0.04/0.09	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.09	% Command    : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM
0.09/0.29	% Computer : n001.cluster.edu
0.09/0.29	% Model    : x86_64 x86_64
0.09/0.29	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.29	% Memory   : 8042.1875MB
0.09/0.29	% OS       : Linux 3.10.0-693.el7.x86_64
0.09/0.29	% CPULimit   : 1920
0.09/0.29	% WCLimit    : 240
0.09/0.29	% DateTime   : Wed Jul 30 06:44:49 EDT 2025
0.09/0.29	% CPUTime    : 
0.14/0.39	Running higher-order theorem proving
0.14/0.43	Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p
13.54/2.16	# Version: 3.0.0-ho
13.54/2.16	# Preprocessing class: HSLMSLSSLLLCHFA.
13.54/2.16	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
13.54/2.16	# Starting ehoh_best5 with 240s (1) cores
13.54/2.16	# Starting almost_fo_3_lam with 240s (1) cores
13.54/2.16	# Starting new_bool_5 with 240s (1) cores
13.54/2.16	# Starting pre_casc_3 with 240s (1) cores
13.54/2.16	# Starting ho_unfolding_8 with 240s (1) cores
13.54/2.16	# Starting new_ho_10_cnf2 with 240s (1) cores
13.54/2.16	# Starting new_bool_3 with 240s (1) cores
13.54/2.16	# Starting new_ho_5 with 240s (1) cores
13.54/2.16	# new_bool_3 with pid 20368 completed with status 0
13.54/2.16	# Result found by new_bool_3
13.54/2.16	# Preprocessing class: HSLMSLSSLLLCHFA.
13.54/2.16	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
13.54/2.16	# Starting ehoh_best5 with 240s (1) cores
13.54/2.16	# Starting almost_fo_3_lam with 240s (1) cores
13.54/2.16	# Starting new_bool_5 with 240s (1) cores
13.54/2.16	# Starting pre_casc_3 with 240s (1) cores
13.54/2.16	# Starting ho_unfolding_8 with 240s (1) cores
13.54/2.16	# Starting new_ho_10_cnf2 with 240s (1) cores
13.54/2.16	# Starting new_bool_3 with 240s (1) cores
13.54/2.16	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
13.54/2.16	# Search class: HGHSM-FSLM31-MHFMMSBN
13.54/2.16	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
13.54/2.16	# Starting new_ho_10_cnf2 with 130s (1) cores
13.54/2.16	# new_ho_10_cnf2 with pid 20372 completed with status 0
13.54/2.16	# Result found by new_ho_10_cnf2
13.54/2.16	# Preprocessing class: HSLMSLSSLLLCHFA.
13.54/2.16	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
13.54/2.16	# Starting ehoh_best5 with 240s (1) cores
13.54/2.16	# Starting almost_fo_3_lam with 240s (1) cores
13.54/2.16	# Starting new_bool_5 with 240s (1) cores
13.54/2.16	# Starting pre_casc_3 with 240s (1) cores
13.54/2.16	# Starting ho_unfolding_8 with 240s (1) cores
13.54/2.16	# Starting new_ho_10_cnf2 with 240s (1) cores
13.54/2.16	# Starting new_bool_3 with 240s (1) cores
13.54/2.16	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
13.54/2.16	# Search class: HGHSM-FSLM31-MHFMMSBN
13.54/2.16	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
13.54/2.16	# Starting new_ho_10_cnf2 with 130s (1) cores
13.54/2.16	# Preprocessing time       : 0.005 s
13.54/2.16	# Presaturation interreduction done
13.54/2.16	
13.54/2.16	# Proof found!
13.54/2.16	# SZS status Theorem
13.54/2.16	# SZS output start CNFRefutation
13.54/2.16	thf(decl_23, type, in: $i > $i > $o).
13.54/2.16	thf(decl_24, type, exu: ($i > $o) > $o).
13.54/2.16	thf(decl_25, type, setextAx: $o).
13.54/2.16	thf(decl_26, type, emptyset: $i).
13.54/2.16	thf(decl_27, type, emptysetAx: $o).
13.54/2.16	thf(decl_28, type, setadjoin: $i > $i > $i).
13.54/2.16	thf(decl_29, type, setadjoinAx: $o).
13.54/2.16	thf(decl_30, type, powerset: $i > $i).
13.54/2.16	thf(decl_31, type, powersetAx: $o).
13.54/2.16	thf(decl_32, type, setunion: $i > $i).
13.54/2.16	thf(decl_33, type, setunionAx: $o).
13.54/2.16	thf(decl_34, type, omega: $i).
13.54/2.16	thf(decl_35, type, omega0Ax: $o).
13.54/2.16	thf(decl_36, type, omegaSAx: $o).
13.54/2.16	thf(decl_37, type, omegaIndAx: $o).
13.54/2.16	thf(decl_38, type, replAx: $o).
13.54/2.16	thf(decl_39, type, foundationAx: $o).
13.54/2.16	thf(decl_40, type, wellorderingAx: $o).
13.54/2.16	thf(decl_41, type, descr: ($i > $o) > $i).
13.54/2.16	thf(decl_42, type, descrp: $o).
13.54/2.16	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_44, type, dsetconstrI: $o).
13.54/2.16	thf(decl_45, type, dsetconstrEL: $o).
13.54/2.16	thf(decl_46, type, dsetconstrER: $o).
13.54/2.16	thf(decl_47, type, exuE1: $o).
13.54/2.16	thf(decl_48, type, prop2set: $o > $i).
13.54/2.16	thf(decl_49, type, prop2setE: $o).
13.54/2.16	thf(decl_50, type, emptysetE: $o).
13.54/2.16	thf(decl_51, type, emptysetimpfalse: $o).
13.54/2.16	thf(decl_52, type, notinemptyset: $o).
13.54/2.16	thf(decl_53, type, exuE3e: $o).
13.54/2.16	thf(decl_54, type, setext: $o).
13.54/2.16	thf(decl_55, type, emptyI: $o).
13.54/2.16	thf(decl_56, type, noeltsimpempty: $o).
13.54/2.16	thf(decl_57, type, setbeta: $o).
13.54/2.16	thf(decl_58, type, nonempty: $i > $o).
13.54/2.16	thf(decl_59, type, nonemptyE1: $o).
13.54/2.16	thf(decl_60, type, nonemptyI: $o).
13.54/2.16	thf(decl_61, type, nonemptyI1: $o).
13.54/2.16	thf(decl_62, type, setadjoinIL: $o).
13.54/2.16	thf(decl_63, type, emptyinunitempty: $o).
13.54/2.16	thf(decl_64, type, setadjoinIR: $o).
13.54/2.16	thf(decl_65, type, setadjoinE: $o).
13.54/2.16	thf(decl_66, type, setadjoinOr: $o).
13.54/2.16	thf(decl_67, type, setoftrueEq: $o).
13.54/2.16	thf(decl_68, type, powersetI: $o).
13.54/2.16	thf(decl_69, type, emptyinPowerset: $o).
13.54/2.16	thf(decl_70, type, emptyInPowerset: $o).
13.54/2.16	thf(decl_71, type, powersetE: $o).
13.54/2.16	thf(decl_72, type, setunionI: $o).
13.54/2.16	thf(decl_73, type, setunionE: $o).
13.54/2.16	thf(decl_74, type, subPowSU: $o).
13.54/2.16	thf(decl_75, type, exuE2: $o).
13.54/2.16	thf(decl_76, type, nonemptyImpWitness: $o).
13.54/2.16	thf(decl_77, type, uniqinunit: $o).
13.54/2.16	thf(decl_78, type, notinsingleton: $o).
13.54/2.16	thf(decl_79, type, eqinunit: $o).
13.54/2.16	thf(decl_80, type, singletonsswitch: $o).
13.54/2.16	thf(decl_81, type, upairsetE: $o).
13.54/2.16	thf(decl_82, type, upairsetIL: $o).
13.54/2.16	thf(decl_83, type, upairsetIR: $o).
13.54/2.16	thf(decl_84, type, emptyE1: $o).
13.54/2.16	thf(decl_85, type, vacuousDall: $o).
13.54/2.16	thf(decl_86, type, quantDeMorgan1: $o).
13.54/2.16	thf(decl_87, type, quantDeMorgan2: $o).
13.54/2.16	thf(decl_88, type, quantDeMorgan3: $o).
13.54/2.16	thf(decl_89, type, quantDeMorgan4: $o).
13.54/2.16	thf(decl_90, type, prop2setI: $o).
13.54/2.16	thf(decl_92, type, prop2set2propI: $o).
13.54/2.16	thf(decl_93, type, notdexE: $o).
13.54/2.16	thf(decl_94, type, notdallE: $o).
13.54/2.16	thf(decl_95, type, exuI1: $o).
13.54/2.16	thf(decl_96, type, exuI3: $o).
13.54/2.16	thf(decl_97, type, exuI2: $o).
13.54/2.16	thf(decl_98, type, inCongP: $o).
13.54/2.16	thf(decl_99, type, in__Cong: $o).
13.54/2.16	thf(decl_100, type, exuE3u: $o).
13.54/2.16	thf(decl_101, type, exu__Cong: $o).
13.54/2.16	thf(decl_102, type, emptyset__Cong: $o).
13.54/2.16	thf(decl_103, type, setadjoin__Cong: $o).
13.54/2.16	thf(decl_104, type, powerset__Cong: $o).
13.54/2.16	thf(decl_105, type, setunion__Cong: $o).
13.54/2.16	thf(decl_106, type, omega__Cong: $o).
13.54/2.16	thf(decl_107, type, exuEu: $o).
13.54/2.16	thf(decl_108, type, descr__Cong: $o).
13.54/2.16	thf(decl_109, type, dsetconstr__Cong: $o).
13.54/2.16	thf(decl_110, type, subset: $i > $i > $o).
13.54/2.16	thf(decl_113, type, subsetI1: $o).
13.54/2.16	thf(decl_114, type, eqimpsubset2: $o).
13.54/2.16	thf(decl_115, type, eqimpsubset1: $o).
13.54/2.16	thf(decl_116, type, subsetI2: $o).
13.54/2.16	thf(decl_117, type, emptysetsubset: $o).
13.54/2.16	thf(decl_118, type, subsetE: $o).
13.54/2.16	thf(decl_119, type, subsetE2: $o).
13.54/2.16	thf(decl_120, type, notsubsetI: $o).
13.54/2.16	thf(decl_121, type, notequalI1: $o).
13.54/2.16	thf(decl_122, type, notequalI2: $o).
13.54/2.16	thf(decl_123, type, subsetRefl: $o).
13.54/2.16	thf(decl_124, type, subsetTrans: $o).
13.54/2.16	thf(decl_125, type, setadjoinSub: $o).
13.54/2.16	thf(decl_126, type, setadjoinSub2: $o).
13.54/2.16	thf(decl_127, type, subset2powerset: $o).
13.54/2.16	thf(decl_128, type, setextsub: $o).
13.54/2.16	thf(decl_129, type, subsetemptysetimpeq: $o).
13.54/2.16	thf(decl_130, type, powersetI1: $o).
13.54/2.16	thf(decl_131, type, powersetE1: $o).
13.54/2.16	thf(decl_132, type, inPowerset: $o).
13.54/2.16	thf(decl_133, type, powersetsubset: $o).
13.54/2.16	thf(decl_134, type, sepInPowerset: $o).
13.54/2.16	thf(decl_135, type, sepSubset: $o).
13.54/2.16	thf(decl_136, type, binunion: $i > $i > $i).
13.54/2.16	thf(decl_137, type, binunionIL: $o).
13.54/2.16	thf(decl_138, type, upairset2IR: $o).
13.54/2.16	thf(decl_139, type, binunionIR: $o).
13.54/2.16	thf(decl_140, type, binunionEcases: $o).
13.54/2.16	thf(decl_141, type, binunionE: $o).
13.54/2.16	thf(decl_142, type, binunionLsub: $o).
13.54/2.16	thf(decl_143, type, binunionRsub: $o).
13.54/2.16	thf(decl_144, type, binintersect: $i > $i > $i).
13.54/2.16	thf(decl_145, type, binintersectI: $o).
13.54/2.16	thf(decl_146, type, binintersectSubset5: $o).
13.54/2.16	thf(decl_147, type, binintersectEL: $o).
13.54/2.16	thf(decl_148, type, binintersectLsub: $o).
13.54/2.16	thf(decl_149, type, binintersectSubset2: $o).
13.54/2.16	thf(decl_150, type, binintersectSubset3: $o).
13.54/2.16	thf(decl_151, type, binintersectER: $o).
13.54/2.16	thf(decl_152, type, disjointsetsI1: $o).
13.54/2.16	thf(decl_153, type, binintersectRsub: $o).
13.54/2.16	thf(decl_154, type, binintersectSubset4: $o).
13.54/2.16	thf(decl_155, type, binintersectSubset1: $o).
13.54/2.16	thf(decl_156, type, bs114d: $o).
13.54/2.16	thf(decl_158, type, setminus: $i > $i > $i).
13.54/2.16	thf(decl_159, type, setminusI: $o).
13.54/2.16	thf(decl_160, type, setminusEL: $o).
13.54/2.16	thf(decl_161, type, setminusER: $o).
13.54/2.16	thf(decl_162, type, setminusSubset2: $o).
13.54/2.16	thf(decl_163, type, setminusERneg: $o).
13.54/2.16	thf(decl_164, type, setminusELneg: $o).
13.54/2.16	thf(decl_165, type, setminusILneg: $o).
13.54/2.16	thf(decl_166, type, setminusIRneg: $o).
13.54/2.16	thf(decl_167, type, setminusLsub: $o).
13.54/2.16	thf(decl_168, type, setminusSubset1: $o).
13.54/2.16	thf(decl_169, type, symdiff: $i > $i > $i).
13.54/2.16	thf(decl_170, type, symdiffE: $o).
13.54/2.16	thf(decl_171, type, symdiffI1: $o).
13.54/2.16	thf(decl_172, type, symdiffI2: $o).
13.54/2.16	thf(decl_173, type, symdiffIneg1: $o).
13.54/2.16	thf(decl_174, type, symdiffIneg2: $o).
13.54/2.16	thf(decl_175, type, iskpair: $i > $o).
13.54/2.16	thf(decl_176, type, secondinupair: $o).
13.54/2.16	thf(decl_177, type, setukpairIL: $o).
13.54/2.16	thf(decl_178, type, setukpairIR: $o).
13.54/2.16	thf(decl_179, type, kpairiskpair: $o).
13.54/2.16	thf(decl_180, type, kpair: $i > $i > $i).
13.54/2.16	thf(decl_181, type, kpairp: $o).
13.54/2.16	thf(decl_182, type, cartprod: $i > $i > $i).
13.54/2.16	thf(decl_183, type, singletonsubset: $o).
13.54/2.16	thf(decl_184, type, singletoninpowerset: $o).
13.54/2.16	thf(decl_185, type, singletoninpowunion: $o).
13.54/2.16	thf(decl_186, type, upairset2E: $o).
13.54/2.16	thf(decl_187, type, upairsubunion: $o).
13.54/2.16	thf(decl_188, type, upairinpowunion: $o).
13.54/2.16	thf(decl_189, type, ubforcartprodlem1: $o).
13.54/2.16	thf(decl_190, type, ubforcartprodlem2: $o).
13.54/2.16	thf(decl_191, type, ubforcartprodlem3: $o).
13.54/2.16	thf(decl_192, type, cartprodpairin: $o).
13.54/2.16	thf(decl_193, type, cartprodmempair1: $o).
13.54/2.16	thf(decl_194, type, cartprodmempair: $o).
13.54/2.16	thf(decl_195, type, setunionE2: $o).
13.54/2.16	thf(decl_196, type, setunionsingleton1: $o).
13.54/2.16	thf(decl_197, type, setunionsingleton2: $o).
13.54/2.16	thf(decl_198, type, setunionsingleton: $o).
13.54/2.16	thf(decl_199, type, singleton: $i > $o).
13.54/2.16	thf(decl_200, type, singletonprop: $o).
13.54/2.16	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
13.54/2.16	thf(decl_202, type, ex1E1: $o).
13.54/2.16	thf(decl_203, type, ex1I: $o).
13.54/2.16	thf(decl_204, type, ex1I2: $o).
13.54/2.16	thf(decl_205, type, singletonsuniq: $o).
13.54/2.16	thf(decl_210, type, setukpairinjL1: $o).
13.54/2.16	thf(decl_211, type, kfstsingleton: $o).
13.54/2.16	thf(decl_212, type, theprop: $o).
13.54/2.16	thf(decl_213, type, kfst: $i > $i).
13.54/2.16	thf(decl_214, type, kfstpairEq: $o).
13.54/2.16	thf(decl_215, type, cartprodfstin: $o).
13.54/2.16	thf(decl_216, type, setukpairinjL2: $o).
13.54/2.16	thf(decl_217, type, setukpairinjL: $o).
13.54/2.16	thf(decl_218, type, setukpairinjR11: $o).
13.54/2.16	thf(decl_219, type, setukpairinjR12: $o).
13.54/2.16	thf(decl_220, type, setukpairinjR1: $o).
13.54/2.16	thf(decl_221, type, upairequniteq: $o).
13.54/2.16	thf(decl_222, type, epred1_0: $o).
13.54/2.16	thf(decl_223, type, esk1_2: $i > $i > $i).
13.54/2.16	thf(decl_224, type, esk2_2: $i > $i > $i).
13.54/2.16	thf(decl_225, type, esk3_2: $i > $i > $i).
13.54/2.16	thf(decl_226, type, esk4_1: $i > $i).
13.54/2.16	thf(decl_227, type, esk5_2: ($i > $i > $o) > $i > $i).
13.54/2.16	thf(decl_228, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
13.54/2.16	thf(decl_229, type, esk7_2: ($i > $i > $o) > $i > $i).
13.54/2.16	thf(decl_230, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
13.54/2.16	thf(decl_231, type, esk9_1: $i > $i).
13.54/2.16	thf(decl_232, type, esk10_2: ($i > $o) > $i > $i).
13.54/2.16	thf(decl_233, type, esk11_2: ($i > $o) > $i > $i).
13.54/2.16	thf(decl_234, type, esk12_1: ($i > $o) > $i).
13.54/2.16	thf(decl_235, type, esk13_2: ($i > $o) > $i > $i).
13.54/2.16	thf(decl_236, type, esk14_1: ($i > $o) > $i).
13.54/2.16	thf(decl_237, type, esk15_2: $i > $i > $i).
13.54/2.16	thf(decl_238, type, esk16_2: $i > $i > $i).
13.54/2.16	thf(decl_239, type, esk17_1: $i > $i).
13.54/2.16	thf(decl_240, type, esk18_1: $i > $i).
13.54/2.16	thf(decl_241, type, esk19_1: $i > $i).
13.54/2.16	thf(decl_242, type, esk20_2: $i > $i > $i).
13.54/2.16	thf(decl_243, type, esk21_3: $i > $i > $o > $i).
13.54/2.16	thf(decl_244, type, esk22_2: ($i > $o) > $i > $i).
13.54/2.16	thf(decl_245, type, esk23_1: ($i > $o) > $i).
13.54/2.16	thf(decl_246, type, esk24_1: $i > $i).
13.54/2.16	thf(decl_247, type, esk25_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_248, type, esk26_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_249, type, esk27_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_250, type, esk28_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_251, type, esk29_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_252, type, esk30_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_253, type, esk31_2: ($i > $o) > $i > $i).
13.54/2.16	thf(decl_254, type, esk32_1: ($i > $o) > $i).
13.54/2.16	thf(decl_255, type, esk33_1: ($i > $o) > $i).
13.54/2.16	thf(decl_256, type, esk34_1: ($i > $o) > $i).
13.54/2.16	thf(decl_257, type, esk35_1: ($i > $o) > $i).
13.54/2.16	thf(decl_258, type, esk36_2: ($i > $o) > $i > $i).
13.54/2.16	thf(decl_259, type, esk37_1: ($i > $o) > $i).
13.54/2.16	thf(decl_260, type, esk38_2: ($i > $o) > $i > $i).
13.54/2.16	thf(decl_261, type, esk39_2: ($i > $o) > ($i > $o) > $i).
13.54/2.16	thf(decl_262, type, esk40_2: ($i > $o) > ($i > $o) > $i).
13.54/2.16	thf(decl_263, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
13.54/2.16	thf(decl_264, type, esk42_2: ($i > $o) > ($i > $o) > $i).
13.54/2.16	thf(decl_265, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
13.54/2.16	thf(decl_266, type, esk44_2: ($i > $o) > ($i > $o) > $i).
13.54/2.16	thf(decl_267, type, esk45_2: ($i > $o) > $i > $i).
13.54/2.16	thf(decl_268, type, esk46_2: ($i > $o) > ($i > $o) > $i).
13.54/2.16	thf(decl_269, type, esk47_2: ($i > $o) > ($i > $o) > $i).
13.54/2.16	thf(decl_270, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
13.54/2.16	thf(decl_271, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
13.54/2.16	thf(decl_272, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
13.54/2.16	thf(decl_273, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
13.54/2.16	thf(decl_274, type, esk52_2: $i > $i > $i).
13.54/2.16	thf(decl_275, type, esk53_2: $i > $i > $i).
13.54/2.16	thf(decl_276, type, esk54_2: $i > $i > $i).
13.54/2.16	thf(decl_277, type, esk55_2: $i > $i > $i).
13.54/2.16	thf(decl_278, type, esk56_2: $i > $i > $i).
13.54/2.16	thf(decl_279, type, esk57_2: $i > $i > $i).
13.54/2.16	thf(decl_280, type, esk58_2: $i > $i > $i).
13.54/2.16	thf(decl_281, type, esk59_3: $i > $i > $i > $i).
13.54/2.16	thf(decl_282, type, esk60_3: $i > $i > $i > $i).
13.54/2.16	thf(decl_283, type, esk61_3: $i > $i > $i > $i).
13.54/2.16	thf(decl_284, type, esk62_3: $i > $i > $i > $i).
13.54/2.16	thf(decl_285, type, esk63_2: $i > $i > $i).
13.54/2.16	thf(decl_286, type, esk64_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_287, type, esk65_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_288, type, esk66_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_289, type, esk67_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_290, type, esk68_3: $i > ($i > $o) > $i > $i).
13.54/2.16	thf(decl_291, type, esk69_3: $i > ($i > $o) > $i > $i).
13.54/2.16	thf(decl_292, type, esk70_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_293, type, esk71_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_294, type, esk72_2: $i > ($i > $o) > $i).
13.54/2.16	thf(decl_295, type, esk73_1: $i > $i).
13.54/2.16	thf(decl_296, type, esk74_0: $i).
13.54/2.16	thf(decl_297, type, esk75_0: $i).
13.54/2.16	thf(decl_298, type, esk76_0: $i).
13.54/2.16	thf(decl_299, type, esk77_0: $i).
13.54/2.16	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', ex1)).
13.54/2.16	thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', singleton)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', exuEu)).
13.54/2.16	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', exu)).
13.54/2.16	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', exuI1)).
13.54/2.16	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', nonempty)).
13.54/2.16	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', exuE3u)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', exuE1)).
13.54/2.16	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', exu__Cong)).
13.54/2.16	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', descrp)).
13.54/2.16	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', replAx)).
13.54/2.16	thf(iskpair, axiom, ((iskpair)=(^[X4:$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.LaL3KlXi4I/E---3.1_20284.p', iskpair)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', kpair)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', ex1I)).
13.54/2.16	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', ex1I2)).
13.54/2.16	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', kfstsingleton)).
13.54/2.16	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', ex1E1)).
13.54/2.16	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', singletonprop)).
13.54/2.16	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', descr__Cong)).
13.54/2.16	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', exuI2)).
13.54/2.16	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', exuI3)).
13.54/2.16	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', exuE2)).
13.54/2.16	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', nonemptyI)).
13.54/2.16	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', exuE3e)).
13.54/2.16	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.LaL3KlXi4I/E---3.1_20284.p', emptyE1)).
13.54/2.16	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', nonemptyI1)).
13.54/2.16	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setbeta)).
13.54/2.16	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', dsetconstrER)).
13.54/2.16	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', sepInPowerset)).
13.54/2.16	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', sepSubset)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', kpairiskpair)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', ubforcartprodlem3)).
13.54/2.16	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', theprop)).
13.54/2.16	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', kfstpairEq)).
13.54/2.16	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setukpairinjL)).
13.54/2.16	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', cartprodmempair)).
13.54/2.16	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', cartprodmempair1)).
13.54/2.16	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', cartprodpairin)).
13.54/2.16	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', kpairp)).
13.54/2.16	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', dsetconstr__Cong)).
13.54/2.16	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', nonemptyImpWitness)).
13.54/2.16	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setoftrueEq)).
13.54/2.16	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', nonemptyE1)).
13.54/2.16	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', dsetconstrEL)).
13.54/2.16	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', dsetconstrI)).
13.54/2.16	thf(setukpairinjR2, conjecture, ((((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((((omegaIndAx)=>(((foundationAx)=>((wellorderingAx)=>(((dsetconstrI)=>((dsetconstrEL)=>((((((emptysetimpfalse)=>(((exuE3e)=>(((emptyI)=>((noeltsimpempty)=>(((nonemptyE1)=>((nonemptyI)=>(((setadjoinIL)=>((emptyinunitempty)=>(((((setoftrueEq)=>(((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>(((eqinunit)=>((((upairsetIL)=>((upairsetIR)=>(((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((((exuI3)=>((exuI2)=>(((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>(((setunion__Cong)=>((omega__Cong)=>((((((eqimpsubset2)=>(((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>(((notequalI2)=>((subsetRefl)=>((subsetTrans)=>(((setadjoinSub2)=>((((subsetemptysetimpeq)=>((powersetI1)=>((((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>(((binunionLsub)=>(((binintersectI)=>((((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>(((disjointsetsI1)=>((binintersectRsub)=>((((((setminusEL)=>((setminusER)=>(((((((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((((symdiffIneg2)=>(((((kpairiskpair)=>((((((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>(((((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((((ex1I)=>((ex1I2)=>((((kfstsingleton)=>((theprop)=>((kfstpairEq)=>(((((setukpairinjR11)=>(((setukpairinjR1)=>(![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))<=(upairequniteq)))<=(setukpairinjR12)))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin)))))<=(setukpairinjL1))<=(singletonsuniq))))<=(ex1E1))<=(singletonprop))))))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin))))))))<=(singletoninpowunion))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp)))<=(setukpairIR))<=(setukpairIL))<=(secondinupair)))<=(symdiffIneg1))<=(symdiffI2))))))<=(setminusIRneg))<=(setminusILneg))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2))))<=(setminusI))<=(bs114d))<=(binintersectSubset1))<=(binintersectSubset4))))<=(binintersectER)))))<=(binintersectEL))<=(binintersectSubset5)))<=(binunionRsub)))<=(binunionE)))))))))<=(inPowerset))<=(powersetE1))))<=(setextsub))<=(subset2powerset)))<=(setadjoinSub)))))<=(notequalI1)))))))<=(eqimpsubset1)))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu))))<=(powerset__Cong)))))))<=(inCongP))))<=(exuI1))<=(notdallE))))))))))<=(emptyE1))))<=(upairsetE))<=(singletonsswitch)))<=(notinsingleton)))))))))))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR))))<=(nonemptyI1))))<=(setbeta))))<=(setext)))<=(notinemptyset)))<=(emptysetE))<=(prop2setE))<=(exuE1))<=(dsetconstrER))))<=(descrp))))<=(replAx)))<=(omegaSAx))<=(omega0Ax)))))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setukpairinjR2)).
13.54/2.16	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', subsetE2)).
13.54/2.16	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setextAx)).
13.54/2.16	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', powerset__Cong)).
13.54/2.16	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', inCongP)).
13.54/2.16	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setunion__Cong)).
13.54/2.16	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', notdallE)).
13.54/2.16	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', omega__Cong)).
13.54/2.16	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', upairsetE)).
13.54/2.16	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', singletonsswitch)).
13.54/2.16	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', eqimpsubset2)).
13.54/2.16	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', notinsingleton)).
13.54/2.16	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', powersetI)).
13.54/2.16	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', subsetI2)).
13.54/2.16	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setadjoinOr)).
13.54/2.16	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setadjoinE)).
13.54/2.16	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setadjoinIR)).
13.54/2.16	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', emptysetsubset)).
13.54/2.16	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setext)).
13.54/2.16	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', subsetE)).
13.54/2.16	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', notinemptyset)).
13.54/2.16	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', emptysetE)).
13.54/2.16	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', prop2setE)).
13.54/2.16	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binunionLsub)).
13.54/2.16	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', notsubsetI)).
13.54/2.16	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', omegaSAx)).
13.54/2.16	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', omega0Ax)).
13.54/2.16	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', emptysetAx)).
13.54/2.16	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', notequalI2)).
13.54/2.16	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', subsetRefl)).
13.54/2.16	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', subsetTrans)).
13.54/2.16	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setadjoinSub2)).
13.54/2.16	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', subsetemptysetimpeq)).
13.54/2.16	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', powersetI1)).
13.54/2.16	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', powersetsubset)).
13.54/2.16	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', emptyset__Cong)).
13.54/2.16	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binunionIL)).
13.54/2.16	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', upairset2IR)).
13.54/2.16	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binunionIR)).
13.54/2.16	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binunionEcases)).
13.54/2.16	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', upairequniteq)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', setukpairinjR12)).
13.54/2.16	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binintersectI)).
13.54/2.16	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binintersectLsub)).
13.54/2.16	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binintersectSubset2)).
13.54/2.16	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binintersectSubset3)).
13.54/2.16	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', disjointsetsI1)).
13.54/2.16	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binintersectRsub)).
13.54/2.16	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setminusEL)).
13.54/2.16	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setminusER)).
13.54/2.16	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setminusLsub)).
13.54/2.16	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setminusSubset1)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', setadjoin__Cong)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', symdiffE)).
13.54/2.16	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', symdiffI1)).
13.54/2.16	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', symdiffIneg2)).
13.54/2.16	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', upairset2E)).
13.54/2.16	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', upairsubunion)).
13.54/2.16	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', upairinpowunion)).
13.54/2.16	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', ubforcartprodlem1)).
13.54/2.16	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', ubforcartprodlem2)).
13.54/2.16	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setunionE2)).
13.54/2.16	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setunionsingleton1)).
13.54/2.16	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setunionsingleton2)).
13.54/2.16	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setunionsingleton)).
13.54/2.16	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setukpairinjR11)).
13.54/2.16	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setukpairinjR1)).
13.54/2.16	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setukpairinjL2)).
13.54/2.16	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', cartprodfstin)).
13.54/2.16	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setukpairinjL1)).
13.54/2.16	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', singletonsuniq)).
13.54/2.16	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', singletoninpowunion)).
13.54/2.16	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', singletoninpowerset)).
13.54/2.16	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', singletonsubset)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', setukpairIR)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', setukpairIL)).
13.54/2.16	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', secondinupair)).
13.54/2.16	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', symdiffIneg1)).
13.54/2.16	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', symdiffI2)).
13.54/2.16	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setminusIRneg)).
13.54/2.16	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setminusILneg)).
13.54/2.16	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setminusELneg)).
13.54/2.16	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setminusERneg)).
13.54/2.16	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setminusSubset2)).
13.54/2.16	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setminusI)).
13.54/2.16	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', bs114d)).
13.54/2.16	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binintersectSubset1)).
13.54/2.16	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binintersectSubset4)).
13.54/2.16	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binintersectER)).
13.54/2.16	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binintersectEL)).
13.54/2.16	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binintersectSubset5)).
13.54/2.16	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binunionRsub)).
13.54/2.16	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', binunionE)).
13.54/2.16	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', inPowerset)).
13.54/2.16	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', powersetE1)).
13.54/2.16	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setextsub)).
13.54/2.16	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', subset2powerset)).
13.54/2.16	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setadjoinSub)).
13.54/2.16	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', notequalI1)).
13.54/2.16	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', eqimpsubset1)).
13.54/2.16	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', subsetI1)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', in__Cong)).
13.54/2.16	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', notdexE)).
13.54/2.16	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', prop2setI)).
13.54/2.16	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', quantDeMorgan4)).
13.54/2.16	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', quantDeMorgan3)).
13.54/2.16	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', quantDeMorgan2)).
13.54/2.16	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', quantDeMorgan1)).
13.54/2.16	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', vacuousDall)).
13.54/2.16	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', upairsetIR)).
13.54/2.16	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', upairsetIL)).
13.54/2.16	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', eqinunit)).
13.54/2.16	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', uniqinunit)).
13.54/2.16	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', subPowSU)).
13.54/2.16	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.LaL3KlXi4I/E---3.1_20284.p', setunionE)).
13.54/2.16	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setunionI)).
13.54/2.16	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', powersetE)).
13.54/2.16	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', emptyInPowerset)).
13.54/2.16	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', emptyinPowerset)).
13.54/2.16	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', emptyinunitempty)).
13.54/2.16	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setadjoinIL)).
13.54/2.16	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', noeltsimpempty)).
13.54/2.16	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', emptyI)).
13.54/2.16	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', emptysetimpfalse)).
13.54/2.16	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', wellorderingAx)).
13.54/2.16	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', foundationAx)).
13.54/2.16	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.LaL3KlXi4I/E---3.1_20284.p', omegaIndAx)).
13.54/2.16	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setunionAx)).
13.54/2.16	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', powersetAx)).
13.54/2.16	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LaL3KlXi4I/E---3.1_20284.p', setadjoinAx)).
13.54/2.16	thf(c_0_175, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X520:$i]:(((in @ X520 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X520 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
13.54/2.16	thf(c_0_176, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
13.54/2.16	thf(c_0_177, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
13.54/2.16	thf(c_0_178, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
13.54/2.16	thf(c_0_179, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
13.54/2.16	thf(c_0_180, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
13.54/2.16	thf(c_0_181, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
13.54/2.16	thf(c_0_182, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
13.54/2.16	thf(c_0_183, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
13.54/2.16	thf(c_0_184, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
13.54/2.16	thf(c_0_185, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
13.54/2.16	thf(c_0_186, plain, ((iskpair)=(^[Z0/* 5 */:$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])).
13.54/2.16	thf(c_0_187, plain, ((kpair)=(^[Z0/* 19 */:$i, Z1:$i]:(setadjoin @ (setadjoin @ Z0 @ emptyset) @ (setadjoin @ (setadjoin @ Z0 @ (setadjoin @ Z1 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[kpair])).
13.54/2.16	thf(c_0_188, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
13.54/2.16	thf(c_0_189, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X520:$i]:(((in @ X520 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X520 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_175, c_0_176])).
13.54/2.16	thf(c_0_190, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
13.54/2.16	thf(c_0_191, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
13.54/2.16	thf(c_0_192, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
13.54/2.16	thf(c_0_193, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
13.54/2.16	thf(c_0_194, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
13.54/2.16	thf(c_0_195, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
13.54/2.16	thf(c_0_196, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
13.54/2.16	thf(c_0_197, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
13.54/2.16	thf(c_0_198, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
13.54/2.16	thf(c_0_199, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
13.54/2.16	thf(c_0_200, plain, ((exuEu)=(![X1:$i > $o]:(((?[X507:$i]:((((X1 @ X507))&![X508:$i]:((((X1 @ X508))=>((X507)=(X508)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_177, c_0_178])).
13.54/2.16	thf(c_0_201, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X495:$i]:((((X1 @ X495))&![X496:$i]:((((X1 @ X496))=>((X495)=(X496))))))))))), inference(apply_def,[status(thm)],[c_0_179, c_0_178])).
13.54/2.16	thf(c_0_202, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
13.54/2.16	thf(c_0_203, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_180])).
13.54/2.16	thf(c_0_204, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X501:$i]:((((X1 @ X501))&![X502:$i]:((((X1 @ X502))=>((X501)=(X502)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_181, c_0_178])).
13.54/2.16	thf(c_0_205, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
13.54/2.16	thf(c_0_206, plain, ((exuE1)=(![X1:$i > $o]:(((?[X489:$i]:((((X1 @ X489))&![X490:$i]:((((X1 @ X490))=>((X489)=(X490)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_182, c_0_178])).
13.54/2.16	thf(c_0_207, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
13.54/2.16	thf(c_0_208, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X503:$i]:((((X1 @ X503))&![X504:$i]:((((X1 @ X504))=>((X503)=(X504)))))))<=>(?[X505:$i]:((((X17 @ X505))&![X506:$i]:((((X17 @ X506))=>((X505)=(X506)))))))))))), inference(apply_def,[status(thm)],[c_0_183, c_0_178])).
13.54/2.16	thf(c_0_209, plain, ((descrp)=(![X1:$i > $o]:(((?[X487:$i]:((((X1 @ X487))&![X488:$i]:((((X1 @ X488))=>((X487)=(X488)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_184, c_0_178])).
13.54/2.16	thf(c_0_210, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X485:$i]:((((X6 @ X2 @ X485))&![X486:$i]:((((X6 @ X2 @ X486))=>((X485)=(X486)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_185, c_0_178])).
13.54/2.16	thf(c_0_211, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
13.54/2.16	thf(c_0_212, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
13.54/2.16	thf(c_0_213, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X513:$i]:(((in @ X513 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X514:$i]:(((in @ X514 @ (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 @ X513 @ emptyset) @ (setadjoin @ (setadjoin @ X513 @ (setadjoin @ X514 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_186])).
13.54/2.16	thf(c_0_214, axiom, ((ubforcartprodlem3)=(![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)))))))))), inference(apply_def,[status(thm)],[ubforcartprodlem3, c_0_187])).
13.54/2.16	thf(c_0_215, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X522:$i]:(((in @ X522 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X522 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_188, c_0_189])).
13.54/2.16	thf(c_0_216, 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)))=>(?[X523:$i]:(((in @ X523 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X523 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_190, c_0_189])).
13.54/2.16	thf(c_0_217, plain, ((kfstsingleton)=(![X18:$i]:(((?[X524:$i]:(((in @ X524 @ (setunion @ X18))&?[X525:$i]:(((in @ X525 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X524 @ emptyset) @ (setadjoin @ (setadjoin @ X524 @ (setadjoin @ X525 @ emptyset)) @ emptyset))))))))=>(?[X526:$i]:(((in @ X526 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X526 @ emptyset))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_191, c_0_186]), c_0_176])).
13.54/2.16	thf(c_0_218, axiom, ((theprop)=(![X21:$i]:(((?[X527:$i]:(((in @ X527 @ X21)&((X21)=(setadjoin @ X527 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_176])).
13.54/2.16	thf(c_0_219, axiom, ((kfstpairEq)=(![X2:$i, X3:$i]:(((kfst @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=(X2))))), inference(apply_def,[status(thm)],[kfstpairEq, c_0_187])).
13.54/2.16	thf(c_0_220, axiom, ((setukpairinjL)=(![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14)))))), inference(apply_def,[status(thm)],[setukpairinjL, c_0_187])).
13.54/2.16	thf(c_0_221, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X521:$i]:(((in @ X521 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X521 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_192, c_0_189])).
13.54/2.16	thf(c_0_222, plain, ((singletonprop)=(![X4:$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)))=>(?[X519:$i]:(((in @ X519 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X519 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_193, c_0_176])).
13.54/2.16	thf(c_0_223, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(?[X517:$i]:(((in @ X517 @ (setunion @ X18))&?[X518:$i]:(((in @ X518 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X517 @ emptyset) @ (setadjoin @ (setadjoin @ X517 @ (setadjoin @ X518 @ emptyset)) @ emptyset)))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_186])).
13.54/2.16	thf(c_0_224, axiom, ((cartprodmempair1)=(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[cartprodmempair1, c_0_187])).
13.54/2.16	thf(c_0_225, axiom, ((cartprodpairin)=(![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (cartprod @ X4 @ X5)))))))), inference(apply_def,[status(thm)],[cartprodpairin, c_0_187])).
13.54/2.16	thf(c_0_226, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X515:$i]:(((in @ X515 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X516:$i]:(((in @ X516 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X515 @ emptyset) @ (setadjoin @ (setadjoin @ X515 @ (setadjoin @ X516 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[kpairp, c_0_186]), c_0_187])).
13.54/2.16	thf(c_0_227, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
13.54/2.16	thf(c_0_228, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X509:$i]:((((X1 @ X509))&![X510:$i]:((((X1 @ X510))=>((X509)=(X510)))))))=>((?[X511:$i]:((((X17 @ X511))&![X512:$i]:((((X17 @ X512))=>((X511)=(X512)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_194, c_0_178])).
13.54/2.16	thf(c_0_229, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X499:$i]:((((X1 @ X499))&![X500:$i]:((((X1 @ X500))=>((X499)=(X500))))))))))), inference(apply_def,[status(thm)],[c_0_195, c_0_178])).
13.54/2.16	thf(c_0_230, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X497:$i]:((((X1 @ X497))&![X498:$i]:((((X1 @ X498))=>((X497)=(X498)))))))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_178])).
13.54/2.16	thf(c_0_231, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_180])).
13.54/2.16	thf(c_0_232, plain, ((exuE2)=(![X1:$i > $o]:(((?[X493:$i]:((((X1 @ X493))&![X494:$i]:((((X1 @ X494))=>((X493)=(X494)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_197, c_0_178])).
13.54/2.16	thf(c_0_233, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
13.54/2.16	thf(c_0_234, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_198, c_0_180])).
13.54/2.16	thf(c_0_235, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_180])).
13.54/2.16	thf(c_0_236, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X491:$i]:((((X1 @ X491))&![X492:$i]:((((X1 @ X492))=>((X491)=(X492)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_199, c_0_178])).
13.54/2.16	thf(c_0_237, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
13.54/2.16	thf(c_0_238, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
13.54/2.16	thf(c_0_239, plain, ((epred1_0)<=>![X544:$i]:(?[X545:$i]:((((![X546:$i]:(((in @ X546 @ X545)=>![X547:$i]:(((in @ X547 @ X546)=>(in @ X547 @ X544)))))&![X548:$i, X549:$i]:((((in @ X548 @ X544)&(in @ X549 @ X544))=>(![X550:$i]:(((in @ X550 @ X545)=>((in @ X548 @ X550)<=>(in @ X549 @ X550))))=>((X548)=(X549))))))&![X551:$i, X552:$i]:((((in @ X551 @ X545)&(in @ X552 @ X545))=>(![X553:$i]:(((in @ X553 @ X551)=>(in @ X553 @ X552)))|![X554:$i]:(((in @ X554 @ X552)=>(in @ X554 @ X551)))))))&![X555:$i]:(((![X556:$i]:(((in @ X556 @ X555)=>(in @ X556 @ X544)))&?[X557:$i]:((in @ X557 @ X555)))=>?[X558:$i, X559:$i]:(((((in @ X558 @ X545)&(in @ X559 @ X555))&~(?[X560:$i]:(((in @ X560 @ X558)&(in @ X560 @ X555)))))&![X561:$i]:(((in @ X561 @ X545)=>(![X562:$i]:(((in @ X562 @ X561)=>(in @ X562 @ X558)))|(in @ X559 @ X561)))))))))))), introduced(definition)).
13.54/2.16	thf(c_0_240, negated_conjecture, ~((![X1026:$i, X1027:$i]:((![X1028:$i]:(((in @ X1028 @ X1026)<=>(in @ X1028 @ X1027)))=>((X1026)=(X1027))))=>(![X1025:$i]:(~(in @ X1025 @ emptyset))=>(![X528:$i, X529:$i, X530:$i]:(((in @ X530 @ (setadjoin @ X528 @ X529))<=>(((X530)=(X528))|(in @ X530 @ X529))))=>(![X531:$i, X532:$i]:(((in @ X532 @ (powerset @ X531))<=>![X533:$i]:(((in @ X533 @ X532)=>(in @ X533 @ X531)))))=>(![X534:$i, X535:$i]:(((in @ X535 @ (setunion @ X534))<=>?[X536:$i]:(((in @ X535 @ X536)&(in @ X536 @ X534)))))=>((in @ emptyset @ omega)=>(![X1024:$i]:(((in @ X1024 @ omega)=>(in @ (setadjoin @ X1024 @ X1024) @ omega)))=>(![X537:$i]:((((in @ emptyset @ X537)&![X538:$i]:((((in @ X538 @ omega)&(in @ X538 @ X537))=>(in @ (setadjoin @ X538 @ X538) @ X537))))=>![X539:$i]:(((in @ X539 @ omega)=>(in @ X539 @ X537)))))=>(![X1016:$i > $i > $o, X1017:$i]:((![X1018:$i]:(((in @ X1018 @ X1017)=>?[X1019:$i]:(((X1016 @ X1018 @ X1019)&![X1020:$i]:(((X1016 @ X1018 @ X1020)=>((X1019)=(X1020))))))))=>?[X1021:$i]:(![X1022:$i]:(((in @ X1022 @ X1021)<=>?[X1023:$i]:(((in @ X1023 @ X1017)&(X1016 @ X1023 @ X1022))))))))=>(![X540:$i]:((?[X541:$i]:((in @ X541 @ X540))=>?[X542:$i]:(((in @ X542 @ X540)&~(?[X543:$i]:(((in @ X543 @ X542)&(in @ X543 @ X540))))))))=>((epred1_0)=>(![X1013:$i > $o]:((?[X1014:$i]:(((X1013 @ X1014)&![X1015:$i]:(((X1013 @ X1015)=>((X1014)=(X1015))))))=>(X1013 @ (descr @ (^[Z0/* 17 */:$i]:(X1013 @ Z0))))))=>(![X563:$i, X564:$i > $o, X565:$i]:(((in @ X565 @ X563)=>((X564 @ X565)=>(in @ X565 @ (dsetconstr @ X563 @ X564)))))=>(![X566:$i, X567:$i > $o, X568:$i]:(((in @ X568 @ (dsetconstr @ X566 @ X567))=>(in @ X568 @ X566)))=>(![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:$i]:(((X1005 @ X1009)=>((X1008)=(X1009))))))))=>(![X1003:$o, X1004:$i]:(((in @ X1004 @ (prop2set @ ((X1003))))=>(X1003)))=>(![X1001:$i]:(((in @ X1001 @ emptyset)=>![X1002:$o]:((X1002))))=>(![X569:$i]:(((in @ X569 @ emptyset)=>~($true)))=>(![X1000:$i]:(~(in @ X1000 @ emptyset))=>(![X570:$i > $o]:((?[X571:$i]:(((X570 @ X571)&![X572:$i]:(((X570 @ X572)=>((X571)=(X572))))))=>?[X573:$i]:((X570 @ X573))))=>(![X996:$i, X997:$i]:((![X998:$i]:(((in @ X998 @ X996)=>(in @ X998 @ X997)))=>(![X999:$i]:(((in @ X999 @ X997)=>(in @ X999 @ X996)))=>((X996)=(X997)))))=>(![X574:$i]:((![X575:$i]:(~(in @ X575 @ X574))=>((X574)=(emptyset))))=>(![X576:$i]:((![X577:$i]:(~(in @ X577 @ X576))=>((X576)=(emptyset))))=>(![X993:$i, X994:$i > $o, X995:$i]:(((in @ X995 @ X993)=>((in @ X995 @ (dsetconstr @ X993 @ X994))<=>(X994 @ X995))))=>(![X578:$i]:((((X578)!=(emptyset))=>?[X579:$i]:((in @ X579 @ X578))))=>(![X580:$i, X581:$i > $o, X582:$i]:(((in @ X582 @ X580)=>((X581 @ X582)=>((dsetconstr @ X580 @ X581)!=(emptyset)))))=>(![X991:$i]:((?[X992:$i]:((in @ X992 @ X991))=>((X991)!=(emptyset))))=>(![X583:$i, X584:$i]:((in @ X583 @ (setadjoin @ X583 @ X584)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X988:$i, X989:$i, X990:$i]:(((in @ X990 @ X989)=>(in @ X990 @ (setadjoin @ X988 @ X989))))=>(![X984:$i, X985:$i, X986:$i]:(((in @ X986 @ (setadjoin @ X984 @ X985))=>![X987:$o]:(((((X986)=(X984))=>(X987))=>(((in @ X986 @ X985)=>(X987))=>(X987))))))=>(![X981:$i, X982:$i, X983:$i]:(((in @ X983 @ (setadjoin @ X981 @ X982))=>(((X983)=(X981))|(in @ X983 @ X982))))=>(![X585:$i]:(((dsetconstr @ X585 @ (^[Z0/* 1 */:$i]:($true)))=(X585)))=>(![X978:$i, X979:$i]:((![X980:$i]:(((in @ X980 @ X979)=>(in @ X980 @ X978)))=>(in @ X979 @ (powerset @ X978))))=>(![X586:$i]:((in @ emptyset @ (powerset @ X586)))=>(![X587:$i]:((in @ emptyset @ (powerset @ X587)))=>(![X588:$i, X589:$i, X590:$i]:(((in @ X589 @ (powerset @ X588))=>((in @ X590 @ X589)=>(in @ X590 @ X588))))=>(![X591:$i, X592:$i, X593:$i]:(((in @ X592 @ X593)=>((in @ X593 @ X591)=>(in @ X592 @ (setunion @ X591)))))=>(![X594:$i, X595:$i]:(((in @ X595 @ (setunion @ X594))=>![X596:$o]:((![X597:$i]:(((in @ X595 @ X597)=>((in @ X597 @ X594)=>(X596))))=>(X596)))))=>(![X598:$i, X599:$i]:(((in @ X599 @ X598)=>(in @ X599 @ (powerset @ (setunion @ X598)))))=>(![X600:$i > $o]:((?[X601:$i]:(((X600 @ X601)&![X602:$i]:(((X600 @ X602)=>((X601)=(X602))))))=>?[X603:$i]:(![X604:$i]:(((X600 @ X604)<=>((X604)=(X603)))))))=>(![X605:$i]:((((X605)!=(emptyset))=>?[X606:$i]:(((in @ X606 @ X605)&$true))))=>(![X607:$i, X608:$i]:(((in @ X607 @ (setadjoin @ X608 @ emptyset))=>((X607)=(X608))))=>(![X976:$i, X977:$i]:((((X976)!=(X977))=>~(in @ X977 @ (setadjoin @ X976 @ emptyset))))=>(![X609:$i, X610:$i]:((((X609)=(X610))=>(in @ X609 @ (setadjoin @ X610 @ emptyset))))=>(![X974:$i, X975:$i]:(((in @ X974 @ (setadjoin @ X975 @ emptyset))=>(in @ X975 @ (setadjoin @ X974 @ emptyset))))=>(![X971:$i, X972:$i, X973:$i]:(((in @ X973 @ (setadjoin @ X971 @ (setadjoin @ X972 @ emptyset)))=>(((X973)=(X971))|((X973)=(X972)))))=>(![X611:$i, X612:$i]:((in @ X611 @ (setadjoin @ X611 @ (setadjoin @ X612 @ emptyset))))=>(![X613:$i, X614:$i]:((in @ X614 @ (setadjoin @ X613 @ (setadjoin @ X614 @ emptyset))))=>(![X968:$i, X969:$i > $o]:((?[X970:$i]:(((in @ X970 @ X968)&(X969 @ X970)))=>(((dsetconstr @ X968 @ X969)=(emptyset))=>~($true))))=>(![X615:$i > $o, X616:$i]:(((in @ X616 @ emptyset)=>(X615 @ X616)))=>(![X617:$i, X618:$i > $o]:((~(![X619:$i]:(((in @ X619 @ X617)=>(X618 @ X619))))=>?[X620:$i]:(((in @ X620 @ X617)&~((X618 @ X620))))))=>(![X621:$i, X622:$i > $o]:((![X623:$i]:(((in @ X623 @ X621)=>~((X622 @ X623))))=>~(?[X624:$i]:(((in @ X624 @ X621)&(X622 @ X624))))))=>(![X625:$i, X626:$i > $o]:((~(?[X627:$i]:(((in @ X627 @ X625)&(X626 @ X627))))=>![X628:$i]:(((in @ X628 @ X625)=>~((X626 @ X628))))))=>(![X629:$i, X630:$i > $o]:((?[X631:$i]:(((in @ X631 @ X629)&~((X630 @ X631))))=>~(![X632:$i]:(((in @ X632 @ X629)=>(X630 @ X632))))))=>(![X633:$o]:(((X633)=>(in @ emptyset @ (prop2set @ ((X633))))))=>((prop2set2propI)=>(![X634:$i, X635:$i > $o]:((~(?[X636:$i]:(((in @ X636 @ X634)&(X635 @ X636))))=>![X637:$i]:(((in @ X637 @ X634)=>~((X635 @ X637))))))=>(![X964:$i, X965:$i > $o]:((~(![X966:$i]:(((in @ X966 @ X964)=>(X965 @ X966))))=>?[X967:$i]:(((in @ X967 @ X964)&~((X965 @ X967))))))=>(![X959:$i > $o]:((?[X960:$i]:(((X959 @ X960)&![X961:$i]:(((X959 @ X961)=>((X960)=(X961))))))=>?[X962:$i]:(((X959 @ X962)&![X963:$i]:(((X959 @ X963)=>((X962)=(X963))))))))=>(![X638:$i > $o]:((?[X639:$i]:((X638 @ X639))=>(![X640:$i, X641:$i]:(((X638 @ X640)=>((X638 @ X641)=>((X640)=(X641)))))=>?[X642:$i]:(((X638 @ X642)&![X643:$i]:(((X638 @ X643)=>((X642)=(X643)))))))))=>(![X644:$i > $o]:((?[X645:$i]:(![X646:$i]:(((X644 @ X646)<=>((X646)=(X645)))))=>?[X647:$i]:(((X644 @ X647)&![X648:$i]:(((X644 @ X648)=>((X647)=(X648))))))))=>(![X955:$i, X956:$i]:((((X955)=(X956))=>![X957:$i, X958:$i]:((((X957)=(X958))=>((in @ X957 @ X955)=>(in @ X958 @ X956))))))=>(![X649:$i, X650:$i]:((((X649)=(X650))=>![X651:$i, X652:$i]:((((X651)=(X652))=>((in @ X651 @ X649)<=>(in @ X652 @ X650))))))=>(![X653:$i > $o]:((?[X654:$i]:(((X653 @ X654)&![X655:$i]:(((X653 @ X655)=>((X654)=(X655))))))=>![X656:$i, X657:$i]:(((X653 @ X656)=>((X653 @ X657)=>((X656)=(X657)))))))=>(![X658:$i > $o, X659:$i > $o]:((![X660:$i, X661:$i]:((((X660)=(X661))=>((X658 @ X660)<=>(X659 @ X661))))=>(?[X662:$i]:(((X658 @ X662)&![X663:$i]:(((X658 @ X663)=>((X662)=(X663))))))<=>?[X664:$i]:(((X659 @ X664)&![X665:$i]:(((X659 @ X665)=>((X664)=(X665)))))))))=>(((emptyset)=(emptyset))=>(![X666:$i, X667:$i]:((((X666)=(X667))=>![X668:$i, X669:$i]:((((X668)=(X669))=>((setadjoin @ X666 @ X668)=(setadjoin @ X667 @ X669))))))=>(![X953:$i, X954:$i]:((((X953)=(X954))=>((powerset @ X953)=(powerset @ X954))))=>(![X670:$i, X671:$i]:((((X670)=(X671))=>((setunion @ X670)=(setunion @ X671))))=>(((omega)=(omega))=>(![X948:$i > $o]:((?[X949:$i]:(((X948 @ X949)&![X950:$i]:(((X948 @ X950)=>((X949)=(X950))))))=>![X951:$i, X952:$i]:(((X948 @ X951)=>((X948 @ X952)=>((X951)=(X952)))))))=>(![X940:$i > $o, X941:$i > $o]:((![X942:$i, X943:$i]:((((X942)=(X943))=>((X940 @ X942)<=>(X941 @ X943))))=>(?[X944:$i]:(((X940 @ X944)&![X945:$i]:(((X940 @ X945)=>((X944)=(X945))))))=>(?[X946:$i]:(((X941 @ X946)&![X947:$i]:(((X941 @ X947)=>((X946)=(X947))))))=>((descr @ X940)=(descr @ X941))))))=>(![X934:$i, X935:$i]:((((X934)=(X935))=>![X936:$i > $o, X937:$i > $o]:((![X938:$i]:(((in @ X938 @ X934)=>![X939:$i]:(((in @ X939 @ X935)=>(((X938)=(X939))=>((X936 @ X938)<=>(X937 @ X939)))))))=>((dsetconstr @ X934 @ X936)=(dsetconstr @ X935 @ X937))))))=>(![X931:$i, X932:$i]:((![X933:$i]:(((in @ X933 @ X931)=>(in @ X933 @ X932)))=>(subset @ X931 @ X932)))=>(![X672:$i, X673:$i]:((((X672)=(X673))=>(subset @ X673 @ X672)))=>(![X929:$i, X930:$i]:((((X929)=(X930))=>(subset @ X929 @ X930)))=>(![X674:$i, X675:$i]:((![X676:$i]:(((in @ X676 @ X674)=>(in @ X676 @ X675)))=>(subset @ X674 @ X675)))=>(![X677:$i]:((subset @ emptyset @ X677))=>(![X678:$i, X679:$i, X680:$i]:(((subset @ X678 @ X679)=>((in @ X680 @ X678)=>(in @ X680 @ X679))))=>(![X681:$i, X682:$i, X683:$i]:(((subset @ X681 @ X682)=>(~(in @ X683 @ X682)=>~(in @ X683 @ X681))))=>(![X684:$i, X685:$i, X686:$i]:(((in @ X686 @ X684)=>(~(in @ X686 @ X685)=>~(subset @ X684 @ X685))))=>(![X927:$i, X928:$i]:((~(subset @ X927 @ X928)=>((X927)!=(X928))))=>(![X687:$i, X688:$i, X689:$i]:(((in @ X689 @ X687)=>(~(in @ X689 @ X688)=>((X687)!=(X688)))))=>(![X690:$i]:((subset @ X690 @ X690))=>(![X691:$i, X692:$i, X693:$i]:(((subset @ X691 @ X692)=>((subset @ X692 @ X693)=>(subset @ X691 @ X693))))=>(![X925:$i, X926:$i]:((subset @ X926 @ (setadjoin @ X925 @ X926)))=>(![X694:$i, X695:$i, X696:$i]:(((subset @ X694 @ X696)=>(subset @ X694 @ (setadjoin @ X695 @ X696))))=>(![X923:$i, X924:$i]:(((subset @ X923 @ X924)=>(in @ X923 @ (powerset @ X924))))=>(![X921:$i, X922:$i]:(((subset @ X921 @ X922)=>((subset @ X922 @ X921)=>((X921)=(X922)))))=>(![X697:$i]:(((subset @ X697 @ 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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(assume_negation,[status(cth)],[setukpairinjR2]), subsetE2]), setextAx]), c_0_200]), powerset__Cong]), inCongP]), setunion__Cong]), c_0_201]), notdallE]), omega__Cong]), c_0_202]), upairsetE]), singletonsswitch]), eqimpsubset2]), notinsingleton]), powersetI]), subsetI2]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptysetsubset]), c_0_203]), c_0_204]), c_0_205]), setext]), subsetE]), notinemptyset]), emptysetE]), prop2setE]), binunionLsub]), c_0_206]), c_0_207]), c_0_208]), c_0_209]), notsubsetI]), c_0_210]), omegaSAx]), omega0Ax]), emptysetAx]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub2]), subsetemptysetimpeq]), powersetI1]), powersetsubset]), emptyset__Cong]), c_0_211]), c_0_212]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), upairequniteq]), setukpairinjR12]), binintersectI]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), disjointsetsI1]), binintersectRsub]), setminusEL]), setminusER]), setminusLsub]), setminusSubset1]), setadjoin__Cong]), symdiffE]), symdiffI1]), symdiffIneg2]), c_0_213]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), c_0_214]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_215]), c_0_216]), c_0_217]), c_0_218]), c_0_219]), setukpairinjR11]), setukpairinjR1]), c_0_220]), setukpairinjL2]), cartprodfstin]), setukpairinjL1]), singletonsuniq]), c_0_221]), c_0_222]), c_0_223]), c_0_224]), c_0_225]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), c_0_226]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg1]), symdiffI2]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectER]), binintersectEL]), binintersectSubset5]), binunionRsub]), binunionE]), inPowerset]), powersetE1]), setextsub]), subset2powerset]), setadjoinSub]), notequalI1]), eqimpsubset1]), subsetI1]), c_0_227]), c_0_228]), in__Cong]), c_0_229]), c_0_230]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), upairsetIR]), upairsetIL]), eqinunit]), uniqinunit]), c_0_231]), c_0_232]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), c_0_233]), emptyinunitempty]), setadjoinIL]), c_0_234]), c_0_235]), noeltsimpempty]), emptyI]), c_0_236]), emptysetimpfalse]), c_0_237]), c_0_238]), wellorderingAx]), foundationAx]), omegaIndAx]), setunionAx]), powersetAx]), setadjoinAx])])]), c_0_239])).
13.54/2.16	thf(c_0_241, negated_conjecture, ![X1029:$i, X1030:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1042:$i, X1043:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1051:$i, X1052:$i > $i > $o, X1053:$i, X1055:$i, X1058:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1065:$i, X1066:$i > $o, X1067:$i, X1069:$i, X1070:$i > $o, X1071:$i, X1072:$i, X1073:$i > $o, X1074:$i, X1075:$i, X1076:$i > $o, X1077:$i, X1078:$i > $o, X1079:$i, X1082:$i, X1083:$o, X1084:$i, X1085:$i, X1086:$o, X1087:$i, X1088:$i, X1089:$i > $o, X1090:$i, X1093:$i, X1094:$i, X1097:$i, X1099:$i, X1101:$i, X1102:$i > $o, X1103:$i, X1104:$i, X1106:$i, X1107:$i > $o, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$o, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$o, X1139:$i, X1140:$i, X1141:$i > $o, X1142:$i, X1145:$i, X1146:$i, X1147:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i > $o, X1166:$i, X1167:$i > $o, X1168:$i, X1169:$i, X1170:$i > $o, X1171:$i, X1173:$i, X1174:$i > $o, X1176:$i, X1177:$i, X1178:$i > $o, X1180:$i, X1181:$i, X1182:$i > $o, X1183:$i, X1185:$o, X1186:$i, X1187:$i > $o, X1189:$i, X1190:$i, X1191:$i > $o, X1192:$i, X1194:$i > $o, X1195:$i, X1198:$i, X1199:$i > $o, X1200:$i, X1204:$i, X1205:$i > $o, X1206:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i > $o, X1219:$i, X1221:$i, X1222:$i, X1223:$i > $o, X1224:$i > $o, X1227:$i, X1230:$i, X1231:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i > $o, X1244:$i, X1246:$i, X1247:$i, X1248:$i > $o, X1249:$i > $o, X1252:$i, X1254:$i, X1256:$i, X1257:$i, X1258:$i > $o, X1259:$i > $o, X1262:$i, X1263:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i > $o, X1310:$i, X1311:$i > $o, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$o, X1324:$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, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$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, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$o, 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, X1414:$i, X1415:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$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:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1457:$i, X1458:$i, X1459:$i, X1462:$i, X1463:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i > $o, X1472:$i, X1474:$i, X1475:$i > $o, X1476:$i, X1478:$i, X1479:$i > $o, X1480:$i, X1483:$i, X1484:$i > $o, X1487:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i]:((((~(in @ (esk1_2 @ X1029 @ X1030) @ X1029)|~(in @ (esk1_2 @ X1029 @ X1030) @ X1030)|((X1029)=(X1030)))&((in @ (esk1_2 @ X1029 @ X1030) @ X1029)|(in @ (esk1_2 @ X1029 @ X1030) @ X1030)|((X1029)=(X1030))))&(~(in @ X1032 @ emptyset)&(((~(in @ X1035 @ (setadjoin @ X1033 @ X1034))|(((X1035)=(X1033))|(in @ X1035 @ X1034)))&((((X1035)!=(X1033))|(in @ X1035 @ (setadjoin @ X1033 @ X1034)))&(~(in @ X1035 @ X1034)|(in @ X1035 @ (setadjoin @ X1033 @ X1034)))))&(((~(in @ X1037 @ (powerset @ X1036))|(~(in @ X1038 @ X1037)|(in @ X1038 @ X1036)))&(((in @ (esk2_2 @ X1039 @ X1040) @ X1040)|(in @ X1040 @ (powerset @ X1039)))&(~(in @ (esk2_2 @ X1039 @ X1040) @ X1039)|(in @ X1040 @ (powerset @ X1039)))))&(((((in @ X1043 @ (esk3_2 @ X1042 @ X1043))|~(in @ X1043 @ (setunion @ X1042)))&((in @ (esk3_2 @ X1042 @ X1043) @ X1042)|~(in @ X1043 @ (setunion @ X1042))))&(~(in @ X1046 @ X1047)|~(in @ X1047 @ X1045)|(in @ X1046 @ (setunion @ X1045))))&((in @ emptyset @ omega)&((~(in @ X1048 @ omega)|(in @ (setadjoin @ X1048 @ X1048) @ omega))&(((((in @ (esk4_1 @ X1049) @ omega)|~(in @ emptyset @ X1049)|(~(in @ X1051 @ omega)|(in @ X1051 @ X1049)))&((in @ (esk4_1 @ X1049) @ X1049)|~(in @ emptyset @ X1049)|(~(in @ X1051 @ omega)|(in @ X1051 @ X1049))))&(~(in @ (setadjoin @ (esk4_1 @ X1049) @ (esk4_1 @ X1049)) @ X1049)|~(in @ emptyset @ X1049)|(~(in @ X1051 @ omega)|(in @ X1051 @ X1049))))&((((((in @ (esk8_3 @ X1052 @ X1053 @ X1058) @ X1053)|~(in @ X1058 @ (esk7_2 @ X1052 @ X1053))|(in @ (esk5_2 @ X1052 @ X1053) @ X1053))&((X1052 @ (esk8_3 @ X1052 @ X1053 @ X1058) @ X1058)|~(in @ X1058 @ (esk7_2 @ X1052 @ X1053))|(in @ (esk5_2 @ X1052 @ X1053) @ X1053)))&(~(in @ X1061 @ X1053)|~(X1052 @ X1061 @ X1060)|(in @ X1060 @ (esk7_2 @ X1052 @ X1053))|(in @ (esk5_2 @ X1052 @ X1053) @ X1053)))&(((((in @ (esk8_3 @ X1052 @ X1053 @ X1058) @ X1053)|~(in @ X1058 @ (esk7_2 @ X1052 @ X1053))|((X1052 @ (esk5_2 @ X1052 @ X1053) @ (esk6_3 @ X1052 @ X1053 @ X1055))|~(X1052 @ (esk5_2 @ X1052 @ X1053) @ X1055)))&((X1052 @ (esk8_3 @ X1052 @ X1053 @ X1058) @ X1058)|~(in @ X1058 @ (esk7_2 @ X1052 @ X1053))|((X1052 @ (esk5_2 @ X1052 @ X1053) @ (esk6_3 @ X1052 @ X1053 @ X1055))|~(X1052 @ (esk5_2 @ X1052 @ X1053) @ X1055))))&(~(in @ X1061 @ X1053)|~(X1052 @ X1061 @ X1060)|(in @ X1060 @ (esk7_2 @ X1052 @ X1053))|((X1052 @ (esk5_2 @ X1052 @ X1053) @ (esk6_3 @ X1052 @ X1053 @ X1055))|~(X1052 @ (esk5_2 @ X1052 @ X1053) @ X1055))))&((((in @ (esk8_3 @ X1052 @ X1053 @ X1058) @ X1053)|~(in @ X1058 @ (esk7_2 @ X1052 @ X1053))|(((X1055)!=(esk6_3 @ X1052 @ X1053 @ X1055))|~(X1052 @ (esk5_2 @ X1052 @ X1053) @ X1055)))&((X1052 @ (esk8_3 @ X1052 @ X1053 @ X1058) @ X1058)|~(in @ X1058 @ (esk7_2 @ X1052 @ X1053))|(((X1055)!=(esk6_3 @ X1052 @ X1053 @ X1055))|~(X1052 @ (esk5_2 @ X1052 @ X1053) @ X1055))))&(~(in @ X1061 @ X1053)|~(X1052 @ X1061 @ X1060)|(in @ X1060 @ (esk7_2 @ X1052 @ X1053))|(((X1055)!=(esk6_3 @ X1052 @ X1053 @ X1055))|~(X1052 @ (esk5_2 @ X1052 @ X1053) @ X1055))))))&((((in @ (esk9_1 @ X1062) @ X1062)|~(in @ X1063 @ X1062))&(~(in @ X1065 @ (esk9_1 @ X1062))|~(in @ X1065 @ X1062)|~(in @ X1063 @ X1062)))&((epred1_0)&((((X1066 @ (esk10_2 @ X1066 @ X1067))|~(X1066 @ X1067)|(X1066 @ (descr @ X1066)))&(((X1067)!=(esk10_2 @ X1066 @ X1067))|~(X1066 @ X1067)|(X1066 @ (descr @ X1066))))&((~(in @ X1071 @ X1069)|(~(X1070 @ X1071)|(in @ X1071 @ (dsetconstr @ X1069 @ X1070))))&((~(in @ X1074 @ (dsetconstr @ X1072 @ X1073))|(in @ X1074 @ X1072))&((~(in @ X1077 @ (dsetconstr @ X1075 @ X1076))|(X1076 @ X1077))&(((((X1078 @ (esk12_1 @ X1078))|((X1078 @ 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X1469))|(~(in @ X1472 @ X1468)|~(X1469 @ X1472))|(X1469 @ (esk64_2 @ X1468 @ X1469)))&(((dsetconstr @ X1468 @ X1469)=(setadjoin @ (esk66_2 @ X1468 @ X1469) @ emptyset))|(~(in @ X1472 @ X1468)|~(X1469 @ X1472))|(X1469 @ (esk64_2 @ X1468 @ X1469))))&((((in @ (esk66_2 @ X1468 @ X1469) @ (dsetconstr @ X1468 @ X1469))|(~(in @ X1472 @ X1468)|~(X1469 @ X1472))|(X1469 @ (esk65_2 @ X1468 @ X1469)))&(((dsetconstr @ X1468 @ X1469)=(setadjoin @ (esk66_2 @ X1468 @ X1469) @ emptyset))|(~(in @ X1472 @ X1468)|~(X1469 @ X1472))|(X1469 @ (esk65_2 @ X1468 @ X1469))))&(((in @ (esk66_2 @ X1468 @ X1469) @ (dsetconstr @ X1468 @ X1469))|(~(in @ X1472 @ X1468)|~(X1469 @ X1472))|((esk64_2 @ X1468 @ X1469)!=(esk65_2 @ X1468 @ X1469)))&(((dsetconstr @ X1468 @ X1469)=(setadjoin @ (esk66_2 @ X1468 @ X1469) @ emptyset))|(~(in @ X1472 @ X1468)|~(X1469 @ X1472))|((esk64_2 @ X1468 @ X1469)!=(esk65_2 @ X1468 @ X1469))))))))&((((in @ (esk67_2 @ X1474 @ X1475) @ X1474)|(~(in @ X1476 @ (dsetconstr @ X1474 @ X1475))|((dsetconstr @ X1474 @ X1475)!=(setadjoin @ X1476 @ emptyset))))&((X1475 @ (esk67_2 @ X1474 @ X1475))|(~(in @ X1476 @ (dsetconstr @ X1474 @ X1475))|((dsetconstr @ X1474 @ X1475)!=(setadjoin @ X1476 @ emptyset)))))&(((((in @ (esk69_3 @ X1478 @ X1479 @ X1480) @ (dsetconstr @ X1478 @ X1479))|(in @ (esk68_3 @ X1478 @ X1479 @ X1480) @ X1478)|~(X1479 @ X1480)|~(in @ X1480 @ X1478))&(((dsetconstr @ X1478 @ X1479)=(setadjoin @ (esk69_3 @ X1478 @ X1479 @ X1480) @ emptyset))|(in @ (esk68_3 @ X1478 @ X1479 @ X1480) @ X1478)|~(X1479 @ X1480)|~(in @ X1480 @ X1478)))&((((in @ (esk69_3 @ X1478 @ X1479 @ X1480) @ (dsetconstr @ X1478 @ X1479))|(X1479 @ (esk68_3 @ X1478 @ X1479 @ X1480))|~(X1479 @ X1480)|~(in @ X1480 @ X1478))&(((dsetconstr @ X1478 @ X1479)=(setadjoin @ (esk69_3 @ X1478 @ X1479 @ X1480) @ emptyset))|(X1479 @ (esk68_3 @ X1478 @ X1479 @ X1480))|~(X1479 @ X1480)|~(in @ X1480 @ X1478)))&(((in @ (esk69_3 @ X1478 @ X1479 @ X1480) @ (dsetconstr @ X1478 @ X1479))|((esk68_3 @ X1478 @ X1479 @ X1480)!=(X1480))|~(X1479 @ X1480)|~(in @ X1480 @ X1478))&(((dsetconstr @ X1478 @ X1479)=(setadjoin @ (esk69_3 @ X1478 @ X1479 @ X1480) @ emptyset))|((esk68_3 @ X1478 @ X1479 @ X1480)!=(X1480))|~(X1479 @ X1480)|~(in @ X1480 @ X1478)))))&(((((in @ (esk72_2 @ X1483 @ X1484) @ (dsetconstr @ X1483 @ X1484))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|(in @ (esk70_2 @ X1483 @ X1484) @ X1483))&(((dsetconstr @ X1483 @ X1484)=(setadjoin @ (esk72_2 @ X1483 @ X1484) @ emptyset))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|(in @ (esk70_2 @ X1483 @ X1484) @ X1483)))&((((in @ (esk72_2 @ X1483 @ X1484) @ (dsetconstr @ X1483 @ X1484))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|(in @ (esk71_2 @ X1483 @ X1484) @ X1483))&(((dsetconstr @ X1483 @ X1484)=(setadjoin @ (esk72_2 @ X1483 @ X1484) @ emptyset))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|(in @ (esk71_2 @ X1483 @ X1484) @ X1483)))&((((in @ (esk72_2 @ X1483 @ X1484) @ (dsetconstr @ X1483 @ X1484))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|(X1484 @ (esk70_2 @ X1483 @ X1484)))&(((dsetconstr @ X1483 @ X1484)=(setadjoin @ (esk72_2 @ X1483 @ X1484) @ emptyset))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|(X1484 @ (esk70_2 @ X1483 @ X1484))))&((((in @ (esk72_2 @ X1483 @ X1484) @ (dsetconstr @ X1483 @ X1484))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|(X1484 @ (esk71_2 @ X1483 @ X1484)))&(((dsetconstr @ X1483 @ X1484)=(setadjoin @ (esk72_2 @ X1483 @ X1484) @ emptyset))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|(X1484 @ (esk71_2 @ X1483 @ X1484))))&(((in @ (esk72_2 @ X1483 @ X1484) @ (dsetconstr @ X1483 @ X1484))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|((esk70_2 @ X1483 @ X1484)!=(esk71_2 @ X1483 @ X1484)))&(((dsetconstr @ X1483 @ X1484)=(setadjoin @ (esk72_2 @ X1483 @ X1484) @ emptyset))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|((esk70_2 @ X1483 @ X1484)!=(esk71_2 @ X1483 @ X1484))))))))&((((setadjoin @ X1489 @ emptyset)!=(setadjoin @ X1490 @ emptyset))|((X1489)=(X1490)))&((~(in @ (setadjoin @ X1493 @ emptyset) @ (setadjoin @ (setadjoin @ X1491 @ emptyset) @ (setadjoin @ (setadjoin @ X1491 @ (setadjoin @ X1492 @ emptyset)) @ emptyset)))|((X1491)=(X1493)))&((((in @ (esk73_1 @ X1494) @ (dsetconstr @ (setunion @ X1494) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1494)))))|(~(in @ X1495 @ (setunion @ X1494))|(~(in @ X1496 @ (setunion @ X1494))|((X1494)!=(setadjoin @ (setadjoin @ X1495 @ emptyset) @ (setadjoin @ (setadjoin @ X1495 @ (setadjoin @ X1496 @ emptyset)) @ emptyset))))))&(((dsetconstr @ (setunion @ X1494) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1494))))=(setadjoin @ (esk73_1 @ X1494) @ emptyset))|(~(in @ X1495 @ (setunion @ X1494))|(~(in @ X1496 @ (setunion @ X1494))|((X1494)!=(setadjoin @ (setadjoin @ X1495 @ emptyset) @ (setadjoin @ (setadjoin @ X1495 @ (setadjoin @ X1496 @ emptyset)) @ emptyset)))))))&((~(in @ X1499 @ X1498)|((X1498)!=(setadjoin @ X1499 @ emptyset))|(in @ (setunion @ X1498) @ X1498))&(((kfst @ (setadjoin @ (setadjoin @ X1500 @ emptyset) @ (setadjoin @ (setadjoin @ X1500 @ (setadjoin @ X1501 @ emptyset)) @ emptyset)))=(X1500))&((~(in @ X1504 @ (cartprod @ X1502 @ X1503))|(in @ (kfst @ X1504) @ X1502))&((((setadjoin @ (setadjoin @ X1505 @ emptyset) @ (setadjoin @ (setadjoin @ X1505 @ (setadjoin @ X1506 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1507 @ emptyset) @ (setadjoin @ (setadjoin @ X1507 @ (setadjoin @ X1508 @ emptyset)) @ emptyset)))|((X1505)=(X1507)))&((((setadjoin @ (setadjoin @ X1509 @ emptyset) @ (setadjoin @ (setadjoin @ X1509 @ (setadjoin @ X1510 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1511 @ emptyset) @ (setadjoin @ (setadjoin @ X1511 @ (setadjoin @ X1512 @ emptyset)) @ emptyset)))|((X1509)=(X1511)))&((((X1513)!=(X1514))|((setadjoin @ X1513 @ (setadjoin @ X1514 @ emptyset))=(setadjoin @ X1513 @ emptyset)))&((((X1515)!=(X1516))|((setadjoin @ (setadjoin @ X1515 @ emptyset) @ (setadjoin @ (setadjoin @ X1515 @ (setadjoin @ X1516 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1515 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1517 @ emptyset) @ (setadjoin @ (setadjoin @ X1517 @ (setadjoin @ X1518 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1519 @ emptyset) @ (setadjoin @ (setadjoin @ X1519 @ (setadjoin @ X1520 @ emptyset)) @ emptyset)))|(((X1519)!=(X1520))|((X1518)=(X1520))))&((((setadjoin @ X1521 @ (setadjoin @ X1522 @ emptyset))!=(setadjoin @ X1523 @ emptyset))|((X1521)=(X1522)))&(((setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk74_0 @ (setadjoin @ esk75_0 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset)))&((esk75_0)!=(esk77_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_240])])])])])])])).
13.54/2.16	thf(c_0_242, negated_conjecture, ![X3:$i, X2:$i]:((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_241])).
13.54/2.16	thf(c_0_243, negated_conjecture, ((setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk74_0 @ (setadjoin @ esk75_0 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_241])).
13.54/2.16	thf(c_0_244, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=(X2))), inference(split_conjunct,[status(thm)],[c_0_241])).
13.54/2.16	thf(c_0_245, negated_conjecture, (in @ (setadjoin @ esk74_0 @ (setadjoin @ esk75_0 @ emptyset)) @ (setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset))), inference(spm,[status(thm)],[c_0_242, c_0_243])).
13.54/2.16	thf(c_0_246, negated_conjecture, ((esk74_0)=(esk76_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244, c_0_243]), c_0_244])).
13.54/2.16	thf(c_0_247, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(X3))|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)))))), inference(split_conjunct,[status(thm)],[c_0_241])).
13.54/2.16	thf(c_0_248, negated_conjecture, (in @ (setadjoin @ esk76_0 @ (setadjoin @ esk75_0 @ emptyset)) @ (setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset))), inference(spm,[status(thm)],[c_0_245, c_0_246])).
13.54/2.16	thf(c_0_249, negated_conjecture, (((setadjoin @ esk76_0 @ (setadjoin @ esk75_0 @ emptyset))=(setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)))|((setadjoin @ esk76_0 @ (setadjoin @ esk75_0 @ emptyset))=(setadjoin @ esk76_0 @ emptyset))), inference(spm,[status(thm)],[c_0_247, c_0_248])).
13.54/2.16	thf(c_0_250, negated_conjecture, (((setadjoin @ esk76_0 @ (setadjoin @ esk75_0 @ emptyset))=(setadjoin @ esk76_0 @ emptyset))|(in @ esk75_0 @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)))), inference(spm,[status(thm)],[c_0_242, c_0_249])).
13.54/2.16	thf(c_0_251, negated_conjecture, ((esk75_0)!=(esk77_0)), inference(split_conjunct,[status(thm)],[c_0_241])).
13.54/2.16	thf(c_0_252, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(X3))|((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))!=(setadjoin @ X4 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_241])).
13.54/2.16	thf(c_0_253, negated_conjecture, ![X2:$i, X3:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))|((X2)!=(X3)))), inference(split_conjunct,[status(thm)],[c_0_241])).
13.54/2.16	thf(c_0_254, negated_conjecture, ![X2:$i]:((((X2)=(setadjoin @ esk76_0 @ (setadjoin @ esk75_0 @ emptyset)))|((X2)=(setadjoin @ esk76_0 @ emptyset))|~((in @ X2 @ (setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247, c_0_243]), c_0_246]), c_0_246])).
13.54/2.16	thf(c_0_255, negated_conjecture, ((esk75_0)=(esk76_0)), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_247, c_0_250]), c_0_251]), c_0_252])).
13.54/2.16	thf(c_0_256, negated_conjecture, ![X2:$i]:(((setadjoin @ X2 @ (setadjoin @ X2 @ emptyset))=(setadjoin @ X2 @ emptyset))), inference(er,[status(thm)],[c_0_253])).
13.54/2.16	thf(c_0_257, negated_conjecture, ((setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset))=(setadjoin @ esk76_0 @ emptyset)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254, c_0_242]), c_0_255]), c_0_256])])).
13.54/2.16	thf(c_0_258, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_241])])])).
13.54/2.16	thf(c_0_259, negated_conjecture, (in @ esk77_0 @ (setadjoin @ esk76_0 @ emptyset)), inference(spm,[status(thm)],[c_0_242, c_0_257])).
13.54/2.16	thf(c_0_260, negated_conjecture, ((esk77_0)!=(esk76_0)), inference(rw,[status(thm)],[c_0_251, c_0_255])).
13.54/2.16	thf(c_0_261, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_241])).
13.54/2.16	thf(c_0_262, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_258, c_0_259]), c_0_260]), c_0_261]), ['proof']).
13.54/2.16	# SZS output end CNFRefutation
13.54/2.16	# Parsed axioms                        : 375
13.54/2.16	# Removed by relevancy pruning/SinE    : 200
13.54/2.16	# Initial clauses                      : 327
13.54/2.16	# Removed in clause preprocessing      : 24
13.54/2.16	# Initial clauses in saturation        : 303
13.54/2.16	# Processed clauses                    : 2002
13.54/2.16	# ...of these trivial                  : 38
13.54/2.16	# ...subsumed                          : 620
13.54/2.16	# ...remaining for further processing  : 1344
13.54/2.16	# Other redundant clauses eliminated   : 41
13.54/2.16	# Clauses deleted for lack of memory   : 0
13.54/2.16	# Backward-subsumed                    : 11
13.54/2.16	# Backward-rewritten                   : 40
13.54/2.16	# Generated clauses                    : 65080
13.54/2.16	# ...of the previous two non-redundant : 63942
13.54/2.16	# ...aggressively subsumed             : 0
13.54/2.16	# Contextual simplify-reflections      : 1
13.54/2.16	# Paramodulations                      : 65033
13.54/2.16	# Factorizations                       : 4
13.54/2.16	# NegExts                              : 0
13.54/2.16	# Equation resolutions                 : 43
13.54/2.16	# Disequality decompositions           : 0
13.54/2.16	# Total rewrite steps                  : 5579
13.54/2.16	# ...of those cached                   : 5328
13.54/2.16	# Propositional unsat checks           : 0
13.54/2.16	#    Propositional check models        : 0
13.54/2.16	#    Propositional check unsatisfiable : 0
13.54/2.16	#    Propositional clauses             : 0
13.54/2.16	#    Propositional clauses after purity: 0
13.54/2.16	#    Propositional unsat core size     : 0
13.54/2.16	#    Propositional preprocessing time  : 0.000
13.54/2.16	#    Propositional encoding time       : 0.000
13.54/2.16	#    Propositional solver time         : 0.000
13.54/2.16	#    Success case prop preproc time    : 0.000
13.54/2.16	#    Success case prop encoding time   : 0.000
13.54/2.16	#    Success case prop solver time     : 0.000
13.54/2.16	# Current number of processed clauses  : 1013
13.54/2.16	#    Positive orientable unit clauses  : 75
13.54/2.16	#    Positive unorientable unit clauses: 0
13.54/2.16	#    Negative unit clauses             : 42
13.54/2.16	#    Non-unit-clauses                  : 896
13.54/2.16	# Current number of unprocessed clauses: 62312
13.54/2.16	# ...number of literals in the above   : 230845
13.54/2.16	# Current number of archived formulas  : 0
13.54/2.16	# Current number of archived clauses   : 312
13.54/2.16	# Clause-clause subsumption calls (NU) : 86573
13.54/2.16	# Rec. Clause-clause subsumption calls : 56459
13.54/2.16	# Non-unit clause-clause subsumptions  : 412
13.54/2.16	# Unit Clause-clause subsumption calls : 8362
13.54/2.16	# Rewrite failures with RHS unbound    : 0
13.54/2.16	# BW rewrite match attempts            : 41
13.54/2.16	# BW rewrite match successes           : 13
13.54/2.16	# Condensation attempts                : 2002
13.54/2.16	# Condensation successes               : 16
13.54/2.16	# Termbank termtop insertions          : 1327304
13.54/2.16	# Search garbage collected termcells   : 16822
13.54/2.16	
13.54/2.16	# -------------------------------------------------
13.54/2.16	# User time                : 1.515 s
13.54/2.16	# System time              : 0.058 s
13.54/2.16	# Total time               : 1.574 s
13.54/2.16	# Maximum resident set size: 6212 pages
13.54/2.16	
13.54/2.16	# -------------------------------------------------
13.54/2.16	# User time                : 1.524 s
13.54/2.16	# System time              : 0.062 s
13.54/2.16	# Total time               : 1.586 s
13.54/2.16	# Maximum resident set size: 2216 pages
13.54/2.16	% E exiting
13.54/2.16	% E exiting
13.54/2.16	EOF