0.08/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.12	% Command    : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.11/0.32	% Computer : n011.cluster.edu
0.11/0.32	% Model    : x86_64 x86_64
0.11/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory   : 8042.1875MB
0.11/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 1920
0.11/0.32	% WCLimit    : 240
0.11/0.32	% DateTime   : Wed Jul 30 09:33:19 EDT 2025
0.11/0.32	% CPUTime    : 
0.18/0.46	Running higher-order theorem proving
0.18/0.51	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.hv8VQiADgy/E---3.1_12799.p
13.82/2.27	# Version: 3.0.0-ho
13.82/2.27	# Preprocessing class: HSLMSLSSLLLCHFA.
13.82/2.27	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
13.82/2.27	# Starting ehoh_best5 with 240s (1) cores
13.82/2.27	# Starting almost_fo_3_lam with 240s (1) cores
13.82/2.27	# Starting new_bool_5 with 240s (1) cores
13.82/2.27	# Starting pre_casc_3 with 240s (1) cores
13.82/2.27	# Starting ho_unfolding_8 with 240s (1) cores
13.82/2.27	# Starting new_ho_10_cnf2 with 240s (1) cores
13.82/2.27	# Starting new_bool_3 with 240s (1) cores
13.82/2.27	# Starting new_ho_5 with 240s (1) cores
13.82/2.27	# ho_unfolding_8 with pid 12881 completed with status 0
13.82/2.27	# Result found by ho_unfolding_8
13.82/2.27	# Preprocessing class: HSLMSLSSLLLCHFA.
13.82/2.27	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
13.82/2.27	# Starting ehoh_best5 with 240s (1) cores
13.82/2.27	# Starting almost_fo_3_lam with 240s (1) cores
13.82/2.27	# Starting new_bool_5 with 240s (1) cores
13.82/2.27	# Starting pre_casc_3 with 240s (1) cores
13.82/2.27	# Starting ho_unfolding_8 with 240s (1) cores
13.82/2.27	# No SInE strategy applied
13.82/2.27	# Search class: HGHSM-FSLM32-MHFMMSBN
13.82/2.27	# Scheduled 9 strats onto 1 cores with 240 seconds (240 total)
13.82/2.27	# Starting ho_unfolding_8 with 49s (1) cores
13.82/2.27	# ho_unfolding_8 with pid 12887 completed with status 0
13.82/2.27	# Result found by ho_unfolding_8
13.82/2.27	# Preprocessing class: HSLMSLSSLLLCHFA.
13.82/2.27	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
13.82/2.27	# Starting ehoh_best5 with 240s (1) cores
13.82/2.27	# Starting almost_fo_3_lam with 240s (1) cores
13.82/2.27	# Starting new_bool_5 with 240s (1) cores
13.82/2.27	# Starting pre_casc_3 with 240s (1) cores
13.82/2.27	# Starting ho_unfolding_8 with 240s (1) cores
13.82/2.27	# No SInE strategy applied
13.82/2.27	# Search class: HGHSM-FSLM32-MHFMMSBN
13.82/2.27	# Scheduled 9 strats onto 1 cores with 240 seconds (240 total)
13.82/2.27	# Starting ho_unfolding_8 with 49s (1) cores
13.82/2.27	# Preprocessing time       : 0.058 s
13.82/2.27	# Presaturation interreduction done
13.82/2.27	
13.82/2.27	# Proof found!
13.82/2.27	# SZS status Theorem
13.82/2.27	# SZS output start CNFRefutation
13.82/2.27	thf(decl_23, type, in: $i > $i > $o).
13.82/2.27	thf(decl_24, type, exu: ($i > $o) > $o).
13.82/2.27	thf(decl_25, type, setextAx: $o).
13.82/2.27	thf(decl_26, type, emptyset: $i).
13.82/2.27	thf(decl_27, type, emptysetAx: $o).
13.82/2.27	thf(decl_28, type, setadjoin: $i > $i > $i).
13.82/2.27	thf(decl_29, type, setadjoinAx: $o).
13.82/2.27	thf(decl_30, type, powerset: $i > $i).
13.82/2.27	thf(decl_31, type, powersetAx: $o).
13.82/2.27	thf(decl_32, type, setunion: $i > $i).
13.82/2.27	thf(decl_33, type, setunionAx: $o).
13.82/2.27	thf(decl_34, type, omega: $i).
13.82/2.27	thf(decl_35, type, omega0Ax: $o).
13.82/2.27	thf(decl_36, type, omegaSAx: $o).
13.82/2.27	thf(decl_37, type, omegaIndAx: $o).
13.82/2.27	thf(decl_38, type, replAx: $o).
13.82/2.27	thf(decl_39, type, foundationAx: $o).
13.82/2.27	thf(decl_40, type, wellorderingAx: $o).
13.82/2.27	thf(decl_41, type, descr: ($i > $o) > $i).
13.82/2.27	thf(decl_42, type, descrp: $o).
13.82/2.27	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_44, type, dsetconstrI: $o).
13.82/2.27	thf(decl_45, type, dsetconstrEL: $o).
13.82/2.27	thf(decl_46, type, dsetconstrER: $o).
13.82/2.27	thf(decl_47, type, exuE1: $o).
13.82/2.27	thf(decl_48, type, prop2set: $o > $i).
13.82/2.27	thf(decl_49, type, prop2setE: $o).
13.82/2.27	thf(decl_50, type, emptysetE: $o).
13.82/2.27	thf(decl_51, type, emptysetimpfalse: $o).
13.82/2.27	thf(decl_52, type, notinemptyset: $o).
13.82/2.27	thf(decl_53, type, exuE3e: $o).
13.82/2.27	thf(decl_54, type, setext: $o).
13.82/2.27	thf(decl_55, type, emptyI: $o).
13.82/2.27	thf(decl_56, type, noeltsimpempty: $o).
13.82/2.27	thf(decl_57, type, setbeta: $o).
13.82/2.27	thf(decl_58, type, nonempty: $i > $o).
13.82/2.27	thf(decl_59, type, nonemptyE1: $o).
13.82/2.27	thf(decl_60, type, nonemptyI: $o).
13.82/2.27	thf(decl_61, type, nonemptyI1: $o).
13.82/2.27	thf(decl_62, type, setadjoinIL: $o).
13.82/2.27	thf(decl_63, type, emptyinunitempty: $o).
13.82/2.27	thf(decl_64, type, setadjoinIR: $o).
13.82/2.27	thf(decl_65, type, setadjoinE: $o).
13.82/2.27	thf(decl_66, type, setadjoinOr: $o).
13.82/2.27	thf(decl_67, type, setoftrueEq: $o).
13.82/2.27	thf(decl_68, type, powersetI: $o).
13.82/2.27	thf(decl_69, type, emptyinPowerset: $o).
13.82/2.27	thf(decl_70, type, emptyInPowerset: $o).
13.82/2.27	thf(decl_71, type, powersetE: $o).
13.82/2.27	thf(decl_72, type, setunionI: $o).
13.82/2.27	thf(decl_73, type, setunionE: $o).
13.82/2.27	thf(decl_74, type, subPowSU: $o).
13.82/2.27	thf(decl_75, type, exuE2: $o).
13.82/2.27	thf(decl_76, type, nonemptyImpWitness: $o).
13.82/2.27	thf(decl_77, type, uniqinunit: $o).
13.82/2.27	thf(decl_78, type, notinsingleton: $o).
13.82/2.27	thf(decl_79, type, eqinunit: $o).
13.82/2.27	thf(decl_80, type, singletonsswitch: $o).
13.82/2.27	thf(decl_81, type, upairsetE: $o).
13.82/2.27	thf(decl_82, type, upairsetIL: $o).
13.82/2.27	thf(decl_83, type, upairsetIR: $o).
13.82/2.27	thf(decl_84, type, emptyE1: $o).
13.82/2.27	thf(decl_85, type, vacuousDall: $o).
13.82/2.27	thf(decl_86, type, quantDeMorgan1: $o).
13.82/2.27	thf(decl_87, type, quantDeMorgan2: $o).
13.82/2.27	thf(decl_88, type, quantDeMorgan3: $o).
13.82/2.27	thf(decl_89, type, quantDeMorgan4: $o).
13.82/2.27	thf(decl_90, type, prop2setI: $o).
13.82/2.27	thf(decl_91, type, set2prop: $i > $o).
13.82/2.27	thf(decl_92, type, prop2set2propI: $o).
13.82/2.27	thf(decl_93, type, notdexE: $o).
13.82/2.27	thf(decl_94, type, notdallE: $o).
13.82/2.27	thf(decl_95, type, exuI1: $o).
13.82/2.27	thf(decl_96, type, exuI3: $o).
13.82/2.27	thf(decl_97, type, exuI2: $o).
13.82/2.27	thf(decl_98, type, inCongP: $o).
13.82/2.27	thf(decl_99, type, in__Cong: $o).
13.82/2.27	thf(decl_100, type, exuE3u: $o).
13.82/2.27	thf(decl_101, type, exu__Cong: $o).
13.82/2.27	thf(decl_102, type, emptyset__Cong: $o).
13.82/2.27	thf(decl_103, type, setadjoin__Cong: $o).
13.82/2.27	thf(decl_104, type, powerset__Cong: $o).
13.82/2.27	thf(decl_105, type, setunion__Cong: $o).
13.82/2.27	thf(decl_106, type, omega__Cong: $o).
13.82/2.27	thf(decl_107, type, exuEu: $o).
13.82/2.27	thf(decl_108, type, descr__Cong: $o).
13.82/2.27	thf(decl_109, type, dsetconstr__Cong: $o).
13.82/2.27	thf(decl_110, type, subset: $i > $i > $o).
13.82/2.27	thf(decl_113, type, subsetI1: $o).
13.82/2.27	thf(decl_114, type, eqimpsubset2: $o).
13.82/2.27	thf(decl_115, type, eqimpsubset1: $o).
13.82/2.27	thf(decl_116, type, subsetI2: $o).
13.82/2.27	thf(decl_117, type, emptysetsubset: $o).
13.82/2.27	thf(decl_118, type, subsetE: $o).
13.82/2.27	thf(decl_119, type, subsetE2: $o).
13.82/2.27	thf(decl_120, type, notsubsetI: $o).
13.82/2.27	thf(decl_121, type, notequalI1: $o).
13.82/2.27	thf(decl_122, type, notequalI2: $o).
13.82/2.27	thf(decl_123, type, subsetRefl: $o).
13.82/2.27	thf(decl_124, type, subsetTrans: $o).
13.82/2.27	thf(decl_125, type, setadjoinSub: $o).
13.82/2.27	thf(decl_126, type, setadjoinSub2: $o).
13.82/2.27	thf(decl_127, type, subset2powerset: $o).
13.82/2.27	thf(decl_128, type, setextsub: $o).
13.82/2.27	thf(decl_129, type, subsetemptysetimpeq: $o).
13.82/2.27	thf(decl_130, type, powersetI1: $o).
13.82/2.27	thf(decl_131, type, powersetE1: $o).
13.82/2.27	thf(decl_132, type, inPowerset: $o).
13.82/2.27	thf(decl_133, type, powersetsubset: $o).
13.82/2.27	thf(decl_134, type, sepInPowerset: $o).
13.82/2.27	thf(decl_135, type, sepSubset: $o).
13.82/2.27	thf(decl_136, type, binunion: $i > $i > $i).
13.82/2.27	thf(decl_137, type, binunionIL: $o).
13.82/2.27	thf(decl_138, type, upairset2IR: $o).
13.82/2.27	thf(decl_139, type, binunionIR: $o).
13.82/2.27	thf(decl_140, type, binunionEcases: $o).
13.82/2.27	thf(decl_141, type, binunionE: $o).
13.82/2.27	thf(decl_142, type, binunionLsub: $o).
13.82/2.27	thf(decl_143, type, binunionRsub: $o).
13.82/2.27	thf(decl_144, type, binintersect: $i > $i > $i).
13.82/2.27	thf(decl_145, type, binintersectI: $o).
13.82/2.27	thf(decl_146, type, binintersectSubset5: $o).
13.82/2.27	thf(decl_147, type, binintersectEL: $o).
13.82/2.27	thf(decl_148, type, binintersectLsub: $o).
13.82/2.27	thf(decl_149, type, binintersectSubset2: $o).
13.82/2.27	thf(decl_150, type, binintersectSubset3: $o).
13.82/2.27	thf(decl_151, type, binintersectER: $o).
13.82/2.27	thf(decl_152, type, disjointsetsI1: $o).
13.82/2.27	thf(decl_153, type, binintersectRsub: $o).
13.82/2.27	thf(decl_154, type, binintersectSubset4: $o).
13.82/2.27	thf(decl_155, type, binintersectSubset1: $o).
13.82/2.27	thf(decl_156, type, bs114d: $o).
13.82/2.27	thf(decl_158, type, setminus: $i > $i > $i).
13.82/2.27	thf(decl_159, type, setminusI: $o).
13.82/2.27	thf(decl_160, type, setminusEL: $o).
13.82/2.27	thf(decl_161, type, setminusER: $o).
13.82/2.27	thf(decl_162, type, setminusSubset2: $o).
13.82/2.27	thf(decl_163, type, setminusERneg: $o).
13.82/2.27	thf(decl_164, type, setminusELneg: $o).
13.82/2.27	thf(decl_165, type, setminusILneg: $o).
13.82/2.27	thf(decl_166, type, setminusIRneg: $o).
13.82/2.27	thf(decl_167, type, setminusLsub: $o).
13.82/2.27	thf(decl_168, type, setminusSubset1: $o).
13.82/2.27	thf(decl_169, type, symdiff: $i > $i > $i).
13.82/2.27	thf(decl_170, type, symdiffE: $o).
13.82/2.27	thf(decl_171, type, symdiffI1: $o).
13.82/2.27	thf(decl_172, type, symdiffI2: $o).
13.82/2.27	thf(decl_173, type, symdiffIneg1: $o).
13.82/2.27	thf(decl_174, type, symdiffIneg2: $o).
13.82/2.27	thf(decl_175, type, iskpair: $i > $o).
13.82/2.27	thf(decl_176, type, secondinupair: $o).
13.82/2.27	thf(decl_177, type, setukpairIL: $o).
13.82/2.27	thf(decl_178, type, setukpairIR: $o).
13.82/2.27	thf(decl_179, type, kpairiskpair: $o).
13.82/2.27	thf(decl_180, type, kpair: $i > $i > $i).
13.82/2.27	thf(decl_181, type, kpairp: $o).
13.82/2.27	thf(decl_182, type, cartprod: $i > $i > $i).
13.82/2.27	thf(decl_183, type, singletonsubset: $o).
13.82/2.27	thf(decl_184, type, singletoninpowerset: $o).
13.82/2.27	thf(decl_185, type, singletoninpowunion: $o).
13.82/2.27	thf(decl_186, type, upairset2E: $o).
13.82/2.27	thf(decl_187, type, upairsubunion: $o).
13.82/2.27	thf(decl_188, type, upairinpowunion: $o).
13.82/2.27	thf(decl_189, type, ubforcartprodlem1: $o).
13.82/2.27	thf(decl_190, type, ubforcartprodlem2: $o).
13.82/2.27	thf(decl_191, type, ubforcartprodlem3: $o).
13.82/2.27	thf(decl_192, type, cartprodpairin: $o).
13.82/2.27	thf(decl_193, type, cartprodmempair1: $o).
13.82/2.27	thf(decl_194, type, cartprodmempair: $o).
13.82/2.27	thf(decl_195, type, setunionE2: $o).
13.82/2.27	thf(decl_196, type, setunionsingleton1: $o).
13.82/2.27	thf(decl_197, type, setunionsingleton2: $o).
13.82/2.27	thf(decl_198, type, setunionsingleton: $o).
13.82/2.27	thf(decl_199, type, singleton: $i > $o).
13.82/2.27	thf(decl_200, type, singletonprop: $o).
13.82/2.27	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
13.82/2.27	thf(decl_202, type, ex1E1: $o).
13.82/2.27	thf(decl_203, type, ex1I: $o).
13.82/2.27	thf(decl_204, type, ex1I2: $o).
13.82/2.27	thf(decl_205, type, singletonsuniq: $o).
13.82/2.27	thf(decl_210, type, setukpairinjL1: $o).
13.82/2.27	thf(decl_211, type, kfstsingleton: $o).
13.82/2.27	thf(decl_212, type, theprop: $o).
13.82/2.27	thf(decl_213, type, kfst: $i > $i).
13.82/2.27	thf(decl_214, type, kfstpairEq: $o).
13.82/2.27	thf(decl_215, type, cartprodfstin: $o).
13.82/2.27	thf(decl_216, type, setukpairinjL2: $o).
13.82/2.27	thf(decl_217, type, setukpairinjL: $o).
13.82/2.27	thf(decl_218, type, setukpairinjR11: $o).
13.82/2.27	thf(decl_219, type, setukpairinjR12: $o).
13.82/2.27	thf(decl_220, type, setukpairinjR1: $o).
13.82/2.27	thf(decl_221, type, upairequniteq: $o).
13.82/2.27	thf(decl_222, type, setukpairinjR2: $o).
13.82/2.27	thf(decl_223, type, setukpairinjR: $o).
13.82/2.27	thf(decl_224, type, ksndsingleton: $o).
13.82/2.27	thf(decl_225, type, ksnd: $i > $i).
13.82/2.27	thf(decl_226, type, ksndpairEq: $o).
13.82/2.27	thf(decl_227, type, kpairsurjEq: $o).
13.82/2.27	thf(decl_228, type, cartprodsndin: $o).
13.82/2.27	thf(decl_229, type, cartprodpairmemEL: $o).
13.82/2.27	thf(decl_230, type, cartprodpairmemER: $o).
13.82/2.27	thf(decl_231, type, cartprodmempaircEq: $o).
13.82/2.27	thf(decl_232, type, cartprodfstpairEq: $o).
13.82/2.27	thf(decl_233, type, cartprodsndpairEq: $o).
13.82/2.27	thf(decl_234, type, cartprodpairsurjEq: $o).
13.82/2.27	thf(decl_235, type, breln: $i > $i > $i > $o).
13.82/2.27	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
13.82/2.27	thf(decl_237, type, dpsetconstrI: $o).
13.82/2.27	thf(decl_238, type, dpsetconstrSub: $o).
13.82/2.27	thf(decl_239, type, setOfPairsIsBReln: $o).
13.82/2.27	thf(decl_240, type, dpsetconstrERa: $o).
13.82/2.27	thf(decl_241, type, dpsetconstrEL1: $o).
13.82/2.27	thf(decl_242, type, dpsetconstrEL2: $o).
13.82/2.27	thf(decl_243, type, dpsetconstrER: $o).
13.82/2.27	thf(decl_244, type, func: $i > $i > $i > $o).
13.82/2.27	thf(decl_245, type, funcSet: $i > $i > $i).
13.82/2.27	thf(decl_246, type, funcImageSingleton: $o).
13.82/2.27	thf(decl_247, type, apProp: $o).
13.82/2.27	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
13.82/2.27	thf(decl_249, type, app: $o).
13.82/2.27	thf(decl_250, type, infuncsetfunc: $o).
13.82/2.27	thf(decl_251, type, ap2p: $o).
13.82/2.27	thf(decl_252, type, funcinfuncset: $o).
13.82/2.27	thf(decl_253, type, lamProp: $o).
13.82/2.27	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
13.82/2.27	thf(decl_255, type, lamp: $o).
13.82/2.27	thf(decl_256, type, lam2p: $o).
13.82/2.27	thf(decl_257, type, brelnall1: $o).
13.82/2.27	thf(decl_258, type, brelnall2: $o).
13.82/2.27	thf(decl_259, type, ex1E2: $o).
13.82/2.27	thf(decl_260, type, funcGraphProp1: $o).
13.82/2.27	thf(decl_261, type, funcGraphProp3: $o).
13.82/2.27	thf(decl_262, type, funcGraphProp2: $o).
13.82/2.27	thf(decl_263, type, funcextLem: $o).
13.82/2.27	thf(decl_264, type, funcGraphProp4: $o).
13.82/2.27	thf(decl_265, type, subbreln: $o).
13.82/2.27	thf(decl_266, type, eqbreln: $o).
13.82/2.27	thf(decl_267, type, funcext: $o).
13.82/2.27	thf(decl_268, type, funcext2: $o).
13.82/2.27	thf(decl_269, type, ap2apEq1: $o).
13.82/2.27	thf(decl_270, type, ap2apEq2: $o).
13.82/2.27	thf(decl_271, type, beta1: $o).
13.82/2.27	thf(decl_272, type, eta1: $o).
13.82/2.27	thf(decl_273, type, lam2lamEq: $o).
13.82/2.27	thf(decl_274, type, beta2: $o).
13.82/2.27	thf(decl_275, type, eta2: $o).
13.82/2.27	thf(decl_276, type, iffalseProp1: $o).
13.82/2.27	thf(decl_277, type, iffalseProp2: $o).
13.82/2.27	thf(decl_278, type, iftrueProp1: $o).
13.82/2.27	thf(decl_279, type, iftrueProp2: $o).
13.82/2.27	thf(decl_280, type, ifSingleton: $o).
13.82/2.27	thf(decl_281, type, if: $i > $o > $i > $i > $i).
13.82/2.27	thf(decl_282, type, ifp: $o).
13.82/2.27	thf(decl_283, type, theeq: $o).
13.82/2.27	thf(decl_284, type, iftrue: $o).
13.82/2.27	thf(decl_285, type, iffalse: $o).
13.82/2.27	thf(decl_286, type, iftrueorfalse: $o).
13.82/2.27	thf(decl_287, type, binintersectT_lem: $o).
13.82/2.27	thf(decl_288, type, binunionT_lem: $o).
13.82/2.27	thf(decl_289, type, powersetT_lem: $o).
13.82/2.27	thf(decl_290, type, setminusT_lem: $o).
13.82/2.27	thf(decl_291, type, complementT_lem: $o).
13.82/2.27	thf(decl_292, type, setextT: $o).
13.82/2.27	thf(decl_293, type, subsetTI: $o).
13.82/2.27	thf(decl_294, type, powersetTI1: $o).
13.82/2.27	thf(decl_295, type, powersetTE1: $o).
13.82/2.27	thf(decl_296, type, complementTI1: $o).
13.82/2.27	thf(decl_297, type, complementTE1: $o).
13.82/2.27	thf(decl_298, type, binintersectTELcontra: $o).
13.82/2.27	thf(decl_299, type, binintersectTERcontra: $o).
13.82/2.27	thf(decl_300, type, contrasubsetT: $o).
13.82/2.27	thf(decl_301, type, contrasubsetT1: $o).
13.82/2.27	thf(decl_302, type, contrasubsetT2: $o).
13.82/2.27	thf(decl_303, type, epred1_0: $o).
13.82/2.27	thf(decl_304, type, esk1_2: $i > $i > $i).
13.82/2.27	thf(decl_305, type, esk2_2: $i > $i > $i).
13.82/2.27	thf(decl_306, type, esk3_2: $i > $i > $i).
13.82/2.27	thf(decl_307, type, esk4_1: $i > $i).
13.82/2.27	thf(decl_308, type, esk5_2: ($i > $i > $o) > $i > $i).
13.82/2.27	thf(decl_309, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
13.82/2.27	thf(decl_310, type, esk7_2: ($i > $i > $o) > $i > $i).
13.82/2.27	thf(decl_311, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
13.82/2.27	thf(decl_312, type, esk9_1: $i > $i).
13.82/2.27	thf(decl_313, type, esk10_2: ($i > $o) > $i > $i).
13.82/2.27	thf(decl_314, type, esk11_2: ($i > $o) > $i > $i).
13.82/2.27	thf(decl_315, type, esk12_1: ($i > $o) > $i).
13.82/2.27	thf(decl_316, type, esk13_2: ($i > $o) > $i > $i).
13.82/2.27	thf(decl_317, type, esk14_1: ($i > $o) > $i).
13.82/2.27	thf(decl_318, type, esk15_2: $i > $i > $i).
13.82/2.27	thf(decl_319, type, esk16_2: $i > $i > $i).
13.82/2.27	thf(decl_320, type, esk17_1: $i > $i).
13.82/2.27	thf(decl_321, type, esk18_1: $i > $i).
13.82/2.27	thf(decl_322, type, esk19_1: $i > $i).
13.82/2.27	thf(decl_323, type, esk20_2: $i > $i > $i).
13.82/2.27	thf(decl_324, type, esk21_3: $i > $i > $o > $i).
13.82/2.27	thf(decl_325, type, esk22_2: ($i > $o) > $i > $i).
13.82/2.27	thf(decl_326, type, esk23_1: ($i > $o) > $i).
13.82/2.27	thf(decl_327, type, esk24_1: $i > $i).
13.82/2.27	thf(decl_328, type, esk25_2: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_329, type, esk26_2: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_330, type, esk27_2: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_331, type, esk28_2: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_332, type, esk29_2: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_333, type, esk30_2: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_334, type, esk31_2: ($i > $o) > $i > $i).
13.82/2.27	thf(decl_335, type, esk32_1: ($i > $o) > $i).
13.82/2.27	thf(decl_336, type, esk33_1: ($i > $o) > $i).
13.82/2.27	thf(decl_337, type, esk34_1: ($i > $o) > $i).
13.82/2.27	thf(decl_338, type, esk35_1: ($i > $o) > $i).
13.82/2.27	thf(decl_339, type, esk36_2: ($i > $o) > $i > $i).
13.82/2.27	thf(decl_340, type, esk37_1: ($i > $o) > $i).
13.82/2.27	thf(decl_341, type, esk38_2: ($i > $o) > $i > $i).
13.82/2.27	thf(decl_342, type, esk39_2: ($i > $o) > ($i > $o) > $i).
13.82/2.27	thf(decl_343, type, esk40_2: ($i > $o) > ($i > $o) > $i).
13.82/2.27	thf(decl_344, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
13.82/2.27	thf(decl_345, type, esk42_2: ($i > $o) > ($i > $o) > $i).
13.82/2.27	thf(decl_346, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
13.82/2.27	thf(decl_347, type, esk44_2: ($i > $o) > ($i > $o) > $i).
13.82/2.27	thf(decl_348, type, esk45_2: ($i > $o) > $i > $i).
13.82/2.27	thf(decl_349, type, esk46_2: ($i > $o) > ($i > $o) > $i).
13.82/2.27	thf(decl_350, type, esk47_2: ($i > $o) > ($i > $o) > $i).
13.82/2.27	thf(decl_351, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
13.82/2.27	thf(decl_352, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
13.82/2.27	thf(decl_353, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
13.82/2.27	thf(decl_354, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
13.82/2.27	thf(decl_355, type, esk52_2: $i > $i > $i).
13.82/2.27	thf(decl_356, type, esk53_2: $i > $i > $i).
13.82/2.27	thf(decl_357, type, esk54_2: $i > $i > $i).
13.82/2.27	thf(decl_358, type, esk55_3: $i > $i > $i > $i).
13.82/2.27	thf(decl_359, type, esk56_3: $i > $i > $i > $i).
13.82/2.27	thf(decl_360, type, esk57_2: $i > $i > $i).
13.82/2.27	thf(decl_361, type, esk58_2: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_362, type, esk59_2: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_363, type, esk60_2: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_364, type, esk61_3: $i > ($i > $o) > $i > $i).
13.82/2.27	thf(decl_365, type, esk62_2: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_366, type, esk63_2: $i > ($i > $o) > $i).
13.82/2.27	thf(decl_367, type, esk64_3: $i > $i > ($i > $i) > $i).
13.82/2.27	thf(decl_368, type, esk65_3: $i > $i > ($i > $i) > $i).
13.82/2.27	thf(decl_369, type, esk66_3: $i > $i > ($i > $i) > $i).
13.82/2.27	thf(decl_370, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
13.82/2.27	thf(decl_371, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
13.82/2.27	thf(decl_372, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
13.82/2.27	thf(decl_373, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
13.82/2.27	thf(decl_374, type, esk71_4: $i > $i > $i > $i > $i).
13.82/2.27	thf(decl_375, type, esk72_4: $i > $i > $i > $i > $i).
13.82/2.27	thf(decl_376, type, esk73_4: $i > $i > $i > $i > $i).
13.82/2.27	thf(decl_377, type, esk74_4: $i > $i > $i > $i > $i).
13.82/2.27	thf(decl_378, type, esk75_4: $i > $i > $i > $i > $i).
13.82/2.27	thf(decl_379, type, esk76_4: $i > $i > $i > $i > $i).
13.82/2.27	thf(decl_380, type, esk77_4: $i > $i > $i > $i > $i).
13.82/2.27	thf(decl_381, type, esk78_4: $i > $i > $i > $i > $i).
13.82/2.27	thf(decl_382, type, esk79_4: $i > $i > $i > $i > $i).
13.82/2.27	thf(decl_383, type, esk80_3: $i > $i > ($i > $i) > $i).
13.82/2.27	thf(decl_384, type, esk81_3: $i > $i > ($i > $i) > $i).
13.82/2.27	thf(decl_385, type, esk82_3: $i > $i > ($i > $i) > $i).
13.82/2.27	thf(decl_386, type, esk83_3: $i > $i > $i > $i).
13.82/2.27	thf(decl_387, type, esk84_3: $i > $i > $i > $i).
13.82/2.27	thf(decl_388, type, esk85_3: $i > $i > $i > $i).
13.82/2.27	thf(decl_389, type, esk86_3: $i > $i > $i > $i).
13.82/2.27	thf(decl_390, type, esk87_0: $i).
13.82/2.27	thf(decl_391, type, esk88_0: $i).
13.82/2.27	thf(decl_392, type, esk89_0: $i).
13.82/2.27	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', replAx)).
13.82/2.27	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', exu)).
13.82/2.27	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', descrp)).
13.82/2.27	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', exuE1)).
13.82/2.27	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', exuE3e)).
13.82/2.27	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', nonempty)).
13.82/2.27	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', nonemptyI)).
13.82/2.27	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', exuE2)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', exuI1)).
13.82/2.27	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', exuI3)).
13.82/2.27	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', exuI2)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', exuE3u)).
13.82/2.27	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', exu__Cong)).
13.82/2.27	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', exuEu)).
13.82/2.27	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', descr__Cong)).
13.82/2.27	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ex1E1)).
13.82/2.27	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ex1)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', ex1I)).
13.82/2.27	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ex1I2)).
13.82/2.27	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setOfPairsIsBReln)).
13.82/2.27	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', breln)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', ex1E2)).
13.82/2.27	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', dsetconstrI)).
13.82/2.27	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', dsetconstrEL)).
13.82/2.27	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', dsetconstrER)).
13.82/2.27	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setbeta)).
13.82/2.27	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', nonemptyE1)).
13.82/2.27	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', nonemptyI1)).
13.82/2.27	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setoftrueEq)).
13.82/2.27	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', nonemptyImpWitness)).
13.82/2.27	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.hv8VQiADgy/E---3.1_12799.p', emptyE1)).
13.82/2.27	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', dsetconstr__Cong)).
13.82/2.27	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', sepInPowerset)).
13.82/2.27	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', sepSubset)).
13.82/2.27	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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', singletonprop)).
13.82/2.27	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', kfstsingleton)).
13.82/2.27	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ksndsingleton)).
13.82/2.27	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', dpsetconstrI)).
13.82/2.27	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', dpsetconstrSub)).
13.82/2.27	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', dpsetconstrERa)).
13.82/2.27	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', dpsetconstrEL1)).
13.82/2.27	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', dpsetconstrEL2)).
13.82/2.27	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', dpsetconstrER)).
13.82/2.27	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.hv8VQiADgy/E---3.1_12799.p', funcImageSingleton)).
13.82/2.27	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', apProp)).
13.82/2.27	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.hv8VQiADgy/E---3.1_12799.p', lamProp)).
13.82/2.27	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', lamp)).
13.82/2.27	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', lam2p)).
13.82/2.27	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.hv8VQiADgy/E---3.1_12799.p', brelnall1)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', brelnall2)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', subbreln)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', eqbreln)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', beta1)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', eta1)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', lam2lamEq)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', beta2)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', eta2)).
13.82/2.27	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', iffalseProp1)).
13.82/2.27	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.hv8VQiADgy/E---3.1_12799.p', iffalseProp2)).
13.82/2.27	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', iftrueProp1)).
13.82/2.27	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.hv8VQiADgy/E---3.1_12799.p', iftrueProp2)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', ifSingleton)).
13.82/2.27	thf(contrasubsetT3, conjecture, ((setextAx)=>((((powersetAx)=>(((omega0Ax)=>(((((foundationAx)=>(((descrp)=>(((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>(((emptysetE)=>((emptysetimpfalse)=>((((setext)=>(((((nonemptyE1)=>((nonemptyI)=>(((setadjoinIL)=>(((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((((emptyinPowerset)=>((((setunionI)=>(((subPowSU)=>(((nonemptyImpWitness)=>((((eqinunit)=>((singletonsswitch)=>((upairsetE)=>(((((vacuousDall)=>(((((quantDeMorgan4)=>((((notdexE)=>((notdallE)=>(((((inCongP)=>((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>(((powerset__Cong)=>((((exuEu)=>(((dsetconstr__Cong)=>(((((subsetI2)=>(((subsetE)=>((subsetE2)=>((((notequalI2)=>((subsetRefl)=>((((setadjoinSub2)=>(((((((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>(((((binunionIR)=>(((((binunionRsub)=>(((binintersectSubset5)=>((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>(((binintersectSubset4)=>(((bs114d)=>((setminusI)=>(((((setminusERneg)=>(((((setminusLsub)=>((((((symdiffIneg1)=>((symdiffIneg2)=>((((((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>(((upairinpowunion)=>(((((((((setunionsingleton1)=>((setunionsingleton2)=>(((singletonprop)=>((ex1E1)=>((ex1I)=>((((setukpairinjL1)=>(((theprop)=>((((setukpairinjL2)=>(((((setukpairinjR1)=>((((setukpairinjR)=>(((ksndpairEq)=>((((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((((cartprodpairsurjEq)=>((((((((dpsetconstrER)=>(((((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((((((brelnall2)=>((ex1E2)=>((((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(((((((((eta1)=>((lam2lamEq)=>(((((iffalseProp2)=>((iftrueProp1)=>(((((((((((powersetT_lem)=>(((complementT_lem)=>(((subsetTI)=>((powersetTI1)=>((((complementTE1)=>(((binintersectTERcontra)=>((contrasubsetT)=>((![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)<=(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))<=(contrasubsetT2))<=(contrasubsetT1))))<=(binintersectTELcontra)))<=(complementTI1))<=(powersetTE1))))<=(setextT)))<=(setminusT_lem)))<=(binunionT_lem))<=(binintersectT_lem))<=(iftrueorfalse))<=(iffalse))<=(iftrue))<=(theeq))<=(ifp))<=(ifSingleton))<=(iftrueProp2))))<=(iffalseProp1))<=(eta2))<=(beta2))))<=(beta1))<=(ap2apEq2))<=(ap2apEq1))<=(funcext2))<=(funcext))<=(eqbreln))<=(subbreln)))))<=(funcGraphProp3))<=(funcGraphProp1))))<=(brelnall1))<=(lam2p))<=(lamp))<=(lamProp)))))<=(app))<=(apProp))<=(funcImageSingleton)))<=(dpsetconstrEL2))<=(dpsetconstrEL1))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI)))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))))<=(cartprodsndin))<=(kpairsurjEq)))<=(ksndsingleton)))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12))<=(setukpairinjR11))<=(setukpairinjL)))<=(cartprodfstin))<=(kfstpairEq)))<=(kfstsingleton)))<=(singletonsuniq))<=(ex1I2)))))<=(setunionsingleton))))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2))<=(ubforcartprodlem1)))<=(upairsubunion)))))))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))<=(secondinupair))))<=(symdiffI2))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1)))<=(setminusIRneg))<=(setminusILneg))<=(setminusELneg)))<=(setminusSubset2))<=(setminusER))<=(setminusEL))))<=(binintersectSubset1)))<=(binintersectRsub))))))<=(binintersectLsub))))<=(binintersectI)))<=(binunionLsub))<=(binunionE))<=(binunionEcases)))<=(upairset2IR))<=(binunionIL))<=(sepSubset)))))<=(powersetE1))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset)))<=(setadjoinSub))<=(subsetTrans))))<=(notequalI1))<=(notsubsetI))))<=(emptysetsubset)))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1)))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong)))<=(setadjoin__Cong))))<=(exuE3u))))<=(exuI2))<=(exuI3))<=(exuI1))))<=(prop2set2propI))<=(prop2setI)))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1)))<=(emptyE1))<=(upairsetIR))<=(upairsetIL)))))<=(notinsingleton))<=(uniqinunit)))<=(exuE2)))<=(setunionE)))<=(powersetE))<=(emptyInPowerset)))<=(powersetI))<=(setoftrueEq)))))<=(emptyinunitempty)))<=(nonemptyI1))))<=(setbeta))<=(noeltsimpempty))<=(emptyI)))<=(exuE3e))<=(notinemptyset))))<=(prop2setE)))))<=(dsetconstrI)))<=(wellorderingAx)))<=(replAx))<=(omegaIndAx))<=(omegaSAx)))<=(setunionAx)))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', contrasubsetT3)).
13.82/2.27	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setextAx)).
13.82/2.27	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', emptysetAx)).
13.82/2.27	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setadjoinAx)).
13.82/2.27	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', powersetAx)).
13.82/2.27	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setunionAx)).
13.82/2.27	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', omega0Ax)).
13.82/2.27	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', omegaSAx)).
13.82/2.27	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', omegaIndAx)).
13.82/2.27	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', foundationAx)).
13.82/2.27	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.hv8VQiADgy/E---3.1_12799.p', wellorderingAx)).
13.82/2.27	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', prop2setE)).
13.82/2.27	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', emptysetE)).
13.82/2.27	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', emptysetimpfalse)).
13.82/2.27	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', notinemptyset)).
13.82/2.27	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setext)).
13.82/2.27	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', emptyI)).
13.82/2.27	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', noeltsimpempty)).
13.82/2.27	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setadjoinIL)).
13.82/2.27	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', emptyinunitempty)).
13.82/2.27	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setadjoinIR)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', setadjoinE)).
13.82/2.27	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setadjoinOr)).
13.82/2.27	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', powersetI)).
13.82/2.27	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', emptyinPowerset)).
13.82/2.27	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', emptyInPowerset)).
13.82/2.27	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', powersetE)).
13.82/2.27	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setunionI)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', setunionE)).
13.82/2.27	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', subPowSU)).
13.82/2.27	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', uniqinunit)).
13.82/2.27	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', notinsingleton)).
13.82/2.27	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', eqinunit)).
13.82/2.27	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', singletonsswitch)).
13.82/2.27	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', upairsetE)).
13.82/2.27	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', upairsetIL)).
13.82/2.27	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', upairsetIR)).
13.82/2.27	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', vacuousDall)).
13.82/2.27	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', quantDeMorgan1)).
13.82/2.27	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', quantDeMorgan2)).
13.82/2.27	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', quantDeMorgan3)).
13.82/2.27	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', quantDeMorgan4)).
13.82/2.27	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', prop2setI)).
13.82/2.27	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', prop2set2propI)).
13.82/2.27	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', notdexE)).
13.82/2.27	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', notdallE)).
13.82/2.27	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', inCongP)).
13.82/2.27	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', in__Cong)).
13.82/2.27	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', emptyset__Cong)).
13.82/2.27	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setadjoin__Cong)).
13.82/2.27	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', powerset__Cong)).
13.82/2.27	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setunion__Cong)).
13.82/2.27	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', omega__Cong)).
13.82/2.27	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', subsetI1)).
13.82/2.27	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', eqimpsubset2)).
13.82/2.27	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', eqimpsubset1)).
13.82/2.27	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', subsetI2)).
13.82/2.27	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', emptysetsubset)).
13.82/2.27	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', subsetE)).
13.82/2.27	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', subsetE2)).
13.82/2.27	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', notsubsetI)).
13.82/2.27	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', notequalI1)).
13.82/2.27	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', notequalI2)).
13.82/2.27	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', subsetRefl)).
13.82/2.27	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', subsetTrans)).
13.82/2.27	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setadjoinSub)).
13.82/2.27	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setadjoinSub2)).
13.82/2.27	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', subset2powerset)).
13.82/2.27	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setextsub)).
13.82/2.27	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', subsetemptysetimpeq)).
13.82/2.27	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', powersetI1)).
13.82/2.27	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', powersetE1)).
13.82/2.27	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', inPowerset)).
13.82/2.27	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', powersetsubset)).
13.82/2.27	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binunionIL)).
13.82/2.27	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', upairset2IR)).
13.82/2.27	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binunionIR)).
13.82/2.27	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binunionEcases)).
13.82/2.27	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binunionE)).
13.82/2.27	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binunionLsub)).
13.82/2.27	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binunionRsub)).
13.82/2.27	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectI)).
13.82/2.27	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectSubset5)).
13.82/2.27	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectEL)).
13.82/2.27	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectLsub)).
13.82/2.27	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectSubset2)).
13.82/2.27	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectSubset3)).
13.82/2.27	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectER)).
13.82/2.27	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', disjointsetsI1)).
13.82/2.27	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectRsub)).
13.82/2.27	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectSubset4)).
13.82/2.27	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectSubset1)).
13.82/2.27	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', bs114d)).
13.82/2.27	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setminusI)).
13.82/2.27	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setminusEL)).
13.82/2.27	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setminusER)).
13.82/2.27	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setminusSubset2)).
13.82/2.27	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setminusERneg)).
13.82/2.27	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setminusELneg)).
13.82/2.27	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setminusILneg)).
13.82/2.27	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setminusIRneg)).
13.82/2.27	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setminusLsub)).
13.82/2.27	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setminusSubset1)).
13.82/2.27	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', symdiffE)).
13.82/2.27	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', symdiffI1)).
13.82/2.27	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', symdiffI2)).
13.82/2.27	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', symdiffIneg1)).
13.82/2.27	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', symdiffIneg2)).
13.82/2.27	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', secondinupair)).
13.82/2.27	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setukpairIL)).
13.82/2.27	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setukpairIR)).
13.82/2.27	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', kpairiskpair)).
13.82/2.27	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', kpairp)).
13.82/2.27	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', singletonsubset)).
13.82/2.27	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', singletoninpowerset)).
13.82/2.27	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', singletoninpowunion)).
13.82/2.27	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', upairset2E)).
13.82/2.27	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', upairsubunion)).
13.82/2.27	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', upairinpowunion)).
13.82/2.27	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ubforcartprodlem1)).
13.82/2.27	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ubforcartprodlem2)).
13.82/2.27	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ubforcartprodlem3)).
13.82/2.27	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', cartprodpairin)).
13.82/2.27	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.hv8VQiADgy/E---3.1_12799.p', cartprodmempair1)).
13.82/2.27	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', cartprodmempair)).
13.82/2.27	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setunionE2)).
13.82/2.27	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setunionsingleton1)).
13.82/2.27	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setunionsingleton2)).
13.82/2.27	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setunionsingleton)).
13.82/2.27	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', singletonsuniq)).
13.82/2.27	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.hv8VQiADgy/E---3.1_12799.p', setukpairinjL1)).
13.82/2.27	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', theprop)).
13.82/2.27	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', kfstpairEq)).
13.82/2.27	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', cartprodfstin)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', setukpairinjL2)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', setukpairinjL)).
13.82/2.27	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setukpairinjR11)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', setukpairinjR12)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', setukpairinjR1)).
13.82/2.27	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', upairequniteq)).
13.82/2.27	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setukpairinjR2)).
13.82/2.27	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setukpairinjR)).
13.82/2.27	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ksndpairEq)).
13.82/2.27	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', kpairsurjEq)).
13.82/2.27	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', cartprodsndin)).
13.82/2.27	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', cartprodpairmemEL)).
13.82/2.27	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', cartprodpairmemER)).
13.82/2.27	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', cartprodmempaircEq)).
13.82/2.27	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', cartprodfstpairEq)).
13.82/2.27	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', cartprodsndpairEq)).
13.82/2.27	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', cartprodpairsurjEq)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', app)).
13.82/2.27	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', infuncsetfunc)).
13.82/2.27	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ap2p)).
13.82/2.27	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', funcinfuncset)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', funcGraphProp1)).
13.82/2.27	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.hv8VQiADgy/E---3.1_12799.p', funcGraphProp3)).
13.82/2.27	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', funcGraphProp2)).
13.82/2.27	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.hv8VQiADgy/E---3.1_12799.p', funcextLem)).
13.82/2.27	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', funcGraphProp4)).
13.82/2.27	thf(funcext, axiom, ((funcext)<=>![X4:$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.hv8VQiADgy/E---3.1_12799.p', funcext)).
13.82/2.27	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', funcext2)).
13.82/2.27	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ap2apEq1)).
13.82/2.27	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ap2apEq2)).
13.82/2.27	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', ifp)).
13.82/2.27	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', theeq)).
13.82/2.27	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', iftrue)).
13.82/2.27	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', iffalse)).
13.82/2.27	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', iftrueorfalse)).
13.82/2.27	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectT_lem)).
13.82/2.27	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binunionT_lem)).
13.82/2.27	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', powersetT_lem)).
13.82/2.27	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setminusT_lem)).
13.82/2.27	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', complementT_lem)).
13.82/2.27	thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', setextT)).
13.82/2.27	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', subsetTI)).
13.82/2.27	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', powersetTI1)).
13.82/2.27	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', powersetTE1)).
13.82/2.27	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', complementTI1)).
13.82/2.27	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', complementTE1)).
13.82/2.27	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectTELcontra)).
13.82/2.27	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', binintersectTERcontra)).
13.82/2.27	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', contrasubsetT)).
13.82/2.27	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', contrasubsetT1)).
13.82/2.27	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.hv8VQiADgy/E---3.1_12799.p', contrasubsetT2)).
13.82/2.27	thf(c_0_247, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
13.82/2.27	thf(c_0_248, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
13.82/2.27	thf(c_0_249, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
13.82/2.27	thf(c_0_250, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
13.82/2.27	thf(c_0_251, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
13.82/2.27	thf(c_0_252, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
13.82/2.27	thf(c_0_253, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
13.82/2.27	thf(c_0_254, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
13.82/2.27	thf(c_0_255, 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])).
13.82/2.27	thf(c_0_256, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
13.82/2.27	thf(c_0_257, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
13.82/2.27	thf(c_0_258, 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])).
13.82/2.27	thf(c_0_259, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
13.82/2.27	thf(c_0_260, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
13.82/2.27	thf(c_0_261, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
13.82/2.27	thf(c_0_262, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
13.82/2.27	thf(c_0_263, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
13.82/2.27	thf(c_0_264, 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])).
13.82/2.27	thf(c_0_265, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
13.82/2.27	thf(c_0_266, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
13.82/2.27	thf(c_0_267, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
13.82/2.27	thf(c_0_268, 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])).
13.82/2.27	thf(c_0_269, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X803:$i]:((((X6 @ X2 @ X803))&![X804:$i]:((((X6 @ X2 @ X804))=>((X803)=(X804)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_247, c_0_248])).
13.82/2.27	thf(c_0_270, plain, ((descrp)=(![X1:$i > $o]:(((?[X805:$i]:((((X1 @ X805))&![X806:$i]:((((X1 @ X806))=>((X805)=(X806)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_249, c_0_248])).
13.82/2.27	thf(c_0_271, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
13.82/2.27	thf(c_0_272, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
13.82/2.27	thf(c_0_273, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
13.82/2.27	thf(c_0_274, plain, ((exuE1)=(![X1:$i > $o]:(((?[X807:$i]:((((X1 @ X807))&![X808:$i]:((((X1 @ X808))=>((X807)=(X808)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_250, c_0_248])).
13.82/2.27	thf(c_0_275, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X809:$i]:((((X1 @ X809))&![X810:$i]:((((X1 @ X810))=>((X809)=(X810)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_251, c_0_248])).
13.82/2.27	thf(c_0_276, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
13.82/2.27	thf(c_0_277, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_252])).
13.82/2.27	thf(c_0_278, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_253, c_0_252])).
13.82/2.27	thf(c_0_279, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_252])).
13.82/2.27	thf(c_0_280, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
13.82/2.27	thf(c_0_281, plain, ((exuE2)=(![X1:$i > $o]:(((?[X811:$i]:((((X1 @ X811))&![X812:$i]:((((X1 @ X812))=>((X811)=(X812)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_254, c_0_248])).
13.82/2.27	thf(c_0_282, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_252])).
13.82/2.27	thf(c_0_283, 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])).
13.82/2.27	thf(c_0_284, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X813:$i]:((((X1 @ X813))&![X814:$i]:((((X1 @ X814))=>((X813)=(X814))))))))))), inference(apply_def,[status(thm)],[c_0_255, c_0_248])).
13.82/2.27	thf(c_0_285, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X815:$i]:((((X1 @ X815))&![X816:$i]:((((X1 @ X816))=>((X815)=(X816)))))))))))), inference(apply_def,[status(thm)],[c_0_256, c_0_248])).
13.82/2.27	thf(c_0_286, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X817:$i]:((((X1 @ X817))&![X818:$i]:((((X1 @ X818))=>((X817)=(X818))))))))))), inference(apply_def,[status(thm)],[c_0_257, c_0_248])).
13.82/2.27	thf(c_0_287, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X819:$i]:((((X1 @ X819))&![X820:$i]:((((X1 @ X820))=>((X819)=(X820)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_258, c_0_248])).
13.82/2.27	thf(c_0_288, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X821:$i]:((((X1 @ X821))&![X822:$i]:((((X1 @ X822))=>((X821)=(X822)))))))<=>(?[X823:$i]:((((X17 @ X823))&![X824:$i]:((((X17 @ X824))=>((X823)=(X824)))))))))))), inference(apply_def,[status(thm)],[c_0_259, c_0_248])).
13.82/2.27	thf(c_0_289, plain, ((exuEu)=(![X1:$i > $o]:(((?[X825:$i]:((((X1 @ X825))&![X826:$i]:((((X1 @ X826))=>((X825)=(X826)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_260, c_0_248])).
13.82/2.27	thf(c_0_290, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X827:$i]:((((X1 @ X827))&![X828:$i]:((((X1 @ X828))=>((X827)=(X828)))))))=>((?[X829:$i]:((((X17 @ X829))&![X830:$i]:((((X17 @ X830))=>((X829)=(X830)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_261, c_0_248])).
13.82/2.27	thf(c_0_291, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
13.82/2.27	thf(c_0_292, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
13.82/2.27	thf(c_0_293, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
13.82/2.27	thf(c_0_294, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
13.82/2.27	thf(c_0_295, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_262, c_0_263])).
13.82/2.27	thf(c_0_296, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))))))))), inference(apply_def,[status(thm)],[c_0_264, c_0_263])).
13.82/2.27	thf(c_0_297, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))))))), inference(apply_def,[status(thm)],[c_0_265, c_0_263])).
13.82/2.27	thf(c_0_298, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
13.82/2.27	thf(c_0_299, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
13.82/2.27	thf(c_0_300, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
13.82/2.27	thf(c_0_301, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
13.82/2.27	thf(c_0_302, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_266, c_0_267])).
13.82/2.27	thf(c_0_303, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
13.82/2.27	thf(c_0_304, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
13.82/2.27	thf(c_0_305, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
13.82/2.27	thf(c_0_306, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
13.82/2.27	thf(c_0_307, plain, ((funcImageSingleton)<=>![X4:$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])).
13.82/2.27	thf(c_0_308, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
13.82/2.27	thf(c_0_309, plain, ((lamProp)<=>![X4:$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])).
13.82/2.27	thf(c_0_310, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
13.82/2.27	thf(c_0_311, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
13.82/2.27	thf(c_0_312, axiom, ((brelnall1)=(![X4:$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_267])).
13.82/2.27	thf(c_0_313, 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_267])).
13.82/2.27	thf(c_0_314, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_268, c_0_263])).
13.82/2.27	thf(c_0_315, 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_267])).
13.82/2.27	thf(c_0_316, 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_267])).
13.82/2.27	thf(c_0_317, 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])).
13.82/2.27	thf(c_0_318, 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])).
13.82/2.27	thf(c_0_319, 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])).
13.82/2.27	thf(c_0_320, 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])).
13.82/2.27	thf(c_0_321, 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])).
13.82/2.27	thf(c_0_322, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
13.82/2.27	thf(c_0_323, plain, ((iffalseProp2)<=>![X4:$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])).
13.82/2.27	thf(c_0_324, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
13.82/2.27	thf(c_0_325, plain, ((iftrueProp2)<=>![X4:$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])).
13.82/2.27	thf(c_0_326, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
13.82/2.27	thf(c_0_327, plain, ((epred1_0)<=>![X1572:$i]:(?[X1573:$i]:((((![X1574:$i]:(((in @ X1574 @ X1573)=>![X1575:$i]:(((in @ X1575 @ X1574)=>(in @ X1575 @ X1572)))))&![X1576:$i, X1577:$i]:((((in @ X1576 @ X1572)&(in @ X1577 @ X1572))=>(![X1578:$i]:(((in @ X1578 @ X1573)=>((in @ X1576 @ X1578)<=>(in @ X1577 @ X1578))))=>((X1576)=(X1577))))))&![X1579:$i, X1580:$i]:((((in @ X1579 @ X1573)&(in @ X1580 @ X1573))=>(![X1581:$i]:(((in @ X1581 @ X1579)=>(in @ X1581 @ X1580)))|![X1582:$i]:(((in @ X1582 @ X1580)=>(in @ X1582 @ X1579)))))))&![X1583:$i]:(((![X1584:$i]:(((in @ X1584 @ X1583)=>(in @ X1584 @ X1572)))&?[X1585:$i]:((in @ X1585 @ X1583)))=>?[X1586:$i, X1587:$i]:(((((in @ X1586 @ X1573)&(in @ X1587 @ X1583))&~(?[X1588:$i]:(((in @ X1588 @ X1586)&(in @ X1588 @ X1583)))))&![X1589:$i]:(((in @ X1589 @ X1573)=>(![X1590:$i]:(((in @ X1590 @ X1589)=>(in @ X1590 @ X1586)))|(in @ X1587 @ X1589)))))))))))), introduced(definition)).
13.82/2.27	thf(c_0_328, negated_conjecture, ~((![X831:$i, X832:$i]:((![X833:$i]:(((in @ X833 @ X831)<=>(in @ X833 @ X832)))=>((X831)=(X832))))=>(![X1609:$i]:(~(in @ X1609 @ emptyset))=>(![X1606:$i, X1607:$i, X1608:$i]:(((in @ X1608 @ (setadjoin @ X1606 @ X1607))<=>(((X1608)=(X1606))|(in @ X1608 @ X1607))))=>(![X834:$i, X835:$i]:(((in @ X835 @ (powerset @ X834))<=>![X836:$i]:(((in @ X836 @ X835)=>(in @ X836 @ X834)))))=>(![X1603:$i, X1604:$i]:(((in @ X1604 @ (setunion @ X1603))<=>?[X1605:$i]:(((in @ X1604 @ X1605)&(in @ X1605 @ X1603)))))=>((in @ emptyset @ omega)=>(![X1602:$i]:(((in @ X1602 @ omega)=>(in @ (setadjoin @ X1602 @ X1602) @ omega)))=>(![X1599:$i]:((((in @ emptyset @ X1599)&![X1600:$i]:((((in @ X1600 @ omega)&(in @ X1600 @ X1599))=>(in @ (setadjoin @ X1600 @ X1600) @ X1599))))=>![X1601:$i]:(((in @ X1601 @ omega)=>(in @ X1601 @ X1599)))))=>(![X1591:$i > $i > $o, X1592:$i]:((![X1593:$i]:(((in @ X1593 @ X1592)=>?[X1594:$i]:(((X1591 @ X1593 @ X1594)&![X1595:$i]:(((X1591 @ X1593 @ X1595)=>((X1594)=(X1595))))))))=>?[X1596:$i]:(![X1597:$i]:(((in @ X1597 @ X1596)<=>?[X1598:$i]:(((in @ X1598 @ X1592)&(X1591 @ X1598 @ X1597))))))))=>(![X837:$i]:((?[X838:$i]:((in @ X838 @ X837))=>?[X839:$i]:(((in @ X839 @ X837)&~(?[X840:$i]:(((in @ X840 @ X839)&(in @ X840 @ X837))))))))=>((epred1_0)=>(![X841:$i > $o]:((?[X842:$i]:(((X841 @ X842)&![X843:$i]:(((X841 @ X843)=>((X842)=(X843))))))=>(X841 @ (descr @ (^[Z0/* 17 */:$i]:(X841 @ Z0))))))=>(![X1569:$i, X1570:$i > $o, X1571:$i]:(((in @ X1571 @ X1569)=>((X1570 @ X1571)=>(in @ X1571 @ (dsetconstr @ X1569 @ X1570)))))=>(![X844:$i, X845:$i > $o, X846:$i]:(((in @ X846 @ (dsetconstr @ X844 @ X845))=>(in @ X846 @ X844)))=>(![X847:$i, X848:$i > $o, X849:$i]:(((in @ X849 @ (dsetconstr @ X847 @ X848))=>(X848 @ X849)))=>(![X850:$i > $o]:((?[X851:$i]:(((X850 @ X851)&![X852:$i]:(((X850 @ X852)=>((X851)=(X852))))))=>?[X853:$i]:(((X850 @ X853)&![X854:$i]:(((X850 @ X854)=>((X853)=(X854))))))))=>(![X1567:$o, X1568:$i]:(((in @ X1568 @ (prop2set @ ((X1567))))=>(X1567)))=>(![X855:$i]:(((in @ X855 @ emptyset)=>![X856:$o]:((X856))))=>(![X857:$i]:(((in @ X857 @ emptyset)=>~($true)))=>(![X1566:$i]:(~(in @ X1566 @ emptyset))=>(![X1562:$i > $o]:((?[X1563:$i]:(((X1562 @ X1563)&![X1564:$i]:(((X1562 @ X1564)=>((X1563)=(X1564))))))=>?[X1565:$i]:((X1562 @ X1565))))=>(![X858:$i, X859:$i]:((![X860:$i]:(((in @ X860 @ X858)=>(in @ X860 @ X859)))=>(![X861:$i]:(((in @ X861 @ X859)=>(in @ X861 @ X858)))=>((X858)=(X859)))))=>(![X1560:$i]:((![X1561:$i]:(~(in @ X1561 @ X1560))=>((X1560)=(emptyset))))=>(![X1558:$i]:((![X1559:$i]:(~(in @ X1559 @ X1558))=>((X1558)=(emptyset))))=>(![X1555:$i, X1556:$i > $o, X1557:$i]:(((in @ X1557 @ X1555)=>((in @ X1557 @ (dsetconstr @ X1555 @ X1556))<=>(X1556 @ X1557))))=>(![X862:$i]:((((X862)!=(emptyset))=>?[X863:$i]:((in @ X863 @ X862))))=>(![X864:$i, X865:$i > $o, X866:$i]:(((in @ X866 @ X864)=>((X865 @ X866)=>((dsetconstr @ X864 @ X865)!=(emptyset)))))=>(![X1553:$i]:((?[X1554:$i]:((in @ X1554 @ X1553))=>((X1553)!=(emptyset))))=>(![X867:$i, X868:$i]:((in @ X867 @ (setadjoin @ X867 @ X868)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X869:$i, X870:$i, X871:$i]:(((in @ X871 @ X870)=>(in @ X871 @ (setadjoin @ X869 @ X870))))=>(![X872:$i, X873:$i, X874:$i]:(((in @ X874 @ (setadjoin @ X872 @ X873))=>![X875:$o]:(((((X874)=(X872))=>(X875))=>(((in @ X874 @ X873)=>(X875))=>(X875))))))=>(![X876:$i, X877:$i, X878:$i]:(((in @ X878 @ (setadjoin @ X876 @ X877))=>(((X878)=(X876))|(in @ X878 @ X877))))=>(![X1552:$i]:(((dsetconstr @ X1552 @ (^[Z0/* 1 */:$i]:($true)))=(X1552)))=>(![X1549:$i, X1550:$i]:((![X1551:$i]:(((in @ X1551 @ X1550)=>(in @ X1551 @ X1549)))=>(in @ X1550 @ (powerset @ X1549))))=>(![X879:$i]:((in @ emptyset @ (powerset @ X879)))=>(![X1548:$i]:((in @ emptyset @ (powerset @ X1548)))=>(![X1545:$i, X1546:$i, X1547:$i]:(((in @ X1546 @ (powerset @ X1545))=>((in @ X1547 @ X1546)=>(in @ X1547 @ X1545))))=>(![X880:$i, X881:$i, X882:$i]:(((in @ X881 @ X882)=>((in @ X882 @ X880)=>(in @ X881 @ (setunion @ X880)))))=>(![X1541:$i, X1542:$i]:(((in @ X1542 @ (setunion @ X1541))=>![X1543:$o]:((![X1544:$i]:(((in @ X1542 @ X1544)=>((in @ X1544 @ X1541)=>(X1543))))=>(X1543)))))=>(![X883:$i, X884:$i]:(((in @ X884 @ X883)=>(in @ X884 @ (powerset @ (setunion @ X883)))))=>(![X1536:$i > $o]:((?[X1537:$i]:(((X1536 @ X1537)&![X1538:$i]:(((X1536 @ X1538)=>((X1537)=(X1538))))))=>?[X1539:$i]:(![X1540:$i]:(((X1536 @ X1540)<=>((X1540)=(X1539)))))))=>(![X885:$i]:((((X885)!=(emptyset))=>?[X886:$i]:(((in @ X886 @ X885)&$true))))=>(![X1534:$i, X1535:$i]:(((in @ X1534 @ (setadjoin @ X1535 @ emptyset))=>((X1534)=(X1535))))=>(![X1532:$i, X1533:$i]:((((X1532)!=(X1533))=>~(in @ X1533 @ (setadjoin @ X1532 @ emptyset))))=>(![X887:$i, X888:$i]:((((X887)=(X888))=>(in @ X887 @ (setadjoin @ X888 @ emptyset))))=>(![X889:$i, X890:$i]:(((in @ X889 @ (setadjoin @ X890 @ emptyset))=>(in @ X890 @ (setadjoin @ X889 @ emptyset))))=>(![X891:$i, X892:$i, X893:$i]:(((in @ X893 @ (setadjoin @ X891 @ (setadjoin @ X892 @ emptyset)))=>(((X893)=(X891))|((X893)=(X892)))))=>(![X1530:$i, X1531:$i]:((in @ X1530 @ (setadjoin @ X1530 @ (setadjoin @ X1531 @ emptyset))))=>(![X1528:$i, X1529:$i]:((in @ X1529 @ (setadjoin @ X1528 @ (setadjoin @ X1529 @ emptyset))))=>(![X1525:$i, X1526:$i > $o]:((?[X1527:$i]:(((in @ X1527 @ X1525)&(X1526 @ X1527)))=>(((dsetconstr @ X1525 @ X1526)=(emptyset))=>~($true))))=>(![X894:$i > $o, X895:$i]:(((in @ X895 @ emptyset)=>(X894 @ X895)))=>(![X1521:$i, X1522:$i > $o]:((~(![X1523:$i]:(((in @ X1523 @ X1521)=>(X1522 @ X1523))))=>?[X1524:$i]:(((in @ X1524 @ X1521)&~((X1522 @ X1524))))))=>(![X1517:$i, X1518:$i > $o]:((![X1519:$i]:(((in @ X1519 @ X1517)=>~((X1518 @ X1519))))=>~(?[X1520:$i]:(((in @ X1520 @ X1517)&(X1518 @ X1520))))))=>(![X1513:$i, X1514:$i > $o]:((~(?[X1515:$i]:(((in @ X1515 @ X1513)&(X1514 @ X1515))))=>![X1516:$i]:(((in @ X1516 @ X1513)=>~((X1514 @ X1516))))))=>(![X896:$i, X897:$i > $o]:((?[X898:$i]:(((in @ X898 @ X896)&~((X897 @ X898))))=>~(![X899:$i]:(((in @ X899 @ X896)=>(X897 @ X899))))))=>(![X1512:$o]:(((X1512)=>(in @ emptyset @ (prop2set @ ((X1512))))))=>(![X1511:$o]:(((X1511)=>(set2prop @ (prop2set @ ((X1511))))))=>(![X900:$i, X901:$i > $o]:((~(?[X902:$i]:(((in @ X902 @ X900)&(X901 @ X902))))=>![X903:$i]:(((in @ X903 @ X900)=>~((X901 @ X903))))))=>(![X904:$i, X905:$i > $o]:((~(![X906:$i]:(((in @ X906 @ X904)=>(X905 @ X906))))=>?[X907:$i]:(((in @ X907 @ X904)&~((X905 @ X907))))))=>(![X1506:$i > $o]:((?[X1507:$i]:(((X1506 @ X1507)&![X1508:$i]:(((X1506 @ X1508)=>((X1507)=(X1508))))))=>?[X1509:$i]:(((X1506 @ X1509)&![X1510:$i]:(((X1506 @ X1510)=>((X1509)=(X1510))))))))=>(![X1500:$i > $o]:((?[X1501:$i]:((X1500 @ X1501))=>(![X1502:$i, X1503:$i]:(((X1500 @ X1502)=>((X1500 @ X1503)=>((X1502)=(X1503)))))=>?[X1504:$i]:(((X1500 @ X1504)&![X1505:$i]:(((X1500 @ X1505)=>((X1504)=(X1505)))))))))=>(![X1495:$i > $o]:((?[X1496:$i]:(![X1497:$i]:(((X1495 @ X1497)<=>((X1497)=(X1496)))))=>?[X1498:$i]:(((X1495 @ X1498)&![X1499:$i]:(((X1495 @ X1499)=>((X1498)=(X1499))))))))=>(![X908:$i, X909:$i]:((((X908)=(X909))=>![X910:$i, X911:$i]:((((X910)=(X911))=>((in @ X910 @ X908)=>(in @ X911 @ X909))))))=>(![X912:$i, X913:$i]:((((X912)=(X913))=>![X914:$i, X915:$i]:((((X914)=(X915))=>((in @ X914 @ X912)<=>(in @ X915 @ X913))))))=>(![X1490:$i > $o]:((?[X1491:$i]:(((X1490 @ X1491)&![X1492:$i]:(((X1490 @ X1492)=>((X1491)=(X1492))))))=>![X1493:$i, X1494:$i]:(((X1490 @ X1493)=>((X1490 @ X1494)=>((X1493)=(X1494)))))))=>(![X916:$i > $o, X917:$i > $o]:((![X918:$i, X919:$i]:((((X918)=(X919))=>((X916 @ X918)<=>(X917 @ X919))))=>(?[X920:$i]:(((X916 @ X920)&![X921:$i]:(((X916 @ X921)=>((X920)=(X921))))))<=>?[X922:$i]:(((X917 @ X922)&![X923:$i]:(((X917 @ X923)=>((X922)=(X923)))))))))=>(((emptyset)=(emptyset))=>(![X1486:$i, X1487:$i]:((((X1486)=(X1487))=>![X1488:$i, X1489:$i]:((((X1488)=(X1489))=>((setadjoin @ X1486 @ X1488)=(setadjoin @ X1487 @ X1489))))))=>(![X924:$i, X925:$i]:((((X924)=(X925))=>((powerset @ X924)=(powerset @ X925))))=>(![X1484:$i, X1485:$i]:((((X1484)=(X1485))=>((setunion @ X1484)=(setunion @ X1485))))=>(((omega)=(omega))=>(![X926:$i > $o]:((?[X927:$i]:(((X926 @ X927)&![X928:$i]:(((X926 @ X928)=>((X927)=(X928))))))=>![X929:$i, X930:$i]:(((X926 @ X929)=>((X926 @ X930)=>((X929)=(X930)))))))=>(![X1476:$i > $o, X1477:$i > $o]:((![X1478:$i, X1479:$i]:((((X1478)=(X1479))=>((X1476 @ X1478)<=>(X1477 @ X1479))))=>(?[X1480:$i]:(((X1476 @ X1480)&![X1481:$i]:(((X1476 @ X1481)=>((X1480)=(X1481))))))=>(?[X1482:$i]:(((X1477 @ X1482)&![X1483:$i]:(((X1477 @ X1483)=>((X1482)=(X1483))))))=>((descr @ X1476)=(descr @ X1477))))))=>(![X931:$i, X932:$i]:((((X931)=(X932))=>![X933:$i > $o, X934:$i > $o]:((![X935:$i]:(((in @ X935 @ X931)=>![X936:$i]:(((in @ X936 @ X932)=>(((X935)=(X936))=>((X933 @ X935)<=>(X934 @ X936)))))))=>((dsetconstr @ X931 @ X933)=(dsetconstr @ X932 @ X934))))))=>(![X1473:$i, X1474:$i]:((![X1475:$i]:(((in @ X1475 @ X1473)=>(in @ X1475 @ X1474)))=>(subset @ X1473 @ X1474)))=>(![X1471:$i, X1472:$i]:((((X1471)=(X1472))=>(subset @ X1472 @ X1471)))=>(![X1469:$i, X1470:$i]:((((X1469)=(X1470))=>(subset @ X1469 @ X1470)))=>(![X937:$i, X938:$i]:((![X939:$i]:(((in @ X939 @ X937)=>(in @ X939 @ X938)))=>(subset @ X937 @ X938)))=>(![X1468:$i]:((subset @ emptyset @ X1468))=>(![X940:$i, X941:$i, X942:$i]:(((subset @ X940 @ X941)=>((in @ X942 @ X940)=>(in @ X942 @ X941))))=>(![X943:$i, X944:$i, X945:$i]:(((subset @ X943 @ X944)=>(~(in @ X945 @ X944)=>~(in @ X945 @ X943))))=>(![X1465:$i, X1466:$i, X1467:$i]:(((in @ X1467 @ X1465)=>(~(in @ X1467 @ X1466)=>~(subset @ X1465 @ X1466))))=>(![X1463:$i, X1464:$i]:((~(subset @ X1463 @ X1464)=>((X1463)!=(X1464))))=>(![X946:$i, X947:$i, X948:$i]:(((in @ X948 @ X946)=>(~(in @ X948 @ X947)=>((X946)!=(X947)))))=>(![X949:$i]:((subset @ X949 @ X949))=>(![X1460:$i, X1461:$i, X1462:$i]:(((subset @ X1460 @ X1461)=>((subset @ X1461 @ X1462)=>(subset @ X1460 @ X1462))))=>(![X1458:$i, X1459:$i]:((subset @ X1459 @ (setadjoin @ X1458 @ X1459)))=>(![X950:$i, X951:$i, X952:$i]:(((subset @ X950 @ X952)=>(subset @ X950 @ (setadjoin @ X951 @ X952))))=>(![X1456:$i, X1457:$i]:(((subset @ X1456 @ X1457)=>(in @ X1456 @ (powerset @ X1457))))=>(![X1454:$i, X1455:$i]:(((subset @ X1454 @ X1455)=>((subset @ X1455 @ X1454)=>((X1454)=(X1455)))))=>(![X1453:$i]:(((subset @ X1453 @ emptyset)=>((X1453)=(emptyset))))=>(![X1451:$i, X1452:$i]:(((subset @ X1452 @ X1451)=>(in @ X1452 @ (powerset @ X1451))))=>(![X1449:$i, X1450:$i]:(((in @ X1450 @ (powerset @ X1449))=>(subset @ X1450 @ X1449)))=>(![X953:$i]:((in @ X953 @ (powerset @ X953)))=>(![X954:$i, X955:$i]:(((subset @ X954 @ X955)=>(subset @ (powerset @ X954) @ (powerset @ X955))))=>(![X956:$i, X957:$i > $o]:((in @ (dsetconstr @ X956 @ X957) @ (powerset @ X956)))=>(![X1447:$i, X1448:$i > $o]:((subset @ (dsetconstr @ X1447 @ X1448) @ X1447))=>(![X1444:$i, X1445:$i, X1446:$i]:(((in @ X1446 @ X1444)=>(in @ X1446 @ (binunion @ X1444 @ X1445))))=>(![X1442:$i, X1443:$i]:((in @ X1443 @ 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X1255)))))=>(![X1249:$i, X1250:$i, X1251:$i]:(((in @ X1251 @ (funcSet @ X1249 @ X1250))=>![X1252:$i]:(((in @ X1252 @ X1249)=>(in @ (kpair @ X1252 @ (ap @ X1249 @ X1250 @ X1251 @ X1252)) @ X1251)))))=>(![X1087:$i, X1088:$i, X1089:$i]:(((func @ X1087 @ X1088 @ X1089)=>![X1090:$i]:(((in @ X1090 @ X1087)=>![X1091:$i]:(((in @ X1091 @ X1088)=>((in @ (kpair @ X1090 @ X1091) @ X1089)=>((ap @ X1087 @ X1088 @ X1089 @ X1090)=(X1091)))))))))=>(![X1092:$i, X1093:$i, X1094:$i]:(((func @ X1092 @ X1093 @ X1094)=>![X1095:$i]:(((func @ X1092 @ X1093 @ X1095)=>(![X1096:$i]:(((in @ X1096 @ X1092)=>((ap @ X1092 @ X1093 @ X1094 @ X1096)=(ap @ X1092 @ X1093 @ X1095 @ X1096))))=>![X1097:$i]:(((in @ X1097 @ X1092)=>![X1098:$i]:(((in @ X1098 @ X1093)=>((in @ (kpair @ X1097 @ X1098) @ X1095)=>(in @ (kpair @ X1097 @ X1098) @ X1094)))))))))))=>(![X1099:$i, X1100:$i, X1101:$i]:(((in @ X1101 @ (funcSet @ X1099 @ X1100))=>![X1102:$i]:(((in @ X1102 @ X1099)=>![X1103:$i]:(((in @ X1103 @ X1100)=>((in @ (kpair @ X1102 @ 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(setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[contrasubsetT3]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_269]), foundationAx]), wellorderingAx]), c_0_270]), c_0_271]), c_0_272]), c_0_273]), c_0_274]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_275]), setext]), emptyI]), noeltsimpempty]), c_0_276]), c_0_277]), c_0_278]), c_0_279]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_280]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_281]), c_0_282]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_283]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_284]), c_0_285]), c_0_286]), inCongP]), in__Cong]), c_0_287]), c_0_288]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_289]), c_0_290]), c_0_291]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_292]), c_0_293]), 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_294]), c_0_295]), c_0_296]), c_0_297]), singletonsuniq]), setukpairinjL1]), c_0_298]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_299]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), c_0_306]), c_0_307]), c_0_308]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_309]), c_0_310]), c_0_311]), c_0_312]), c_0_313]), c_0_314]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_315]), c_0_316]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_317]), c_0_318]), c_0_319]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), c_0_324]), c_0_325]), c_0_326]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2])])]), c_0_327])).
13.82/2.27	thf(c_0_329, negated_conjecture, ![X1610:$i, X1611:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1623:$i, X1624:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1632:$i, X1633:$i > $i > $o, X1634:$i, X1636:$i, X1639:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1646:$i, X1647:$i > $o, X1648:$i, X1650:$i, X1651:$i > $o, X1652:$i, X1653:$i, X1654:$i > $o, X1655:$i, X1656:$i, X1657:$i > $o, X1658:$i, X1659:$i > $o, X1660:$i, X1663:$i, X1664:$o, X1665:$i, X1666:$i, X1667:$o, X1668:$i, X1669:$i, X1670:$i > $o, X1671:$i, X1674:$i, X1675:$i, X1678:$i, X1680:$i, X1682:$i, X1683:$i > $o, X1684:$i, X1685:$i, X1687:$i, X1688:$i > $o, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$o, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$o, X1720:$i, X1721:$i, X1722:$i > $o, X1723:$i, X1726:$i, X1727:$i, X1728:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i > $o, X1747:$i, X1748:$i > $o, X1749:$i, X1750:$i, X1751:$i > $o, X1752:$i, X1754:$i, X1755:$i > $o, X1757:$i, X1758:$i, X1759:$i > $o, X1761:$i, X1762:$i, X1763:$i > $o, X1764:$i, X1766:$o, X1767:$o, X1768:$i, X1769:$i > $o, X1771:$i, X1772:$i, X1773:$i > $o, X1774:$i, X1776:$i > $o, X1777:$i, X1780:$i, X1781:$i > $o, X1782:$i, X1786:$i, X1787:$i > $o, X1788:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i > $o, X1801:$i, X1803:$i, X1804:$i, X1805:$i > $o, X1806:$i > $o, X1809:$i, X1812:$i, X1813:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i > $o, X1826:$i, X1828:$i, X1829:$i, X1830:$i > $o, X1831:$i > $o, X1834:$i, X1836:$i, X1838:$i, X1839:$i, X1840:$i > $o, X1841:$i > $o, X1844:$i, X1845:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1854:$i, 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 > $o, X1892:$i, X1893:$i > $o, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$o, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$o, 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, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i > $o, X2048:$i, X2049:$i, X2050:$i > $o, X2052:$i, X2053:$i > $o, X2054:$i, X2056:$i, X2057:$i > $o, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$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:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i > $i > $o, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i > $i > $o, X2138:$i, X2139:$i, X2140:$i > $i > $o, X2141:$i, X2142:$i, X2143:$i > $i > $o, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i > $i > $o, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i > $i > $o, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i > $i > $o, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i > $i, X2187:$i, X2188:$i, X2189:$i > $i, X2191:$i, X2192:$i, X2193:$i > $i, X2195:$i, X2196:$i, X2197:$i, X2198:$i > $o, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i > $o, X2208:$i, X2209:$i, X2210:$i > $o, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i > $i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i > $i, X2282:$i, X2283:$i, X2284:$i > $i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$o, X2292:$i, X2293:$i, X2294:$i, X2295:$o, X2296:$i, X2297:$i, X2298:$i, X2299:$o, X2300:$i, X2301:$i, X2302:$i, X2303:$o, X2304:$i, X2305:$i, X2306:$i, X2307:$o, X2308:$i, X2309:$i, X2310:$i, X2311:$o, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$o, X2318:$i, X2319:$i, X2320:$i, X2321:$o, X2322:$i, X2323:$i, X2324:$i, X2325:$o, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2346:$i, X2347:$i, X2348:$i, X2350:$i, X2351:$i, X2352:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, 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(esk75_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2246)|~(subset @ X2247 @ (cartprod @ X2244 @ X2245))|~(subset @ X2246 @ (cartprod @ X2244 @ X2245)))&(((in @ (esk77_4 @ X2244 @ X2245 @ X2246 @ X2247) @ X2245)|((X2246)=(X2247))|(in @ (kpair @ (esk74_4 @ X2244 @ X2245 @ X2246 @ X2247) @ (esk75_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2246)|~(subset @ X2247 @ (cartprod @ X2244 @ X2245))|~(subset @ X2246 @ (cartprod @ X2244 @ X2245)))&(((in @ (kpair @ (esk76_4 @ X2244 @ X2245 @ X2246 @ X2247) @ (esk77_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2247)|((X2246)=(X2247))|(in @ (kpair @ (esk74_4 @ X2244 @ X2245 @ X2246 @ X2247) @ (esk75_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2246)|~(subset @ X2247 @ (cartprod @ X2244 @ X2245))|~(subset @ X2246 @ (cartprod @ X2244 @ X2245)))&(~(in @ (kpair @ (esk76_4 @ X2244 @ X2245 @ X2246 @ X2247) @ (esk77_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2246)|((X2246)=(X2247))|(in @ (kpair @ (esk74_4 @ X2244 @ X2245 @ X2246 @ X2247) @ (esk75_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2246)|~(subset @ X2247 @ (cartprod @ X2244 @ X2245))|~(subset @ X2246 @ (cartprod @ X2244 @ X2245))))))&(((in @ (esk76_4 @ X2244 @ X2245 @ X2246 @ X2247) @ X2244)|((X2246)=(X2247))|~(in @ (kpair @ (esk74_4 @ X2244 @ X2245 @ X2246 @ X2247) @ (esk75_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2247)|~(subset @ X2247 @ (cartprod @ X2244 @ X2245))|~(subset @ X2246 @ (cartprod @ X2244 @ X2245)))&(((in @ (esk77_4 @ X2244 @ X2245 @ X2246 @ X2247) @ X2245)|((X2246)=(X2247))|~(in @ (kpair @ (esk74_4 @ X2244 @ X2245 @ X2246 @ X2247) @ (esk75_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2247)|~(subset @ X2247 @ (cartprod @ X2244 @ X2245))|~(subset @ X2246 @ (cartprod @ X2244 @ X2245)))&(((in @ (kpair @ (esk76_4 @ X2244 @ X2245 @ X2246 @ X2247) @ (esk77_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2247)|((X2246)=(X2247))|~(in @ (kpair @ (esk74_4 @ X2244 @ X2245 @ X2246 @ X2247) @ (esk75_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2247)|~(subset @ X2247 @ (cartprod @ X2244 @ X2245))|~(subset @ X2246 @ (cartprod @ X2244 @ X2245)))&(~(in @ (kpair @ (esk76_4 @ X2244 @ X2245 @ X2246 @ X2247) @ (esk77_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2246)|((X2246)=(X2247))|~(in @ (kpair @ (esk74_4 @ X2244 @ X2245 @ X2246 @ X2247) @ (esk75_4 @ X2244 @ X2245 @ X2246 @ X2247)) @ X2247)|~(subset @ X2247 @ (cartprod @ X2244 @ X2245))|~(subset @ X2246 @ (cartprod @ X2244 @ X2245)))))))))&((((in @ (esk78_4 @ X2252 @ X2253 @ X2254 @ X2255) @ X2252)|((X2254)=(X2255))|~(func @ X2252 @ X2253 @ X2255)|~(func @ X2252 @ X2253 @ X2254))&(((ap @ X2252 @ X2253 @ X2254 @ (esk78_4 @ X2252 @ X2253 @ X2254 @ X2255))!=(ap @ X2252 @ X2253 @ X2255 @ (esk78_4 @ X2252 @ X2253 @ X2254 @ X2255)))|((X2254)=(X2255))|~(func @ X2252 @ X2253 @ X2255)|~(func @ X2252 @ X2253 @ X2254)))&((((in @ (esk79_4 @ X2257 @ X2258 @ X2259 @ X2260) @ X2257)|((X2259)=(X2260))|~(in @ X2260 @ (funcSet @ X2257 @ X2258))|~(in @ X2259 @ (funcSet @ X2257 @ X2258)))&(((ap @ X2257 @ X2258 @ X2259 @ (esk79_4 @ X2257 @ X2258 @ X2259 @ X2260))!=(ap @ X2257 @ X2258 @ X2260 @ (esk79_4 @ X2257 @ X2258 @ X2259 @ X2260)))|((X2259)=(X2260))|~(in @ X2260 @ (funcSet @ X2257 @ X2258))|~(in @ X2259 @ (funcSet @ X2257 @ X2258))))&((~(in @ X2264 @ (funcSet @ X2262 @ X2263))|(~(in @ X2265 @ X2262)|((ap @ X2262 @ X2263 @ X2264 @ X2265)=(ap @ X2262 @ X2263 @ X2264 @ X2265))))&((~(func @ X2266 @ X2267 @ X2268)|(~(in @ X2269 @ X2266)|((ap @ X2266 @ X2267 @ X2268 @ X2269)=(ap @ X2266 @ X2267 @ X2268 @ X2269))))&((((in @ (esk80_3 @ X2270 @ X2271 @ X2272) @ X2270)|(~(in @ X2274 @ X2270)|((ap @ X2270 @ X2271 @ (lam @ X2270 @ X2271 @ X2272) @ X2274)=(X2272 @ X2274))))&(~(in @ (X2272 @ (esk80_3 @ X2270 @ X2271 @ X2272)) @ X2271)|(~(in @ X2274 @ X2270)|((ap @ X2270 @ X2271 @ (lam @ X2270 @ X2271 @ X2272) @ X2274)=(X2272 @ X2274)))))&((~(func @ X2275 @ X2276 @ X2277)|((lam @ X2275 @ X2276 @ (ap @ X2275 @ X2276 @ X2277))=(X2277)))&((((in @ (esk81_3 @ X2278 @ X2279 @ X2280) @ X2278)|((lam @ X2278 @ X2279 @ X2280)=(lam @ X2278 @ X2279 @ X2280)))&(~(in @ (X2280 @ (esk81_3 @ X2278 @ X2279 @ X2280)) @ X2279)|((lam @ X2278 @ X2279 @ X2280)=(lam @ X2278 @ X2279 @ X2280))))&((((in @ (esk82_3 @ X2282 @ X2283 @ X2284) @ X2282)|(~(in @ X2286 @ X2282)|((ap @ X2282 @ X2283 @ (lam @ X2282 @ X2283 @ X2284) @ X2286)=(X2284 @ X2286))))&(~(in @ (X2284 @ (esk82_3 @ X2282 @ X2283 @ X2284)) @ X2283)|(~(in @ X2286 @ X2282)|((ap @ X2282 @ X2283 @ (lam @ X2282 @ X2283 @ X2284) @ X2286)=(X2284 @ X2286)))))&((~(in @ X2289 @ (funcSet @ X2287 @ X2288))|((lam @ X2287 @ X2288 @ (ap @ X2287 @ X2288 @ X2289))=(X2289)))&((~(in @ X2292 @ X2290)|(~(in @ X2293 @ X2290)|((X2291)|(in @ X2293 @ (dsetconstr @ X2290 @ (^[Z0/* 9 */:$i]:((((X2291)&((Z0)=(X2292)))|(~((X2291))&((Z0)=(X2293)))))))))))&((~(in @ X2296 @ X2294)|(~(in @ X2297 @ X2294)|((X2295)|((dsetconstr @ X2294 @ (^[Z0/* 9 */:$i]:((((X2295)&((Z0)=(X2296)))|(~((X2295))&((Z0)=(X2297)))))))=(setadjoin @ X2297 @ emptyset)))))&((~(in @ X2300 @ X2298)|(~(in @ X2301 @ X2298)|(~(X2299)|(in @ X2300 @ (dsetconstr @ X2298 @ (^[Z0/* 9 */:$i]:((((X2299)&((Z0)=(X2300)))|(~((X2299))&((Z0)=(X2301)))))))))))&((~(in @ X2304 @ X2302)|(~(in @ X2305 @ X2302)|(~(X2303)|((dsetconstr @ X2302 @ (^[Z0/* 9 */:$i]:((((X2303)&((Z0)=(X2304)))|(~((X2303))&((Z0)=(X2305)))))))=(setadjoin @ X2304 @ emptyset)))))&((~(in @ X2308 @ X2306)|(~(in @ X2309 @ X2306)|(singleton @ (dsetconstr @ X2306 @ (^[Z0/* 9 */:$i]:((((X2307)&((Z0)=(X2308)))|(~((X2307))&((Z0)=(X2309))))))))))&((~(in @ X2312 @ X2310)|(~(in @ X2313 @ X2310)|(in @ (if @ X2310 @ ((X2311)) @ X2312 @ X2313) @ X2310)))&((~(singleton @ X2314)|(~(in @ X2315 @ X2314)|((setunion @ X2314)=(X2315))))&((~(in @ X2318 @ X2316)|(~(in @ X2319 @ X2316)|(~(X2317)|((if @ X2316 @ ((X2317)) @ X2318 @ X2319)=(X2318)))))&((~(in @ X2322 @ X2320)|(~(in @ X2323 @ X2320)|((X2321)|((if @ X2320 @ ((X2321)) @ X2322 @ X2323)=(X2323)))))&((~(in @ X2326 @ X2324)|(~(in @ X2327 @ X2324)|(in @ (if @ X2324 @ ((X2325)) @ X2326 @ X2327) @ (setadjoin @ X2326 @ (setadjoin @ X2327 @ emptyset)))))&((~(in @ X2329 @ (powerset @ X2328))|(~(in @ X2330 @ (powerset @ X2328))|(in @ (binintersect @ X2329 @ X2330) @ (powerset @ X2328))))&((~(in @ X2332 @ (powerset @ X2331))|(~(in @ X2333 @ (powerset @ X2331))|(in @ (binunion @ X2332 @ X2333) @ (powerset @ X2331))))&((~(in @ X2335 @ (powerset @ X2334))|(in @ (powerset @ X2335) @ (powerset @ (powerset @ X2334))))&((~(in @ X2337 @ (powerset @ X2336))|(~(in @ X2338 @ (powerset @ X2336))|(in @ (setminus @ X2337 @ X2338) @ (powerset @ X2336))))&((~(in @ X2340 @ (powerset @ X2339))|(in @ (setminus @ X2339 @ X2340) @ (powerset @ X2339)))&(((((in @ (esk84_3 @ X2341 @ X2342 @ X2343) @ X2341)|((X2342)=(X2343))|(in @ (esk83_3 @ X2341 @ X2342 @ X2343) @ X2341)|~(in @ X2343 @ (powerset @ X2341))|~(in @ X2342 @ (powerset @ X2341)))&(((in @ (esk84_3 @ X2341 @ X2342 @ X2343) @ X2343)|((X2342)=(X2343))|(in @ (esk83_3 @ X2341 @ X2342 @ X2343) @ X2341)|~(in @ X2343 @ (powerset @ X2341))|~(in @ X2342 @ (powerset @ X2341)))&(~(in @ (esk84_3 @ X2341 @ X2342 @ X2343) @ X2342)|((X2342)=(X2343))|(in @ (esk83_3 @ X2341 @ X2342 @ X2343) @ X2341)|~(in @ X2343 @ (powerset @ X2341))|~(in @ X2342 @ (powerset @ X2341)))))&((((in @ (esk84_3 @ X2341 @ X2342 @ X2343) @ X2341)|((X2342)=(X2343))|(in @ (esk83_3 @ X2341 @ X2342 @ X2343) @ X2342)|~(in @ X2343 @ (powerset @ X2341))|~(in @ X2342 @ (powerset @ X2341)))&(((in @ (esk84_3 @ X2341 @ X2342 @ X2343) @ X2343)|((X2342)=(X2343))|(in @ (esk83_3 @ X2341 @ X2342 @ X2343) @ X2342)|~(in @ X2343 @ (powerset @ X2341))|~(in @ X2342 @ (powerset @ X2341)))&(~(in @ (esk84_3 @ X2341 @ X2342 @ X2343) @ X2342)|((X2342)=(X2343))|(in @ (esk83_3 @ X2341 @ X2342 @ X2343) @ X2342)|~(in @ X2343 @ (powerset @ X2341))|~(in @ X2342 @ (powerset @ X2341)))))&(((in @ (esk84_3 @ X2341 @ X2342 @ X2343) @ X2341)|((X2342)=(X2343))|~(in @ (esk83_3 @ X2341 @ X2342 @ X2343) @ X2343)|~(in @ X2343 @ (powerset @ X2341))|~(in @ X2342 @ (powerset @ X2341)))&(((in @ (esk84_3 @ X2341 @ X2342 @ X2343) @ X2343)|((X2342)=(X2343))|~(in @ (esk83_3 @ X2341 @ X2342 @ X2343) @ X2343)|~(in @ X2343 @ (powerset @ X2341))|~(in @ X2342 @ (powerset @ X2341)))&(~(in @ (esk84_3 @ X2341 @ X2342 @ X2343) @ X2342)|((X2342)=(X2343))|~(in @ (esk83_3 @ X2341 @ X2342 @ X2343) @ X2343)|~(in @ X2343 @ (powerset @ X2341))|~(in @ X2342 @ (powerset @ X2341)))))))&((((in @ (esk85_3 @ X2346 @ X2347 @ X2348) @ X2346)|(subset @ X2347 @ X2348)|~(in @ X2348 @ (powerset @ X2346))|~(in @ X2347 @ (powerset @ X2346)))&(((in @ (esk85_3 @ X2346 @ X2347 @ X2348) @ X2347)|(subset @ X2347 @ X2348)|~(in @ X2348 @ (powerset @ X2346))|~(in @ X2347 @ (powerset @ X2346)))&(~(in @ (esk85_3 @ X2346 @ X2347 @ X2348) @ X2348)|(subset @ X2347 @ X2348)|~(in @ X2348 @ (powerset @ X2346))|~(in @ X2347 @ (powerset @ X2346)))))&((((in @ (esk86_3 @ X2350 @ X2351 @ X2352) @ X2350)|(in @ X2351 @ (powerset @ X2352))|~(in @ X2352 @ (powerset @ X2350))|~(in @ X2351 @ (powerset @ X2350)))&(((in @ (esk86_3 @ X2350 @ X2351 @ X2352) @ X2351)|(in @ X2351 @ (powerset @ X2352))|~(in @ X2352 @ (powerset @ X2350))|~(in @ X2351 @ (powerset @ X2350)))&(~(in @ (esk86_3 @ X2350 @ X2351 @ X2352) @ X2352)|(in @ X2351 @ (powerset @ X2352))|~(in @ X2352 @ (powerset @ X2350))|~(in @ X2351 @ (powerset @ X2350)))))&((~(in @ X2355 @ (powerset @ X2354))|(~(in @ X2356 @ (powerset @ X2354))|(~(in @ X2357 @ X2354)|(~(in @ X2355 @ (powerset @ X2356))|(~(in @ X2357 @ X2355)|(in @ X2357 @ X2356))))))&((~(in @ X2359 @ (powerset @ X2358))|(~(in @ X2360 @ X2358)|(~(in @ X2360 @ X2359)|~(in @ X2360 @ (setminus @ X2358 @ X2359)))))&((~(in @ X2362 @ (powerset @ X2361))|(~(in @ X2363 @ X2361)|((in @ X2363 @ (setminus @ X2361 @ X2362))|(in @ X2363 @ X2362))))&((~(in @ X2365 @ (powerset @ X2364))|(~(in @ X2366 @ (powerset @ X2364))|(~(in @ X2367 @ X2364)|((in @ X2367 @ X2365)|~(in @ X2367 @ (binintersect @ X2365 @ X2366))))))&((~(in @ X2369 @ (powerset @ X2368))|(~(in @ X2370 @ (powerset @ X2368))|(~(in @ X2371 @ X2368)|((in @ X2371 @ X2370)|~(in @ X2371 @ (binintersect @ X2369 @ X2370))))))&((~(in @ X2373 @ (powerset @ X2372))|(~(in @ X2374 @ (powerset @ X2372))|(~(in @ X2375 @ X2372)|(~(subset @ X2373 @ (setminus @ X2372 @ X2374))|(~(in @ X2375 @ X2374)|~(in @ X2375 @ X2373))))))&((~(in @ X2377 @ (powerset @ X2376))|(~(in @ X2378 @ (powerset @ X2376))|(~(in @ X2379 @ X2376)|(~(subset @ X2377 @ X2378)|((in @ X2379 @ X2378)|~(in @ X2379 @ X2377))))))&((~(in @ X2381 @ (powerset @ X2380))|(~(in @ X2382 @ (powerset @ X2380))|(~(subset @ X2381 @ X2382)|(subset @ (setminus @ X2380 @ X2382) @ (setminus @ X2380 @ X2381)))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((subset @ (setminus @ esk87_0 @ esk89_0) @ (setminus @ esk87_0 @ esk88_0))&~(subset @ esk88_0 @ esk89_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_328])])])])])])])).
13.82/2.27	thf(c_0_330, negated_conjecture, ![X3:$i, X5:$i, X4:$i, X2:$i]:((~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((in @ X5 @ X3))|~((subset @ X2 @ (setminus @ X3 @ X4)))|~((in @ X5 @ X4))|~((in @ X5 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_329])).
13.82/2.27	thf(c_0_331, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_329])).
13.82/2.27	thf(c_0_332, negated_conjecture, ![X3:$i, X5:$i, X4:$i, X2:$i]:((~((subset @ X2 @ (setminus @ X3 @ X4)))|~((in @ X4 @ (powerset @ X3)))|~((in @ X2 @ (powerset @ X3)))|~((in @ X5 @ X4))|~((in @ X5 @ X2)))), inference(csr,[status(thm)],[c_0_330, c_0_331])).
13.82/2.27	thf(c_0_333, negated_conjecture, (subset @ (setminus @ esk87_0 @ esk89_0) @ (setminus @ esk87_0 @ esk88_0)), inference(split_conjunct,[status(thm)],[c_0_329])).
13.82/2.27	thf(c_0_334, negated_conjecture, (in @ esk88_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_329])).
13.82/2.27	thf(c_0_335, negated_conjecture, ![X2:$i]:((~((in @ (setminus @ esk87_0 @ esk89_0) @ (powerset @ esk87_0)))|~((in @ X2 @ (setminus @ esk87_0 @ esk89_0)))|~((in @ X2 @ esk88_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_332, c_0_333]), c_0_334])])).
13.82/2.27	thf(c_0_336, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_329])).
13.82/2.27	thf(c_0_337, negated_conjecture, ![X3:$i, X2:$i]:((subset @ (setminus @ X2 @ X3) @ X2)), inference(split_conjunct,[status(thm)],[c_0_329])).
13.82/2.27	thf(c_0_338, negated_conjecture, ![X2:$i]:((~((in @ X2 @ (setminus @ esk87_0 @ esk89_0)))|~((in @ X2 @ esk88_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_335, c_0_336]), c_0_337])])).
13.82/2.27	thf(c_0_339, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_329])).
13.82/2.27	thf(c_0_340, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk87_0)|~((in @ X2 @ esk88_0)))), inference(spm,[status(thm)],[c_0_331, c_0_334])).
13.82/2.27	thf(c_0_341, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_329])).
13.82/2.27	thf(c_0_342, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk89_0)|~((in @ X2 @ esk88_0)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_338, c_0_339]), c_0_340])).
13.82/2.27	thf(c_0_343, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk89_0)|~((in @ (esk53_2 @ X2 @ esk89_0) @ esk88_0)))), inference(spm,[status(thm)],[c_0_341, c_0_342])).
13.82/2.27	thf(c_0_344, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_329])).
13.82/2.27	thf(c_0_345, negated_conjecture, ~((subset @ esk88_0 @ esk89_0)), inference(split_conjunct,[status(thm)],[c_0_329])).
13.82/2.27	thf(c_0_346, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_343, c_0_344]), c_0_345]), ['proof']).
13.82/2.27	# SZS output end CNFRefutation
13.82/2.27	# Parsed axioms                        : 527
13.82/2.27	# Removed by relevancy pruning/SinE    : 0
13.82/2.27	# Initial clauses                      : 707
13.82/2.27	# Removed in clause preprocessing      : 309
13.82/2.27	# Initial clauses in saturation        : 398
13.82/2.27	# Processed clauses                    : 3474
13.82/2.27	# ...of these trivial                  : 50
13.82/2.27	# ...subsumed                          : 1556
13.82/2.27	# ...remaining for further processing  : 1868
13.82/2.27	# Other redundant clauses eliminated   : 66
13.82/2.27	# Clauses deleted for lack of memory   : 0
13.82/2.27	# Backward-subsumed                    : 123
13.82/2.27	# Backward-rewritten                   : 16
13.82/2.27	# Generated clauses                    : 76211
13.82/2.27	# ...of the previous two non-redundant : 74641
13.82/2.27	# ...aggressively subsumed             : 0
13.82/2.27	# Contextual simplify-reflections      : 8
13.82/2.27	# Paramodulations                      : 76097
13.82/2.27	# Factorizations                       : 22
13.82/2.27	# NegExts                              : 2
13.82/2.27	# Equation resolutions                 : 74
13.82/2.27	# Disequality decompositions           : 0
13.82/2.27	# Total rewrite steps                  : 4739
13.82/2.27	# ...of those cached                   : 4518
13.82/2.27	# Propositional unsat checks           : 0
13.82/2.27	#    Propositional check models        : 0
13.82/2.27	#    Propositional check unsatisfiable : 0
13.82/2.27	#    Propositional clauses             : 0
13.82/2.27	#    Propositional clauses after purity: 0
13.82/2.27	#    Propositional unsat core size     : 0
13.82/2.27	#    Propositional preprocessing time  : 0.000
13.82/2.27	#    Propositional encoding time       : 0.000
13.82/2.27	#    Propositional solver time         : 0.000
13.82/2.27	#    Success case prop preproc time    : 0.000
13.82/2.27	#    Success case prop encoding time   : 0.000
13.82/2.27	#    Success case prop solver time     : 0.000
13.82/2.27	# Current number of processed clauses  : 1367
13.82/2.27	#    Positive orientable unit clauses  : 54
13.82/2.27	#    Positive unorientable unit clauses: 0
13.82/2.27	#    Negative unit clauses             : 88
13.82/2.27	#    Non-unit-clauses                  : 1225
13.82/2.27	# Current number of unprocessed clauses: 71815
13.82/2.27	# ...number of literals in the above   : 272685
13.82/2.27	# Current number of archived formulas  : 0
13.82/2.27	# Current number of archived clauses   : 486
13.82/2.27	# Clause-clause subsumption calls (NU) : 180841
13.82/2.27	# Rec. Clause-clause subsumption calls : 92290
13.82/2.27	# Non-unit clause-clause subsumptions  : 1143
13.82/2.27	# Unit Clause-clause subsumption calls : 2579
13.82/2.27	# Rewrite failures with RHS unbound    : 0
13.82/2.27	# BW rewrite match attempts            : 47
13.82/2.27	# BW rewrite match successes           : 11
13.82/2.27	# Condensation attempts                : 0
13.82/2.27	# Condensation successes               : 0
13.82/2.27	# Termbank termtop insertions          : 1491260
13.82/2.27	# Search garbage collected termcells   : 25271
13.82/2.27	
13.82/2.27	# -------------------------------------------------
13.82/2.27	# User time                : 1.585 s
13.82/2.27	# System time              : 0.072 s
13.82/2.27	# Total time               : 1.657 s
13.82/2.27	# Maximum resident set size: 7988 pages
13.82/2.27	
13.82/2.27	# -------------------------------------------------
13.82/2.27	# User time                : 1.599 s
13.82/2.27	# System time              : 0.076 s
13.82/2.27	# Total time               : 1.675 s
13.82/2.27	# Maximum resident set size: 2608 pages
13.82/2.27	% E exiting
13.82/2.27	% E exiting
13.82/2.27	EOF