))&![X743:$i]:((((X1 @ X743))=>((X742)=(X743))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_231])).
114.24/15.04	thf(c_0_275, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X744:$i]:((((X1 @ X744))&![X745:$i]:((((X1 @ X745))=>((X744)=(X745)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_231])).
114.24/15.04	thf(c_0_276, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X746:$i]:((((X1 @ X746))&![X747:$i]:((((X1 @ X747))=>((X746)=(X747)))))))<=>(?[X748:$i]:((((X17 @ X748))&![X749:$i]:((((X17 @ X749))=>((X748)=(X749)))))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_231])).
114.24/15.04	thf(c_0_277, plain, ((exuEu)=(![X1:$i > $o]:(((?[X750:$i]:((((X1 @ X750))&![X751:$i]:((((X1 @ X751))=>((X750)=(X751)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_231])).
114.24/15.04	thf(c_0_278, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X752:$i]:((((X1 @ X752))&![X753:$i]:((((X1 @ X753))=>((X752)=(X753)))))))=>((?[X754:$i]:((((X17 @ X754))&![X755:$i]:((((X17 @ X755))=>((X754)=(X755)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_231])).
114.24/15.04	thf(c_0_279, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
114.24/15.04	thf(c_0_280, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
114.24/15.04	thf(c_0_281, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
114.24/15.04	thf(c_0_282, 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)))=>(?[X756:$i]:(((in @ X756 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X756 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_229])).
114.24/15.04	thf(c_0_283, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X758:$i]:(((in @ X758 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X758 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_247])).
114.24/15.04	thf(c_0_284, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X759:$i]:(((in @ X759 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X759 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_248, c_0_247])).
114.24/15.04	thf(c_0_285, 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)))=>(?[X760:$i]:(((in @ X760 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X760 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_249, c_0_247])).
114.24/15.04	thf(c_0_286, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X761:$i]:(((in @ X761 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X761 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_250, c_0_229])).
114.24/15.04	thf(c_0_287, axiom, ((theprop)=(![X21:$i]:(((?[X762:$i]:(((in @ X762 @ X21)&((X21)=(setadjoin @ X762 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_229])).
114.24/15.04	thf(c_0_288, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X763:$i]:(((in @ X763 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X763 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_251, c_0_229])).
114.24/15.04	thf(c_0_289, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
114.24/15.04	thf(c_0_290, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
114.24/15.04	thf(c_0_291, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_252, c_0_253])).
114.24/15.04	thf(c_0_292, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
114.24/15.04	thf(c_0_293, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
114.24/15.04	thf(c_0_294, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
114.24/15.04	thf(c_0_295, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
114.24/15.04	thf(c_0_296, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(?[X764:$i]:(((in @ X764 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X764 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_254, c_0_229])).
114.24/15.04	thf(c_0_297, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
114.24/15.04	thf(c_0_298, plain, ((lamProp)<=>![X4:$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])).
114.24/15.04	thf(c_0_299, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
114.24/15.04	thf(c_0_300, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
114.24/15.04	thf(c_0_301, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_253])).
114.24/15.04	thf(c_0_302, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_253])).
114.24/15.04	thf(c_0_303, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((?[X765:$i]:(((in @ X765 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X765 @ emptyset)))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_255, c_0_247])).
114.24/15.04	thf(c_0_304, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_253])).
114.24/15.04	thf(c_0_305, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_253])).
114.24/15.04	thf(c_0_306, 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])).
114.24/15.04	thf(c_0_307, 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])).
114.24/15.04	thf(c_0_308, 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])).
114.24/15.04	thf(c_0_309, 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])).
114.24/15.04	thf(c_0_310, 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])).
114.24/15.04	thf(c_0_311, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
114.24/15.04	thf(c_0_312, plain, ((iffalseProp2)<=>![X4:$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])).
114.24/15.04	thf(c_0_313, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
114.24/15.04	thf(c_0_314, plain, ((iftrueProp2)<=>![X4:$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])).
114.24/15.04	thf(c_0_315, plain, ((ifSingleton)=(![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(?[X766:$i]:(((in @ X766 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))&((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3)))))))=(setadjoin @ X766 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_256, c_0_229])).
114.24/15.04	thf(c_0_316, plain, ((epred1_0)<=>![X1442:$i]:(?[X1443:$i]:((((![X1444:$i]:(((in @ X1444 @ X1443)=>![X1445:$i]:(((in @ X1445 @ X1444)=>(in @ X1445 @ X1442)))))&![X1446:$i, X1447:$i]:((((in @ X1446 @ X1442)&(in @ X1447 @ X1442))=>(![X1448:$i]:(((in @ X1448 @ X1443)=>((in @ X1446 @ X1448)<=>(in @ X1447 @ X1448))))=>((X1446)=(X1447))))))&![X1449:$i, X1450:$i]:((((in @ X1449 @ X1443)&(in @ X1450 @ X1443))=>(![X1451:$i]:(((in @ X1451 @ X1449)=>(in @ X1451 @ X1450)))|![X1452:$i]:(((in @ X1452 @ X1450)=>(in @ X1452 @ X1449)))))))&![X1453:$i]:(((![X1454:$i]:(((in @ X1454 @ X1453)=>(in @ X1454 @ X1442)))&?[X1455:$i]:((in @ X1455 @ X1453)))=>?[X1456:$i, X1457:$i]:(((((in @ X1456 @ X1443)&(in @ X1457 @ X1453))&~(?[X1458:$i]:(((in @ X1458 @ X1456)&(in @ X1458 @ X1453)))))&![X1459:$i]:(((in @ X1459 @ X1443)=>(![X1460:$i]:(((in @ X1460 @ X1459)=>(in @ X1460 @ X1456)))|(in @ X1457 @ X1459)))))))))))), introduced(definition)).
114.24/15.04	thf(c_0_317, negated_conjecture, ~((![X767:$i, X768:$i]:((![X769:$i]:(((in @ X769 @ X767)<=>(in @ X769 @ X768)))=>((X767)=(X768))))=>(![X1482:$i]:(~(in @ X1482 @ emptyset))=>(![X1479:$i, X1480:$i, X1481:$i]:(((in @ X1481 @ (setadjoin @ X1479 @ X1480))<=>(((X1481)=(X1479))|(in @ X1481 @ X1480))))=>(![X1476:$i, X1477:$i]:(((in @ X1477 @ (powerset @ X1476))<=>![X1478:$i]:(((in @ X1478 @ X1477)=>(in @ X1478 @ X1476)))))=>(![X1473:$i, X1474:$i]:(((in @ X1474 @ (setunion @ X1473))<=>?[X1475:$i]:(((in @ X1474 @ X1475)&(in @ X1475 @ X1473)))))=>((in @ emptyset @ omega)=>(![X770:$i]:(((in @ X770 @ omega)=>(in @ (setadjoin @ X770 @ X770) @ omega)))=>(![X771:$i]:((((in @ emptyset @ X771)&![X772:$i]:((((in @ X772 @ omega)&(in @ X772 @ X771))=>(in @ (setadjoin @ X772 @ X772) @ X771))))=>![X773:$i]:(((in @ X773 @ omega)=>(in @ X773 @ X771)))))=>(![X1465:$i > $i > $o, X1466:$i]:((![X1467:$i]:(((in @ X1467 @ X1466)=>?[X1468:$i]:(((X1465 @ X1467 @ X1468)&![X1469:$i]:(((X1465 @ X1467 @ X1469)=>((X1468)=(X1469))))))))=>?[X1470:$i]:(![X1471:$i]:(((in @ X1471 @ X1470)<=>?[X1472:$i]:(((in @ X1472 @ X1466)&(X1465 @ X1472 @ X1471))))))))=>(![X1461:$i]:((?[X1462:$i]:((in @ X1462 @ X1461))=>?[X1463:$i]:(((in @ X1463 @ X1461)&~(?[X1464:$i]:(((in @ X1464 @ X1463)&(in @ X1464 @ X1461))))))))=>((epred1_0)=>(![X1439:$i > $o]:((?[X1440:$i]:(((X1439 @ X1440)&![X1441:$i]:(((X1439 @ X1441)=>((X1440)=(X1441))))))=>(X1439 @ (descr @ (^[Z0/* 17 */:$i]:(X1439 @ Z0))))))=>(![X774:$i, X775:$i > $o, X776:$i]:(((in @ X776 @ X774)=>((X775 @ X776)=>(in @ X776 @ (dsetconstr @ X774 @ X775)))))=>(![X777:$i, X778:$i > $o, X779:$i]:(((in @ X779 @ (dsetconstr @ X777 @ X778))=>(in @ X779 @ X777)))=>(![X780:$i, X781:$i > $o, X782:$i]:(((in @ X782 @ (dsetconstr @ X780 @ X781))=>(X781 @ X782)))=>(![X783:$i > $o]:((?[X784:$i]:(((X783 @ X784)&![X785:$i]:(((X783 @ X785)=>((X784)=(X785))))))=>?[X786:$i]:(((X783 @ X786)&![X787:$i]:(((X783 @ X787)=>((X786)=(X787))))))))=>(![X1437:$o, X1438:$i]:(((in @ X1438 @ (prop2set @ ((X1437))))=>(X1437)))=>(![X1435:$i]:(((in @ X1435 @ emptyset)=>![X1436:$o]:((X1436))))=>(![X788:$i]:(((in @ X788 @ emptyset)=>~($true)))=>(![X789:$i]:(~(in @ X789 @ emptyset))=>(![X790:$i > $o]:((?[X791:$i]:(((X790 @ X791)&![X792:$i]:(((X790 @ X792)=>((X791)=(X792))))))=>?[X793:$i]:((X790 @ X793))))=>(![X1431:$i, X1432:$i]:((![X1433:$i]:(((in @ X1433 @ X1431)=>(in @ X1433 @ X1432)))=>(![X1434:$i]:(((in @ X1434 @ X1432)=>(in @ X1434 @ X1431)))=>((X1431)=(X1432)))))=>(![X794:$i]:((![X795:$i]:(~(in @ X795 @ X794))=>((X794)=(emptyset))))=>(![X796:$i]:((![X797:$i]:(~(in @ X797 @ X796))=>((X796)=(emptyset))))=>(![X1428:$i, X1429:$i > $o, X1430:$i]:(((in @ X1430 @ X1428)=>((in @ X1430 @ (dsetconstr @ X1428 @ X1429))<=>(X1429 @ X1430))))=>(![X798:$i]:((((X798)!=(emptyset))=>?[X799:$i]:((in @ X799 @ X798))))=>(![X1425:$i, X1426:$i > $o, X1427:$i]:(((in @ X1427 @ X1425)=>((X1426 @ X1427)=>((dsetconstr @ X1425 @ X1426)!=(emptyset)))))=>(![X800:$i]:((?[X801:$i]:((in @ X801 @ X800))=>((X800)!=(emptyset))))=>(![X802:$i, X803:$i]:((in @ X802 @ (setadjoin @ X802 @ X803)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X804:$i, X805:$i, X806:$i]:(((in @ X806 @ X805)=>(in @ X806 @ (setadjoin @ X804 @ X805))))=>(![X1421:$i, X1422:$i, X1423:$i]:(((in @ X1423 @ (setadjoin @ X1421 @ X1422))=>![X1424:$o]:(((((X1423)=(X1421))=>(X1424))=>(((in @ X1423 @ X1422)=>(X1424))=>(X1424))))))=>(![X807:$i, X808:$i, X809:$i]:(((in @ X809 @ (setadjoin @ X807 @ X808))=>(((X809)=(X807))|(in @ X809 @ X808))))=>(![X810:$i]:(((dsetconstr @ X810 @ (^[Z0/* 1 */:$i]:($true)))=(X810)))=>(![X1418:$i, X1419:$i]:((![X1420:$i]:(((in @ X1420 @ X1419)=>(in @ X1420 @ X1418)))=>(in @ X1419 @ (powerset @ X1418))))=>(![X1417:$i]:((in @ emptyset @ (powerset @ X1417)))=>(![X811:$i]:((in @ emptyset @ (powerset @ X811)))=>(![X1414:$i, X1415:$i, X1416:$i]:(((in @ X1415 @ (powerset @ X1414))=>((in @ X1416 @ X1415)=>(in @ X1416 @ X1414))))=>(![X1411:$i, X1412:$i, X1413:$i]:(((in @ X1412 @ X1413)=>((in @ X1413 @ X1411)=>(in @ X1412 @ (setunion @ X1411)))))=>(![X1407:$i, X1408:$i]:(((in @ X1408 @ (setunion @ X1407))=>![X1409:$o]:((![X1410:$i]:(((in @ X1408 @ X1410)=>((in @ X1410 @ X1407)=>(X1409))))=>(X1409)))))=>(![X1405:$i, X1406:$i]:(((in @ X1406 @ X1405)=>(in @ X1406 @ (powerset @ (setunion @ X1405)))))=>(![X1400:$i > $o]:((?[X1401:$i]:(((X1400 @ X1401)&![X1402:$i]:(((X1400 @ X1402)=>((X1401)=(X1402))))))=>?[X1403:$i]:(![X1404:$i]:(((X1400 @ X1404)<=>((X1404)=(X1403)))))))=>(![X1398:$i]:((((X1398)!=(emptyset))=>?[X1399:$i]:(((in @ X1399 @ X1398)&$true))))=>(![X1396:$i, X1397:$i]:(((in @ X1396 @ (setadjoin @ X1397 @ emptyset))=>((X1396)=(X1397))))=>(![X812:$i, X813:$i]:((((X812)!=(X813))=>~(in @ X813 @ (setadjoin @ X812 @ emptyset))))=>(![X814:$i, X815:$i]:((((X814)=(X815))=>(in @ X814 @ (setadjoin @ X815 @ emptyset))))=>(![X816:$i, X817:$i]:(((in @ X816 @ (setadjoin @ X817 @ emptyset))=>(in @ X817 @ (setadjoin @ X816 @ emptyset))))=>(![X1393:$i, X1394:$i, X1395:$i]:(((in @ X1395 @ (setadjoin @ X1393 @ (setadjoin @ X1394 @ emptyset)))=>(((X1395)=(X1393))|((X1395)=(X1394)))))=>(![X1391:$i, X1392:$i]:((in @ X1391 @ (setadjoin @ X1391 @ (setadjoin @ X1392 @ emptyset))))=>(![X818:$i, X819:$i]:((in @ X819 @ (setadjoin @ X818 @ (setadjoin @ X819 @ emptyset))))=>(![X820:$i, X821:$i > $o]:((?[X822:$i]:(((in @ X822 @ X820)&(X821 @ X822)))=>(((dsetconstr @ X820 @ X821)=(emptyset))=>~($true))))=>(![X823:$i > $o, X824:$i]:(((in @ X824 @ emptyset)=>(X823 @ X824)))=>(![X825:$i, X826:$i > $o]:((~(![X827:$i]:(((in @ X827 @ X825)=>(X826 @ X827))))=>?[X828:$i]:(((in @ X828 @ X825)&~((X826 @ X828))))))=>(![X829:$i, X830:$i > $o]:((![X831:$i]:(((in @ X831 @ X829)=>~((X830 @ X831))))=>~(?[X832:$i]:(((in @ X832 @ X829)&(X830 @ X832))))))=>(![X1387:$i, X1388:$i > $o]:((~(?[X1389:$i]:(((in @ X1389 @ X1387)&(X1388 @ X1389))))=>![X1390:$i]:(((in @ X1390 @ X1387)=>~((X1388 @ X1390))))))=>(![X1383:$i, X1384:$i > $o]:((?[X1385:$i]:(((in @ X1385 @ X1383)&~((X1384 @ X1385))))=>~(![X1386:$i]:(((in @ X1386 @ X1383)=>(X1384 @ X1386))))))=>(![X833:$o]:(((X833)=>(in @ emptyset @ (prop2set @ ((X833))))))=>(![X1382:$o]:(((X1382)=>(set2prop @ (prop2set @ ((X1382))))))=>(![X834:$i, X835:$i > $o]:((~(?[X836:$i]:(((in @ X836 @ X834)&(X835 @ X836))))=>![X837:$i]:(((in @ X837 @ X834)=>~((X835 @ X837))))))=>(![X1378:$i, X1379:$i > $o]:((~(![X1380:$i]:(((in @ X1380 @ X1378)=>(X1379 @ X1380))))=>?[X1381:$i]:(((in @ X1381 @ X1378)&~((X1379 @ X1381))))))=>(![X838:$i > $o]:((?[X839:$i]:(((X838 @ X839)&![X840:$i]:(((X838 @ X840)=>((X839)=(X840))))))=>?[X841:$i]:(((X838 @ X841)&![X842:$i]:(((X838 @ X842)=>((X841)=(X842))))))))=>(![X1372:$i > $o]:((?[X1373:$i]:((X1372 @ X1373))=>(![X1374:$i, X1375:$i]:(((X1372 @ X1374)=>((X1372 @ X1375)=>((X1374)=(X1375)))))=>?[X1376:$i]:(((X1372 @ X1376)&![X1377:$i]:(((X1372 @ X1377)=>((X1376)=(X1377)))))))))=>(![X843:$i > $o]:((?[X844:$i]:(![X845:$i]:(((X843 @ X845)<=>((X845)=(X844)))))=>?[X846:$i]:(((X843 @ X846)&![X847:$i]:(((X843 @ X847)=>((X846)=(X847))))))))=>(![X1368:$i, X1369:$i]:((((X1368)=(X1369))=>![X1370:$i, X1371:$i]:((((X1370)=(X1371))=>((in @ X1370 @ X1368)=>(in @ X1371 @ X1369))))))=>(![X848:$i, X849:$i]:((((X848)=(X849))=>![X850:$i, X851:$i]:((((X850)=(X851))=>((in @ X850 @ X848)<=>(in @ X851 @ X849))))))=>(![X1363:$i > $o]:((?[X1364:$i]:(((X1363 @ X1364)&![X1365:$i]:(((X1363 @ X1365)=>((X1364)=(X1365))))))=>![X1366:$i, X1367:$i]:(((X1363 @ X1366)=>((X1363 @ X1367)=>((X1366)=(X1367)))))))=>(![X852:$i > $o, X853:$i > $o]:((![X854:$i, X855:$i]:((((X854)=(X855))=>((X852 @ X854)<=>(X853 @ X855))))=>(?[X856:$i]:(((X852 @ X856)&![X857:$i]:(((X852 @ X857)=>((X856)=(X857))))))<=>?[X858:$i]:(((X853 @ X858)&![X859:$i]:(((X853 @ X859)=>((X858)=(X859)))))))))=>(((emptyset)=(emptyset))=>(![X860:$i, X861:$i]:((((X860)=(X861))=>![X862:$i, X863:$i]:((((X862)=(X863))=>((setadjoin @ X860 @ X862)=(setadjoin @ X861 @ X863))))))=>(![X864:$i, X865:$i]:((((X864)=(X865))=>((powerset @ X864)=(powerset @ X865))))=>(![X866:$i, X867:$i]:((((X866)=(X867))=>((setunion @ X866)=(setunion @ X867))))=>(((omega)=(omega))=>(![X868:$i > $o]:((?[X869:$i]:(((X868 @ X869)&![X870:$i]:(((X868 @ X870)=>((X869)=(X870))))))=>![X871:$i, X872:$i]:(((X868 @ X871)=>((X868 @ X872)=>((X871)=(X872)))))))=>(![X1355:$i > $o, X1356:$i > $o]:((![X1357:$i, X1358:$i]:((((X1357)=(X1358))=>((X1355 @ X1357)<=>(X1356 @ X1358))))=>(?[X1359:$i]:(((X1355 @ X1359)&![X1360:$i]:(((X1355 @ X1360)=>((X1359)=(X1360))))))=>(?[X1361:$i]:(((X1356 @ X1361)&![X1362:$i]:(((X1356 @ X1362)=>((X1361)=(X1362))))))=>((descr @ X1355)=(descr @ X1356))))))=>(![X1349:$i, X1350:$i]:((((X1349)=(X1350))=>![X1351:$i > $o, X1352:$i > $o]:((![X1353:$i]:(((in @ X1353 @ X1349)=>![X1354:$i]:(((in @ X1354 @ X1350)=>(((X1353)=(X1354))=>((X1351 @ X1353)<=>(X1352 @ X1354)))))))=>((dsetconstr @ X1349 @ X1351)=(dsetconstr @ X1350 @ X1352))))))=>(![X1346:$i, X1347:$i]:((![X1348:$i]:(((in @ X1348 @ X1346)=>(in @ X1348 @ X1347)))=>(subset @ X1346 @ X1347)))=>(![X1344:$i, X1345:$i]:((((X1344)=(X1345))=>(subset @ X1345 @ X1344)))=>(![X873:$i, X874:$i]:((((X873)=(X874))=>(subset @ X873 @ X874)))=>(![X875:$i, X876:$i]:((![X877:$i]:(((in @ X877 @ X875)=>(in @ X877 @ X876)))=>(subset @ X875 @ X876)))=>(![X1343:$i]:((subset @ emptyset @ X1343))=>(![X878:$i, X879:$i, X880:$i]:(((subset @ X878 @ X879)=>((in @ X880 @ X878)=>(in @ X880 @ X879))))=>(![X881:$i, X882:$i, X883:$i]:(((subset @ X881 @ X882)=>(~(in @ X883 @ X882)=>~(in @ X883 @ X881))))=>(![X1340:$i, X1341:$i, X1342:$i]:(((in @ X1342 @ X1340)=>(~(in @ X1342 @ X1341)=>~(subset @ X1340 @ X1341))))=>(![X1338:$i, X1339:$i]:((~(subset @ X1338 @ X1339)=>((X1338)!=(X1339))))=>(![X884:$i, X885:$i, X886:$i]:(((in @ X886 @ X884)=>(~(in @ X886 @ X885)=>((X884)!=(X885)))))=>(![X887:$i]:((subset @ X887 @ X887))=>(![X888:$i, X889:$i, X890:$i]:(((subset @ X888 @ X889)=>((subset @ X889 @ X890)=>(subset @ X888 @ X890))))=>(![X1336:$i, X1337:$i]:((subset @ X1337 @ (setadjoin @ X1336 @ X1337)))=>(![X1333:$i, X1334:$i, X1335:$i]:(((subset @ X1333 @ X1335)=>(subset @ X1333 @ (setadjoin @ X1334 @ X1335))))=>(![X1331:$i, X1332:$i]:(((subset @ X1331 @ X1332)=>(in @ X1331 @ (powerset @ X1332))))=>(![X1329:$i, X1330:$i]:(((subset @ X1329 @ X1330)=>((subset @ X1330 @ X1329)=>((X1329)=(X1330)))))=>(![X1328:$i]:(((subset @ X1328 @ emptyset)=>((X1328)=(emptyset))))=>(![X1326:$i, X1327:$i]:(((subset @ X1327 @ X1326)=>(in @ X1327 @ (powerset @ X1326))))=>(![X891:$i, X892:$i]:(((in @ X892 @ (powerset @ X891))=>(subset @ X892 @ X891)))=>(![X1325:$i]:((in @ X1325 @ (powerset @ X1325)))=>(![X893:$i, X894:$i]:(((subset @ X893 @ X894)=>(subset @ (powerset @ X893) @ (powerset @ X894))))=>(![X1323:$i, X1324:$i > $o]:((in @ (dsetconstr @ X1323 @ X1324) @ (powerset @ X1323)))=>(![X895:$i, X896:$i > $o]:((subset @ (dsetconstr @ X895 @ X896) @ X895))=>(![X897:$i, X898:$i, X899:$i]:(((in @ X899 @ X897)=>(in @ X899 @ (binunion @ X897 @ X898))))=>(![X1321:$i, X1322:$i]:((in @ X1322 @ (setadjoin @ X1321 @ (setadjoin @ X1322 @ emptyset))))=>(![X1318:$i, X1319:$i, X1320:$i]:(((in @ X1320 @ X1319)=>(in @ X1320 @ (binunion @ X1318 @ X1319))))=>(![X1314:$i, X1315:$i, X1316:$i, X1317:$o]:(((in @ X1316 @ (binunion @ X1314 @ X1315))=>(((in @ X1316 @ X1314)=>(X1317))=>(((in @ X1316 @ X1315)=>(X1317))=>(X1317)))))=>(![X900:$i, X901:$i, X902:$i]:(((in @ X902 @ (binunion @ X900 @ X901))=>((in @ X902 @ X900)|(in @ X902 @ X901))))=>(![X1312:$i, X1313:$i]:((subset @ X1312 @ (binunion @ X1312 @ X1313)))=>(![X903:$i, X904:$i]:((subset @ X904 @ (binunion @ X903 @ X904)))=>(![X1309:$i, X1310:$i, X1311:$i]:(((in @ X1311 @ X1309)=>((in @ X1311 @ X1310)=>(in @ X1311 @ (binintersect @ X1309 @ X1310)))))=>(![X1306:$i, X1307:$i, X1308:$i]:(((subset @ X1308 @ X1306)=>((subset @ X1308 @ X1307)=>(subset @ X1308 @ (binintersect @ X1306 @ X1307)))))=>(![X1303:$i, X1304:$i, X1305:$i]:(((in @ X1305 @ (binintersect @ X1303 @ X1304))=>(in @ X1305 @ X1303)))=>(![X1301:$i, X1302:$i]:((subset @ (binintersect @ X1301 @ X1302) @ X1301))=>(![X905:$i, X906:$i]:(((subset @ X905 @ X906)=>((binintersect @ X905 @ X906)=(X905))))=>(![X907:$i, X908:$i]:((((binintersect @ X907 @ X908)=(X908))=>(subset @ X908 @ X907)))=>(![X1298:$i, X1299:$i, X1300:$i]:(((in @ X1300 @ (binintersect @ X1298 @ X1299))=>(in @ X1300 @ X1299)))=>(![X909:$i, X910:$i]:((~(?[X911:$i]:(((in @ X911 @ X909)&(in @ X911 @ X910))))=>((binintersect @ X909 @ X910)=(emptyset))))=>(![X1296:$i, X1297:$i]:((subset @ (binintersect @ X1296 @ X1297) @ X1297))=>(![X912:$i, X913:$i]:(((subset @ X913 @ X912)=>((binintersect @ X912 @ X913)=(X913))))=>(![X1294:$i, X1295:$i]:((((binintersect @ X1294 @ X1295)=(X1294))=>(subset @ X1294 @ X1295)))=>(![X1291:$i, X1292:$i, X1293:$i]:(((binintersect @ X1291 @ (binunion @ X1292 @ X1293))=(binunion @ (binintersect @ X1291 @ X1292) @ (binintersect @ X1291 @ X1293))))=>(![X1288:$i, X1289:$i, X1290:$i]:(((in @ X1290 @ X1288)=>(~(in @ X1290 @ X1289)=>(in @ X1290 @ (setminus @ X1288 @ X1289)))))=>(![X914:$i, X915:$i, X916:$i]:(((in @ X916 @ (setminus @ X914 @ X915))=>(in @ X916 @ X914)))=>(![X917:$i, X918:$i, X919:$i]:(((in @ X919 @ (setminus @ X917 @ X918))=>~(in @ X919 @ X918)))=>(![X920:$i, X921:$i]:(((subset @ X920 @ X921)=>((setminus @ X920 @ X921)=(emptyset))))=>(![X922:$i, X923:$i, X924:$i]:((~(in @ X924 @ (setminus @ X922 @ X923))=>((in @ X924 @ X922)=>(in @ X924 @ X923))))=>(![X925:$i, X926:$i, X927:$i]:((~(in @ X927 @ (setminus @ X925 @ X926))=>(~(in @ X927 @ X926)=>~(in @ X927 @ X925))))=>(![X1285:$i, X1286:$i, X1287:$i]:((~(in @ X1287 @ X1285)=>~(in @ X1287 @ (setminus @ X1285 @ X1286))))=>(![X1282:$i, X1283:$i, X1284:$i]:(((in @ X1284 @ X1283)=>~(in @ X1284 @ (setminus @ X1282 @ X1283))))=>(![X1280:$i, X1281:$i]:((subset @ (setminus @ X1280 @ X1281) @ X1280))=>(![X1278:$i, X1279:$i]:((((setminus @ X1278 @ X1279)=(emptyset))=>(subset @ X1278 @ X1279)))=>(![X928:$i, X929:$i, X930:$i]:(((in @ X930 @ (symdiff @ X928 @ X929))=>![X931:$o]:((((in @ X930 @ X928)=>(~(in @ X930 @ X929)=>(X931)))=>((~(in @ X930 @ X928)=>((in @ X930 @ X929)=>(X931)))=>(X931))))))=>(![X932:$i, X933:$i, X934:$i]:(((in @ X934 @ X932)=>(~(in @ X934 @ X933)=>(in @ X934 @ (symdiff @ X932 @ X933)))))=>(![X1275:$i, X1276:$i, X1277:$i]:((~(in @ X1277 @ X1275)=>((in @ X1277 @ X1276)=>(in @ X1277 @ (symdiff @ X1275 @ X1276)))))=>(![X935:$i, X936:$i, X937:$i]:(((in @ X937 @ X935)=>((in @ X937 @ X936)=>~(in @ X937 @ (symdiff @ X935 @ X936)))))=>(![X938:$i, X939:$i, X940:$i]:((~(in @ X940 @ X938)=>(~(in @ X940 @ X939)=>~(in @ X940 @ (symdiff @ X938 @ X939)))))=>(![X1273:$i, X1274:$i]:((in @ X1274 @ (setadjoin @ X1273 @ (setadjoin @ X1274 @ emptyset))))=>(![X1271:$i, X1272:$i]:((in @ X1271 @ (setunion @ (setadjoin @ (setadjoin @ X1271 @ emptyset) @ (setadjoin @ (setadjoin @ X1271 @ (setadjoin @ X1272 @ emptyset)) @ emptyset)))))=>(![X941:$i, X942:$i]:((in @ X942 @ (setunion @ (setadjoin @ (setadjoin @ X941 @ emptyset) @ (setadjoin @ (setadjoin @ X941 @ (setadjoin @ X942 @ emptyset)) @ 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X1062)=(lam @ X1060 @ X1061 @ X1062))))=>(![X1088:$i, X1089:$i, X1090:$i > $i]:((![X1091:$i]:(((in @ X1091 @ X1088)=>(in @ (X1090 @ X1091) @ X1089)))=>![X1092:$i]:(((in @ X1092 @ X1088)=>((ap @ X1088 @ X1089 @ (lam @ X1088 @ X1089 @ X1090) @ X1092)=(X1090 @ X1092))))))=>(![X1064:$i, X1065:$i, X1066:$i]:(((in @ X1066 @ (funcSet @ X1064 @ X1065))=>((lam @ X1064 @ X1065 @ (ap @ X1064 @ X1065 @ X1066))=(X1066))))=>(![X1067:$i, X1068:$o, X1069:$i]:(((in @ X1069 @ X1067)=>![X1070:$i]:(((in @ X1070 @ X1067)=>(~(X1068)=>(in @ X1070 @ (dsetconstr @ X1067 @ (^[Z0/* 9 */:$i]:((((X1068)&((Z0)=(X1069)))|(~((X1068))&((Z0)=(X1070)))))))))))))=>(![X1084:$i, X1085:$o, X1086:$i]:(((in @ X1086 @ X1084)=>![X1087:$i]:(((in @ X1087 @ X1084)=>(~(X1085)=>((dsetconstr @ X1084 @ (^[Z0/* 9 */:$i]:((((X1085)&((Z0)=(X1086)))|(~((X1085))&((Z0)=(X1087)))))))=(setadjoin @ X1087 @ emptyset)))))))=>(![X1080:$i, X1081:$o, X1082:$i]:(((in @ X1082 @ X1080)=>![X1083:$i]:(((in @ X1083 @ X1080)=>((X1081)=>(in @ X1082 @ (dsetconstr @ X1080 @ (^[Z0/* 9 */:$i]:((((X1081)&((Z0)=(X1082)))|(~((X1081))&((Z0)=(X1083)))))))))))))=>(![X1076:$i, X1077:$o, X1078:$i]:(((in @ X1078 @ X1076)=>![X1079:$i]:(((in @ X1079 @ X1076)=>((X1077)=>((dsetconstr @ X1076 @ (^[Z0/* 9 */:$i]:((((X1077)&((Z0)=(X1078)))|(~((X1077))&((Z0)=(X1079)))))))=(setadjoin @ X1078 @ emptyset)))))))=>(![X1071:$i, X1072:$o, X1073:$i]:(((in @ X1073 @ X1071)=>![X1074:$i]:(((in @ X1074 @ X1071)=>?[X1075:$i]:(((in @ X1075 @ (dsetconstr @ X1071 @ (^[Z0/* 9 */:$i]:((((X1072)&((Z0)=(X1073)))|(~((X1072))&((Z0)=(X1074))))))))&((dsetconstr @ X1071 @ (^[Z0/* 9 */:$i]:((((X1072)&((Z0)=(X1073)))|(~((X1072))&((Z0)=(X1074)))))))=(setadjoin @ X1075 @ emptyset))))))))=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X45)) @ X2 @ X3) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[ifp]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_257]), foundationAx]), wellorderingAx]), c_0_258]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_263]), setext]), emptyI]), noeltsimpempty]), c_0_264]), c_0_265]), c_0_266]), c_0_267]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_268]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_269]), c_0_270]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_271]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_272]), c_0_273]), c_0_274]), inCongP]), in__Cong]), c_0_275]), c_0_276]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_277]), c_0_278]), c_0_279]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_280]), c_0_281]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_282]), c_0_283]), c_0_284]), c_0_285]), singletonsuniq]), setukpairinjL1]), c_0_286]), c_0_287]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_288]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_289]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), c_0_297]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_298]), c_0_299]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_304]), c_0_305]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_306]), c_0_307]), c_0_308]), c_0_309]), c_0_310]), c_0_311]), c_0_312]), c_0_313]), c_0_314]), c_0_315])])]), c_0_316])).
114.24/15.04	thf(c_0_318, plain, ![X1483:$i, X1484:$o, X1485:$i, X1486:$i]:(((if @ X1483 @ ((X1484)) @ X1485 @ X1486)=(setunion @ (dsetconstr @ X1483 @ (^[Z0/* 9 */:$i]:((((X1484)&((Z0)=(X1485)))|(~((X1484))&((Z0)=(X1486)))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[if])])).
114.24/15.04	thf(c_0_319, negated_conjecture, ![X1491:$i, X1492:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1504:$i, X1505:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1513:$i, X1514:$i > $i > $o, X1515:$i, X1517:$i, X1520:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1527:$i, X1528:$i > $o, X1529:$i, X1531:$i, X1532:$i > $o, X1533:$i, X1534:$i, X1535:$i > $o, X1536:$i, X1537:$i, X1538:$i > $o, X1539:$i, X1540:$i > $o, X1541:$i, X1544:$i, X1545:$o, X1546:$i, X1547:$i, X1548:$o, X1549:$i, X1550:$i, X1551:$i > $o, X1552:$i, X1555:$i, X1556:$i, X1559:$i, X1561:$i, X1563:$i, X1564:$i > $o, X1565:$i, X1566:$i, X1568:$i, X1569:$i > $o, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$o, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$o, X1601:$i, X1602:$i, X1603:$i > $o, X1604:$i, X1607:$i, X1608:$i, X1609:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i > $o, X1628:$i, X1629:$i > $o, X1630:$i, X1631:$i, X1632:$i > $o, X1633:$i, X1635:$i, X1636:$i > $o, X1638:$i, X1639:$i, X1640:$i > $o, X1642:$i, X1643:$i, X1644:$i > $o, X1645:$i, X1647:$o, X1648:$o, X1649:$i, X1650:$i > $o, X1652:$i, X1653:$i, X1654:$i > $o, X1655:$i, X1657:$i > $o, X1658:$i, X1661:$i, X1662:$i > $o, X1663:$i, X1667:$i, X1668:$i > $o, X1669:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i > $o, X1682:$i, X1684:$i, X1685:$i, X1686:$i > $o, X1687:$i > $o, X1690:$i, X1693:$i, X1694:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i > $o, X1707:$i, X1709:$i, X1710:$i, X1711:$i > $o, X1712:$i > $o, X1715:$i, X1717:$i, X1719:$i, X1720:$i, X1721:$i > $o, X1722:$i > $o, X1725:$i, X1726:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1735:$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, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i > $o, X1773:$i, X1774:$i > $o, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$o, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, 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:$i, X1854:$o, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, 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:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i > $o, X1929:$i, X1931:$i, X1932:$i > $o, X1933:$i, X1935:$i, X1936:$i > $o, X1937:$i, X1940:$i, X1941:$i > $o, X1944:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i > $i > $o, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i > $i > $o, X2026:$i, X2027:$i, X2028:$i > $i > $o, X2029:$i, X2030:$i, X2031:$i > $i > $o, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i > $i > $o, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i > $i > $o, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i > $i > $o, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i > $i, X2076:$i, X2077:$i, X2078:$i > $i, X2080:$i, X2081:$i, X2082:$i > $i, X2084:$i, X2085:$i, X2086:$i, X2087:$i > $o, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i > $o, X2097:$i, X2098:$i, X2099:$i > $o, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i > $i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i > $i, X2172:$i, X2173:$i, X2174:$i > $i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$o, X2182:$i, X2183:$i, X2184:$i, X2185:$o, X2186:$i, X2187:$i, X2188:$i, X2189:$o, X2190:$i, X2191:$i, X2192:$i, X2193:$o, X2194:$i, X2195:$i, X2196:$i, X2197:$o, X2198:$i, X2199:$i]:((((~(in @ (esk1_2 @ X1491 @ X1492) @ X1491)|~(in @ (esk1_2 @ X1491 @ X1492) @ X1492)|((X1491)=(X1492)))&((in @ (esk1_2 @ X1491 @ X1492) @ X1491)|(in @ (esk1_2 @ X1491 @ X1492) @ X1492)|((X1491)=(X1492))))&(~(in @ X1494 @ emptyset)&(((~(in @ X1497 @ (setadjoin @ X1495 @ X1496))|(((X1497)=(X1495))|(in @ X1497 @ X1496)))&((((X1497)!=(X1495))|(in @ X1497 @ (setadjoin @ X1495 @ X1496)))&(~(in @ X1497 @ X1496)|(in @ X1497 @ (setadjoin @ X1495 @ X1496)))))&(((~(in @ X1499 @ (powerset @ X1498))|(~(in @ X1500 @ X1499)|(in @ X1500 @ X1498)))&(((in @ (esk2_2 @ X1501 @ X1502) @ X1502)|(in @ X1502 @ (powerset @ X1501)))&(~(in @ (esk2_2 @ X1501 @ X1502) @ X1501)|(in @ X1502 @ (powerset @ X1501)))))&(((((in @ X1505 @ (esk3_2 @ X1504 @ X1505))|~(in @ X1505 @ (setunion @ X1504)))&((in @ (esk3_2 @ X1504 @ X1505) @ X1504)|~(in @ X1505 @ (setunion @ X1504))))&(~(in @ X1508 @ X1509)|~(in @ X1509 @ X1507)|(in @ X1508 @ (setunion @ X1507))))&((in @ emptyset @ omega)&((~(in @ X1510 @ omega)|(in @ (setadjoin @ X1510 @ X1510) @ omega))&(((((in @ (esk4_1 @ X1511) @ omega)|~(in @ emptyset @ X1511)|(~(in @ X1513 @ omega)|(in @ X1513 @ X1511)))&((in @ (esk4_1 @ X1511) @ X1511)|~(in @ emptyset @ X1511)|(~(in @ X1513 @ omega)|(in @ X1513 @ X1511))))&(~(in @ (setadjoin @ (esk4_1 @ X1511) @ (esk4_1 @ X1511)) @ X1511)|~(in @ emptyset @ X1511)|(~(in @ X1513 @ omega)|(in @ X1513 @ X1511))))&((((((in @ (esk8_3 @ X1514 @ X1515 @ X1520) @ X1515)|~(in @ X1520 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X2085)|(~(in @ X2090 @ X2086)|(X2087 @ X2090))|~(subset @ X2086 @ (cartprod @ X2084 @ X2085)))&(((in @ (kpair @ (esk73_4 @ X2084 @ X2085 @ X2086 @ X2087) @ (esk74_4 @ X2084 @ X2085 @ X2086 @ X2087)) @ X2086)|(~(in @ X2090 @ X2086)|(X2087 @ X2090))|~(subset @ X2086 @ (cartprod @ X2084 @ X2085)))&(~(X2087 @ (kpair @ (esk73_4 @ X2084 @ X2085 @ X2086 @ X2087) @ (esk74_4 @ X2084 @ X2085 @ X2086 @ X2087)))|(~(in @ X2090 @ X2086)|(X2087 @ X2090))|~(subset @ X2086 @ (cartprod @ X2084 @ X2085))))))&((((in @ (esk75_4 @ X2091 @ X2092 @ X2093 @ X2094) @ X2091)|(~(in @ X2097 @ X2093)|(X2094 @ X2097))|~(subset @ X2093 @ (cartprod @ X2091 @ X2092)))&(((in @ (esk76_4 @ X2091 @ X2092 @ X2093 @ X2094) @ X2092)|(~(in @ X2097 @ X2093)|(X2094 @ X2097))|~(subset @ X2093 @ (cartprod @ X2091 @ X2092)))&(((in @ (kpair @ (esk75_4 @ X2091 @ X2092 @ X2093 @ X2094) @ (esk76_4 @ X2091 @ X2092 @ X2093 @ X2094)) @ X2093)|(~(in @ X2097 @ X2093)|(X2094 @ X2097))|~(subset @ X2093 @ (cartprod @ X2091 @ X2092)))&(~(X2094 @ (kpair @ (esk75_4 @ X2091 @ X2092 @ X2093 @ X2094) @ (esk76_4 @ X2091 @ X2092 @ X2093 @ X2094)))|(~(in @ X2097 @ X2093)|(X2094 @ X2097))|~(subset @ X2093 @ (cartprod @ X2091 @ X2092))))))&((~(in @ X2100 @ (dsetconstr @ X2098 @ X2099))|((dsetconstr @ X2098 @ X2099)!=(setadjoin @ X2100 @ emptyset))|(~(in @ X2101 @ X2098)|(~(in @ X2102 @ X2098)|(~(X2099 @ X2101)|(~(X2099 @ X2102)|((X2101)=(X2102)))))))&((~(func @ X2103 @ X2104 @ X2105)|(~(in @ X2106 @ X2103)|(in @ (kpair @ X2106 @ (ap @ X2103 @ X2104 @ X2105 @ X2106)) @ X2105)))&((~(in @ X2109 @ (funcSet @ X2107 @ X2108))|(~(in @ X2110 @ X2107)|(in @ (kpair @ X2110 @ (ap @ X2107 @ X2108 @ X2109 @ X2110)) @ X2109)))&((~(func @ X2111 @ X2112 @ X2113)|(~(in @ X2114 @ X2111)|(~(in @ X2115 @ X2112)|(~(in @ (kpair @ X2114 @ X2115) @ X2113)|((ap @ X2111 @ X2112 @ X2113 @ X2114)=(X2115))))))&((((in @ (esk77_4 @ X2116 @ X2117 @ X2118 @ X2119) @ X2116)|(~(in @ X2121 @ X2116)|(~(in @ X2122 @ X2117)|(~(in @ (kpair @ X2121 @ X2122) @ X2119)|(in @ (kpair @ X2121 @ X2122) @ X2118))))|~(func @ X2116 @ X2117 @ X2119)|~(func @ X2116 @ X2117 @ X2118))&(((ap @ X2116 @ X2117 @ X2118 @ (esk77_4 @ X2116 @ X2117 @ X2118 @ X2119))!=(ap @ X2116 @ X2117 @ X2119 @ (esk77_4 @ X2116 @ X2117 @ X2118 @ X2119)))|(~(in @ X2121 @ X2116)|(~(in @ X2122 @ X2117)|(~(in @ (kpair @ X2121 @ X2122) @ X2119)|(in @ (kpair @ X2121 @ X2122) @ X2118))))|~(func @ X2116 @ X2117 @ X2119)|~(func @ X2116 @ X2117 @ X2118)))&((~(in @ X2125 @ (funcSet @ X2123 @ X2124))|(~(in @ X2126 @ X2123)|(~(in @ X2127 @ X2124)|(~(in @ (kpair @ X2126 @ X2127) @ X2125)|((ap @ X2123 @ X2124 @ X2125 @ X2126)=(X2127))))))&((((in @ (esk78_4 @ X2128 @ X2129 @ X2130 @ X2131) @ X2128)|(subset @ X2130 @ X2131)|~(subset @ X2131 @ (cartprod @ X2128 @ X2129))|~(subset @ X2130 @ (cartprod @ X2128 @ X2129)))&(((in @ (esk79_4 @ X2128 @ X2129 @ X2130 @ X2131) @ X2129)|(subset @ X2130 @ X2131)|~(subset @ X2131 @ (cartprod @ X2128 @ X2129))|~(subset @ X2130 @ (cartprod @ X2128 @ X2129)))&(((in @ (kpair @ (esk78_4 @ X2128 @ X2129 @ X2130 @ X2131) @ (esk79_4 @ X2128 @ X2129 @ X2130 @ X2131)) @ X2130)|(subset @ X2130 @ X2131)|~(subset @ X2131 @ (cartprod @ X2128 @ X2129))|~(subset @ X2130 @ (cartprod @ X2128 @ X2129)))&(~(in @ (kpair @ (esk78_4 @ X2128 @ X2129 @ X2130 @ X2131) @ (esk79_4 @ X2128 @ X2129 @ X2130 @ X2131)) @ X2131)|(subset @ X2130 @ X2131)|~(subset @ X2131 @ (cartprod @ X2128 @ X2129))|~(subset @ X2130 @ (cartprod @ X2128 @ X2129))))))&(((((in @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|((X2136)=(X2137))|(in @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|((X2136)=(X2137))|(in @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|((X2136)=(X2137))|(in @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(~(in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|((X2136)=(X2137))|(in @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135))))))&((((in @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|((X2136)=(X2137))|(in @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|((X2136)=(X2137))|(in @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|((X2136)=(X2137))|(in @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(~(in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|((X2136)=(X2137))|(in @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135))))))&((((in @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|((X2136)=(X2137))|(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|((X2136)=(X2137))|(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|((X2136)=(X2137))|(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(~(in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|((X2136)=(X2137))|(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135))))))&(((in @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|((X2136)=(X2137))|~(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|((X2136)=(X2137))|~(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|((X2136)=(X2137))|~(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(~(in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|((X2136)=(X2137))|~(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))))))))&((((in @ (esk84_4 @ X2142 @ X2143 @ X2144 @ X2145) @ X2142)|((X2144)=(X2145))|~(func @ X2142 @ X2143 @ X2145)|~(func @ X2142 @ X2143 @ X2144))&(((ap @ X2142 @ X2143 @ X2144 @ (esk84_4 @ X2142 @ X2143 @ X2144 @ X2145))!=(ap @ X2142 @ X2143 @ X2145 @ (esk84_4 @ X2142 @ X2143 @ X2144 @ X2145)))|((X2144)=(X2145))|~(func @ X2142 @ X2143 @ X2145)|~(func @ X2142 @ X2143 @ X2144)))&((((in @ (esk85_4 @ X2147 @ X2148 @ X2149 @ X2150) @ X2147)|((X2149)=(X2150))|~(in @ X2150 @ (funcSet @ X2147 @ X2148))|~(in @ X2149 @ (funcSet @ X2147 @ X2148)))&(((ap @ X2147 @ X2148 @ X2149 @ (esk85_4 @ X2147 @ X2148 @ X2149 @ X2150))!=(ap @ X2147 @ X2148 @ X2150 @ (esk85_4 @ X2147 @ X2148 @ X2149 @ X2150)))|((X2149)=(X2150))|~(in @ X2150 @ (funcSet @ X2147 @ X2148))|~(in @ X2149 @ (funcSet @ X2147 @ X2148))))&((~(in @ X2154 @ (funcSet @ X2152 @ X2153))|(~(in @ X2155 @ X2152)|((ap @ X2152 @ X2153 @ X2154 @ X2155)=(ap @ X2152 @ X2153 @ X2154 @ X2155))))&((~(func @ X2156 @ X2157 @ X2158)|(~(in @ X2159 @ X2156)|((ap @ X2156 @ X2157 @ X2158 @ X2159)=(ap @ X2156 @ X2157 @ X2158 @ X2159))))&((((in @ (esk86_3 @ X2160 @ X2161 @ X2162) @ X2160)|(~(in @ X2164 @ X2160)|((ap @ X2160 @ X2161 @ (lam @ X2160 @ X2161 @ X2162) @ X2164)=(X2162 @ X2164))))&(~(in @ (X2162 @ (esk86_3 @ X2160 @ X2161 @ X2162)) @ X2161)|(~(in @ X2164 @ X2160)|((ap @ X2160 @ X2161 @ (lam @ X2160 @ X2161 @ X2162) @ X2164)=(X2162 @ X2164)))))&((~(func @ X2165 @ X2166 @ X2167)|((lam @ X2165 @ X2166 @ (ap @ X2165 @ X2166 @ X2167))=(X2167)))&((((in @ (esk87_3 @ X2168 @ X2169 @ X2170) @ X2168)|((lam @ X2168 @ X2169 @ X2170)=(lam @ X2168 @ X2169 @ X2170)))&(~(in @ (X2170 @ (esk87_3 @ X2168 @ X2169 @ X2170)) @ X2169)|((lam @ X2168 @ X2169 @ X2170)=(lam @ X2168 @ X2169 @ X2170))))&((((in @ (esk88_3 @ X2172 @ X2173 @ X2174) @ X2172)|(~(in @ X2176 @ X2172)|((ap @ X2172 @ X2173 @ (lam @ X2172 @ X2173 @ X2174) @ X2176)=(X2174 @ X2176))))&(~(in @ (X2174 @ (esk88_3 @ X2172 @ X2173 @ X2174)) @ X2173)|(~(in @ X2176 @ X2172)|((ap @ X2172 @ X2173 @ (lam @ X2172 @ X2173 @ X2174) @ X2176)=(X2174 @ X2176)))))&((~(in @ X2179 @ (funcSet @ X2177 @ X2178))|((lam @ X2177 @ X2178 @ (ap @ X2177 @ X2178 @ X2179))=(X2179)))&((~(in @ X2182 @ X2180)|(~(in @ X2183 @ X2180)|((X2181)|(in @ X2183 @ (dsetconstr @ X2180 @ (^[Z0/* 9 */:$i]:((((X2181)&((Z0)=(X2182)))|(~((X2181))&((Z0)=(X2183)))))))))))&((~(in @ X2186 @ X2184)|(~(in @ X2187 @ X2184)|((X2185)|((dsetconstr @ X2184 @ (^[Z0/* 9 */:$i]:((((X2185)&((Z0)=(X2186)))|(~((X2185))&((Z0)=(X2187)))))))=(setadjoin @ X2187 @ emptyset)))))&((~(in @ X2190 @ X2188)|(~(in @ X2191 @ X2188)|(~(X2189)|(in @ X2190 @ (dsetconstr @ X2188 @ (^[Z0/* 9 */:$i]:((((X2189)&((Z0)=(X2190)))|(~((X2189))&((Z0)=(X2191)))))))))))&((~(in @ X2194 @ X2192)|(~(in @ X2195 @ X2192)|(~(X2193)|((dsetconstr @ X2192 @ (^[Z0/* 9 */:$i]:((((X2193)&((Z0)=(X2194)))|(~((X2193))&((Z0)=(X2195)))))))=(setadjoin @ X2194 @ emptyset)))))&((((in @ (esk89_4 @ X2196 @ X2197 @ X2198 @ X2199) @ (dsetconstr @ X2196 @ (^[Z0/* 9 */:$i]:((((X2197)&((Z0)=(X2198)))|(~((X2197))&((Z0)=(X2199))))))))|~(in @ X2199 @ X2196)|~(in @ X2198 @ X2196))&(((dsetconstr @ X2196 @ (^[Z0/* 9 */:$i]:((((X2197)&((Z0)=(X2198)))|(~((X2197))&((Z0)=(X2199)))))))=(setadjoin @ (esk89_4 @ X2196 @ X2197 @ X2198 @ X2199) @ emptyset))|~(in @ X2199 @ X2196)|~(in @ X2198 @ X2196)))&((in @ esk91_0 @ esk90_0)&((in @ esk92_0 @ esk90_0)&(((~(epred2_0)|(epred2_0))&(~(in @ (if @ esk90_0 @ $false @ esk91_0 @ esk92_0) @ esk90_0)|(epred2_0)))&((~(epred2_0)|~(in @ (if @ esk90_0 @ $true @ esk91_0 @ esk92_0) @ esk90_0))&(~(in @ (if @ esk90_0 @ $false @ esk91_0 @ esk92_0) @ esk90_0)|~(in @ (if @ esk90_0 @ $true @ esk91_0 @ esk92_0) @ esk90_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_317])])])])])])])])).
114.24/15.04	thf(c_0_320, plain, ![X1487:$i, X1488:$o, X1489:$i, X1490:$i]:(((if @ X1487 @ ((X1488)) @ X1489 @ X1490)=(setunion @ (dsetconstr @ X1487 @ (^[Z0/* 9 */:$i]:((((X1488)&((Z0)=(X1489)))|(~((X1488))&((Z0)=(X1490)))))))))), inference(variable_rename,[status(thm)],[c_0_318])).
114.24/15.04	thf(c_0_321, negated_conjecture, (~((epred2_0))|~((in @ (if @ esk90_0 @ (($true)) @ esk91_0 @ esk92_0) @ esk90_0))), inference(split_conjunct,[status(thm)],[c_0_319])).
114.24/15.04	thf(c_0_322, plain, ![X2:$i, X3:$i, X10:$o, X4:$i]:(((if @ X2 @ ((X10)) @ X3 @ X4)=(setunion @ (dsetconstr @ X2 @ (^[Z0/* 9 */:$i]:((((X10)&((Z0)=(X3)))|(~((X10))&((Z0)=(X4)))))))))), inference(split_conjunct,[status(thm)],[c_0_320])).
114.24/15.04	thf(c_0_323, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((dsetconstr @ X3 @ (^[Z0/* 9 */:$i]:(((~($true)&((Z0)=(X2)))|(~(~($true))&((Z0)=(X4)))))))=(setadjoin @ X4 @ emptyset))|~((in @ X2 @ X3))|~((in @ X4 @ X3)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_319])])])).
114.24/15.04	thf(c_0_324, negated_conjecture, ((epred2_0)|~((in @ (if @ esk90_0 @ (~($true)) @ esk91_0 @ esk92_0) @ esk90_0))), inference(split_conjunct,[status(thm)],[c_0_319])).
114.24/15.04	thf(c_0_325, negated_conjecture, (~((epred2_0))|~((in @ (setunion @ (dsetconstr @ esk90_0 @ (^[Z0/* 9 */:$i]:(((($true)&((Z0)=(esk91_0)))|(~(($true))&((Z0)=(esk92_0)))))))) @ esk90_0))), inference(rw,[status(thm)],[c_0_321, c_0_322])).
114.24/15.04	thf(c_0_326, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:((((dsetconstr @ X2 @ (^[Z0/* 3 */:$i]:(((Z0)=(X3)))))=(setadjoin @ X3 @ emptyset))|~((in @ X3 @ X2))|~((in @ X4 @ X2)))), inference(cn,[status(thm)],[c_0_323])).
114.24/15.04	thf(c_0_327, negated_conjecture, (in @ esk92_0 @ esk90_0), inference(split_conjunct,[status(thm)],[c_0_319])).
114.24/15.04	thf(c_0_328, negated_conjecture, ((epred2_0)|~((in @ (setunion @ (dsetconstr @ esk90_0 @ (^[Z0/* 9 */:$i]:(((~($true)&((Z0)=(esk91_0)))|(~(~($true))&((Z0)=(esk92_0)))))))) @ esk90_0))), inference(rw,[status(thm)],[c_0_324, c_0_322])).
114.24/15.04	thf(c_0_329, negated_conjecture, (~((in @ (setunion @ (dsetconstr @ esk90_0 @ (^[Z0/* 3 */:$i]:(((Z0)=(esk91_0)))))) @ esk90_0))|~((epred2_0))), inference(cn,[status(thm)],[c_0_325])).
114.24/15.04	thf(c_0_330, negated_conjecture, ![X2:$i]:((((dsetconstr @ esk90_0 @ (^[Z0/* 3 */:$i]:(((Z0)=(X2)))))=(setadjoin @ X2 @ emptyset))|~((in @ X2 @ esk90_0)))), inference(spm,[status(thm)],[c_0_326, c_0_327])).
114.24/15.04	thf(c_0_331, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_319])).
114.24/15.04	thf(c_0_332, negated_conjecture, (in @ esk91_0 @ esk90_0), inference(split_conjunct,[status(thm)],[c_0_319])).
114.24/15.04	thf(c_0_333, negated_conjecture, ((epred2_0)|~((in @ (setunion @ (dsetconstr @ esk90_0 @ (^[Z0/* 3 */:$i]:(((Z0)=(esk92_0)))))) @ esk90_0))), inference(cn,[status(thm)],[c_0_328])).
114.24/15.04	thf(c_0_334, negated_conjecture, ~((epred2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_329, c_0_330]), c_0_331]), c_0_332]), c_0_332])])).
114.24/15.04	thf(c_0_335, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333, c_0_330]), c_0_331]), c_0_327]), c_0_327])]), c_0_334]), ['proof']).
114.24/15.04	# SZS output end CNFRefutation
114.24/15.04	# Parsed axioms                        : 487
114.24/15.04	# Removed by relevancy pruning/SinE    : 0
114.24/15.04	# Initial clauses                      : 673
114.24/15.04	# Removed in clause preprocessing      : 290
114.24/15.04	# Initial clauses in saturation        : 383
114.24/15.04	# Processed clauses                    : 8558
114.24/15.04	# ...of these trivial                  : 43
114.24/15.04	# ...subsumed                          : 4855
114.24/15.04	# ...remaining for further processing  : 3659
114.24/15.04	# Other redundant clauses eliminated   : 188
114.24/15.04	# Clauses deleted for lack of memory   : 0
114.24/15.04	# Backward-subsumed                    : 371
114.24/15.04	# Backward-rewritten                   : 7
114.24/15.04	# Generated clauses                    : 612528
114.24/15.04	# ...of the previous two non-redundant : 606876
114.24/15.04	# ...aggressively subsumed             : 0
114.24/15.04	# Contextual simplify-reflections      : 89
114.24/15.04	# Paramodulations                      : 611918
114.24/15.04	# Factorizations                       : 120
114.24/15.04	# NegExts                              : 131
114.24/15.04	# Equation resolutions                 : 202
114.24/15.04	# Disequality decompositions           : 0
114.24/15.04	# Total rewrite steps                  : 59480
114.24/15.04	# ...of those cached                   : 59153
114.24/15.04	# Propositional unsat checks           : 0
114.24/15.04	#    Propositional check models        : 0
114.24/15.04	#    Propositional check unsatisfiable : 0
114.24/15.04	#    Propositional clauses             : 0
114.24/15.04	#    Propositional clauses after purity: 0
114.24/15.04	#    Propositional unsat core size     : 0
114.24/15.04	#    Propositional preprocessing time  : 0.000
114.24/15.04	#    Propositional encoding time       : 0.000
114.24/15.04	#    Propositional solver time         : 0.000
114.24/15.04	#    Success case prop preproc time    : 0.000
114.24/15.04	#    Success case prop encoding time   : 0.000
114.24/15.04	#    Success case prop solver time     : 0.000
114.24/15.04	# Current number of processed clauses  : 2892
114.24/15.04	#    Positive orientable unit clauses  : 54
114.24/15.04	#    Positive unorientable unit clauses: 0
114.24/15.04	#    Negative unit clauses             : 50
114.24/15.04	#    Non-unit-clauses                  : 2788
114.24/15.04	# Current number of unprocessed clauses: 598681
114.24/15.04	# ...number of literals in the above   : 2749842
114.24/15.04	# Current number of archived formulas  : 0
114.24/15.04	# Current number of archived clauses   : 752
114.24/15.04	# Clause-clause subsumption calls (NU) : 1367808
114.24/15.04	# Rec. Clause-clause subsumption calls : 596206
114.24/15.04	# Non-unit clause-clause subsumptions  : 3088
114.24/15.04	# Unit Clause-clause subsumption calls : 6176
114.24/15.04	# Rewrite failures with RHS unbound    : 0
114.24/15.04	# BW rewrite match attempts            : 33
114.24/15.04	# BW rewrite match successes           : 7
114.24/15.04	# Condensation attempts                : 0
114.24/15.04	# Condensation successes               : 0
114.24/15.04	# Termbank termtop insertions          : 14351164
114.24/15.04	# Search garbage collected termcells   : 24889
114.24/15.04	
114.24/15.04	# -------------------------------------------------
114.24/15.04	# User time                : 13.608 s
114.24/15.04	# System time              : 0.450 s
114.24/15.04	# Total time               : 14.058 s
114.24/15.04	# Maximum resident set size: 7552 pages
114.24/15.04	
114.24/15.04	# -------------------------------------------------
114.24/15.04	# User time                : 13.621 s
114.24/15.04	# System time              : 0.454 s
114.24/15.04	# Total time               : 14.075 s
114.24/15.04	# Maximum resident set size: 2608 pages
114.24/15.04	% E exiting
114.24/15.04	% E exiting
114.24/15.04	EOF