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 : n026.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 11:16:53 EDT 2024
0.12/0.33	% CPUTime    : 
0.19/0.47	Running higher-order theorem proving
0.19/0.50	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.sEpEmjvSnc/E---3.1_4511.p
15.33/2.44	# Version: 3.2.0-ho
15.33/2.44	# Preprocessing class: HSLMSLSSLLLCHFA.
15.33/2.44	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
15.33/2.44	# Starting ehoh_best5 with 180s (1) cores
15.33/2.44	# Starting almost_fo_3_lam with 180s (1) cores
15.33/2.44	# Starting new_bool_5 with 180s (1) cores
15.33/2.44	# Starting pre_casc_3 with 180s (1) cores
15.33/2.44	# Starting ho_unfolding_8 with 180s (1) cores
15.33/2.44	# Starting new_ho_10_cnf2 with 180s (1) cores
15.33/2.44	# Starting new_bool_3 with 180s (1) cores
15.33/2.44	# Starting new_ho_5 with 180s (1) cores
15.33/2.44	# new_ho_10_cnf2 with pid 4594 completed with status 0
15.33/2.44	# Result found by new_ho_10_cnf2
15.33/2.44	# Preprocessing class: HSLMSLSSLLLCHFA.
15.33/2.44	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
15.33/2.44	# Starting ehoh_best5 with 180s (1) cores
15.33/2.44	# Starting almost_fo_3_lam with 180s (1) cores
15.33/2.44	# Starting new_bool_5 with 180s (1) cores
15.33/2.44	# Starting pre_casc_3 with 180s (1) cores
15.33/2.44	# Starting ho_unfolding_8 with 180s (1) cores
15.33/2.44	# Starting new_ho_10_cnf2 with 180s (1) cores
15.33/2.44	# No SInE strategy applied
15.33/2.44	# Search class: HGHSM-FSLS31-MHFMMSBN
15.33/2.44	# Scheduled 5 strats onto 1 cores with 180 seconds (180 total)
15.33/2.44	# Starting pre_casc_7 with 109s (1) cores
15.33/2.44	# pre_casc_7 with pid 4600 completed with status 0
15.33/2.44	# Result found by pre_casc_7
15.33/2.44	# Preprocessing class: HSLMSLSSLLLCHFA.
15.33/2.44	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
15.33/2.44	# Starting ehoh_best5 with 180s (1) cores
15.33/2.44	# Starting almost_fo_3_lam with 180s (1) cores
15.33/2.44	# Starting new_bool_5 with 180s (1) cores
15.33/2.44	# Starting pre_casc_3 with 180s (1) cores
15.33/2.44	# Starting ho_unfolding_8 with 180s (1) cores
15.33/2.44	# Starting new_ho_10_cnf2 with 180s (1) cores
15.33/2.44	# No SInE strategy applied
15.33/2.44	# Search class: HGHSM-FSLS31-MHFMMSBN
15.33/2.44	# Scheduled 5 strats onto 1 cores with 180 seconds (180 total)
15.33/2.44	# Starting pre_casc_7 with 109s (1) cores
15.33/2.44	# Preprocessing time       : 0.006 s
15.33/2.44	
15.33/2.44	# Proof found!
15.33/2.44	# SZS status Theorem
15.33/2.44	# SZS output start CNFRefutation
15.33/2.44	thf(decl_22, type, in: $i > $i > $o).
15.33/2.44	thf(decl_23, type, exu: ($i > $o) > $o).
15.33/2.44	thf(decl_24, type, setextAx: $o).
15.33/2.44	thf(decl_25, type, emptyset: $i).
15.33/2.44	thf(decl_26, type, emptysetAx: $o).
15.33/2.44	thf(decl_27, type, setadjoin: $i > $i > $i).
15.33/2.44	thf(decl_28, type, setadjoinAx: $o).
15.33/2.44	thf(decl_29, type, powerset: $i > $i).
15.33/2.44	thf(decl_30, type, powersetAx: $o).
15.33/2.44	thf(decl_31, type, setunion: $i > $i).
15.33/2.44	thf(decl_32, type, setunionAx: $o).
15.33/2.44	thf(decl_33, type, omega: $i).
15.33/2.44	thf(decl_34, type, omega0Ax: $o).
15.33/2.44	thf(decl_35, type, omegaSAx: $o).
15.33/2.44	thf(decl_36, type, omegaIndAx: $o).
15.33/2.44	thf(decl_37, type, replAx: $o).
15.33/2.44	thf(decl_38, type, foundationAx: $o).
15.33/2.44	thf(decl_39, type, wellorderingAx: $o).
15.33/2.44	thf(decl_40, type, descr: ($i > $o) > $i).
15.33/2.44	thf(decl_41, type, descrp: $o).
15.33/2.44	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_43, type, dsetconstrI: $o).
15.33/2.44	thf(decl_44, type, dsetconstrEL: $o).
15.33/2.44	thf(decl_45, type, dsetconstrER: $o).
15.33/2.44	thf(decl_46, type, exuE1: $o).
15.33/2.44	thf(decl_47, type, prop2set: $o > $i).
15.33/2.44	thf(decl_48, type, prop2setE: $o).
15.33/2.44	thf(decl_49, type, emptysetE: $o).
15.33/2.44	thf(decl_50, type, emptysetimpfalse: $o).
15.33/2.44	thf(decl_51, type, notinemptyset: $o).
15.33/2.44	thf(decl_52, type, exuE3e: $o).
15.33/2.44	thf(decl_53, type, setext: $o).
15.33/2.44	thf(decl_54, type, emptyI: $o).
15.33/2.44	thf(decl_55, type, noeltsimpempty: $o).
15.33/2.44	thf(decl_56, type, setbeta: $o).
15.33/2.44	thf(decl_57, type, nonempty: $i > $o).
15.33/2.44	thf(decl_58, type, nonemptyE1: $o).
15.33/2.44	thf(decl_59, type, nonemptyI: $o).
15.33/2.44	thf(decl_60, type, nonemptyI1: $o).
15.33/2.44	thf(decl_61, type, setadjoinIL: $o).
15.33/2.44	thf(decl_62, type, emptyinunitempty: $o).
15.33/2.44	thf(decl_63, type, setadjoinIR: $o).
15.33/2.44	thf(decl_64, type, setadjoinE: $o).
15.33/2.44	thf(decl_65, type, setadjoinOr: $o).
15.33/2.44	thf(decl_66, type, setoftrueEq: $o).
15.33/2.44	thf(decl_67, type, powersetI: $o).
15.33/2.44	thf(decl_68, type, emptyinPowerset: $o).
15.33/2.44	thf(decl_69, type, emptyInPowerset: $o).
15.33/2.44	thf(decl_70, type, powersetE: $o).
15.33/2.44	thf(decl_71, type, setunionI: $o).
15.33/2.44	thf(decl_72, type, setunionE: $o).
15.33/2.44	thf(decl_73, type, subPowSU: $o).
15.33/2.44	thf(decl_74, type, exuE2: $o).
15.33/2.44	thf(decl_75, type, nonemptyImpWitness: $o).
15.33/2.44	thf(decl_76, type, uniqinunit: $o).
15.33/2.44	thf(decl_77, type, notinsingleton: $o).
15.33/2.44	thf(decl_78, type, eqinunit: $o).
15.33/2.44	thf(decl_79, type, singletonsswitch: $o).
15.33/2.44	thf(decl_80, type, upairsetE: $o).
15.33/2.44	thf(decl_81, type, upairsetIL: $o).
15.33/2.44	thf(decl_82, type, upairsetIR: $o).
15.33/2.44	thf(decl_83, type, emptyE1: $o).
15.33/2.44	thf(decl_84, type, vacuousDall: $o).
15.33/2.44	thf(decl_85, type, quantDeMorgan1: $o).
15.33/2.44	thf(decl_86, type, quantDeMorgan2: $o).
15.33/2.44	thf(decl_87, type, quantDeMorgan3: $o).
15.33/2.44	thf(decl_88, type, quantDeMorgan4: $o).
15.33/2.44	thf(decl_89, type, prop2setI: $o).
15.33/2.44	thf(decl_90, type, set2prop: $i > $o).
15.33/2.44	thf(decl_91, type, prop2set2propI: $o).
15.33/2.44	thf(decl_92, type, notdexE: $o).
15.33/2.44	thf(decl_93, type, notdallE: $o).
15.33/2.44	thf(decl_94, type, exuI1: $o).
15.33/2.44	thf(decl_95, type, exuI3: $o).
15.33/2.44	thf(decl_96, type, exuI2: $o).
15.33/2.44	thf(decl_97, type, inCongP: $o).
15.33/2.44	thf(decl_98, type, in__Cong: $o).
15.33/2.44	thf(decl_99, type, exuE3u: $o).
15.33/2.44	thf(decl_100, type, exu__Cong: $o).
15.33/2.44	thf(decl_101, type, emptyset__Cong: $o).
15.33/2.44	thf(decl_102, type, setadjoin__Cong: $o).
15.33/2.44	thf(decl_103, type, powerset__Cong: $o).
15.33/2.44	thf(decl_104, type, setunion__Cong: $o).
15.33/2.44	thf(decl_105, type, omega__Cong: $o).
15.33/2.44	thf(decl_106, type, exuEu: $o).
15.33/2.44	thf(decl_107, type, descr__Cong: $o).
15.33/2.44	thf(decl_108, type, dsetconstr__Cong: $o).
15.33/2.44	thf(decl_109, type, subset: $i > $i > $o).
15.33/2.44	thf(decl_112, type, subsetI1: $o).
15.33/2.44	thf(decl_113, type, eqimpsubset2: $o).
15.33/2.44	thf(decl_114, type, eqimpsubset1: $o).
15.33/2.44	thf(decl_115, type, subsetI2: $o).
15.33/2.44	thf(decl_116, type, emptysetsubset: $o).
15.33/2.44	thf(decl_117, type, subsetE: $o).
15.33/2.44	thf(decl_118, type, subsetE2: $o).
15.33/2.44	thf(decl_119, type, notsubsetI: $o).
15.33/2.44	thf(decl_120, type, notequalI1: $o).
15.33/2.44	thf(decl_121, type, notequalI2: $o).
15.33/2.44	thf(decl_122, type, subsetRefl: $o).
15.33/2.44	thf(decl_123, type, subsetTrans: $o).
15.33/2.44	thf(decl_124, type, setadjoinSub: $o).
15.33/2.44	thf(decl_125, type, setadjoinSub2: $o).
15.33/2.44	thf(decl_126, type, subset2powerset: $o).
15.33/2.44	thf(decl_127, type, setextsub: $o).
15.33/2.44	thf(decl_128, type, subsetemptysetimpeq: $o).
15.33/2.44	thf(decl_129, type, powersetI1: $o).
15.33/2.44	thf(decl_130, type, powersetE1: $o).
15.33/2.44	thf(decl_131, type, inPowerset: $o).
15.33/2.44	thf(decl_132, type, powersetsubset: $o).
15.33/2.44	thf(decl_133, type, sepInPowerset: $o).
15.33/2.44	thf(decl_134, type, sepSubset: $o).
15.33/2.44	thf(decl_135, type, binunion: $i > $i > $i).
15.33/2.44	thf(decl_136, type, binunionIL: $o).
15.33/2.44	thf(decl_137, type, upairset2IR: $o).
15.33/2.44	thf(decl_138, type, binunionIR: $o).
15.33/2.44	thf(decl_139, type, binunionEcases: $o).
15.33/2.44	thf(decl_140, type, binunionE: $o).
15.33/2.44	thf(decl_141, type, binunionLsub: $o).
15.33/2.44	thf(decl_142, type, binunionRsub: $o).
15.33/2.44	thf(decl_143, type, binintersect: $i > $i > $i).
15.33/2.44	thf(decl_144, type, binintersectI: $o).
15.33/2.44	thf(decl_145, type, binintersectSubset5: $o).
15.33/2.44	thf(decl_146, type, binintersectEL: $o).
15.33/2.44	thf(decl_147, type, binintersectLsub: $o).
15.33/2.44	thf(decl_148, type, binintersectSubset2: $o).
15.33/2.44	thf(decl_149, type, binintersectSubset3: $o).
15.33/2.44	thf(decl_150, type, binintersectER: $o).
15.33/2.44	thf(decl_151, type, disjointsetsI1: $o).
15.33/2.44	thf(decl_152, type, binintersectRsub: $o).
15.33/2.44	thf(decl_153, type, binintersectSubset4: $o).
15.33/2.44	thf(decl_154, type, binintersectSubset1: $o).
15.33/2.44	thf(decl_155, type, bs114d: $o).
15.33/2.44	thf(decl_157, type, setminus: $i > $i > $i).
15.33/2.44	thf(decl_158, type, setminusI: $o).
15.33/2.44	thf(decl_159, type, setminusEL: $o).
15.33/2.44	thf(decl_160, type, setminusER: $o).
15.33/2.44	thf(decl_161, type, setminusSubset2: $o).
15.33/2.44	thf(decl_162, type, setminusERneg: $o).
15.33/2.44	thf(decl_163, type, setminusELneg: $o).
15.33/2.44	thf(decl_164, type, setminusILneg: $o).
15.33/2.44	thf(decl_165, type, setminusIRneg: $o).
15.33/2.44	thf(decl_166, type, setminusLsub: $o).
15.33/2.44	thf(decl_167, type, setminusSubset1: $o).
15.33/2.44	thf(decl_168, type, symdiff: $i > $i > $i).
15.33/2.44	thf(decl_169, type, symdiffE: $o).
15.33/2.44	thf(decl_170, type, symdiffI1: $o).
15.33/2.44	thf(decl_171, type, symdiffI2: $o).
15.33/2.44	thf(decl_172, type, symdiffIneg1: $o).
15.33/2.44	thf(decl_173, type, symdiffIneg2: $o).
15.33/2.44	thf(decl_174, type, iskpair: $i > $o).
15.33/2.44	thf(decl_175, type, secondinupair: $o).
15.33/2.44	thf(decl_176, type, setukpairIL: $o).
15.33/2.44	thf(decl_177, type, setukpairIR: $o).
15.33/2.44	thf(decl_178, type, kpairiskpair: $o).
15.33/2.44	thf(decl_179, type, kpair: $i > $i > $i).
15.33/2.44	thf(decl_180, type, kpairp: $o).
15.33/2.44	thf(decl_181, type, cartprod: $i > $i > $i).
15.33/2.44	thf(decl_182, type, singletonsubset: $o).
15.33/2.44	thf(decl_183, type, singletoninpowerset: $o).
15.33/2.44	thf(decl_184, type, singletoninpowunion: $o).
15.33/2.44	thf(decl_185, type, upairset2E: $o).
15.33/2.44	thf(decl_186, type, upairsubunion: $o).
15.33/2.44	thf(decl_187, type, upairinpowunion: $o).
15.33/2.44	thf(decl_188, type, ubforcartprodlem1: $o).
15.33/2.44	thf(decl_189, type, ubforcartprodlem2: $o).
15.33/2.44	thf(decl_190, type, ubforcartprodlem3: $o).
15.33/2.44	thf(decl_191, type, cartprodpairin: $o).
15.33/2.44	thf(decl_192, type, cartprodmempair1: $o).
15.33/2.44	thf(decl_193, type, cartprodmempair: $o).
15.33/2.44	thf(decl_194, type, setunionE2: $o).
15.33/2.44	thf(decl_195, type, setunionsingleton1: $o).
15.33/2.44	thf(decl_196, type, setunionsingleton2: $o).
15.33/2.44	thf(decl_197, type, setunionsingleton: $o).
15.33/2.44	thf(decl_198, type, singleton: $i > $o).
15.33/2.44	thf(decl_199, type, singletonprop: $o).
15.33/2.44	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
15.33/2.44	thf(decl_201, type, ex1E1: $o).
15.33/2.44	thf(decl_202, type, ex1I: $o).
15.33/2.44	thf(decl_203, type, ex1I2: $o).
15.33/2.44	thf(decl_204, type, singletonsuniq: $o).
15.33/2.44	thf(decl_209, type, setukpairinjL1: $o).
15.33/2.44	thf(decl_210, type, kfstsingleton: $o).
15.33/2.44	thf(decl_211, type, theprop: $o).
15.33/2.44	thf(decl_212, type, kfst: $i > $i).
15.33/2.44	thf(decl_213, type, kfstpairEq: $o).
15.33/2.44	thf(decl_214, type, cartprodfstin: $o).
15.33/2.44	thf(decl_215, type, setukpairinjL2: $o).
15.33/2.44	thf(decl_216, type, setukpairinjL: $o).
15.33/2.44	thf(decl_217, type, setukpairinjR11: $o).
15.33/2.44	thf(decl_218, type, setukpairinjR12: $o).
15.33/2.44	thf(decl_219, type, setukpairinjR1: $o).
15.33/2.44	thf(decl_220, type, upairequniteq: $o).
15.33/2.44	thf(decl_221, type, setukpairinjR2: $o).
15.33/2.44	thf(decl_222, type, setukpairinjR: $o).
15.33/2.44	thf(decl_223, type, ksndsingleton: $o).
15.33/2.44	thf(decl_224, type, ksnd: $i > $i).
15.33/2.44	thf(decl_225, type, epred1_0: $o).
15.33/2.44	thf(decl_226, type, esk1_2: $i > $i > $i).
15.33/2.44	thf(decl_227, type, esk2_2: $i > $i > $i).
15.33/2.44	thf(decl_228, type, esk3_2: $i > $i > $i).
15.33/2.44	thf(decl_229, type, esk4_1: $i > $i).
15.33/2.44	thf(decl_230, type, esk5_2: ($i > $i > $o) > $i > $i).
15.33/2.44	thf(decl_231, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
15.33/2.44	thf(decl_232, type, esk7_2: ($i > $i > $o) > $i > $i).
15.33/2.44	thf(decl_233, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
15.33/2.44	thf(decl_234, type, esk9_1: $i > $i).
15.33/2.44	thf(decl_235, type, esk10_2: ($i > $o) > $i > $i).
15.33/2.44	thf(decl_236, type, esk11_2: ($i > $o) > $i > $i).
15.33/2.44	thf(decl_237, type, esk12_1: ($i > $o) > $i).
15.33/2.44	thf(decl_238, type, esk13_2: ($i > $o) > $i > $i).
15.33/2.44	thf(decl_239, type, esk14_1: ($i > $o) > $i).
15.33/2.44	thf(decl_240, type, esk15_2: $i > $i > $i).
15.33/2.44	thf(decl_241, type, esk16_2: $i > $i > $i).
15.33/2.44	thf(decl_242, type, esk17_1: $i > $i).
15.33/2.44	thf(decl_243, type, esk18_1: $i > $i).
15.33/2.44	thf(decl_244, type, esk19_1: $i > $i).
15.33/2.44	thf(decl_245, type, esk20_2: $i > $i > $i).
15.33/2.44	thf(decl_246, type, esk21_3: $i > $i > $o > $i).
15.33/2.44	thf(decl_247, type, esk22_2: ($i > $o) > $i > $i).
15.33/2.44	thf(decl_248, type, esk23_1: ($i > $o) > $i).
15.33/2.44	thf(decl_249, type, esk24_1: $i > $i).
15.33/2.44	thf(decl_250, type, esk25_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_251, type, esk26_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_252, type, esk27_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_253, type, esk28_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_254, type, esk29_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_255, type, esk30_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_256, type, esk31_2: ($i > $o) > $i > $i).
15.33/2.44	thf(decl_257, type, esk32_1: ($i > $o) > $i).
15.33/2.44	thf(decl_258, type, esk33_1: ($i > $o) > $i).
15.33/2.44	thf(decl_259, type, esk34_1: ($i > $o) > $i).
15.33/2.44	thf(decl_260, type, esk35_1: ($i > $o) > $i).
15.33/2.44	thf(decl_261, type, esk36_2: ($i > $o) > $i > $i).
15.33/2.44	thf(decl_262, type, esk37_1: ($i > $o) > $i).
15.33/2.44	thf(decl_263, type, esk38_2: ($i > $o) > $i > $i).
15.33/2.44	thf(decl_264, type, esk39_2: ($i > $o) > ($i > $o) > $i).
15.33/2.44	thf(decl_265, type, esk40_2: ($i > $o) > ($i > $o) > $i).
15.33/2.44	thf(decl_266, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
15.33/2.44	thf(decl_267, type, esk42_2: ($i > $o) > ($i > $o) > $i).
15.33/2.44	thf(decl_268, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
15.33/2.44	thf(decl_269, type, esk44_2: ($i > $o) > ($i > $o) > $i).
15.33/2.44	thf(decl_270, type, esk45_2: ($i > $o) > $i > $i).
15.33/2.44	thf(decl_271, type, esk46_2: ($i > $o) > ($i > $o) > $i).
15.33/2.44	thf(decl_272, type, esk47_2: ($i > $o) > ($i > $o) > $i).
15.33/2.44	thf(decl_273, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
15.33/2.44	thf(decl_274, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
15.33/2.44	thf(decl_275, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
15.33/2.44	thf(decl_276, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
15.33/2.44	thf(decl_277, type, esk52_2: $i > $i > $i).
15.33/2.44	thf(decl_278, type, esk53_2: $i > $i > $i).
15.33/2.44	thf(decl_279, type, esk54_2: $i > $i > $i).
15.33/2.44	thf(decl_280, type, esk55_2: $i > $i > $i).
15.33/2.44	thf(decl_281, type, esk56_2: $i > $i > $i).
15.33/2.44	thf(decl_282, type, esk57_2: $i > $i > $i).
15.33/2.44	thf(decl_283, type, esk58_2: $i > $i > $i).
15.33/2.44	thf(decl_284, type, esk59_3: $i > $i > $i > $i).
15.33/2.44	thf(decl_285, type, esk60_3: $i > $i > $i > $i).
15.33/2.44	thf(decl_286, type, esk61_3: $i > $i > $i > $i).
15.33/2.44	thf(decl_287, type, esk62_3: $i > $i > $i > $i).
15.33/2.44	thf(decl_288, type, esk63_2: $i > $i > $i).
15.33/2.44	thf(decl_289, type, esk64_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_290, type, esk65_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_291, type, esk66_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_292, type, esk67_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_293, type, esk68_3: $i > ($i > $o) > $i > $i).
15.33/2.44	thf(decl_294, type, esk69_3: $i > ($i > $o) > $i > $i).
15.33/2.44	thf(decl_295, type, esk70_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_296, type, esk71_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_297, type, esk72_2: $i > ($i > $o) > $i).
15.33/2.44	thf(decl_298, type, esk73_1: $i > $i).
15.33/2.44	thf(decl_299, type, esk74_1: $i > $i).
15.33/2.44	thf(decl_300, type, esk75_0: $i).
15.33/2.44	thf(decl_301, type, esk76_0: $i).
15.33/2.44	thf(decl_307, type, epred2_1: $i > $i > $o).
15.33/2.44	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', ex1)).
15.33/2.44	thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', singleton)).
15.33/2.44	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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', replAx)).
15.33/2.44	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', exu)).
15.33/2.44	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', descrp)).
15.33/2.44	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', exuE1)).
15.33/2.44	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', exuE3e)).
15.33/2.44	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', nonempty)).
15.33/2.44	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', nonemptyI)).
15.33/2.44	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', exuE2)).
15.33/2.44	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.sEpEmjvSnc/E---3.1_4511.p', exuI1)).
15.33/2.44	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', exuI3)).
15.33/2.44	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', exuI2)).
15.33/2.44	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.sEpEmjvSnc/E---3.1_4511.p', exuE3u)).
15.33/2.44	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', exu__Cong)).
15.33/2.44	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', exuEu)).
15.33/2.44	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', descr__Cong)).
15.33/2.44	thf(iskpair, axiom, ((iskpair)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ (setunion @ X4))&?[X3:$i]:(((in @ X3 @ (setunion @ X4))&((X4)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', iskpair)).
15.33/2.44	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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', singletonprop)).
15.33/2.44	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', ex1E1)).
15.33/2.44	thf(ex1I, axiom, ((ex1I)<=>![X4:$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.sEpEmjvSnc/E---3.1_4511.p', ex1I)).
15.33/2.44	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', ex1I2)).
15.33/2.44	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', kfstsingleton)).
15.33/2.44	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', ksndsingleton)).
15.33/2.44	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', dsetconstrI)).
15.33/2.44	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', dsetconstrEL)).
15.33/2.44	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', dsetconstrER)).
15.33/2.44	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setbeta)).
15.33/2.44	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', nonemptyE1)).
15.33/2.44	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', nonemptyI1)).
15.33/2.44	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setoftrueEq)).
15.33/2.44	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', nonemptyImpWitness)).
15.33/2.44	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.sEpEmjvSnc/E---3.1_4511.p', emptyE1)).
15.33/2.44	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', dsetconstr__Cong)).
15.33/2.44	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', sepInPowerset)).
15.33/2.44	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', sepSubset)).
15.33/2.44	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.sEpEmjvSnc/E---3.1_4511.p', kpairiskpair)).
15.33/2.44	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', kpairp)).
15.33/2.44	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', cartprodmempair)).
15.33/2.44	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', theprop)).
15.33/2.44	thf(ksndpairEq, conjecture, (((emptysetAx)=>(((powersetAx)=>((setunionAx)=>((((((foundationAx)=>((((dsetconstrI)=>((dsetconstrEL)=>((((prop2setE)=>((emptysetE)=>((((exuE3e)=>((setext)=>((emptyI)=>(((setbeta)=>((((((emptyinunitempty)=>((setadjoinIR)=>(((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>(((((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>(((notinsingleton)=>(((singletonsswitch)=>(((upairsetIL)=>((upairsetIR)=>((((quantDeMorgan1)=>(((quantDeMorgan3)=>((((prop2set2propI)=>(((notdallE)=>((exuI1)=>(((((((((((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((((((((emptysetsubset)=>((subsetE)=>((subsetE2)=>(((notequalI1)=>((((subsetTrans)=>(((setadjoinSub2)=>((((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>(((sepInPowerset)=>((((upairset2IR)=>((((((binunionRsub)=>((binintersectI)=>(((binintersectEL)=>(((((binintersectER)=>(((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((((setminusEL)=>((setminusER)=>((((setminusELneg)=>(((((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((((((setukpairIR)=>((((singletonsubset)=>((((upairset2E)=>(((upairinpowunion)=>(((((((cartprodmempair)=>(((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(((((ex1I2)=>(((setukpairinjL1)=>((((kfstpairEq)=>((((setukpairinjL)=>(((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))<=(ksndsingleton))<=(setukpairinjR))))))<=(setukpairinjR11)))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop))<=(kfstsingleton)))<=(singletonsuniq)))<=(ex1I))<=(ex1E1))<=(singletonprop)))))<=(setunionE2)))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2))<=(ubforcartprodlem1)))<=(upairsubunion)))<=(singletoninpowunion))<=(singletoninpowerset)))<=(kpairp))<=(kpairiskpair)))<=(setukpairIL))<=(secondinupair))<=(symdiffIneg2))<=(symdiffIneg1))))))<=(setminusLsub))<=(setminusIRneg))<=(setminusILneg)))<=(setminusERneg))<=(setminusSubset2))))<=(setminusI))<=(bs114d)))))<=(disjointsetsI1)))<=(binintersectSubset3))<=(binintersectSubset2))<=(binintersectLsub)))<=(binintersectSubset5))))<=(binunionLsub))<=(binunionE))<=(binunionEcases))<=(binunionIR)))<=(binunionIL))<=(sepSubset)))<=(powersetsubset)))<=(powersetE1))))<=(setextsub))<=(subset2powerset)))<=(setadjoinSub)))<=(subsetRefl))<=(notequalI2)))<=(notsubsetI)))))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong)))))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))<=(in__Cong))<=(inCongP))<=(exuI2))<=(exuI3))))<=(notdexE)))<=(prop2setI))<=(quantDeMorgan4)))<=(quantDeMorgan2)))<=(vacuousDall))<=(emptyE1))))<=(upairsetE)))<=(eqinunit)))<=(uniqinunit)))))))<=(powersetE))<=(emptyInPowerset))<=(emptyinPowerset)))))<=(setadjoinE))))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1)))<=(noeltsimpempty)))))<=(notinemptyset))<=(emptysetimpfalse))))<=(exuE1))<=(dsetconstrER))))<=(descrp))<=(wellorderingAx)))<=(replAx))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))))<=(setadjoinAx)))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', ksndpairEq)).
15.33/2.44	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setextAx)).
15.33/2.44	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', emptysetAx)).
15.33/2.44	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setadjoinAx)).
15.33/2.44	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', powersetAx)).
15.33/2.44	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setunionAx)).
15.33/2.44	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', omega0Ax)).
15.33/2.44	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', omegaSAx)).
15.33/2.44	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', omegaIndAx)).
15.33/2.44	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', foundationAx)).
15.33/2.44	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.sEpEmjvSnc/E---3.1_4511.p', wellorderingAx)).
15.33/2.44	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', prop2setE)).
15.33/2.44	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', emptysetE)).
15.33/2.44	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', emptysetimpfalse)).
15.33/2.44	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', notinemptyset)).
15.33/2.44	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setext)).
15.33/2.44	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', emptyI)).
15.33/2.44	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', noeltsimpempty)).
15.33/2.44	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setadjoinIL)).
15.33/2.44	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', emptyinunitempty)).
15.33/2.44	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setadjoinIR)).
15.33/2.44	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.sEpEmjvSnc/E---3.1_4511.p', setadjoinE)).
15.33/2.44	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setadjoinOr)).
15.33/2.44	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', powersetI)).
15.33/2.44	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', emptyinPowerset)).
15.33/2.44	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', emptyInPowerset)).
15.33/2.44	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', powersetE)).
15.33/2.44	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setunionI)).
15.33/2.44	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.sEpEmjvSnc/E---3.1_4511.p', setunionE)).
15.33/2.44	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', subPowSU)).
15.33/2.44	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', uniqinunit)).
15.33/2.44	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', notinsingleton)).
15.33/2.44	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', eqinunit)).
15.33/2.44	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', singletonsswitch)).
15.33/2.44	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', upairsetE)).
15.33/2.44	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', upairsetIL)).
15.33/2.44	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', upairsetIR)).
15.33/2.44	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', vacuousDall)).
15.33/2.44	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', quantDeMorgan1)).
15.33/2.44	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', quantDeMorgan2)).
15.33/2.44	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', quantDeMorgan3)).
15.33/2.44	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', quantDeMorgan4)).
15.33/2.44	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', prop2setI)).
15.33/2.44	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', prop2set2propI)).
15.33/2.44	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', notdexE)).
15.33/2.44	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', notdallE)).
15.33/2.44	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', inCongP)).
15.33/2.44	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', in__Cong)).
15.33/2.44	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', emptyset__Cong)).
15.33/2.44	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setadjoin__Cong)).
15.33/2.44	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', powerset__Cong)).
15.33/2.44	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setunion__Cong)).
15.33/2.44	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', omega__Cong)).
15.33/2.44	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', subsetI1)).
15.33/2.44	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', eqimpsubset2)).
15.33/2.44	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', eqimpsubset1)).
15.33/2.44	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', subsetI2)).
15.33/2.44	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', emptysetsubset)).
15.33/2.44	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', subsetE)).
15.33/2.44	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', subsetE2)).
15.33/2.44	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', notsubsetI)).
15.33/2.44	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', notequalI1)).
15.33/2.44	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', notequalI2)).
15.33/2.44	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', subsetRefl)).
15.33/2.44	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', subsetTrans)).
15.33/2.44	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setadjoinSub)).
15.33/2.44	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setadjoinSub2)).
15.33/2.44	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', subset2powerset)).
15.33/2.44	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setextsub)).
15.33/2.44	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', subsetemptysetimpeq)).
15.33/2.44	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', powersetI1)).
15.33/2.44	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', powersetE1)).
15.33/2.44	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', inPowerset)).
15.33/2.44	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', powersetsubset)).
15.33/2.44	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binunionIL)).
15.33/2.44	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', upairset2IR)).
15.33/2.44	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binunionIR)).
15.33/2.44	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binunionEcases)).
15.33/2.44	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binunionE)).
15.33/2.44	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binunionLsub)).
15.33/2.44	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binunionRsub)).
15.33/2.44	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binintersectI)).
15.33/2.44	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binintersectSubset5)).
15.33/2.44	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binintersectEL)).
15.33/2.44	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binintersectLsub)).
15.33/2.44	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binintersectSubset2)).
15.33/2.44	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binintersectSubset3)).
15.33/2.44	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binintersectER)).
15.33/2.44	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', disjointsetsI1)).
15.33/2.44	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binintersectRsub)).
15.33/2.44	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binintersectSubset4)).
15.33/2.44	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', binintersectSubset1)).
15.33/2.44	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', bs114d)).
15.33/2.44	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setminusI)).
15.33/2.44	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setminusEL)).
15.33/2.44	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setminusER)).
15.33/2.44	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setminusSubset2)).
15.33/2.44	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setminusERneg)).
15.33/2.44	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setminusELneg)).
15.33/2.44	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setminusILneg)).
15.33/2.44	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setminusIRneg)).
15.33/2.44	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setminusLsub)).
15.33/2.44	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setminusSubset1)).
15.33/2.44	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', symdiffE)).
15.33/2.44	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', symdiffI1)).
15.33/2.44	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', symdiffI2)).
15.33/2.44	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', symdiffIneg1)).
15.33/2.44	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', symdiffIneg2)).
15.33/2.44	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', secondinupair)).
15.33/2.44	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setukpairIL)).
15.33/2.44	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setukpairIR)).
15.33/2.44	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', singletonsubset)).
15.33/2.44	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', singletoninpowerset)).
15.33/2.44	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', singletoninpowunion)).
15.33/2.44	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', upairset2E)).
15.33/2.44	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', upairsubunion)).
15.33/2.44	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', upairinpowunion)).
15.33/2.44	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', ubforcartprodlem1)).
15.33/2.44	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', ubforcartprodlem2)).
15.33/2.44	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', ubforcartprodlem3)).
15.33/2.44	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', cartprodpairin)).
15.33/2.44	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.sEpEmjvSnc/E---3.1_4511.p', cartprodmempair1)).
15.33/2.44	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setunionE2)).
15.33/2.44	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setunionsingleton1)).
15.33/2.44	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setunionsingleton2)).
15.33/2.44	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setunionsingleton)).
15.33/2.44	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', singletonsuniq)).
15.33/2.44	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setukpairinjL1)).
15.33/2.44	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', kfstpairEq)).
15.33/2.44	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', cartprodfstin)).
15.33/2.44	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.sEpEmjvSnc/E---3.1_4511.p', setukpairinjL2)).
15.33/2.44	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.sEpEmjvSnc/E---3.1_4511.p', setukpairinjL)).
15.33/2.44	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setukpairinjR11)).
15.33/2.44	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.sEpEmjvSnc/E---3.1_4511.p', setukpairinjR12)).
15.33/2.44	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.sEpEmjvSnc/E---3.1_4511.p', setukpairinjR1)).
15.33/2.44	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', upairequniteq)).
15.33/2.44	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setukpairinjR2)).
15.33/2.44	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', setukpairinjR)).
15.33/2.44	thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', kpair)).
15.33/2.44	thf(ksnd, axiom, ((ksnd)=(^[X18:$i]:(setunion @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sEpEmjvSnc/E---3.1_4511.p', ksnd)).
15.33/2.44	thf(c_0_180, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X528:$i]:(((in @ X528 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X528 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
15.33/2.44	thf(c_0_181, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
15.33/2.44	thf(c_0_182, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
15.33/2.44	thf(c_0_183, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
15.33/2.44	thf(c_0_184, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
15.33/2.44	thf(c_0_185, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
15.33/2.44	thf(c_0_186, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
15.33/2.44	thf(c_0_187, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
15.33/2.44	thf(c_0_188, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
15.33/2.44	thf(c_0_189, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
15.33/2.44	thf(c_0_190, 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])).
15.33/2.44	thf(c_0_191, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
15.33/2.44	thf(c_0_192, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
15.33/2.44	thf(c_0_193, 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])).
15.33/2.44	thf(c_0_194, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
15.33/2.44	thf(c_0_195, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
15.33/2.44	thf(c_0_196, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
15.33/2.44	thf(c_0_197, plain, ((iskpair)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ (setunion @ Z0))&?[X3:$i]:(((in @ X3 @ (setunion @ Z0))&((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))), inference(fof_simplification,[status(thm)],[iskpair])).
15.33/2.44	thf(c_0_198, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
15.33/2.44	thf(c_0_199, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
15.33/2.44	thf(c_0_200, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X528:$i]:(((in @ X528 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X528 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_180, c_0_181])).
15.33/2.44	thf(c_0_201, 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])).
15.33/2.44	thf(c_0_202, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
15.33/2.44	thf(c_0_203, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
15.33/2.44	thf(c_0_204, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
15.33/2.44	thf(c_0_205, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X493:$i]:((((X6 @ X2 @ X493))&![X494:$i]:((((X6 @ X2 @ X494))=>((X493)=(X494)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_182, c_0_183])).
15.33/2.44	thf(c_0_206, plain, ((descrp)=(![X1:$i > $o]:(((?[X495:$i]:((((X1 @ X495))&![X496:$i]:((((X1 @ X496))=>((X495)=(X496)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_184, c_0_183])).
15.33/2.44	thf(c_0_207, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
15.33/2.44	thf(c_0_208, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
15.33/2.44	thf(c_0_209, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
15.33/2.44	thf(c_0_210, plain, ((exuE1)=(![X1:$i > $o]:(((?[X497:$i]:((((X1 @ X497))&![X498:$i]:((((X1 @ X498))=>((X497)=(X498)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_185, c_0_183])).
15.33/2.44	thf(c_0_211, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X499:$i]:((((X1 @ X499))&![X500:$i]:((((X1 @ X500))=>((X499)=(X500)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_186, c_0_183])).
15.33/2.44	thf(c_0_212, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
15.33/2.44	thf(c_0_213, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_187])).
15.33/2.44	thf(c_0_214, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_188, c_0_187])).
15.33/2.44	thf(c_0_215, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_187])).
15.33/2.44	thf(c_0_216, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
15.33/2.44	thf(c_0_217, plain, ((exuE2)=(![X1:$i > $o]:(((?[X501:$i]:((((X1 @ X501))&![X502:$i]:((((X1 @ X502))=>((X501)=(X502)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_189, c_0_183])).
15.33/2.44	thf(c_0_218, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_187])).
15.33/2.44	thf(c_0_219, 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])).
15.33/2.44	thf(c_0_220, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X503:$i]:((((X1 @ X503))&![X504:$i]:((((X1 @ X504))=>((X503)=(X504))))))))))), inference(apply_def,[status(thm)],[c_0_190, c_0_183])).
15.33/2.44	thf(c_0_221, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X505:$i]:((((X1 @ X505))&![X506:$i]:((((X1 @ X506))=>((X505)=(X506)))))))))))), inference(apply_def,[status(thm)],[c_0_191, c_0_183])).
15.33/2.44	thf(c_0_222, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X507:$i]:((((X1 @ X507))&![X508:$i]:((((X1 @ X508))=>((X507)=(X508))))))))))), inference(apply_def,[status(thm)],[c_0_192, c_0_183])).
15.33/2.44	thf(c_0_223, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X509:$i]:((((X1 @ X509))&![X510:$i]:((((X1 @ X510))=>((X509)=(X510)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_193, c_0_183])).
15.33/2.44	thf(c_0_224, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X511:$i]:((((X1 @ X511))&![X512:$i]:((((X1 @ X512))=>((X511)=(X512)))))))<=>(?[X513:$i]:((((X17 @ X513))&![X514:$i]:((((X17 @ X514))=>((X513)=(X514)))))))))))), inference(apply_def,[status(thm)],[c_0_194, c_0_183])).
15.33/2.44	thf(c_0_225, plain, ((exuEu)=(![X1:$i > $o]:(((?[X515:$i]:((((X1 @ X515))&![X516:$i]:((((X1 @ X516))=>((X515)=(X516)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_195, c_0_183])).
15.33/2.44	thf(c_0_226, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X517:$i]:((((X1 @ X517))&![X518:$i]:((((X1 @ X518))=>((X517)=(X518)))))))=>((?[X519:$i]:((((X17 @ X519))&![X520:$i]:((((X17 @ X520))=>((X519)=(X520)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_183])).
15.33/2.44	thf(c_0_227, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
15.33/2.44	thf(c_0_228, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
15.33/2.44	thf(c_0_229, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
15.33/2.44	thf(c_0_230, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X521:$i]:(((in @ X521 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X522:$i]:(((in @ X522 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X521 @ emptyset) @ (setadjoin @ (setadjoin @ X521 @ (setadjoin @ X522 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_197])).
15.33/2.44	thf(c_0_231, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X523:$i]:(((in @ X523 @ (setunion @ (kpair @ X2 @ X3)))&?[X524:$i]:(((in @ X524 @ (setunion @ (kpair @ X2 @ X3)))&((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X523 @ emptyset) @ (setadjoin @ (setadjoin @ X523 @ (setadjoin @ X524 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_197])).
15.33/2.44	thf(c_0_232, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(?[X525:$i]:(((in @ X525 @ (setunion @ X18))&?[X526:$i]:(((in @ X526 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X525 @ emptyset) @ (setadjoin @ (setadjoin @ X525 @ (setadjoin @ X526 @ emptyset)) @ emptyset)))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_197])).
15.33/2.44	thf(c_0_233, plain, ((singletonprop)=(![X4:$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)))=>(?[X527:$i]:(((in @ X527 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X527 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_198, c_0_181])).
15.33/2.44	thf(c_0_234, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X529:$i]:(((in @ X529 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X529 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_199, c_0_200])).
15.33/2.44	thf(c_0_235, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X530:$i]:(((in @ X530 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X530 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_201, c_0_200])).
15.33/2.44	thf(c_0_236, 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)))=>(?[X531:$i]:(((in @ X531 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X531 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_202, c_0_200])).
15.33/2.44	thf(c_0_237, plain, ((kfstsingleton)=(![X18:$i]:(((?[X532:$i]:(((in @ X532 @ (setunion @ X18))&?[X533:$i]:(((in @ X533 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X532 @ emptyset) @ (setadjoin @ (setadjoin @ X532 @ (setadjoin @ X533 @ emptyset)) @ emptyset))))))))=>(?[X534:$i]:(((in @ X534 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X534 @ emptyset))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_203, c_0_197]), c_0_181])).
15.33/2.44	thf(c_0_238, axiom, ((theprop)=(![X21:$i]:(((?[X535:$i]:(((in @ X535 @ X21)&((X21)=(setadjoin @ X535 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_181])).
15.33/2.44	thf(c_0_239, plain, ((ksndsingleton)=(![X18:$i]:(((?[X536:$i]:(((in @ X536 @ (setunion @ X18))&?[X537:$i]:(((in @ X537 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X536 @ emptyset) @ (setadjoin @ (setadjoin @ X536 @ (setadjoin @ X537 @ emptyset)) @ emptyset))))))))=>(?[X538:$i]:(((in @ X538 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X538 @ emptyset))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_204, c_0_197]), c_0_181])).
15.33/2.44	thf(c_0_240, plain, ((epred1_0)<=>![X1016:$i]:(?[X1017:$i]:((((![X1018:$i]:(((in @ X1018 @ X1017)=>![X1019:$i]:(((in @ X1019 @ X1018)=>(in @ X1019 @ X1016)))))&![X1020:$i, X1021:$i]:((((in @ X1020 @ X1016)&(in @ X1021 @ X1016))=>(![X1022:$i]:(((in @ X1022 @ X1017)=>((in @ X1020 @ X1022)<=>(in @ X1021 @ X1022))))=>((X1020)=(X1021))))))&![X1023:$i, X1024:$i]:((((in @ X1023 @ X1017)&(in @ X1024 @ X1017))=>(![X1025:$i]:(((in @ X1025 @ X1023)=>(in @ X1025 @ X1024)))|![X1026:$i]:(((in @ X1026 @ X1024)=>(in @ X1026 @ X1023)))))))&![X1027:$i]:(((![X1028:$i]:(((in @ X1028 @ X1027)=>(in @ X1028 @ X1016)))&?[X1029:$i]:((in @ X1029 @ X1027)))=>?[X1030:$i, X1031:$i]:(((((in @ X1030 @ X1017)&(in @ X1031 @ X1027))&~(?[X1032:$i]:(((in @ X1032 @ X1030)&(in @ X1032 @ X1027)))))&![X1033:$i]:(((in @ X1033 @ X1017)=>(![X1034:$i]:(((in @ X1034 @ X1033)=>(in @ X1034 @ X1030)))|(in @ X1031 @ X1033)))))))))))), introduced(definition)).
15.33/2.44	thf(c_0_241, negated_conjecture, ~((![X1050:$i, X1051:$i]:((![X1052:$i]:(((in @ X1052 @ X1050)<=>(in @ X1052 @ X1051)))=>((X1050)=(X1051))))=>(![X539:$i]:(~(in @ X539 @ emptyset))=>(![X1047:$i, X1048:$i, X1049:$i]:(((in @ X1049 @ (setadjoin @ X1047 @ X1048))<=>(((X1049)=(X1047))|(in @ X1049 @ X1048))))=>(![X540:$i, X541:$i]:(((in @ X541 @ (powerset @ X540))<=>![X542:$i]:(((in @ X542 @ X541)=>(in @ X542 @ X540)))))=>(![X543:$i, X544:$i]:(((in @ X544 @ (setunion @ X543))<=>?[X545:$i]:(((in @ X544 @ X545)&(in @ X545 @ X543)))))=>((in @ emptyset @ omega)=>(![X1046:$i]:(((in @ X1046 @ omega)=>(in @ (setadjoin @ X1046 @ X1046) @ omega)))=>(![X1043:$i]:((((in @ emptyset @ X1043)&![X1044:$i]:((((in @ X1044 @ omega)&(in @ X1044 @ X1043))=>(in @ (setadjoin @ X1044 @ X1044) @ X1043))))=>![X1045:$i]:(((in @ X1045 @ omega)=>(in @ X1045 @ X1043)))))=>(![X1035:$i > $i > $o, X1036:$i]:((![X1037:$i]:(((in @ X1037 @ X1036)=>?[X1038:$i]:(((X1035 @ X1037 @ X1038)&![X1039:$i]:(((X1035 @ X1037 @ X1039)=>((X1038)=(X1039))))))))=>?[X1040:$i]:(![X1041:$i]:(((in @ X1041 @ X1040)<=>?[X1042:$i]:(((in @ X1042 @ X1036)&(X1035 @ X1042 @ X1041))))))))=>(![X546:$i]:((?[X547:$i]:((in @ X547 @ X546))=>?[X548:$i]:(((in @ X548 @ X546)&~(?[X549:$i]:(((in @ X549 @ X548)&(in @ X549 @ X546))))))))=>((epred1_0)=>(![X1013:$i > $o]:((?[X1014:$i]:(((X1013 @ X1014)&![X1015:$i]:(((X1013 @ X1015)=>((X1014)=(X1015))))))=>(X1013 @ (descr @ (^[Z0/* 17 */:$i]:(X1013 @ Z0))))))=>(![X550:$i, X551:$i > $o, X552:$i]:(((in @ X552 @ X550)=>((X551 @ X552)=>(in @ X552 @ (dsetconstr @ X550 @ X551)))))=>(![X553:$i, X554:$i > $o, X555:$i]:(((in @ X555 @ (dsetconstr @ X553 @ X554))=>(in @ X555 @ X553)))=>(![X1010:$i, X1011:$i > $o, X1012:$i]:(((in @ X1012 @ (dsetconstr @ X1010 @ X1011))=>(X1011 @ X1012)))=>(![X1005:$i > $o]:((?[X1006:$i]:(((X1005 @ X1006)&![X1007:$i]:(((X1005 @ X1007)=>((X1006)=(X1007))))))=>?[X1008:$i]:(((X1005 @ X1008)&![X1009:$i]:(((X1005 @ X1009)=>((X1008)=(X1009))))))))=>(![X556:$o, X557:$i]:(((in @ X557 @ (prop2set @ ((X556))))=>(X556)))=>(![X558:$i]:(((in @ X558 @ emptyset)=>![X559:$o]:((X559))))=>(![X1004:$i]:(((in @ X1004 @ emptyset)=>~($true)))=>(![X1003:$i]:(~(in @ X1003 @ emptyset))=>(![X560:$i > $o]:((?[X561:$i]:(((X560 @ X561)&![X562:$i]:(((X560 @ X562)=>((X561)=(X562))))))=>?[X563:$i]:((X560 @ X563))))=>(![X564:$i, X565:$i]:((![X566:$i]:(((in @ X566 @ X564)=>(in @ X566 @ X565)))=>(![X567:$i]:(((in @ X567 @ X565)=>(in @ X567 @ X564)))=>((X564)=(X565)))))=>(![X568:$i]:((![X569:$i]:(~(in @ X569 @ X568))=>((X568)=(emptyset))))=>(![X1001:$i]:((![X1002:$i]:(~(in @ X1002 @ X1001))=>((X1001)=(emptyset))))=>(![X570:$i, X571:$i > $o, X572:$i]:(((in @ X572 @ X570)=>((in @ X572 @ (dsetconstr @ X570 @ X571))<=>(X571 @ X572))))=>(![X999:$i]:((((X999)!=(emptyset))=>?[X1000:$i]:((in @ X1000 @ X999))))=>(![X996:$i, X997:$i > $o, X998:$i]:(((in @ X998 @ X996)=>((X997 @ X998)=>((dsetconstr @ X996 @ X997)!=(emptyset)))))=>(![X994:$i]:((?[X995:$i]:((in @ X995 @ X994))=>((X994)!=(emptyset))))=>(![X992:$i, X993:$i]:((in @ X992 @ (setadjoin @ X992 @ X993)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X573:$i, X574:$i, X575:$i]:(((in @ X575 @ X574)=>(in @ X575 @ (setadjoin @ X573 @ X574))))=>(![X988:$i, X989:$i, X990:$i]:(((in @ X990 @ (setadjoin @ X988 @ X989))=>![X991:$o]:(((((X990)=(X988))=>(X991))=>(((in @ X990 @ X989)=>(X991))=>(X991))))))=>(![X576:$i, X577:$i, X578:$i]:(((in @ X578 @ (setadjoin @ X576 @ X577))=>(((X578)=(X576))|(in @ X578 @ X577))))=>(![X579:$i]:(((dsetconstr @ X579 @ (^[Z0/* 1 */:$i]:($true)))=(X579)))=>(![X580:$i, X581:$i]:((![X582:$i]:(((in @ X582 @ X581)=>(in @ X582 @ X580)))=>(in @ X581 @ (powerset @ X580))))=>(![X987:$i]:((in @ emptyset @ (powerset @ X987)))=>(![X986:$i]:((in @ emptyset @ (powerset @ X986)))=>(![X983:$i, X984:$i, X985:$i]:(((in @ X984 @ (powerset @ X983))=>((in @ X985 @ X984)=>(in @ X985 @ X983))))=>(![X583:$i, X584:$i, X585:$i]:(((in @ X584 @ X585)=>((in @ X585 @ X583)=>(in @ X584 @ (setunion @ X583)))))=>(![X586:$i, X587:$i]:(((in @ X587 @ (setunion @ X586))=>![X588:$o]:((![X589:$i]:(((in @ X587 @ X589)=>((in @ X589 @ X586)=>(X588))))=>(X588)))))=>(![X590:$i, X591:$i]:(((in @ X591 @ X590)=>(in @ X591 @ (powerset @ (setunion @ X590)))))=>(![X592:$i > $o]:((?[X593:$i]:(((X592 @ X593)&![X594:$i]:(((X592 @ X594)=>((X593)=(X594))))))=>?[X595:$i]:(![X596:$i]:(((X592 @ X596)<=>((X596)=(X595)))))))=>(![X597:$i]:((((X597)!=(emptyset))=>?[X598:$i]:(((in @ X598 @ X597)&$true))))=>(![X981:$i, X982:$i]:(((in @ X981 @ (setadjoin @ X982 @ emptyset))=>((X981)=(X982))))=>(![X599:$i, X600:$i]:((((X599)!=(X600))=>~(in @ X600 @ (setadjoin @ X599 @ emptyset))))=>(![X979:$i, X980:$i]:((((X979)=(X980))=>(in @ X979 @ (setadjoin @ X980 @ emptyset))))=>(![X601:$i, X602:$i]:(((in @ X601 @ (setadjoin @ X602 @ emptyset))=>(in @ X602 @ (setadjoin @ X601 @ emptyset))))=>(![X976:$i, X977:$i, X978:$i]:(((in @ X978 @ (setadjoin @ X976 @ (setadjoin @ X977 @ emptyset)))=>(((X978)=(X976))|((X978)=(X977)))))=>(![X603:$i, X604:$i]:((in @ X603 @ (setadjoin @ X603 @ (setadjoin @ X604 @ emptyset))))=>(![X605:$i, X606:$i]:((in @ X606 @ (setadjoin @ X605 @ (setadjoin @ X606 @ emptyset))))=>(![X973:$i, X974:$i > $o]:((?[X975:$i]:(((in @ X975 @ X973)&(X974 @ X975)))=>(((dsetconstr @ X973 @ X974)=(emptyset))=>~($true))))=>(![X971:$i > $o, X972:$i]:(((in @ X972 @ emptyset)=>(X971 @ X972)))=>(![X607:$i, X608:$i > $o]:((~(![X609:$i]:(((in @ X609 @ X607)=>(X608 @ X609))))=>?[X610:$i]:(((in @ X610 @ X607)&~((X608 @ X610))))))=>(![X967:$i, X968:$i > $o]:((![X969:$i]:(((in @ X969 @ X967)=>~((X968 @ X969))))=>~(?[X970:$i]:(((in @ X970 @ X967)&(X968 @ X970))))))=>(![X611:$i, X612:$i > $o]:((~(?[X613:$i]:(((in @ X613 @ X611)&(X612 @ X613))))=>![X614:$i]:(((in @ X614 @ X611)=>~((X612 @ X614))))))=>(![X963:$i, X964:$i > $o]:((?[X965:$i]:(((in @ X965 @ X963)&~((X964 @ X965))))=>~(![X966:$i]:(((in @ X966 @ X963)=>(X964 @ X966))))))=>(![X962:$o]:(((X962)=>(in @ emptyset @ (prop2set @ ((X962))))))=>(![X615:$o]:(((X615)=>(set2prop @ (prop2set @ ((X615))))))=>(![X958:$i, X959:$i > $o]:((~(?[X960:$i]:(((in @ X960 @ X958)&(X959 @ X960))))=>![X961:$i]:(((in @ X961 @ X958)=>~((X959 @ X961))))))=>(![X616:$i, X617:$i > $o]:((~(![X618:$i]:(((in @ X618 @ X616)=>(X617 @ X618))))=>?[X619:$i]:(((in @ X619 @ X616)&~((X617 @ X619))))))=>(![X620:$i > $o]:((?[X621:$i]:(((X620 @ X621)&![X622:$i]:(((X620 @ X622)=>((X621)=(X622))))))=>?[X623:$i]:(((X620 @ X623)&![X624:$i]:(((X620 @ X624)=>((X623)=(X624))))))))=>(![X952:$i > $o]:((?[X953:$i]:((X952 @ X953))=>(![X954:$i, X955:$i]:(((X952 @ X954)=>((X952 @ X955)=>((X954)=(X955)))))=>?[X956:$i]:(((X952 @ X956)&![X957:$i]:(((X952 @ X957)=>((X956)=(X957)))))))))=>(![X947:$i > $o]:((?[X948:$i]:(![X949:$i]:(((X947 @ X949)<=>((X949)=(X948)))))=>?[X950:$i]:(((X947 @ X950)&![X951:$i]:(((X947 @ X951)=>((X950)=(X951))))))))=>(![X943:$i, X944:$i]:((((X943)=(X944))=>![X945:$i, X946:$i]:((((X945)=(X946))=>((in @ X945 @ X943)=>(in @ X946 @ X944))))))=>(![X939:$i, X940:$i]:((((X939)=(X940))=>![X941:$i, X942:$i]:((((X941)=(X942))=>((in @ X941 @ X939)<=>(in @ X942 @ X940))))))=>(![X934:$i > $o]:((?[X935:$i]:(((X934 @ X935)&![X936:$i]:(((X934 @ X936)=>((X935)=(X936))))))=>![X937:$i, X938:$i]:(((X934 @ X937)=>((X934 @ X938)=>((X937)=(X938)))))))=>(![X926:$i > $o, X927:$i > $o]:((![X928:$i, X929:$i]:((((X928)=(X929))=>((X926 @ X928)<=>(X927 @ X929))))=>(?[X930:$i]:(((X926 @ X930)&![X931:$i]:(((X926 @ X931)=>((X930)=(X931))))))<=>?[X932:$i]:(((X927 @ X932)&![X933:$i]:(((X927 @ X933)=>((X932)=(X933)))))))))=>(((emptyset)=(emptyset))=>(![X922:$i, X923:$i]:((((X922)=(X923))=>![X924:$i, X925:$i]:((((X924)=(X925))=>((setadjoin @ X922 @ X924)=(setadjoin @ X923 @ X925))))))=>(![X920:$i, X921:$i]:((((X920)=(X921))=>((powerset @ X920)=(powerset @ X921))))=>(![X625:$i, X626:$i]:((((X625)=(X626))=>((setunion @ X625)=(setunion @ X626))))=>(((omega)=(omega))=>(![X627:$i > $o]:((?[X628:$i]:(((X627 @ X628)&![X629:$i]:(((X627 @ X629)=>((X628)=(X629))))))=>![X630:$i, X631:$i]:(((X627 @ X630)=>((X627 @ X631)=>((X630)=(X631)))))))=>(![X912:$i > $o, X913:$i > $o]:((![X914:$i, X915:$i]:((((X914)=(X915))=>((X912 @ X914)<=>(X913 @ X915))))=>(?[X916:$i]:(((X912 @ X916)&![X917:$i]:(((X912 @ X917)=>((X916)=(X917))))))=>(?[X918:$i]:(((X913 @ X918)&![X919:$i]:(((X913 @ X919)=>((X918)=(X919))))))=>((descr @ X912)=(descr @ X913))))))=>(![X906:$i, X907:$i]:((((X906)=(X907))=>![X908:$i > $o, X909:$i > $o]:((![X910:$i]:(((in @ X910 @ X906)=>![X911:$i]:(((in @ X911 @ X907)=>(((X910)=(X911))=>((X908 @ X910)<=>(X909 @ X911)))))))=>((dsetconstr @ X906 @ X908)=(dsetconstr @ X907 @ X909))))))=>(![X903:$i, X904:$i]:((![X905:$i]:(((in @ X905 @ X903)=>(in @ X905 @ X904)))=>(subset @ X903 @ X904)))=>(![X901:$i, X902:$i]:((((X901)=(X902))=>(subset @ X902 @ X901)))=>(![X899:$i, X900:$i]:((((X899)=(X900))=>(subset @ X899 @ X900)))=>(![X896:$i, X897:$i]:((![X898:$i]:(((in @ X898 @ X896)=>(in @ X898 @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[ksndpairEq]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_205]), foundationAx]), wellorderingAx]), c_0_206]), c_0_207]), c_0_208]), c_0_209]), c_0_210]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_211]), setext]), emptyI]), noeltsimpempty]), c_0_212]), c_0_213]), c_0_214]), c_0_215]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_216]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_217]), c_0_218]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_219]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_220]), c_0_221]), c_0_222]), inCongP]), in__Cong]), c_0_223]), c_0_224]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_225]), c_0_226]), c_0_227]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_228]), c_0_229]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), c_0_230]), c_0_231]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), c_0_232]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_233]), c_0_234]), c_0_235]), c_0_236]), singletonsuniq]), setukpairinjL1]), c_0_237]), c_0_238]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_239])])]), c_0_240])).
15.33/2.44	thf(c_0_242, plain, ![X1053:$i, X1054:$i]:(((kpair @ X1053 @ X1054)=(setadjoin @ (setadjoin @ X1053 @ emptyset) @ (setadjoin @ (setadjoin @ X1053 @ (setadjoin @ X1054 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])])).
15.33/2.44	thf(c_0_243, negated_conjecture, ![X1059:$i, X1060:$i, X1062:$i, X1063:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1072:$i, X1073:$i, X1075:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i, X1081:$i, X1082:$i > $i > $o, X1083:$i, X1085:$i, X1088:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1095:$i, X1096:$i > $o, X1097:$i, X1099:$i, X1100:$i > $o, X1101:$i, X1102:$i, X1103:$i > $o, X1104:$i, X1105:$i, X1106:$i > $o, X1107:$i, X1108:$i > $o, X1109:$i, X1112:$i, X1113:$o, X1114:$i, X1115:$i, X1116:$o, X1117:$i, X1118:$i, X1119:$i > $o, X1120:$i, X1123:$i, X1124:$i, X1127:$i, X1129:$i, X1131:$i, X1132:$i > $o, X1133:$i, X1134:$i, X1136:$i, X1137:$i > $o, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$o, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$o, X1169:$i, X1170:$i, X1171:$i > $o, X1172:$i, X1175:$i, X1176:$i, X1177:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i > $o, X1196:$i, X1197:$i > $o, X1198:$i, X1199:$i, X1200:$i > $o, X1201:$i, X1203:$i, X1204:$i > $o, X1206:$i, X1207:$i, X1208:$i > $o, X1210:$i, X1211:$i, X1212:$i > $o, X1213:$i, X1215:$o, X1216:$o, X1217:$i, X1218:$i > $o, X1220:$i, X1221:$i, X1222:$i > $o, X1223:$i, X1225:$i > $o, X1226:$i, X1229:$i, X1230:$i > $o, X1231:$i, X1235:$i, X1236:$i > $o, X1237:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i > $o, X1250:$i, X1252:$i, X1253:$i, X1254:$i > $o, X1255:$i > $o, X1258:$i, X1261:$i, X1262:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i > $o, X1275:$i, X1277:$i, X1278:$i, X1279:$i > $o, X1280:$i > $o, X1283:$i, X1285:$i, X1287:$i, X1288:$i, X1289:$i > $o, X1290:$i > $o, X1293:$i, X1294:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i > $o, X1341:$i, X1342:$i > $o, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$o, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$o, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1445:$i, X1446:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1488:$i, X1489:$i, X1490:$i, X1493:$i, X1494:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i > $o, X1503:$i, X1505:$i, X1506:$i > $o, X1507:$i, X1509:$i, X1510:$i > $o, X1511:$i, X1514:$i, X1515:$i > $o, X1518:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i]:((((~(in @ (esk1_2 @ X1059 @ X1060) @ X1059)|~(in @ (esk1_2 @ X1059 @ X1060) @ X1060)|((X1059)=(X1060)))&((in @ (esk1_2 @ X1059 @ X1060) @ X1059)|(in @ (esk1_2 @ X1059 @ X1060) @ X1060)|((X1059)=(X1060))))&(~(in @ X1062 @ emptyset)&(((~(in @ X1065 @ (setadjoin @ X1063 @ X1064))|(((X1065)=(X1063))|(in @ X1065 @ X1064)))&((((X1065)!=(X1063))|(in @ X1065 @ (setadjoin @ X1063 @ X1064)))&(~(in @ X1065 @ X1064)|(in @ X1065 @ (setadjoin @ X1063 @ X1064)))))&(((~(in @ X1067 @ (powerset @ X1066))|(~(in @ X1068 @ X1067)|(in @ X1068 @ X1066)))&(((in @ (esk2_2 @ X1069 @ X1070) @ X1070)|(in @ X1070 @ (powerset @ X1069)))&(~(in @ (esk2_2 @ X1069 @ X1070) @ X1069)|(in @ X1070 @ (powerset @ X1069)))))&(((((in @ X1073 @ (esk3_2 @ X1072 @ X1073))|~(in @ X1073 @ (setunion @ X1072)))&((in @ (esk3_2 @ X1072 @ X1073) @ X1072)|~(in @ X1073 @ (setunion @ X1072))))&(~(in @ X1076 @ X1077)|~(in @ X1077 @ X1075)|(in @ X1076 @ (setunion @ X1075))))&((in @ emptyset @ omega)&((~(in @ X1078 @ omega)|(in @ (setadjoin @ X1078 @ X1078) @ omega))&(((((in @ (esk4_1 @ X1079) @ omega)|~(in @ emptyset @ X1079)|(~(in @ X1081 @ omega)|(in @ X1081 @ X1079)))&((in @ (esk4_1 @ X1079) @ X1079)|~(in @ emptyset @ X1079)|(~(in @ X1081 @ omega)|(in @ X1081 @ X1079))))&(~(in @ (setadjoin @ (esk4_1 @ X1079) @ (esk4_1 @ X1079)) @ X1079)|~(in @ emptyset @ X1079)|(~(in @ X1081 @ omega)|(in @ X1081 @ X1079))))&((((((in @ (esk8_3 @ X1082 @ X1083 @ X1088) @ X1083)|~(in @ X1088 @ (esk7_2 @ X1082 @ X1083))|(in @ (esk5_2 @ X1082 @ X1083) @ X1083))&((X1082 @ (esk8_3 @ X1082 @ X1083 @ X1088) @ X1088)|~(in @ X1088 @ (esk7_2 @ X1082 @ X1083))|(in @ (esk5_2 @ X1082 @ X1083) @ X1083)))&(~(in @ X1091 @ X1083)|~(X1082 @ X1091 @ X1090)|(in @ X1090 @ (esk7_2 @ X1082 @ X1083))|(in @ (esk5_2 @ X1082 @ X1083) @ X1083)))&(((((in @ (esk8_3 @ X1082 @ X1083 @ X1088) @ X1083)|~(in @ X1088 @ (esk7_2 @ X1082 @ X1083))|((X1082 @ (esk5_2 @ X1082 @ X1083) @ (esk6_3 @ X1082 @ X1083 @ X1085))|~(X1082 @ (esk5_2 @ X1082 @ X1083) @ X1085)))&((X1082 @ (esk8_3 @ X1082 @ X1083 @ X1088) @ X1088)|~(in @ X1088 @ (esk7_2 @ X1082 @ X1083))|((X1082 @ (esk5_2 @ X1082 @ X1083) @ (esk6_3 @ X1082 @ X1083 @ X1085))|~(X1082 @ (esk5_2 @ X1082 @ X1083) @ X1085))))&(~(in @ X1091 @ X1083)|~(X1082 @ X1091 @ X1090)|(in @ X1090 @ (esk7_2 @ X1082 @ X1083))|((X1082 @ (esk5_2 @ X1082 @ X1083) @ (esk6_3 @ X1082 @ X1083 @ X1085))|~(X1082 @ (esk5_2 @ X1082 @ X1083) @ X1085))))&((((in @ (esk8_3 @ 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@ X1499 @ X1500)=(setadjoin @ (esk66_2 @ X1499 @ X1500) @ emptyset))|(~(in @ X1503 @ X1499)|~(X1500 @ X1503))|(in @ (esk64_2 @ X1499 @ X1500) @ X1499)))&((((in @ (esk66_2 @ X1499 @ X1500) @ (dsetconstr @ X1499 @ X1500))|(~(in @ X1503 @ X1499)|~(X1500 @ X1503))|(in @ (esk65_2 @ X1499 @ X1500) @ X1499))&(((dsetconstr @ X1499 @ X1500)=(setadjoin @ (esk66_2 @ X1499 @ X1500) @ emptyset))|(~(in @ X1503 @ X1499)|~(X1500 @ X1503))|(in @ (esk65_2 @ X1499 @ X1500) @ X1499)))&((((in @ (esk66_2 @ X1499 @ X1500) @ (dsetconstr @ X1499 @ X1500))|(~(in @ X1503 @ X1499)|~(X1500 @ X1503))|(X1500 @ (esk64_2 @ X1499 @ X1500)))&(((dsetconstr @ X1499 @ X1500)=(setadjoin @ (esk66_2 @ X1499 @ X1500) @ emptyset))|(~(in @ X1503 @ X1499)|~(X1500 @ X1503))|(X1500 @ (esk64_2 @ X1499 @ X1500))))&((((in @ (esk66_2 @ X1499 @ X1500) @ (dsetconstr @ X1499 @ X1500))|(~(in @ X1503 @ X1499)|~(X1500 @ X1503))|(X1500 @ (esk65_2 @ X1499 @ X1500)))&(((dsetconstr @ X1499 @ X1500)=(setadjoin @ (esk66_2 @ X1499 @ X1500) @ emptyset))|(~(in @ X1503 @ X1499)|~(X1500 @ X1503))|(X1500 @ (esk65_2 @ X1499 @ X1500))))&(((in @ (esk66_2 @ X1499 @ X1500) @ (dsetconstr @ X1499 @ X1500))|(~(in @ X1503 @ X1499)|~(X1500 @ X1503))|((esk64_2 @ X1499 @ X1500)!=(esk65_2 @ X1499 @ X1500)))&(((dsetconstr @ X1499 @ X1500)=(setadjoin @ (esk66_2 @ X1499 @ X1500) @ emptyset))|(~(in @ X1503 @ X1499)|~(X1500 @ X1503))|((esk64_2 @ X1499 @ X1500)!=(esk65_2 @ X1499 @ X1500))))))))&((((in @ (esk67_2 @ X1505 @ X1506) @ X1505)|(~(in @ X1507 @ (dsetconstr @ X1505 @ X1506))|((dsetconstr @ X1505 @ X1506)!=(setadjoin @ X1507 @ emptyset))))&((X1506 @ (esk67_2 @ X1505 @ X1506))|(~(in @ X1507 @ (dsetconstr @ X1505 @ X1506))|((dsetconstr @ X1505 @ X1506)!=(setadjoin @ X1507 @ emptyset)))))&(((((in @ (esk69_3 @ X1509 @ X1510 @ X1511) @ (dsetconstr @ X1509 @ X1510))|(in @ (esk68_3 @ X1509 @ X1510 @ X1511) @ X1509)|~(X1510 @ X1511)|~(in @ X1511 @ X1509))&(((dsetconstr @ X1509 @ X1510)=(setadjoin @ (esk69_3 @ X1509 @ X1510 @ X1511) @ emptyset))|(in @ (esk68_3 @ X1509 @ X1510 @ X1511) @ X1509)|~(X1510 @ X1511)|~(in @ X1511 @ X1509)))&((((in @ (esk69_3 @ X1509 @ X1510 @ X1511) @ (dsetconstr @ X1509 @ X1510))|(X1510 @ (esk68_3 @ X1509 @ X1510 @ X1511))|~(X1510 @ X1511)|~(in @ X1511 @ X1509))&(((dsetconstr @ X1509 @ X1510)=(setadjoin @ (esk69_3 @ X1509 @ X1510 @ X1511) @ emptyset))|(X1510 @ (esk68_3 @ X1509 @ X1510 @ X1511))|~(X1510 @ X1511)|~(in @ X1511 @ X1509)))&(((in @ (esk69_3 @ X1509 @ X1510 @ X1511) @ (dsetconstr @ X1509 @ X1510))|((esk68_3 @ X1509 @ X1510 @ X1511)!=(X1511))|~(X1510 @ X1511)|~(in @ X1511 @ X1509))&(((dsetconstr @ X1509 @ X1510)=(setadjoin @ (esk69_3 @ X1509 @ X1510 @ X1511) @ emptyset))|((esk68_3 @ X1509 @ X1510 @ X1511)!=(X1511))|~(X1510 @ X1511)|~(in @ X1511 @ X1509)))))&(((((in @ (esk72_2 @ X1514 @ X1515) @ (dsetconstr @ X1514 @ X1515))|(~(in @ X1518 @ X1514)|~(X1515 @ X1518))|(in @ (esk70_2 @ X1514 @ X1515) @ X1514))&(((dsetconstr @ X1514 @ X1515)=(setadjoin @ (esk72_2 @ X1514 @ X1515) @ emptyset))|(~(in @ X1518 @ X1514)|~(X1515 @ X1518))|(in @ (esk70_2 @ X1514 @ X1515) @ X1514)))&((((in @ (esk72_2 @ X1514 @ X1515) @ (dsetconstr @ X1514 @ X1515))|(~(in @ X1518 @ X1514)|~(X1515 @ X1518))|(in @ (esk71_2 @ X1514 @ X1515) @ X1514))&(((dsetconstr @ X1514 @ X1515)=(setadjoin @ (esk72_2 @ X1514 @ X1515) @ emptyset))|(~(in @ X1518 @ X1514)|~(X1515 @ X1518))|(in @ (esk71_2 @ X1514 @ X1515) @ X1514)))&((((in @ (esk72_2 @ X1514 @ X1515) @ (dsetconstr @ X1514 @ X1515))|(~(in @ X1518 @ X1514)|~(X1515 @ X1518))|(X1515 @ (esk70_2 @ X1514 @ X1515)))&(((dsetconstr @ X1514 @ X1515)=(setadjoin @ (esk72_2 @ X1514 @ X1515) @ emptyset))|(~(in @ X1518 @ X1514)|~(X1515 @ X1518))|(X1515 @ (esk70_2 @ X1514 @ X1515))))&((((in @ (esk72_2 @ X1514 @ X1515) @ (dsetconstr @ X1514 @ X1515))|(~(in @ X1518 @ X1514)|~(X1515 @ X1518))|(X1515 @ (esk71_2 @ X1514 @ X1515)))&(((dsetconstr @ X1514 @ X1515)=(setadjoin @ (esk72_2 @ X1514 @ X1515) @ emptyset))|(~(in @ X1518 @ X1514)|~(X1515 @ X1518))|(X1515 @ (esk71_2 @ X1514 @ X1515))))&(((in @ (esk72_2 @ X1514 @ X1515) @ (dsetconstr @ X1514 @ X1515))|(~(in @ X1518 @ X1514)|~(X1515 @ X1518))|((esk70_2 @ X1514 @ X1515)!=(esk71_2 @ X1514 @ X1515)))&(((dsetconstr @ X1514 @ X1515)=(setadjoin @ (esk72_2 @ X1514 @ X1515) @ emptyset))|(~(in @ X1518 @ X1514)|~(X1515 @ X1518))|((esk70_2 @ X1514 @ X1515)!=(esk71_2 @ X1514 @ X1515))))))))&((((setadjoin @ X1520 @ emptyset)!=(setadjoin @ X1521 @ emptyset))|((X1520)=(X1521)))&((~(in @ (setadjoin @ X1524 @ emptyset) @ (setadjoin @ (setadjoin @ X1522 @ emptyset) @ (setadjoin @ (setadjoin @ X1522 @ (setadjoin @ X1523 @ emptyset)) @ emptyset)))|((X1522)=(X1524)))&((((in @ (esk73_1 @ X1525) @ (dsetconstr @ (setunion @ X1525) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1525)))))|(~(in @ X1526 @ (setunion @ X1525))|(~(in @ X1527 @ (setunion @ X1525))|((X1525)!=(setadjoin @ (setadjoin @ X1526 @ emptyset) @ (setadjoin @ (setadjoin @ X1526 @ (setadjoin @ X1527 @ emptyset)) @ emptyset))))))&(((dsetconstr @ (setunion @ X1525) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1525))))=(setadjoin @ (esk73_1 @ X1525) @ emptyset))|(~(in @ X1526 @ (setunion @ X1525))|(~(in @ X1527 @ (setunion @ X1525))|((X1525)!=(setadjoin @ (setadjoin @ X1526 @ emptyset) @ (setadjoin @ (setadjoin @ X1526 @ (setadjoin @ X1527 @ emptyset)) @ emptyset)))))))&((~(in @ X1530 @ X1529)|((X1529)!=(setadjoin @ X1530 @ emptyset))|(in @ (setunion @ X1529) @ X1529))&(((kfst @ (kpair @ X1531 @ X1532))=(X1531))&((~(in @ X1535 @ (cartprod @ X1533 @ X1534))|(in @ (kfst @ X1535) @ X1533))&((((setadjoin @ (setadjoin @ X1536 @ emptyset) @ (setadjoin @ (setadjoin @ X1536 @ (setadjoin @ X1537 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1538 @ emptyset) @ (setadjoin @ (setadjoin @ X1538 @ (setadjoin @ X1539 @ emptyset)) @ emptyset)))|((X1536)=(X1538)))&((((kpair @ X1540 @ X1541)!=(kpair @ X1542 @ X1543))|((X1540)=(X1542)))&((((X1544)!=(X1545))|((setadjoin @ X1544 @ (setadjoin @ X1545 @ emptyset))=(setadjoin @ X1544 @ emptyset)))&((((X1546)!=(X1547))|((setadjoin @ (setadjoin @ X1546 @ emptyset) @ (setadjoin @ (setadjoin @ X1546 @ (setadjoin @ X1547 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1546 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1548 @ emptyset) @ (setadjoin @ (setadjoin @ X1548 @ (setadjoin @ X1549 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1550 @ emptyset) @ (setadjoin @ (setadjoin @ X1550 @ (setadjoin @ X1551 @ emptyset)) @ emptyset)))|(((X1550)!=(X1551))|((X1549)=(X1551))))&((((setadjoin @ X1552 @ (setadjoin @ X1553 @ emptyset))!=(setadjoin @ X1554 @ emptyset))|((X1552)=(X1553)))&((((setadjoin @ (setadjoin @ X1555 @ emptyset) @ (setadjoin @ (setadjoin @ X1555 @ (setadjoin @ X1556 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1557 @ emptyset) @ (setadjoin @ (setadjoin @ X1557 @ (setadjoin @ X1558 @ emptyset)) @ emptyset)))|((X1556)=(X1558)))&((((kpair @ X1559 @ X1560)!=(kpair @ X1561 @ X1562))|((X1560)=(X1562)))&((((in @ (esk74_1 @ X1563) @ (dsetconstr @ (setunion @ X1563) @ (^[Z0/* 3 */:$i]:(((X1563)=(kpair @ (kfst @ X1563) @ Z0))))))|(~(in @ X1564 @ (setunion @ X1563))|(~(in @ X1565 @ (setunion @ X1563))|((X1563)!=(setadjoin @ (setadjoin @ X1564 @ emptyset) @ (setadjoin @ (setadjoin @ X1564 @ (setadjoin @ X1565 @ emptyset)) @ emptyset))))))&(((dsetconstr @ (setunion @ X1563) @ (^[Z0/* 3 */:$i]:(((X1563)=(kpair @ (kfst @ X1563) @ Z0)))))=(setadjoin @ (esk74_1 @ X1563) @ emptyset))|(~(in @ X1564 @ (setunion @ X1563))|(~(in @ X1565 @ (setunion @ X1563))|((X1563)!=(setadjoin @ (setadjoin @ X1564 @ emptyset) @ (setadjoin @ (setadjoin @ X1564 @ (setadjoin @ X1565 @ emptyset)) @ emptyset)))))))&((ksnd @ (kpair @ esk75_0 @ esk76_0))!=(esk76_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_241])])])])])])])).
15.33/2.44	thf(c_0_244, plain, ![X1056:$i, X1057:$i]:(((kpair @ X1056 @ X1057)=(setadjoin @ (setadjoin @ X1056 @ emptyset) @ (setadjoin @ (setadjoin @ X1056 @ (setadjoin @ X1057 @ emptyset)) @ emptyset)))), inference(variable_rename,[status(thm)],[c_0_242])).
15.33/2.44	thf(c_0_245, negated_conjecture, ![X2:$i, X3:$i]:(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ (esk57_2 @ X2 @ X3) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X2 @ X3) @ (setadjoin @ (esk58_2 @ X2 @ X3) @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_243])).
15.33/2.44	thf(c_0_246, plain, ![X2:$i, X3:$i]:(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_244])).
15.33/2.44	thf(c_0_247, plain, ![X1588:$i, X2:$i]:(((epred2_1 @ X2 @ X1588)<=>((X2)=(kpair @ (kfst @ X2) @ X1588)))), introduced(definition)).
15.33/2.44	thf(c_0_248, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_243])).
15.33/2.44	thf(c_0_249, negated_conjecture, ![X2:$i, X3:$i]:(((kpair @ (esk57_2 @ X2 @ X3) @ (esk58_2 @ X2 @ X3))=(kpair @ X2 @ X3))), inference(rw,[status(thm)],[c_0_245, c_0_246])).
15.33/2.44	thf(c_0_250, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((((in @ (esk74_1 @ X2) @ (dsetconstr @ (setunion @ X2) @ (epred2_1 @ X2))))=(($true)))|~((in @ X3 @ (setunion @ X2)))|~((in @ X4 @ (setunion @ X2)))|((X2)!=(setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_243]), c_0_247])).
15.33/2.44	thf(c_0_251, negated_conjecture, ![X2:$i, X3:$i]:((in @ (esk57_2 @ X2 @ X3) @ (setunion @ (kpair @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_243])).
15.33/2.44	thf(c_0_252, negated_conjecture, ![X3:$i, X2:$i]:(((esk57_2 @ X2 @ X3)=(X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248, c_0_249]), c_0_248])).
15.33/2.44	thf(c_0_253, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((dsetconstr @ (setunion @ X2) @ (epred2_1 @ X2))=(setadjoin @ (esk74_1 @ X2) @ emptyset))|~((in @ X3 @ (setunion @ X2)))|~((in @ X4 @ (setunion @ X2)))|((X2)!=(setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_243]), c_0_247])).
15.33/2.44	thf(c_0_254, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk74_1 @ (kpair @ X2 @ X3)) @ (dsetconstr @ (setunion @ (kpair @ X2 @ X3)) @ (epred2_1 @ (kpair @ X2 @ X3))))|~((in @ X3 @ (setunion @ (kpair @ X2 @ X3))))|~((in @ X2 @ (setunion @ (kpair @ X2 @ X3)))))), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[c_0_250]), c_0_246])])).
15.33/2.44	thf(c_0_255, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (kpair @ X2 @ X3)))), inference(rw,[status(thm)],[c_0_251, c_0_252])).
15.33/2.44	thf(c_0_256, negated_conjecture, ![X3:$i, X2:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_243])).
15.33/2.44	thf(c_0_257, plain, ![X1055:$i]:(((ksnd @ X1055)=(setunion @ (dsetconstr @ (setunion @ X1055) @ (^[Z0/* 3 */:$i]:(((X1055)=(kpair @ (kfst @ X1055) @ Z0)))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ksnd])])).
15.33/2.44	thf(c_0_258, negated_conjecture, ![X2:$i, X3:$i]:((((dsetconstr @ (setunion @ (kpair @ X2 @ X3)) @ (epred2_1 @ (kpair @ X2 @ X3)))=(setadjoin @ (esk74_1 @ (kpair @ X2 @ X3)) @ emptyset))|~((in @ X3 @ (setunion @ (kpair @ X2 @ X3))))|~((in @ X2 @ (setunion @ (kpair @ X2 @ X3)))))), inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_253, c_0_246])])).
15.33/2.44	thf(c_0_259, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk74_1 @ (kpair @ X2 @ X3)) @ (dsetconstr @ (setunion @ (kpair @ X2 @ X3)) @ (epred2_1 @ (kpair @ X2 @ X3))))|~((in @ X3 @ (setunion @ (kpair @ X2 @ X3)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_254, c_0_255])])).
15.33/2.44	thf(c_0_260, negated_conjecture, ![X3:$i, X2:$i]:((in @ X2 @ (setunion @ (kpair @ X3 @ X2)))), inference(rw,[status(thm)],[c_0_256, c_0_246])).
15.33/2.44	thf(c_0_261, plain, ![X1058:$i]:(((ksnd @ X1058)=(setunion @ (dsetconstr @ (setunion @ X1058) @ (^[Z0/* 3 */:$i]:(((X1058)=(kpair @ (kfst @ X1058) @ Z0)))))))), inference(variable_rename,[status(thm)],[c_0_257])).
15.33/2.44	thf(c_0_262, negated_conjecture, ![X2:$i, X3:$i]:((((dsetconstr @ (setunion @ (kpair @ X2 @ X3)) @ (epred2_1 @ (kpair @ X2 @ X3)))=(setadjoin @ (esk74_1 @ (kpair @ X2 @ X3)) @ emptyset))|~((in @ X3 @ (setunion @ (kpair @ X2 @ X3)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_258, c_0_255])])).
15.33/2.44	thf(c_0_263, plain, ![X1594:$i, X1595:$i]:(((~(epred2_1 @ X1595 @ X1594)|((X1595)=(kpair @ (kfst @ X1595) @ X1594)))&(((X1595)!=(kpair @ (kfst @ X1595) @ X1594))|(epred2_1 @ X1595 @ X1594)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])).
15.33/2.44	thf(c_0_264, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_243])).
15.33/2.44	thf(c_0_265, negated_conjecture, ![X2:$i, X3:$i]:((in @ (esk74_1 @ (kpair @ X2 @ X3)) @ (dsetconstr @ (setunion @ (kpair @ X2 @ X3)) @ (epred2_1 @ (kpair @ X2 @ X3))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_259, c_0_260])])).
15.33/2.44	thf(c_0_266, plain, ![X2:$i]:(((ksnd @ X2)=(setunion @ (dsetconstr @ (setunion @ X2) @ (epred2_1 @ X2))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_261]), c_0_247])).
15.33/2.44	thf(c_0_267, negated_conjecture, ![X2:$i, X3:$i]:(((dsetconstr @ (setunion @ (kpair @ X2 @ X3)) @ (epred2_1 @ (kpair @ X2 @ X3)))=(setadjoin @ (esk74_1 @ (kpair @ X2 @ X3)) @ emptyset))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_262, c_0_260])])).
15.33/2.44	thf(c_0_268, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_243])).
15.33/2.44	thf(c_0_269, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i]:((((X3)=(X5))|((kpair @ X2 @ X3)!=(kpair @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_243])).
15.33/2.44	thf(c_0_270, plain, ![X2:$i, X3:$i]:((((X2)=(kpair @ (kfst @ X2) @ X3))|~((epred2_1 @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_263])).
15.33/2.44	thf(c_0_271, negated_conjecture, ![X2:$i, X3:$i]:((epred2_1 @ (kpair @ X2 @ X3) @ (esk74_1 @ (kpair @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_264, c_0_265])).
15.33/2.44	thf(c_0_272, negated_conjecture, ![X2:$i, X3:$i]:(((esk74_1 @ (kpair @ X2 @ X3))=(ksnd @ (kpair @ X2 @ X3)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266, c_0_267]), c_0_268])).
15.33/2.44	thf(c_0_273, plain, ![X2:$i, X4:$i, X3:$i]:((((X2)=(X3))|~((epred2_1 @ (kpair @ X4 @ X2) @ X3)))), inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_269, c_0_270])])).
15.33/2.44	thf(c_0_274, negated_conjecture, ![X2:$i, X3:$i]:((epred2_1 @ (kpair @ X2 @ X3) @ (ksnd @ (kpair @ X2 @ X3)))), inference(rw,[status(thm)],[c_0_271, c_0_272])).
15.33/2.44	thf(c_0_275, negated_conjecture, ((ksnd @ (kpair @ esk75_0 @ esk76_0))!=(esk76_0)), inference(split_conjunct,[status(thm)],[c_0_243])).
15.33/2.44	thf(c_0_276, negated_conjecture, ![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3))), inference(spm,[status(thm)],[c_0_273, c_0_274])).
15.33/2.44	thf(c_0_277, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_275, c_0_276])]), ['proof']).
15.33/2.44	# SZS output end CNFRefutation
15.33/2.44	# Parsed axioms                        : 383
15.33/2.44	# Removed by relevancy pruning/SinE    : 0
15.33/2.44	# Initial clauses                      : 541
15.33/2.44	# Removed in clause preprocessing      : 228
15.33/2.44	# Initial clauses in saturation        : 313
15.33/2.44	# Processed clauses                    : 7475
15.33/2.44	# ...of these trivial                  : 255
15.33/2.44	# ...subsumed                          : 4756
15.33/2.44	# ...remaining for further processing  : 2464
15.33/2.44	# Other redundant clauses eliminated   : 204
15.33/2.44	# Clauses deleted for lack of memory   : 0
15.33/2.44	# Backward-subsumed                    : 92
15.33/2.44	# Backward-rewritten                   : 154
15.33/2.44	# Generated clauses                    : 119782
15.33/2.44	# ...of the previous two non-redundant : 103500
15.33/2.44	# ...aggressively subsumed             : 0
15.33/2.44	# Contextual simplify-reflections      : 15
15.33/2.44	# Paramodulations                      : 119412
15.33/2.44	# Factorizations                       : 10
15.33/2.44	# NegExts                              : 121
15.33/2.44	# Equation resolutions                 : 208
15.33/2.44	# Disequality decompositions           : 0
15.33/2.44	# Total rewrite steps                  : 28264
15.33/2.44	# ...of those cached                   : 24931
15.33/2.44	# Propositional unsat checks           : 0
15.33/2.44	#    Propositional check models        : 0
15.33/2.44	#    Propositional check unsatisfiable : 0
15.33/2.44	#    Propositional clauses             : 0
15.33/2.44	#    Propositional clauses after purity: 0
15.33/2.44	#    Propositional unsat core size     : 0
15.33/2.44	#    Propositional preprocessing time  : 0.000
15.33/2.44	#    Propositional encoding time       : 0.000
15.33/2.44	#    Propositional solver time         : 0.000
15.33/2.44	#    Success case prop preproc time    : 0.000
15.33/2.44	#    Success case prop encoding time   : 0.000
15.33/2.44	#    Success case prop solver time     : 0.000
15.33/2.44	# Current number of processed clauses  : 2169
15.33/2.44	#    Positive orientable unit clauses  : 393
15.33/2.44	#    Positive unorientable unit clauses: 1
15.33/2.44	#    Negative unit clauses             : 241
15.33/2.44	#    Non-unit-clauses                  : 1534
15.33/2.44	# Current number of unprocessed clauses: 95233
15.33/2.44	# ...number of literals in the above   : 341656
15.33/2.44	# Current number of archived formulas  : 0
15.33/2.44	# Current number of archived clauses   : 275
15.33/2.44	# Clause-clause subsumption calls (NU) : 243121
15.33/2.44	# Rec. Clause-clause subsumption calls : 147340
15.33/2.44	# Non-unit clause-clause subsumptions  : 3409
15.33/2.44	# Unit Clause-clause subsumption calls : 33672
15.33/2.44	# Rewrite failures with RHS unbound    : 0
15.33/2.44	# BW rewrite match attempts            : 809
15.33/2.44	# BW rewrite match successes           : 98
15.33/2.44	# Condensation attempts                : 7475
15.33/2.44	# Condensation successes               : 104
15.33/2.44	# Termbank termtop insertions          : 2223876
15.33/2.44	# Search garbage collected termcells   : 17228
15.33/2.44	
15.33/2.44	# -------------------------------------------------
15.33/2.44	# User time                : 1.800 s
15.33/2.44	# System time              : 0.063 s
15.33/2.44	# Total time               : 1.863 s
15.33/2.44	# Maximum resident set size: 5864 pages
15.33/2.44	
15.33/2.44	# -------------------------------------------------
15.33/2.44	# User time                : 1.808 s
15.33/2.44	# System time              : 0.067 s
15.33/2.44	# Total time               : 1.875 s
15.33/2.44	# Maximum resident set size: 2200 pages
15.33/2.44	% E---3.1 exiting
15.33/2.44	% E exiting
15.33/2.44	EOF