0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : run_E %s %d THM
0.12/0.33	% Computer : n001.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1440
0.12/0.33	% WCLimit    : 180
0.12/0.33	% DateTime   : Thu Jul  4 08:44:38 EDT 2024
0.12/0.33	% CPUTime    : 
0.19/0.47	Running higher-order theorem proving
0.19/0.51	Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p
4.52/1.09	# Version: 3.2.0-ho
4.52/1.09	# Preprocessing class: HSLMSLSSLLLCHFA.
4.52/1.09	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
4.52/1.09	# Starting ehoh_best5 with 180s (1) cores
4.52/1.09	# Starting almost_fo_3_lam with 180s (1) cores
4.52/1.09	# Starting new_bool_5 with 180s (1) cores
4.52/1.09	# Starting pre_casc_3 with 180s (1) cores
4.52/1.09	# Starting ho_unfolding_8 with 180s (1) cores
4.52/1.09	# Starting new_ho_10_cnf2 with 180s (1) cores
4.52/1.09	# Starting new_bool_3 with 180s (1) cores
4.52/1.09	# Starting new_ho_5 with 180s (1) cores
4.52/1.09	# new_bool_3 with pid 2749 completed with status 0
4.52/1.09	# Result found by new_bool_3
4.52/1.09	# Preprocessing class: HSLMSLSSLLLCHFA.
4.52/1.09	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
4.52/1.09	# Starting ehoh_best5 with 180s (1) cores
4.52/1.09	# Starting almost_fo_3_lam with 180s (1) cores
4.52/1.09	# Starting new_bool_5 with 180s (1) cores
4.52/1.09	# Starting pre_casc_3 with 180s (1) cores
4.52/1.09	# Starting ho_unfolding_8 with 180s (1) cores
4.52/1.09	# Starting new_ho_10_cnf2 with 180s (1) cores
4.52/1.09	# Starting new_bool_3 with 180s (1) cores
4.52/1.09	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
4.52/1.09	# Search class: HGHSM-FSLM32-DHFMMSBN
4.52/1.09	# partial match(1): HGHSM-FSLM32-MHFMMSBN
4.52/1.09	# Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
4.52/1.09	# Starting ho_unfolding_8 with 37s (1) cores
4.52/1.09	# ho_unfolding_8 with pid 2752 completed with status 0
4.52/1.09	# Result found by ho_unfolding_8
4.52/1.09	# Preprocessing class: HSLMSLSSLLLCHFA.
4.52/1.09	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
4.52/1.09	# Starting ehoh_best5 with 180s (1) cores
4.52/1.09	# Starting almost_fo_3_lam with 180s (1) cores
4.52/1.09	# Starting new_bool_5 with 180s (1) cores
4.52/1.09	# Starting pre_casc_3 with 180s (1) cores
4.52/1.09	# Starting ho_unfolding_8 with 180s (1) cores
4.52/1.09	# Starting new_ho_10_cnf2 with 180s (1) cores
4.52/1.09	# Starting new_bool_3 with 180s (1) cores
4.52/1.09	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
4.52/1.09	# Search class: HGHSM-FSLM32-DHFMMSBN
4.52/1.09	# partial match(1): HGHSM-FSLM32-MHFMMSBN
4.52/1.09	# Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
4.52/1.09	# Starting ho_unfolding_8 with 37s (1) cores
4.52/1.09	# Preprocessing time       : 0.112 s
4.52/1.09	# Presaturation interreduction done
4.52/1.09	
4.52/1.09	# Proof found!
4.52/1.09	# SZS status Theorem
4.52/1.09	# SZS output start CNFRefutation
4.52/1.09	thf(decl_22, type, in: $i > $i > $o).
4.52/1.09	thf(decl_23, type, exu: ($i > $o) > $o).
4.52/1.09	thf(decl_24, type, setextAx: $o).
4.52/1.09	thf(decl_25, type, emptyset: $i).
4.52/1.09	thf(decl_26, type, emptysetAx: $o).
4.52/1.09	thf(decl_27, type, setadjoin: $i > $i > $i).
4.52/1.09	thf(decl_28, type, setadjoinAx: $o).
4.52/1.09	thf(decl_29, type, powerset: $i > $i).
4.52/1.09	thf(decl_30, type, powersetAx: $o).
4.52/1.09	thf(decl_31, type, setunion: $i > $i).
4.52/1.09	thf(decl_32, type, setunionAx: $o).
4.52/1.09	thf(decl_33, type, omega: $i).
4.52/1.09	thf(decl_34, type, omega0Ax: $o).
4.52/1.09	thf(decl_35, type, omegaSAx: $o).
4.52/1.09	thf(decl_36, type, omegaIndAx: $o).
4.52/1.09	thf(decl_37, type, replAx: $o).
4.52/1.09	thf(decl_38, type, foundationAx: $o).
4.52/1.09	thf(decl_39, type, wellorderingAx: $o).
4.52/1.09	thf(decl_40, type, descr: ($i > $o) > $i).
4.52/1.09	thf(decl_41, type, descrp: $o).
4.52/1.09	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_43, type, dsetconstrI: $o).
4.52/1.09	thf(decl_44, type, dsetconstrEL: $o).
4.52/1.09	thf(decl_45, type, dsetconstrER: $o).
4.52/1.09	thf(decl_46, type, exuE1: $o).
4.52/1.09	thf(decl_47, type, prop2set: $o > $i).
4.52/1.09	thf(decl_48, type, prop2setE: $o).
4.52/1.09	thf(decl_49, type, emptysetE: $o).
4.52/1.09	thf(decl_50, type, emptysetimpfalse: $o).
4.52/1.09	thf(decl_51, type, notinemptyset: $o).
4.52/1.09	thf(decl_52, type, exuE3e: $o).
4.52/1.09	thf(decl_53, type, setext: $o).
4.52/1.09	thf(decl_54, type, emptyI: $o).
4.52/1.09	thf(decl_55, type, noeltsimpempty: $o).
4.52/1.09	thf(decl_56, type, setbeta: $o).
4.52/1.09	thf(decl_57, type, nonempty: $i > $o).
4.52/1.09	thf(decl_58, type, nonemptyE1: $o).
4.52/1.09	thf(decl_59, type, nonemptyI: $o).
4.52/1.09	thf(decl_60, type, nonemptyI1: $o).
4.52/1.09	thf(decl_61, type, setadjoinIL: $o).
4.52/1.09	thf(decl_62, type, emptyinunitempty: $o).
4.52/1.09	thf(decl_63, type, setadjoinIR: $o).
4.52/1.09	thf(decl_64, type, setadjoinE: $o).
4.52/1.09	thf(decl_65, type, setadjoinOr: $o).
4.52/1.09	thf(decl_66, type, setoftrueEq: $o).
4.52/1.09	thf(decl_67, type, powersetI: $o).
4.52/1.09	thf(decl_68, type, emptyinPowerset: $o).
4.52/1.09	thf(decl_69, type, emptyInPowerset: $o).
4.52/1.09	thf(decl_70, type, powersetE: $o).
4.52/1.09	thf(decl_71, type, setunionI: $o).
4.52/1.09	thf(decl_72, type, setunionE: $o).
4.52/1.09	thf(decl_73, type, subPowSU: $o).
4.52/1.09	thf(decl_74, type, exuE2: $o).
4.52/1.09	thf(decl_75, type, nonemptyImpWitness: $o).
4.52/1.09	thf(decl_76, type, uniqinunit: $o).
4.52/1.09	thf(decl_77, type, notinsingleton: $o).
4.52/1.09	thf(decl_78, type, eqinunit: $o).
4.52/1.09	thf(decl_79, type, singletonsswitch: $o).
4.52/1.09	thf(decl_80, type, upairsetE: $o).
4.52/1.09	thf(decl_81, type, upairsetIL: $o).
4.52/1.09	thf(decl_82, type, upairsetIR: $o).
4.52/1.09	thf(decl_83, type, emptyE1: $o).
4.52/1.09	thf(decl_84, type, vacuousDall: $o).
4.52/1.09	thf(decl_85, type, quantDeMorgan1: $o).
4.52/1.09	thf(decl_86, type, quantDeMorgan2: $o).
4.52/1.09	thf(decl_87, type, quantDeMorgan3: $o).
4.52/1.09	thf(decl_88, type, quantDeMorgan4: $o).
4.52/1.09	thf(decl_89, type, prop2setI: $o).
4.52/1.09	thf(decl_91, type, prop2set2propI: $o).
4.52/1.09	thf(decl_92, type, notdexE: $o).
4.52/1.09	thf(decl_93, type, notdallE: $o).
4.52/1.09	thf(decl_94, type, exuI1: $o).
4.52/1.09	thf(decl_95, type, exuI3: $o).
4.52/1.09	thf(decl_96, type, exuI2: $o).
4.52/1.09	thf(decl_97, type, inCongP: $o).
4.52/1.09	thf(decl_98, type, in__Cong: $o).
4.52/1.09	thf(decl_99, type, exuE3u: $o).
4.52/1.09	thf(decl_100, type, exu__Cong: $o).
4.52/1.09	thf(decl_101, type, emptyset__Cong: $o).
4.52/1.09	thf(decl_102, type, setadjoin__Cong: $o).
4.52/1.09	thf(decl_103, type, powerset__Cong: $o).
4.52/1.09	thf(decl_104, type, setunion__Cong: $o).
4.52/1.09	thf(decl_105, type, omega__Cong: $o).
4.52/1.09	thf(decl_106, type, exuEu: $o).
4.52/1.09	thf(decl_107, type, descr__Cong: $o).
4.52/1.09	thf(decl_108, type, dsetconstr__Cong: $o).
4.52/1.09	thf(decl_109, type, subset: $i > $i > $o).
4.52/1.09	thf(decl_112, type, subsetI1: $o).
4.52/1.09	thf(decl_113, type, eqimpsubset2: $o).
4.52/1.09	thf(decl_114, type, eqimpsubset1: $o).
4.52/1.09	thf(decl_115, type, subsetI2: $o).
4.52/1.09	thf(decl_116, type, emptysetsubset: $o).
4.52/1.09	thf(decl_117, type, subsetE: $o).
4.52/1.09	thf(decl_118, type, subsetE2: $o).
4.52/1.09	thf(decl_119, type, notsubsetI: $o).
4.52/1.09	thf(decl_120, type, notequalI1: $o).
4.52/1.09	thf(decl_121, type, notequalI2: $o).
4.52/1.09	thf(decl_122, type, subsetRefl: $o).
4.52/1.09	thf(decl_123, type, subsetTrans: $o).
4.52/1.09	thf(decl_124, type, setadjoinSub: $o).
4.52/1.09	thf(decl_125, type, setadjoinSub2: $o).
4.52/1.09	thf(decl_126, type, subset2powerset: $o).
4.52/1.09	thf(decl_127, type, setextsub: $o).
4.52/1.09	thf(decl_128, type, subsetemptysetimpeq: $o).
4.52/1.09	thf(decl_129, type, powersetI1: $o).
4.52/1.09	thf(decl_130, type, powersetE1: $o).
4.52/1.09	thf(decl_131, type, inPowerset: $o).
4.52/1.09	thf(decl_132, type, powersetsubset: $o).
4.52/1.09	thf(decl_133, type, sepInPowerset: $o).
4.52/1.09	thf(decl_134, type, sepSubset: $o).
4.52/1.09	thf(decl_135, type, binunion: $i > $i > $i).
4.52/1.09	thf(decl_136, type, binunionIL: $o).
4.52/1.09	thf(decl_137, type, upairset2IR: $o).
4.52/1.09	thf(decl_138, type, binunionIR: $o).
4.52/1.09	thf(decl_139, type, binunionEcases: $o).
4.52/1.09	thf(decl_140, type, binunionE: $o).
4.52/1.09	thf(decl_141, type, binunionLsub: $o).
4.52/1.09	thf(decl_142, type, binunionRsub: $o).
4.52/1.09	thf(decl_143, type, binintersect: $i > $i > $i).
4.52/1.09	thf(decl_144, type, binintersectI: $o).
4.52/1.09	thf(decl_145, type, binintersectSubset5: $o).
4.52/1.09	thf(decl_146, type, binintersectEL: $o).
4.52/1.09	thf(decl_147, type, binintersectLsub: $o).
4.52/1.09	thf(decl_148, type, binintersectSubset2: $o).
4.52/1.09	thf(decl_149, type, binintersectSubset3: $o).
4.52/1.09	thf(decl_150, type, binintersectER: $o).
4.52/1.09	thf(decl_151, type, disjointsetsI1: $o).
4.52/1.09	thf(decl_152, type, binintersectRsub: $o).
4.52/1.09	thf(decl_153, type, binintersectSubset4: $o).
4.52/1.09	thf(decl_154, type, binintersectSubset1: $o).
4.52/1.09	thf(decl_155, type, bs114d: $o).
4.52/1.09	thf(decl_157, type, setminus: $i > $i > $i).
4.52/1.09	thf(decl_158, type, setminusI: $o).
4.52/1.09	thf(decl_159, type, setminusEL: $o).
4.52/1.09	thf(decl_160, type, setminusER: $o).
4.52/1.09	thf(decl_161, type, setminusSubset2: $o).
4.52/1.09	thf(decl_162, type, setminusERneg: $o).
4.52/1.09	thf(decl_163, type, setminusELneg: $o).
4.52/1.09	thf(decl_164, type, setminusILneg: $o).
4.52/1.09	thf(decl_165, type, setminusIRneg: $o).
4.52/1.09	thf(decl_166, type, setminusLsub: $o).
4.52/1.09	thf(decl_167, type, setminusSubset1: $o).
4.52/1.09	thf(decl_168, type, symdiff: $i > $i > $i).
4.52/1.09	thf(decl_169, type, symdiffE: $o).
4.52/1.09	thf(decl_170, type, symdiffI1: $o).
4.52/1.09	thf(decl_171, type, symdiffI2: $o).
4.52/1.09	thf(decl_172, type, symdiffIneg1: $o).
4.52/1.09	thf(decl_173, type, symdiffIneg2: $o).
4.52/1.09	thf(decl_174, type, iskpair: $i > $o).
4.52/1.09	thf(decl_175, type, secondinupair: $o).
4.52/1.09	thf(decl_176, type, setukpairIL: $o).
4.52/1.09	thf(decl_177, type, setukpairIR: $o).
4.52/1.09	thf(decl_178, type, kpairiskpair: $o).
4.52/1.09	thf(decl_179, type, kpair: $i > $i > $i).
4.52/1.09	thf(decl_180, type, kpairp: $o).
4.52/1.09	thf(decl_181, type, cartprod: $i > $i > $i).
4.52/1.09	thf(decl_182, type, singletonsubset: $o).
4.52/1.09	thf(decl_183, type, singletoninpowerset: $o).
4.52/1.09	thf(decl_184, type, singletoninpowunion: $o).
4.52/1.09	thf(decl_185, type, upairset2E: $o).
4.52/1.09	thf(decl_186, type, upairsubunion: $o).
4.52/1.09	thf(decl_187, type, upairinpowunion: $o).
4.52/1.09	thf(decl_188, type, ubforcartprodlem1: $o).
4.52/1.09	thf(decl_189, type, ubforcartprodlem2: $o).
4.52/1.09	thf(decl_190, type, ubforcartprodlem3: $o).
4.52/1.09	thf(decl_191, type, cartprodpairin: $o).
4.52/1.09	thf(decl_192, type, cartprodmempair1: $o).
4.52/1.09	thf(decl_193, type, cartprodmempair: $o).
4.52/1.09	thf(decl_194, type, setunionE2: $o).
4.52/1.09	thf(decl_195, type, setunionsingleton1: $o).
4.52/1.09	thf(decl_196, type, setunionsingleton2: $o).
4.52/1.09	thf(decl_197, type, setunionsingleton: $o).
4.52/1.09	thf(decl_198, type, singleton: $i > $o).
4.52/1.09	thf(decl_199, type, singletonprop: $o).
4.52/1.09	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
4.52/1.09	thf(decl_201, type, ex1E1: $o).
4.52/1.09	thf(decl_202, type, ex1I: $o).
4.52/1.09	thf(decl_203, type, ex1I2: $o).
4.52/1.09	thf(decl_204, type, singletonsuniq: $o).
4.52/1.09	thf(decl_209, type, setukpairinjL1: $o).
4.52/1.09	thf(decl_210, type, kfstsingleton: $o).
4.52/1.09	thf(decl_211, type, theprop: $o).
4.52/1.09	thf(decl_212, type, kfst: $i > $i).
4.52/1.09	thf(decl_213, type, kfstpairEq: $o).
4.52/1.09	thf(decl_214, type, cartprodfstin: $o).
4.52/1.09	thf(decl_215, type, setukpairinjL2: $o).
4.52/1.09	thf(decl_216, type, setukpairinjL: $o).
4.52/1.09	thf(decl_217, type, setukpairinjR11: $o).
4.52/1.09	thf(decl_218, type, setukpairinjR12: $o).
4.52/1.09	thf(decl_219, type, setukpairinjR1: $o).
4.52/1.09	thf(decl_220, type, upairequniteq: $o).
4.52/1.09	thf(decl_221, type, setukpairinjR2: $o).
4.52/1.09	thf(decl_222, type, setukpairinjR: $o).
4.52/1.09	thf(decl_223, type, ksndsingleton: $o).
4.52/1.09	thf(decl_224, type, ksnd: $i > $i).
4.52/1.09	thf(decl_225, type, ksndpairEq: $o).
4.52/1.09	thf(decl_226, type, kpairsurjEq: $o).
4.52/1.09	thf(decl_227, type, cartprodsndin: $o).
4.52/1.09	thf(decl_228, type, cartprodpairmemEL: $o).
4.52/1.09	thf(decl_229, type, cartprodpairmemER: $o).
4.52/1.09	thf(decl_230, type, cartprodmempaircEq: $o).
4.52/1.09	thf(decl_231, type, cartprodfstpairEq: $o).
4.52/1.09	thf(decl_232, type, cartprodsndpairEq: $o).
4.52/1.09	thf(decl_233, type, cartprodpairsurjEq: $o).
4.52/1.09	thf(decl_234, type, breln: $i > $i > $i > $o).
4.52/1.09	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
4.52/1.09	thf(decl_236, type, dpsetconstrI: $o).
4.52/1.09	thf(decl_237, type, dpsetconstrSub: $o).
4.52/1.09	thf(decl_238, type, setOfPairsIsBReln: $o).
4.52/1.09	thf(decl_239, type, dpsetconstrERa: $o).
4.52/1.09	thf(decl_240, type, dpsetconstrEL1: $o).
4.52/1.09	thf(decl_241, type, dpsetconstrEL2: $o).
4.52/1.09	thf(decl_242, type, dpsetconstrER: $o).
4.52/1.09	thf(decl_243, type, func: $i > $i > $i > $o).
4.52/1.09	thf(decl_244, type, funcSet: $i > $i > $i).
4.52/1.09	thf(decl_245, type, funcImageSingleton: $o).
4.52/1.09	thf(decl_246, type, apProp: $o).
4.52/1.09	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
4.52/1.09	thf(decl_248, type, app: $o).
4.52/1.09	thf(decl_249, type, infuncsetfunc: $o).
4.52/1.09	thf(decl_250, type, ap2p: $o).
4.52/1.09	thf(decl_251, type, funcinfuncset: $o).
4.52/1.09	thf(decl_252, type, lamProp: $o).
4.52/1.09	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
4.52/1.09	thf(decl_254, type, lamp: $o).
4.52/1.09	thf(decl_255, type, lam2p: $o).
4.52/1.09	thf(decl_256, type, brelnall1: $o).
4.52/1.09	thf(decl_257, type, brelnall2: $o).
4.52/1.09	thf(decl_258, type, ex1E2: $o).
4.52/1.09	thf(decl_259, type, epred1_0: $o).
4.52/1.09	thf(decl_260, type, esk1_2: $i > $i > $i).
4.52/1.09	thf(decl_261, type, esk2_2: $i > $i > $i).
4.52/1.09	thf(decl_262, type, esk3_2: $i > $i > $i).
4.52/1.09	thf(decl_263, type, esk4_1: $i > $i).
4.52/1.09	thf(decl_264, type, esk5_2: ($i > $i > $o) > $i > $i).
4.52/1.09	thf(decl_265, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
4.52/1.09	thf(decl_266, type, esk7_2: ($i > $i > $o) > $i > $i).
4.52/1.09	thf(decl_267, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
4.52/1.09	thf(decl_268, type, esk9_1: $i > $i).
4.52/1.09	thf(decl_269, type, esk10_2: ($i > $o) > $i > $i).
4.52/1.09	thf(decl_270, type, esk11_2: ($i > $o) > $i > $i).
4.52/1.09	thf(decl_271, type, esk12_1: ($i > $o) > $i).
4.52/1.09	thf(decl_272, type, esk13_2: ($i > $o) > $i > $i).
4.52/1.09	thf(decl_273, type, esk14_1: ($i > $o) > $i).
4.52/1.09	thf(decl_274, type, esk15_2: $i > $i > $i).
4.52/1.09	thf(decl_275, type, esk16_2: $i > $i > $i).
4.52/1.09	thf(decl_276, type, esk17_1: $i > $i).
4.52/1.09	thf(decl_277, type, esk18_1: $i > $i).
4.52/1.09	thf(decl_278, type, esk19_1: $i > $i).
4.52/1.09	thf(decl_279, type, esk20_2: $i > $i > $i).
4.52/1.09	thf(decl_280, type, esk21_3: $i > $i > $o > $i).
4.52/1.09	thf(decl_281, type, esk22_2: ($i > $o) > $i > $i).
4.52/1.09	thf(decl_282, type, esk23_1: ($i > $o) > $i).
4.52/1.09	thf(decl_283, type, esk24_1: $i > $i).
4.52/1.09	thf(decl_284, type, esk25_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_285, type, esk26_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_286, type, esk27_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_287, type, esk28_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_288, type, esk29_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_289, type, esk30_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_290, type, esk31_2: ($i > $o) > $i > $i).
4.52/1.09	thf(decl_291, type, esk32_1: ($i > $o) > $i).
4.52/1.09	thf(decl_292, type, esk33_1: ($i > $o) > $i).
4.52/1.09	thf(decl_293, type, esk34_1: ($i > $o) > $i).
4.52/1.09	thf(decl_294, type, esk35_1: ($i > $o) > $i).
4.52/1.09	thf(decl_295, type, esk36_2: ($i > $o) > $i > $i).
4.52/1.09	thf(decl_296, type, esk37_1: ($i > $o) > $i).
4.52/1.09	thf(decl_297, type, esk38_2: ($i > $o) > $i > $i).
4.52/1.09	thf(decl_298, type, esk39_2: ($i > $o) > ($i > $o) > $i).
4.52/1.09	thf(decl_299, type, esk40_2: ($i > $o) > ($i > $o) > $i).
4.52/1.09	thf(decl_300, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
4.52/1.09	thf(decl_301, type, esk42_2: ($i > $o) > ($i > $o) > $i).
4.52/1.09	thf(decl_302, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
4.52/1.09	thf(decl_303, type, esk44_2: ($i > $o) > ($i > $o) > $i).
4.52/1.09	thf(decl_304, type, esk45_2: ($i > $o) > $i > $i).
4.52/1.09	thf(decl_305, type, esk46_2: ($i > $o) > ($i > $o) > $i).
4.52/1.09	thf(decl_306, type, esk47_2: ($i > $o) > ($i > $o) > $i).
4.52/1.09	thf(decl_307, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
4.52/1.09	thf(decl_308, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
4.52/1.09	thf(decl_309, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
4.52/1.09	thf(decl_310, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
4.52/1.09	thf(decl_311, type, esk52_2: $i > $i > $i).
4.52/1.09	thf(decl_312, type, esk53_2: $i > $i > $i).
4.52/1.09	thf(decl_313, type, esk54_2: $i > $i > $i).
4.52/1.09	thf(decl_314, type, esk55_3: $i > $i > $i > $i).
4.52/1.09	thf(decl_315, type, esk56_3: $i > $i > $i > $i).
4.52/1.09	thf(decl_316, type, esk57_2: $i > $i > $i).
4.52/1.09	thf(decl_317, type, esk58_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_318, type, esk59_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_319, type, esk60_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_320, type, esk61_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_321, type, esk62_3: $i > ($i > $o) > $i > $i).
4.52/1.09	thf(decl_322, type, esk63_3: $i > ($i > $o) > $i > $i).
4.52/1.09	thf(decl_323, type, esk64_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_324, type, esk65_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_325, type, esk66_2: $i > ($i > $o) > $i).
4.52/1.09	thf(decl_326, type, esk67_1: $i > $i).
4.52/1.09	thf(decl_327, type, esk68_1: $i > $i).
4.52/1.09	thf(decl_328, type, esk69_3: $i > $i > $i > $i).
4.52/1.09	thf(decl_329, type, esk70_4: $i > $i > $i > $i > $i).
4.52/1.09	thf(decl_330, type, esk71_3: $i > $i > $i > $i).
4.52/1.09	thf(decl_331, type, esk72_3: $i > $i > $i > $i).
4.52/1.09	thf(decl_332, type, esk73_4: $i > $i > $i > $i > $i).
4.52/1.09	thf(decl_333, type, esk74_3: $i > $i > $i > $i).
4.52/1.09	thf(decl_334, type, esk75_3: $i > $i > ($i > $i) > $i).
4.52/1.09	thf(decl_335, type, esk76_4: $i > $i > ($i > $i) > $i > $i).
4.52/1.09	thf(decl_336, type, esk77_3: $i > $i > ($i > $i) > $i).
4.52/1.09	thf(decl_337, type, esk78_4: $i > $i > ($i > $i) > $i > $i).
4.52/1.09	thf(decl_338, type, esk79_3: $i > $i > ($i > $i) > $i).
4.52/1.09	thf(decl_339, type, esk80_4: $i > $i > $i > ($i > $o) > $i).
4.52/1.09	thf(decl_340, type, esk81_4: $i > $i > $i > ($i > $o) > $i).
4.52/1.09	thf(decl_341, type, esk82_4: $i > $i > $i > ($i > $o) > $i).
4.52/1.09	thf(decl_342, type, esk83_4: $i > $i > $i > ($i > $o) > $i).
4.52/1.09	thf(decl_343, type, esk84_0: $i).
4.52/1.09	thf(decl_344, type, esk85_0: $i).
4.52/1.09	thf(decl_345, type, esk86_0: $i).
4.52/1.09	thf(decl_346, type, esk87_1: $i > $i).
4.52/1.09	thf(decl_347, type, esk88_0: $i).
4.52/1.09	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ex1)).
4.52/1.09	thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', singleton)).
4.52/1.09	thf(func, axiom, ((func)=(^[X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)&![X2:$i]:(((in @ X2 @ X4)=>(ex1 @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', func)).
4.52/1.09	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', breln)).
4.52/1.09	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', nonempty)).
4.52/1.09	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', exuE2)).
4.52/1.09	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', exu)).
4.52/1.09	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ex1E1)).
4.52/1.09	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', descrp)).
4.52/1.09	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', replAx)).
4.52/1.09	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', singletonprop)).
4.52/1.09	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ex1I)).
4.52/1.09	thf(ap, axiom, ((ap)=(^[X4:$i, X5:$i, X30:$i, X2:$i]:(setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ap)).
4.52/1.09	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X31 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', lamProp)).
4.52/1.09	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X34 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', lam2p)).
4.52/1.09	thf(lam, axiom, ((lam)=(^[X4:$i, X5:$i, X32:$i > $i]:(dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X32 @ X2)=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', lam)).
4.52/1.09	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ex1E2)).
4.52/1.09	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X33 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', lamp)).
4.52/1.09	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', apProp)).
4.52/1.09	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', funcImageSingleton)).
4.52/1.09	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setOfPairsIsBReln)).
4.52/1.09	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ksndsingleton)).
4.52/1.09	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', kfstsingleton)).
4.52/1.09	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ex1I2)).
4.52/1.09	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', descr__Cong)).
4.52/1.09	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', exu__Cong)).
4.52/1.09	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', exuE3u)).
4.52/1.09	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', exuI3)).
4.52/1.09	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', exuEu)).
4.52/1.09	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', exuI2)).
4.52/1.09	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', exuI1)).
4.52/1.09	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', nonemptyI)).
4.52/1.09	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', exuE3e)).
4.52/1.09	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', exuE1)).
4.52/1.09	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', nonemptyImpWitness)).
4.52/1.09	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', nonemptyI1)).
4.52/1.09	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', nonemptyE1)).
4.52/1.09	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setbeta)).
4.52/1.09	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', dsetconstrEL)).
4.52/1.09	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', dsetconstrI)).
4.52/1.09	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', dpsetconstrI)).
4.52/1.09	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', theprop)).
4.52/1.09	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', dpsetconstrSub)).
4.52/1.09	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', dpsetconstrEL1)).
4.52/1.09	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', dpsetconstrEL2)).
4.52/1.09	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', app)).
4.52/1.09	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', infuncsetfunc)).
4.52/1.09	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', brelnall1)).
4.52/1.09	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', brelnall2)).
4.52/1.09	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>(in @ X30 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', funcinfuncset)).
4.52/1.09	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ap2p)).
4.52/1.09	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', dpsetconstrER)).
4.52/1.09	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', dpsetconstrERa)).
4.52/1.09	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', sepSubset)).
4.52/1.09	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', dsetconstr__Cong)).
4.52/1.09	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', sepInPowerset)).
4.52/1.09	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', emptyE1)).
4.52/1.09	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setoftrueEq)).
4.52/1.09	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', dsetconstrER)).
4.52/1.09	thf(funcGraphProp1, conjecture, ((((((setunionAx)=>((((((foundationAx)=>((wellorderingAx)=>(((((dsetconstrER)=>((exuE1)=>((prop2setE)=>(((emptysetimpfalse)=>(((exuE3e)=>((setext)=>((((((nonemptyI)=>(((((setadjoinIR)=>((setadjoinE)=>(((setoftrueEq)=>((powersetI)=>((((powersetE)=>(((setunionE)=>((((((((singletonsswitch)=>((upairsetE)=>(((upairsetIR)=>((emptyE1)=>(((quantDeMorgan1)=>((quantDeMorgan2)=>(((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>(((notdallE)=>((exuI1)=>(((exuI2)=>((inCongP)=>(((((((powerset__Cong)=>(((omega__Cong)=>((exuEu)=>((((subsetI1)=>((eqimpsubset2)=>(((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>(((subsetRefl)=>(((setadjoinSub)=>((setadjoinSub2)=>(((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>(((sepInPowerset)=>(((binunionIL)=>(((binunionIR)=>(((((((binintersectSubset5)=>((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>(((binintersectSubset4)=>(((bs114d)=>((setminusI)=>((setminusEL)=>(((((setminusELneg)=>((((((symdiffE)=>((symdiffI1)=>(((symdiffIneg1)=>(((secondinupair)=>((((kpairiskpair)=>((kpairp)=>(((singletoninpowerset)=>(((upairset2E)=>((upairsubunion)=>(((((ubforcartprodlem3)=>(((((((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>(((singletonsuniq)=>((setukpairinjL1)=>(((theprop)=>((((setukpairinjL2)=>(((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>(((setukpairinjR2)=>((setukpairinjR)=>((((((cartprodpairmemEL)=>(((cartprodmempaircEq)=>((((((dpsetconstrSub)=>((((dpsetconstrEL1)=>((dpsetconstrEL2)=>(((((app)=>((infuncsetfunc)=>((((lamProp)=>(((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)<=(in @ X2 @ X4)))))))))<=(lamp)))<=(funcinfuncset))<=(ap2p))))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER))))<=(dpsetconstrERa))<=(setOfPairsIsBReln)))<=(dpsetconstrI))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))<=(cartprodpairmemER)))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton))))<=(upairequniteq)))))<=(setukpairinjL)))<=(cartprodfstin))<=(kfstpairEq)))<=(kfstsingleton))))<=(ex1I2)))))))<=(setunionsingleton1))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin)))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion))))<=(singletoninpowunion)))<=(singletonsubset))))<=(setukpairIR))<=(setukpairIL)))<=(symdiffIneg2)))<=(symdiffI2))))<=(setminusSubset1))<=(setminusLsub))<=(setminusIRneg))<=(setminusILneg)))<=(setminusERneg))<=(setminusSubset2))<=(setminusER)))))<=(binintersectSubset1)))<=(binintersectRsub))))))<=(binintersectLsub))))<=(binintersectI))<=(binunionRsub))<=(binunionLsub))<=(binunionE))<=(binunionEcases)))<=(upairset2IR)))<=(sepSubset)))<=(powersetsubset)))<=(powersetE1)))))<=(subset2powerset))))<=(subsetTrans)))<=(notequalI2))))))))<=(eqimpsubset1))))<=(dsetconstr__Cong))<=(descr__Cong))))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))<=(in__Cong))))<=(exuI3))))<=(notdexE)))))<=(quantDeMorgan3))))<=(vacuousDall))))<=(upairsetIL))))<=(eqinunit))<=(notinsingleton))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))<=(setunionI)))<=(emptyInPowerset))<=(emptyinPowerset))))<=(setadjoinOr))))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1)))<=(nonemptyE1))<=(setbeta))<=(noeltsimpempty))<=(emptyI))))<=(notinemptyset)))<=(emptysetE)))))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))))<=(replAx))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', funcGraphProp1)).
4.52/1.09	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binunionIR)).
4.52/1.09	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', emptysetE)).
4.52/1.09	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setextAx)).
4.52/1.09	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', vacuousDall)).
4.52/1.09	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binunionIL)).
4.52/1.09	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', upairsetIL)).
4.52/1.09	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binintersectSubset2)).
4.52/1.09	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', eqinunit)).
4.52/1.09	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', notinsingleton)).
4.52/1.09	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', uniqinunit)).
4.52/1.09	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binintersectSubset3)).
4.52/1.09	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binintersectER)).
4.52/1.09	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', subPowSU)).
4.52/1.09	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setunionI)).
4.52/1.09	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', emptyInPowerset)).
4.52/1.09	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', disjointsetsI1)).
4.52/1.09	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', emptyinPowerset)).
4.52/1.09	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setadjoinOr)).
4.52/1.09	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binintersectSubset4)).
4.52/1.09	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', emptyinunitempty)).
4.52/1.09	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setadjoinIL)).
4.52/1.09	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', bs114d)).
4.52/1.09	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', noeltsimpempty)).
4.52/1.09	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setminusI)).
4.52/1.09	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', emptyI)).
4.52/1.09	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', notinemptyset)).
4.52/1.09	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setminusEL)).
4.52/1.09	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setminusELneg)).
4.52/1.09	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', omegaIndAx)).
4.52/1.09	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', omegaSAx)).
4.52/1.09	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', symdiffE)).
4.52/1.09	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', omega0Ax)).
4.52/1.09	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', powersetAx)).
4.52/1.09	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', symdiffI1)).
4.52/1.09	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setadjoinAx)).
4.52/1.09	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', emptysetAx)).
4.52/1.09	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', symdiffIneg1)).
4.52/1.09	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', secondinupair)).
4.52/1.09	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', kpairiskpair)).
4.52/1.09	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', kpairp)).
4.52/1.09	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', singletoninpowerset)).
4.52/1.09	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', upairset2E)).
4.52/1.09	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', upairsubunion)).
4.52/1.09	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ubforcartprodlem3)).
4.52/1.09	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setunionsingleton2)).
4.52/1.09	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setunionsingleton)).
4.52/1.09	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', cartprodpairsurjEq)).
4.52/1.09	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', singletonsuniq)).
4.52/1.09	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setukpairinjL1)).
4.52/1.09	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setukpairinjL2)).
4.52/1.09	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setukpairinjR11)).
4.52/1.09	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setukpairinjR12)).
4.52/1.09	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setukpairinjR1)).
4.52/1.09	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binintersectSubset5)).
4.52/1.09	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setukpairinjR2)).
4.52/1.09	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binintersectEL)).
4.52/1.09	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setukpairinjR)).
4.52/1.09	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', cartprodpairmemEL)).
4.52/1.09	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', cartprodmempaircEq)).
4.52/1.09	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', cartprodsndpairEq)).
4.52/1.09	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', cartprodfstpairEq)).
4.52/1.09	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', cartprodpairmemER)).
4.52/1.09	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', cartprodsndin)).
4.52/1.09	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', kpairsurjEq)).
4.52/1.09	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ksndpairEq)).
4.52/1.09	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', upairequniteq)).
4.52/1.09	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setukpairinjL)).
4.52/1.09	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', cartprodfstin)).
4.52/1.09	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', kfstpairEq)).
4.52/1.09	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setunionsingleton1)).
4.52/1.09	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setunionE2)).
4.52/1.09	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', cartprodmempair)).
4.52/1.09	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', cartprodmempair1)).
4.52/1.09	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', cartprodpairin)).
4.52/1.09	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ubforcartprodlem2)).
4.52/1.09	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', ubforcartprodlem1)).
4.52/1.09	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', upairinpowunion)).
4.52/1.09	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', singletoninpowunion)).
4.52/1.09	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', singletonsubset)).
4.52/1.09	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setukpairIR)).
4.52/1.09	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setukpairIL)).
4.52/1.09	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', symdiffIneg2)).
4.52/1.09	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', symdiffI2)).
4.52/1.09	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setminusSubset1)).
4.52/1.09	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setminusLsub)).
4.52/1.09	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setminusIRneg)).
4.52/1.09	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setminusILneg)).
4.52/1.09	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setminusERneg)).
4.52/1.09	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setminusSubset2)).
4.52/1.09	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setminusER)).
4.52/1.09	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binintersectSubset1)).
4.52/1.09	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binintersectRsub)).
4.52/1.09	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binintersectLsub)).
4.52/1.09	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binintersectI)).
4.52/1.09	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binunionRsub)).
4.52/1.09	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binunionLsub)).
4.52/1.09	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binunionE)).
4.52/1.09	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', binunionEcases)).
4.52/1.09	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', upairset2IR)).
4.52/1.09	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', powersetsubset)).
4.52/1.09	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', powersetE1)).
4.52/1.09	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', subset2powerset)).
4.52/1.09	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', subsetTrans)).
4.52/1.09	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', notequalI2)).
4.52/1.09	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', eqimpsubset1)).
4.52/1.09	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setunion__Cong)).
4.52/1.09	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setadjoin__Cong)).
4.52/1.09	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', emptyset__Cong)).
4.52/1.09	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', in__Cong)).
4.52/1.09	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', notdexE)).
4.52/1.09	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', quantDeMorgan3)).
4.52/1.09	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', inPowerset)).
4.52/1.09	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', powersetI1)).
4.52/1.09	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', subsetemptysetimpeq)).
4.52/1.09	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setextsub)).
4.52/1.09	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setadjoinSub2)).
4.52/1.09	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setadjoinSub)).
4.52/1.09	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', subsetRefl)).
4.52/1.09	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', notequalI1)).
4.52/1.09	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', notsubsetI)).
4.52/1.09	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', subsetE2)).
4.52/1.09	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', subsetE)).
4.52/1.09	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', emptysetsubset)).
4.52/1.09	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', subsetI2)).
4.52/1.09	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', eqimpsubset2)).
4.52/1.09	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', subsetI1)).
4.52/1.09	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', omega__Cong)).
4.52/1.09	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', powerset__Cong)).
4.52/1.09	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', inCongP)).
4.52/1.09	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', notdallE)).
4.52/1.09	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', prop2setI)).
4.52/1.09	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', quantDeMorgan4)).
4.52/1.09	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', quantDeMorgan2)).
4.52/1.09	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', quantDeMorgan1)).
4.52/1.09	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', upairsetIR)).
4.52/1.09	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', upairsetE)).
4.52/1.09	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', singletonsswitch)).
4.52/1.09	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setunionE)).
4.52/1.09	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', powersetE)).
4.52/1.09	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', powersetI)).
4.52/1.09	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setadjoinE)).
4.52/1.09	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setadjoinIR)).
4.52/1.09	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setext)).
4.52/1.09	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', emptysetimpfalse)).
4.52/1.09	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', prop2setE)).
4.52/1.09	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', wellorderingAx)).
4.52/1.09	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', foundationAx)).
4.52/1.09	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.IQYS7rT5vD/E---3.1_2664.p', setunionAx)).
4.52/1.09	thf(c_0_208, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X648:$i]:(((in @ X648 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X648 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
4.52/1.09	thf(c_0_209, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
4.52/1.09	thf(c_0_210, plain, ((func)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((((subset @ Z2 @ (cartprod @ Z0 @ Z1)))&![X2:$i]:(((in @ X2 @ Z0)=>(?[X655:$i]:(((in @ X655 @ (dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2))))))&((dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X655 @ emptyset))))))))))), inference(fof_simplification,[status(thm)],[func])).
4.52/1.09	thf(c_0_211, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X648:$i]:(((in @ X648 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X648 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_208, c_0_209])).
4.52/1.09	thf(c_0_212, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
4.52/1.09	thf(c_0_213, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
4.52/1.09	thf(c_0_214, 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])).
4.52/1.09	thf(c_0_215, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
4.52/1.09	thf(c_0_216, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
4.52/1.09	thf(c_0_217, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
4.52/1.09	thf(c_0_218, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
4.52/1.09	thf(c_0_219, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
4.52/1.09	thf(c_0_220, plain, ((ex1I)<=>![X4:$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])).
4.52/1.09	thf(c_0_221, plain, ((ap)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i, Z3:$i]:(setunion @ (dsetconstr @ Z1 @ (^[Z4/* 3 */:$i]:((in @ (kpair @ Z3 @ Z4) @ Z2))))))), inference(fof_simplification,[status(thm)],[ap])).
4.52/1.09	thf(c_0_222, plain, ((func)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((((subset @ Z2 @ (cartprod @ Z0 @ Z1)))&![X2:$i]:(((in @ X2 @ Z0)=>(?[X655:$i]:(((in @ X655 @ (dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2))))))&((dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X655 @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_210, c_0_211]), c_0_212])).
4.52/1.09	thf(c_0_223, plain, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
4.52/1.09	thf(c_0_224, plain, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X34 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
4.52/1.09	thf(c_0_225, plain, ((lam)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i > $i]:(dpsetconstr @ Z0 @ Z1 @ (^[Z3/* 19 */:$i, Z4:$i]:(((Z2 @ Z3)=(Z4))))))), inference(fof_simplification,[status(thm)],[lam])).
4.52/1.09	thf(c_0_226, plain, ((ex1E2)<=>![X4:$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])).
4.52/1.09	thf(c_0_227, plain, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X33 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
4.52/1.09	thf(c_0_228, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
4.52/1.09	thf(c_0_229, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
4.52/1.09	thf(c_0_230, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
4.52/1.09	thf(c_0_231, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
4.52/1.09	thf(c_0_232, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
4.52/1.09	thf(c_0_233, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
4.52/1.09	thf(c_0_234, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
4.52/1.09	thf(c_0_235, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
4.52/1.09	thf(c_0_236, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
4.52/1.09	thf(c_0_237, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
4.52/1.09	thf(c_0_238, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
4.52/1.09	thf(c_0_239, 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])).
4.52/1.09	thf(c_0_240, 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])).
4.52/1.09	thf(c_0_241, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
4.52/1.09	thf(c_0_242, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
4.52/1.09	thf(c_0_243, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
4.52/1.09	thf(c_0_244, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_213])).
4.52/1.09	thf(c_0_245, plain, ((exuE2)=(![X1:$i > $o]:(((?[X627:$i]:((((X1 @ X627))&![X628:$i]:((((X1 @ X628))=>((X627)=(X628)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_214, c_0_215])).
4.52/1.09	thf(c_0_246, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_213])).
4.52/1.09	thf(c_0_247, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_213])).
4.52/1.09	thf(c_0_248, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
4.52/1.09	thf(c_0_249, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X649:$i]:(((in @ X649 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X649 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_216, c_0_211])).
4.52/1.09	thf(c_0_250, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
4.52/1.09	thf(c_0_251, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
4.52/1.09	thf(c_0_252, plain, ((descrp)=(![X1:$i > $o]:(((?[X621:$i]:((((X1 @ X621))&![X622:$i]:((((X1 @ X622))=>((X621)=(X622)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_217, c_0_215])).
4.52/1.09	thf(c_0_253, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X619:$i]:((((X6 @ X2 @ X619))&![X620:$i]:((((X6 @ X2 @ X620))=>((X619)=(X620)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_218, c_0_215])).
4.52/1.09	thf(c_0_254, 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)))=>(?[X647:$i]:(((in @ X647 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X647 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_219, c_0_209])).
4.52/1.09	thf(c_0_255, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
4.52/1.09	thf(c_0_256, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X650:$i]:(((in @ X650 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X650 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_220, c_0_211])).
4.52/1.09	thf(c_0_257, axiom, ((theprop)=(![X21:$i]:(((?[X653:$i]:(((in @ X653 @ X21)&((X21)=(setadjoin @ X653 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_209])).
4.52/1.09	thf(c_0_258, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
4.52/1.09	thf(c_0_259, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
4.52/1.09	thf(c_0_260, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
4.52/1.09	thf(c_0_261, axiom, ((app)=(![X4:$i, X5:$i, X30:$i]:((((((subset @ X30 @ (cartprod @ X4 @ X5)))&![X661:$i]:(((in @ X661 @ X4)=>(?[X662:$i]:(((in @ X662 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X661 @ Z0) @ X30))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X661 @ Z0) @ X30)))))=(setadjoin @ X662 @ emptyset)))))))))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[app, c_0_221]), c_0_222])).
4.52/1.09	thf(c_0_262, axiom, ((infuncsetfunc)=(![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>((((subset @ X30 @ (cartprod @ X4 @ X5)))&![X663:$i]:(((in @ X663 @ X4)=>(?[X664:$i]:(((in @ X664 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X663 @ Z0) @ X30))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X663 @ Z0) @ X30)))))=(setadjoin @ X664 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[infuncsetfunc, c_0_222])).
4.52/1.09	thf(c_0_263, plain, ((lamProp)=(![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>((((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))) @ (cartprod @ X4 @ X5)))&![X667:$i]:(((in @ X667 @ X4)=>(?[X668:$i]:(((in @ X668 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X667 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1/* 19 */:$i, Z2:$i]:(((X31 @ Z1)=(Z2)))))))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X667 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1/* 19 */:$i, Z2:$i]:(((X31 @ Z1)=(Z2))))))))))=(setadjoin @ X668 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_223, c_0_222])).
4.52/1.09	thf(c_0_264, plain, ((lam2p)=(![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X34 @ Z0)=(Z1))))) @ (funcSet @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_224, c_0_225])).
4.52/1.09	thf(c_0_265, axiom, ((brelnall1)=(![X4:$i, X5:$i, X29:$i]:((((subset @ X29 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_212])).
4.52/1.09	thf(c_0_266, axiom, ((brelnall2)=(![X4:$i, X5:$i, X29:$i]:((((subset @ X29 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_212])).
4.52/1.09	thf(c_0_267, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((?[X671:$i]:(((in @ X671 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X671 @ emptyset)))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_211])).
4.52/1.09	thf(c_0_268, plain, ((lamp)=(![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>((((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X33 @ Z0)=(Z1))))) @ (cartprod @ X4 @ X5)))&![X669:$i]:(((in @ X669 @ X4)=>(?[X670:$i]:(((in @ X670 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X669 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1/* 19 */:$i, Z2:$i]:(((X33 @ Z1)=(Z2)))))))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X669 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1/* 19 */:$i, Z2:$i]:(((X33 @ Z1)=(Z2))))))))))=(setadjoin @ X670 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_227, c_0_222]), c_0_225])).
4.52/1.09	thf(c_0_269, axiom, ((funcinfuncset)=(![X4:$i, X5:$i, X30:$i]:((((((subset @ X30 @ (cartprod @ X4 @ X5)))&![X665:$i]:(((in @ X665 @ X4)=>(?[X666:$i]:(((in @ X666 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X665 @ Z0) @ X30))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X665 @ Z0) @ X30)))))=(setadjoin @ X666 @ emptyset)))))))))=>(in @ X30 @ (funcSet @ X4 @ X5)))))), inference(apply_def,[status(thm)],[funcinfuncset, c_0_222])).
4.52/1.09	thf(c_0_270, axiom, ((ap2p)=(![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5))))))), inference(apply_def,[status(thm)],[ap2p, c_0_221])).
4.52/1.09	thf(c_0_271, plain, ((apProp)=(![X4:$i, X5:$i, X30:$i]:((((((subset @ X30 @ (cartprod @ X4 @ X5)))&![X659:$i]:(((in @ X659 @ X4)=>(?[X660:$i]:(((in @ X660 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X659 @ Z0) @ X30))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X659 @ Z0) @ X30)))))=(setadjoin @ X660 @ emptyset)))))))))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_222])).
4.52/1.09	thf(c_0_272, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X30:$i]:((((((subset @ X30 @ (cartprod @ X4 @ X5)))&![X656:$i]:(((in @ X656 @ X4)=>(?[X657:$i]:(((in @ X657 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X656 @ Z0) @ X30))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X656 @ Z0) @ X30)))))=(setadjoin @ X657 @ emptyset)))))))))=>![X2:$i]:(((in @ X2 @ X4)=>(?[X658:$i]:(((in @ X658 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))=(setadjoin @ X658 @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_229, c_0_222]), c_0_209])).
4.52/1.09	thf(c_0_273, 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:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
4.52/1.09	thf(c_0_274, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
4.52/1.09	thf(c_0_275, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_230, c_0_212])).
4.52/1.09	thf(c_0_276, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X654:$i]:(((in @ X654 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X654 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_231, c_0_209])).
4.52/1.09	thf(c_0_277, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X652:$i]:(((in @ X652 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X652 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_209])).
4.52/1.09	thf(c_0_278, plain, ((ex1I2)=(![X4:$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)))=>(?[X651:$i]:(((in @ X651 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X651 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_211])).
4.52/1.09	thf(c_0_279, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
4.52/1.09	thf(c_0_280, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
4.52/1.09	thf(c_0_281, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X643:$i]:((((X1 @ X643))&![X644:$i]:((((X1 @ X644))=>((X643)=(X644)))))))=>((?[X645:$i]:((((X17 @ X645))&![X646:$i]:((((X17 @ X646))=>((X645)=(X646)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_215])).
4.52/1.09	thf(c_0_282, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X637:$i]:((((X1 @ X637))&![X638:$i]:((((X1 @ X638))=>((X637)=(X638)))))))<=>(?[X639:$i]:((((X17 @ X639))&![X640:$i]:((((X17 @ X640))=>((X639)=(X640)))))))))))), inference(apply_def,[status(thm)],[c_0_235, c_0_215])).
4.52/1.09	thf(c_0_283, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X635:$i]:((((X1 @ X635))&![X636:$i]:((((X1 @ X636))=>((X635)=(X636)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_215])).
4.52/1.09	thf(c_0_284, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X631:$i]:((((X1 @ X631))&![X632:$i]:((((X1 @ X632))=>((X631)=(X632)))))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_215])).
4.52/1.09	thf(c_0_285, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
4.52/1.09	thf(c_0_286, plain, ((exuEu)=(![X1:$i > $o]:(((?[X641:$i]:((((X1 @ X641))&![X642:$i]:((((X1 @ X642))=>((X641)=(X642)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_215])).
4.52/1.09	thf(c_0_287, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X633:$i]:((((X1 @ X633))&![X634:$i]:((((X1 @ X634))=>((X633)=(X634))))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_215])).
4.52/1.09	thf(c_0_288, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X629:$i]:((((X1 @ X629))&![X630:$i]:((((X1 @ X630))=>((X629)=(X630))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_215])).
4.52/1.09	thf(c_0_289, plain, ((emptyE1)<=>![X4:$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])).
4.52/1.09	thf(c_0_290, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
4.52/1.09	thf(c_0_291, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_213])).
4.52/1.09	thf(c_0_292, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X625:$i]:((((X1 @ X625))&![X626:$i]:((((X1 @ X626))=>((X625)=(X626)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_242, c_0_215])).
4.52/1.09	thf(c_0_293, plain, ((exuE1)=(![X1:$i > $o]:(((?[X623:$i]:((((X1 @ X623))&![X624:$i]:((((X1 @ X624))=>((X623)=(X624)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_215])).
4.52/1.09	thf(c_0_294, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
4.52/1.09	thf(c_0_295, plain, ((epred1_0)<=>![X679:$i]:(?[X680:$i]:((((![X681:$i]:(((in @ X681 @ X680)=>![X682:$i]:(((in @ X682 @ X681)=>(in @ X682 @ X679)))))&![X683:$i, X684:$i]:((((in @ X683 @ X679)&(in @ X684 @ X679))=>(![X685:$i]:(((in @ X685 @ X680)=>((in @ X683 @ X685)<=>(in @ X684 @ X685))))=>((X683)=(X684))))))&![X686:$i, X687:$i]:((((in @ X686 @ X680)&(in @ X687 @ X680))=>(![X688:$i]:(((in @ X688 @ X686)=>(in @ X688 @ X687)))|![X689:$i]:(((in @ X689 @ X687)=>(in @ X689 @ X686)))))))&![X690:$i]:(((![X691:$i]:(((in @ X691 @ X690)=>(in @ X691 @ X679)))&?[X692:$i]:((in @ X692 @ X690)))=>?[X693:$i, X694:$i]:(((((in @ X693 @ X680)&(in @ X694 @ X690))&~(?[X695:$i]:(((in @ X695 @ X693)&(in @ X695 @ X690)))))&![X696:$i]:(((in @ X696 @ X680)=>(![X697:$i]:(((in @ X697 @ X696)=>(in @ X697 @ X693)))|(in @ X694 @ X696)))))))))))), introduced(definition)).
4.52/1.09	thf(c_0_296, negated_conjecture, ~((![X1302:$i, X1303:$i]:((![X1304:$i]:(((in @ X1304 @ X1302)<=>(in @ X1304 @ X1303)))=>((X1302)=(X1303))))=>(![X1301:$i]:(~(in @ X1301 @ emptyset))=>(![X1298:$i, X1299:$i, X1300:$i]:(((in @ X1300 @ (setadjoin @ X1298 @ X1299))<=>(((X1300)=(X1298))|(in @ X1300 @ X1299))))=>(![X1295:$i, X1296:$i]:(((in @ X1296 @ (powerset @ X1295))<=>![X1297:$i]:(((in @ X1297 @ X1296)=>(in @ X1297 @ X1295)))))=>(![X672:$i, X673:$i]:(((in @ X673 @ (setunion @ X672))<=>?[X674:$i]:(((in @ X673 @ X674)&(in @ X674 @ X672)))))=>((in @ emptyset @ omega)=>(![X1294:$i]:(((in @ X1294 @ omega)=>(in @ (setadjoin @ X1294 @ X1294) @ omega)))=>(![X1291:$i]:((((in @ emptyset @ X1291)&![X1292:$i]:((((in @ X1292 @ omega)&(in @ X1292 @ X1291))=>(in @ (setadjoin @ X1292 @ X1292) @ X1291))))=>![X1293:$i]:(((in @ X1293 @ omega)=>(in @ X1293 @ X1291)))))=>(![X1283:$i > $i > $o, X1284:$i]:((![X1285:$i]:(((in @ X1285 @ X1284)=>?[X1286:$i]:(((X1283 @ X1285 @ X1286)&![X1287:$i]:(((X1283 @ X1285 @ X1287)=>((X1286)=(X1287))))))))=>?[X1288:$i]:(![X1289:$i]:(((in @ X1289 @ X1288)<=>?[X1290:$i]:(((in @ X1290 @ X1284)&(X1283 @ X1290 @ X1289))))))))=>(![X675:$i]:((?[X676:$i]:((in @ X676 @ X675))=>?[X677:$i]:(((in @ X677 @ X675)&~(?[X678:$i]:(((in @ X678 @ X677)&(in @ X678 @ X675))))))))=>((epred1_0)=>(![X1280:$i > $o]:((?[X1281:$i]:(((X1280 @ X1281)&![X1282:$i]:(((X1280 @ X1282)=>((X1281)=(X1282))))))=>(X1280 @ (descr @ (^[Z0/* 17 */:$i]:(X1280 @ Z0))))))=>(![X1277:$i, X1278:$i > $o, X1279:$i]:(((in @ X1279 @ X1277)=>((X1278 @ X1279)=>(in @ X1279 @ (dsetconstr @ X1277 @ X1278)))))=>(![X1274:$i, X1275:$i > $o, X1276:$i]:(((in @ X1276 @ (dsetconstr @ X1274 @ X1275))=>(in @ X1276 @ X1274)))=>(![X698:$i, X699:$i > $o, X700:$i]:(((in @ X700 @ (dsetconstr @ X698 @ X699))=>(X699 @ X700)))=>(![X701:$i > $o]:((?[X702:$i]:(((X701 @ X702)&![X703:$i]:(((X701 @ X703)=>((X702)=(X703))))))=>?[X704:$i]:(((X701 @ X704)&![X705:$i]:(((X701 @ X705)=>((X704)=(X705))))))))=>(![X706:$o, X707:$i]:(((in @ X707 @ (prop2set @ ((X706))))=>(X706)))=>(![X1272:$i]:(((in @ X1272 @ emptyset)=>![X1273:$o]:((X1273))))=>(![X708:$i]:(((in @ X708 @ emptyset)=>~($true)))=>(![X1271:$i]:(~(in @ X1271 @ emptyset))=>(![X709:$i > $o]:((?[X710:$i]:(((X709 @ X710)&![X711:$i]:(((X709 @ X711)=>((X710)=(X711))))))=>?[X712:$i]:((X709 @ X712))))=>(![X713:$i, X714:$i]:((![X715:$i]:(((in @ X715 @ X713)=>(in @ X715 @ X714)))=>(![X716:$i]:(((in @ X716 @ X714)=>(in @ X716 @ X713)))=>((X713)=(X714)))))=>(![X1269:$i]:((![X1270:$i]:(~(in @ X1270 @ X1269))=>((X1269)=(emptyset))))=>(![X1267:$i]:((![X1268:$i]:(~(in @ X1268 @ X1267))=>((X1267)=(emptyset))))=>(![X1264:$i, X1265:$i > $o, X1266:$i]:(((in @ X1266 @ X1264)=>((in @ X1266 @ (dsetconstr @ X1264 @ X1265))<=>(X1265 @ X1266))))=>(![X1262:$i]:((((X1262)!=(emptyset))=>?[X1263:$i]:((in @ X1263 @ X1262))))=>(![X717:$i, X718:$i > $o, X719:$i]:(((in @ X719 @ X717)=>((X718 @ X719)=>((dsetconstr @ X717 @ X718)!=(emptyset)))))=>(![X1260:$i]:((?[X1261:$i]:((in @ X1261 @ X1260))=>((X1260)!=(emptyset))))=>(![X1258:$i, X1259:$i]:((in @ X1258 @ (setadjoin @ X1258 @ X1259)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X720:$i, X721:$i, X722:$i]:(((in @ X722 @ X721)=>(in @ X722 @ (setadjoin @ X720 @ X721))))=>(![X723:$i, X724:$i, X725:$i]:(((in @ X725 @ (setadjoin @ X723 @ X724))=>![X726:$o]:(((((X725)=(X723))=>(X726))=>(((in @ X725 @ X724)=>(X726))=>(X726))))))=>(![X1255:$i, X1256:$i, X1257:$i]:(((in @ X1257 @ (setadjoin @ X1255 @ X1256))=>(((X1257)=(X1255))|(in @ X1257 @ X1256))))=>(![X727:$i]:(((dsetconstr @ X727 @ (^[Z0/* 1 */:$i]:($true)))=(X727)))=>(![X728:$i, X729:$i]:((![X730:$i]:(((in @ X730 @ X729)=>(in @ X730 @ X728)))=>(in @ X729 @ (powerset @ X728))))=>(![X1254:$i]:((in @ emptyset @ (powerset @ X1254)))=>(![X1253:$i]:((in @ emptyset @ (powerset @ X1253)))=>(![X731:$i, X732:$i, X733:$i]:(((in @ X732 @ (powerset @ X731))=>((in @ X733 @ X732)=>(in @ X733 @ X731))))=>(![X1250:$i, X1251:$i, X1252:$i]:(((in @ X1251 @ X1252)=>((in @ X1252 @ X1250)=>(in @ X1251 @ (setunion @ X1250)))))=>(![X734:$i, X735:$i]:(((in @ X735 @ (setunion @ X734))=>![X736:$o]:((![X737:$i]:(((in @ X735 @ X737)=>((in @ X737 @ X734)=>(X736))))=>(X736)))))=>(![X1248:$i, X1249:$i]:(((in @ X1249 @ X1248)=>(in @ X1249 @ (powerset @ (setunion @ X1248)))))=>(![X1243:$i > $o]:((?[X1244:$i]:(((X1243 @ X1244)&![X1245:$i]:(((X1243 @ X1245)=>((X1244)=(X1245))))))=>?[X1246:$i]:(![X1247:$i]:(((X1243 @ X1247)<=>((X1247)=(X1246)))))))=>(![X1241:$i]:((((X1241)!=(emptyset))=>?[X1242:$i]:(((in @ X1242 @ X1241)&$true))))=>(![X1239:$i, X1240:$i]:(((in @ X1239 @ (setadjoin @ X1240 @ emptyset))=>((X1239)=(X1240))))=>(![X1237:$i, X1238:$i]:((((X1237)!=(X1238))=>~(in @ X1238 @ (setadjoin @ X1237 @ emptyset))))=>(![X1235:$i, X1236:$i]:((((X1235)=(X1236))=>(in @ X1235 @ (setadjoin @ X1236 @ emptyset))))=>(![X738:$i, X739:$i]:(((in @ X738 @ (setadjoin @ X739 @ emptyset))=>(in @ X739 @ (setadjoin @ X738 @ emptyset))))=>(![X740:$i, X741:$i, X742:$i]:(((in @ X742 @ (setadjoin @ X740 @ (setadjoin @ X741 @ emptyset)))=>(((X742)=(X740))|((X742)=(X741)))))=>(![X1233:$i, X1234:$i]:((in @ X1233 @ (setadjoin @ X1233 @ (setadjoin @ X1234 @ emptyset))))=>(![X743:$i, X744:$i]:((in @ X744 @ (setadjoin @ X743 @ (setadjoin @ X744 @ emptyset))))=>(![X745:$i, X746:$i > $o]:((?[X747:$i]:(((in @ X747 @ X745)&(X746 @ X747)))=>(((dsetconstr @ X745 @ X746)=(emptyset))=>~($true))))=>(![X1231:$i > $o, X1232:$i]:(((in @ X1232 @ emptyset)=>(X1231 @ X1232)))=>(![X748:$i, X749:$i > $o]:((~(![X750:$i]:(((in @ X750 @ X748)=>(X749 @ X750))))=>?[X751:$i]:(((in @ X751 @ X748)&~((X749 @ X751))))))=>(![X752:$i, X753:$i > $o]:((![X754:$i]:(((in @ X754 @ X752)=>~((X753 @ X754))))=>~(?[X755:$i]:(((in @ X755 @ X752)&(X753 @ X755))))))=>(![X1227:$i, X1228:$i > $o]:((~(?[X1229:$i]:(((in @ X1229 @ X1227)&(X1228 @ X1229))))=>![X1230:$i]:(((in @ X1230 @ X1227)=>~((X1228 @ X1230))))))=>(![X756:$i, X757:$i > $o]:((?[X758:$i]:(((in @ X758 @ X756)&~((X757 @ 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binunionIR]), emptysetE]), setextAx]), vacuousDall]), binunionIL]), upairsetIL]), binintersectSubset2]), eqinunit]), notinsingleton]), uniqinunit]), binintersectSubset3]), c_0_244]), c_0_245]), binintersectER]), subPowSU]), setunionI]), emptyInPowerset]), disjointsetsI1]), emptyinPowerset]), setadjoinOr]), binintersectSubset4]), emptyinunitempty]), setadjoinIL]), c_0_246]), c_0_247]), bs114d]), c_0_248]), noeltsimpempty]), setminusI]), emptyI]), notinemptyset]), c_0_249]), c_0_250]), setminusEL]), c_0_251]), c_0_252]), setminusELneg]), c_0_253]), omegaIndAx]), omegaSAx]), symdiffE]), omega0Ax]), powersetAx]), symdiffI1]), setadjoinAx]), emptysetAx]), symdiffIneg1]), secondinupair]), kpairiskpair]), kpairp]), singletoninpowerset]), upairset2E]), upairsubunion]), ubforcartprodlem3]), setunionsingleton2]), setunionsingleton]), c_0_254]), c_0_255]), cartprodpairsurjEq]), c_0_256]), singletonsuniq]), setukpairinjL1]), c_0_257]), setukpairinjL2]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), binintersectSubset5]), setukpairinjR2]), binintersectEL]), setukpairinjR]), cartprodpairmemEL]), cartprodmempaircEq]), c_0_258]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), c_0_263]), c_0_264]), c_0_265]), c_0_266]), c_0_267]), c_0_221]), c_0_268]), c_0_269]), c_0_270]), c_0_271]), c_0_272]), c_0_273]), c_0_274]), c_0_275]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodpairmemER]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), c_0_276]), upairequniteq]), setukpairinjL]), cartprodfstin]), kfstpairEq]), c_0_277]), c_0_278]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), singletoninpowunion]), singletonsubset]), setukpairIR]), setukpairIL]), symdiffIneg2]), symdiffI2]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusERneg]), setminusSubset2]), setminusER]), binintersectSubset1]), binintersectRsub]), binintersectLsub]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), binunionEcases]), upairset2IR]), c_0_279]), powersetsubset]), powersetE1]), subset2powerset]), subsetTrans]), notequalI2]), eqimpsubset1]), c_0_280]), c_0_281]), setunion__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_282]), c_0_283]), in__Cong]), c_0_284]), notdexE]), quantDeMorgan3]), c_0_285]), inPowerset]), powersetI1]), subsetemptysetimpeq]), setextsub]), setadjoinSub2]), setadjoinSub]), subsetRefl]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset2]), subsetI1]), c_0_286]), omega__Cong]), powerset__Cong]), inCongP]), c_0_287]), c_0_288]), notdallE]), prop2setI]), quantDeMorgan4]), quantDeMorgan2]), quantDeMorgan1]), c_0_289]), upairsetIR]), upairsetE]), singletonsswitch]), setunionE]), powersetE]), powersetI]), c_0_290]), setadjoinE]), setadjoinIR]), c_0_291]), setext]), c_0_292]), emptysetimpfalse]), prop2setE]), c_0_293]), c_0_294]), wellorderingAx]), foundationAx]), setunionAx]), c_0_222])])]), c_0_295])).
4.52/1.09	thf(c_0_297, negated_conjecture, ![X1305:$i, X1306:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1318:$i, X1319:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1327:$i, X1328:$i > $i > $o, X1329:$i, X1331:$i, X1334:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1341:$i, X1342:$i > $o, X1343:$i, X1345:$i, X1346:$i > $o, X1347:$i, X1348:$i, X1349:$i > $o, X1350:$i, X1351:$i, X1352:$i > $o, X1353:$i, X1354:$i > $o, X1355:$i, X1358:$i, X1359:$o, X1360:$i, X1361:$i, X1362:$o, X1363:$i, X1364:$i, X1365:$i > $o, X1366:$i, X1369:$i, X1370:$i, X1373:$i, X1375:$i, X1377:$i, X1378:$i > $o, X1379:$i, X1380:$i, X1382:$i, X1383:$i > $o, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$o, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$o, X1415:$i, X1416:$i, X1417:$i > $o, X1418:$i, X1421:$i, X1422:$i, X1423:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i > $o, X1442:$i, X1443:$i > $o, X1444:$i, X1445:$i, X1446:$i > $o, X1447:$i, X1449:$i, X1450:$i > $o, X1452:$i, X1453:$i, X1454:$i > $o, X1456:$i, X1457:$i, X1458:$i > $o, X1459:$i, X1461:$o, X1462:$i, X1463:$i > $o, X1465:$i, X1466:$i, X1467:$i > $o, X1468:$i, X1470:$i > $o, X1471:$i, X1474:$i, X1475:$i > $o, X1476:$i, X1480:$i, X1481:$i > $o, X1482:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i > $o, X1495:$i, X1497:$i, X1498:$i, X1499:$i > $o, X1500:$i > $o, X1503:$i, X1506:$i, X1507:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i > $o, X1520:$i, X1522:$i, X1523:$i, X1524:$i > $o, X1525:$i > $o, X1528:$i, X1530:$i, X1532:$i, X1533:$i, X1534:$i > $o, X1535:$i > $o, X1538:$i, X1539:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i > $o, X1586:$i, X1587:$i > $o, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$o, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$o, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i > $o, X1742:$i, X1744:$i, X1745:$i > $o, X1746:$i, X1748:$i, X1749:$i > $o, X1750:$i, X1753:$i, X1754:$i > $o, X1757:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i > $i > $o, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i > $i > $o, X1839:$i, X1840:$i, X1841:$i > $i > $o, X1842:$i, X1843:$i, X1844:$i > $i > $o, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i > $i > $o, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i > $i > $o, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i > $i > $o, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1866:$i, X1867:$i, X1869:$i, X1870:$i, X1871:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i > $i, X1899:$i, X1901:$i, X1902:$i, X1903:$i > $i, X1905:$i, X1907:$i, X1908:$i, X1909:$i > $i, X1911:$i, X1912:$i, X1913:$i, X1914:$i > $o, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i > $o, X1924:$i, X1925:$i, X1926:$i > $o, X1927:$i, X1928:$i, X1929:$i, X1933:$i]:((((~(in @ (esk1_2 @ X1305 @ X1306) @ X1305)|~(in @ (esk1_2 @ X1305 @ X1306) @ X1306)|((X1305)=(X1306)))&((in @ (esk1_2 @ X1305 @ X1306) @ X1305)|(in @ (esk1_2 @ X1305 @ X1306) @ X1306)|((X1305)=(X1306))))&(~(in @ X1308 @ emptyset)&(((~(in @ X1311 @ (setadjoin @ X1309 @ X1310))|(((X1311)=(X1309))|(in @ X1311 @ X1310)))&((((X1311)!=(X1309))|(in @ X1311 @ (setadjoin @ X1309 @ X1310)))&(~(in @ X1311 @ X1310)|(in @ X1311 @ (setadjoin @ X1309 @ X1310)))))&(((~(in @ X1313 @ (powerset @ X1312))|(~(in @ X1314 @ X1313)|(in @ X1314 @ X1312)))&(((in @ (esk2_2 @ X1315 @ X1316) @ X1316)|(in @ X1316 @ (powerset @ X1315)))&(~(in @ (esk2_2 @ X1315 @ X1316) @ X1315)|(in @ X1316 @ (powerset @ X1315)))))&(((((in @ X1319 @ (esk3_2 @ X1318 @ X1319))|~(in @ X1319 @ (setunion @ X1318)))&((in @ (esk3_2 @ X1318 @ X1319) @ X1318)|~(in @ X1319 @ (setunion @ X1318))))&(~(in @ X1322 @ X1323)|~(in @ X1323 @ X1321)|(in @ X1322 @ (setunion @ X1321))))&((in @ emptyset @ omega)&((~(in @ X1324 @ omega)|(in @ (setadjoin @ X1324 @ X1324) @ omega))&(((((in @ (esk4_1 @ X1325) @ omega)|~(in @ emptyset @ X1325)|(~(in @ X1327 @ omega)|(in @ X1327 @ X1325)))&((in @ (esk4_1 @ X1325) @ X1325)|~(in @ emptyset @ X1325)|(~(in @ X1327 @ omega)|(in @ X1327 @ X1325))))&(~(in @ (setadjoin @ (esk4_1 @ X1325) @ (esk4_1 @ X1325)) @ X1325)|~(in @ emptyset @ X1325)|(~(in @ X1327 @ omega)|(in @ X1327 @ X1325))))&((((((in @ (esk8_3 @ X1328 @ X1329 @ X1334) @ X1329)|~(in @ X1334 @ (esk7_2 @ X1328 @ X1329))|(in @ (esk5_2 @ X1328 @ X1329) @ X1329))&((X1328 @ (esk8_3 @ X1328 @ X1329 @ X1334) @ X1334)|~(in @ X1334 @ (esk7_2 @ X1328 @ X1329))|(in @ (esk5_2 @ X1328 @ X1329) @ X1329)))&(~(in @ X1337 @ X1329)|~(X1328 @ X1337 @ X1336)|(in @ X1336 @ (esk7_2 @ X1328 @ X1329))|(in @ (esk5_2 @ X1328 @ X1329) @ X1329)))&(((((in @ (esk8_3 @ X1328 @ X1329 @ X1334) @ X1329)|~(in @ X1334 @ (esk7_2 @ X1328 @ X1329))|((X1328 @ (esk5_2 @ X1328 @ X1329) @ (esk6_3 @ X1328 @ X1329 @ X1331))|~(X1328 @ (esk5_2 @ X1328 @ X1329) @ X1331)))&((X1328 @ (esk8_3 @ X1328 @ X1329 @ X1334) @ X1334)|~(in @ X1334 @ (esk7_2 @ X1328 @ X1329))|((X1328 @ (esk5_2 @ X1328 @ X1329) @ (esk6_3 @ X1328 @ X1329 @ X1331))|~(X1328 @ (esk5_2 @ X1328 @ X1329) @ X1331))))&(~(in @ X1337 @ X1329)|~(X1328 @ X1337 @ X1336)|(in @ X1336 @ (esk7_2 @ X1328 @ X1329))|((X1328 @ (esk5_2 @ X1328 @ X1329) @ (esk6_3 @ X1328 @ X1329 @ X1331))|~(X1328 @ (esk5_2 @ X1328 @ X1329) @ X1331))))&((((in @ (esk8_3 @ X1328 @ X1329 @ X1334) @ X1329)|~(in @ X1334 @ (esk7_2 @ X1328 @ X1329))|(((X1331)!=(esk6_3 @ X1328 @ X1329 @ X1331))|~(X1328 @ (esk5_2 @ X1328 @ X1329) @ X1331)))&((X1328 @ (esk8_3 @ X1328 @ X1329 @ X1334) @ X1334)|~(in @ X1334 @ (esk7_2 @ X1328 @ X1329))|(((X1331)!=(esk6_3 @ X1328 @ X1329 @ X1331))|~(X1328 @ (esk5_2 @ X1328 @ X1329) @ X1331))))&(~(in @ X1337 @ X1329)|~(X1328 @ X1337 @ X1336)|(in @ X1336 @ (esk7_2 @ X1328 @ X1329))|(((X1331)!=(esk6_3 @ X1328 @ X1329 @ X1331))|~(X1328 @ (esk5_2 @ X1328 @ X1329) @ X1331))))))&((((in @ (esk9_1 @ X1338) @ X1338)|~(in @ X1339 @ X1338))&(~(in @ X1341 @ (esk9_1 @ X1338))|~(in @ X1341 @ X1338)|~(in @ X1339 @ X1338)))&((epred1_0)&((((X1342 @ (esk10_2 @ X1342 @ X1343))|~(X1342 @ X1343)|(X1342 @ (descr @ X1342)))&(((X1343)!=(esk10_2 @ X1342 @ X1343))|~(X1342 @ X1343)|(X1342 @ (descr @ X1342))))&((~(in @ X1347 @ X1345)|(~(X1346 @ X1347)|(in @ X1347 @ (dsetconstr @ X1345 @ X1346))))&((~(in @ X1350 @ (dsetconstr @ X1348 @ X1349))|(in @ X1350 @ X1348))&((~(in @ X1353 @ (dsetconstr @ X1351 @ X1352))|(X1352 @ X1353))&(((((X1354 @ (esk12_1 @ X1354))|((X1354 @ (esk11_2 @ X1354 @ X1355))|~(X1354 @ X1355)))&(~(X1354 @ X1358)|((esk12_1 @ X1354)=(X1358))|((X1354 @ (esk11_2 @ X1354 @ X1355))|~(X1354 @ X1355))))&(((X1354 @ (esk12_1 @ X1354))|(((X1355)!=(esk11_2 @ X1354 @ X1355))|~(X1354 @ X1355)))&(~(X1354 @ X1358)|((esk12_1 @ X1354)=(X1358))|(((X1355)!=(esk11_2 @ X1354 @ X1355))|~(X1354 @ X1355)))))&((~(in @ X1360 @ (prop2set @ ((X1359))))|(X1359))&((~(in @ X1361 @ emptyset)|(X1362))&((~(in @ X1363 @ emptyset)|~($true))&(~(in @ X1364 @ emptyset)&((((X1365 @ (esk13_2 @ X1365 @ X1366))|~(X1365 @ X1366)|(X1365 @ (esk14_1 @ X1365)))&(((X1366)!=(esk13_2 @ X1365 @ X1366))|~(X1365 @ X1366)|(X1365 @ (esk14_1 @ X1365))))&(((((in @ (esk16_2 @ X1369 @ X1370) @ X1370)|((X1369)=(X1370))|(in @ (esk15_2 @ X1369 @ X1370) @ X1369))&(~(in @ (esk16_2 @ X1369 @ X1370) @ X1369)|((X1369)=(X1370))|(in @ (esk15_2 @ X1369 @ X1370) @ X1369)))&(((in @ (esk16_2 @ X1369 @ X1370) @ X1370)|((X1369)=(X1370))|~(in @ (esk15_2 @ X1369 @ X1370) @ X1370))&(~(in @ (esk16_2 @ X1369 @ X1370) @ X1369)|((X1369)=(X1370))|~(in @ (esk15_2 @ X1369 @ X1370) @ X1370))))&(((in @ (esk17_1 @ X1373) @ X1373)|((X1373)=(emptyset)))&(((in @ (esk18_1 @ X1375) @ X1375)|((X1375)=(emptyset)))&(((~(in @ X1379 @ (dsetconstr @ X1377 @ X1378))|(X1378 @ X1379)|~(in @ X1379 @ X1377))&(~(X1378 @ X1379)|(in @ X1379 @ (dsetconstr @ X1377 @ X1378))|~(in @ X1379 @ X1377)))&((((X1380)=(emptyset))|(in @ (esk19_1 @ X1380) @ X1380))&((~(in @ X1384 @ X1382)|(~(X1383 @ X1384)|((dsetconstr @ X1382 @ X1383)!=(emptyset))))&((~(in @ X1386 @ X1385)|((X1385)!=(emptyset)))&((in @ X1387 @ (setadjoin @ X1387 @ X1388))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1391 @ X1390)|(in @ X1391 @ (setadjoin @ X1389 @ X1390)))&(((((in @ X1394 @ X1393)|(X1395)|((X1394)=(X1392))|~(in @ X1394 @ (setadjoin @ X1392 @ X1393)))&(~(X1395)|(X1395)|((X1394)=(X1392))|~(in @ X1394 @ (setadjoin @ X1392 @ X1393))))&(((in @ X1394 @ X1393)|(X1395)|~(X1395)|~(in @ X1394 @ (setadjoin @ X1392 @ X1393)))&(~(X1395)|(X1395)|~(X1395)|~(in @ X1394 @ (setadjoin @ X1392 @ X1393)))))&((~(in @ X1398 @ (setadjoin @ X1396 @ X1397))|(((X1398)=(X1396))|(in @ X1398 @ X1397)))&(((dsetconstr @ X1399 @ (^[Z0/* 1 */:$i]:($true)))=(X1399))&((((in @ (esk20_2 @ X1400 @ X1401) @ X1401)|(in @ X1401 @ (powerset @ X1400)))&(~(in @ (esk20_2 @ X1400 @ X1401) @ X1400)|(in @ X1401 @ (powerset @ X1400))))&((in @ emptyset @ (powerset @ X1403))&((in @ emptyset @ (powerset @ X1404))&((~(in @ X1406 @ (powerset @ X1405))|(~(in @ X1407 @ X1406)|(in @ X1407 @ X1405)))&((~(in @ X1409 @ X1410)|(~(in @ X1410 @ X1408)|(in @ X1409 @ (setunion @ X1408))))&((((in @ X1412 @ (esk21_3 @ X1411 @ X1412 @ X1413))|(X1413)|~(in @ X1412 @ 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emptyset)))|(((X1787)!=(X1788))|((X1786)=(X1788))))&((((setadjoin @ X1789 @ (setadjoin @ X1790 @ emptyset))!=(setadjoin @ X1791 @ emptyset))|((X1789)=(X1790)))&((((setadjoin @ (setadjoin @ X1792 @ emptyset) @ (setadjoin @ (setadjoin @ X1792 @ (setadjoin @ X1793 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1794 @ emptyset) @ (setadjoin @ (setadjoin @ X1794 @ (setadjoin @ X1795 @ emptyset)) @ emptyset)))|((X1793)=(X1795)))&((((kpair @ X1796 @ X1797)!=(kpair @ X1798 @ X1799))|((X1797)=(X1799)))&((((in @ (esk68_1 @ X1800) @ (dsetconstr @ (setunion @ X1800) @ (^[Z0/* 3 */:$i]:(((X1800)=(kpair @ (kfst @ X1800) @ Z0))))))|~(iskpair @ X1800))&(((dsetconstr @ (setunion @ X1800) @ (^[Z0/* 3 */:$i]:(((X1800)=(kpair @ (kfst @ X1800) @ Z0)))))=(setadjoin @ (esk68_1 @ X1800) @ emptyset))|~(iskpair @ X1800)))&(((ksnd @ (kpair @ X1802 @ X1803))=(X1803))&((~(iskpair @ X1804)|((kpair @ (kfst @ X1804) @ (ksnd @ X1804))=(X1804)))&((~(in @ X1807 @ (cartprod @ X1805 @ X1806))|(in @ (ksnd @ X1807) @ X1806))&((~(in @ (kpair @ X1810 @ X1811) @ (cartprod @ X1808 @ X1809))|(in @ X1810 @ X1808))&((~(in @ (kpair @ X1814 @ X1815) @ (cartprod @ X1812 @ X1813))|(in @ X1815 @ X1813))&((~(in @ X1818 @ X1816)|(~(in @ X1819 @ X1817)|((kpair @ X1818 @ X1819)=(kpair @ X1818 @ X1819))))&((~(in @ X1822 @ X1820)|(~(in @ X1823 @ X1821)|((kfst @ (kpair @ X1822 @ X1823))=(X1822))))&((~(in @ X1826 @ X1824)|(~(in @ X1827 @ X1825)|((ksnd @ (kpair @ X1826 @ X1827))=(X1827))))&((~(in @ X1830 @ (cartprod @ X1828 @ X1829))|((kpair @ (kfst @ X1830) @ (ksnd @ X1830))=(X1830)))&((~(in @ X1834 @ X1831)|(~(in @ X1835 @ X1832)|(~(X1833 @ X1834 @ X1835)|(in @ (kpair @ X1834 @ X1835) @ (dpsetconstr @ X1831 @ X1832 @ X1833)))))&((subset @ (dpsetconstr @ X1836 @ X1837 @ X1838) @ (cartprod @ X1836 @ X1837))&((subset @ (dpsetconstr @ X1839 @ X1840 @ X1841) @ (cartprod @ X1839 @ X1840))&((~(in @ X1845 @ X1842)|(~(in @ X1846 @ X1843)|(~(in @ (kpair @ X1845 @ X1846) @ (dpsetconstr @ X1842 @ X1843 @ X1844))|(X1844 @ X1845 @ X1846))))&((~(in @ (kpair @ X1850 @ X1851) @ (dpsetconstr @ X1847 @ X1848 @ X1849))|(in @ X1850 @ X1847))&((~(in @ (kpair @ X1855 @ X1856) @ (dpsetconstr @ X1852 @ X1853 @ X1854))|(in @ X1856 @ X1853))&((~(in @ (kpair @ X1860 @ X1861) @ (dpsetconstr @ X1857 @ X1858 @ X1859))|(X1859 @ X1860 @ X1861))&(((((in @ (esk70_4 @ X1862 @ X1863 @ X1864 @ X1867) @ (dsetconstr @ X1863 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1867 @ Z0) @ X1864)))))|~(in @ X1867 @ X1862)|((in @ (esk69_3 @ X1862 @ X1863 @ X1864) @ X1862)|~(subset @ X1864 @ (cartprod @ X1862 @ X1863))))&(((dsetconstr @ X1863 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1867 @ Z0) @ X1864))))=(setadjoin @ (esk70_4 @ X1862 @ X1863 @ X1864 @ X1867) @ emptyset))|~(in @ X1867 @ X1862)|((in @ (esk69_3 @ X1862 @ X1863 @ X1864) @ X1862)|~(subset @ X1864 @ (cartprod @ X1862 @ X1863)))))&(((in @ (esk70_4 @ X1862 @ X1863 @ X1864 @ X1867) @ (dsetconstr @ X1863 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1867 @ Z0) @ X1864)))))|~(in @ X1867 @ X1862)|(~(in @ X1866 @ (dsetconstr @ X1863 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk69_3 @ X1862 @ X1863 @ X1864) @ Z0) @ X1864)))))|((dsetconstr @ X1863 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk69_3 @ X1862 @ X1863 @ X1864) @ Z0) @ X1864))))!=(setadjoin @ X1866 @ emptyset))|~(subset @ X1864 @ (cartprod @ X1862 @ X1863))))&(((dsetconstr @ X1863 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1867 @ Z0) @ X1864))))=(setadjoin @ (esk70_4 @ X1862 @ X1863 @ X1864 @ X1867) @ emptyset))|~(in @ X1867 @ X1862)|(~(in @ X1866 @ (dsetconstr @ X1863 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk69_3 @ X1862 @ X1863 @ X1864) @ Z0) @ X1864)))))|((dsetconstr @ X1863 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk69_3 @ X1862 @ X1863 @ X1864) @ Z0) @ X1864))))!=(setadjoin @ X1866 @ emptyset))|~(subset @ X1864 @ (cartprod @ X1862 @ X1863))))))&((((in @ (esk71_3 @ X1869 @ X1870 @ X1871) @ X1869)|~(subset @ X1871 @ (cartprod @ X1869 @ X1870))|(~(in @ X1874 @ X1869)|(in @ (setunion @ (dsetconstr @ X1870 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1874 @ Z0) @ X1871))))) @ X1870)))&(~(in @ X1873 @ (dsetconstr @ X1870 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk71_3 @ X1869 @ X1870 @ X1871) @ Z0) @ X1871)))))|((dsetconstr @ X1870 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk71_3 @ X1869 @ X1870 @ X1871) @ Z0) @ X1871))))!=(setadjoin @ X1873 @ emptyset))|~(subset @ X1871 @ (cartprod @ X1869 @ X1870))|(~(in @ X1874 @ X1869)|(in @ (setunion @ (dsetconstr @ X1870 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1874 @ Z0) @ X1871))))) @ X1870))))&((((in @ (esk72_3 @ X1875 @ X1876 @ X1877) @ X1875)|~(subset @ X1877 @ (cartprod @ X1875 @ X1876))|(~(in @ X1880 @ X1875)|(in @ (setunion @ (dsetconstr @ X1876 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1880 @ Z0) @ X1877))))) @ X1876)))&(~(in @ X1879 @ (dsetconstr @ X1876 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk72_3 @ X1875 @ X1876 @ X1877) @ Z0) @ X1877)))))|((dsetconstr @ X1876 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk72_3 @ X1875 @ X1876 @ X1877) @ Z0) @ X1877))))!=(setadjoin @ X1879 @ emptyset))|~(subset @ X1877 @ (cartprod @ X1875 @ X1876))|(~(in @ X1880 @ X1875)|(in @ (setunion @ (dsetconstr @ X1876 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1880 @ Z0) @ X1877))))) @ X1876))))&((((subset @ X1883 @ (cartprod @ X1881 @ X1882))|~(in @ X1883 @ (funcSet @ X1881 @ X1882)))&(((in @ (esk73_4 @ X1881 @ X1882 @ X1883 @ X1884) @ (dsetconstr @ X1882 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1884 @ Z0) @ X1883)))))|~(in @ X1884 @ X1881)|~(in @ X1883 @ (funcSet @ X1881 @ X1882)))&(((dsetconstr @ X1882 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1884 @ Z0) @ X1883))))=(setadjoin @ (esk73_4 @ X1881 @ X1882 @ X1883 @ X1884) @ emptyset))|~(in @ X1884 @ X1881)|~(in @ X1883 @ (funcSet @ X1881 @ X1882)))))&((~(in @ X1888 @ (funcSet @ X1886 @ X1887))|(~(in @ X1889 @ X1886)|(in @ (setunion @ (dsetconstr @ X1887 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1889 @ Z0) @ X1888))))) @ X1887)))&((((in @ (esk74_3 @ X1890 @ X1891 @ X1892) @ X1890)|~(subset @ X1892 @ (cartprod @ X1890 @ X1891))|(in @ X1892 @ (funcSet @ X1890 @ X1891)))&(~(in @ X1894 @ (dsetconstr @ X1891 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk74_3 @ X1890 @ X1891 @ X1892) @ Z0) @ X1892)))))|((dsetconstr @ X1891 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk74_3 @ X1890 @ X1891 @ X1892) @ Z0) @ X1892))))!=(setadjoin @ X1894 @ emptyset))|~(subset @ X1892 @ (cartprod @ X1890 @ X1891))|(in @ X1892 @ (funcSet @ X1890 @ X1891))))&(((((subset @ (dpsetconstr @ X1895 @ X1896 @ (^[Z0/* 3 */:$i]:($eq @ (X1897 @ Z0)))) @ (cartprod @ X1895 @ X1896))|(in @ (esk75_3 @ X1895 @ X1896 @ X1897) @ X1895))&(((in @ (esk76_4 @ X1895 @ X1896 @ X1897 @ X1899) @ (dsetconstr @ X1896 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1899 @ Z0) @ (dpsetconstr @ X1895 @ X1896 @ (^[Z1/* 3 */:$i]:($eq @ (X1897 @ Z1)))))))))|~(in @ X1899 @ X1895)|(in @ (esk75_3 @ X1895 @ X1896 @ X1897) @ X1895))&(((dsetconstr @ X1896 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1899 @ Z0) @ (dpsetconstr @ X1895 @ X1896 @ (^[Z1/* 3 */:$i]:($eq @ (X1897 @ Z1))))))))=(setadjoin @ (esk76_4 @ X1895 @ X1896 @ X1897 @ X1899) @ emptyset))|~(in @ X1899 @ X1895)|(in @ (esk75_3 @ X1895 @ X1896 @ X1897) @ X1895))))&(((subset @ (dpsetconstr @ X1895 @ X1896 @ (^[Z0/* 3 */:$i]:($eq @ (X1897 @ Z0)))) @ (cartprod @ X1895 @ X1896))|~(in @ (X1897 @ (esk75_3 @ X1895 @ X1896 @ X1897)) @ X1896))&(((in @ (esk76_4 @ X1895 @ X1896 @ X1897 @ X1899) @ (dsetconstr @ X1896 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1899 @ Z0) @ (dpsetconstr @ X1895 @ X1896 @ (^[Z1/* 3 */:$i]:($eq @ (X1897 @ Z1)))))))))|~(in @ X1899 @ X1895)|~(in @ (X1897 @ (esk75_3 @ X1895 @ X1896 @ X1897)) @ X1896))&(((dsetconstr @ X1896 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1899 @ Z0) @ (dpsetconstr @ X1895 @ X1896 @ (^[Z1/* 3 */:$i]:($eq @ (X1897 @ Z1))))))))=(setadjoin @ (esk76_4 @ X1895 @ X1896 @ X1897 @ X1899) @ emptyset))|~(in @ X1899 @ X1895)|~(in @ (X1897 @ (esk75_3 @ X1895 @ X1896 @ X1897)) @ X1896)))))&(((((subset @ (dpsetconstr @ X1901 @ X1902 @ (^[Z0/* 3 */:$i]:($eq @ (X1903 @ Z0)))) @ (cartprod @ X1901 @ X1902))|(in @ (esk77_3 @ X1901 @ X1902 @ X1903) @ X1901))&(((in @ (esk78_4 @ X1901 @ X1902 @ X1903 @ X1905) @ (dsetconstr @ X1902 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1905 @ Z0) @ (dpsetconstr @ X1901 @ X1902 @ (^[Z1/* 3 */:$i]:($eq @ (X1903 @ Z1)))))))))|~(in @ X1905 @ X1901)|(in @ (esk77_3 @ X1901 @ X1902 @ X1903) @ X1901))&(((dsetconstr @ X1902 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1905 @ Z0) @ (dpsetconstr @ X1901 @ X1902 @ (^[Z1/* 3 */:$i]:($eq @ (X1903 @ Z1))))))))=(setadjoin @ (esk78_4 @ X1901 @ X1902 @ X1903 @ X1905) @ emptyset))|~(in @ X1905 @ X1901)|(in @ (esk77_3 @ X1901 @ X1902 @ X1903) @ X1901))))&(((subset @ (dpsetconstr @ X1901 @ X1902 @ (^[Z0/* 3 */:$i]:($eq @ (X1903 @ Z0)))) @ (cartprod @ X1901 @ X1902))|~(in @ (X1903 @ (esk77_3 @ X1901 @ X1902 @ X1903)) @ X1902))&(((in @ (esk78_4 @ X1901 @ X1902 @ X1903 @ X1905) @ (dsetconstr @ X1902 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1905 @ Z0) @ (dpsetconstr @ X1901 @ X1902 @ (^[Z1/* 3 */:$i]:($eq @ (X1903 @ Z1)))))))))|~(in @ X1905 @ X1901)|~(in @ (X1903 @ (esk77_3 @ X1901 @ X1902 @ X1903)) @ X1902))&(((dsetconstr @ X1902 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1905 @ Z0) @ (dpsetconstr @ X1901 @ X1902 @ (^[Z1/* 3 */:$i]:($eq @ (X1903 @ Z1))))))))=(setadjoin @ (esk78_4 @ X1901 @ X1902 @ X1903 @ X1905) @ emptyset))|~(in @ X1905 @ X1901)|~(in @ (X1903 @ (esk77_3 @ X1901 @ X1902 @ X1903)) @ X1902)))))&((((in @ (esk79_3 @ X1907 @ X1908 @ X1909) @ X1907)|(in @ (dpsetconstr @ X1907 @ X1908 @ (^[Z0/* 3 */:$i]:($eq @ (X1909 @ Z0)))) @ (funcSet @ X1907 @ X1908)))&(~(in @ (X1909 @ (esk79_3 @ X1907 @ X1908 @ X1909)) @ X1908)|(in @ (dpsetconstr @ X1907 @ X1908 @ (^[Z0/* 3 */:$i]:($eq @ (X1909 @ Z0)))) @ (funcSet @ X1907 @ X1908))))&((((in @ (esk80_4 @ X1911 @ X1912 @ X1913 @ X1914) @ X1911)|(~(in @ X1917 @ X1913)|(X1914 @ X1917))|~(subset @ X1913 @ (cartprod @ X1911 @ X1912)))&(((in @ (esk81_4 @ X1911 @ X1912 @ X1913 @ X1914) @ X1912)|(~(in @ X1917 @ X1913)|(X1914 @ X1917))|~(subset @ X1913 @ (cartprod @ X1911 @ X1912)))&(((in @ (kpair @ (esk80_4 @ X1911 @ X1912 @ X1913 @ X1914) @ (esk81_4 @ X1911 @ X1912 @ X1913 @ X1914)) @ X1913)|(~(in @ X1917 @ X1913)|(X1914 @ X1917))|~(subset @ X1913 @ (cartprod @ X1911 @ X1912)))&(~(X1914 @ (kpair @ (esk80_4 @ X1911 @ X1912 @ X1913 @ X1914) @ (esk81_4 @ X1911 @ X1912 @ X1913 @ X1914)))|(~(in @ X1917 @ X1913)|(X1914 @ X1917))|~(subset @ X1913 @ (cartprod @ X1911 @ X1912))))))&((((in @ (esk82_4 @ X1918 @ X1919 @ X1920 @ X1921) @ X1918)|(~(in @ X1924 @ X1920)|(X1921 @ X1924))|~(subset @ X1920 @ (cartprod @ X1918 @ X1919)))&(((in @ (esk83_4 @ X1918 @ X1919 @ X1920 @ X1921) @ X1919)|(~(in @ X1924 @ X1920)|(X1921 @ X1924))|~(subset @ X1920 @ (cartprod @ X1918 @ X1919)))&(((in @ (kpair @ (esk82_4 @ X1918 @ X1919 @ X1920 @ X1921) @ (esk83_4 @ X1918 @ X1919 @ X1920 @ X1921)) @ X1920)|(~(in @ X1924 @ X1920)|(X1921 @ X1924))|~(subset @ X1920 @ (cartprod @ X1918 @ X1919)))&(~(X1921 @ (kpair @ (esk82_4 @ X1918 @ X1919 @ X1920 @ X1921) @ (esk83_4 @ X1918 @ X1919 @ X1920 @ X1921)))|(~(in @ X1924 @ X1920)|(X1921 @ X1924))|~(subset @ X1920 @ (cartprod @ X1918 @ X1919))))))&((~(in @ X1927 @ (dsetconstr @ X1925 @ X1926))|((dsetconstr @ X1925 @ X1926)!=(setadjoin @ X1927 @ emptyset))|(~(in @ X1928 @ X1925)|(~(in @ X1929 @ X1925)|(~(X1926 @ X1928)|(~(X1926 @ X1929)|((X1928)=(X1929)))))))&(((subset @ esk86_0 @ (cartprod @ esk84_0 @ esk85_0))&(((in @ (esk87_1 @ X1933) @ (dsetconstr @ esk85_0 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1933 @ Z0) @ esk86_0)))))|~(in @ X1933 @ esk84_0))&(((dsetconstr @ esk85_0 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1933 @ Z0) @ esk86_0))))=(setadjoin @ (esk87_1 @ X1933) @ emptyset))|~(in @ X1933 @ esk84_0))))&((in @ esk88_0 @ esk84_0)&~(in @ (kpair @ esk88_0 @ (setunion @ (dsetconstr @ esk85_0 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ esk88_0 @ Z0) @ esk86_0)))))) @ esk86_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_296])])])])])])])).
4.52/1.09	thf(c_0_298, negated_conjecture, ~((in @ (kpair @ esk88_0 @ (setunion @ (dsetconstr @ esk85_0 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ esk88_0 @ Z0) @ esk86_0)))))) @ esk86_0)), inference(split_conjunct,[status(thm)],[c_0_297])).
4.52/1.09	thf(c_0_299, negated_conjecture, ![X2:$i]:((((dsetconstr @ esk85_0 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ esk86_0))))=(setadjoin @ (esk87_1 @ X2) @ emptyset))|~((in @ X2 @ esk84_0)))), inference(split_conjunct,[status(thm)],[c_0_297])).
4.52/1.09	thf(c_0_300, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_297])).
4.52/1.09	thf(c_0_301, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_297])).
4.52/1.09	thf(c_0_302, negated_conjecture, ![X2:$i]:(((in @ (esk87_1 @ X2) @ (dsetconstr @ esk85_0 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ esk86_0)))))|~((in @ X2 @ esk84_0)))), inference(split_conjunct,[status(thm)],[c_0_297])).
4.52/1.09	thf(c_0_303, plain, ![X2:$i]:((((^[Z0/* 3 */:$i]:((in @ (kpair @ esk88_0 @ Z0) @ esk86_0)))!=(^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ esk86_0))))|~((in @ (kpair @ esk88_0 @ (esk87_1 @ X2)) @ esk86_0))|~((in @ X2 @ esk84_0)))), inference(rw,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_298, c_0_299]), c_0_300])).
4.52/1.09	thf(c_0_304, negated_conjecture, ![X2:$i]:(((in @ (kpair @ X2 @ (esk87_1 @ X2)) @ esk86_0)|~((in @ X2 @ esk84_0)))), inference(spm,[status(thm)],[c_0_301, c_0_302])).
4.52/1.09	thf(c_0_305, negated_conjecture, (in @ esk88_0 @ esk84_0), inference(split_conjunct,[status(thm)],[c_0_297])).
4.52/1.09	thf(c_0_306, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_303, c_0_304]), c_0_305])]), ['proof']).
4.52/1.09	# SZS output end CNFRefutation
4.52/1.09	# Parsed axioms                        : 446
4.52/1.09	# Removed by relevancy pruning/SinE    : 238
4.52/1.09	# Initial clauses                      : 381
4.52/1.09	# Removed in clause preprocessing      : 25
4.52/1.09	# Initial clauses in saturation        : 356
4.52/1.09	# Processed clauses                    : 1139
4.52/1.09	# ...of these trivial                  : 19
4.52/1.09	# ...subsumed                          : 243
4.52/1.09	# ...remaining for further processing  : 877
4.52/1.09	# Other redundant clauses eliminated   : 480
4.52/1.09	# Clauses deleted for lack of memory   : 0
4.52/1.09	# Backward-subsumed                    : 8
4.52/1.09	# Backward-rewritten                   : 7
4.52/1.09	# Generated clauses                    : 16807
4.52/1.09	# ...of the previous two non-redundant : 16110
4.52/1.09	# ...aggressively subsumed             : 0
4.52/1.09	# Contextual simplify-reflections      : 3
4.52/1.09	# Paramodulations                      : 15883
4.52/1.09	# Factorizations                       : 2
4.52/1.09	# NegExts                              : 26
4.52/1.09	# Equation resolutions                 : 487
4.52/1.09	# Disequality decompositions           : 0
4.52/1.09	# Total rewrite steps                  : 417
4.52/1.09	# ...of those cached                   : 319
4.52/1.09	# Propositional unsat checks           : 0
4.52/1.09	#    Propositional check models        : 0
4.52/1.09	#    Propositional check unsatisfiable : 0
4.52/1.09	#    Propositional clauses             : 0
4.52/1.09	#    Propositional clauses after purity: 0
4.52/1.09	#    Propositional unsat core size     : 0
4.52/1.09	#    Propositional preprocessing time  : 0.000
4.52/1.09	#    Propositional encoding time       : 0.000
4.52/1.09	#    Propositional solver time         : 0.000
4.52/1.09	#    Success case prop preproc time    : 0.000
4.52/1.09	#    Success case prop encoding time   : 0.000
4.52/1.09	#    Success case prop solver time     : 0.000
4.52/1.09	# Current number of processed clauses  : 532
4.52/1.09	#    Positive orientable unit clauses  : 48
4.52/1.09	#    Positive unorientable unit clauses: 0
4.52/1.09	#    Negative unit clauses             : 18
4.52/1.09	#    Non-unit-clauses                  : 466
4.52/1.09	# Current number of unprocessed clauses: 15512
4.52/1.09	# ...number of literals in the above   : 62958
4.52/1.09	# Current number of archived formulas  : 0
4.52/1.09	# Current number of archived clauses   : 329
4.52/1.09	# Clause-clause subsumption calls (NU) : 47666
4.52/1.09	# Rec. Clause-clause subsumption calls : 22246
4.52/1.09	# Non-unit clause-clause subsumptions  : 153
4.52/1.09	# Unit Clause-clause subsumption calls : 1358
4.52/1.09	# Rewrite failures with RHS unbound    : 0
4.52/1.09	# BW rewrite match attempts            : 31
4.52/1.09	# BW rewrite match successes           : 7
4.52/1.09	# Condensation attempts                : 0
4.52/1.09	# Condensation successes               : 0
4.52/1.09	# Termbank termtop insertions          : 466318
4.52/1.09	# Search garbage collected termcells   : 21081
4.52/1.09	
4.52/1.09	# -------------------------------------------------
4.52/1.09	# User time                : 0.506 s
4.52/1.09	# System time              : 0.027 s
4.52/1.09	# Total time               : 0.533 s
4.52/1.09	# Maximum resident set size: 7056 pages
4.52/1.09	
4.52/1.09	# -------------------------------------------------
4.52/1.09	# User time                : 0.517 s
4.52/1.09	# System time              : 0.030 s
4.52/1.09	# Total time               : 0.547 s
4.52/1.09	# Maximum resident set size: 2344 pages
4.52/1.09	% E---3.1 exiting
4.52/1.09	% E exiting
4.52/1.09	EOF