0.02/0.08	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.08	% Command    : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM
0.08/0.28	% Computer : n003.cluster.edu
0.08/0.28	% Model    : x86_64 x86_64
0.08/0.28	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.08/0.28	% Memory   : 8042.1875MB
0.08/0.28	% OS       : Linux 3.10.0-693.el7.x86_64
0.08/0.28	% CPULimit   : 1920
0.08/0.28	% WCLimit    : 240
0.08/0.28	% DateTime   : Wed Jul 30 02:53:34 EDT 2025
0.08/0.28	% CPUTime    : 
0.13/0.38	Running higher-order theorem proving
0.13/0.41	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.0NfCQWCtNq/E---3.1_18927.p
980.25/124.10	# Version: 3.0.0-ho
980.25/124.10	# Preprocessing class: HSLMSLSSLLLCHFA.
980.25/124.10	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
980.25/124.10	# Starting ehoh_best5 with 240s (1) cores
980.25/124.10	# Starting almost_fo_3_lam with 240s (1) cores
980.25/124.10	# Starting new_bool_5 with 240s (1) cores
980.25/124.10	# Starting pre_casc_3 with 240s (1) cores
980.25/124.10	# Starting ho_unfolding_8 with 240s (1) cores
980.25/124.10	# Starting new_ho_10_cnf2 with 240s (1) cores
980.25/124.10	# Starting new_bool_3 with 240s (1) cores
980.25/124.10	# Starting new_ho_5 with 240s (1) cores
980.25/124.10	# ho_unfolding_8 with pid 19009 completed with status 0
980.25/124.10	# Result found by ho_unfolding_8
980.25/124.10	# Preprocessing class: HSLMSLSSLLLCHFA.
980.25/124.10	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
980.25/124.10	# Starting ehoh_best5 with 240s (1) cores
980.25/124.10	# Starting almost_fo_3_lam with 240s (1) cores
980.25/124.10	# Starting new_bool_5 with 240s (1) cores
980.25/124.10	# Starting pre_casc_3 with 240s (1) cores
980.25/124.10	# Starting ho_unfolding_8 with 240s (1) cores
980.25/124.10	# No SInE strategy applied
980.25/124.10	# Search class: HGHSM-FSLM31-MHFMMSBN
980.25/124.10	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
980.25/124.10	# Starting new_ho_10_cnf2 with 130s (1) cores
980.25/124.10	# new_ho_10_cnf2 with pid 19020 completed with status 0
980.25/124.10	# Result found by new_ho_10_cnf2
980.25/124.10	# Preprocessing class: HSLMSLSSLLLCHFA.
980.25/124.10	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
980.25/124.10	# Starting ehoh_best5 with 240s (1) cores
980.25/124.10	# Starting almost_fo_3_lam with 240s (1) cores
980.25/124.10	# Starting new_bool_5 with 240s (1) cores
980.25/124.10	# Starting pre_casc_3 with 240s (1) cores
980.25/124.10	# Starting ho_unfolding_8 with 240s (1) cores
980.25/124.10	# No SInE strategy applied
980.25/124.10	# Search class: HGHSM-FSLM31-MHFMMSBN
980.25/124.10	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
980.25/124.10	# Starting new_ho_10_cnf2 with 130s (1) cores
980.25/124.10	# Preprocessing time       : 0.004 s
980.25/124.10	# Presaturation interreduction done
980.25/124.10	
980.25/124.10	# Proof found!
980.25/124.10	# SZS status Theorem
980.25/124.10	# SZS output start CNFRefutation
980.25/124.10	thf(decl_23, type, in: $i > $i > $o).
980.25/124.10	thf(decl_24, type, exu: ($i > $o) > $o).
980.25/124.10	thf(decl_25, type, setextAx: $o).
980.25/124.10	thf(decl_26, type, emptyset: $i).
980.25/124.10	thf(decl_27, type, emptysetAx: $o).
980.25/124.10	thf(decl_28, type, setadjoin: $i > $i > $i).
980.25/124.10	thf(decl_29, type, setadjoinAx: $o).
980.25/124.10	thf(decl_30, type, powerset: $i > $i).
980.25/124.10	thf(decl_31, type, powersetAx: $o).
980.25/124.10	thf(decl_32, type, setunion: $i > $i).
980.25/124.10	thf(decl_33, type, setunionAx: $o).
980.25/124.10	thf(decl_34, type, omega: $i).
980.25/124.10	thf(decl_35, type, omega0Ax: $o).
980.25/124.10	thf(decl_36, type, omegaSAx: $o).
980.25/124.10	thf(decl_37, type, omegaIndAx: $o).
980.25/124.10	thf(decl_38, type, replAx: $o).
980.25/124.10	thf(decl_39, type, foundationAx: $o).
980.25/124.10	thf(decl_40, type, wellorderingAx: $o).
980.25/124.10	thf(decl_41, type, descr: ($i > $o) > $i).
980.25/124.10	thf(decl_42, type, descrp: $o).
980.25/124.10	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
980.25/124.10	thf(decl_44, type, dsetconstrI: $o).
980.25/124.10	thf(decl_45, type, dsetconstrEL: $o).
980.25/124.10	thf(decl_46, type, dsetconstrER: $o).
980.25/124.10	thf(decl_47, type, exuE1: $o).
980.25/124.10	thf(decl_48, type, prop2set: $o > $i).
980.25/124.10	thf(decl_49, type, prop2setE: $o).
980.25/124.10	thf(decl_50, type, emptysetE: $o).
980.25/124.10	thf(decl_51, type, emptysetimpfalse: $o).
980.25/124.10	thf(decl_52, type, notinemptyset: $o).
980.25/124.10	thf(decl_53, type, exuE3e: $o).
980.25/124.10	thf(decl_54, type, setext: $o).
980.25/124.10	thf(decl_55, type, emptyI: $o).
980.25/124.10	thf(decl_56, type, noeltsimpempty: $o).
980.25/124.10	thf(decl_57, type, setbeta: $o).
980.25/124.10	thf(decl_58, type, nonempty: $i > $o).
980.25/124.10	thf(decl_59, type, nonemptyE1: $o).
980.25/124.10	thf(decl_60, type, nonemptyI: $o).
980.25/124.10	thf(decl_61, type, nonemptyI1: $o).
980.25/124.10	thf(decl_62, type, setadjoinIL: $o).
980.25/124.10	thf(decl_63, type, emptyinunitempty: $o).
980.25/124.10	thf(decl_64, type, setadjoinIR: $o).
980.25/124.10	thf(decl_65, type, setadjoinE: $o).
980.25/124.10	thf(decl_66, type, setadjoinOr: $o).
980.25/124.10	thf(decl_67, type, setoftrueEq: $o).
980.25/124.10	thf(decl_68, type, powersetI: $o).
980.25/124.10	thf(decl_69, type, emptyinPowerset: $o).
980.25/124.10	thf(decl_70, type, emptyInPowerset: $o).
980.25/124.10	thf(decl_71, type, powersetE: $o).
980.25/124.10	thf(decl_72, type, setunionI: $o).
980.25/124.10	thf(decl_73, type, setunionE: $o).
980.25/124.10	thf(decl_74, type, subPowSU: $o).
980.25/124.10	thf(decl_75, type, exuE2: $o).
980.25/124.10	thf(decl_76, type, nonemptyImpWitness: $o).
980.25/124.10	thf(decl_77, type, uniqinunit: $o).
980.25/124.10	thf(decl_78, type, notinsingleton: $o).
980.25/124.10	thf(decl_79, type, eqinunit: $o).
980.25/124.10	thf(decl_80, type, singletonsswitch: $o).
980.25/124.10	thf(decl_81, type, upairsetE: $o).
980.25/124.10	thf(decl_82, type, upairsetIL: $o).
980.25/124.10	thf(decl_83, type, upairsetIR: $o).
980.25/124.10	thf(decl_84, type, emptyE1: $o).
980.25/124.10	thf(decl_85, type, vacuousDall: $o).
980.25/124.10	thf(decl_86, type, quantDeMorgan1: $o).
980.25/124.10	thf(decl_87, type, quantDeMorgan2: $o).
980.25/124.10	thf(decl_88, type, quantDeMorgan3: $o).
980.25/124.10	thf(decl_89, type, quantDeMorgan4: $o).
980.25/124.10	thf(decl_90, type, prop2setI: $o).
980.25/124.10	thf(decl_91, type, set2prop: $i > $o).
980.25/124.10	thf(decl_92, type, prop2set2propI: $o).
980.25/124.10	thf(decl_93, type, notdexE: $o).
980.25/124.10	thf(decl_94, type, notdallE: $o).
980.25/124.10	thf(decl_95, type, exuI1: $o).
980.25/124.10	thf(decl_96, type, exuI3: $o).
980.25/124.10	thf(decl_97, type, exuI2: $o).
980.25/124.10	thf(decl_98, type, inCongP: $o).
980.25/124.10	thf(decl_99, type, in__Cong: $o).
980.25/124.10	thf(decl_100, type, exuE3u: $o).
980.25/124.10	thf(decl_101, type, exu__Cong: $o).
980.25/124.10	thf(decl_102, type, emptyset__Cong: $o).
980.25/124.10	thf(decl_103, type, setadjoin__Cong: $o).
980.25/124.10	thf(decl_104, type, powerset__Cong: $o).
980.25/124.10	thf(decl_105, type, setunion__Cong: $o).
980.25/124.10	thf(decl_106, type, omega__Cong: $o).
980.25/124.10	thf(decl_107, type, exuEu: $o).
980.25/124.10	thf(decl_108, type, descr__Cong: $o).
980.25/124.10	thf(decl_109, type, dsetconstr__Cong: $o).
980.25/124.10	thf(decl_110, type, subset: $i > $i > $o).
980.25/124.10	thf(decl_113, type, subsetI1: $o).
980.25/124.10	thf(decl_114, type, eqimpsubset2: $o).
980.25/124.10	thf(decl_115, type, eqimpsubset1: $o).
980.25/124.10	thf(decl_116, type, subsetI2: $o).
980.25/124.10	thf(decl_117, type, emptysetsubset: $o).
980.25/124.10	thf(decl_118, type, subsetE: $o).
980.25/124.10	thf(decl_119, type, subsetE2: $o).
980.25/124.10	thf(decl_120, type, notsubsetI: $o).
980.25/124.10	thf(decl_121, type, notequalI1: $o).
980.25/124.10	thf(decl_122, type, notequalI2: $o).
980.25/124.10	thf(decl_123, type, subsetRefl: $o).
980.25/124.10	thf(decl_124, type, subsetTrans: $o).
980.25/124.10	thf(decl_125, type, setadjoinSub: $o).
980.25/124.10	thf(decl_126, type, setadjoinSub2: $o).
980.25/124.10	thf(decl_127, type, subset2powerset: $o).
980.25/124.10	thf(decl_128, type, setextsub: $o).
980.25/124.10	thf(decl_129, type, subsetemptysetimpeq: $o).
980.25/124.10	thf(decl_130, type, powersetI1: $o).
980.25/124.10	thf(decl_131, type, powersetE1: $o).
980.25/124.10	thf(decl_132, type, inPowerset: $o).
980.25/124.10	thf(decl_133, type, powersetsubset: $o).
980.25/124.10	thf(decl_134, type, sepInPowerset: $o).
980.25/124.10	thf(decl_135, type, sepSubset: $o).
980.25/124.10	thf(decl_136, type, binunion: $i > $i > $i).
980.25/124.10	thf(decl_137, type, binunionIL: $o).
980.25/124.10	thf(decl_138, type, upairset2IR: $o).
980.25/124.10	thf(decl_139, type, binunionIR: $o).
980.25/124.10	thf(decl_140, type, binunionEcases: $o).
980.25/124.10	thf(decl_141, type, binunionE: $o).
980.25/124.10	thf(decl_142, type, binunionLsub: $o).
980.25/124.10	thf(decl_143, type, binunionRsub: $o).
980.25/124.10	thf(decl_144, type, binintersect: $i > $i > $i).
980.25/124.10	thf(decl_145, type, binintersectI: $o).
980.25/124.10	thf(decl_146, type, binintersectSubset5: $o).
980.25/124.10	thf(decl_147, type, binintersectEL: $o).
980.25/124.10	thf(decl_148, type, binintersectLsub: $o).
980.25/124.10	thf(decl_149, type, binintersectSubset2: $o).
980.25/124.10	thf(decl_150, type, binintersectSubset3: $o).
980.25/124.10	thf(decl_151, type, binintersectER: $o).
980.25/124.10	thf(decl_152, type, disjointsetsI1: $o).
980.25/124.10	thf(decl_153, type, binintersectRsub: $o).
980.25/124.10	thf(decl_154, type, binintersectSubset4: $o).
980.25/124.10	thf(decl_155, type, binintersectSubset1: $o).
980.25/124.10	thf(decl_156, type, bs114d: $o).
980.25/124.10	thf(decl_158, type, setminus: $i > $i > $i).
980.25/124.10	thf(decl_159, type, setminusI: $o).
980.25/124.10	thf(decl_160, type, setminusEL: $o).
980.25/124.10	thf(decl_161, type, setminusER: $o).
980.25/124.10	thf(decl_162, type, setminusSubset2: $o).
980.25/124.10	thf(decl_163, type, setminusERneg: $o).
980.25/124.10	thf(decl_164, type, setminusELneg: $o).
980.25/124.10	thf(decl_165, type, setminusILneg: $o).
980.25/124.10	thf(decl_166, type, setminusIRneg: $o).
980.25/124.10	thf(decl_167, type, setminusLsub: $o).
980.25/124.10	thf(decl_168, type, setminusSubset1: $o).
980.25/124.10	thf(decl_169, type, symdiff: $i > $i > $i).
980.25/124.10	thf(decl_170, type, symdiffE: $o).
980.25/124.10	thf(decl_171, type, symdiffI1: $o).
980.25/124.10	thf(decl_172, type, symdiffI2: $o).
980.25/124.10	thf(decl_173, type, symdiffIneg1: $o).
980.25/124.10	thf(decl_174, type, symdiffIneg2: $o).
980.25/124.10	thf(decl_175, type, iskpair: $i > $o).
980.25/124.10	thf(decl_176, type, secondinupair: $o).
980.25/124.10	thf(decl_177, type, setukpairIL: $o).
980.25/124.10	thf(decl_178, type, setukpairIR: $o).
980.25/124.10	thf(decl_179, type, kpairiskpair: $o).
980.25/124.10	thf(decl_180, type, kpair: $i > $i > $i).
980.25/124.10	thf(decl_181, type, kpairp: $o).
980.25/124.10	thf(decl_182, type, cartprod: $i > $i > $i).
980.25/124.10	thf(decl_183, type, singletonsubset: $o).
980.25/124.10	thf(decl_184, type, singletoninpowerset: $o).
980.25/124.10	thf(decl_185, type, singletoninpowunion: $o).
980.25/124.10	thf(decl_186, type, upairset2E: $o).
980.25/124.10	thf(decl_187, type, upairsubunion: $o).
980.25/124.10	thf(decl_188, type, upairinpowunion: $o).
980.25/124.10	thf(decl_189, type, ubforcartprodlem1: $o).
980.25/124.10	thf(decl_190, type, ubforcartprodlem2: $o).
980.25/124.10	thf(decl_191, type, ubforcartprodlem3: $o).
980.25/124.10	thf(decl_192, type, cartprodpairin: $o).
980.25/124.10	thf(decl_193, type, cartprodmempair1: $o).
980.25/124.10	thf(decl_194, type, epred1_0: $o).
980.25/124.10	thf(decl_195, type, esk1_2: $i > $i > $i).
980.25/124.10	thf(decl_196, type, esk2_2: $i > $i > $i).
980.25/124.10	thf(decl_197, type, esk3_2: $i > $i > $i).
980.25/124.10	thf(decl_198, type, esk4_1: $i > $i).
980.25/124.10	thf(decl_199, type, esk5_2: ($i > $i > $o) > $i > $i).
980.25/124.10	thf(decl_200, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
980.25/124.10	thf(decl_201, type, esk7_2: ($i > $i > $o) > $i > $i).
980.25/124.10	thf(decl_202, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
980.25/124.10	thf(decl_203, type, esk9_1: $i > $i).
980.25/124.10	thf(decl_204, type, esk10_2: ($i > $o) > $i > $i).
980.25/124.10	thf(decl_205, type, esk11_2: ($i > $o) > $i > $i).
980.25/124.10	thf(decl_206, type, esk12_1: ($i > $o) > $i).
980.25/124.10	thf(decl_207, type, esk13_2: ($i > $o) > $i > $i).
980.25/124.10	thf(decl_208, type, esk14_1: ($i > $o) > $i).
980.25/124.10	thf(decl_209, type, esk15_2: $i > $i > $i).
980.25/124.10	thf(decl_210, type, esk16_2: $i > $i > $i).
980.25/124.10	thf(decl_211, type, esk17_1: $i > $i).
980.25/124.10	thf(decl_212, type, esk18_1: $i > $i).
980.25/124.10	thf(decl_213, type, esk19_1: $i > $i).
980.25/124.10	thf(decl_214, type, esk20_2: $i > $i > $i).
980.25/124.10	thf(decl_215, type, esk21_3: $i > $i > $o > $i).
980.25/124.10	thf(decl_216, type, esk22_2: ($i > $o) > $i > $i).
980.25/124.10	thf(decl_217, type, esk23_1: ($i > $o) > $i).
980.25/124.10	thf(decl_218, type, esk24_1: $i > $i).
980.25/124.10	thf(decl_219, type, esk25_2: $i > ($i > $o) > $i).
980.25/124.10	thf(decl_220, type, esk26_2: $i > ($i > $o) > $i).
980.25/124.10	thf(decl_221, type, esk27_2: $i > ($i > $o) > $i).
980.25/124.10	thf(decl_222, type, esk28_2: $i > ($i > $o) > $i).
980.25/124.10	thf(decl_223, type, esk29_2: $i > ($i > $o) > $i).
980.25/124.10	thf(decl_224, type, esk30_2: $i > ($i > $o) > $i).
980.25/124.10	thf(decl_225, type, esk31_2: ($i > $o) > $i > $i).
980.25/124.10	thf(decl_226, type, esk32_1: ($i > $o) > $i).
980.25/124.10	thf(decl_227, type, esk33_1: ($i > $o) > $i).
980.25/124.10	thf(decl_228, type, esk34_1: ($i > $o) > $i).
980.25/124.10	thf(decl_229, type, esk35_1: ($i > $o) > $i).
980.25/124.10	thf(decl_230, type, esk36_2: ($i > $o) > $i > $i).
980.25/124.10	thf(decl_231, type, esk37_1: ($i > $o) > $i).
980.25/124.10	thf(decl_232, type, esk38_2: ($i > $o) > $i > $i).
980.25/124.10	thf(decl_233, type, esk39_2: ($i > $o) > ($i > $o) > $i).
980.25/124.10	thf(decl_234, type, esk40_2: ($i > $o) > ($i > $o) > $i).
980.25/124.10	thf(decl_235, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
980.25/124.10	thf(decl_236, type, esk42_2: ($i > $o) > ($i > $o) > $i).
980.25/124.10	thf(decl_237, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
980.25/124.10	thf(decl_238, type, esk44_2: ($i > $o) > ($i > $o) > $i).
980.25/124.10	thf(decl_239, type, esk45_2: ($i > $o) > $i > $i).
980.25/124.10	thf(decl_240, type, esk46_2: ($i > $o) > ($i > $o) > $i).
980.25/124.10	thf(decl_241, type, esk47_2: ($i > $o) > ($i > $o) > $i).
980.25/124.10	thf(decl_242, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
980.25/124.10	thf(decl_243, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
980.25/124.10	thf(decl_244, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
980.25/124.10	thf(decl_245, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
980.25/124.10	thf(decl_246, type, esk52_2: $i > $i > $i).
980.25/124.10	thf(decl_247, type, esk53_2: $i > $i > $i).
980.25/124.10	thf(decl_248, type, esk54_2: $i > $i > $i).
980.25/124.10	thf(decl_249, type, esk55_2: $i > $i > $i).
980.25/124.10	thf(decl_250, type, esk56_2: $i > $i > $i).
980.25/124.10	thf(decl_251, type, esk57_2: $i > $i > $i).
980.25/124.10	thf(decl_252, type, esk58_2: $i > $i > $i).
980.25/124.10	thf(decl_253, type, esk59_3: $i > $i > $i > $i).
980.25/124.10	thf(decl_254, type, esk60_3: $i > $i > $i > $i).
980.25/124.10	thf(decl_255, type, esk61_0: $i).
980.25/124.10	thf(decl_256, type, esk62_0: $i).
980.25/124.10	thf(decl_257, type, esk63_0: $i).
980.25/124.10	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', replAx)).
980.25/124.10	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', exu)).
980.25/124.10	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', descrp)).
980.25/124.10	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', exuE1)).
980.25/124.10	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', exuE3e)).
980.25/124.10	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', nonempty)).
980.25/124.10	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', nonemptyI)).
980.25/124.10	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', exuE2)).
980.25/124.10	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.0NfCQWCtNq/E---3.1_18927.p', exuI1)).
980.25/124.10	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', exuI3)).
980.25/124.10	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', exuI2)).
980.25/124.10	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.0NfCQWCtNq/E---3.1_18927.p', exuE3u)).
980.25/124.10	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', exu__Cong)).
980.25/124.10	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', exuEu)).
980.25/124.10	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', descr__Cong)).
980.25/124.10	thf(iskpair, axiom, ((iskpair)=(^[X4:$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.0NfCQWCtNq/E---3.1_18927.p', iskpair)).
980.25/124.10	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', dsetconstrI)).
980.25/124.10	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', dsetconstrEL)).
980.25/124.10	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', dsetconstrER)).
980.25/124.10	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setbeta)).
980.25/124.10	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', nonemptyE1)).
980.25/124.10	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', nonemptyI1)).
980.25/124.10	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setoftrueEq)).
980.25/124.10	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', nonemptyImpWitness)).
980.25/124.10	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.0NfCQWCtNq/E---3.1_18927.p', emptyE1)).
980.25/124.10	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', dsetconstr__Cong)).
980.25/124.10	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', sepInPowerset)).
980.25/124.10	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', sepSubset)).
980.25/124.10	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.0NfCQWCtNq/E---3.1_18927.p', kpairiskpair)).
980.25/124.10	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', kpairp)).
980.25/124.10	thf(cartprodmempair, conjecture, (((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>(((omegaSAx)=>(((((wellorderingAx)=>(((dsetconstrI)=>(((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((((exuE3e)=>((setext)=>((emptyI)=>(((setbeta)=>(((nonemptyI)=>((nonemptyI1)=>((((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>(((emptyInPowerset)=>((((setunionE)=>(((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>(((eqinunit)=>(((((((((((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>(((((exuI2)=>((inCongP)=>((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>(((powerset__Cong)=>(((((descr__Cong)=>(((subsetI1)=>(((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>((((subsetRefl)=>((((((setextsub)=>(((((inPowerset)=>((((sepSubset)=>(((upairset2IR)=>((((binunionE)=>(((((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>(((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>(((((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>(((((((secondinupair)=>((((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>(((upairsubunion)=>((upairinpowunion)=>((((((cartprodmempair1)=>![X4:$i, X5:$i, X18:$i]:(((iskpair @ X18)<=(in @ X18 @ (cartprod @ X4 @ X5)))))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2))<=(ubforcartprodlem1))))<=(upairset2E)))))))<=(setukpairIR))<=(setukpairIL)))<=(symdiffIneg2))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1))<=(symdiffE))))))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2)))))))))<=(disjointsetsI1))))))))<=(binintersectI))<=(binunionRsub))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR)))<=(binunionIL)))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1))<=(powersetI1))<=(subsetemptysetimpeq)))<=(subset2powerset))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans)))<=(notequalI2))<=(notequalI1))))<=(subsetE)))))<=(eqimpsubset2)))<=(dsetconstr__Cong)))<=(exuEu))<=(omega__Cong))<=(setunion__Cong)))<=(setadjoin__Cong))))<=(exuE3u)))))<=(exuI3))<=(exuI1))<=(notdallE)))<=(prop2set2propI))))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch)))<=(notinsingleton)))))<=(subPowSU)))<=(setunionI))<=(powersetE)))<=(emptyinPowerset)))))))<=(emptyinunitempty))<=(setadjoinIL))))<=(nonemptyE1)))<=(noeltsimpempty)))))<=(notinemptyset))<=(emptysetimpfalse))))))<=(dsetconstrEL)))<=(descrp)))<=(foundationAx))<=(replAx))<=(omegaIndAx)))<=(omega0Ax))))))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', cartprodmempair)).
980.25/124.10	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setextAx)).
980.25/124.10	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', emptysetAx)).
980.25/124.10	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setadjoinAx)).
980.25/124.10	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', powersetAx)).
980.25/124.10	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setunionAx)).
980.25/124.10	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', omega0Ax)).
980.25/124.10	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', omegaSAx)).
980.25/124.10	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.0NfCQWCtNq/E---3.1_18927.p', omegaIndAx)).
980.25/124.10	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.0NfCQWCtNq/E---3.1_18927.p', foundationAx)).
980.25/124.10	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', wellorderingAx)).
980.25/124.10	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', prop2setE)).
980.25/124.10	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', emptysetE)).
980.25/124.10	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', emptysetimpfalse)).
980.25/124.10	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', notinemptyset)).
980.25/124.10	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.0NfCQWCtNq/E---3.1_18927.p', setext)).
980.25/124.10	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', emptyI)).
980.25/124.10	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', noeltsimpempty)).
980.25/124.10	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setadjoinIL)).
980.25/124.10	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', emptyinunitempty)).
980.25/124.10	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setadjoinIR)).
980.25/124.10	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setadjoinE)).
980.25/124.10	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setadjoinOr)).
980.25/124.10	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', powersetI)).
980.25/124.10	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', emptyinPowerset)).
980.25/124.10	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', emptyInPowerset)).
980.25/124.10	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', powersetE)).
980.25/124.10	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setunionI)).
980.25/124.10	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setunionE)).
980.25/124.10	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', subPowSU)).
980.25/124.10	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', uniqinunit)).
980.25/124.10	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', notinsingleton)).
980.25/124.10	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', eqinunit)).
980.25/124.10	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', singletonsswitch)).
980.25/124.10	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', upairsetE)).
980.25/124.10	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', upairsetIL)).
980.25/124.10	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', upairsetIR)).
980.25/124.10	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', vacuousDall)).
980.25/124.10	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', quantDeMorgan1)).
980.25/124.10	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', quantDeMorgan2)).
980.25/124.10	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', quantDeMorgan3)).
980.25/124.10	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', quantDeMorgan4)).
980.25/124.10	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', prop2setI)).
980.25/124.10	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', prop2set2propI)).
980.25/124.10	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', notdexE)).
980.25/124.10	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', notdallE)).
980.25/124.10	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', inCongP)).
980.25/124.10	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', in__Cong)).
980.25/124.10	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', emptyset__Cong)).
980.25/124.10	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setadjoin__Cong)).
980.25/124.10	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', powerset__Cong)).
980.25/124.10	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setunion__Cong)).
980.25/124.10	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', omega__Cong)).
980.25/124.10	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', subsetI1)).
980.25/124.10	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', eqimpsubset2)).
980.25/124.10	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', eqimpsubset1)).
980.25/124.10	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', subsetI2)).
980.25/124.10	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', emptysetsubset)).
980.25/124.10	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', subsetE)).
980.25/124.10	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', subsetE2)).
980.25/124.10	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', notsubsetI)).
980.25/124.10	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', notequalI1)).
980.25/124.10	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', notequalI2)).
980.25/124.10	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', subsetRefl)).
980.25/124.10	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', subsetTrans)).
980.25/124.10	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setadjoinSub)).
980.25/124.10	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setadjoinSub2)).
980.25/124.10	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', subset2powerset)).
980.25/124.10	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setextsub)).
980.25/124.10	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', subsetemptysetimpeq)).
980.25/124.10	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', powersetI1)).
980.25/124.10	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', powersetE1)).
980.25/124.10	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', inPowerset)).
980.25/124.10	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', powersetsubset)).
980.25/124.10	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binunionIL)).
980.25/124.10	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', upairset2IR)).
980.25/124.10	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binunionIR)).
980.25/124.10	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binunionEcases)).
980.25/124.10	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binunionE)).
980.25/124.10	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binunionLsub)).
980.25/124.10	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binunionRsub)).
980.25/124.10	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binintersectI)).
980.25/124.10	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binintersectSubset5)).
980.25/124.10	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binintersectEL)).
980.25/124.10	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binintersectLsub)).
980.25/124.10	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binintersectSubset2)).
980.25/124.10	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binintersectSubset3)).
980.25/124.10	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binintersectER)).
980.25/124.10	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', disjointsetsI1)).
980.25/124.10	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binintersectRsub)).
980.25/124.10	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binintersectSubset4)).
980.25/124.10	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', binintersectSubset1)).
980.25/124.10	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', bs114d)).
980.25/124.10	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setminusI)).
980.25/124.10	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setminusEL)).
980.25/124.10	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setminusER)).
980.25/124.10	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setminusSubset2)).
980.25/124.10	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setminusERneg)).
980.25/124.10	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setminusELneg)).
980.25/124.10	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setminusILneg)).
980.25/124.10	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setminusIRneg)).
980.25/124.10	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setminusLsub)).
980.25/124.10	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setminusSubset1)).
980.25/124.10	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', symdiffE)).
980.25/124.10	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', symdiffI1)).
980.25/124.10	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', symdiffI2)).
980.25/124.10	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', symdiffIneg1)).
980.25/124.10	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', symdiffIneg2)).
980.25/124.10	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', secondinupair)).
980.25/124.10	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setukpairIL)).
980.25/124.10	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', setukpairIR)).
980.25/124.10	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', singletonsubset)).
980.25/124.10	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', singletoninpowerset)).
980.25/124.10	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', singletoninpowunion)).
980.25/124.10	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', upairset2E)).
980.25/124.10	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', upairsubunion)).
980.25/124.10	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', upairinpowunion)).
980.25/124.10	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', ubforcartprodlem1)).
980.25/124.10	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', ubforcartprodlem2)).
980.25/124.10	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', ubforcartprodlem3)).
980.25/124.10	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0NfCQWCtNq/E---3.1_18927.p', cartprodpairin)).
980.25/124.10	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.0NfCQWCtNq/E---3.1_18927.p', cartprodmempair1)).
980.25/124.10	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.0NfCQWCtNq/E---3.1_18927.p', kpair)).
980.25/124.10	thf(c_0_153, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
980.25/124.10	thf(c_0_154, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
980.25/124.10	thf(c_0_155, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
980.25/124.10	thf(c_0_156, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
980.25/124.10	thf(c_0_157, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
980.25/124.10	thf(c_0_158, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
980.25/124.10	thf(c_0_159, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
980.25/124.10	thf(c_0_160, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
980.25/124.10	thf(c_0_161, 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])).
980.25/124.10	thf(c_0_162, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
980.25/124.10	thf(c_0_163, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
980.25/124.10	thf(c_0_164, 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])).
980.25/124.10	thf(c_0_165, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
980.25/124.10	thf(c_0_166, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
980.25/124.10	thf(c_0_167, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
980.25/124.10	thf(c_0_168, plain, ((iskpair)=(^[Z0/* 5 */:$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])).
980.25/124.10	thf(c_0_169, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X427:$i]:((((X6 @ X2 @ X427))&![X428:$i]:((((X6 @ X2 @ X428))=>((X427)=(X428)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_153, c_0_154])).
980.25/124.10	thf(c_0_170, plain, ((descrp)=(![X1:$i > $o]:(((?[X429:$i]:((((X1 @ X429))&![X430:$i]:((((X1 @ X430))=>((X429)=(X430)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_155, c_0_154])).
980.25/124.10	thf(c_0_171, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
980.25/124.10	thf(c_0_172, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
980.25/124.10	thf(c_0_173, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
980.25/124.10	thf(c_0_174, plain, ((exuE1)=(![X1:$i > $o]:(((?[X431:$i]:((((X1 @ X431))&![X432:$i]:((((X1 @ X432))=>((X431)=(X432)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_156, c_0_154])).
980.25/124.10	thf(c_0_175, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X433:$i]:((((X1 @ X433))&![X434:$i]:((((X1 @ X434))=>((X433)=(X434)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_157, c_0_154])).
980.25/124.10	thf(c_0_176, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
980.25/124.10	thf(c_0_177, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_158])).
980.25/124.10	thf(c_0_178, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_159, c_0_158])).
980.25/124.10	thf(c_0_179, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_158])).
980.25/124.10	thf(c_0_180, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
980.25/124.10	thf(c_0_181, plain, ((exuE2)=(![X1:$i > $o]:(((?[X435:$i]:((((X1 @ X435))&![X436:$i]:((((X1 @ X436))=>((X435)=(X436)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_160, c_0_154])).
980.25/124.10	thf(c_0_182, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_158])).
980.25/124.10	thf(c_0_183, 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])).
980.25/124.10	thf(c_0_184, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X437:$i]:((((X1 @ X437))&![X438:$i]:((((X1 @ X438))=>((X437)=(X438))))))))))), inference(apply_def,[status(thm)],[c_0_161, c_0_154])).
980.25/124.10	thf(c_0_185, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X439:$i]:((((X1 @ X439))&![X440:$i]:((((X1 @ X440))=>((X439)=(X440)))))))))))), inference(apply_def,[status(thm)],[c_0_162, c_0_154])).
980.25/124.10	thf(c_0_186, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X441:$i]:((((X1 @ X441))&![X442:$i]:((((X1 @ X442))=>((X441)=(X442))))))))))), inference(apply_def,[status(thm)],[c_0_163, c_0_154])).
980.25/124.10	thf(c_0_187, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X443:$i]:((((X1 @ X443))&![X444:$i]:((((X1 @ X444))=>((X443)=(X444)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_164, c_0_154])).
980.25/124.10	thf(c_0_188, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X445:$i]:((((X1 @ X445))&![X446:$i]:((((X1 @ X446))=>((X445)=(X446)))))))<=>(?[X447:$i]:((((X17 @ X447))&![X448:$i]:((((X17 @ X448))=>((X447)=(X448)))))))))))), inference(apply_def,[status(thm)],[c_0_165, c_0_154])).
980.25/124.10	thf(c_0_189, plain, ((exuEu)=(![X1:$i > $o]:(((?[X449:$i]:((((X1 @ X449))&![X450:$i]:((((X1 @ X450))=>((X449)=(X450)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_166, c_0_154])).
980.25/124.10	thf(c_0_190, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X451:$i]:((((X1 @ X451))&![X452:$i]:((((X1 @ X452))=>((X451)=(X452)))))))=>((?[X453:$i]:((((X17 @ X453))&![X454:$i]:((((X17 @ X454))=>((X453)=(X454)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_167, c_0_154])).
980.25/124.10	thf(c_0_191, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
980.25/124.10	thf(c_0_192, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
980.25/124.10	thf(c_0_193, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
980.25/124.10	thf(c_0_194, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X455:$i]:(((in @ X455 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X456:$i]:(((in @ X456 @ (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 @ X455 @ emptyset) @ (setadjoin @ (setadjoin @ X455 @ (setadjoin @ X456 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_168])).
980.25/124.10	thf(c_0_195, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X457:$i]:(((in @ X457 @ (setunion @ (kpair @ X2 @ X3)))&?[X458:$i]:(((in @ X458 @ (setunion @ (kpair @ X2 @ X3)))&((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X457 @ emptyset) @ (setadjoin @ (setadjoin @ X457 @ (setadjoin @ X458 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_168])).
980.25/124.10	thf(c_0_196, plain, ((epred1_0)<=>![X470:$i]:(?[X471:$i]:((((![X472:$i]:(((in @ X472 @ X471)=>![X473:$i]:(((in @ X473 @ X472)=>(in @ X473 @ X470)))))&![X474:$i, X475:$i]:((((in @ X474 @ X470)&(in @ X475 @ X470))=>(![X476:$i]:(((in @ X476 @ X471)=>((in @ X474 @ X476)<=>(in @ X475 @ X476))))=>((X474)=(X475))))))&![X477:$i, X478:$i]:((((in @ X477 @ X471)&(in @ X478 @ X471))=>(![X479:$i]:(((in @ X479 @ X477)=>(in @ X479 @ X478)))|![X480:$i]:(((in @ X480 @ X478)=>(in @ X480 @ X477)))))))&![X481:$i]:(((![X482:$i]:(((in @ X482 @ X481)=>(in @ X482 @ X470)))&?[X483:$i]:((in @ X483 @ X481)))=>?[X484:$i, X485:$i]:(((((in @ X484 @ X471)&(in @ X485 @ X481))&~(?[X486:$i]:(((in @ X486 @ X484)&(in @ X486 @ X481)))))&![X487:$i]:(((in @ X487 @ X471)=>(![X488:$i]:(((in @ X488 @ X487)=>(in @ X488 @ X484)))|(in @ X485 @ X487)))))))))))), introduced(definition)).
980.25/124.10	thf(c_0_197, negated_conjecture, ~((![X893:$i, X894:$i]:((![X895:$i]:(((in @ X895 @ X893)<=>(in @ X895 @ X894)))=>((X893)=(X894))))=>(![X459:$i]:(~(in @ X459 @ emptyset))=>(![X460:$i, X461:$i, X462:$i]:(((in @ X462 @ (setadjoin @ X460 @ X461))<=>(((X462)=(X460))|(in @ X462 @ X461))))=>(![X463:$i, X464:$i]:(((in @ X464 @ (powerset @ X463))<=>![X465:$i]:(((in @ X465 @ X464)=>(in @ X465 @ X463)))))=>(![X466:$i, X467:$i]:(((in @ X467 @ (setunion @ X466))<=>?[X468:$i]:(((in @ X467 @ X468)&(in @ X468 @ X466)))))=>((in @ emptyset @ omega)=>(![X469:$i]:(((in @ X469 @ omega)=>(in @ (setadjoin @ X469 @ X469) @ omega)))=>(![X890:$i]:((((in @ emptyset @ X890)&![X891:$i]:((((in @ X891 @ omega)&(in @ X891 @ X890))=>(in @ (setadjoin @ X891 @ X891) @ X890))))=>![X892:$i]:(((in @ X892 @ omega)=>(in @ X892 @ X890)))))=>(![X882:$i > $i > $o, X883:$i]:((![X884:$i]:(((in @ X884 @ X883)=>?[X885:$i]:(((X882 @ X884 @ X885)&![X886:$i]:(((X882 @ X884 @ X886)=>((X885)=(X886))))))))=>?[X887:$i]:(![X888:$i]:(((in @ X888 @ X887)<=>?[X889:$i]:(((in @ X889 @ X883)&(X882 @ X889 @ X888))))))))=>(![X878:$i]:((?[X879:$i]:((in @ X879 @ X878))=>?[X880:$i]:(((in @ X880 @ X878)&~(?[X881:$i]:(((in @ X881 @ X880)&(in @ X881 @ X878))))))))=>((epred1_0)=>(![X875:$i > $o]:((?[X876:$i]:(((X875 @ X876)&![X877:$i]:(((X875 @ X877)=>((X876)=(X877))))))=>(X875 @ (descr @ (^[Z0/* 17 */:$i]:(X875 @ Z0))))))=>(![X489:$i, X490:$i > $o, X491:$i]:(((in @ X491 @ X489)=>((X490 @ X491)=>(in @ X491 @ (dsetconstr @ X489 @ X490)))))=>(![X872:$i, X873:$i > $o, X874:$i]:(((in @ X874 @ (dsetconstr @ X872 @ X873))=>(in @ X874 @ X872)))=>(![X492:$i, X493:$i > $o, X494:$i]:(((in @ X494 @ (dsetconstr @ X492 @ X493))=>(X493 @ X494)))=>(![X495:$i > $o]:((?[X496:$i]:(((X495 @ X496)&![X497:$i]:(((X495 @ X497)=>((X496)=(X497))))))=>?[X498:$i]:(((X495 @ X498)&![X499:$i]:(((X495 @ X499)=>((X498)=(X499))))))))=>(![X500:$o, X501:$i]:(((in @ X501 @ (prop2set @ ((X500))))=>(X500)))=>(![X502:$i]:(((in @ X502 @ emptyset)=>![X503:$o]:((X503))))=>(![X871:$i]:(((in @ X871 @ emptyset)=>~($true)))=>(![X870:$i]:(~(in @ X870 @ emptyset))=>(![X504:$i > $o]:((?[X505:$i]:(((X504 @ X505)&![X506:$i]:(((X504 @ X506)=>((X505)=(X506))))))=>?[X507:$i]:((X504 @ X507))))=>(![X508:$i, X509:$i]:((![X510:$i]:(((in @ X510 @ X508)=>(in @ X510 @ X509)))=>(![X511:$i]:(((in @ X511 @ X509)=>(in @ X511 @ X508)))=>((X508)=(X509)))))=>(![X512:$i]:((![X513:$i]:(~(in @ X513 @ X512))=>((X512)=(emptyset))))=>(![X868:$i]:((![X869:$i]:(~(in @ X869 @ X868))=>((X868)=(emptyset))))=>(![X514:$i, X515:$i > $o, X516:$i]:(((in @ X516 @ X514)=>((in @ X516 @ (dsetconstr @ X514 @ X515))<=>(X515 @ X516))))=>(![X866:$i]:((((X866)!=(emptyset))=>?[X867:$i]:((in @ X867 @ X866))))=>(![X517:$i, X518:$i > $o, X519:$i]:(((in @ X519 @ X517)=>((X518 @ X519)=>((dsetconstr @ X517 @ X518)!=(emptyset)))))=>(![X520:$i]:((?[X521:$i]:((in @ X521 @ X520))=>((X520)!=(emptyset))))=>(![X864:$i, X865:$i]:((in @ X864 @ (setadjoin @ X864 @ X865)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X522:$i, X523:$i, X524:$i]:(((in @ X524 @ X523)=>(in @ X524 @ (setadjoin @ X522 @ X523))))=>(![X525:$i, X526:$i, X527:$i]:(((in @ X527 @ (setadjoin @ X525 @ X526))=>![X528:$o]:(((((X527)=(X525))=>(X528))=>(((in @ X527 @ X526)=>(X528))=>(X528))))))=>(![X529:$i, X530:$i, X531:$i]:(((in @ X531 @ (setadjoin @ X529 @ X530))=>(((X531)=(X529))|(in @ X531 @ X530))))=>(![X532:$i]:(((dsetconstr @ X532 @ (^[Z0/* 1 */:$i]:($true)))=(X532)))=>(![X533:$i, X534:$i]:((![X535:$i]:(((in @ X535 @ X534)=>(in @ X535 @ X533)))=>(in @ X534 @ (powerset @ X533))))=>(![X863:$i]:((in @ emptyset @ (powerset @ X863)))=>(![X536:$i]:((in @ emptyset @ (powerset @ X536)))=>(![X860:$i, X861:$i, X862:$i]:(((in @ X861 @ (powerset @ X860))=>((in @ X862 @ X861)=>(in @ X862 @ X860))))=>(![X857:$i, X858:$i, X859:$i]:(((in @ X858 @ X859)=>((in @ X859 @ X857)=>(in @ X858 @ (setunion @ X857)))))=>(![X537:$i, X538:$i]:(((in @ X538 @ (setunion @ X537))=>![X539:$o]:((![X540:$i]:(((in @ X538 @ X540)=>((in @ X540 @ X537)=>(X539))))=>(X539)))))=>(![X855:$i, X856:$i]:(((in @ X856 @ X855)=>(in @ X856 @ (powerset @ (setunion @ X855)))))=>(![X541:$i > $o]:((?[X542:$i]:(((X541 @ X542)&![X543:$i]:(((X541 @ X543)=>((X542)=(X543))))))=>?[X544:$i]:(![X545:$i]:(((X541 @ X545)<=>((X545)=(X544)))))))=>(![X546:$i]:((((X546)!=(emptyset))=>?[X547:$i]:(((in @ X547 @ X546)&$true))))=>(![X548:$i, X549:$i]:(((in @ X548 @ (setadjoin @ X549 @ emptyset))=>((X548)=(X549))))=>(![X853:$i, X854:$i]:((((X853)!=(X854))=>~(in @ X854 @ (setadjoin @ X853 @ emptyset))))=>(![X550:$i, X551:$i]:((((X550)=(X551))=>(in @ X550 @ (setadjoin @ X551 @ emptyset))))=>(![X851:$i, X852:$i]:(((in @ X851 @ (setadjoin @ X852 @ emptyset))=>(in @ X852 @ (setadjoin @ X851 @ emptyset))))=>(![X848:$i, X849:$i, X850:$i]:(((in @ X850 @ (setadjoin @ X848 @ (setadjoin @ X849 @ emptyset)))=>(((X850)=(X848))|((X850)=(X849)))))=>(![X846:$i, X847:$i]:((in @ X846 @ (setadjoin @ X846 @ (setadjoin @ X847 @ emptyset))))=>(![X844:$i, X845:$i]:((in @ X845 @ (setadjoin @ X844 @ (setadjoin @ X845 @ emptyset))))=>(![X841:$i, X842:$i > $o]:((?[X843:$i]:(((in @ X843 @ X841)&(X842 @ X843)))=>(((dsetconstr @ X841 @ X842)=(emptyset))=>~($true))))=>(![X839:$i > $o, X840:$i]:(((in @ X840 @ emptyset)=>(X839 @ X840)))=>(![X835:$i, X836:$i > $o]:((~(![X837:$i]:(((in @ X837 @ X835)=>(X836 @ X837))))=>?[X838:$i]:(((in @ X838 @ X835)&~((X836 @ X838))))))=>(![X831:$i, X832:$i > $o]:((![X833:$i]:(((in @ X833 @ X831)=>~((X832 @ X833))))=>~(?[X834:$i]:(((in @ X834 @ X831)&(X832 @ X834))))))=>(![X827:$i, X828:$i > $o]:((~(?[X829:$i]:(((in @ X829 @ X827)&(X828 @ X829))))=>![X830:$i]:(((in @ X830 @ X827)=>~((X828 @ X830))))))=>(![X552:$i, X553:$i > $o]:((?[X554:$i]:(((in @ X554 @ X552)&~((X553 @ X554))))=>~(![X555:$i]:(((in @ X555 @ X552)=>(X553 @ X555))))))=>(![X556:$o]:(((X556)=>(in @ emptyset @ (prop2set @ ((X556))))))=>(![X826:$o]:(((X826)=>(set2prop @ (prop2set @ ((X826))))))=>(![X557:$i, X558:$i > $o]:((~(?[X559:$i]:(((in @ X559 @ X557)&(X558 @ X559))))=>![X560:$i]:(((in @ X560 @ X557)=>~((X558 @ X560))))))=>(![X822:$i, X823:$i > $o]:((~(![X824:$i]:(((in @ X824 @ X822)=>(X823 @ X824))))=>?[X825:$i]:(((in @ X825 @ X822)&~((X823 @ X825))))))=>(![X817:$i > $o]:((?[X818:$i]:(((X817 @ X818)&![X819:$i]:(((X817 @ X819)=>((X818)=(X819))))))=>?[X820:$i]:(((X817 @ X820)&![X821:$i]:(((X817 @ X821)=>((X820)=(X821))))))))=>(![X811:$i > $o]:((?[X812:$i]:((X811 @ X812))=>(![X813:$i, X814:$i]:(((X811 @ X813)=>((X811 @ X814)=>((X813)=(X814)))))=>?[X815:$i]:(((X811 @ X815)&![X816:$i]:(((X811 @ X816)=>((X815)=(X816)))))))))=>(![X561:$i > $o]:((?[X562:$i]:(![X563:$i]:(((X561 @ X563)<=>((X563)=(X562)))))=>?[X564:$i]:(((X561 @ X564)&![X565:$i]:(((X561 @ X565)=>((X564)=(X565))))))))=>(![X566:$i, X567:$i]:((((X566)=(X567))=>![X568:$i, X569:$i]:((((X568)=(X569))=>((in @ X568 @ X566)=>(in @ X569 @ X567))))))=>(![X570:$i, X571:$i]:((((X570)=(X571))=>![X572:$i, X573:$i]:((((X572)=(X573))=>((in @ X572 @ X570)<=>(in @ X573 @ X571))))))=>(![X806:$i > $o]:((?[X807:$i]:(((X806 @ X807)&![X808:$i]:(((X806 @ X808)=>((X807)=(X808))))))=>![X809:$i, X810:$i]:(((X806 @ X809)=>((X806 @ X810)=>((X809)=(X810)))))))=>(![X574:$i > $o, X575:$i > $o]:((![X576:$i, X577:$i]:((((X576)=(X577))=>((X574 @ X576)<=>(X575 @ X577))))=>(?[X578:$i]:(((X574 @ X578)&![X579:$i]:(((X574 @ X579)=>((X578)=(X579))))))<=>?[X580:$i]:(((X575 @ X580)&![X581:$i]:(((X575 @ X581)=>((X580)=(X581)))))))))=>(((emptyset)=(emptyset))=>(![X802:$i, X803:$i]:((((X802)=(X803))=>![X804:$i, X805:$i]:((((X804)=(X805))=>((setadjoin @ X802 @ X804)=(setadjoin @ X803 @ X805))))))=>(![X582:$i, X583:$i]:((((X582)=(X583))=>((powerset @ X582)=(powerset @ X583))))=>(![X800:$i, X801:$i]:((((X800)=(X801))=>((setunion @ X800)=(setunion @ X801))))=>(((omega)=(omega))=>(![X795:$i > $o]:((?[X796:$i]:(((X795 @ X796)&![X797:$i]:(((X795 @ X797)=>((X796)=(X797))))))=>![X798:$i, X799:$i]:(((X795 @ X798)=>((X795 @ X799)=>((X798)=(X799)))))))=>(![X584:$i > $o, X585:$i > $o]:((![X586:$i, X587:$i]:((((X586)=(X587))=>((X584 @ X586)<=>(X585 @ X587))))=>(?[X588:$i]:(((X584 @ X588)&![X589:$i]:(((X584 @ X589)=>((X588)=(X589))))))=>(?[X590:$i]:(((X585 @ X590)&![X591:$i]:(((X585 @ X591)=>((X590)=(X591))))))=>((descr @ X584)=(descr @ X585))))))=>(![X789:$i, X790:$i]:((((X789)=(X790))=>![X791:$i > $o, X792:$i > $o]:((![X793:$i]:(((in @ X793 @ X789)=>![X794:$i]:(((in @ X794 @ X790)=>(((X793)=(X794))=>((X791 @ X793)<=>(X792 @ X794)))))))=>((dsetconstr @ X789 @ X791)=(dsetconstr @ X790 @ X792))))))=>(![X592:$i, X593:$i]:((![X594:$i]:(((in @ X594 @ X592)=>(in @ X594 @ X593)))=>(subset @ X592 @ X593)))=>(![X787:$i, X788:$i]:((((X787)=(X788))=>(subset @ X788 @ X787)))=>(![X595:$i, X596:$i]:((((X595)=(X596))=>(subset @ X595 @ X596)))=>(![X597:$i, X598:$i]:((![X599:$i]:(((in @ X599 @ X597)=>(in @ X599 @ X598)))=>(subset @ X597 @ X598)))=>(![X600:$i]:((subset @ emptyset @ X600))=>(![X784:$i, X785:$i, X786:$i]:(((subset @ X784 @ X785)=>((in @ X786 @ X784)=>(in @ X786 @ X785))))=>(![X601:$i, X602:$i, X603:$i]:(((subset @ X601 @ X602)=>(~(in @ X603 @ X602)=>~(in @ X603 @ X601))))=>(![X604:$i, X605:$i, X606:$i]:(((in @ X606 @ X604)=>(~(in @ X606 @ X605)=>~(subset @ X604 @ X605))))=>(![X782:$i, X783:$i]:((~(subset @ X782 @ X783)=>((X782)!=(X783))))=>(![X779:$i, X780:$i, X781:$i]:(((in @ X781 @ X779)=>(~(in @ X781 @ X780)=>((X779)!=(X780)))))=>(![X607:$i]:((subset @ X607 @ X607))=>(![X776:$i, X777:$i, X778:$i]:(((subset @ X776 @ X777)=>((subset @ X777 @ X778)=>(subset @ X776 @ X778))))=>(![X774:$i, X775:$i]:((subset @ X775 @ (setadjoin @ X774 @ X775)))=>(![X771:$i, X772:$i, X773:$i]:(((subset @ X771 @ X773)=>(subset @ X771 @ (setadjoin @ X772 @ X773))))=>(![X769:$i, X770:$i]:(((subset @ X769 @ X770)=>(in @ X769 @ (powerset @ X770))))=>(![X608:$i, X609:$i]:(((subset @ X608 @ X609)=>((subset @ X609 @ X608)=>((X608)=(X609)))))=>(![X768:$i]:(((subset @ X768 @ emptyset)=>((X768)=(emptyset))))=>(![X766:$i, X767:$i]:(((subset @ X767 @ X766)=>(in @ X767 @ (powerset @ X766))))=>(![X764:$i, X765:$i]:(((in @ X765 @ (powerset @ X764))=>(subset @ X765 @ X764)))=>(![X610:$i]:((in @ X610 @ (powerset @ X610)))=>(![X762:$i, X763:$i]:(((subset @ X762 @ X763)=>(subset @ (powerset @ X762) @ (powerset @ X763))))=>(![X760:$i, X761:$i > $o]:((in @ (dsetconstr @ X760 @ X761) @ (powerset @ X760)))=>(![X611:$i, X612:$i > $o]:((subset @ (dsetconstr @ X611 @ X612) @ X611))=>(![X757:$i, X758:$i, X759:$i]:(((in @ X759 @ X757)=>(in @ X759 @ (binunion @ X757 @ X758))))=>(![X613:$i, X614:$i]:((in @ X614 @ (setadjoin @ X613 @ (setadjoin @ X614 @ emptyset))))=>(![X754:$i, X755:$i, X756:$i]:(((in @ X756 @ X755)=>(in @ X756 @ (binunion @ X754 @ X755))))=>(![X750:$i, X751:$i, X752:$i, X753:$o]:(((in @ X752 @ (binunion @ X750 @ X751))=>(((in @ X752 @ X750)=>(X753))=>(((in @ X752 @ X751)=>(X753))=>(X753)))))=>(![X615:$i, X616:$i, X617:$i]:(((in @ X617 @ (binunion @ X615 @ X616))=>((in @ X617 @ X615)|(in @ X617 @ X616))))=>(![X748:$i, X749:$i]:((subset @ X748 @ (binunion @ X748 @ X749)))=>(![X746:$i, X747:$i]:((subset @ X747 @ (binunion @ X746 @ X747)))=>(![X743:$i, X744:$i, X745:$i]:(((in @ X745 @ X743)=>((in @ X745 @ X744)=>(in @ X745 @ (binintersect @ X743 @ X744)))))=>(![X618:$i, X619:$i, X620:$i]:(((subset @ X620 @ X618)=>((subset @ X620 @ X619)=>(subset @ X620 @ (binintersect @ X618 @ X619)))))=>(![X621:$i, X622:$i, X623:$i]:(((in @ X623 @ (binintersect @ X621 @ X622))=>(in @ X623 @ X621)))=>(![X624:$i, X625:$i]:((subset @ (binintersect @ X624 @ X625) @ X624))=>(![X626:$i, X627:$i]:(((subset @ X626 @ X627)=>((binintersect @ X626 @ X627)=(X626))))=>(![X628:$i, X629:$i]:((((binintersect @ X628 @ X629)=(X629))=>(subset @ X629 @ X628)))=>(![X630:$i, X631:$i, X632:$i]:(((in @ X632 @ (binintersect @ X630 @ X631))=>(in @ X632 @ X631)))=>(![X740:$i, X741:$i]:((~(?[X742:$i]:(((in @ X742 @ X740)&(in @ X742 @ X741))))=>((binintersect @ X740 @ X741)=(emptyset))))=>(![X633:$i, X634:$i]:((subset @ (binintersect @ X633 @ X634) @ X634))=>(![X635:$i, X636:$i]:(((subset @ X636 @ X635)=>((binintersect @ X635 @ X636)=(X636))))=>(![X637:$i, X638:$i]:((((binintersect @ X637 @ X638)=(X637))=>(subset @ X637 @ X638)))=>(![X639:$i, X640:$i, X641:$i]:(((binintersect @ X639 @ (binunion @ X640 @ X641))=(binunion @ (binintersect @ X639 @ X640) @ (binintersect @ X639 @ X641))))=>(![X642:$i, X643:$i, X644:$i]:(((in @ X644 @ X642)=>(~(in @ X644 @ X643)=>(in @ X644 @ (setminus @ X642 @ X643)))))=>(![X645:$i, X646:$i, X647:$i]:(((in @ X647 @ (setminus @ X645 @ X646))=>(in @ X647 @ X645)))=>(![X648:$i, X649:$i, X650:$i]:(((in @ X650 @ (setminus @ X648 @ X649))=>~(in @ X650 @ X649)))=>(![X738:$i, X739:$i]:(((subset @ X738 @ X739)=>((setminus @ X738 @ X739)=(emptyset))))=>(![X735:$i, X736:$i, X737:$i]:((~(in @ X737 @ (setminus @ X735 @ X736))=>((in @ X737 @ X735)=>(in @ X737 @ X736))))=>(![X732:$i, X733:$i, X734:$i]:((~(in @ X734 @ (setminus @ X732 @ X733))=>(~(in @ X734 @ X733)=>~(in @ X734 @ X732))))=>(![X651:$i, X652:$i, X653:$i]:((~(in @ X653 @ X651)=>~(in @ X653 @ (setminus @ X651 @ X652))))=>(![X654:$i, X655:$i, X656:$i]:(((in @ X656 @ X655)=>~(in @ X656 @ (setminus @ X654 @ X655))))=>(![X657:$i, X658:$i]:((subset @ (setminus @ X657 @ X658) @ X657))=>(![X659:$i, X660:$i]:((((setminus @ X659 @ X660)=(emptyset))=>(subset @ X659 @ X660)))=>(![X728:$i, X729:$i, X730:$i]:(((in @ X730 @ (symdiff @ X728 @ X729))=>![X731:$o]:((((in @ X730 @ X728)=>(~(in @ X730 @ X729)=>(X731)))=>((~(in @ X730 @ X728)=>((in @ X730 @ X729)=>(X731)))=>(X731))))))=>(![X725:$i, X726:$i, X727:$i]:(((in @ X727 @ X725)=>(~(in @ X727 @ X726)=>(in @ X727 @ (symdiff @ X725 @ X726)))))=>(![X722:$i, X723:$i, X724:$i]:((~(in @ X724 @ X722)=>((in @ X724 @ X723)=>(in @ X724 @ (symdiff @ X722 @ X723)))))=>(![X719:$i, X720:$i, X721:$i]:(((in @ X721 @ X719)=>((in @ X721 @ X720)=>~(in @ X721 @ (symdiff @ X719 @ X720)))))=>(![X716:$i, X717:$i, X718:$i]:((~(in @ X718 @ X716)=>(~(in @ X718 @ X717)=>~(in @ X718 @ (symdiff @ X716 @ X717)))))=>(![X661:$i, X662:$i]:((in @ X662 @ (setadjoin @ X661 @ (setadjoin @ X662 @ emptyset))))=>(![X714:$i, X715:$i]:((in @ X714 @ (setunion @ (setadjoin @ (setadjoin @ X714 @ emptyset) @ (setadjoin @ (setadjoin @ X714 @ (setadjoin @ X715 @ emptyset)) @ emptyset)))))=>(![X712:$i, X713:$i]:((in @ X713 @ (setunion @ (setadjoin @ (setadjoin @ X712 @ emptyset) @ (setadjoin @ (setadjoin @ X712 @ (setadjoin @ X713 @ emptyset)) @ emptyset)))))=>(![X663:$i, X664:$i]:(?[X665:$i]:(((in @ X665 @ (setunion @ (setadjoin @ (setadjoin @ X663 @ emptyset) @ (setadjoin @ (setadjoin @ X663 @ (setadjoin @ X664 @ emptyset)) @ emptyset))))&?[X666:$i]:(((in @ X666 @ (setunion @ (setadjoin @ (setadjoin @ X663 @ emptyset) @ (setadjoin @ (setadjoin @ X663 @ (setadjoin @ X664 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X663 @ emptyset) @ (setadjoin @ (setadjoin @ X663 @ (setadjoin @ X664 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X665 @ emptyset) @ (setadjoin @ (setadjoin @ X665 @ (setadjoin @ X666 @ emptyset)) @ emptyset))))))))=>(![X667:$i, X668:$i]:(?[X669:$i]:(((in @ X669 @ (setunion @ (kpair @ X667 @ X668)))&?[X670:$i]:(((in @ X670 @ (setunion @ (kpair @ X667 @ X668)))&((kpair @ X667 @ X668)=(setadjoin @ (setadjoin @ X669 @ emptyset) @ (setadjoin @ (setadjoin @ X669 @ (setadjoin @ X670 @ emptyset)) @ emptyset))))))))=>(![X671:$i, X672:$i]:(((in @ X672 @ X671)=>(subset @ (setadjoin @ X672 @ emptyset) @ X671)))=>(![X673:$i, X674:$i]:(((in @ X674 @ X673)=>(in @ (setadjoin @ X674 @ emptyset) @ (powerset @ X673))))=>(![X675:$i, X676:$i, X677:$i]:(((in @ X677 @ X675)=>(in @ (setadjoin @ X677 @ emptyset) @ (powerset @ (binunion @ X675 @ X676)))))=>(![X709:$i, X710:$i, X711:$i]:(((in @ X711 @ (setadjoin @ X709 @ (setadjoin @ X710 @ emptyset)))=>(((X711)=(X709))|((X711)=(X710)))))=>(![X678:$i, X679:$i, X680:$i]:(((in @ X680 @ X678)=>![X681:$i]:(((in @ X681 @ X679)=>(subset @ (setadjoin @ X680 @ (setadjoin @ X681 @ emptyset)) @ (binunion @ X678 @ X679))))))=>(![X682:$i, X683:$i, X684:$i]:(((in @ X684 @ X682)=>![X685:$i]:(((in @ X685 @ X683)=>(in @ (setadjoin @ X684 @ (setadjoin @ X685 @ emptyset)) @ (powerset @ (binunion @ X682 @ X683)))))))=>(![X705:$i, X706:$i, X707:$i]:(((in @ X707 @ X705)=>![X708:$i]:(((in @ X708 @ X706)=>(subset @ (setadjoin @ (setadjoin @ X707 @ emptyset) @ (setadjoin @ (setadjoin @ X707 @ (setadjoin @ X708 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X705 @ X706)))))))=>(![X701:$i, X702:$i, X703:$i]:(((in @ X703 @ X701)=>![X704:$i]:(((in @ X704 @ X702)=>(in @ (setadjoin @ (setadjoin @ X703 @ emptyset) @ (setadjoin @ (setadjoin @ X703 @ (setadjoin @ X704 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X701 @ X702))))))))=>(![X697:$i, X698:$i, X699:$i]:(((in @ X699 @ X697)=>![X700:$i]:(((in @ X700 @ X698)=>(in @ (kpair @ X699 @ X700) @ (powerset @ (powerset @ (binunion @ X697 @ X698))))))))=>(![X693:$i, X694:$i, X695:$i]:(((in @ X695 @ X693)=>![X696:$i]:(((in @ X696 @ X694)=>(in @ (kpair @ X695 @ X696) @ (cartprod @ X693 @ X694))))))=>(![X686:$i, X687:$i, X688:$i]:(((in @ X688 @ (cartprod @ X686 @ X687))=>?[X689:$i]:(((in @ X689 @ X686)&?[X690:$i]:(((in @ X690 @ X687)&((X688)=(kpair @ X689 @ X690))))))))=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X691:$i]:(((in @ X691 @ (setunion @ X18))&?[X692:$i]:(((in @ X692 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X691 @ emptyset) @ (setadjoin @ (setadjoin @ X691 @ (setadjoin @ X692 @ emptyset)) @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(assume_negation,[status(cth)],[cartprodmempair]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_169]), foundationAx]), wellorderingAx]), c_0_170]), c_0_171]), c_0_172]), c_0_173]), c_0_174]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_175]), setext]), emptyI]), noeltsimpempty]), c_0_176]), c_0_177]), c_0_178]), c_0_179]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_180]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_181]), c_0_182]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_183]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_184]), c_0_185]), c_0_186]), inCongP]), in__Cong]), c_0_187]), c_0_188]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_189]), c_0_190]), c_0_191]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_192]), c_0_193]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), c_0_168]), secondinupair]), setukpairIL]), setukpairIR]), c_0_194]), c_0_195]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1])])]), c_0_196])).
980.25/124.10	thf(c_0_198, plain, ![X896:$i, X897:$i]:(((kpair @ X896 @ X897)=(setadjoin @ (setadjoin @ X896 @ emptyset) @ (setadjoin @ (setadjoin @ X896 @ (setadjoin @ X897 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])])).
980.25/124.10	thf(c_0_199, negated_conjecture, ![X900:$i, X901:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X913:$i, X914:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X922:$i, X923:$i > $i > $o, X924:$i, X926:$i, X929:$i, X931:$i, X932:$i, X933:$i, X934:$i, X936:$i, X937:$i > $o, X938:$i, X940:$i, X941:$i > $o, X942:$i, X943:$i, X944:$i > $o, X945:$i, X946:$i, X947:$i > $o, X948:$i, X949:$i > $o, X950:$i, X953:$i, X954:$o, X955:$i, X956:$i, X957:$o, X958:$i, X959:$i, X960:$i > $o, X961:$i, X964:$i, X965:$i, X968:$i, X970:$i, X972:$i, X973:$i > $o, X974:$i, X975:$i, X977:$i, X978:$i > $o, X979:$i, X980:$i, X981:$i, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i, X989:$i, X990:$o, X991:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1004:$i, X1005:$i, X1006:$i, X1007:$i, X1008:$o, X1010:$i, X1011:$i, X1012:$i > $o, X1013:$i, X1016:$i, X1017:$i, X1018:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i > $o, X1037:$i, X1038:$i > $o, X1039:$i, X1040:$i, X1041:$i > $o, X1042:$i, X1044:$i, X1045:$i > $o, X1047:$i, X1048:$i, X1049:$i > $o, X1051:$i, X1052:$i, X1053:$i > $o, X1054:$i, X1056:$o, X1057:$o, X1058:$i, X1059:$i > $o, X1061:$i, X1062:$i, X1063:$i > $o, X1064:$i, X1066:$i > $o, X1067:$i, X1070:$i, X1071:$i > $o, X1072:$i, X1076:$i, X1077:$i > $o, X1078:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i > $o, X1091:$i, X1093:$i, X1094:$i, X1095:$i > $o, X1096:$i > $o, X1099:$i, X1102:$i, X1103:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i > $o, X1116:$i, X1118:$i, X1119:$i, X1120:$i > $o, X1121:$i > $o, X1124:$i, X1126:$i, X1128:$i, X1129:$i, X1130:$i > $o, X1131:$i > $o, X1134:$i, X1135:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$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:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i > $o, X1182:$i, X1183:$i > $o, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$o, X1196:$i, X1197:$i, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$o, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$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, X1286:$i, X1287:$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, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1332:$i, X1333:$i]:((((~(in @ (esk1_2 @ X900 @ X901) @ X900)|~(in @ (esk1_2 @ X900 @ X901) @ X901)|((X900)=(X901)))&((in @ (esk1_2 @ X900 @ X901) @ X900)|(in @ (esk1_2 @ 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X1099))|~(X1095 @ X1099))|((X1095 @ (esk39_2 @ X1095 @ X1096))|(X1096 @ (esk40_2 @ X1095 @ X1096))))&(~(X1096 @ X1102)|((esk42_2 @ X1095 @ X1096)=(X1102))|((X1095 @ (esk41_3 @ X1095 @ X1096 @ X1099))|~(X1095 @ X1099))|((X1095 @ (esk39_2 @ X1095 @ X1096))|(X1096 @ (esk40_2 @ X1095 @ X1096)))))&(((X1096 @ (esk42_2 @ X1095 @ X1096))|(((X1099)!=(esk41_3 @ X1095 @ X1096 @ X1099))|~(X1095 @ X1099))|((X1095 @ (esk39_2 @ X1095 @ X1096))|(X1096 @ (esk40_2 @ X1095 @ X1096))))&(~(X1096 @ X1102)|((esk42_2 @ X1095 @ X1096)=(X1102))|(((X1099)!=(esk41_3 @ X1095 @ X1096 @ X1099))|~(X1095 @ X1099))|((X1095 @ (esk39_2 @ X1095 @ X1096))|(X1096 @ (esk40_2 @ X1095 @ X1096))))))&((((X1095 @ (esk44_2 @ X1095 @ X1096))|((X1096 @ (esk43_3 @ X1095 @ X1096 @ X1103))|~(X1096 @ X1103))|((X1095 @ (esk39_2 @ X1095 @ X1096))|(X1096 @ (esk40_2 @ X1095 @ X1096))))&(~(X1095 @ X1106)|((esk44_2 @ X1095 @ X1096)=(X1106))|((X1096 @ (esk43_3 @ X1095 @ X1096 @ X1103))|~(X1096 @ X1103))|((X1095 @ (esk39_2 @ X1095 @ X1096))|(X1096 @ (esk40_2 @ X1095 @ X1096)))))&(((X1095 @ (esk44_2 @ X1095 @ X1096))|(((X1103)!=(esk43_3 @ X1095 @ X1096 @ X1103))|~(X1096 @ X1103))|((X1095 @ (esk39_2 @ X1095 @ X1096))|(X1096 @ (esk40_2 @ X1095 @ X1096))))&(~(X1095 @ X1106)|((esk44_2 @ X1095 @ X1096)=(X1106))|(((X1103)!=(esk43_3 @ X1095 @ X1096 @ X1103))|~(X1096 @ X1103))|((X1095 @ (esk39_2 @ X1095 @ X1096))|(X1096 @ (esk40_2 @ X1095 @ X1096)))))))))&(((emptyset)=(emptyset))&((((X1107)!=(X1108))|(((X1109)!=(X1110))|((setadjoin @ X1107 @ X1109)=(setadjoin @ X1108 @ X1110))))&((((X1111)!=(X1112))|((powerset @ X1111)=(powerset @ X1112)))&((((X1113)!=(X1114))|((setunion @ X1113)=(setunion @ X1114)))&(((omega)=(omega))&((((X1115 @ (esk45_2 @ X1115 @ X1116))|~(X1115 @ X1116)|(~(X1115 @ X1118)|(~(X1115 @ X1119)|((X1118)=(X1119)))))&(((X1116)!=(esk45_2 @ X1115 @ X1116))|~(X1115 @ X1116)|(~(X1115 @ X1118)|(~(X1115 @ X1119)|((X1118)=(X1119))))))&((((((X1121 @ (esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|((X1120 @ (esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|((esk46_2 @ X1120 @ X1121)=(esk47_2 @ X1120 @ X1121)))&(((X1126)!=(esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|((X1120 @ (esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|((esk46_2 @ X1120 @ X1121)=(esk47_2 @ X1120 @ X1121))))&(((X1121 @ (esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|(((X1124)!=(esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|((esk46_2 @ X1120 @ X1121)=(esk47_2 @ X1120 @ X1121)))&(((X1126)!=(esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|(((X1124)!=(esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|((esk46_2 @ X1120 @ X1121)=(esk47_2 @ X1120 @ X1121)))))&(((((X1121 @ (esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|((X1120 @ (esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|(~(X1120 @ (esk46_2 @ X1120 @ X1121))|~(X1121 @ (esk47_2 @ X1120 @ X1121))))&(((X1126)!=(esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|((X1120 @ (esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|(~(X1120 @ (esk46_2 @ X1120 @ X1121))|~(X1121 @ (esk47_2 @ X1120 @ X1121)))))&(((X1121 @ (esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|(((X1124)!=(esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|(~(X1120 @ (esk46_2 @ X1120 @ X1121))|~(X1121 @ (esk47_2 @ X1120 @ X1121))))&(((X1126)!=(esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|(((X1124)!=(esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|(~(X1120 @ (esk46_2 @ X1120 @ X1121))|~(X1121 @ (esk47_2 @ X1120 @ X1121))))))&((((X1121 @ (esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|((X1120 @ (esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|((X1120 @ (esk46_2 @ X1120 @ X1121))|(X1121 @ (esk47_2 @ X1120 @ X1121))))&(((X1126)!=(esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|((X1120 @ (esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|((X1120 @ (esk46_2 @ X1120 @ X1121))|(X1121 @ (esk47_2 @ X1120 @ X1121)))))&(((X1121 @ (esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|(((X1124)!=(esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|((X1120 @ (esk46_2 @ X1120 @ X1121))|(X1121 @ (esk47_2 @ X1120 @ X1121))))&(((X1126)!=(esk49_3 @ X1120 @ X1121 @ X1126))|~(X1121 @ X1126)|((descr @ X1120)=(descr @ X1121))|(((X1124)!=(esk48_3 @ X1120 @ X1121 @ X1124))|~(X1120 @ X1124))|((X1120 @ (esk46_2 @ X1120 @ X1121))|(X1121 @ (esk47_2 @ X1120 @ X1121))))))))&((((in @ (esk50_4 @ X1128 @ X1129 @ X1130 @ X1131) @ X1128)|((dsetconstr @ X1128 @ X1130)=(dsetconstr @ X1129 @ X1131))|((X1128)!=(X1129)))&(((in @ (esk51_4 @ X1128 @ X1129 @ X1130 @ X1131) @ X1129)|((dsetconstr @ X1128 @ X1130)=(dsetconstr @ X1129 @ X1131))|((X1128)!=(X1129)))&((((esk50_4 @ X1128 @ X1129 @ X1130 @ X1131)=(esk51_4 @ X1128 @ X1129 @ X1130 @ X1131))|((dsetconstr @ X1128 @ X1130)=(dsetconstr @ X1129 @ X1131))|((X1128)!=(X1129)))&((~(X1130 @ (esk50_4 @ X1128 @ X1129 @ X1130 @ X1131))|~(X1131 @ (esk51_4 @ X1128 @ X1129 @ X1130 @ X1131))|((dsetconstr @ X1128 @ X1130)=(dsetconstr @ X1129 @ X1131))|((X1128)!=(X1129)))&((X1130 @ (esk50_4 @ X1128 @ X1129 @ X1130 @ X1131))|(X1131 @ (esk51_4 @ X1128 @ X1129 @ X1130 @ X1131))|((dsetconstr @ X1128 @ X1130)=(dsetconstr @ X1129 @ X1131))|((X1128)!=(X1129)))))))&((((in @ (esk52_2 @ X1134 @ X1135) @ X1134)|(subset @ X1134 @ X1135))&(~(in @ (esk52_2 @ X1134 @ X1135) @ X1135)|(subset @ X1134 @ X1135)))&((((X1137)!=(X1138))|(subset @ X1138 @ X1137))&((((X1139)!=(X1140))|(subset @ X1139 @ X1140))&((((in @ (esk53_2 @ X1141 @ X1142) @ X1141)|(subset @ X1141 @ X1142))&(~(in @ (esk53_2 @ X1141 @ X1142) @ X1142)|(subset @ X1141 @ X1142)))&((subset @ emptyset @ X1144)&((~(subset @ X1145 @ X1146)|(~(in @ X1147 @ X1145)|(in @ X1147 @ X1146)))&((~(subset @ X1148 @ X1149)|((in @ X1150 @ X1149)|~(in @ X1150 @ X1148)))&((~(in @ X1153 @ X1151)|((in @ X1153 @ X1152)|~(subset @ X1151 @ X1152)))&(((subset @ X1154 @ X1155)|((X1154)!=(X1155)))&((~(in @ X1158 @ X1156)|((in @ X1158 @ X1157)|((X1156)!=(X1157))))&((subset @ X1159 @ X1159)&((~(subset @ X1160 @ X1161)|(~(subset @ X1161 @ X1162)|(subset @ X1160 @ X1162)))&((subset @ X1164 @ (setadjoin @ X1163 @ X1164))&((~(subset @ X1165 @ X1167)|(subset @ X1165 @ (setadjoin @ X1166 @ X1167)))&((~(subset @ X1168 @ X1169)|(in @ X1168 @ (powerset @ X1169)))&((~(subset @ X1170 @ X1171)|(~(subset @ X1171 @ X1170)|((X1170)=(X1171))))&((~(subset @ X1172 @ emptyset)|((X1172)=(emptyset)))&((~(subset @ X1174 @ X1173)|(in @ X1174 @ (powerset @ X1173)))&((~(in @ X1176 @ (powerset @ X1175))|(subset @ X1176 @ X1175))&((in @ X1177 @ (powerset @ X1177))&((~(subset @ X1178 @ X1179)|(subset @ (powerset @ X1178) @ (powerset @ X1179)))&((in @ (dsetconstr @ X1180 @ X1181) @ (powerset @ X1180))&((subset @ (dsetconstr @ X1182 @ X1183) @ X1182)&((~(in @ X1186 @ X1184)|(in @ X1186 @ (binunion @ X1184 @ X1185)))&((in @ X1188 @ (setadjoin @ X1187 @ (setadjoin @ X1188 @ emptyset)))&((~(in @ X1191 @ X1190)|(in @ X1191 @ (binunion @ X1189 @ X1190)))&(((((in @ X1194 @ X1193)|(X1195)|(in @ X1194 @ X1192)|~(in @ X1194 @ (binunion @ X1192 @ X1193)))&(~(X1195)|(X1195)|(in @ X1194 @ X1192)|~(in @ X1194 @ (binunion @ X1192 @ X1193))))&(((in @ X1194 @ X1193)|(X1195)|~(X1195)|~(in @ X1194 @ (binunion @ X1192 @ X1193)))&(~(X1195)|(X1195)|~(X1195)|~(in @ X1194 @ (binunion @ X1192 @ X1193)))))&((~(in @ X1198 @ (binunion @ X1196 @ X1197))|((in @ X1198 @ X1196)|(in @ X1198 @ X1197)))&((subset @ X1199 @ (binunion @ X1199 @ X1200))&((subset @ X1202 @ (binunion @ X1201 @ X1202))&((~(in @ X1205 @ X1203)|(~(in @ X1205 @ X1204)|(in @ X1205 @ (binintersect @ X1203 @ X1204))))&((~(subset @ X1208 @ X1206)|(~(subset @ X1208 @ X1207)|(subset @ X1208 @ (binintersect @ X1206 @ X1207))))&((~(in @ X1211 @ (binintersect @ X1209 @ X1210))|(in @ X1211 @ X1209))&((subset @ (binintersect @ X1212 @ X1213) @ X1212)&((~(subset @ X1214 @ X1215)|((binintersect @ X1214 @ X1215)=(X1214)))&((((binintersect @ X1216 @ X1217)!=(X1217))|(subset @ X1217 @ X1216))&((~(in @ X1220 @ (binintersect @ X1218 @ X1219))|(in @ X1220 @ X1219))&((((in @ (esk54_2 @ X1221 @ X1222) @ X1221)|((binintersect @ X1221 @ X1222)=(emptyset)))&((in @ (esk54_2 @ X1221 @ X1222) @ X1222)|((binintersect @ X1221 @ X1222)=(emptyset))))&((subset @ (binintersect @ X1224 @ X1225) @ X1225)&((~(subset @ X1227 @ X1226)|((binintersect @ X1226 @ X1227)=(X1227)))&((((binintersect @ X1228 @ X1229)!=(X1228))|(subset @ X1228 @ X1229))&(((binintersect @ X1230 @ (binunion @ X1231 @ X1232))=(binunion @ (binintersect @ X1230 @ X1231) @ (binintersect @ X1230 @ X1232)))&((~(in @ X1235 @ X1233)|((in @ X1235 @ X1234)|(in @ X1235 @ (setminus @ X1233 @ X1234))))&((~(in @ X1238 @ (setminus @ X1236 @ X1237))|(in @ X1238 @ X1236))&((~(in @ X1241 @ (setminus @ X1239 @ X1240))|~(in @ X1241 @ X1240))&((~(subset @ X1242 @ X1243)|((setminus @ X1242 @ X1243)=(emptyset)))&(((in @ X1246 @ (setminus @ X1244 @ X1245))|(~(in @ X1246 @ X1244)|(in @ X1246 @ X1245)))&(((in @ X1249 @ (setminus @ X1247 @ X1248))|((in @ X1249 @ X1248)|~(in @ X1249 @ X1247)))&(((in @ X1252 @ X1250)|~(in @ X1252 @ (setminus @ X1250 @ X1251)))&((~(in @ X1255 @ X1254)|~(in @ X1255 @ (setminus @ X1253 @ X1254)))&((subset @ (setminus @ X1256 @ X1257) @ X1256)&((((setminus @ X1258 @ X1259)!=(emptyset))|(subset @ X1258 @ X1259))&((((~(in @ X1262 @ X1260)|(X1263)|(in @ X1262 @ X1260)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(((in @ X1262 @ X1261)|(X1263)|(in @ X1262 @ X1260)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(~(X1263)|(X1263)|(in @ X1262 @ X1260)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))))&(((~(in @ X1262 @ X1260)|(X1263)|~(in @ X1262 @ X1261)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(((in @ X1262 @ X1261)|(X1263)|~(in @ X1262 @ X1261)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(~(X1263)|(X1263)|~(in @ X1262 @ X1261)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))))&((~(in @ X1262 @ X1260)|(X1263)|~(X1263)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(((in @ X1262 @ X1261)|(X1263)|~(X1263)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(~(X1263)|(X1263)|~(X1263)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))))))&((~(in @ X1266 @ X1264)|((in @ X1266 @ X1265)|(in @ X1266 @ (symdiff @ X1264 @ X1265))))&(((in @ X1269 @ X1267)|(~(in @ X1269 @ X1268)|(in @ X1269 @ (symdiff @ X1267 @ X1268))))&((~(in @ X1272 @ X1270)|(~(in @ X1272 @ X1271)|~(in @ X1272 @ (symdiff @ X1270 @ X1271))))&(((in @ X1275 @ X1273)|((in @ X1275 @ X1274)|~(in @ X1275 @ (symdiff @ X1273 @ X1274))))&((in @ X1277 @ (setadjoin @ X1276 @ (setadjoin @ X1277 @ emptyset)))&((in @ X1278 @ (setunion @ (setadjoin @ (setadjoin @ X1278 @ emptyset) @ (setadjoin @ (setadjoin @ X1278 @ (setadjoin @ X1279 @ emptyset)) @ emptyset))))&((in @ X1281 @ (setunion @ (setadjoin @ (setadjoin @ X1280 @ emptyset) @ (setadjoin @ (setadjoin @ X1280 @ (setadjoin @ X1281 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1282 @ X1283) @ (setunion @ (setadjoin @ (setadjoin @ X1282 @ emptyset) @ (setadjoin @ (setadjoin @ X1282 @ (setadjoin @ X1283 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1282 @ X1283) @ (setunion @ (setadjoin @ (setadjoin @ X1282 @ emptyset) @ (setadjoin @ (setadjoin @ X1282 @ (setadjoin @ X1283 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1282 @ emptyset) @ (setadjoin @ (setadjoin @ X1282 @ (setadjoin @ X1283 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1282 @ X1283) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1282 @ X1283) @ (setadjoin @ (esk56_2 @ X1282 @ X1283) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1286 @ X1287) @ (setunion @ (kpair @ X1286 @ X1287)))&((in @ (esk58_2 @ X1286 @ X1287) @ (setunion @ (kpair @ X1286 @ X1287)))&((kpair @ X1286 @ X1287)=(setadjoin @ (setadjoin @ (esk57_2 @ X1286 @ X1287) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1286 @ X1287) @ (setadjoin @ (esk58_2 @ X1286 @ X1287) @ emptyset)) @ emptyset)))))&((~(in @ X1291 @ X1290)|(subset @ (setadjoin @ X1291 @ emptyset) @ X1290))&((~(in @ X1293 @ X1292)|(in @ (setadjoin @ X1293 @ emptyset) @ (powerset @ X1292)))&((~(in @ X1296 @ X1294)|(in @ (setadjoin @ X1296 @ emptyset) @ (powerset @ (binunion @ X1294 @ X1295))))&((~(in @ X1299 @ (setadjoin @ X1297 @ (setadjoin @ X1298 @ emptyset)))|(((X1299)=(X1297))|((X1299)=(X1298))))&((~(in @ X1302 @ X1300)|(~(in @ X1303 @ X1301)|(subset @ (setadjoin @ X1302 @ (setadjoin @ X1303 @ emptyset)) @ (binunion @ X1300 @ X1301))))&((~(in @ X1306 @ X1304)|(~(in @ X1307 @ X1305)|(in @ (setadjoin @ X1306 @ (setadjoin @ X1307 @ emptyset)) @ (powerset @ (binunion @ X1304 @ X1305)))))&((~(in @ X1310 @ X1308)|(~(in @ X1311 @ X1309)|(subset @ (setadjoin @ (setadjoin @ X1310 @ emptyset) @ (setadjoin @ (setadjoin @ X1310 @ (setadjoin @ X1311 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1308 @ X1309)))))&((~(in @ X1314 @ X1312)|(~(in @ X1315 @ X1313)|(in @ (setadjoin @ (setadjoin @ X1314 @ emptyset) @ (setadjoin @ (setadjoin @ X1314 @ (setadjoin @ X1315 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1312 @ X1313))))))&((~(in @ X1318 @ X1316)|(~(in @ X1319 @ X1317)|(in @ (kpair @ X1318 @ X1319) @ (powerset @ (powerset @ (binunion @ X1316 @ X1317))))))&((~(in @ X1322 @ X1320)|(~(in @ X1323 @ X1321)|(in @ (kpair @ X1322 @ X1323) @ (cartprod @ X1320 @ X1321))))&((((in @ (esk59_3 @ X1324 @ X1325 @ X1326) @ X1324)|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))&(((in @ (esk60_3 @ X1324 @ X1325 @ X1326) @ X1325)|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))&(((X1326)=(kpair @ (esk59_3 @ X1324 @ X1325 @ X1326) @ (esk60_3 @ X1324 @ X1325 @ X1326)))|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))))&((in @ esk63_0 @ (cartprod @ esk61_0 @ esk62_0))&(~(in @ X1332 @ (setunion @ esk63_0))|(~(in @ X1333 @ (setunion @ esk63_0))|((esk63_0)!=(setadjoin @ (setadjoin @ X1332 @ emptyset) @ (setadjoin @ (setadjoin @ X1332 @ (setadjoin @ X1333 @ emptyset)) @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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_197])])])])])])])).
980.25/124.10	thf(c_0_200, plain, ![X898:$i, X899:$i]:(((kpair @ X898 @ X899)=(setadjoin @ (setadjoin @ X898 @ emptyset) @ (setadjoin @ (setadjoin @ X898 @ (setadjoin @ X899 @ emptyset)) @ emptyset)))), inference(variable_rename,[status(thm)],[c_0_198])).
980.25/124.10	thf(c_0_201, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(kpair @ (esk59_3 @ X3 @ X4 @ X2) @ (esk60_3 @ X3 @ X4 @ X2)))|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_199])).
980.25/124.10	thf(c_0_202, plain, ![X2:$i, X3:$i]:(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_200])).
980.25/124.10	thf(c_0_203, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_199])).
980.25/124.10	thf(c_0_204, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(setadjoin @ (setadjoin @ (esk59_3 @ X3 @ X4 @ X2) @ emptyset) @ (setadjoin @ (setadjoin @ (esk59_3 @ X3 @ X4 @ X2) @ (setadjoin @ (esk60_3 @ X3 @ X4 @ X2) @ emptyset)) @ emptyset)))|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(rw,[status(thm)],[c_0_201, c_0_202])).
980.25/124.10	thf(c_0_205, negated_conjecture, ![X3:$i, X2:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_199])).
980.25/124.10	thf(c_0_206, negated_conjecture, ![X2:$i, X3:$i]:((~((in @ X2 @ (setunion @ esk63_0)))|~((in @ X3 @ (setunion @ esk63_0)))|((esk63_0)!=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_199])).
980.25/124.10	thf(c_0_207, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ (esk59_3 @ X2 @ X3 @ X4) @ (setunion @ X4))|~((in @ X4 @ (cartprod @ X2 @ X3))))), inference(spm,[status(thm)],[c_0_203, c_0_204])).
980.25/124.10	thf(c_0_208, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ (esk60_3 @ X2 @ X3 @ X4) @ (setunion @ X4))|~((in @ X4 @ (cartprod @ X2 @ X3))))), inference(spm,[status(thm)],[c_0_205, c_0_204])).
980.25/124.10	thf(c_0_209, negated_conjecture, (in @ esk63_0 @ (cartprod @ esk61_0 @ esk62_0)), inference(split_conjunct,[status(thm)],[c_0_199])).
980.25/124.10	thf(c_0_210, negated_conjecture, ![X2:$i, X3:$i]:(~((in @ esk63_0 @ (cartprod @ X2 @ X3)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_206, c_0_204])]), c_0_207]), c_0_208])).
980.25/124.10	thf(c_0_211, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_209, c_0_210]), ['proof']).
980.25/124.10	# SZS output end CNFRefutation
980.25/124.10	# Parsed axioms                        : 324
980.25/124.10	# Removed by relevancy pruning/SinE    : 0
980.25/124.10	# Initial clauses                      : 450
980.25/124.10	# Removed in clause preprocessing      : 196
980.25/124.10	# Initial clauses in saturation        : 254
980.25/124.10	# Processed clauses                    : 9957
980.25/124.10	# ...of these trivial                  : 107
980.25/124.10	# ...subsumed                          : 3940
980.25/124.10	# ...remaining for further processing  : 5910
980.25/124.10	# Other redundant clauses eliminated   : 410
980.25/124.10	# Clauses deleted for lack of memory   : 83982
980.25/124.10	# Backward-subsumed                    : 129
980.25/124.10	# Backward-rewritten                   : 218
980.25/124.10	# Generated clauses                    : 2865924
980.25/124.10	# ...of the previous two non-redundant : 2857120
980.25/124.10	# ...aggressively subsumed             : 0
980.25/124.10	# Contextual simplify-reflections      : 13
980.25/124.10	# Paramodulations                      : 2865376
980.25/124.10	# Factorizations                       : 137
980.25/124.10	# NegExts                              : 0
980.25/124.10	# Equation resolutions                 : 410
980.25/124.10	# Disequality decompositions           : 0
980.25/124.10	# Total rewrite steps                  : 20066
980.25/124.10	# ...of those cached                   : 19151
980.25/124.10	# Propositional unsat checks           : 0
980.25/124.10	#    Propositional check models        : 0
980.25/124.10	#    Propositional check unsatisfiable : 0
980.25/124.10	#    Propositional clauses             : 0
980.25/124.10	#    Propositional clauses after purity: 0
980.25/124.10	#    Propositional unsat core size     : 0
980.25/124.10	#    Propositional preprocessing time  : 0.000
980.25/124.10	#    Propositional encoding time       : 0.000
980.25/124.10	#    Propositional solver time         : 0.000
980.25/124.10	#    Success case prop preproc time    : 0.000
980.25/124.10	#    Success case prop encoding time   : 0.000
980.25/124.10	#    Success case prop solver time     : 0.000
980.25/124.10	# Current number of processed clauses  : 5331
980.25/124.10	#    Positive orientable unit clauses  : 122
980.25/124.10	#    Positive unorientable unit clauses: 0
980.25/124.10	#    Negative unit clauses             : 226
980.25/124.10	#    Non-unit-clauses                  : 4983
980.25/124.10	# Current number of unprocessed clauses: 1015925
980.25/124.10	# ...number of literals in the above   : 4619923
980.25/124.10	# Current number of archived formulas  : 0
980.25/124.10	# Current number of archived clauses   : 567
980.25/124.10	# Clause-clause subsumption calls (NU) : 3053245
980.25/124.10	# Rec. Clause-clause subsumption calls : 743806
980.25/124.10	# Non-unit clause-clause subsumptions  : 2545
980.25/124.10	# Unit Clause-clause subsumption calls : 122026
980.25/124.10	# Rewrite failures with RHS unbound    : 0
980.25/124.10	# BW rewrite match attempts            : 74
980.25/124.10	# BW rewrite match successes           : 29
980.25/124.10	# Condensation attempts                : 9957
980.25/124.10	# Condensation successes               : 137
980.25/124.10	# Termbank termtop insertions          : 102165214
980.25/124.10	# Search garbage collected termcells   : 2485066
980.25/124.10	
980.25/124.10	# -------------------------------------------------
980.25/124.10	# User time                : 120.844 s
980.25/124.10	# System time              : 1.707 s
980.25/124.10	# Total time               : 122.550 s
980.25/124.10	# Maximum resident set size: 5284 pages
980.25/124.10	
980.25/124.10	# -------------------------------------------------
980.25/124.10	# User time                : 120.857 s
980.25/124.10	# System time              : 1.709 s
980.25/124.10	# Total time               : 122.566 s
980.25/124.10	# Maximum resident set size: 2108 pages
980.25/124.10	% E exiting
980.25/124.10	% E exiting
980.25/124.10	EOF