0.07/0.14	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.14	% Command    : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.13/0.36	% Computer : n024.cluster.edu
0.13/0.36	% Model    : x86_64 x86_64
0.13/0.36	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.36	% Memory   : 8042.1875MB
0.13/0.36	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.36	% CPULimit   : 1920
0.13/0.36	% WCLimit    : 240
0.13/0.36	% DateTime   : Wed Jul 30 05:42:19 EDT 2025
0.13/0.36	% CPUTime    : 
0.23/0.52	Running higher-order theorem proving
0.23/0.56	Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p
0.69/0.67	# Version: 3.0.0-ho
0.69/0.67	# Preprocessing class: HSLMSLSSLLLCHFA.
0.69/0.67	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
0.69/0.67	# Starting ehoh_best5 with 240s (1) cores
0.69/0.67	# Starting almost_fo_3_lam with 240s (1) cores
0.69/0.67	# Starting new_bool_5 with 240s (1) cores
0.69/0.67	# Starting pre_casc_3 with 240s (1) cores
0.69/0.67	# Starting ho_unfolding_8 with 240s (1) cores
0.69/0.67	# Starting new_ho_10_cnf2 with 240s (1) cores
0.69/0.67	# Starting new_bool_3 with 240s (1) cores
0.69/0.67	# Starting new_ho_5 with 240s (1) cores
0.69/0.67	# ehoh_best5 with pid 17682 completed with status 0
0.69/0.67	# Result found by ehoh_best5
0.69/0.67	# Preprocessing class: HSLMSLSSLLLCHFA.
0.69/0.67	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
0.69/0.67	# Starting ehoh_best5 with 240s (1) cores
0.69/0.67	# No SInE strategy applied
0.69/0.67	# Search class: HGHSM-FSLM31-MHFMMSBN
0.69/0.67	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
0.69/0.67	# Starting new_ho_10_cnf2 with 130s (1) cores
0.69/0.67	# new_ho_10_cnf2 with pid 17693 completed with status 0
0.69/0.67	# Result found by new_ho_10_cnf2
0.69/0.67	# Preprocessing class: HSLMSLSSLLLCHFA.
0.69/0.67	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
0.69/0.67	# Starting ehoh_best5 with 240s (1) cores
0.69/0.67	# No SInE strategy applied
0.69/0.67	# Search class: HGHSM-FSLM31-MHFMMSBN
0.69/0.67	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
0.69/0.67	# Starting new_ho_10_cnf2 with 130s (1) cores
0.69/0.67	# Preprocessing time       : 0.004 s
0.69/0.67	# Presaturation interreduction done
0.69/0.67	
0.69/0.67	# Proof found!
0.69/0.67	# SZS status Theorem
0.69/0.67	# SZS output start CNFRefutation
0.69/0.67	thf(decl_23, type, in: $i > $i > $o).
0.69/0.67	thf(decl_24, type, exu: ($i > $o) > $o).
0.69/0.67	thf(decl_25, type, setextAx: $o).
0.69/0.67	thf(decl_26, type, emptyset: $i).
0.69/0.67	thf(decl_27, type, emptysetAx: $o).
0.69/0.67	thf(decl_28, type, setadjoin: $i > $i > $i).
0.69/0.67	thf(decl_29, type, setadjoinAx: $o).
0.69/0.67	thf(decl_30, type, powerset: $i > $i).
0.69/0.67	thf(decl_31, type, powersetAx: $o).
0.69/0.67	thf(decl_32, type, setunion: $i > $i).
0.69/0.67	thf(decl_33, type, setunionAx: $o).
0.69/0.67	thf(decl_34, type, omega: $i).
0.69/0.67	thf(decl_35, type, omega0Ax: $o).
0.69/0.67	thf(decl_36, type, omegaSAx: $o).
0.69/0.67	thf(decl_37, type, omegaIndAx: $o).
0.69/0.67	thf(decl_38, type, replAx: $o).
0.69/0.67	thf(decl_39, type, foundationAx: $o).
0.69/0.67	thf(decl_40, type, wellorderingAx: $o).
0.69/0.67	thf(decl_41, type, descr: ($i > $o) > $i).
0.69/0.67	thf(decl_42, type, descrp: $o).
0.69/0.67	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_44, type, dsetconstrI: $o).
0.69/0.67	thf(decl_45, type, dsetconstrEL: $o).
0.69/0.67	thf(decl_46, type, dsetconstrER: $o).
0.69/0.67	thf(decl_47, type, exuE1: $o).
0.69/0.67	thf(decl_48, type, prop2set: $o > $i).
0.69/0.67	thf(decl_49, type, prop2setE: $o).
0.69/0.67	thf(decl_50, type, emptysetE: $o).
0.69/0.67	thf(decl_51, type, emptysetimpfalse: $o).
0.69/0.67	thf(decl_52, type, notinemptyset: $o).
0.69/0.67	thf(decl_53, type, exuE3e: $o).
0.69/0.67	thf(decl_54, type, setext: $o).
0.69/0.67	thf(decl_55, type, emptyI: $o).
0.69/0.67	thf(decl_56, type, noeltsimpempty: $o).
0.69/0.67	thf(decl_57, type, setbeta: $o).
0.69/0.67	thf(decl_58, type, nonempty: $i > $o).
0.69/0.67	thf(decl_59, type, nonemptyE1: $o).
0.69/0.67	thf(decl_60, type, nonemptyI: $o).
0.69/0.67	thf(decl_61, type, nonemptyI1: $o).
0.69/0.67	thf(decl_62, type, setadjoinIL: $o).
0.69/0.67	thf(decl_63, type, emptyinunitempty: $o).
0.69/0.67	thf(decl_64, type, setadjoinIR: $o).
0.69/0.67	thf(decl_65, type, setadjoinE: $o).
0.69/0.67	thf(decl_66, type, setadjoinOr: $o).
0.69/0.67	thf(decl_67, type, setoftrueEq: $o).
0.69/0.67	thf(decl_68, type, powersetI: $o).
0.69/0.67	thf(decl_69, type, emptyinPowerset: $o).
0.69/0.67	thf(decl_70, type, emptyInPowerset: $o).
0.69/0.67	thf(decl_71, type, powersetE: $o).
0.69/0.67	thf(decl_72, type, setunionI: $o).
0.69/0.67	thf(decl_73, type, setunionE: $o).
0.69/0.67	thf(decl_74, type, subPowSU: $o).
0.69/0.67	thf(decl_75, type, exuE2: $o).
0.69/0.67	thf(decl_76, type, nonemptyImpWitness: $o).
0.69/0.67	thf(decl_77, type, uniqinunit: $o).
0.69/0.67	thf(decl_78, type, notinsingleton: $o).
0.69/0.67	thf(decl_79, type, eqinunit: $o).
0.69/0.67	thf(decl_80, type, singletonsswitch: $o).
0.69/0.67	thf(decl_81, type, upairsetE: $o).
0.69/0.67	thf(decl_82, type, upairsetIL: $o).
0.69/0.67	thf(decl_83, type, upairsetIR: $o).
0.69/0.67	thf(decl_84, type, emptyE1: $o).
0.69/0.67	thf(decl_85, type, vacuousDall: $o).
0.69/0.67	thf(decl_86, type, quantDeMorgan1: $o).
0.69/0.67	thf(decl_87, type, quantDeMorgan2: $o).
0.69/0.67	thf(decl_88, type, quantDeMorgan3: $o).
0.69/0.67	thf(decl_89, type, quantDeMorgan4: $o).
0.69/0.67	thf(decl_90, type, prop2setI: $o).
0.69/0.67	thf(decl_91, type, set2prop: $i > $o).
0.69/0.67	thf(decl_92, type, prop2set2propI: $o).
0.69/0.67	thf(decl_93, type, notdexE: $o).
0.69/0.67	thf(decl_94, type, notdallE: $o).
0.69/0.67	thf(decl_95, type, exuI1: $o).
0.69/0.67	thf(decl_96, type, exuI3: $o).
0.69/0.67	thf(decl_97, type, exuI2: $o).
0.69/0.67	thf(decl_98, type, inCongP: $o).
0.69/0.67	thf(decl_99, type, in__Cong: $o).
0.69/0.67	thf(decl_100, type, exuE3u: $o).
0.69/0.67	thf(decl_101, type, exu__Cong: $o).
0.69/0.67	thf(decl_102, type, emptyset__Cong: $o).
0.69/0.67	thf(decl_103, type, setadjoin__Cong: $o).
0.69/0.67	thf(decl_104, type, powerset__Cong: $o).
0.69/0.67	thf(decl_105, type, setunion__Cong: $o).
0.69/0.67	thf(decl_106, type, omega__Cong: $o).
0.69/0.67	thf(decl_107, type, exuEu: $o).
0.69/0.67	thf(decl_108, type, descr__Cong: $o).
0.69/0.67	thf(decl_109, type, dsetconstr__Cong: $o).
0.69/0.67	thf(decl_110, type, subset: $i > $i > $o).
0.69/0.67	thf(decl_113, type, subsetI1: $o).
0.69/0.67	thf(decl_114, type, eqimpsubset2: $o).
0.69/0.67	thf(decl_115, type, eqimpsubset1: $o).
0.69/0.67	thf(decl_116, type, subsetI2: $o).
0.69/0.67	thf(decl_117, type, emptysetsubset: $o).
0.69/0.67	thf(decl_118, type, subsetE: $o).
0.69/0.67	thf(decl_119, type, subsetE2: $o).
0.69/0.67	thf(decl_120, type, notsubsetI: $o).
0.69/0.67	thf(decl_121, type, notequalI1: $o).
0.69/0.67	thf(decl_122, type, notequalI2: $o).
0.69/0.67	thf(decl_123, type, subsetRefl: $o).
0.69/0.67	thf(decl_124, type, subsetTrans: $o).
0.69/0.67	thf(decl_125, type, setadjoinSub: $o).
0.69/0.67	thf(decl_126, type, setadjoinSub2: $o).
0.69/0.67	thf(decl_127, type, subset2powerset: $o).
0.69/0.67	thf(decl_128, type, setextsub: $o).
0.69/0.67	thf(decl_129, type, subsetemptysetimpeq: $o).
0.69/0.67	thf(decl_130, type, powersetI1: $o).
0.69/0.67	thf(decl_131, type, powersetE1: $o).
0.69/0.67	thf(decl_132, type, inPowerset: $o).
0.69/0.67	thf(decl_133, type, powersetsubset: $o).
0.69/0.67	thf(decl_134, type, sepInPowerset: $o).
0.69/0.67	thf(decl_135, type, sepSubset: $o).
0.69/0.67	thf(decl_136, type, binunion: $i > $i > $i).
0.69/0.67	thf(decl_137, type, binunionIL: $o).
0.69/0.67	thf(decl_138, type, upairset2IR: $o).
0.69/0.67	thf(decl_139, type, binunionIR: $o).
0.69/0.67	thf(decl_140, type, binunionEcases: $o).
0.69/0.67	thf(decl_141, type, binunionE: $o).
0.69/0.67	thf(decl_142, type, binunionLsub: $o).
0.69/0.67	thf(decl_143, type, binunionRsub: $o).
0.69/0.67	thf(decl_144, type, binintersect: $i > $i > $i).
0.69/0.67	thf(decl_145, type, binintersectI: $o).
0.69/0.67	thf(decl_146, type, binintersectSubset5: $o).
0.69/0.67	thf(decl_147, type, binintersectEL: $o).
0.69/0.67	thf(decl_148, type, binintersectLsub: $o).
0.69/0.67	thf(decl_149, type, binintersectSubset2: $o).
0.69/0.67	thf(decl_150, type, binintersectSubset3: $o).
0.69/0.67	thf(decl_151, type, binintersectER: $o).
0.69/0.67	thf(decl_152, type, disjointsetsI1: $o).
0.69/0.67	thf(decl_153, type, binintersectRsub: $o).
0.69/0.67	thf(decl_154, type, binintersectSubset4: $o).
0.69/0.67	thf(decl_155, type, binintersectSubset1: $o).
0.69/0.67	thf(decl_156, type, bs114d: $o).
0.69/0.67	thf(decl_158, type, setminus: $i > $i > $i).
0.69/0.67	thf(decl_159, type, setminusI: $o).
0.69/0.67	thf(decl_160, type, setminusEL: $o).
0.69/0.67	thf(decl_161, type, setminusER: $o).
0.69/0.67	thf(decl_162, type, setminusSubset2: $o).
0.69/0.67	thf(decl_163, type, setminusERneg: $o).
0.69/0.67	thf(decl_164, type, setminusELneg: $o).
0.69/0.67	thf(decl_165, type, setminusILneg: $o).
0.69/0.67	thf(decl_166, type, setminusIRneg: $o).
0.69/0.67	thf(decl_167, type, setminusLsub: $o).
0.69/0.67	thf(decl_168, type, setminusSubset1: $o).
0.69/0.67	thf(decl_169, type, symdiff: $i > $i > $i).
0.69/0.67	thf(decl_170, type, symdiffE: $o).
0.69/0.67	thf(decl_171, type, symdiffI1: $o).
0.69/0.67	thf(decl_172, type, symdiffI2: $o).
0.69/0.67	thf(decl_173, type, symdiffIneg1: $o).
0.69/0.67	thf(decl_174, type, symdiffIneg2: $o).
0.69/0.67	thf(decl_175, type, iskpair: $i > $o).
0.69/0.67	thf(decl_176, type, secondinupair: $o).
0.69/0.67	thf(decl_177, type, setukpairIL: $o).
0.69/0.67	thf(decl_178, type, setukpairIR: $o).
0.69/0.67	thf(decl_179, type, kpairiskpair: $o).
0.69/0.67	thf(decl_180, type, kpair: $i > $i > $i).
0.69/0.67	thf(decl_181, type, kpairp: $o).
0.69/0.67	thf(decl_182, type, cartprod: $i > $i > $i).
0.69/0.67	thf(decl_183, type, singletonsubset: $o).
0.69/0.67	thf(decl_184, type, singletoninpowerset: $o).
0.69/0.67	thf(decl_185, type, singletoninpowunion: $o).
0.69/0.67	thf(decl_186, type, upairset2E: $o).
0.69/0.67	thf(decl_187, type, upairsubunion: $o).
0.69/0.67	thf(decl_188, type, upairinpowunion: $o).
0.69/0.67	thf(decl_189, type, ubforcartprodlem1: $o).
0.69/0.67	thf(decl_190, type, ubforcartprodlem2: $o).
0.69/0.67	thf(decl_191, type, ubforcartprodlem3: $o).
0.69/0.67	thf(decl_192, type, cartprodpairin: $o).
0.69/0.67	thf(decl_193, type, cartprodmempair1: $o).
0.69/0.67	thf(decl_194, type, cartprodmempair: $o).
0.69/0.67	thf(decl_195, type, setunionE2: $o).
0.69/0.67	thf(decl_196, type, setunionsingleton1: $o).
0.69/0.67	thf(decl_197, type, setunionsingleton2: $o).
0.69/0.67	thf(decl_198, type, setunionsingleton: $o).
0.69/0.67	thf(decl_199, type, singleton: $i > $o).
0.69/0.67	thf(decl_200, type, singletonprop: $o).
0.69/0.67	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
0.69/0.67	thf(decl_202, type, ex1E1: $o).
0.69/0.67	thf(decl_203, type, ex1I: $o).
0.69/0.67	thf(decl_204, type, ex1I2: $o).
0.69/0.67	thf(decl_205, type, singletonsuniq: $o).
0.69/0.67	thf(decl_210, type, setukpairinjL1: $o).
0.69/0.67	thf(decl_211, type, kfstsingleton: $o).
0.69/0.67	thf(decl_212, type, theprop: $o).
0.69/0.67	thf(decl_213, type, kfst: $i > $i).
0.69/0.67	thf(decl_214, type, kfstpairEq: $o).
0.69/0.67	thf(decl_215, type, cartprodfstin: $o).
0.69/0.67	thf(decl_216, type, setukpairinjL2: $o).
0.69/0.67	thf(decl_217, type, setukpairinjL: $o).
0.69/0.67	thf(decl_218, type, setukpairinjR11: $o).
0.69/0.67	thf(decl_219, type, setukpairinjR12: $o).
0.69/0.67	thf(decl_220, type, setukpairinjR1: $o).
0.69/0.67	thf(decl_221, type, upairequniteq: $o).
0.69/0.67	thf(decl_222, type, setukpairinjR2: $o).
0.69/0.67	thf(decl_223, type, setukpairinjR: $o).
0.69/0.67	thf(decl_224, type, ksndsingleton: $o).
0.69/0.67	thf(decl_225, type, ksnd: $i > $i).
0.69/0.67	thf(decl_226, type, ksndpairEq: $o).
0.69/0.67	thf(decl_227, type, epred1_0: $o).
0.69/0.67	thf(decl_228, type, esk1_2: $i > $i > $i).
0.69/0.67	thf(decl_229, type, esk2_2: $i > $i > $i).
0.69/0.67	thf(decl_230, type, esk3_2: $i > $i > $i).
0.69/0.67	thf(decl_231, type, esk4_1: $i > $i).
0.69/0.67	thf(decl_232, type, esk5_2: ($i > $i > $o) > $i > $i).
0.69/0.67	thf(decl_233, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
0.69/0.67	thf(decl_234, type, esk7_2: ($i > $i > $o) > $i > $i).
0.69/0.67	thf(decl_235, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
0.69/0.67	thf(decl_236, type, esk9_1: $i > $i).
0.69/0.67	thf(decl_237, type, esk10_2: ($i > $o) > $i > $i).
0.69/0.67	thf(decl_238, type, esk11_2: ($i > $o) > $i > $i).
0.69/0.67	thf(decl_239, type, esk12_1: ($i > $o) > $i).
0.69/0.67	thf(decl_240, type, esk13_2: ($i > $o) > $i > $i).
0.69/0.67	thf(decl_241, type, esk14_1: ($i > $o) > $i).
0.69/0.67	thf(decl_242, type, esk15_2: $i > $i > $i).
0.69/0.67	thf(decl_243, type, esk16_2: $i > $i > $i).
0.69/0.67	thf(decl_244, type, esk17_1: $i > $i).
0.69/0.67	thf(decl_245, type, esk18_1: $i > $i).
0.69/0.67	thf(decl_246, type, esk19_1: $i > $i).
0.69/0.67	thf(decl_247, type, esk20_2: $i > $i > $i).
0.69/0.67	thf(decl_248, type, esk21_3: $i > $i > $o > $i).
0.69/0.67	thf(decl_249, type, esk22_2: ($i > $o) > $i > $i).
0.69/0.67	thf(decl_250, type, esk23_1: ($i > $o) > $i).
0.69/0.67	thf(decl_251, type, esk24_1: $i > $i).
0.69/0.67	thf(decl_252, type, esk25_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_253, type, esk26_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_254, type, esk27_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_255, type, esk28_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_256, type, esk29_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_257, type, esk30_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_258, type, esk31_2: ($i > $o) > $i > $i).
0.69/0.67	thf(decl_259, type, esk32_1: ($i > $o) > $i).
0.69/0.67	thf(decl_260, type, esk33_1: ($i > $o) > $i).
0.69/0.67	thf(decl_261, type, esk34_1: ($i > $o) > $i).
0.69/0.67	thf(decl_262, type, esk35_1: ($i > $o) > $i).
0.69/0.67	thf(decl_263, type, esk36_2: ($i > $o) > $i > $i).
0.69/0.67	thf(decl_264, type, esk37_1: ($i > $o) > $i).
0.69/0.67	thf(decl_265, type, esk38_2: ($i > $o) > $i > $i).
0.69/0.67	thf(decl_266, type, esk39_2: ($i > $o) > ($i > $o) > $i).
0.69/0.67	thf(decl_267, type, esk40_2: ($i > $o) > ($i > $o) > $i).
0.69/0.67	thf(decl_268, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
0.69/0.67	thf(decl_269, type, esk42_2: ($i > $o) > ($i > $o) > $i).
0.69/0.67	thf(decl_270, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
0.69/0.67	thf(decl_271, type, esk44_2: ($i > $o) > ($i > $o) > $i).
0.69/0.67	thf(decl_272, type, esk45_2: ($i > $o) > $i > $i).
0.69/0.67	thf(decl_273, type, esk46_2: ($i > $o) > ($i > $o) > $i).
0.69/0.67	thf(decl_274, type, esk47_2: ($i > $o) > ($i > $o) > $i).
0.69/0.67	thf(decl_275, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
0.69/0.67	thf(decl_276, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
0.69/0.67	thf(decl_277, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.69/0.67	thf(decl_278, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.69/0.67	thf(decl_279, type, esk52_2: $i > $i > $i).
0.69/0.67	thf(decl_280, type, esk53_2: $i > $i > $i).
0.69/0.67	thf(decl_281, type, esk54_2: $i > $i > $i).
0.69/0.67	thf(decl_282, type, esk55_2: $i > $i > $i).
0.69/0.67	thf(decl_283, type, esk56_2: $i > $i > $i).
0.69/0.67	thf(decl_284, type, esk57_2: $i > $i > $i).
0.69/0.67	thf(decl_285, type, esk58_2: $i > $i > $i).
0.69/0.67	thf(decl_286, type, esk59_3: $i > $i > $i > $i).
0.69/0.67	thf(decl_287, type, esk60_3: $i > $i > $i > $i).
0.69/0.67	thf(decl_288, type, esk61_3: $i > $i > $i > $i).
0.69/0.67	thf(decl_289, type, esk62_3: $i > $i > $i > $i).
0.69/0.67	thf(decl_290, type, esk63_2: $i > $i > $i).
0.69/0.67	thf(decl_291, type, esk64_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_292, type, esk65_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_293, type, esk66_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_294, type, esk67_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_295, type, esk68_3: $i > ($i > $o) > $i > $i).
0.69/0.67	thf(decl_296, type, esk69_3: $i > ($i > $o) > $i > $i).
0.69/0.67	thf(decl_297, type, esk70_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_298, type, esk71_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_299, type, esk72_2: $i > ($i > $o) > $i).
0.69/0.67	thf(decl_300, type, esk73_1: $i > $i).
0.69/0.67	thf(decl_301, type, esk74_1: $i > $i).
0.69/0.67	thf(decl_302, type, esk75_0: $i).
0.69/0.67	thf(decl_303, type, esk76_0: $i).
0.69/0.67	thf(decl_304, type, esk77_0: $i).
0.69/0.67	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', ex1)).
0.69/0.67	thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', singleton)).
0.69/0.67	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', replAx)).
0.69/0.67	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', exu)).
0.69/0.67	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', descrp)).
0.69/0.67	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', exuE1)).
0.69/0.67	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', exuE3e)).
0.69/0.67	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', nonempty)).
0.69/0.67	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', nonemptyI)).
0.69/0.67	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', exuE2)).
0.69/0.67	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', exuI1)).
0.69/0.67	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', exuI3)).
0.69/0.67	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', exuI2)).
0.69/0.67	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', exuE3u)).
0.69/0.67	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', exu__Cong)).
0.69/0.67	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', exuEu)).
0.69/0.67	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', descr__Cong)).
0.69/0.67	thf(iskpair, axiom, ((iskpair)=(^[X4:$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/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', iskpair)).
0.69/0.67	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', singletonprop)).
0.69/0.67	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', ex1E1)).
0.69/0.67	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', ex1I)).
0.69/0.67	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', ex1I2)).
0.69/0.67	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', kfstsingleton)).
0.69/0.67	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', ksndsingleton)).
0.69/0.67	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', dsetconstrI)).
0.69/0.67	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', dsetconstrEL)).
0.69/0.67	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', dsetconstrER)).
0.69/0.67	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setbeta)).
0.69/0.67	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', nonemptyE1)).
0.69/0.67	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', nonemptyI1)).
0.69/0.67	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setoftrueEq)).
0.69/0.67	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', nonemptyImpWitness)).
0.69/0.67	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', emptyE1)).
0.69/0.67	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', dsetconstr__Cong)).
0.69/0.67	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', sepInPowerset)).
0.69/0.67	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', sepSubset)).
0.69/0.67	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', kpairiskpair)).
0.69/0.67	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', kpairp)).
0.69/0.67	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', cartprodmempair)).
0.69/0.67	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', theprop)).
0.69/0.67	thf(kpairsurjEq, conjecture, (((emptysetAx)=>((setadjoinAx)=>(((((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>(((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>(((((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>(((emptyI)=>((noeltsimpempty)=>((((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((((((((powersetE)=>(((setunionE)=>((subPowSU)=>(((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>(((((((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>(((quantDeMorgan3)=>((quantDeMorgan4)=>(((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>(((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>(((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>(((exuEu)=>(((((((subsetI2)=>(((((notsubsetI)=>(((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((((setextsub)=>((subsetemptysetimpeq)=>(((powersetE1)=>((inPowerset)=>(((sepInPowerset)=>((sepSubset)=>((((((binunionE)=>((((binintersectI)=>(((binintersectEL)=>((binintersectLsub)=>((((binintersectER)=>(((binintersectRsub)=>((((bs114d)=>((setminusI)=>((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>(((symdiffI1)=>((symdiffI2)=>(((symdiffIneg2)=>(((setukpairIL)=>((setukpairIR)=>(((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((((upairinpowunion)=>((ubforcartprodlem1)=>((((((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(((ex1E1)=>(((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>(((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>(((setukpairinjR1)=>((upairequniteq)=>(((((ksndpairEq)=>![X18:$i]:((((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))<=(iskpair @ X18))))<=(ksndsingleton))<=(setukpairinjR))<=(setukpairinjR2))))<=(setukpairinjR12))))))<=(kfstpairEq)))))))<=(ex1I)))<=(singletonprop)))))))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2))))<=(upairsubunion))<=(upairset2E))))))<=(kpairiskpair))))<=(secondinupair)))<=(symdiffIneg1))))<=(symdiffE))))))<=(setminusELneg))))<=(setminusER)))))<=(binintersectSubset1))<=(binintersectSubset4)))<=(disjointsetsI1)))<=(binintersectSubset3))<=(binintersectSubset2))))<=(binintersectSubset5)))<=(binunionRsub))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR))<=(upairset2IR))<=(binunionIL))))<=(powersetsubset))))<=(powersetI1))))<=(subset2powerset))<=(setadjoinSub2))))))<=(notequalI1)))<=(subsetE2))<=(subsetE))<=(emptysetsubset)))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong)))))<=(emptyset__Cong)))))))<=(exuI3))))))<=(prop2setI))))<=(quantDeMorgan2)))))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch))<=(eqinunit)))))<=(exuE2))))<=(setunionI)))<=(emptyInPowerset))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE)))))))<=(nonemptyE1))<=(setbeta))))<=(setext)))))<=(emptysetE))<=(prop2setE))<=(exuE1))))))<=(wellorderingAx))))))<=(omega0Ax))<=(setunionAx))<=(powersetAx))))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', kpairsurjEq)).
0.69/0.67	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setextAx)).
0.69/0.67	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', emptysetAx)).
0.69/0.67	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setadjoinAx)).
0.69/0.67	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', powersetAx)).
0.69/0.67	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setunionAx)).
0.69/0.67	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', omega0Ax)).
0.69/0.67	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', omegaSAx)).
0.69/0.67	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', omegaIndAx)).
0.69/0.67	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', foundationAx)).
0.69/0.67	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', wellorderingAx)).
0.69/0.67	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', prop2setE)).
0.69/0.67	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', emptysetE)).
0.69/0.67	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', emptysetimpfalse)).
0.69/0.67	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', notinemptyset)).
0.69/0.67	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setext)).
0.69/0.67	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', emptyI)).
0.69/0.67	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', noeltsimpempty)).
0.69/0.67	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setadjoinIL)).
0.69/0.67	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', emptyinunitempty)).
0.69/0.67	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setadjoinIR)).
0.69/0.67	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setadjoinE)).
0.69/0.67	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setadjoinOr)).
0.69/0.67	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', powersetI)).
0.69/0.67	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', emptyinPowerset)).
0.69/0.67	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', emptyInPowerset)).
0.69/0.67	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', powersetE)).
0.69/0.67	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setunionI)).
0.69/0.67	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setunionE)).
0.69/0.67	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', subPowSU)).
0.69/0.67	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', uniqinunit)).
0.69/0.67	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', notinsingleton)).
0.69/0.67	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', eqinunit)).
0.69/0.67	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', singletonsswitch)).
0.69/0.67	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', upairsetE)).
0.69/0.67	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', upairsetIL)).
0.69/0.67	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', upairsetIR)).
0.69/0.67	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', vacuousDall)).
0.69/0.67	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', quantDeMorgan1)).
0.69/0.67	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', quantDeMorgan2)).
0.69/0.67	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', quantDeMorgan3)).
0.69/0.67	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', quantDeMorgan4)).
0.69/0.67	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', prop2setI)).
0.69/0.67	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', prop2set2propI)).
0.69/0.67	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', notdexE)).
0.69/0.67	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', notdallE)).
0.69/0.67	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', inCongP)).
0.69/0.67	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', in__Cong)).
0.69/0.67	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', emptyset__Cong)).
0.69/0.67	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setadjoin__Cong)).
0.69/0.67	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', powerset__Cong)).
0.69/0.67	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setunion__Cong)).
0.69/0.67	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', omega__Cong)).
0.69/0.67	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', subsetI1)).
0.69/0.67	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', eqimpsubset2)).
0.69/0.67	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', eqimpsubset1)).
0.69/0.67	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', subsetI2)).
0.69/0.67	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', emptysetsubset)).
0.69/0.67	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', subsetE)).
0.69/0.67	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', subsetE2)).
0.69/0.67	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', notsubsetI)).
0.69/0.67	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', notequalI1)).
0.69/0.67	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', notequalI2)).
0.69/0.67	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', subsetRefl)).
0.69/0.67	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', subsetTrans)).
0.69/0.67	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setadjoinSub)).
0.69/0.67	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setadjoinSub2)).
0.69/0.67	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', subset2powerset)).
0.69/0.67	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setextsub)).
0.69/0.67	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', subsetemptysetimpeq)).
0.69/0.67	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', powersetI1)).
0.69/0.67	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', powersetE1)).
0.69/0.67	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', inPowerset)).
0.69/0.67	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', powersetsubset)).
0.69/0.67	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binunionIL)).
0.69/0.67	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', upairset2IR)).
0.69/0.67	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binunionIR)).
0.69/0.67	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binunionEcases)).
0.69/0.67	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binunionE)).
0.69/0.67	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binunionLsub)).
0.69/0.67	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binunionRsub)).
0.69/0.67	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binintersectI)).
0.69/0.67	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binintersectSubset5)).
0.69/0.67	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binintersectEL)).
0.69/0.67	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binintersectLsub)).
0.69/0.67	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binintersectSubset2)).
0.69/0.67	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binintersectSubset3)).
0.69/0.67	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binintersectER)).
0.69/0.67	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', disjointsetsI1)).
0.69/0.67	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binintersectRsub)).
0.69/0.67	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binintersectSubset4)).
0.69/0.67	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', binintersectSubset1)).
0.69/0.67	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', bs114d)).
0.69/0.67	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setminusI)).
0.69/0.67	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setminusEL)).
0.69/0.67	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setminusER)).
0.69/0.67	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setminusSubset2)).
0.69/0.67	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setminusERneg)).
0.69/0.67	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setminusELneg)).
0.69/0.67	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setminusILneg)).
0.69/0.67	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setminusIRneg)).
0.69/0.67	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setminusLsub)).
0.69/0.67	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setminusSubset1)).
0.69/0.67	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', symdiffE)).
0.69/0.67	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', symdiffI1)).
0.69/0.67	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', symdiffI2)).
0.69/0.67	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', symdiffIneg1)).
0.69/0.67	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', symdiffIneg2)).
0.69/0.67	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', secondinupair)).
0.69/0.67	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setukpairIL)).
0.69/0.67	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setukpairIR)).
0.69/0.67	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', singletonsubset)).
0.69/0.67	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', singletoninpowerset)).
0.69/0.67	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', singletoninpowunion)).
0.69/0.67	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', upairset2E)).
0.69/0.67	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', upairsubunion)).
0.69/0.67	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', upairinpowunion)).
0.69/0.67	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', ubforcartprodlem1)).
0.69/0.67	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', ubforcartprodlem2)).
0.69/0.67	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', ubforcartprodlem3)).
0.69/0.67	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', cartprodpairin)).
0.69/0.67	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', cartprodmempair1)).
0.69/0.67	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setunionE2)).
0.69/0.67	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setunionsingleton1)).
0.69/0.67	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setunionsingleton2)).
0.69/0.67	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setunionsingleton)).
0.69/0.67	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', singletonsuniq)).
0.69/0.67	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setukpairinjL1)).
0.69/0.67	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', kfstpairEq)).
0.69/0.67	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', cartprodfstin)).
0.69/0.67	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setukpairinjL2)).
0.69/0.67	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setukpairinjL)).
0.69/0.67	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setukpairinjR11)).
0.69/0.67	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setukpairinjR12)).
0.69/0.67	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setukpairinjR1)).
0.69/0.67	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', upairequniteq)).
0.69/0.67	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setukpairinjR2)).
0.69/0.67	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', setukpairinjR)).
0.69/0.67	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', ksndpairEq)).
0.69/0.67	thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.rhJX8kM7xO/E---3.1_17604.p', kpair)).
0.69/0.67	thf(c_0_180, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X529:$i]:(((in @ X529 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X529 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
0.69/0.67	thf(c_0_181, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
0.69/0.67	thf(c_0_182, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
0.69/0.67	thf(c_0_183, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
0.69/0.67	thf(c_0_184, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
0.69/0.67	thf(c_0_185, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
0.69/0.67	thf(c_0_186, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
0.69/0.67	thf(c_0_187, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
0.69/0.67	thf(c_0_188, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
0.69/0.67	thf(c_0_189, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
0.69/0.67	thf(c_0_190, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
0.69/0.67	thf(c_0_191, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
0.69/0.67	thf(c_0_192, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
0.69/0.67	thf(c_0_193, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
0.69/0.67	thf(c_0_194, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
0.69/0.67	thf(c_0_195, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
0.69/0.67	thf(c_0_196, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
0.69/0.67	thf(c_0_197, plain, ((iskpair)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ (setunion @ Z0))&?[X3:$i]:(((in @ X3 @ (setunion @ Z0))&((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))), inference(fof_simplification,[status(thm)],[iskpair])).
0.69/0.67	thf(c_0_198, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
0.69/0.67	thf(c_0_199, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
0.69/0.67	thf(c_0_200, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X529:$i]:(((in @ X529 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X529 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_180, c_0_181])).
0.69/0.67	thf(c_0_201, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
0.69/0.67	thf(c_0_202, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
0.69/0.67	thf(c_0_203, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
0.69/0.67	thf(c_0_204, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
0.69/0.67	thf(c_0_205, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X494:$i]:((((X6 @ X2 @ X494))&![X495:$i]:((((X6 @ X2 @ X495))=>((X494)=(X495)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_182, c_0_183])).
0.69/0.67	thf(c_0_206, plain, ((descrp)=(![X1:$i > $o]:(((?[X496:$i]:((((X1 @ X496))&![X497:$i]:((((X1 @ X497))=>((X496)=(X497)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_184, c_0_183])).
0.69/0.67	thf(c_0_207, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
0.69/0.67	thf(c_0_208, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
0.69/0.67	thf(c_0_209, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
0.69/0.67	thf(c_0_210, plain, ((exuE1)=(![X1:$i > $o]:(((?[X498:$i]:((((X1 @ X498))&![X499:$i]:((((X1 @ X499))=>((X498)=(X499)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_185, c_0_183])).
0.69/0.67	thf(c_0_211, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X500:$i]:((((X1 @ X500))&![X501:$i]:((((X1 @ X501))=>((X500)=(X501)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_186, c_0_183])).
0.69/0.67	thf(c_0_212, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
0.69/0.67	thf(c_0_213, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_187])).
0.69/0.67	thf(c_0_214, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_188, c_0_187])).
0.69/0.67	thf(c_0_215, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_187])).
0.69/0.67	thf(c_0_216, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
0.69/0.67	thf(c_0_217, plain, ((exuE2)=(![X1:$i > $o]:(((?[X502:$i]:((((X1 @ X502))&![X503:$i]:((((X1 @ X503))=>((X502)=(X503)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_189, c_0_183])).
0.69/0.67	thf(c_0_218, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_187])).
0.69/0.67	thf(c_0_219, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
0.69/0.67	thf(c_0_220, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X504:$i]:((((X1 @ X504))&![X505:$i]:((((X1 @ X505))=>((X504)=(X505))))))))))), inference(apply_def,[status(thm)],[c_0_190, c_0_183])).
0.69/0.67	thf(c_0_221, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X506:$i]:((((X1 @ X506))&![X507:$i]:((((X1 @ X507))=>((X506)=(X507)))))))))))), inference(apply_def,[status(thm)],[c_0_191, c_0_183])).
0.69/0.67	thf(c_0_222, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X508:$i]:((((X1 @ X508))&![X509:$i]:((((X1 @ X509))=>((X508)=(X509))))))))))), inference(apply_def,[status(thm)],[c_0_192, c_0_183])).
0.69/0.67	thf(c_0_223, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X510:$i]:((((X1 @ X510))&![X511:$i]:((((X1 @ X511))=>((X510)=(X511)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_193, c_0_183])).
0.69/0.67	thf(c_0_224, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X512:$i]:((((X1 @ X512))&![X513:$i]:((((X1 @ X513))=>((X512)=(X513)))))))<=>(?[X514:$i]:((((X17 @ X514))&![X515:$i]:((((X17 @ X515))=>((X514)=(X515)))))))))))), inference(apply_def,[status(thm)],[c_0_194, c_0_183])).
0.69/0.67	thf(c_0_225, plain, ((exuEu)=(![X1:$i > $o]:(((?[X516:$i]:((((X1 @ X516))&![X517:$i]:((((X1 @ X517))=>((X516)=(X517)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_195, c_0_183])).
0.69/0.67	thf(c_0_226, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X518:$i]:((((X1 @ X518))&![X519:$i]:((((X1 @ X519))=>((X518)=(X519)))))))=>((?[X520:$i]:((((X17 @ X520))&![X521:$i]:((((X17 @ X521))=>((X520)=(X521)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_183])).
0.69/0.67	thf(c_0_227, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
0.69/0.67	thf(c_0_228, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
0.69/0.67	thf(c_0_229, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
0.69/0.67	thf(c_0_230, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X522:$i]:(((in @ X522 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X523:$i]:(((in @ X523 @ (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 @ X522 @ emptyset) @ (setadjoin @ (setadjoin @ X522 @ (setadjoin @ X523 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_197])).
0.69/0.67	thf(c_0_231, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X524:$i]:(((in @ X524 @ (setunion @ (kpair @ X2 @ X3)))&?[X525:$i]:(((in @ X525 @ (setunion @ (kpair @ X2 @ X3)))&((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X524 @ emptyset) @ (setadjoin @ (setadjoin @ X524 @ (setadjoin @ X525 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_197])).
0.69/0.67	thf(c_0_232, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(?[X526:$i]:(((in @ X526 @ (setunion @ X18))&?[X527:$i]:(((in @ X527 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X526 @ emptyset) @ (setadjoin @ (setadjoin @ X526 @ (setadjoin @ X527 @ emptyset)) @ emptyset)))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_197])).
0.69/0.67	thf(c_0_233, plain, ((singletonprop)=(![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(?[X528:$i]:(((in @ X528 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X528 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_198, c_0_181])).
0.69/0.67	thf(c_0_234, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X530:$i]:(((in @ X530 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X530 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_199, c_0_200])).
0.69/0.67	thf(c_0_235, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X531:$i]:(((in @ X531 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X531 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_201, c_0_200])).
0.69/0.67	thf(c_0_236, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(?[X532:$i]:(((in @ X532 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X532 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_202, c_0_200])).
0.69/0.67	thf(c_0_237, plain, ((kfstsingleton)=(![X18:$i]:(((?[X533:$i]:(((in @ X533 @ (setunion @ X18))&?[X534:$i]:(((in @ X534 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X533 @ emptyset) @ (setadjoin @ (setadjoin @ X533 @ (setadjoin @ X534 @ emptyset)) @ emptyset))))))))=>(?[X535:$i]:(((in @ X535 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X535 @ emptyset))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_203, c_0_197]), c_0_181])).
0.69/0.67	thf(c_0_238, axiom, ((theprop)=(![X21:$i]:(((?[X536:$i]:(((in @ X536 @ X21)&((X21)=(setadjoin @ X536 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_181])).
0.69/0.67	thf(c_0_239, plain, ((ksndsingleton)=(![X18:$i]:(((?[X537:$i]:(((in @ X537 @ (setunion @ X18))&?[X538:$i]:(((in @ X538 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X537 @ emptyset) @ (setadjoin @ (setadjoin @ X537 @ (setadjoin @ X538 @ emptyset)) @ emptyset))))))))=>(?[X539:$i]:(((in @ X539 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X539 @ emptyset))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_204, c_0_197]), c_0_181])).
0.69/0.67	thf(c_0_240, plain, ((epred1_0)<=>![X1030:$i]:(?[X1031:$i]:((((![X1032:$i]:(((in @ X1032 @ X1031)=>![X1033:$i]:(((in @ X1033 @ X1032)=>(in @ X1033 @ X1030)))))&![X1034:$i, X1035:$i]:((((in @ X1034 @ X1030)&(in @ X1035 @ X1030))=>(![X1036:$i]:(((in @ X1036 @ X1031)=>((in @ X1034 @ X1036)<=>(in @ X1035 @ X1036))))=>((X1034)=(X1035))))))&![X1037:$i, X1038:$i]:((((in @ X1037 @ X1031)&(in @ X1038 @ X1031))=>(![X1039:$i]:(((in @ X1039 @ X1037)=>(in @ X1039 @ X1038)))|![X1040:$i]:(((in @ X1040 @ X1038)=>(in @ X1040 @ X1037)))))))&![X1041:$i]:(((![X1042:$i]:(((in @ X1042 @ X1041)=>(in @ X1042 @ X1030)))&?[X1043:$i]:((in @ X1043 @ X1041)))=>?[X1044:$i, X1045:$i]:(((((in @ X1044 @ X1031)&(in @ X1045 @ X1041))&~(?[X1046:$i]:(((in @ X1046 @ X1044)&(in @ X1046 @ X1041)))))&![X1047:$i]:(((in @ X1047 @ X1031)=>(![X1048:$i]:(((in @ X1048 @ X1047)=>(in @ X1048 @ X1044)))|(in @ X1045 @ X1047)))))))))))), introduced(definition)).
0.69/0.67	thf(c_0_241, negated_conjecture, ~((![X1055:$i, X1056:$i]:((![X1057:$i]:(((in @ X1057 @ X1055)<=>(in @ X1057 @ X1056)))=>((X1055)=(X1056))))=>(![X540:$i]:(~(in @ X540 @ emptyset))=>(![X541:$i, X542:$i, X543:$i]:(((in @ X543 @ (setadjoin @ X541 @ X542))<=>(((X543)=(X541))|(in @ X543 @ X542))))=>(![X1052:$i, X1053:$i]:(((in @ X1053 @ (powerset @ X1052))<=>![X1054:$i]:(((in @ X1054 @ X1053)=>(in @ X1054 @ X1052)))))=>(![X1049:$i, X1050:$i]:(((in @ X1050 @ (setunion @ X1049))<=>?[X1051:$i]:(((in @ X1050 @ X1051)&(in @ X1051 @ X1049)))))=>((in @ emptyset @ omega)=>(![X544:$i]:(((in @ X544 @ omega)=>(in @ (setadjoin @ X544 @ X544) @ omega)))=>(![X545:$i]:((((in @ emptyset @ X545)&![X546:$i]:((((in @ X546 @ omega)&(in @ X546 @ X545))=>(in @ (setadjoin @ X546 @ X546) @ X545))))=>![X547:$i]:(((in @ X547 @ omega)=>(in @ X547 @ X545)))))=>(![X548:$i > $i > $o, X549:$i]:((![X550:$i]:(((in @ X550 @ X549)=>?[X551:$i]:(((X548 @ X550 @ X551)&![X552:$i]:(((X548 @ X550 @ X552)=>((X551)=(X552))))))))=>?[X553:$i]:(![X554:$i]:(((in @ X554 @ X553)<=>?[X555:$i]:(((in @ X555 @ X549)&(X548 @ X555 @ X554))))))))=>(![X556:$i]:((?[X557:$i]:((in @ X557 @ X556))=>?[X558:$i]:(((in @ X558 @ X556)&~(?[X559:$i]:(((in @ X559 @ X558)&(in @ X559 @ X556))))))))=>((epred1_0)=>(![X560:$i > $o]:((?[X561:$i]:(((X560 @ X561)&![X562:$i]:(((X560 @ X562)=>((X561)=(X562))))))=>(X560 @ (descr @ (^[Z0/* 17 */:$i]:(X560 @ Z0))))))=>(![X563:$i, X564:$i > $o, X565:$i]:(((in @ X565 @ X563)=>((X564 @ X565)=>(in @ X565 @ (dsetconstr @ X563 @ X564)))))=>(![X566:$i, X567:$i > $o, X568:$i]:(((in @ X568 @ (dsetconstr @ X566 @ X567))=>(in @ X568 @ X566)))=>(![X569:$i, X570:$i > $o, X571:$i]:(((in @ X571 @ (dsetconstr @ X569 @ X570))=>(X570 @ X571)))=>(![X1025:$i > $o]:((?[X1026:$i]:(((X1025 @ X1026)&![X1027:$i]:(((X1025 @ X1027)=>((X1026)=(X1027))))))=>?[X1028:$i]:(((X1025 @ X1028)&![X1029:$i]:(((X1025 @ X1029)=>((X1028)=(X1029))))))))=>(![X1023:$o, X1024:$i]:(((in @ X1024 @ (prop2set @ ((X1023))))=>(X1023)))=>(![X1021:$i]:(((in @ X1021 @ emptyset)=>![X1022:$o]:((X1022))))=>(![X572:$i]:(((in @ X572 @ emptyset)=>~($true)))=>(![X573:$i]:(~(in @ X573 @ emptyset))=>(![X574:$i > $o]:((?[X575:$i]:(((X574 @ X575)&![X576:$i]:(((X574 @ X576)=>((X575)=(X576))))))=>?[X577:$i]:((X574 @ X577))))=>(![X1017:$i, X1018:$i]:((![X1019:$i]:(((in @ X1019 @ X1017)=>(in @ X1019 @ X1018)))=>(![X1020:$i]:(((in @ X1020 @ X1018)=>(in @ X1020 @ X1017)))=>((X1017)=(X1018)))))=>(![X578:$i]:((![X579:$i]:(~(in @ X579 @ X578))=>((X578)=(emptyset))))=>(![X580:$i]:((![X581:$i]:(~(in @ X581 @ X580))=>((X580)=(emptyset))))=>(![X1014:$i, X1015:$i > $o, X1016:$i]:(((in @ X1016 @ X1014)=>((in @ X1016 @ (dsetconstr @ X1014 @ X1015))<=>(X1015 @ X1016))))=>(![X1012:$i]:((((X1012)!=(emptyset))=>?[X1013:$i]:((in @ X1013 @ X1012))))=>(![X582:$i, X583:$i > $o, X584:$i]:(((in @ X584 @ X582)=>((X583 @ X584)=>((dsetconstr @ X582 @ X583)!=(emptyset)))))=>(![X585:$i]:((?[X586:$i]:((in @ X586 @ X585))=>((X585)!=(emptyset))))=>(![X587:$i, X588:$i]:((in @ X587 @ (setadjoin @ X587 @ X588)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X589:$i, X590:$i, X591:$i]:(((in @ X591 @ X590)=>(in @ X591 @ (setadjoin @ X589 @ X590))))=>(![X1008:$i, X1009:$i, X1010:$i]:(((in @ X1010 @ (setadjoin @ X1008 @ X1009))=>![X1011:$o]:(((((X1010)=(X1008))=>(X1011))=>(((in @ X1010 @ X1009)=>(X1011))=>(X1011))))))=>(![X1005:$i, X1006:$i, X1007:$i]:(((in @ X1007 @ (setadjoin @ X1005 @ X1006))=>(((X1007)=(X1005))|(in @ X1007 @ X1006))))=>(![X1004:$i]:(((dsetconstr @ X1004 @ (^[Z0/* 1 */:$i]:($true)))=(X1004)))=>(![X1001:$i, X1002:$i]:((![X1003:$i]:(((in @ X1003 @ X1002)=>(in @ X1003 @ X1001)))=>(in @ X1002 @ (powerset @ X1001))))=>(![X1000:$i]:((in @ emptyset @ (powerset @ X1000)))=>(![X999:$i]:((in @ emptyset @ (powerset @ X999)))=>(![X592:$i, X593:$i, X594:$i]:(((in @ X593 @ (powerset @ X592))=>((in @ X594 @ X593)=>(in @ X594 @ X592))))=>(![X996:$i, X997:$i, X998:$i]:(((in @ X997 @ X998)=>((in @ X998 @ X996)=>(in @ X997 @ (setunion @ X996)))))=>(![X595:$i, X596:$i]:(((in @ X596 @ (setunion @ X595))=>![X597:$o]:((![X598:$i]:(((in @ X596 @ X598)=>((in @ X598 @ X595)=>(X597))))=>(X597)))))=>(![X599:$i, X600:$i]:(((in @ X600 @ X599)=>(in @ X600 @ (powerset @ (setunion @ X599)))))=>(![X991:$i > $o]:((?[X992:$i]:(((X991 @ X992)&![X993:$i]:(((X991 @ X993)=>((X992)=(X993))))))=>?[X994:$i]:(![X995:$i]:(((X991 @ X995)<=>((X995)=(X994)))))))=>(![X601:$i]:((((X601)!=(emptyset))=>?[X602:$i]:(((in @ X602 @ X601)&$true))))=>(![X603:$i, X604:$i]:(((in @ X603 @ (setadjoin @ X604 @ emptyset))=>((X603)=(X604))))=>(![X605:$i, X606:$i]:((((X605)!=(X606))=>~(in @ X606 @ (setadjoin @ X605 @ emptyset))))=>(![X989:$i, X990:$i]:((((X989)=(X990))=>(in @ X989 @ (setadjoin @ X990 @ emptyset))))=>(![X987:$i, X988:$i]:(((in @ X987 @ (setadjoin @ X988 @ emptyset))=>(in @ X988 @ (setadjoin @ X987 @ emptyset))))=>(![X984:$i, X985:$i, X986:$i]:(((in @ X986 @ (setadjoin @ X984 @ (setadjoin @ X985 @ emptyset)))=>(((X986)=(X984))|((X986)=(X985)))))=>(![X982:$i, X983:$i]:((in @ X982 @ (setadjoin @ X982 @ (setadjoin @ X983 @ emptyset))))=>(![X980:$i, X981:$i]:((in @ X981 @ (setadjoin @ X980 @ (setadjoin @ X981 @ emptyset))))=>(![X607:$i, X608:$i > $o]:((?[X609:$i]:(((in @ X609 @ X607)&(X608 @ X609)))=>(((dsetconstr @ X607 @ X608)=(emptyset))=>~($true))))=>(![X610:$i > $o, X611:$i]:(((in @ X611 @ emptyset)=>(X610 @ X611)))=>(![X612:$i, X613:$i > $o]:((~(![X614:$i]:(((in @ X614 @ X612)=>(X613 @ X614))))=>?[X615:$i]:(((in @ X615 @ X612)&~((X613 @ X615))))))=>(![X976:$i, X977:$i > $o]:((![X978:$i]:(((in @ X978 @ X976)=>~((X977 @ X978))))=>~(?[X979:$i]:(((in @ X979 @ X976)&(X977 @ X979))))))=>(![X616:$i, X617:$i > $o]:((~(?[X618:$i]:(((in @ X618 @ X616)&(X617 @ X618))))=>![X619:$i]:(((in @ X619 @ X616)=>~((X617 @ X619))))))=>(![X620:$i, X621:$i > $o]:((?[X622:$i]:(((in @ X622 @ X620)&~((X621 @ X622))))=>~(![X623:$i]:(((in @ X623 @ X620)=>(X621 @ X623))))))=>(![X975:$o]:(((X975)=>(in @ emptyset @ (prop2set @ ((X975))))))=>(![X624:$o]:(((X624)=>(set2prop @ (prop2set @ ((X624))))))=>(![X625:$i, X626:$i > $o]:((~(?[X627:$i]:(((in @ X627 @ X625)&(X626 @ X627))))=>![X628:$i]:(((in @ X628 @ X625)=>~((X626 @ X628))))))=>(![X629:$i, X630:$i > $o]:((~(![X631:$i]:(((in @ X631 @ X629)=>(X630 @ X631))))=>?[X632:$i]:(((in @ X632 @ X629)&~((X630 @ X632))))))=>(![X633:$i > $o]:((?[X634:$i]:(((X633 @ X634)&![X635:$i]:(((X633 @ X635)=>((X634)=(X635))))))=>?[X636:$i]:(((X633 @ X636)&![X637:$i]:(((X633 @ X637)=>((X636)=(X637))))))))=>(![X969:$i > $o]:((?[X970:$i]:((X969 @ X970))=>(![X971:$i, X972:$i]:(((X969 @ X971)=>((X969 @ X972)=>((X971)=(X972)))))=>?[X973:$i]:(((X969 @ X973)&![X974:$i]:(((X969 @ X974)=>((X973)=(X974)))))))))=>(![X638:$i > $o]:((?[X639:$i]:(![X640:$i]:(((X638 @ X640)<=>((X640)=(X639)))))=>?[X641:$i]:(((X638 @ X641)&![X642:$i]:(((X638 @ X642)=>((X641)=(X642))))))))=>(![X643:$i, X644:$i]:((((X643)=(X644))=>![X645:$i, X646:$i]:((((X645)=(X646))=>((in @ X645 @ X643)=>(in @ X646 @ X644))))))=>(![X647:$i, X648:$i]:((((X647)=(X648))=>![X649:$i, X650:$i]:((((X649)=(X650))=>((in @ X649 @ X647)<=>(in @ X650 @ X648))))))=>(![X651:$i > $o]:((?[X652:$i]:(((X651 @ X652)&![X653:$i]:(((X651 @ X653)=>((X652)=(X653))))))=>![X654:$i, X655:$i]:(((X651 @ X654)=>((X651 @ X655)=>((X654)=(X655)))))))=>(![X656:$i > $o, X657:$i > $o]:((![X658:$i, X659:$i]:((((X658)=(X659))=>((X656 @ X658)<=>(X657 @ X659))))=>(?[X660:$i]:(((X656 @ X660)&![X661:$i]:(((X656 @ X661)=>((X660)=(X661))))))<=>?[X662:$i]:(((X657 @ X662)&![X663:$i]:(((X657 @ X663)=>((X662)=(X663)))))))))=>(((emptyset)=(emptyset))=>(![X664:$i, X665:$i]:((((X664)=(X665))=>![X666:$i, X667:$i]:((((X666)=(X667))=>((setadjoin @ X664 @ X666)=(setadjoin @ X665 @ X667))))))=>(![X668:$i, X669:$i]:((((X668)=(X669))=>((powerset @ X668)=(powerset @ X669))))=>(![X670:$i, X671:$i]:((((X670)=(X671))=>((setunion @ X670)=(setunion @ X671))))=>(((omega)=(omega))=>(![X672:$i > $o]:((?[X673:$i]:(((X672 @ X673)&![X674:$i]:(((X672 @ X674)=>((X673)=(X674))))))=>![X675:$i, X676:$i]:(((X672 @ X675)=>((X672 @ X676)=>((X675)=(X676)))))))=>(![X961:$i > $o, X962:$i > $o]:((![X963:$i, X964:$i]:((((X963)=(X964))=>((X961 @ X963)<=>(X962 @ X964))))=>(?[X965:$i]:(((X961 @ X965)&![X966:$i]:(((X961 @ X966)=>((X965)=(X966))))))=>(?[X967:$i]:(((X962 @ X967)&![X968:$i]:(((X962 @ X968)=>((X967)=(X968))))))=>((descr @ X961)=(descr @ X962))))))=>(![X955:$i, X956:$i]:((((X955)=(X956))=>![X957:$i > $o, X958:$i > $o]:((![X959:$i]:(((in @ X959 @ X955)=>![X960:$i]:(((in @ X960 @ X956)=>(((X959)=(X960))=>((X957 @ X959)<=>(X958 @ X960)))))))=>((dsetconstr @ X955 @ X957)=(dsetconstr @ X956 @ X958))))))=>(![X952:$i, X953:$i]:((![X954:$i]:(((in @ X954 @ X952)=>(in @ X954 @ X953)))=>(subset @ X952 @ X953)))=>(![X950:$i, X951:$i]:((((X950)=(X951))=>(subset @ X951 @ X950)))=>(![X948:$i, X949:$i]:((((X948)=(X949))=>(subset @ X948 @ X949)))=>(![X677:$i, X678:$i]:((![X679:$i]:(((in @ X679 @ X677)=>(in @ X679 @ X678)))=>(subset @ X677 @ X678)))=>(![X947:$i]:((subset @ emptyset @ X947))=>(![X944:$i, X945:$i, X946:$i]:(((subset @ X944 @ X945)=>((in @ X946 @ X944)=>(in @ X946 @ X945))))=>(![X941:$i, X942:$i, X943:$i]:(((subset @ X941 @ X942)=>(~(in @ X943 @ X942)=>~(in @ X943 @ X941))))=>(![X680:$i, X681:$i, X682:$i]:(((in @ X682 @ X680)=>(~(in @ X682 @ X681)=>~(subset @ X680 @ X681))))=>(![X939:$i, X940:$i]:((~(subset @ X939 @ X940)=>((X939)!=(X940))))=>(![X683:$i, X684:$i, X685:$i]:(((in @ X685 @ X683)=>(~(in @ X685 @ X684)=>((X683)!=(X684)))))=>(![X686:$i]:((subset @ X686 @ X686))=>(![X687:$i, X688:$i, X689:$i]:(((subset @ X687 @ X688)=>((subset @ X688 @ X689)=>(subset @ X687 @ X689))))=>(![X690:$i, X691:$i]:((subset @ X691 @ (setadjoin @ X690 @ X691)))=>(![X936:$i, X937:$i, X938:$i]:(((subset @ X936 @ X938)=>(subset @ X936 @ (setadjoin @ X937 @ X938))))=>(![X934:$i, X935:$i]:(((subset @ X934 @ X935)=>(in @ X934 @ (powerset @ X935))))=>(![X692:$i, X693:$i]:(((subset @ X692 @ X693)=>((subset @ X693 @ X692)=>((X692)=(X693)))))=>(![X694:$i]:(((subset @ X694 @ emptyset)=>((X694)=(emptyset))))=>(![X932:$i, X933:$i]:(((subset @ X933 @ X932)=>(in @ X933 @ (powerset @ X932))))=>(![X695:$i, X696:$i]:(((in @ X696 @ (powerset @ X695))=>(subset @ X696 @ X695)))=>(![X697:$i]:((in @ X697 @ (powerset @ X697)))=>(![X930:$i, X931:$i]:(((subset @ X930 @ X931)=>(subset @ (powerset @ X930) @ (powerset @ X931))))=>(![X698:$i, X699:$i > $o]:((in @ (dsetconstr @ X698 @ X699) @ (powerset @ X698)))=>(![X700:$i, X701:$i > $o]:((subset @ (dsetconstr @ X700 @ X701) @ X700))=>(![X927:$i, X928:$i, X929:$i]:(((in @ X929 @ X927)=>(in @ X929 @ (binunion @ X927 @ X928))))=>(![X925:$i, X926:$i]:((in @ X926 @ (setadjoin @ X925 @ (setadjoin @ X926 @ emptyset))))=>(![X922:$i, X923:$i, X924:$i]:(((in @ X924 @ X923)=>(in @ X924 @ (binunion @ X922 @ X923))))=>(![X918:$i, X919:$i, X920:$i, X921:$o]:(((in @ X920 @ (binunion @ X918 @ X919))=>(((in @ X920 @ X918)=>(X921))=>(((in @ X920 @ X919)=>(X921))=>(X921)))))=>(![X702:$i, X703:$i, X704:$i]:(((in @ X704 @ (binunion @ X702 @ X703))=>((in @ X704 @ X702)|(in @ X704 @ X703))))=>(![X916:$i, X917:$i]:((subset @ X916 @ (binunion @ X916 @ X917)))=>(![X914:$i, X915:$i]:((subset @ X915 @ (binunion @ X914 @ X915)))=>(![X705:$i, X706:$i, X707:$i]:(((in @ X707 @ X705)=>((in @ X707 @ X706)=>(in @ X707 @ (binintersect @ X705 @ X706)))))=>(![X911:$i, X912:$i, X913:$i]:(((subset @ X913 @ X911)=>((subset @ X913 @ X912)=>(subset @ X913 @ (binintersect @ X911 @ X912)))))=>(![X708:$i, X709:$i, X710:$i]:(((in @ X710 @ (binintersect @ X708 @ X709))=>(in @ X710 @ X708)))=>(![X711:$i, X712:$i]:((subset @ (binintersect @ X711 @ X712) @ X711))=>(![X909:$i, X910:$i]:(((subset @ X909 @ X910)=>((binintersect @ X909 @ X910)=(X909))))=>(![X907:$i, X908:$i]:((((binintersect @ X907 @ X908)=(X908))=>(subset @ X908 @ X907)))=>(![X713:$i, X714:$i, X715:$i]:(((in @ X715 @ (binintersect @ X713 @ X714))=>(in @ X715 @ X714)))=>(![X904:$i, X905:$i]:((~(?[X906:$i]:(((in @ X906 @ X904)&(in @ X906 @ X905))))=>((binintersect @ X904 @ X905)=(emptyset))))=>(![X716:$i, X717:$i]:((subset @ (binintersect @ X716 @ X717) @ X717))=>(![X902:$i, X903:$i]:(((subset @ X903 @ X902)=>((binintersect @ X902 @ X903)=(X903))))=>(![X900:$i, X901:$i]:((((binintersect @ X900 @ X901)=(X900))=>(subset @ X900 @ X901)))=>(![X718:$i, X719:$i, X720:$i]:(((binintersect @ X718 @ (binunion @ X719 @ X720))=(binunion @ (binintersect @ X718 @ X719) @ (binintersect @ X718 @ X720))))=>(![X721:$i, X722:$i, X723:$i]:(((in @ X723 @ X721)=>(~(in @ X723 @ X722)=>(in @ X723 @ (setminus @ X721 @ X722)))))=>(![X724:$i, X725:$i, X726:$i]:(((in @ X726 @ (setminus @ X724 @ X725))=>(in @ X726 @ X724)))=>(![X897:$i, X898:$i, X899:$i]:(((in @ X899 @ (setminus @ X897 @ X898))=>~(in @ X899 @ X898)))=>(![X727:$i, X728:$i]:(((subset @ X727 @ X728)=>((setminus @ X727 @ X728)=(emptyset))))=>(![X729:$i, X730:$i, X731:$i]:((~(in @ X731 @ (setminus @ X729 @ X730))=>((in @ X731 @ X729)=>(in @ X731 @ X730))))=>(![X894:$i, X895:$i, X896:$i]:((~(in @ X896 @ (setminus @ X894 @ X895))=>(~(in @ X896 @ X895)=>~(in @ X896 @ X894))))=>(![X732:$i, X733:$i, X734:$i]:((~(in @ X734 @ X732)=>~(in @ X734 @ (setminus @ X732 @ X733))))=>(![X735:$i, X736:$i, X737:$i]:(((in @ X737 @ X736)=>~(in @ X737 @ (setminus @ X735 @ X736))))=>(![X738:$i, X739:$i]:((subset @ (setminus @ X738 @ X739) @ X738))=>(![X740:$i, X741:$i]:((((setminus @ X740 @ X741)=(emptyset))=>(subset @ X740 @ X741)))=>(![X890:$i, X891:$i, X892:$i]:(((in @ X892 @ (symdiff @ X890 @ X891))=>![X893:$o]:((((in @ X892 @ X890)=>(~(in @ X892 @ X891)=>(X893)))=>((~(in @ X892 @ X890)=>((in @ X892 @ X891)=>(X893)))=>(X893))))))=>(![X742:$i, X743:$i, X744:$i]:(((in @ X744 @ X742)=>(~(in @ X744 @ X743)=>(in @ X744 @ (symdiff @ X742 @ X743)))))=>(![X745:$i, X746:$i, X747:$i]:((~(in @ X747 @ X745)=>((in @ X747 @ X746)=>(in @ X747 @ (symdiff @ X745 @ X746)))))=>(![X887:$i, X888:$i, X889:$i]:(((in @ X889 @ X887)=>((in @ X889 @ X888)=>~(in @ X889 @ (symdiff @ X887 @ X888)))))=>(![X748:$i, X749:$i, X750:$i]:((~(in @ X750 @ X748)=>(~(in @ X750 @ X749)=>~(in @ X750 @ (symdiff @ X748 @ X749)))))=>(![X885:$i, X886:$i]:((in @ X886 @ (setadjoin @ X885 @ (setadjoin @ X886 @ emptyset))))=>(![X751:$i, X752:$i]:((in @ X751 @ (setunion @ (setadjoin @ (setadjoin @ X751 @ emptyset) @ (setadjoin @ (setadjoin @ X751 @ (setadjoin @ X752 @ emptyset)) @ emptyset)))))=>(![X753:$i, X754:$i]:((in @ X754 @ (setunion @ (setadjoin @ (setadjoin @ X753 @ emptyset) @ (setadjoin @ (setadjoin @ X753 @ (setadjoin @ X754 @ emptyset)) @ emptyset)))))=>(![X881:$i, X882:$i]:(?[X883:$i]:(((in @ X883 @ (setunion @ (setadjoin @ (setadjoin @ X881 @ emptyset) @ (setadjoin @ (setadjoin @ X881 @ (setadjoin @ X882 @ emptyset)) @ emptyset))))&?[X884:$i]:(((in @ X884 @ (setunion @ (setadjoin @ (setadjoin @ X881 @ emptyset) @ (setadjoin @ (setadjoin @ X881 @ (setadjoin @ X882 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X881 @ emptyset) @ (setadjoin @ (setadjoin @ X881 @ (setadjoin @ X882 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X883 @ emptyset) @ (setadjoin @ (setadjoin @ X883 @ (setadjoin @ X884 @ emptyset)) @ emptyset))))))))=>(![X755:$i, X756:$i]:(?[X757:$i]:(((in @ X757 @ (setunion @ (kpair @ X755 @ X756)))&?[X758:$i]:(((in @ X758 @ (setunion @ (kpair @ X755 @ X756)))&((kpair @ X755 @ X756)=(setadjoin @ (setadjoin @ X757 @ emptyset) @ (setadjoin @ (setadjoin @ X757 @ (setadjoin @ X758 @ emptyset)) @ emptyset))))))))=>(![X759:$i, X760:$i]:(((in @ X760 @ X759)=>(subset @ (setadjoin @ X760 @ emptyset) @ X759)))=>(![X761:$i, X762:$i]:(((in @ X762 @ X761)=>(in @ (setadjoin @ X762 @ emptyset) @ (powerset @ X761))))=>(![X763:$i, X764:$i, X765:$i]:(((in @ X765 @ X763)=>(in @ (setadjoin @ X765 @ emptyset) @ (powerset @ (binunion @ X763 @ X764)))))=>(![X878:$i, X879:$i, X880:$i]:(((in @ X880 @ (setadjoin @ X878 @ (setadjoin @ X879 @ emptyset)))=>(((X880)=(X878))|((X880)=(X879)))))=>(![X874:$i, X875:$i, X876:$i]:(((in @ X876 @ X874)=>![X877:$i]:(((in @ X877 @ X875)=>(subset @ (setadjoin @ X876 @ (setadjoin @ X877 @ emptyset)) @ (binunion @ X874 @ X875))))))=>(![X766:$i, X767:$i, X768:$i]:(((in @ X768 @ X766)=>![X769:$i]:(((in @ X769 @ X767)=>(in @ (setadjoin @ X768 @ (setadjoin @ X769 @ emptyset)) @ (powerset @ (binunion @ X766 @ X767)))))))=>(![X770:$i, X771:$i, X772:$i]:(((in @ X772 @ X770)=>![X773:$i]:(((in @ X773 @ X771)=>(subset @ (setadjoin @ (setadjoin @ X772 @ emptyset) @ (setadjoin @ (setadjoin @ X772 @ (setadjoin @ X773 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X770 @ X771)))))))=>(![X870:$i, X871:$i, X872:$i]:(((in @ X872 @ X870)=>![X873:$i]:(((in @ X873 @ X871)=>(in @ (setadjoin @ (setadjoin @ X872 @ emptyset) @ (setadjoin @ (setadjoin @ X872 @ (setadjoin @ X873 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X870 @ X871))))))))=>(![X866:$i, X867:$i, X868:$i]:(((in @ X868 @ X866)=>![X869:$i]:(((in @ X869 @ X867)=>(in @ (kpair @ X868 @ X869) @ (powerset @ (powerset @ (binunion @ X866 @ X867))))))))=>(![X862:$i, X863:$i, X864:$i]:(((in @ X864 @ X862)=>![X865:$i]:(((in @ X865 @ X863)=>(in @ (kpair @ X864 @ X865) @ (cartprod @ X862 @ X863))))))=>(![X857:$i, X858:$i, X859:$i]:(((in @ X859 @ (cartprod @ X857 @ X858))=>?[X860:$i]:(((in @ X860 @ X857)&?[X861:$i]:(((in @ X861 @ X858)&((X859)=(kpair @ X860 @ X861))))))))=>(![X774:$i, X775:$i, X776:$i]:(((in @ X776 @ (cartprod @ X774 @ X775))=>?[X777:$i]:(((in @ X777 @ (setunion @ X776))&?[X778:$i]:(((in @ X778 @ (setunion @ X776))&((X776)=(setadjoin @ (setadjoin @ X777 @ emptyset) @ (setadjoin @ (setadjoin @ X777 @ (setadjoin @ X778 @ emptyset)) @ emptyset)))))))))=>(![X779:$i, X780:$i]:(((in @ X780 @ (setunion @ X779))=>?[X781:$i]:(((in @ X781 @ X779)&(in @ X780 @ X781)))))=>(![X782:$i]:((subset @ (setunion @ (setadjoin @ X782 @ emptyset)) @ X782))=>(![X783:$i]:((subset @ X783 @ (setunion @ (setadjoin @ X783 @ emptyset))))=>(![X784:$i]:(((setunion @ (setadjoin @ X784 @ emptyset))=(X784)))=>(![X851:$i, X852:$i > $o]:((![X853:$i]:(((in @ X853 @ X851)=>![X854:$i]:(((in @ X854 @ X851)=>((X852 @ X853)=>((X852 @ X854)=>((X853)=(X854))))))))=>(?[X855:$i]:(((in @ X855 @ X851)&(X852 @ X855)))=>?[X856:$i]:(((in @ X856 @ (dsetconstr @ X851 @ X852))&((dsetconstr @ X851 @ X852)=(setadjoin @ X856 @ emptyset)))))))=>(![X785:$i, X786:$i > $o]:((?[X787:$i]:(((in @ X787 @ (dsetconstr @ X785 @ X786))&((dsetconstr @ X785 @ X786)=(setadjoin @ X787 @ emptyset))))=>?[X788:$i]:(((in @ X788 @ X785)&(X786 @ X788)))))=>(![X846:$i, X847:$i > $o, X848:$i]:(((in @ X848 @ X846)=>((X847 @ X848)=>(![X849:$i]:(((in @ X849 @ X846)=>((X847 @ X849)=>((X849)=(X848)))))=>?[X850:$i]:(((in @ X850 @ (dsetconstr @ X846 @ X847))&((dsetconstr @ X846 @ X847)=(setadjoin @ X850 @ emptyset))))))))=>(![X789:$i, X790:$i > $o]:((![X791:$i]:(((in @ X791 @ X789)=>![X792:$i]:(((in @ X792 @ X789)=>((X790 @ X791)=>((X790 @ X792)=>((X791)=(X792))))))))=>(?[X793:$i]:(((in @ X793 @ X789)&(X790 @ X793)))=>?[X794:$i]:(((in @ X794 @ (dsetconstr @ X789 @ X790))&((dsetconstr @ X789 @ X790)=(setadjoin @ X794 @ emptyset)))))))=>(![X795:$i, X796:$i]:((((setadjoin @ X795 @ emptyset)=(setadjoin @ X796 @ emptyset))=>((X795)=(X796))))=>(![X797:$i, X798:$i, X799:$i]:(((in @ (setadjoin @ X799 @ emptyset) @ (setadjoin @ (setadjoin @ X797 @ emptyset) @ (setadjoin @ (setadjoin @ X797 @ (setadjoin @ X798 @ emptyset)) @ emptyset)))=>((X797)=(X799))))=>(![X800:$i]:((?[X801:$i]:(((in @ X801 @ (setunion @ X800))&?[X802:$i]:(((in @ X802 @ (setunion @ X800))&((X800)=(setadjoin @ (setadjoin @ X801 @ emptyset) @ (setadjoin @ (setadjoin @ X801 @ (setadjoin @ X802 @ emptyset)) @ emptyset)))))))=>?[X803:$i]:(((in @ X803 @ (dsetconstr @ (setunion @ X800) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X800)))))&((dsetconstr @ (setunion @ X800) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X800))))=(setadjoin @ X803 @ emptyset))))))=>(![X804:$i]:((?[X805:$i]:(((in @ X805 @ X804)&((X804)=(setadjoin @ X805 @ emptyset))))=>(in @ (setunion @ X804) @ X804)))=>(![X844:$i, X845:$i]:(((kfst @ (kpair @ X844 @ X845))=(X844)))=>(![X806:$i, X807:$i, X808:$i]:(((in @ X808 @ (cartprod @ X806 @ X807))=>(in @ (kfst @ X808) @ X806)))=>(![X809:$i, X810:$i, X811:$i, X812:$i]:((((setadjoin @ (setadjoin @ X809 @ emptyset) @ (setadjoin @ (setadjoin @ X809 @ (setadjoin @ X810 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X811 @ emptyset) @ (setadjoin @ (setadjoin @ X811 @ (setadjoin @ X812 @ emptyset)) @ emptyset)))=>((X809)=(X811))))=>(![X813:$i, X814:$i, X815:$i, X816:$i]:((((kpair @ X813 @ X814)=(kpair @ X815 @ X816))=>((X813)=(X815))))=>(![X817:$i, X818:$i]:((((X817)=(X818))=>((setadjoin @ X817 @ (setadjoin @ X818 @ emptyset))=(setadjoin @ X817 @ emptyset))))=>(![X842:$i, X843:$i]:((((X842)=(X843))=>((setadjoin @ (setadjoin @ X842 @ emptyset) @ (setadjoin @ (setadjoin @ X842 @ (setadjoin @ X843 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X842 @ emptyset) @ emptyset))))=>(![X819:$i, X820:$i, X821:$i, X822:$i]:((((setadjoin @ (setadjoin @ X819 @ emptyset) @ (setadjoin @ (setadjoin @ X819 @ (setadjoin @ X820 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X821 @ emptyset) @ (setadjoin @ (setadjoin @ X821 @ (setadjoin @ X822 @ emptyset)) @ emptyset)))=>(((X821)=(X822))=>((X820)=(X822)))))=>(![X823:$i, X824:$i, X825:$i]:((((setadjoin @ X823 @ (setadjoin @ X824 @ emptyset))=(setadjoin @ X825 @ emptyset))=>((X823)=(X824))))=>(![X838:$i, X839:$i, X840:$i, X841:$i]:((((setadjoin @ (setadjoin @ X838 @ emptyset) @ (setadjoin @ (setadjoin @ X838 @ (setadjoin @ X839 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X840 @ emptyset) @ (setadjoin @ (setadjoin @ X840 @ (setadjoin @ X841 @ emptyset)) @ emptyset)))=>((X839)=(X841))))=>(![X834:$i, X835:$i, X836:$i, X837:$i]:((((kpair @ X834 @ X835)=(kpair @ X836 @ X837))=>((X835)=(X837))))=>(![X830:$i]:((?[X831:$i]:(((in @ X831 @ (setunion @ X830))&?[X832:$i]:(((in @ X832 @ (setunion @ X830))&((X830)=(setadjoin @ (setadjoin @ X831 @ emptyset) @ (setadjoin @ (setadjoin @ X831 @ (setadjoin @ X832 @ emptyset)) @ emptyset)))))))=>?[X833:$i]:(((in @ X833 @ (dsetconstr @ (setunion @ X830) @ (^[Z0/* 3 */:$i]:(((X830)=(kpair @ (kfst @ X830) @ Z0))))))&((dsetconstr @ (setunion @ X830) @ (^[Z0/* 3 */:$i]:(((X830)=(kpair @ (kfst @ X830) @ Z0)))))=(setadjoin @ X833 @ emptyset))))))=>(![X826:$i, X827:$i]:(((ksnd @ (kpair @ X826 @ X827))=(X827)))=>![X18:$i]:((?[X828:$i]:(((in @ X828 @ (setunion @ X18))&?[X829:$i]:(((in @ X829 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X828 @ emptyset) @ (setadjoin @ (setadjoin @ X828 @ (setadjoin @ X829 @ emptyset)) @ emptyset)))))))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[kpairsurjEq]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_205]), foundationAx]), wellorderingAx]), c_0_206]), c_0_207]), c_0_208]), c_0_209]), c_0_210]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_211]), setext]), emptyI]), noeltsimpempty]), c_0_212]), c_0_213]), c_0_214]), c_0_215]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_216]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_217]), c_0_218]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_219]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_220]), c_0_221]), c_0_222]), inCongP]), in__Cong]), c_0_223]), c_0_224]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_225]), c_0_226]), c_0_227]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_228]), c_0_229]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), c_0_197]), secondinupair]), setukpairIL]), setukpairIR]), c_0_230]), c_0_231]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), c_0_232]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_233]), c_0_234]), c_0_235]), c_0_236]), singletonsuniq]), setukpairinjL1]), c_0_237]), c_0_238]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_239]), ksndpairEq])])]), c_0_240])).
0.69/0.67	thf(c_0_242, plain, ![X1058:$i, X1059:$i]:(((kpair @ X1058 @ X1059)=(setadjoin @ (setadjoin @ X1058 @ emptyset) @ (setadjoin @ (setadjoin @ X1058 @ (setadjoin @ X1059 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])])).
0.69/0.67	thf(c_0_243, negated_conjecture, ![X1062:$i, X1063:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1075:$i, X1076:$i, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1084:$i, X1085:$i > $i > $o, X1086:$i, X1088:$i, X1091:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1098:$i, X1099:$i > $o, X1100:$i, X1102:$i, X1103:$i > $o, X1104:$i, X1105:$i, X1106:$i > $o, X1107:$i, X1108:$i, X1109:$i > $o, X1110:$i, X1111:$i > $o, X1112:$i, X1115:$i, X1116:$o, X1117:$i, X1118:$i, X1119:$o, X1120:$i, X1121:$i, X1122:$i > $o, X1123:$i, X1126:$i, X1127:$i, X1130:$i, X1132:$i, X1134:$i, X1135:$i > $o, X1136:$i, X1137:$i, X1139:$i, X1140:$i > $o, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$o, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$o, X1172:$i, X1173:$i, X1174:$i > $o, X1175:$i, X1178:$i, X1179:$i, X1180:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i > $o, X1199:$i, X1200:$i > $o, X1201:$i, X1202:$i, X1203:$i > $o, X1204:$i, X1206:$i, X1207:$i > $o, X1209:$i, X1210:$i, X1211:$i > $o, X1213:$i, X1214:$i, X1215:$i > $o, X1216:$i, X1218:$o, X1219:$o, X1220:$i, X1221:$i > $o, X1223:$i, X1224:$i, X1225:$i > $o, X1226:$i, X1228:$i > $o, X1229:$i, X1232:$i, X1233:$i > $o, X1234:$i, X1238:$i, X1239:$i > $o, X1240:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i > $o, X1253:$i, X1255:$i, X1256:$i, X1257:$i > $o, X1258:$i > $o, X1261:$i, X1264:$i, X1265:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i > $o, X1278:$i, X1280:$i, X1281:$i, X1282:$i > $o, X1283:$i > $o, X1286:$i, X1288:$i, X1290:$i, X1291:$i, X1292:$i > $o, X1293:$i > $o, X1296:$i, X1297:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i > $o, X1344:$i, X1345:$i > $o, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$o, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$o, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1448:$i, X1449:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1491:$i, X1492:$i, X1493:$i, X1496:$i, X1497:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i > $o, X1506:$i, X1508:$i, X1509:$i > $o, X1510:$i, X1512:$i, X1513:$i > $o, X1514:$i, X1517:$i, X1518:$i > $o, X1521:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1570:$i, X1571:$i]:((((~(in @ (esk1_2 @ X1062 @ X1063) @ X1062)|~(in @ (esk1_2 @ X1062 @ X1063) @ X1063)|((X1062)=(X1063)))&((in @ (esk1_2 @ X1062 @ X1063) @ X1062)|(in @ (esk1_2 @ X1062 @ X1063) @ X1063)|((X1062)=(X1063))))&(~(in @ X1065 @ emptyset)&(((~(in @ X1068 @ (setadjoin @ X1066 @ X1067))|(((X1068)=(X1066))|(in @ X1068 @ X1067)))&((((X1068)!=(X1066))|(in @ X1068 @ (setadjoin @ X1066 @ X1067)))&(~(in @ X1068 @ X1067)|(in @ X1068 @ (setadjoin @ X1066 @ X1067)))))&(((~(in @ X1070 @ (powerset @ X1069))|(~(in @ X1071 @ X1070)|(in @ X1071 @ X1069)))&(((in @ (esk2_2 @ X1072 @ X1073) @ X1073)|(in @ X1073 @ (powerset @ X1072)))&(~(in @ (esk2_2 @ X1072 @ X1073) @ X1072)|(in @ X1073 @ (powerset @ X1072)))))&(((((in @ X1076 @ (esk3_2 @ X1075 @ X1076))|~(in @ X1076 @ (setunion @ X1075)))&((in @ (esk3_2 @ X1075 @ X1076) @ X1075)|~(in @ X1076 @ (setunion @ X1075))))&(~(in @ X1079 @ X1080)|~(in @ X1080 @ X1078)|(in @ X1079 @ (setunion @ X1078))))&((in @ emptyset @ omega)&((~(in @ X1081 @ omega)|(in @ (setadjoin @ X1081 @ X1081) @ omega))&(((((in @ (esk4_1 @ X1082) @ omega)|~(in @ emptyset @ X1082)|(~(in @ X1084 @ omega)|(in @ X1084 @ X1082)))&((in @ (esk4_1 @ X1082) @ X1082)|~(in @ emptyset @ X1082)|(~(in @ X1084 @ omega)|(in @ X1084 @ X1082))))&(~(in @ (setadjoin @ (esk4_1 @ X1082) @ (esk4_1 @ X1082)) @ X1082)|~(in @ emptyset @ X1082)|(~(in @ X1084 @ omega)|(in @ X1084 @ X1082))))&((((((in @ (esk8_3 @ X1085 @ X1086 @ X1091) @ X1086)|~(in @ X1091 @ (esk7_2 @ X1085 @ X1086))|(in @ (esk5_2 @ X1085 @ X1086) @ X1086))&((X1085 @ (esk8_3 @ X1085 @ X1086 @ X1091) @ X1091)|~(in @ X1091 @ (esk7_2 @ X1085 @ X1086))|(in @ (esk5_2 @ X1085 @ X1086) @ X1086)))&(~(in @ X1094 @ X1086)|~(X1085 @ X1094 @ X1093)|(in @ X1093 @ (esk7_2 @ X1085 @ X1086))|(in @ (esk5_2 @ X1085 @ X1086) @ X1086)))&(((((in @ (esk8_3 @ X1085 @ X1086 @ X1091) @ X1086)|~(in @ X1091 @ (esk7_2 @ X1085 @ X1086))|((X1085 @ (esk5_2 @ X1085 @ X1086) @ (esk6_3 @ X1085 @ X1086 @ X1088))|~(X1085 @ (esk5_2 @ X1085 @ X1086) @ X1088)))&((X1085 @ (esk8_3 @ X1085 @ X1086 @ X1091) @ X1091)|~(in @ X1091 @ (esk7_2 @ X1085 @ X1086))|((X1085 @ (esk5_2 @ X1085 @ X1086) @ (esk6_3 @ X1085 @ X1086 @ X1088))|~(X1085 @ (esk5_2 @ X1085 @ X1086) @ X1088))))&(~(in @ X1094 @ X1086)|~(X1085 @ X1094 @ X1093)|(in @ X1093 @ (esk7_2 @ X1085 @ X1086))|((X1085 @ (esk5_2 @ X1085 @ X1086) @ (esk6_3 @ X1085 @ X1086 @ X1088))|~(X1085 @ (esk5_2 @ X1085 @ X1086) @ X1088))))&((((in @ (esk8_3 @ X1085 @ X1086 @ X1091) @ X1086)|~(in @ X1091 @ (esk7_2 @ X1085 @ X1086))|(((X1088)!=(esk6_3 @ X1085 @ X1086 @ X1088))|~(X1085 @ (esk5_2 @ X1085 @ X1086) @ X1088)))&((X1085 @ (esk8_3 @ X1085 @ X1086 @ X1091) @ X1091)|~(in @ X1091 @ (esk7_2 @ X1085 @ X1086))|(((X1088)!=(esk6_3 @ X1085 @ X1086 @ X1088))|~(X1085 @ (esk5_2 @ X1085 @ X1086) @ X1088))))&(~(in @ X1094 @ X1086)|~(X1085 @ X1094 @ X1093)|(in @ X1093 @ (esk7_2 @ X1085 @ X1086))|(((X1088)!=(esk6_3 @ X1085 @ X1086 @ X1088))|~(X1085 @ (esk5_2 @ X1085 @ X1086) @ X1088))))))&((((in @ (esk9_1 @ X1095) @ X1095)|~(in @ X1096 @ X1095))&(~(in @ X1098 @ (esk9_1 @ X1095))|~(in @ X1098 @ X1095)|~(in @ X1096 @ X1095)))&((epred1_0)&((((X1099 @ (esk10_2 @ X1099 @ X1100))|~(X1099 @ X1100)|(X1099 @ (descr @ X1099)))&(((X1100)!=(esk10_2 @ X1099 @ X1100))|~(X1099 @ X1100)|(X1099 @ (descr @ X1099))))&((~(in @ X1104 @ X1102)|(~(X1103 @ X1104)|(in @ X1104 @ (dsetconstr @ X1102 @ X1103))))&((~(in @ X1107 @ (dsetconstr @ X1105 @ X1106))|(in @ X1107 @ X1105))&((~(in @ X1110 @ (dsetconstr @ X1108 @ X1109))|(X1109 @ X1110))&(((((X1111 @ (esk12_1 @ X1111))|((X1111 @ (esk11_2 @ X1111 @ X1112))|~(X1111 @ X1112)))&(~(X1111 @ X1115)|((esk12_1 @ X1111)=(X1115))|((X1111 @ (esk11_2 @ X1111 @ X1112))|~(X1111 @ X1112))))&(((X1111 @ (esk12_1 @ X1111))|(((X1112)!=(esk11_2 @ X1111 @ X1112))|~(X1111 @ X1112)))&(~(X1111 @ X1115)|((esk12_1 @ X1111)=(X1115))|(((X1112)!=(esk11_2 @ X1111 @ X1112))|~(X1111 @ X1112)))))&((~(in @ X1117 @ (prop2set @ ((X1116))))|(X1116))&((~(in @ X1118 @ emptyset)|(X1119))&((~(in @ X1120 @ emptyset)|~($true))&(~(in @ X1121 @ emptyset)&((((X1122 @ (esk13_2 @ X1122 @ X1123))|~(X1122 @ X1123)|(X1122 @ (esk14_1 @ X1122)))&(((X1123)!=(esk13_2 @ X1122 @ X1123))|~(X1122 @ X1123)|(X1122 @ (esk14_1 @ X1122))))&(((((in @ (esk16_2 @ X1126 @ X1127) @ X1127)|((X1126)=(X1127))|(in @ (esk15_2 @ X1126 @ X1127) @ X1126))&(~(in @ (esk16_2 @ X1126 @ X1127) @ X1126)|((X1126)=(X1127))|(in @ (esk15_2 @ X1126 @ X1127) @ X1126)))&(((in @ (esk16_2 @ X1126 @ X1127) @ X1127)|((X1126)=(X1127))|~(in @ (esk15_2 @ X1126 @ X1127) @ X1127))&(~(in @ (esk16_2 @ X1126 @ X1127) @ X1126)|((X1126)=(X1127))|~(in @ (esk15_2 @ X1126 @ X1127) @ X1127))))&(((in @ (esk17_1 @ X1130) @ X1130)|((X1130)=(emptyset)))&(((in @ (esk18_1 @ X1132) @ X1132)|((X1132)=(emptyset)))&(((~(in @ X1136 @ (dsetconstr @ X1134 @ X1135))|(X1135 @ X1136)|~(in @ X1136 @ X1134))&(~(X1135 @ X1136)|(in @ X1136 @ (dsetconstr @ X1134 @ X1135))|~(in @ X1136 @ X1134)))&((((X1137)=(emptyset))|(in @ (esk19_1 @ X1137) @ X1137))&((~(in @ X1141 @ X1139)|(~(X1140 @ X1141)|((dsetconstr @ X1139 @ X1140)!=(emptyset))))&((~(in @ X1143 @ X1142)|((X1142)!=(emptyset)))&((in @ X1144 @ (setadjoin @ X1144 @ X1145))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1148 @ X1147)|(in @ X1148 @ (setadjoin @ X1146 @ X1147)))&(((((in @ X1151 @ X1150)|(X1152)|((X1151)=(X1149))|~(in @ X1151 @ (setadjoin @ X1149 @ X1150)))&(~(X1152)|(X1152)|((X1151)=(X1149))|~(in @ X1151 @ (setadjoin @ X1149 @ X1150))))&(((in @ X1151 @ X1150)|(X1152)|~(X1152)|~(in @ X1151 @ (setadjoin @ X1149 @ X1150)))&(~(X1152)|(X1152)|~(X1152)|~(in @ X1151 @ (setadjoin @ X1149 @ X1150)))))&((~(in @ X1155 @ (setadjoin @ X1153 @ X1154))|(((X1155)=(X1153))|(in @ X1155 @ X1154)))&(((dsetconstr @ X1156 @ (^[Z0/* 1 */:$i]:($true)))=(X1156))&((((in @ (esk20_2 @ X1157 @ X1158) @ X1158)|(in @ X1158 @ (powerset @ X1157)))&(~(in @ (esk20_2 @ X1157 @ X1158) @ X1157)|(in @ X1158 @ (powerset @ X1157))))&((in @ emptyset @ (powerset @ X1160))&((in @ emptyset @ (powerset @ X1161))&((~(in @ X1163 @ (powerset @ X1162))|(~(in @ X1164 @ X1163)|(in @ X1164 @ X1162)))&((~(in @ X1166 @ X1167)|(~(in @ X1167 @ X1165)|(in @ X1166 @ (setunion @ X1165))))&((((in @ X1169 @ (esk21_3 @ X1168 @ X1169 @ X1170))|(X1170)|~(in @ X1169 @ (setunion @ X1168)))&(((in @ (esk21_3 @ X1168 @ X1169 @ X1170) @ X1168)|(X1170)|~(in @ X1169 @ (setunion @ X1168)))&(~(X1170)|(X1170)|~(in @ X1169 @ (setunion @ X1168)))))&((~(in @ X1173 @ X1172)|(in @ X1173 @ (powerset @ (setunion @ X1172))))&((((~(X1174 @ X1178)|((X1178)=(esk23_1 @ X1174))|((X1174 @ (esk22_2 @ X1174 @ X1175))|~(X1174 @ X1175)))&(((X1179)!=(esk23_1 @ X1174))|(X1174 @ X1179)|((X1174 @ (esk22_2 @ X1174 @ X1175))|~(X1174 @ X1175))))&((~(X1174 @ X1178)|((X1178)=(esk23_1 @ X1174))|(((X1175)!=(esk22_2 @ X1174 @ X1175))|~(X1174 @ X1175)))&(((X1179)!=(esk23_1 @ X1174))|(X1174 @ X1179)|(((X1175)!=(esk22_2 @ X1174 @ X1175))|~(X1174 @ X1175)))))&((((in @ (esk24_1 @ X1180) @ X1180)|((X1180)=(emptyset)))&(($true)|((X1180)=(emptyset))))&((~(in @ X1182 @ (setadjoin @ X1183 @ emptyset))|((X1182)=(X1183)))&((((X1184)=(X1185))|~(in @ X1185 @ (setadjoin @ X1184 @ emptyset)))&((((X1186)!=(X1187))|(in @ X1186 @ (setadjoin @ X1187 @ emptyset)))&((~(in @ X1188 @ (setadjoin @ X1189 @ emptyset))|(in @ X1189 @ (setadjoin @ X1188 @ emptyset)))&((~(in @ X1192 @ (setadjoin @ X1190 @ (setadjoin @ X1191 @ emptyset)))|(((X1192)=(X1190))|((X1192)=(X1191))))&((in @ X1193 @ (setadjoin @ X1193 @ (setadjoin @ X1194 @ emptyset)))&((in @ X1196 @ (setadjoin @ X1195 @ (setadjoin @ X1196 @ emptyset)))&((~(in @ X1199 @ X1197)|~(X1198 @ X1199)|(((dsetconstr @ X1197 @ X1198)!=(emptyset))|~($true)))&((~(in @ X1201 @ emptyset)|(X1200 @ X1201))&((((in @ (esk25_2 @ X1202 @ X1203) @ X1202)|(~(in @ X1204 @ X1202)|(X1203 @ X1204)))&(~(X1203 @ (esk25_2 @ X1202 @ X1203))|(~(in @ X1204 @ X1202)|(X1203 @ X1204))))&((((in @ (esk26_2 @ X1206 @ X1207) @ X1206)|(~(in @ X1209 @ X1206)|~(X1207 @ X1209)))&((X1207 @ (esk26_2 @ X1206 @ X1207))|(~(in @ X1209 @ X1206)|~(X1207 @ X1209))))&((((in @ (esk27_2 @ X1210 @ X1211) @ X1210)|(~(in @ X1213 @ X1210)|~(X1211 @ X1213)))&((X1211 @ (esk27_2 @ X1210 @ X1211))|(~(in @ X1213 @ X1210)|~(X1211 @ X1213))))&((((in @ (esk28_2 @ X1214 @ X1215) @ X1214)|(~(in @ X1216 @ X1214)|(X1215 @ X1216)))&(~(X1215 @ (esk28_2 @ X1214 @ X1215))|(~(in @ X1216 @ X1214)|(X1215 @ X1216))))&((~(X1218)|(in @ emptyset @ (prop2set @ ((X1218)))))&((~(X1219)|(set2prop @ (prop2set @ ((X1219)))))&((((in @ (esk29_2 @ X1220 @ X1221) @ X1220)|(~(in @ X1223 @ X1220)|~(X1221 @ X1223)))&((X1221 @ (esk29_2 @ X1220 @ X1221))|(~(in @ X1223 @ X1220)|~(X1221 @ X1223))))&((((in @ (esk30_2 @ X1224 @ X1225) @ X1224)|(~(in @ X1226 @ X1224)|(X1225 @ X1226)))&(~(X1225 @ (esk30_2 @ X1224 @ X1225))|(~(in @ X1226 @ X1224)|(X1225 @ X1226))))&(((((X1228 @ (esk32_1 @ X1228))|((X1228 @ (esk31_2 @ X1228 @ X1229))|~(X1228 @ X1229)))&(~(X1228 @ X1232)|((esk32_1 @ X1228)=(X1232))|((X1228 @ (esk31_2 @ X1228 @ X1229))|~(X1228 @ X1229))))&(((X1228 @ (esk32_1 @ X1228))|(((X1229)!=(esk31_2 @ X1228 @ X1229))|~(X1228 @ X1229)))&(~(X1228 @ X1232)|((esk32_1 @ X1228)=(X1232))|(((X1229)!=(esk31_2 @ X1228 @ X1229))|~(X1228 @ X1229)))))&(((((X1233 @ (esk35_1 @ X1233))|(X1233 @ (esk33_1 @ X1233))|~(X1233 @ X1234))&(~(X1233 @ X1238)|((esk35_1 @ X1233)=(X1238))|(X1233 @ (esk33_1 @ X1233))|~(X1233 @ X1234)))&((((X1233 @ (esk35_1 @ X1233))|(X1233 @ (esk34_1 @ X1233))|~(X1233 @ X1234))&(~(X1233 @ X1238)|((esk35_1 @ X1233)=(X1238))|(X1233 @ (esk34_1 @ X1233))|~(X1233 @ X1234)))&(((X1233 @ (esk35_1 @ X1233))|((esk33_1 @ X1233)!=(esk34_1 @ X1233))|~(X1233 @ X1234))&(~(X1233 @ X1238)|((esk35_1 @ X1233)=(X1238))|((esk33_1 @ X1233)!=(esk34_1 @ X1233))|~(X1233 @ X1234)))))&(((((X1239 @ (esk37_1 @ X1239))|(~(X1239 @ (esk36_2 @ X1239 @ X1240))|((esk36_2 @ X1239 @ X1240)!=(X1240))))&(~(X1239 @ X1243)|((esk37_1 @ X1239)=(X1243))|(~(X1239 @ (esk36_2 @ X1239 @ X1240))|((esk36_2 @ X1239 @ X1240)!=(X1240)))))&(((X1239 @ (esk37_1 @ X1239))|((X1239 @ (esk36_2 @ X1239 @ X1240))|((esk36_2 @ X1239 @ X1240)=(X1240))))&(~(X1239 @ X1243)|((esk37_1 @ X1239)=(X1243))|((X1239 @ (esk36_2 @ X1239 @ X1240))|((esk36_2 @ X1239 @ X1240)=(X1240))))))&((((X1244)!=(X1245))|(((X1246)!=(X1247))|(~(in @ X1246 @ X1244)|(in @ X1247 @ X1245))))&(((~(in @ X1250 @ X1248)|(in @ X1251 @ X1249)|((X1250)!=(X1251))|((X1248)!=(X1249)))&(~(in @ X1251 @ X1249)|(in @ X1250 @ X1248)|((X1250)!=(X1251))|((X1248)!=(X1249))))&((((X1252 @ (esk38_2 @ X1252 @ X1253))|~(X1252 @ X1253)|(~(X1252 @ X1255)|(~(X1252 @ X1256)|((X1255)=(X1256)))))&(((X1253)!=(esk38_2 @ X1252 @ X1253))|~(X1252 @ X1253)|(~(X1252 @ X1255)|(~(X1252 @ X1256)|((X1255)=(X1256))))))&(((((((X1258 @ (esk42_2 @ X1257 @ X1258))|((X1257 @ (esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|((esk39_2 @ X1257 @ X1258)=(esk40_2 @ X1257 @ X1258)))&(~(X1258 @ X1264)|((esk42_2 @ X1257 @ X1258)=(X1264))|((X1257 @ (esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|((esk39_2 @ X1257 @ X1258)=(esk40_2 @ X1257 @ X1258))))&(((X1258 @ (esk42_2 @ X1257 @ X1258))|(((X1261)!=(esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|((esk39_2 @ X1257 @ X1258)=(esk40_2 @ X1257 @ X1258)))&(~(X1258 @ X1264)|((esk42_2 @ X1257 @ X1258)=(X1264))|(((X1261)!=(esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|((esk39_2 @ X1257 @ X1258)=(esk40_2 @ X1257 @ X1258)))))&((((X1257 @ (esk44_2 @ X1257 @ X1258))|((X1258 @ (esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|((esk39_2 @ X1257 @ X1258)=(esk40_2 @ X1257 @ X1258)))&(~(X1257 @ X1268)|((esk44_2 @ X1257 @ X1258)=(X1268))|((X1258 @ (esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|((esk39_2 @ X1257 @ X1258)=(esk40_2 @ X1257 @ X1258))))&(((X1257 @ (esk44_2 @ X1257 @ X1258))|(((X1265)!=(esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|((esk39_2 @ X1257 @ X1258)=(esk40_2 @ X1257 @ X1258)))&(~(X1257 @ X1268)|((esk44_2 @ X1257 @ X1258)=(X1268))|(((X1265)!=(esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|((esk39_2 @ X1257 @ X1258)=(esk40_2 @ X1257 @ X1258))))))&((((((X1258 @ (esk42_2 @ X1257 @ X1258))|((X1257 @ (esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|(~(X1257 @ (esk39_2 @ X1257 @ X1258))|~(X1258 @ (esk40_2 @ X1257 @ X1258))))&(~(X1258 @ X1264)|((esk42_2 @ X1257 @ X1258)=(X1264))|((X1257 @ (esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|(~(X1257 @ (esk39_2 @ X1257 @ X1258))|~(X1258 @ (esk40_2 @ X1257 @ X1258)))))&(((X1258 @ (esk42_2 @ X1257 @ X1258))|(((X1261)!=(esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|(~(X1257 @ (esk39_2 @ X1257 @ X1258))|~(X1258 @ (esk40_2 @ X1257 @ X1258))))&(~(X1258 @ X1264)|((esk42_2 @ X1257 @ X1258)=(X1264))|(((X1261)!=(esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|(~(X1257 @ (esk39_2 @ X1257 @ X1258))|~(X1258 @ (esk40_2 @ X1257 @ X1258))))))&((((X1257 @ (esk44_2 @ X1257 @ X1258))|((X1258 @ (esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|(~(X1257 @ (esk39_2 @ X1257 @ X1258))|~(X1258 @ (esk40_2 @ X1257 @ X1258))))&(~(X1257 @ X1268)|((esk44_2 @ X1257 @ X1258)=(X1268))|((X1258 @ (esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|(~(X1257 @ (esk39_2 @ X1257 @ X1258))|~(X1258 @ (esk40_2 @ X1257 @ X1258)))))&(((X1257 @ (esk44_2 @ X1257 @ X1258))|(((X1265)!=(esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|(~(X1257 @ (esk39_2 @ X1257 @ X1258))|~(X1258 @ (esk40_2 @ X1257 @ X1258))))&(~(X1257 @ X1268)|((esk44_2 @ X1257 @ X1258)=(X1268))|(((X1265)!=(esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|(~(X1257 @ (esk39_2 @ X1257 @ X1258))|~(X1258 @ (esk40_2 @ X1257 @ X1258)))))))&(((((X1258 @ (esk42_2 @ X1257 @ X1258))|((X1257 @ (esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|((X1257 @ (esk39_2 @ X1257 @ X1258))|(X1258 @ (esk40_2 @ X1257 @ X1258))))&(~(X1258 @ X1264)|((esk42_2 @ X1257 @ X1258)=(X1264))|((X1257 @ (esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|((X1257 @ (esk39_2 @ X1257 @ X1258))|(X1258 @ (esk40_2 @ X1257 @ X1258)))))&(((X1258 @ (esk42_2 @ X1257 @ X1258))|(((X1261)!=(esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|((X1257 @ (esk39_2 @ X1257 @ X1258))|(X1258 @ (esk40_2 @ X1257 @ X1258))))&(~(X1258 @ X1264)|((esk42_2 @ X1257 @ X1258)=(X1264))|(((X1261)!=(esk41_3 @ X1257 @ X1258 @ X1261))|~(X1257 @ X1261))|((X1257 @ (esk39_2 @ X1257 @ X1258))|(X1258 @ (esk40_2 @ X1257 @ X1258))))))&((((X1257 @ (esk44_2 @ X1257 @ X1258))|((X1258 @ (esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|((X1257 @ (esk39_2 @ X1257 @ X1258))|(X1258 @ (esk40_2 @ X1257 @ X1258))))&(~(X1257 @ X1268)|((esk44_2 @ X1257 @ X1258)=(X1268))|((X1258 @ (esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|((X1257 @ (esk39_2 @ X1257 @ X1258))|(X1258 @ (esk40_2 @ X1257 @ X1258)))))&(((X1257 @ (esk44_2 @ X1257 @ X1258))|(((X1265)!=(esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|((X1257 @ (esk39_2 @ X1257 @ X1258))|(X1258 @ (esk40_2 @ X1257 @ X1258))))&(~(X1257 @ X1268)|((esk44_2 @ X1257 @ X1258)=(X1268))|(((X1265)!=(esk43_3 @ X1257 @ X1258 @ X1265))|~(X1258 @ X1265))|((X1257 @ (esk39_2 @ X1257 @ X1258))|(X1258 @ (esk40_2 @ X1257 @ X1258)))))))))&(((emptyset)=(emptyset))&((((X1269)!=(X1270))|(((X1271)!=(X1272))|((setadjoin @ X1269 @ X1271)=(setadjoin @ X1270 @ X1272))))&((((X1273)!=(X1274))|((powerset @ X1273)=(powerset @ X1274)))&((((X1275)!=(X1276))|((setunion @ X1275)=(setunion @ X1276)))&(((omega)=(omega))&((((X1277 @ (esk45_2 @ X1277 @ X1278))|~(X1277 @ X1278)|(~(X1277 @ X1280)|(~(X1277 @ X1281)|((X1280)=(X1281)))))&(((X1278)!=(esk45_2 @ X1277 @ X1278))|~(X1277 @ X1278)|(~(X1277 @ X1280)|(~(X1277 @ X1281)|((X1280)=(X1281))))))&((((((X1283 @ (esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|((X1282 @ (esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|((esk46_2 @ X1282 @ X1283)=(esk47_2 @ X1282 @ X1283)))&(((X1288)!=(esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|((X1282 @ (esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|((esk46_2 @ X1282 @ X1283)=(esk47_2 @ X1282 @ X1283))))&(((X1283 @ (esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|(((X1286)!=(esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|((esk46_2 @ X1282 @ X1283)=(esk47_2 @ X1282 @ X1283)))&(((X1288)!=(esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|(((X1286)!=(esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|((esk46_2 @ X1282 @ X1283)=(esk47_2 @ X1282 @ X1283)))))&(((((X1283 @ (esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|((X1282 @ (esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|(~(X1282 @ (esk46_2 @ X1282 @ X1283))|~(X1283 @ (esk47_2 @ X1282 @ X1283))))&(((X1288)!=(esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|((X1282 @ (esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|(~(X1282 @ (esk46_2 @ X1282 @ X1283))|~(X1283 @ (esk47_2 @ X1282 @ X1283)))))&(((X1283 @ (esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|(((X1286)!=(esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|(~(X1282 @ (esk46_2 @ X1282 @ X1283))|~(X1283 @ (esk47_2 @ X1282 @ X1283))))&(((X1288)!=(esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|(((X1286)!=(esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|(~(X1282 @ (esk46_2 @ X1282 @ X1283))|~(X1283 @ (esk47_2 @ X1282 @ X1283))))))&((((X1283 @ (esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|((X1282 @ (esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|((X1282 @ (esk46_2 @ X1282 @ X1283))|(X1283 @ (esk47_2 @ X1282 @ X1283))))&(((X1288)!=(esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|((X1282 @ (esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|((X1282 @ (esk46_2 @ X1282 @ X1283))|(X1283 @ (esk47_2 @ X1282 @ X1283)))))&(((X1283 @ (esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|(((X1286)!=(esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|((X1282 @ (esk46_2 @ X1282 @ X1283))|(X1283 @ (esk47_2 @ X1282 @ X1283))))&(((X1288)!=(esk49_3 @ X1282 @ X1283 @ X1288))|~(X1283 @ X1288)|((descr @ X1282)=(descr @ X1283))|(((X1286)!=(esk48_3 @ X1282 @ X1283 @ X1286))|~(X1282 @ X1286))|((X1282 @ (esk46_2 @ X1282 @ X1283))|(X1283 @ (esk47_2 @ X1282 @ X1283))))))))&((((in @ (esk50_4 @ X1290 @ X1291 @ X1292 @ X1293) @ X1290)|((dsetconstr @ X1290 @ X1292)=(dsetconstr @ X1291 @ X1293))|((X1290)!=(X1291)))&(((in @ (esk51_4 @ X1290 @ X1291 @ X1292 @ X1293) @ X1291)|((dsetconstr @ X1290 @ X1292)=(dsetconstr @ X1291 @ X1293))|((X1290)!=(X1291)))&((((esk50_4 @ X1290 @ X1291 @ X1292 @ X1293)=(esk51_4 @ X1290 @ X1291 @ X1292 @ X1293))|((dsetconstr @ X1290 @ X1292)=(dsetconstr @ X1291 @ X1293))|((X1290)!=(X1291)))&((~(X1292 @ (esk50_4 @ X1290 @ X1291 @ X1292 @ X1293))|~(X1293 @ (esk51_4 @ X1290 @ X1291 @ X1292 @ X1293))|((dsetconstr @ X1290 @ X1292)=(dsetconstr @ X1291 @ X1293))|((X1290)!=(X1291)))&((X1292 @ (esk50_4 @ X1290 @ X1291 @ X1292 @ X1293))|(X1293 @ (esk51_4 @ X1290 @ X1291 @ X1292 @ X1293))|((dsetconstr @ X1290 @ X1292)=(dsetconstr @ X1291 @ X1293))|((X1290)!=(X1291)))))))&((((in @ (esk52_2 @ X1296 @ X1297) @ X1296)|(subset @ X1296 @ X1297))&(~(in @ (esk52_2 @ X1296 @ X1297) @ X1297)|(subset @ X1296 @ X1297)))&((((X1299)!=(X1300))|(subset @ X1300 @ X1299))&((((X1301)!=(X1302))|(subset @ X1301 @ X1302))&((((in @ (esk53_2 @ X1303 @ X1304) @ X1303)|(subset @ X1303 @ X1304))&(~(in @ (esk53_2 @ X1303 @ X1304) @ X1304)|(subset @ X1303 @ X1304)))&((subset @ emptyset @ X1306)&((~(subset @ X1307 @ X1308)|(~(in @ X1309 @ X1307)|(in @ X1309 @ X1308)))&((~(subset @ X1310 @ X1311)|((in @ X1312 @ X1311)|~(in @ X1312 @ X1310)))&((~(in @ X1315 @ X1313)|((in @ X1315 @ X1314)|~(subset @ X1313 @ X1314)))&(((subset @ X1316 @ X1317)|((X1316)!=(X1317)))&((~(in @ X1320 @ X1318)|((in @ X1320 @ X1319)|((X1318)!=(X1319))))&((subset @ X1321 @ X1321)&((~(subset @ X1322 @ X1323)|(~(subset @ X1323 @ X1324)|(subset @ X1322 @ X1324)))&((subset @ X1326 @ (setadjoin @ X1325 @ X1326))&((~(subset @ X1327 @ X1329)|(subset @ X1327 @ (setadjoin @ X1328 @ X1329)))&((~(subset @ X1330 @ X1331)|(in @ X1330 @ (powerset @ X1331)))&((~(subset @ X1332 @ X1333)|(~(subset @ X1333 @ X1332)|((X1332)=(X1333))))&((~(subset @ X1334 @ emptyset)|((X1334)=(emptyset)))&((~(subset @ X1336 @ X1335)|(in @ X1336 @ (powerset @ X1335)))&((~(in @ X1338 @ (powerset @ X1337))|(subset @ X1338 @ X1337))&((in @ X1339 @ (powerset @ X1339))&((~(subset @ X1340 @ X1341)|(subset @ (powerset @ X1340) @ (powerset @ X1341)))&((in @ (dsetconstr @ X1342 @ X1343) @ (powerset @ X1342))&((subset @ (dsetconstr @ X1344 @ X1345) @ X1344)&((~(in @ X1348 @ X1346)|(in @ X1348 @ (binunion @ X1346 @ X1347)))&((in @ X1350 @ (setadjoin @ X1349 @ (setadjoin @ X1350 @ emptyset)))&((~(in @ X1353 @ X1352)|(in @ X1353 @ (binunion @ X1351 @ X1352)))&(((((in @ X1356 @ X1355)|(X1357)|(in @ X1356 @ X1354)|~(in @ X1356 @ (binunion @ X1354 @ X1355)))&(~(X1357)|(X1357)|(in @ X1356 @ X1354)|~(in @ X1356 @ (binunion @ X1354 @ X1355))))&(((in @ X1356 @ X1355)|(X1357)|~(X1357)|~(in @ X1356 @ (binunion @ X1354 @ X1355)))&(~(X1357)|(X1357)|~(X1357)|~(in @ X1356 @ (binunion @ X1354 @ X1355)))))&((~(in @ X1360 @ (binunion @ X1358 @ X1359))|((in @ X1360 @ X1358)|(in @ X1360 @ X1359)))&((subset @ X1361 @ (binunion @ X1361 @ X1362))&((subset @ X1364 @ (binunion @ X1363 @ X1364))&((~(in @ X1367 @ X1365)|(~(in @ X1367 @ X1366)|(in @ X1367 @ (binintersect @ X1365 @ X1366))))&((~(subset @ X1370 @ X1368)|(~(subset @ X1370 @ X1369)|(subset @ X1370 @ (binintersect @ X1368 @ X1369))))&((~(in @ X1373 @ (binintersect @ X1371 @ X1372))|(in @ X1373 @ X1371))&((subset @ (binintersect @ X1374 @ X1375) @ X1374)&((~(subset @ X1376 @ X1377)|((binintersect @ X1376 @ X1377)=(X1376)))&((((binintersect @ X1378 @ X1379)!=(X1379))|(subset @ X1379 @ X1378))&((~(in @ X1382 @ (binintersect @ X1380 @ X1381))|(in @ X1382 @ X1381))&((((in @ (esk54_2 @ X1383 @ X1384) @ X1383)|((binintersect @ X1383 @ X1384)=(emptyset)))&((in @ (esk54_2 @ X1383 @ X1384) @ X1384)|((binintersect @ X1383 @ X1384)=(emptyset))))&((subset @ (binintersect @ X1386 @ X1387) @ X1387)&((~(subset @ X1389 @ X1388)|((binintersect @ X1388 @ X1389)=(X1389)))&((((binintersect @ X1390 @ X1391)!=(X1390))|(subset @ X1390 @ X1391))&(((binintersect @ X1392 @ (binunion @ X1393 @ X1394))=(binunion @ (binintersect @ X1392 @ X1393) @ (binintersect @ X1392 @ X1394)))&((~(in @ X1397 @ X1395)|((in @ X1397 @ X1396)|(in @ X1397 @ (setminus @ X1395 @ X1396))))&((~(in @ X1400 @ (setminus @ X1398 @ X1399))|(in @ X1400 @ X1398))&((~(in @ X1403 @ (setminus @ X1401 @ X1402))|~(in @ X1403 @ X1402))&((~(subset @ X1404 @ X1405)|((setminus @ X1404 @ X1405)=(emptyset)))&(((in @ X1408 @ (setminus @ X1406 @ X1407))|(~(in @ X1408 @ X1406)|(in @ X1408 @ X1407)))&(((in @ X1411 @ (setminus @ X1409 @ X1410))|((in @ X1411 @ X1410)|~(in @ X1411 @ X1409)))&(((in @ X1414 @ X1412)|~(in @ X1414 @ (setminus @ X1412 @ X1413)))&((~(in @ X1417 @ X1416)|~(in @ X1417 @ (setminus @ X1415 @ X1416)))&((subset @ (setminus @ X1418 @ X1419) @ X1418)&((((setminus @ X1420 @ X1421)!=(emptyset))|(subset @ X1420 @ X1421))&((((~(in @ X1424 @ X1422)|(X1425)|(in @ X1424 @ X1422)|~(in @ X1424 @ (symdiff @ X1422 @ X1423)))&(((in @ X1424 @ X1423)|(X1425)|(in @ X1424 @ X1422)|~(in @ X1424 @ (symdiff @ X1422 @ X1423)))&(~(X1425)|(X1425)|(in @ X1424 @ X1422)|~(in @ X1424 @ (symdiff @ X1422 @ X1423)))))&(((~(in @ X1424 @ X1422)|(X1425)|~(in @ X1424 @ X1423)|~(in @ X1424 @ (symdiff @ X1422 @ X1423)))&(((in @ X1424 @ X1423)|(X1425)|~(in @ X1424 @ X1423)|~(in @ X1424 @ (symdiff @ X1422 @ X1423)))&(~(X1425)|(X1425)|~(in @ X1424 @ X1423)|~(in @ X1424 @ (symdiff @ X1422 @ X1423)))))&((~(in @ X1424 @ X1422)|(X1425)|~(X1425)|~(in @ X1424 @ (symdiff @ X1422 @ X1423)))&(((in @ X1424 @ X1423)|(X1425)|~(X1425)|~(in @ X1424 @ (symdiff @ X1422 @ X1423)))&(~(X1425)|(X1425)|~(X1425)|~(in @ X1424 @ (symdiff @ X1422 @ X1423)))))))&((~(in @ X1428 @ X1426)|((in @ X1428 @ X1427)|(in @ X1428 @ (symdiff @ X1426 @ X1427))))&(((in @ X1431 @ X1429)|(~(in @ X1431 @ X1430)|(in @ X1431 @ (symdiff @ X1429 @ X1430))))&((~(in @ X1434 @ X1432)|(~(in @ X1434 @ X1433)|~(in @ X1434 @ (symdiff @ X1432 @ X1433))))&(((in @ X1437 @ X1435)|((in @ X1437 @ X1436)|~(in @ X1437 @ (symdiff @ X1435 @ X1436))))&((in @ X1439 @ (setadjoin @ X1438 @ (setadjoin @ X1439 @ emptyset)))&((in @ X1440 @ (setunion @ (setadjoin @ (setadjoin @ X1440 @ emptyset) @ (setadjoin @ (setadjoin @ X1440 @ (setadjoin @ X1441 @ emptyset)) @ emptyset))))&((in @ X1443 @ (setunion @ (setadjoin @ (setadjoin @ X1442 @ emptyset) @ (setadjoin @ (setadjoin @ X1442 @ (setadjoin @ X1443 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1444 @ X1445) @ (setunion @ (setadjoin @ (setadjoin @ X1444 @ emptyset) @ (setadjoin @ (setadjoin @ X1444 @ (setadjoin @ X1445 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1444 @ X1445) @ (setunion @ (setadjoin @ (setadjoin @ X1444 @ emptyset) @ (setadjoin @ (setadjoin @ X1444 @ (setadjoin @ X1445 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1444 @ emptyset) @ (setadjoin @ (setadjoin @ X1444 @ (setadjoin @ X1445 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1444 @ X1445) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1444 @ X1445) @ (setadjoin @ (esk56_2 @ X1444 @ X1445) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1448 @ X1449) @ (setunion @ (kpair @ X1448 @ X1449)))&((in @ (esk58_2 @ X1448 @ X1449) @ (setunion @ (kpair @ X1448 @ X1449)))&((kpair @ X1448 @ X1449)=(setadjoin @ (setadjoin @ (esk57_2 @ X1448 @ X1449) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1448 @ X1449) @ (setadjoin @ (esk58_2 @ X1448 @ X1449) @ emptyset)) @ emptyset)))))&((~(in @ X1453 @ X1452)|(subset @ (setadjoin @ X1453 @ emptyset) @ X1452))&((~(in @ X1455 @ X1454)|(in @ (setadjoin @ X1455 @ emptyset) @ (powerset @ X1454)))&((~(in @ X1458 @ X1456)|(in @ (setadjoin @ X1458 @ emptyset) @ (powerset @ (binunion @ X1456 @ X1457))))&((~(in @ X1461 @ (setadjoin @ X1459 @ (setadjoin @ X1460 @ emptyset)))|(((X1461)=(X1459))|((X1461)=(X1460))))&((~(in @ X1464 @ X1462)|(~(in @ X1465 @ X1463)|(subset @ (setadjoin @ X1464 @ (setadjoin @ X1465 @ emptyset)) @ (binunion @ X1462 @ X1463))))&((~(in @ X1468 @ X1466)|(~(in @ X1469 @ X1467)|(in @ (setadjoin @ X1468 @ (setadjoin @ X1469 @ emptyset)) @ (powerset @ (binunion @ X1466 @ X1467)))))&((~(in @ X1472 @ X1470)|(~(in @ X1473 @ X1471)|(subset @ (setadjoin @ (setadjoin @ X1472 @ emptyset) @ (setadjoin @ (setadjoin @ X1472 @ (setadjoin @ X1473 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1470 @ X1471)))))&((~(in @ X1476 @ X1474)|(~(in @ X1477 @ X1475)|(in @ (setadjoin @ (setadjoin @ X1476 @ emptyset) @ (setadjoin @ (setadjoin @ X1476 @ (setadjoin @ X1477 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1474 @ X1475))))))&((~(in @ X1480 @ X1478)|(~(in @ X1481 @ X1479)|(in @ (kpair @ X1480 @ X1481) @ (powerset @ (powerset @ (binunion @ X1478 @ X1479))))))&((~(in @ X1484 @ X1482)|(~(in @ X1485 @ X1483)|(in @ (kpair @ X1484 @ X1485) @ (cartprod @ X1482 @ X1483))))&((((in @ (esk59_3 @ X1486 @ X1487 @ X1488) @ X1486)|~(in @ X1488 @ (cartprod @ X1486 @ X1487)))&(((in @ (esk60_3 @ X1486 @ X1487 @ X1488) @ X1487)|~(in @ X1488 @ (cartprod @ X1486 @ X1487)))&(((X1488)=(kpair @ (esk59_3 @ X1486 @ X1487 @ X1488) @ (esk60_3 @ X1486 @ X1487 @ X1488)))|~(in @ X1488 @ (cartprod @ X1486 @ X1487)))))&((((in @ (esk61_3 @ X1491 @ X1492 @ X1493) @ (setunion @ X1493))|~(in @ X1493 @ (cartprod @ X1491 @ X1492)))&(((in @ (esk62_3 @ X1491 @ X1492 @ X1493) @ (setunion @ X1493))|~(in @ X1493 @ (cartprod @ X1491 @ X1492)))&(((X1493)=(setadjoin @ (setadjoin @ (esk61_3 @ X1491 @ X1492 @ X1493) @ emptyset) @ (setadjoin @ (setadjoin @ (esk61_3 @ X1491 @ X1492 @ X1493) @ (setadjoin @ (esk62_3 @ X1491 @ X1492 @ X1493) @ emptyset)) @ emptyset)))|~(in @ X1493 @ (cartprod @ X1491 @ X1492)))))&((((in @ (esk63_2 @ X1496 @ X1497) @ X1496)|~(in @ X1497 @ (setunion @ X1496)))&((in @ X1497 @ (esk63_2 @ X1496 @ X1497))|~(in @ X1497 @ (setunion @ X1496))))&((subset @ (setunion @ (setadjoin @ X1499 @ emptyset)) @ X1499)&((subset @ X1500 @ (setunion @ (setadjoin @ X1500 @ emptyset)))&(((setunion @ (setadjoin @ X1501 @ emptyset))=(X1501))&(((((in @ (esk66_2 @ X1502 @ X1503) @ (dsetconstr @ X1502 @ X1503))|(~(in @ X1506 @ X1502)|~(X1503 @ X1506))|(in @ (esk64_2 @ X1502 @ X1503) @ X1502))&(((dsetconstr @ X1502 @ X1503)=(setadjoin @ (esk66_2 @ X1502 @ X1503) @ emptyset))|(~(in @ X1506 @ X1502)|~(X1503 @ X1506))|(in @ (esk64_2 @ X1502 @ X1503) @ X1502)))&((((in @ (esk66_2 @ X1502 @ X1503) @ (dsetconstr @ X1502 @ X1503))|(~(in @ X1506 @ X1502)|~(X1503 @ X1506))|(in @ (esk65_2 @ X1502 @ X1503) @ X1502))&(((dsetconstr @ X1502 @ X1503)=(setadjoin @ (esk66_2 @ X1502 @ X1503) @ emptyset))|(~(in @ X1506 @ X1502)|~(X1503 @ X1506))|(in @ (esk65_2 @ X1502 @ X1503) @ X1502)))&((((in @ (esk66_2 @ X1502 @ X1503) @ (dsetconstr @ X1502 @ X1503))|(~(in @ X1506 @ X1502)|~(X1503 @ X1506))|(X1503 @ (esk64_2 @ X1502 @ X1503)))&(((dsetconstr @ X1502 @ X1503)=(setadjoin @ (esk66_2 @ X1502 @ X1503) @ emptyset))|(~(in @ X1506 @ X1502)|~(X1503 @ X1506))|(X1503 @ (esk64_2 @ X1502 @ X1503))))&((((in @ (esk66_2 @ X1502 @ X1503) @ (dsetconstr @ X1502 @ X1503))|(~(in @ X1506 @ X1502)|~(X1503 @ X1506))|(X1503 @ (esk65_2 @ X1502 @ X1503)))&(((dsetconstr @ X1502 @ X1503)=(setadjoin @ (esk66_2 @ X1502 @ X1503) @ emptyset))|(~(in @ X1506 @ X1502)|~(X1503 @ X1506))|(X1503 @ (esk65_2 @ X1502 @ X1503))))&(((in @ (esk66_2 @ X1502 @ X1503) @ (dsetconstr @ X1502 @ X1503))|(~(in @ X1506 @ X1502)|~(X1503 @ X1506))|((esk64_2 @ X1502 @ X1503)!=(esk65_2 @ X1502 @ X1503)))&(((dsetconstr @ X1502 @ X1503)=(setadjoin @ (esk66_2 @ X1502 @ X1503) @ emptyset))|(~(in @ X1506 @ X1502)|~(X1503 @ X1506))|((esk64_2 @ X1502 @ X1503)!=(esk65_2 @ X1502 @ X1503))))))))&((((in @ (esk67_2 @ X1508 @ X1509) @ X1508)|(~(in @ X1510 @ (dsetconstr @ X1508 @ X1509))|((dsetconstr @ X1508 @ X1509)!=(setadjoin @ X1510 @ emptyset))))&((X1509 @ (esk67_2 @ X1508 @ X1509))|(~(in @ X1510 @ (dsetconstr @ X1508 @ X1509))|((dsetconstr @ X1508 @ X1509)!=(setadjoin @ X1510 @ emptyset)))))&(((((in @ (esk69_3 @ X1512 @ X1513 @ X1514) @ (dsetconstr @ X1512 @ X1513))|(in @ (esk68_3 @ X1512 @ X1513 @ X1514) @ X1512)|~(X1513 @ X1514)|~(in @ X1514 @ X1512))&(((dsetconstr @ X1512 @ X1513)=(setadjoin @ (esk69_3 @ X1512 @ X1513 @ X1514) @ emptyset))|(in @ (esk68_3 @ X1512 @ X1513 @ X1514) @ X1512)|~(X1513 @ X1514)|~(in @ X1514 @ X1512)))&((((in @ (esk69_3 @ X1512 @ X1513 @ X1514) @ (dsetconstr @ X1512 @ X1513))|(X1513 @ (esk68_3 @ X1512 @ X1513 @ X1514))|~(X1513 @ X1514)|~(in @ X1514 @ X1512))&(((dsetconstr @ X1512 @ X1513)=(setadjoin @ (esk69_3 @ X1512 @ X1513 @ X1514) @ emptyset))|(X1513 @ (esk68_3 @ X1512 @ X1513 @ X1514))|~(X1513 @ X1514)|~(in @ X1514 @ X1512)))&(((in @ (esk69_3 @ X1512 @ X1513 @ X1514) @ (dsetconstr @ X1512 @ X1513))|((esk68_3 @ X1512 @ X1513 @ X1514)!=(X1514))|~(X1513 @ X1514)|~(in @ X1514 @ X1512))&(((dsetconstr @ X1512 @ X1513)=(setadjoin @ (esk69_3 @ X1512 @ X1513 @ X1514) @ emptyset))|((esk68_3 @ X1512 @ X1513 @ X1514)!=(X1514))|~(X1513 @ X1514)|~(in @ X1514 @ X1512)))))&(((((in @ (esk72_2 @ X1517 @ X1518) @ (dsetconstr @ X1517 @ X1518))|(~(in @ X1521 @ X1517)|~(X1518 @ X1521))|(in @ (esk70_2 @ X1517 @ X1518) @ X1517))&(((dsetconstr @ X1517 @ X1518)=(setadjoin @ (esk72_2 @ X1517 @ X1518) @ emptyset))|(~(in @ X1521 @ X1517)|~(X1518 @ X1521))|(in @ (esk70_2 @ X1517 @ X1518) @ X1517)))&((((in @ (esk72_2 @ X1517 @ X1518) @ (dsetconstr @ X1517 @ X1518))|(~(in @ X1521 @ X1517)|~(X1518 @ X1521))|(in @ (esk71_2 @ X1517 @ X1518) @ X1517))&(((dsetconstr @ X1517 @ X1518)=(setadjoin @ (esk72_2 @ X1517 @ X1518) @ emptyset))|(~(in @ X1521 @ X1517)|~(X1518 @ X1521))|(in @ (esk71_2 @ X1517 @ X1518) @ X1517)))&((((in @ (esk72_2 @ X1517 @ X1518) @ (dsetconstr @ X1517 @ X1518))|(~(in @ X1521 @ X1517)|~(X1518 @ X1521))|(X1518 @ (esk70_2 @ X1517 @ X1518)))&(((dsetconstr @ X1517 @ X1518)=(setadjoin @ (esk72_2 @ X1517 @ X1518) @ emptyset))|(~(in @ X1521 @ X1517)|~(X1518 @ X1521))|(X1518 @ (esk70_2 @ X1517 @ X1518))))&((((in @ (esk72_2 @ X1517 @ X1518) @ (dsetconstr @ X1517 @ X1518))|(~(in @ X1521 @ X1517)|~(X1518 @ X1521))|(X1518 @ (esk71_2 @ X1517 @ X1518)))&(((dsetconstr @ X1517 @ X1518)=(setadjoin @ (esk72_2 @ X1517 @ X1518) @ emptyset))|(~(in @ X1521 @ X1517)|~(X1518 @ X1521))|(X1518 @ (esk71_2 @ X1517 @ X1518))))&(((in @ (esk72_2 @ X1517 @ X1518) @ (dsetconstr @ X1517 @ X1518))|(~(in @ X1521 @ X1517)|~(X1518 @ X1521))|((esk70_2 @ X1517 @ X1518)!=(esk71_2 @ X1517 @ X1518)))&(((dsetconstr @ X1517 @ X1518)=(setadjoin @ (esk72_2 @ X1517 @ X1518) @ emptyset))|(~(in @ X1521 @ X1517)|~(X1518 @ X1521))|((esk70_2 @ X1517 @ X1518)!=(esk71_2 @ X1517 @ X1518))))))))&((((setadjoin @ X1523 @ emptyset)!=(setadjoin @ X1524 @ emptyset))|((X1523)=(X1524)))&((~(in @ (setadjoin @ X1527 @ emptyset) @ (setadjoin @ (setadjoin @ X1525 @ emptyset) @ (setadjoin @ (setadjoin @ X1525 @ (setadjoin @ X1526 @ emptyset)) @ emptyset)))|((X1525)=(X1527)))&((((in @ (esk73_1 @ X1528) @ (dsetconstr @ (setunion @ X1528) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1528)))))|(~(in @ X1529 @ (setunion @ X1528))|(~(in @ X1530 @ (setunion @ X1528))|((X1528)!=(setadjoin @ (setadjoin @ X1529 @ emptyset) @ (setadjoin @ (setadjoin @ X1529 @ (setadjoin @ X1530 @ emptyset)) @ emptyset))))))&(((dsetconstr @ (setunion @ X1528) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1528))))=(setadjoin @ (esk73_1 @ X1528) @ emptyset))|(~(in @ X1529 @ (setunion @ X1528))|(~(in @ X1530 @ (setunion @ X1528))|((X1528)!=(setadjoin @ (setadjoin @ X1529 @ emptyset) @ (setadjoin @ (setadjoin @ X1529 @ (setadjoin @ X1530 @ emptyset)) @ emptyset)))))))&((~(in @ X1533 @ X1532)|((X1532)!=(setadjoin @ X1533 @ emptyset))|(in @ (setunion @ X1532) @ X1532))&(((kfst @ (kpair @ X1534 @ X1535))=(X1534))&((~(in @ X1538 @ (cartprod @ X1536 @ X1537))|(in @ (kfst @ X1538) @ X1536))&((((setadjoin @ (setadjoin @ X1539 @ emptyset) @ (setadjoin @ (setadjoin @ X1539 @ (setadjoin @ X1540 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1541 @ emptyset) @ (setadjoin @ (setadjoin @ X1541 @ (setadjoin @ X1542 @ emptyset)) @ emptyset)))|((X1539)=(X1541)))&((((kpair @ X1543 @ X1544)!=(kpair @ X1545 @ X1546))|((X1543)=(X1545)))&((((X1547)!=(X1548))|((setadjoin @ X1547 @ (setadjoin @ X1548 @ emptyset))=(setadjoin @ X1547 @ emptyset)))&((((X1549)!=(X1550))|((setadjoin @ (setadjoin @ X1549 @ emptyset) @ (setadjoin @ (setadjoin @ X1549 @ (setadjoin @ X1550 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1549 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1551 @ emptyset) @ (setadjoin @ (setadjoin @ X1551 @ (setadjoin @ X1552 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1553 @ emptyset) @ (setadjoin @ (setadjoin @ X1553 @ (setadjoin @ X1554 @ emptyset)) @ emptyset)))|(((X1553)!=(X1554))|((X1552)=(X1554))))&((((setadjoin @ X1555 @ (setadjoin @ X1556 @ emptyset))!=(setadjoin @ X1557 @ emptyset))|((X1555)=(X1556)))&((((setadjoin @ (setadjoin @ X1558 @ emptyset) @ (setadjoin @ (setadjoin @ X1558 @ (setadjoin @ X1559 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1560 @ emptyset) @ (setadjoin @ (setadjoin @ X1560 @ (setadjoin @ X1561 @ emptyset)) @ emptyset)))|((X1559)=(X1561)))&((((kpair @ X1562 @ X1563)!=(kpair @ X1564 @ X1565))|((X1563)=(X1565)))&((((in @ (esk74_1 @ X1566) @ (dsetconstr @ (setunion @ X1566) @ (^[Z0/* 3 */:$i]:(((X1566)=(kpair @ (kfst @ X1566) @ Z0))))))|(~(in @ X1567 @ (setunion @ X1566))|(~(in @ X1568 @ (setunion @ X1566))|((X1566)!=(setadjoin @ (setadjoin @ X1567 @ emptyset) @ (setadjoin @ (setadjoin @ X1567 @ (setadjoin @ X1568 @ emptyset)) @ emptyset))))))&(((dsetconstr @ (setunion @ X1566) @ (^[Z0/* 3 */:$i]:(((X1566)=(kpair @ (kfst @ X1566) @ Z0)))))=(setadjoin @ (esk74_1 @ X1566) @ emptyset))|(~(in @ X1567 @ (setunion @ X1566))|(~(in @ X1568 @ (setunion @ X1566))|((X1566)!=(setadjoin @ (setadjoin @ X1567 @ emptyset) @ (setadjoin @ (setadjoin @ X1567 @ (setadjoin @ X1568 @ emptyset)) @ emptyset)))))))&(((ksnd @ (kpair @ X1570 @ X1571))=(X1571))&(((in @ esk76_0 @ (setunion @ esk75_0))&((in @ esk77_0 @ (setunion @ esk75_0))&((esk75_0)=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset)))))&((kpair @ (kfst @ esk75_0) @ (ksnd @ esk75_0))!=(esk75_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_241])])])])])])])).
0.69/0.67	thf(c_0_244, plain, ![X1060:$i, X1061:$i]:(((kpair @ X1060 @ X1061)=(setadjoin @ (setadjoin @ X1060 @ emptyset) @ (setadjoin @ (setadjoin @ X1060 @ (setadjoin @ X1061 @ emptyset)) @ emptyset)))), inference(variable_rename,[status(thm)],[c_0_242])).
0.69/0.67	thf(c_0_245, negated_conjecture, ((esk75_0)=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_243])).
0.69/0.67	thf(c_0_246, plain, ![X2:$i, X3:$i]:(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_244])).
0.69/0.67	thf(c_0_247, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_243])).
0.69/0.67	thf(c_0_248, negated_conjecture, ((kpair @ esk76_0 @ esk77_0)=(esk75_0)), inference(rw,[status(thm)],[c_0_245, c_0_246])).
0.69/0.67	thf(c_0_249, negated_conjecture, ((kpair @ (kfst @ esk75_0) @ (ksnd @ esk75_0))!=(esk75_0)), inference(split_conjunct,[status(thm)],[c_0_243])).
0.69/0.67	thf(c_0_250, negated_conjecture, ((kfst @ esk75_0)=(esk76_0)), inference(spm,[status(thm)],[c_0_247, c_0_248])).
0.69/0.67	thf(c_0_251, negated_conjecture, ![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3))), inference(split_conjunct,[status(thm)],[c_0_243])).
0.69/0.67	thf(c_0_252, negated_conjecture, ((kpair @ esk76_0 @ (ksnd @ esk75_0))!=(esk75_0)), inference(rw,[status(thm)],[c_0_249, c_0_250])).
0.69/0.67	thf(c_0_253, negated_conjecture, ((ksnd @ esk75_0)=(esk77_0)), inference(spm,[status(thm)],[c_0_251, c_0_248])).
0.69/0.67	thf(c_0_254, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_252, c_0_253]), c_0_248])]), ['proof']).
0.69/0.67	# SZS output end CNFRefutation
0.69/0.67	# Parsed axioms                        : 384
0.69/0.67	# Removed by relevancy pruning/SinE    : 0
0.69/0.67	# Initial clauses                      : 545
0.69/0.67	# Removed in clause preprocessing      : 229
0.69/0.67	# Initial clauses in saturation        : 316
0.69/0.67	# Processed clauses                    : 361
0.69/0.67	# ...of these trivial                  : 6
0.69/0.67	# ...subsumed                          : 29
0.69/0.67	# ...remaining for further processing  : 326
0.69/0.67	# Other redundant clauses eliminated   : 21
0.69/0.67	# Clauses deleted for lack of memory   : 0
0.69/0.67	# Backward-subsumed                    : 0
0.69/0.67	# Backward-rewritten                   : 5
0.69/0.67	# Generated clauses                    : 24
0.69/0.67	# ...of the previous two non-redundant : 20
0.69/0.67	# ...aggressively subsumed             : 0
0.69/0.67	# Contextual simplify-reflections      : 0
0.69/0.67	# Paramodulations                      : 3
0.69/0.67	# Factorizations                       : 0
0.69/0.67	# NegExts                              : 0
0.69/0.67	# Equation resolutions                 : 21
0.69/0.67	# Disequality decompositions           : 0
0.69/0.67	# Total rewrite steps                  : 55
0.69/0.67	# ...of those cached                   : 34
0.69/0.67	# Propositional unsat checks           : 0
0.69/0.67	#    Propositional check models        : 0
0.69/0.67	#    Propositional check unsatisfiable : 0
0.69/0.67	#    Propositional clauses             : 0
0.69/0.67	#    Propositional clauses after purity: 0
0.69/0.67	#    Propositional unsat core size     : 0
0.69/0.67	#    Propositional preprocessing time  : 0.000
0.69/0.67	#    Propositional encoding time       : 0.000
0.69/0.67	#    Propositional solver time         : 0.000
0.69/0.67	#    Success case prop preproc time    : 0.000
0.69/0.67	#    Success case prop encoding time   : 0.000
0.69/0.67	#    Success case prop solver time     : 0.000
0.69/0.67	# Current number of processed clauses  : 27
0.69/0.67	#    Positive orientable unit clauses  : 19
0.69/0.67	#    Positive unorientable unit clauses: 0
0.69/0.67	#    Negative unit clauses             : 2
0.69/0.67	#    Non-unit-clauses                  : 6
0.69/0.67	# Current number of unprocessed clauses: 249
0.69/0.67	# ...number of literals in the above   : 807
0.69/0.67	# Current number of archived formulas  : 0
0.69/0.67	# Current number of archived clauses   : 279
0.69/0.67	# Clause-clause subsumption calls (NU) : 11880
0.69/0.67	# Rec. Clause-clause subsumption calls : 4881
0.69/0.67	# Non-unit clause-clause subsumptions  : 27
0.69/0.67	# Unit Clause-clause subsumption calls : 15
0.69/0.67	# Rewrite failures with RHS unbound    : 0
0.69/0.67	# BW rewrite match attempts            : 26
0.69/0.67	# BW rewrite match successes           : 5
0.69/0.67	# Condensation attempts                : 361
0.69/0.67	# Condensation successes               : 3
0.69/0.67	# Termbank termtop insertions          : 54281
0.69/0.67	# Search garbage collected termcells   : 17301
0.69/0.67	
0.69/0.67	# -------------------------------------------------
0.69/0.67	# User time                : 0.060 s
0.69/0.67	# System time              : 0.010 s
0.69/0.67	# Total time               : 0.070 s
0.69/0.67	# Maximum resident set size: 5876 pages
0.69/0.67	
0.69/0.67	# -------------------------------------------------
0.69/0.67	# User time                : 0.069 s
0.69/0.67	# System time              : 0.014 s
0.69/0.67	# Total time               : 0.083 s
0.69/0.67	# Maximum resident set size: 2208 pages
0.69/0.67	% E exiting
0.69/0.67	% E exiting
0.69/0.67	EOF