0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : run_E %s %d THM
0.13/0.33	% Computer : n010.cluster.edu
0.13/0.33	% Model    : x86_64 x86_64
0.13/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory   : 8042.1875MB
0.13/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 1440
0.13/0.33	% WCLimit    : 180
0.13/0.34	% DateTime   : Thu Jul  4 07:01:24 EDT 2024
0.13/0.34	% CPUTime    : 
0.20/0.48	Running higher-order theorem proving
0.20/0.55	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=180 /export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p
2.13/180.04	# Version: 3.2.0-ho
2.13/180.04	# Preprocessing class: HSLMSLSSLLLCHFA.
2.13/180.04	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.13/180.04	# Starting ehoh_best5 with 180s (1) cores
2.13/180.04	# Starting almost_fo_3_lam with 180s (1) cores
2.13/180.04	# Starting new_bool_5 with 180s (1) cores
2.13/180.04	# Starting pre_casc_3 with 180s (1) cores
2.13/180.04	# Starting ho_unfolding_8 with 180s (1) cores
2.13/180.04	# Starting new_ho_10_cnf2 with 180s (1) cores
2.13/180.04	# Starting new_bool_3 with 180s (1) cores
2.13/180.04	# Starting new_ho_5 with 180s (1) cores
2.13/180.04	# ho_unfolding_8 with pid 937 completed with status 0
2.13/180.04	# Result found by ho_unfolding_8
2.13/180.04	# Preprocessing class: HSLMSLSSLLLCHFA.
2.13/180.04	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.13/180.04	# Starting ehoh_best5 with 180s (1) cores
2.13/180.04	# Starting almost_fo_3_lam with 180s (1) cores
2.13/180.04	# Starting new_bool_5 with 180s (1) cores
2.13/180.04	# Starting pre_casc_3 with 180s (1) cores
2.13/180.04	# Starting ho_unfolding_8 with 180s (1) cores
2.13/180.04	# No SInE strategy applied
2.13/180.04	# Search class: HGHSM-FSLM32-MHFMMSBN
2.13/180.04	# Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
2.13/180.04	# Starting ho_unfolding_8 with 37s (1) cores
2.13/180.04	# ho_unfolding_8 with pid 978 completed with status 0
2.13/180.04	# Result found by ho_unfolding_8
2.13/180.04	# Preprocessing class: HSLMSLSSLLLCHFA.
2.13/180.04	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.13/180.04	# Starting ehoh_best5 with 180s (1) cores
2.13/180.04	# Starting almost_fo_3_lam with 180s (1) cores
2.13/180.04	# Starting new_bool_5 with 180s (1) cores
2.13/180.04	# Starting pre_casc_3 with 180s (1) cores
2.13/180.04	# Starting ho_unfolding_8 with 180s (1) cores
2.13/180.04	# No SInE strategy applied
2.13/180.04	# Search class: HGHSM-FSLM32-MHFMMSBN
2.13/180.04	# Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
2.13/180.04	# Starting ho_unfolding_8 with 37s (1) cores
2.13/180.04	# Preprocessing time       : 0.070 s
2.13/180.04	# Presaturation interreduction done
2.13/180.04	
2.13/180.04	# Proof found!
2.13/180.04	# SZS status Theorem
2.13/180.04	# SZS output start CNFRefutation
2.13/180.04	thf(decl_22, type, in: $i > $i > $o).
2.13/180.04	thf(decl_23, type, exu: ($i > $o) > $o).
2.13/180.04	thf(decl_24, type, setextAx: $o).
2.13/180.04	thf(decl_25, type, emptyset: $i).
2.13/180.04	thf(decl_26, type, emptysetAx: $o).
2.13/180.04	thf(decl_27, type, setadjoin: $i > $i > $i).
2.13/180.04	thf(decl_28, type, setadjoinAx: $o).
2.13/180.04	thf(decl_29, type, powerset: $i > $i).
2.13/180.04	thf(decl_30, type, powersetAx: $o).
2.13/180.04	thf(decl_31, type, setunion: $i > $i).
2.13/180.04	thf(decl_32, type, setunionAx: $o).
2.13/180.04	thf(decl_33, type, omega: $i).
2.13/180.04	thf(decl_34, type, omega0Ax: $o).
2.13/180.04	thf(decl_35, type, omegaSAx: $o).
2.13/180.04	thf(decl_36, type, omegaIndAx: $o).
2.13/180.04	thf(decl_37, type, replAx: $o).
2.13/180.04	thf(decl_38, type, foundationAx: $o).
2.13/180.04	thf(decl_39, type, wellorderingAx: $o).
2.13/180.04	thf(decl_40, type, descr: ($i > $o) > $i).
2.13/180.04	thf(decl_41, type, descrp: $o).
2.13/180.04	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_43, type, dsetconstrI: $o).
2.13/180.04	thf(decl_44, type, dsetconstrEL: $o).
2.13/180.04	thf(decl_45, type, dsetconstrER: $o).
2.13/180.04	thf(decl_46, type, exuE1: $o).
2.13/180.04	thf(decl_47, type, prop2set: $o > $i).
2.13/180.04	thf(decl_48, type, prop2setE: $o).
2.13/180.04	thf(decl_49, type, emptysetE: $o).
2.13/180.04	thf(decl_50, type, emptysetimpfalse: $o).
2.13/180.04	thf(decl_51, type, notinemptyset: $o).
2.13/180.04	thf(decl_52, type, exuE3e: $o).
2.13/180.04	thf(decl_53, type, setext: $o).
2.13/180.04	thf(decl_54, type, emptyI: $o).
2.13/180.04	thf(decl_55, type, noeltsimpempty: $o).
2.13/180.04	thf(decl_56, type, setbeta: $o).
2.13/180.04	thf(decl_57, type, nonempty: $i > $o).
2.13/180.04	thf(decl_58, type, nonemptyE1: $o).
2.13/180.04	thf(decl_59, type, nonemptyI: $o).
2.13/180.04	thf(decl_60, type, nonemptyI1: $o).
2.13/180.04	thf(decl_61, type, setadjoinIL: $o).
2.13/180.04	thf(decl_62, type, emptyinunitempty: $o).
2.13/180.04	thf(decl_63, type, setadjoinIR: $o).
2.13/180.04	thf(decl_64, type, setadjoinE: $o).
2.13/180.04	thf(decl_65, type, setadjoinOr: $o).
2.13/180.04	thf(decl_66, type, setoftrueEq: $o).
2.13/180.04	thf(decl_67, type, powersetI: $o).
2.13/180.04	thf(decl_68, type, emptyinPowerset: $o).
2.13/180.04	thf(decl_69, type, emptyInPowerset: $o).
2.13/180.04	thf(decl_70, type, powersetE: $o).
2.13/180.04	thf(decl_71, type, setunionI: $o).
2.13/180.04	thf(decl_72, type, setunionE: $o).
2.13/180.04	thf(decl_73, type, subPowSU: $o).
2.13/180.04	thf(decl_74, type, exuE2: $o).
2.13/180.04	thf(decl_75, type, nonemptyImpWitness: $o).
2.13/180.04	thf(decl_76, type, uniqinunit: $o).
2.13/180.04	thf(decl_77, type, notinsingleton: $o).
2.13/180.04	thf(decl_78, type, eqinunit: $o).
2.13/180.04	thf(decl_79, type, singletonsswitch: $o).
2.13/180.04	thf(decl_80, type, upairsetE: $o).
2.13/180.04	thf(decl_81, type, upairsetIL: $o).
2.13/180.04	thf(decl_82, type, upairsetIR: $o).
2.13/180.04	thf(decl_83, type, emptyE1: $o).
2.13/180.04	thf(decl_84, type, vacuousDall: $o).
2.13/180.04	thf(decl_85, type, quantDeMorgan1: $o).
2.13/180.04	thf(decl_86, type, quantDeMorgan2: $o).
2.13/180.04	thf(decl_87, type, quantDeMorgan3: $o).
2.13/180.04	thf(decl_88, type, quantDeMorgan4: $o).
2.13/180.04	thf(decl_89, type, prop2setI: $o).
2.13/180.04	thf(decl_90, type, set2prop: $i > $o).
2.13/180.04	thf(decl_91, type, prop2set2propI: $o).
2.13/180.04	thf(decl_92, type, notdexE: $o).
2.13/180.04	thf(decl_93, type, notdallE: $o).
2.13/180.04	thf(decl_94, type, exuI1: $o).
2.13/180.04	thf(decl_95, type, exuI3: $o).
2.13/180.04	thf(decl_96, type, exuI2: $o).
2.13/180.04	thf(decl_97, type, inCongP: $o).
2.13/180.04	thf(decl_98, type, in__Cong: $o).
2.13/180.04	thf(decl_99, type, exuE3u: $o).
2.13/180.04	thf(decl_100, type, exu__Cong: $o).
2.13/180.04	thf(decl_101, type, emptyset__Cong: $o).
2.13/180.04	thf(decl_102, type, setadjoin__Cong: $o).
2.13/180.04	thf(decl_103, type, powerset__Cong: $o).
2.13/180.04	thf(decl_104, type, setunion__Cong: $o).
2.13/180.04	thf(decl_105, type, omega__Cong: $o).
2.13/180.04	thf(decl_106, type, exuEu: $o).
2.13/180.04	thf(decl_107, type, descr__Cong: $o).
2.13/180.04	thf(decl_108, type, dsetconstr__Cong: $o).
2.13/180.04	thf(decl_109, type, subset: $i > $i > $o).
2.13/180.04	thf(decl_112, type, subsetI1: $o).
2.13/180.04	thf(decl_113, type, eqimpsubset2: $o).
2.13/180.04	thf(decl_114, type, eqimpsubset1: $o).
2.13/180.04	thf(decl_115, type, subsetI2: $o).
2.13/180.04	thf(decl_116, type, emptysetsubset: $o).
2.13/180.04	thf(decl_117, type, subsetE: $o).
2.13/180.04	thf(decl_118, type, subsetE2: $o).
2.13/180.04	thf(decl_119, type, notsubsetI: $o).
2.13/180.04	thf(decl_120, type, notequalI1: $o).
2.13/180.04	thf(decl_121, type, notequalI2: $o).
2.13/180.04	thf(decl_122, type, subsetRefl: $o).
2.13/180.04	thf(decl_123, type, subsetTrans: $o).
2.13/180.04	thf(decl_124, type, setadjoinSub: $o).
2.13/180.04	thf(decl_125, type, setadjoinSub2: $o).
2.13/180.04	thf(decl_126, type, subset2powerset: $o).
2.13/180.04	thf(decl_127, type, setextsub: $o).
2.13/180.04	thf(decl_128, type, subsetemptysetimpeq: $o).
2.13/180.04	thf(decl_129, type, powersetI1: $o).
2.13/180.04	thf(decl_130, type, powersetE1: $o).
2.13/180.04	thf(decl_131, type, inPowerset: $o).
2.13/180.04	thf(decl_132, type, powersetsubset: $o).
2.13/180.04	thf(decl_133, type, sepInPowerset: $o).
2.13/180.04	thf(decl_134, type, sepSubset: $o).
2.13/180.04	thf(decl_135, type, binunion: $i > $i > $i).
2.13/180.04	thf(decl_136, type, binunionIL: $o).
2.13/180.04	thf(decl_137, type, upairset2IR: $o).
2.13/180.04	thf(decl_138, type, binunionIR: $o).
2.13/180.04	thf(decl_139, type, binunionEcases: $o).
2.13/180.04	thf(decl_140, type, binunionE: $o).
2.13/180.04	thf(decl_141, type, binunionLsub: $o).
2.13/180.04	thf(decl_142, type, binunionRsub: $o).
2.13/180.04	thf(decl_143, type, binintersect: $i > $i > $i).
2.13/180.04	thf(decl_144, type, binintersectI: $o).
2.13/180.04	thf(decl_145, type, binintersectSubset5: $o).
2.13/180.04	thf(decl_146, type, binintersectEL: $o).
2.13/180.04	thf(decl_147, type, binintersectLsub: $o).
2.13/180.04	thf(decl_148, type, binintersectSubset2: $o).
2.13/180.04	thf(decl_149, type, binintersectSubset3: $o).
2.13/180.04	thf(decl_150, type, binintersectER: $o).
2.13/180.04	thf(decl_151, type, disjointsetsI1: $o).
2.13/180.04	thf(decl_152, type, binintersectRsub: $o).
2.13/180.04	thf(decl_153, type, binintersectSubset4: $o).
2.13/180.04	thf(decl_154, type, binintersectSubset1: $o).
2.13/180.04	thf(decl_155, type, bs114d: $o).
2.13/180.04	thf(decl_157, type, setminus: $i > $i > $i).
2.13/180.04	thf(decl_158, type, setminusI: $o).
2.13/180.04	thf(decl_159, type, setminusEL: $o).
2.13/180.04	thf(decl_160, type, setminusER: $o).
2.13/180.04	thf(decl_161, type, setminusSubset2: $o).
2.13/180.04	thf(decl_162, type, setminusERneg: $o).
2.13/180.04	thf(decl_163, type, setminusELneg: $o).
2.13/180.04	thf(decl_164, type, setminusILneg: $o).
2.13/180.04	thf(decl_165, type, setminusIRneg: $o).
2.13/180.04	thf(decl_166, type, setminusLsub: $o).
2.13/180.04	thf(decl_167, type, setminusSubset1: $o).
2.13/180.04	thf(decl_168, type, symdiff: $i > $i > $i).
2.13/180.04	thf(decl_169, type, symdiffE: $o).
2.13/180.04	thf(decl_170, type, symdiffI1: $o).
2.13/180.04	thf(decl_171, type, symdiffI2: $o).
2.13/180.04	thf(decl_172, type, symdiffIneg1: $o).
2.13/180.04	thf(decl_173, type, symdiffIneg2: $o).
2.13/180.04	thf(decl_174, type, iskpair: $i > $o).
2.13/180.04	thf(decl_175, type, secondinupair: $o).
2.13/180.04	thf(decl_176, type, setukpairIL: $o).
2.13/180.04	thf(decl_177, type, setukpairIR: $o).
2.13/180.04	thf(decl_178, type, kpairiskpair: $o).
2.13/180.04	thf(decl_179, type, kpair: $i > $i > $i).
2.13/180.04	thf(decl_180, type, kpairp: $o).
2.13/180.04	thf(decl_181, type, cartprod: $i > $i > $i).
2.13/180.04	thf(decl_182, type, singletonsubset: $o).
2.13/180.04	thf(decl_183, type, singletoninpowerset: $o).
2.13/180.04	thf(decl_184, type, singletoninpowunion: $o).
2.13/180.04	thf(decl_185, type, upairset2E: $o).
2.13/180.04	thf(decl_186, type, upairsubunion: $o).
2.13/180.04	thf(decl_187, type, upairinpowunion: $o).
2.13/180.04	thf(decl_188, type, ubforcartprodlem1: $o).
2.13/180.04	thf(decl_189, type, ubforcartprodlem2: $o).
2.13/180.04	thf(decl_190, type, ubforcartprodlem3: $o).
2.13/180.04	thf(decl_191, type, cartprodpairin: $o).
2.13/180.04	thf(decl_192, type, cartprodmempair1: $o).
2.13/180.04	thf(decl_193, type, cartprodmempair: $o).
2.13/180.04	thf(decl_194, type, setunionE2: $o).
2.13/180.04	thf(decl_195, type, setunionsingleton1: $o).
2.13/180.04	thf(decl_196, type, setunionsingleton2: $o).
2.13/180.04	thf(decl_197, type, setunionsingleton: $o).
2.13/180.04	thf(decl_198, type, singleton: $i > $o).
2.13/180.04	thf(decl_199, type, singletonprop: $o).
2.13/180.04	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
2.13/180.04	thf(decl_201, type, ex1E1: $o).
2.13/180.04	thf(decl_202, type, ex1I: $o).
2.13/180.04	thf(decl_203, type, ex1I2: $o).
2.13/180.04	thf(decl_204, type, singletonsuniq: $o).
2.13/180.04	thf(decl_209, type, setukpairinjL1: $o).
2.13/180.04	thf(decl_210, type, kfstsingleton: $o).
2.13/180.04	thf(decl_211, type, theprop: $o).
2.13/180.04	thf(decl_212, type, kfst: $i > $i).
2.13/180.04	thf(decl_213, type, kfstpairEq: $o).
2.13/180.04	thf(decl_214, type, cartprodfstin: $o).
2.13/180.04	thf(decl_215, type, setukpairinjL2: $o).
2.13/180.04	thf(decl_216, type, setukpairinjL: $o).
2.13/180.04	thf(decl_217, type, setukpairinjR11: $o).
2.13/180.04	thf(decl_218, type, setukpairinjR12: $o).
2.13/180.04	thf(decl_219, type, setukpairinjR1: $o).
2.13/180.04	thf(decl_220, type, upairequniteq: $o).
2.13/180.04	thf(decl_221, type, setukpairinjR2: $o).
2.13/180.04	thf(decl_222, type, setukpairinjR: $o).
2.13/180.04	thf(decl_223, type, ksndsingleton: $o).
2.13/180.04	thf(decl_224, type, ksnd: $i > $i).
2.13/180.04	thf(decl_225, type, ksndpairEq: $o).
2.13/180.04	thf(decl_226, type, kpairsurjEq: $o).
2.13/180.04	thf(decl_227, type, cartprodsndin: $o).
2.13/180.04	thf(decl_228, type, cartprodpairmemEL: $o).
2.13/180.04	thf(decl_229, type, cartprodpairmemER: $o).
2.13/180.04	thf(decl_230, type, cartprodmempaircEq: $o).
2.13/180.04	thf(decl_231, type, cartprodfstpairEq: $o).
2.13/180.04	thf(decl_232, type, cartprodsndpairEq: $o).
2.13/180.04	thf(decl_233, type, cartprodpairsurjEq: $o).
2.13/180.04	thf(decl_234, type, breln: $i > $i > $i > $o).
2.13/180.04	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
2.13/180.04	thf(decl_236, type, dpsetconstrI: $o).
2.13/180.04	thf(decl_237, type, dpsetconstrSub: $o).
2.13/180.04	thf(decl_238, type, setOfPairsIsBReln: $o).
2.13/180.04	thf(decl_239, type, dpsetconstrERa: $o).
2.13/180.04	thf(decl_240, type, dpsetconstrEL1: $o).
2.13/180.04	thf(decl_241, type, dpsetconstrEL2: $o).
2.13/180.04	thf(decl_242, type, dpsetconstrER: $o).
2.13/180.04	thf(decl_243, type, func: $i > $i > $i > $o).
2.13/180.04	thf(decl_244, type, funcSet: $i > $i > $i).
2.13/180.04	thf(decl_245, type, funcImageSingleton: $o).
2.13/180.04	thf(decl_246, type, apProp: $o).
2.13/180.04	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
2.13/180.04	thf(decl_248, type, app: $o).
2.13/180.04	thf(decl_249, type, infuncsetfunc: $o).
2.13/180.04	thf(decl_250, type, ap2p: $o).
2.13/180.04	thf(decl_251, type, funcinfuncset: $o).
2.13/180.04	thf(decl_252, type, lamProp: $o).
2.13/180.04	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
2.13/180.04	thf(decl_254, type, lamp: $o).
2.13/180.04	thf(decl_255, type, lam2p: $o).
2.13/180.04	thf(decl_256, type, brelnall1: $o).
2.13/180.04	thf(decl_257, type, brelnall2: $o).
2.13/180.04	thf(decl_258, type, ex1E2: $o).
2.13/180.04	thf(decl_259, type, funcGraphProp1: $o).
2.13/180.04	thf(decl_260, type, funcGraphProp3: $o).
2.13/180.04	thf(decl_261, type, funcGraphProp2: $o).
2.13/180.04	thf(decl_262, type, funcextLem: $o).
2.13/180.04	thf(decl_263, type, funcGraphProp4: $o).
2.13/180.04	thf(decl_264, type, subbreln: $o).
2.13/180.04	thf(decl_265, type, eqbreln: $o).
2.13/180.04	thf(decl_266, type, funcext: $o).
2.13/180.04	thf(decl_267, type, funcext2: $o).
2.13/180.04	thf(decl_268, type, ap2apEq1: $o).
2.13/180.04	thf(decl_269, type, ap2apEq2: $o).
2.13/180.04	thf(decl_270, type, beta1: $o).
2.13/180.04	thf(decl_271, type, eta1: $o).
2.13/180.04	thf(decl_272, type, lam2lamEq: $o).
2.13/180.04	thf(decl_273, type, beta2: $o).
2.13/180.04	thf(decl_274, type, eta2: $o).
2.13/180.04	thf(decl_275, type, iffalseProp1: $o).
2.13/180.04	thf(decl_276, type, iffalseProp2: $o).
2.13/180.04	thf(decl_277, type, iftrueProp1: $o).
2.13/180.04	thf(decl_278, type, iftrueProp2: $o).
2.13/180.04	thf(decl_279, type, ifSingleton: $o).
2.13/180.04	thf(decl_280, type, if: $i > $o > $i > $i > $i).
2.13/180.04	thf(decl_281, type, ifp: $o).
2.13/180.04	thf(decl_282, type, theeq: $o).
2.13/180.04	thf(decl_283, type, iftrue: $o).
2.13/180.04	thf(decl_284, type, iffalse: $o).
2.13/180.04	thf(decl_285, type, iftrueorfalse: $o).
2.13/180.04	thf(decl_286, type, binintersectT_lem: $o).
2.13/180.04	thf(decl_287, type, binunionT_lem: $o).
2.13/180.04	thf(decl_288, type, powersetT_lem: $o).
2.13/180.04	thf(decl_289, type, setminusT_lem: $o).
2.13/180.04	thf(decl_290, type, complementT_lem: $o).
2.13/180.04	thf(decl_291, type, setextT: $o).
2.13/180.04	thf(decl_292, type, subsetTI: $o).
2.13/180.04	thf(decl_293, type, powersetTI1: $o).
2.13/180.04	thf(decl_294, type, powersetTE1: $o).
2.13/180.04	thf(decl_295, type, complementTI1: $o).
2.13/180.04	thf(decl_296, type, complementTE1: $o).
2.13/180.04	thf(decl_297, type, binintersectTELcontra: $o).
2.13/180.04	thf(decl_298, type, binintersectTERcontra: $o).
2.13/180.04	thf(decl_299, type, contrasubsetT: $o).
2.13/180.04	thf(decl_300, type, contrasubsetT1: $o).
2.13/180.04	thf(decl_301, type, contrasubsetT2: $o).
2.13/180.04	thf(decl_302, type, contrasubsetT3: $o).
2.13/180.04	thf(decl_303, type, doubleComplementI1: $o).
2.13/180.04	thf(decl_304, type, doubleComplementE1: $o).
2.13/180.04	thf(decl_305, type, doubleComplementSub1: $o).
2.13/180.04	thf(decl_306, type, doubleComplementSub2: $o).
2.13/180.04	thf(decl_307, type, doubleComplementEq: $o).
2.13/180.04	thf(decl_308, type, complementTnotintersectT: $o).
2.13/180.04	thf(decl_309, type, complementImpComplementIntersect: $o).
2.13/180.04	thf(decl_310, type, complementSubsetComplementIntersect: $o).
2.13/180.04	thf(decl_311, type, complementInPowersetComplementIntersect: $o).
2.13/180.04	thf(decl_312, type, contraSubsetComplement: $o).
2.13/180.04	thf(decl_313, type, complementTcontraSubset: $o).
2.13/180.04	thf(decl_314, type, binunionTILcontra: $o).
2.13/180.04	thf(decl_315, type, epred1_0: $o).
2.13/180.04	thf(decl_316, type, esk1_2: $i > $i > $i).
2.13/180.04	thf(decl_317, type, esk2_2: $i > $i > $i).
2.13/180.04	thf(decl_318, type, esk3_2: $i > $i > $i).
2.13/180.04	thf(decl_319, type, esk4_1: $i > $i).
2.13/180.04	thf(decl_320, type, esk5_2: ($i > $i > $o) > $i > $i).
2.13/180.04	thf(decl_321, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
2.13/180.04	thf(decl_322, type, esk7_2: ($i > $i > $o) > $i > $i).
2.13/180.04	thf(decl_323, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
2.13/180.04	thf(decl_324, type, esk9_1: $i > $i).
2.13/180.04	thf(decl_325, type, esk10_2: ($i > $o) > $i > $i).
2.13/180.04	thf(decl_326, type, esk11_2: ($i > $o) > $i > $i).
2.13/180.04	thf(decl_327, type, esk12_1: ($i > $o) > $i).
2.13/180.04	thf(decl_328, type, esk13_2: ($i > $o) > $i > $i).
2.13/180.04	thf(decl_329, type, esk14_1: ($i > $o) > $i).
2.13/180.04	thf(decl_330, type, esk15_2: $i > $i > $i).
2.13/180.04	thf(decl_331, type, esk16_2: $i > $i > $i).
2.13/180.04	thf(decl_332, type, esk17_1: $i > $i).
2.13/180.04	thf(decl_333, type, esk18_1: $i > $i).
2.13/180.04	thf(decl_334, type, esk19_1: $i > $i).
2.13/180.04	thf(decl_335, type, esk20_2: $i > $i > $i).
2.13/180.04	thf(decl_336, type, esk21_3: $i > $i > $o > $i).
2.13/180.04	thf(decl_337, type, esk22_2: ($i > $o) > $i > $i).
2.13/180.04	thf(decl_338, type, esk23_1: ($i > $o) > $i).
2.13/180.04	thf(decl_339, type, esk24_1: $i > $i).
2.13/180.04	thf(decl_340, type, esk25_2: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_341, type, esk26_2: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_342, type, esk27_2: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_343, type, esk28_2: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_344, type, esk29_2: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_345, type, esk30_2: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_346, type, esk31_2: ($i > $o) > $i > $i).
2.13/180.04	thf(decl_347, type, esk32_1: ($i > $o) > $i).
2.13/180.04	thf(decl_348, type, esk33_1: ($i > $o) > $i).
2.13/180.04	thf(decl_349, type, esk34_1: ($i > $o) > $i).
2.13/180.04	thf(decl_350, type, esk35_1: ($i > $o) > $i).
2.13/180.04	thf(decl_351, type, esk36_2: ($i > $o) > $i > $i).
2.13/180.04	thf(decl_352, type, esk37_1: ($i > $o) > $i).
2.13/180.04	thf(decl_353, type, esk38_2: ($i > $o) > $i > $i).
2.13/180.04	thf(decl_354, type, esk39_2: ($i > $o) > ($i > $o) > $i).
2.13/180.04	thf(decl_355, type, esk40_2: ($i > $o) > ($i > $o) > $i).
2.13/180.04	thf(decl_356, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
2.13/180.04	thf(decl_357, type, esk42_2: ($i > $o) > ($i > $o) > $i).
2.13/180.04	thf(decl_358, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
2.13/180.04	thf(decl_359, type, esk44_2: ($i > $o) > ($i > $o) > $i).
2.13/180.04	thf(decl_360, type, esk45_2: ($i > $o) > $i > $i).
2.13/180.04	thf(decl_361, type, esk46_2: ($i > $o) > ($i > $o) > $i).
2.13/180.04	thf(decl_362, type, esk47_2: ($i > $o) > ($i > $o) > $i).
2.13/180.04	thf(decl_363, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
2.13/180.04	thf(decl_364, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
2.13/180.04	thf(decl_365, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.13/180.04	thf(decl_366, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.13/180.04	thf(decl_367, type, esk52_2: $i > $i > $i).
2.13/180.04	thf(decl_368, type, esk53_2: $i > $i > $i).
2.13/180.04	thf(decl_369, type, esk54_2: $i > $i > $i).
2.13/180.04	thf(decl_370, type, esk55_3: $i > $i > $i > $i).
2.13/180.04	thf(decl_371, type, esk56_3: $i > $i > $i > $i).
2.13/180.04	thf(decl_372, type, esk57_2: $i > $i > $i).
2.13/180.04	thf(decl_373, type, esk58_2: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_374, type, esk59_2: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_375, type, esk60_2: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_376, type, esk61_3: $i > ($i > $o) > $i > $i).
2.13/180.04	thf(decl_377, type, esk62_2: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_378, type, esk63_2: $i > ($i > $o) > $i).
2.13/180.04	thf(decl_379, type, esk64_3: $i > $i > ($i > $i) > $i).
2.13/180.04	thf(decl_380, type, esk65_3: $i > $i > ($i > $i) > $i).
2.13/180.04	thf(decl_381, type, esk66_3: $i > $i > ($i > $i) > $i).
2.13/180.04	thf(decl_382, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
2.13/180.04	thf(decl_383, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
2.13/180.04	thf(decl_384, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
2.13/180.04	thf(decl_385, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
2.13/180.04	thf(decl_386, type, esk71_4: $i > $i > $i > $i > $i).
2.13/180.04	thf(decl_387, type, esk72_4: $i > $i > $i > $i > $i).
2.13/180.04	thf(decl_388, type, esk73_4: $i > $i > $i > $i > $i).
2.13/180.04	thf(decl_389, type, esk74_4: $i > $i > $i > $i > $i).
2.13/180.04	thf(decl_390, type, esk75_4: $i > $i > $i > $i > $i).
2.13/180.04	thf(decl_391, type, esk76_4: $i > $i > $i > $i > $i).
2.13/180.04	thf(decl_392, type, esk77_4: $i > $i > $i > $i > $i).
2.13/180.04	thf(decl_393, type, esk78_4: $i > $i > $i > $i > $i).
2.13/180.04	thf(decl_394, type, esk79_4: $i > $i > $i > $i > $i).
2.13/180.04	thf(decl_395, type, esk80_3: $i > $i > ($i > $i) > $i).
2.13/180.04	thf(decl_396, type, esk81_3: $i > $i > ($i > $i) > $i).
2.13/180.04	thf(decl_397, type, esk82_3: $i > $i > ($i > $i) > $i).
2.13/180.04	thf(decl_398, type, esk83_3: $i > $i > $i > $i).
2.13/180.04	thf(decl_399, type, esk84_3: $i > $i > $i > $i).
2.13/180.04	thf(decl_400, type, esk85_3: $i > $i > $i > $i).
2.13/180.04	thf(decl_401, type, esk86_3: $i > $i > $i > $i).
2.13/180.04	thf(decl_402, type, esk87_0: $i).
2.13/180.04	thf(decl_403, type, esk88_0: $i).
2.13/180.04	thf(decl_404, type, esk89_0: $i).
2.13/180.04	thf(decl_405, type, esk90_0: $i).
2.13/180.04	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', replAx)).
2.13/180.04	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', exu)).
2.13/180.04	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', descrp)).
2.13/180.04	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', exuE1)).
2.13/180.04	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', exuE3e)).
2.13/180.04	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', nonempty)).
2.13/180.04	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', nonemptyI)).
2.13/180.04	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', exuE2)).
2.13/180.04	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.VHMO5r9Z6J/E---3.1_794.p', exuI1)).
2.13/180.04	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', exuI3)).
2.13/180.04	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', exuI2)).
2.13/180.04	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.VHMO5r9Z6J/E---3.1_794.p', exuE3u)).
2.13/180.04	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', exu__Cong)).
2.13/180.04	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', exuEu)).
2.13/180.04	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', descr__Cong)).
2.13/180.04	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ex1E1)).
2.13/180.04	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ex1)).
2.13/180.04	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.VHMO5r9Z6J/E---3.1_794.p', ex1I)).
2.13/180.04	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ex1I2)).
2.13/180.04	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setOfPairsIsBReln)).
2.13/180.04	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', breln)).
2.13/180.04	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ex1E2)).
2.13/180.04	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', dsetconstrI)).
2.13/180.04	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', dsetconstrEL)).
2.13/180.04	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', dsetconstrER)).
2.13/180.04	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setbeta)).
2.13/180.04	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', nonemptyE1)).
2.13/180.04	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', nonemptyI1)).
2.13/180.04	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setoftrueEq)).
2.13/180.04	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', nonemptyImpWitness)).
2.13/180.04	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.VHMO5r9Z6J/E---3.1_794.p', emptyE1)).
2.13/180.04	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', dsetconstr__Cong)).
2.13/180.04	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', sepInPowerset)).
2.13/180.04	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', sepSubset)).
2.13/180.04	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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', singletonprop)).
2.13/180.04	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', kfstsingleton)).
2.13/180.04	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ksndsingleton)).
2.13/180.04	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', dpsetconstrI)).
2.13/180.04	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', dpsetconstrSub)).
2.13/180.04	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', dpsetconstrERa)).
2.13/180.04	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', dpsetconstrEL1)).
2.13/180.04	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', dpsetconstrEL2)).
2.13/180.04	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', dpsetconstrER)).
2.13/180.04	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', funcImageSingleton)).
2.13/180.04	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', apProp)).
2.13/180.04	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', lamProp)).
2.13/180.04	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', lamp)).
2.13/180.04	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', lam2p)).
2.13/180.04	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', brelnall1)).
2.13/180.04	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', brelnall2)).
2.13/180.04	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', subbreln)).
2.13/180.04	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', eqbreln)).
2.13/180.04	thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', beta1)).
2.13/180.04	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', eta1)).
2.13/180.04	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', lam2lamEq)).
2.13/180.04	thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', beta2)).
2.13/180.04	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', eta2)).
2.13/180.04	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', iffalseProp1)).
2.13/180.04	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', iffalseProp2)).
2.13/180.04	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', iftrueProp1)).
2.13/180.04	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', iftrueProp2)).
2.13/180.04	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ifSingleton)).
2.13/180.04	thf(binunionTIRcontra, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((((((wellorderingAx)=>((descrp)=>(((((exuE1)=>(((emptysetE)=>(((((((noeltsimpempty)=>((((nonemptyI)=>(((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((((setoftrueEq)=>(((((powersetE)=>((((((((notinsingleton)=>(((singletonsswitch)=>((upairsetE)=>(((upairsetIR)=>((emptyE1)=>(((quantDeMorgan1)=>((quantDeMorgan2)=>(((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>(((exuE3u)=>((exu__Cong)=>((((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>(((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((((((((setadjoinSub2)=>(((setextsub)=>((subsetemptysetimpeq)=>(((powersetE1)=>((inPowerset)=>((((sepSubset)=>(((((binunionEcases)=>(((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>(((setminusI)=>(((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>(((kpairiskpair)=>((kpairp)=>((singletonsubset)=>(((singletoninpowunion)=>(((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((((((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>(((theprop)=>(((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>(((setukpairinjR12)=>((setukpairinjR1)=>((((((ksndpairEq)=>((((cartprodpairmemEL)=>(((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((((setOfPairsIsBReln)=>((((((funcImageSingleton)=>(((((((lamProp)=>((lamp)=>((lam2p)=>(((brelnall2)=>((ex1E2)=>(((funcGraphProp3)=>(((funcextLem)=>((funcGraphProp4)=>(((eqbreln)=>(((funcext2)=>(((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>(((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>(((iftrue)=>((((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>(((subsetTI)=>((powersetTI1)=>((powersetTE1)=>(((((binintersectTERcontra)=>(((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>(((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>(((((complementTcontraSubset)=>((binunionTILcontra)=>![X4:$i, X21:$i]:((![X48:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))<=~((in @ X2 @ (binunion @ X21 @ X48))))))<=(in @ X48 @ (powerset @ X4))))<=(in @ X21 @ (powerset @ X4))))))<=(contraSubsetComplement))<=(complementInPowersetComplementIntersect))<=(complementSubsetComplementIntersect)))))))<=(doubleComplementE1))))))<=(contrasubsetT)))<=(binintersectTELcontra))<=(complementTE1))<=(complementTI1)))))<=(setextT)))))))<=(iftrueorfalse))<=(iffalse)))<=(theeq)))))))<=(iffalseProp1))))))))<=(ap2apEq1)))<=(funcext)))<=(subbreln))))<=(funcGraphProp2)))<=(funcGraphProp1))))<=(brelnall1)))))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc))<=(app))<=(apProp)))<=(dpsetconstrER))<=(dpsetconstrEL2))<=(dpsetconstrEL1))<=(dpsetconstrERa)))<=(dpsetconstrSub))<=(dpsetconstrI))))))<=(cartprodpairmemER)))<=(cartprodsndin))<=(kpairsurjEq)))<=(ksndsingleton))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq))))<=(setukpairinjR11)))))<=(kfstpairEq)))<=(kfstsingleton))))))<=(ex1E1))<=(singletonprop)))))))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2)))))<=(upairset2E)))<=(singletoninpowerset)))))<=(setukpairIR))))<=(symdiffIneg2)))))))))<=(setminusILneg))<=(setminusELneg)))))<=(setminusEL)))<=(bs114d)))))))))))))))<=(binunionE)))<=(binunionIR))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset))<=(powersetsubset))))<=(powersetI1))))<=(subset2powerset)))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl))<=(notequalI2))<=(notequalI1))<=(notsubsetI)))))))))<=(dsetconstr__Cong)))))))<=(setadjoin__Cong))<=(emptyset__Cong))))<=(in__Cong))))))<=(notdallE))<=(notdexE)))))<=(quantDeMorgan3))))<=(vacuousDall))))<=(upairsetIL))))<=(eqinunit)))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU))<=(setunionE))<=(setunionI)))<=(emptyInPowerset))<=(emptyinPowerset))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE)))))<=(nonemptyI1)))<=(nonemptyE1))<=(setbeta)))<=(emptyI))<=(setext))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE)))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI))))<=(foundationAx))<=(replAx))<=(omegaIndAx))<=(omegaSAx)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binunionTIRcontra)).
2.13/180.04	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setextAx)).
2.13/180.04	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', emptysetAx)).
2.13/180.04	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setadjoinAx)).
2.13/180.04	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', powersetAx)).
2.13/180.04	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setunionAx)).
2.13/180.04	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', omega0Ax)).
2.13/180.04	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', omegaSAx)).
2.13/180.04	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.VHMO5r9Z6J/E---3.1_794.p', omegaIndAx)).
2.13/180.04	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.VHMO5r9Z6J/E---3.1_794.p', foundationAx)).
2.13/180.04	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', wellorderingAx)).
2.13/180.04	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', prop2setE)).
2.13/180.04	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', emptysetE)).
2.13/180.04	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', emptysetimpfalse)).
2.13/180.04	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', notinemptyset)).
2.13/180.04	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.VHMO5r9Z6J/E---3.1_794.p', setext)).
2.13/180.04	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', emptyI)).
2.13/180.04	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', noeltsimpempty)).
2.13/180.04	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setadjoinIL)).
2.13/180.04	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', emptyinunitempty)).
2.13/180.04	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setadjoinIR)).
2.13/180.04	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setadjoinE)).
2.13/180.04	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setadjoinOr)).
2.13/180.04	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', powersetI)).
2.13/180.04	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', emptyinPowerset)).
2.13/180.04	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', emptyInPowerset)).
2.13/180.04	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', powersetE)).
2.13/180.04	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setunionI)).
2.13/180.04	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setunionE)).
2.13/180.04	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', subPowSU)).
2.13/180.04	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', uniqinunit)).
2.13/180.04	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', notinsingleton)).
2.13/180.04	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', eqinunit)).
2.13/180.04	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', singletonsswitch)).
2.13/180.04	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', upairsetE)).
2.13/180.04	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', upairsetIL)).
2.13/180.04	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', upairsetIR)).
2.13/180.04	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', vacuousDall)).
2.13/180.04	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', quantDeMorgan1)).
2.13/180.04	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', quantDeMorgan2)).
2.13/180.04	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', quantDeMorgan3)).
2.13/180.04	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', quantDeMorgan4)).
2.13/180.04	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', prop2setI)).
2.13/180.04	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', prop2set2propI)).
2.13/180.04	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', notdexE)).
2.13/180.04	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', notdallE)).
2.13/180.04	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', inCongP)).
2.13/180.04	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', in__Cong)).
2.13/180.04	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', emptyset__Cong)).
2.13/180.04	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setadjoin__Cong)).
2.13/180.04	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', powerset__Cong)).
2.13/180.04	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setunion__Cong)).
2.13/180.04	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', omega__Cong)).
2.13/180.04	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', subsetI1)).
2.13/180.04	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', eqimpsubset2)).
2.13/180.04	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', eqimpsubset1)).
2.13/180.04	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', subsetI2)).
2.13/180.04	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', emptysetsubset)).
2.13/180.04	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', subsetE)).
2.13/180.04	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', subsetE2)).
2.13/180.04	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', notsubsetI)).
2.13/180.04	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', notequalI1)).
2.13/180.04	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', notequalI2)).
2.13/180.04	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', subsetRefl)).
2.13/180.04	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', subsetTrans)).
2.13/180.04	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setadjoinSub)).
2.13/180.04	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setadjoinSub2)).
2.13/180.04	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', subset2powerset)).
2.13/180.04	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setextsub)).
2.13/180.04	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', subsetemptysetimpeq)).
2.13/180.04	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', powersetI1)).
2.13/180.04	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', powersetE1)).
2.13/180.04	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', inPowerset)).
2.13/180.04	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', powersetsubset)).
2.13/180.04	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binunionIL)).
2.13/180.04	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', upairset2IR)).
2.13/180.04	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binunionIR)).
2.13/180.04	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binunionEcases)).
2.13/180.04	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binunionE)).
2.13/180.04	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binunionLsub)).
2.13/180.04	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binunionRsub)).
2.13/180.04	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectI)).
2.13/180.04	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectSubset5)).
2.13/180.04	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectEL)).
2.13/180.04	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectLsub)).
2.13/180.04	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectSubset2)).
2.13/180.04	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectSubset3)).
2.13/180.04	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectER)).
2.13/180.04	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', disjointsetsI1)).
2.13/180.04	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectRsub)).
2.13/180.04	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectSubset4)).
2.13/180.04	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectSubset1)).
2.13/180.04	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', bs114d)).
2.13/180.04	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setminusI)).
2.13/180.04	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setminusEL)).
2.13/180.04	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setminusER)).
2.13/180.04	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setminusSubset2)).
2.13/180.04	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setminusERneg)).
2.13/180.04	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setminusELneg)).
2.13/180.04	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setminusILneg)).
2.13/180.04	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setminusIRneg)).
2.13/180.04	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setminusLsub)).
2.13/180.04	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setminusSubset1)).
2.13/180.04	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', symdiffE)).
2.13/180.04	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', symdiffI1)).
2.13/180.04	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', symdiffI2)).
2.13/180.04	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', symdiffIneg1)).
2.13/180.04	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', symdiffIneg2)).
2.13/180.04	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', secondinupair)).
2.13/180.04	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setukpairIL)).
2.13/180.04	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setukpairIR)).
2.13/180.04	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', kpairiskpair)).
2.13/180.04	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', kpairp)).
2.13/180.04	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', singletonsubset)).
2.13/180.04	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', singletoninpowerset)).
2.13/180.04	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', singletoninpowunion)).
2.13/180.04	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', upairset2E)).
2.13/180.04	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', upairsubunion)).
2.13/180.04	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', upairinpowunion)).
2.13/180.04	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ubforcartprodlem1)).
2.13/180.04	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ubforcartprodlem2)).
2.13/180.04	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ubforcartprodlem3)).
2.13/180.04	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', cartprodpairin)).
2.13/180.04	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.VHMO5r9Z6J/E---3.1_794.p', cartprodmempair1)).
2.13/180.04	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', cartprodmempair)).
2.13/180.04	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setunionE2)).
2.13/180.04	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setunionsingleton1)).
2.13/180.04	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setunionsingleton2)).
2.13/180.04	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setunionsingleton)).
2.13/180.04	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', singletonsuniq)).
2.13/180.04	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.VHMO5r9Z6J/E---3.1_794.p', setukpairinjL1)).
2.13/180.04	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', theprop)).
2.13/180.04	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', kfstpairEq)).
2.13/180.04	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', cartprodfstin)).
2.13/180.04	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.VHMO5r9Z6J/E---3.1_794.p', setukpairinjL2)).
2.13/180.04	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.VHMO5r9Z6J/E---3.1_794.p', setukpairinjL)).
2.13/180.04	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setukpairinjR11)).
2.13/180.04	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.VHMO5r9Z6J/E---3.1_794.p', setukpairinjR12)).
2.13/180.04	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.VHMO5r9Z6J/E---3.1_794.p', setukpairinjR1)).
2.13/180.04	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', upairequniteq)).
2.13/180.04	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setukpairinjR2)).
2.13/180.04	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setukpairinjR)).
2.13/180.04	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ksndpairEq)).
2.13/180.04	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', kpairsurjEq)).
2.13/180.04	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', cartprodsndin)).
2.13/180.04	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', cartprodpairmemEL)).
2.13/180.04	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', cartprodpairmemER)).
2.13/180.04	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', cartprodmempaircEq)).
2.13/180.04	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', cartprodfstpairEq)).
2.13/180.04	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', cartprodsndpairEq)).
2.13/180.04	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', cartprodpairsurjEq)).
2.13/180.04	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', app)).
2.13/180.04	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', infuncsetfunc)).
2.13/180.04	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ap2p)).
2.13/180.04	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', funcinfuncset)).
2.13/180.04	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', funcGraphProp1)).
2.13/180.04	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', funcGraphProp3)).
2.13/180.04	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', funcGraphProp2)).
2.13/180.04	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', funcextLem)).
2.13/180.04	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', funcGraphProp4)).
2.13/180.04	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', funcext)).
2.13/180.04	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', funcext2)).
2.13/180.04	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ap2apEq1)).
2.13/180.04	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ap2apEq2)).
2.13/180.04	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', ifp)).
2.13/180.04	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', theeq)).
2.13/180.04	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', iftrue)).
2.13/180.04	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', iffalse)).
2.13/180.04	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', iftrueorfalse)).
2.13/180.04	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectT_lem)).
2.13/180.04	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binunionT_lem)).
2.13/180.04	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', powersetT_lem)).
2.13/180.04	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setminusT_lem)).
2.13/180.04	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', complementT_lem)).
2.13/180.04	thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', setextT)).
2.13/180.04	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', subsetTI)).
2.13/180.04	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', powersetTI1)).
2.13/180.04	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', powersetTE1)).
2.13/180.04	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', complementTI1)).
2.13/180.04	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', complementTE1)).
2.13/180.04	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectTELcontra)).
2.13/180.04	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binintersectTERcontra)).
2.13/180.04	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', contrasubsetT)).
2.13/180.04	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', contrasubsetT1)).
2.13/180.04	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', contrasubsetT2)).
2.13/180.04	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', contrasubsetT3)).
2.13/180.04	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', doubleComplementI1)).
2.13/180.04	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', doubleComplementE1)).
2.13/180.04	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', doubleComplementSub1)).
2.13/180.04	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', doubleComplementSub2)).
2.13/180.04	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', doubleComplementEq)).
2.13/180.04	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', complementTnotintersectT)).
2.13/180.04	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', complementImpComplementIntersect)).
2.13/180.04	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', complementSubsetComplementIntersect)).
2.13/180.04	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', complementInPowersetComplementIntersect)).
2.13/180.04	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', contraSubsetComplement)).
2.13/180.04	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', complementTcontraSubset)).
2.13/180.04	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.VHMO5r9Z6J/E---3.1_794.p', binunionTILcontra)).
2.13/180.04	thf(c_0_260, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
2.13/180.04	thf(c_0_261, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
2.13/180.04	thf(c_0_262, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
2.13/180.04	thf(c_0_263, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
2.13/180.04	thf(c_0_264, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
2.13/180.04	thf(c_0_265, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
2.13/180.04	thf(c_0_266, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
2.13/180.04	thf(c_0_267, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
2.13/180.04	thf(c_0_268, 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])).
2.13/180.04	thf(c_0_269, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
2.13/180.04	thf(c_0_270, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
2.13/180.04	thf(c_0_271, 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])).
2.13/180.04	thf(c_0_272, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
2.13/180.04	thf(c_0_273, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
2.13/180.04	thf(c_0_274, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
2.13/180.04	thf(c_0_275, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
2.13/180.04	thf(c_0_276, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
2.13/180.04	thf(c_0_277, 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])).
2.13/180.04	thf(c_0_278, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
2.13/180.04	thf(c_0_279, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
2.13/180.04	thf(c_0_280, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
2.13/180.04	thf(c_0_281, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
2.13/180.04	thf(c_0_282, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X844:$i]:((((X6 @ X2 @ X844))&![X845:$i]:((((X6 @ X2 @ X845))=>((X844)=(X845)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_260, c_0_261])).
2.13/180.04	thf(c_0_283, plain, ((descrp)=(![X1:$i > $o]:(((?[X846:$i]:((((X1 @ X846))&![X847:$i]:((((X1 @ X847))=>((X846)=(X847)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_262, c_0_261])).
2.13/180.04	thf(c_0_284, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
2.13/180.04	thf(c_0_285, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
2.13/180.04	thf(c_0_286, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
2.13/180.04	thf(c_0_287, plain, ((exuE1)=(![X1:$i > $o]:(((?[X848:$i]:((((X1 @ X848))&![X849:$i]:((((X1 @ X849))=>((X848)=(X849)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_263, c_0_261])).
2.13/180.04	thf(c_0_288, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X850:$i]:((((X1 @ X850))&![X851:$i]:((((X1 @ X851))=>((X850)=(X851)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_264, c_0_261])).
2.13/180.04	thf(c_0_289, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
2.13/180.04	thf(c_0_290, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_265])).
2.13/180.04	thf(c_0_291, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_266, c_0_265])).
2.13/180.04	thf(c_0_292, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_265])).
2.13/180.04	thf(c_0_293, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
2.13/180.04	thf(c_0_294, plain, ((exuE2)=(![X1:$i > $o]:(((?[X852:$i]:((((X1 @ X852))&![X853:$i]:((((X1 @ X853))=>((X852)=(X853)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_267, c_0_261])).
2.13/180.04	thf(c_0_295, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_265])).
2.13/180.04	thf(c_0_296, 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])).
2.13/180.04	thf(c_0_297, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X854:$i]:((((X1 @ X854))&![X855:$i]:((((X1 @ X855))=>((X854)=(X855))))))))))), inference(apply_def,[status(thm)],[c_0_268, c_0_261])).
2.13/180.04	thf(c_0_298, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X856:$i]:((((X1 @ X856))&![X857:$i]:((((X1 @ X857))=>((X856)=(X857)))))))))))), inference(apply_def,[status(thm)],[c_0_269, c_0_261])).
2.13/180.04	thf(c_0_299, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X858:$i]:((((X1 @ X858))&![X859:$i]:((((X1 @ X859))=>((X858)=(X859))))))))))), inference(apply_def,[status(thm)],[c_0_270, c_0_261])).
2.13/180.04	thf(c_0_300, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X860:$i]:((((X1 @ X860))&![X861:$i]:((((X1 @ X861))=>((X860)=(X861)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_271, c_0_261])).
2.13/180.04	thf(c_0_301, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X862:$i]:((((X1 @ X862))&![X863:$i]:((((X1 @ X863))=>((X862)=(X863)))))))<=>(?[X864:$i]:((((X17 @ X864))&![X865:$i]:((((X17 @ X865))=>((X864)=(X865)))))))))))), inference(apply_def,[status(thm)],[c_0_272, c_0_261])).
2.13/180.04	thf(c_0_302, plain, ((exuEu)=(![X1:$i > $o]:(((?[X866:$i]:((((X1 @ X866))&![X867:$i]:((((X1 @ X867))=>((X866)=(X867)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_273, c_0_261])).
2.13/180.04	thf(c_0_303, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X868:$i]:((((X1 @ X868))&![X869:$i]:((((X1 @ X869))=>((X868)=(X869)))))))=>((?[X870:$i]:((((X17 @ X870))&![X871:$i]:((((X17 @ X871))=>((X870)=(X871)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_274, c_0_261])).
2.13/180.04	thf(c_0_304, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
2.13/180.04	thf(c_0_305, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
2.13/180.04	thf(c_0_306, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
2.13/180.04	thf(c_0_307, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
2.13/180.04	thf(c_0_308, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_275, c_0_276])).
2.13/180.04	thf(c_0_309, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))))))))), inference(apply_def,[status(thm)],[c_0_277, c_0_276])).
2.13/180.04	thf(c_0_310, 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)))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))))))), inference(apply_def,[status(thm)],[c_0_278, c_0_276])).
2.13/180.04	thf(c_0_311, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
2.13/180.04	thf(c_0_312, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
2.13/180.04	thf(c_0_313, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
2.13/180.04	thf(c_0_314, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
2.13/180.04	thf(c_0_315, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_279, c_0_280])).
2.13/180.04	thf(c_0_316, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
2.13/180.04	thf(c_0_317, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
2.13/180.04	thf(c_0_318, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
2.13/180.04	thf(c_0_319, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
2.13/180.04	thf(c_0_320, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
2.13/180.04	thf(c_0_321, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
2.13/180.04	thf(c_0_322, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
2.13/180.04	thf(c_0_323, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
2.13/180.04	thf(c_0_324, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
2.13/180.04	thf(c_0_325, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_280])).
2.13/180.04	thf(c_0_326, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_280])).
2.13/180.04	thf(c_0_327, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_281, c_0_276])).
2.13/180.04	thf(c_0_328, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_280])).
2.13/180.04	thf(c_0_329, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_280])).
2.13/180.04	thf(c_0_330, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
2.13/180.04	thf(c_0_331, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
2.13/180.04	thf(c_0_332, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
2.13/180.04	thf(c_0_333, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
2.13/180.04	thf(c_0_334, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
2.13/180.04	thf(c_0_335, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
2.13/180.04	thf(c_0_336, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
2.13/180.04	thf(c_0_337, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
2.13/180.04	thf(c_0_338, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
2.13/180.04	thf(c_0_339, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
2.13/180.04	thf(c_0_340, plain, ((epred1_0)<=>![X885:$i]:(?[X886:$i]:((((![X887:$i]:(((in @ X887 @ X886)=>![X888:$i]:(((in @ X888 @ X887)=>(in @ X888 @ X885)))))&![X889:$i, X890:$i]:((((in @ X889 @ X885)&(in @ X890 @ X885))=>(![X891:$i]:(((in @ X891 @ X886)=>((in @ X889 @ X891)<=>(in @ X890 @ X891))))=>((X889)=(X890))))))&![X892:$i, X893:$i]:((((in @ X892 @ X886)&(in @ X893 @ X886))=>(![X894:$i]:(((in @ X894 @ X892)=>(in @ X894 @ X893)))|![X895:$i]:(((in @ X895 @ X893)=>(in @ X895 @ X892)))))))&![X896:$i]:(((![X897:$i]:(((in @ X897 @ X896)=>(in @ X897 @ X885)))&?[X898:$i]:((in @ X898 @ X896)))=>?[X899:$i, X900:$i]:(((((in @ X899 @ X886)&(in @ X900 @ X896))&~(?[X901:$i]:(((in @ X901 @ X899)&(in @ X901 @ X896)))))&![X902:$i]:(((in @ X902 @ X886)=>(![X903:$i]:(((in @ X903 @ X902)=>(in @ X903 @ X899)))|(in @ X900 @ X902)))))))))))), introduced(definition)).
2.13/180.04	thf(c_0_341, negated_conjecture, ~((![X872:$i, X873:$i]:((![X874:$i]:(((in @ X874 @ X872)<=>(in @ X874 @ X873)))=>((X872)=(X873))))=>(![X875:$i]:(~(in @ X875 @ emptyset))=>(![X876:$i, X877:$i, X878:$i]:(((in @ X878 @ (setadjoin @ X876 @ X877))<=>(((X878)=(X876))|(in @ X878 @ X877))))=>(![X879:$i, X880:$i]:(((in @ X880 @ (powerset @ X879))<=>![X881:$i]:(((in @ X881 @ X880)=>(in @ X881 @ X879)))))=>(![X882:$i, X883:$i]:(((in @ X883 @ (setunion @ X882))<=>?[X884:$i]:(((in @ X883 @ X884)&(in @ X884 @ X882)))))=>((in @ emptyset @ omega)=>(![X1690:$i]:(((in @ X1690 @ omega)=>(in @ (setadjoin @ X1690 @ X1690) @ omega)))=>(![X1687:$i]:((((in @ emptyset @ X1687)&![X1688:$i]:((((in @ X1688 @ omega)&(in @ X1688 @ X1687))=>(in @ (setadjoin @ X1688 @ X1688) @ X1687))))=>![X1689:$i]:(((in @ X1689 @ omega)=>(in @ X1689 @ X1687)))))=>(![X1679:$i > $i > $o, X1680:$i]:((![X1681:$i]:(((in @ X1681 @ X1680)=>?[X1682:$i]:(((X1679 @ X1681 @ X1682)&![X1683:$i]:(((X1679 @ X1681 @ X1683)=>((X1682)=(X1683))))))))=>?[X1684:$i]:(![X1685:$i]:(((in @ X1685 @ X1684)<=>?[X1686:$i]:(((in @ X1686 @ X1680)&(X1679 @ X1686 @ X1685))))))))=>(![X1675:$i]:((?[X1676:$i]:((in @ X1676 @ X1675))=>?[X1677:$i]:(((in @ X1677 @ X1675)&~(?[X1678:$i]:(((in @ X1678 @ X1677)&(in @ X1678 @ X1675))))))))=>((epred1_0)=>(![X904:$i > $o]:((?[X905:$i]:(((X904 @ X905)&![X906:$i]:(((X904 @ X906)=>((X905)=(X906))))))=>(X904 @ (descr @ (^[Z0/* 17 */:$i]:(X904 @ Z0))))))=>(![X1672:$i, X1673:$i > $o, X1674:$i]:(((in @ X1674 @ X1672)=>((X1673 @ X1674)=>(in @ X1674 @ (dsetconstr @ X1672 @ X1673)))))=>(![X1669:$i, X1670:$i > $o, X1671:$i]:(((in @ X1671 @ (dsetconstr @ X1669 @ X1670))=>(in @ X1671 @ X1669)))=>(![X1666:$i, X1667:$i > $o, X1668:$i]:(((in @ X1668 @ (dsetconstr @ X1666 @ X1667))=>(X1667 @ X1668)))=>(![X907:$i > $o]:((?[X908:$i]:(((X907 @ X908)&![X909:$i]:(((X907 @ X909)=>((X908)=(X909))))))=>?[X910:$i]:(((X907 @ X910)&![X911:$i]:(((X907 @ X911)=>((X910)=(X911))))))))=>(![X1664:$o, X1665:$i]:(((in @ X1665 @ (prop2set @ ((X1664))))=>(X1664)))=>(![X912:$i]:(((in @ X912 @ emptyset)=>![X913:$o]:((X913))))=>(![X1663:$i]:(((in @ X1663 @ emptyset)=>~($true)))=>(![X1662:$i]:(~(in @ X1662 @ emptyset))=>(![X1658:$i > $o]:((?[X1659:$i]:(((X1658 @ X1659)&![X1660:$i]:(((X1658 @ X1660)=>((X1659)=(X1660))))))=>?[X1661:$i]:((X1658 @ X1661))))=>(![X1654:$i, X1655:$i]:((![X1656:$i]:(((in @ X1656 @ X1654)=>(in @ X1656 @ X1655)))=>(![X1657:$i]:(((in @ X1657 @ X1655)=>(in @ X1657 @ X1654)))=>((X1654)=(X1655)))))=>(![X1652:$i]:((![X1653:$i]:(~(in @ X1653 @ X1652))=>((X1652)=(emptyset))))=>(![X914:$i]:((![X915:$i]:(~(in @ X915 @ X914))=>((X914)=(emptyset))))=>(![X1649:$i, X1650:$i > $o, X1651:$i]:(((in @ X1651 @ X1649)=>((in @ X1651 @ (dsetconstr @ X1649 @ X1650))<=>(X1650 @ X1651))))=>(![X1647:$i]:((((X1647)!=(emptyset))=>?[X1648:$i]:((in @ X1648 @ X1647))))=>(![X916:$i, X917:$i > $o, X918:$i]:(((in @ X918 @ X916)=>((X917 @ X918)=>((dsetconstr @ X916 @ X917)!=(emptyset)))))=>(![X1645:$i]:((?[X1646:$i]:((in @ X1646 @ X1645))=>((X1645)!=(emptyset))))=>(![X919:$i, X920:$i]:((in @ X919 @ (setadjoin @ X919 @ X920)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X921:$i, X922:$i, X923:$i]:(((in @ X923 @ X922)=>(in @ X923 @ (setadjoin @ X921 @ X922))))=>(![X1641:$i, X1642:$i, X1643:$i]:(((in @ X1643 @ (setadjoin @ X1641 @ X1642))=>![X1644:$o]:(((((X1643)=(X1641))=>(X1644))=>(((in @ X1643 @ X1642)=>(X1644))=>(X1644))))))=>(![X1638:$i, X1639:$i, X1640:$i]:(((in @ X1640 @ (setadjoin @ X1638 @ X1639))=>(((X1640)=(X1638))|(in @ X1640 @ X1639))))=>(![X924:$i]:(((dsetconstr @ X924 @ (^[Z0/* 1 */:$i]:($true)))=(X924)))=>(![X1635:$i, X1636:$i]:((![X1637:$i]:(((in @ X1637 @ X1636)=>(in @ X1637 @ X1635)))=>(in @ X1636 @ (powerset @ X1635))))=>(![X1634:$i]:((in @ emptyset @ (powerset @ X1634)))=>(![X1633:$i]:((in @ emptyset @ (powerset @ X1633)))=>(![X925:$i, X926:$i, X927:$i]:(((in @ X926 @ (powerset @ X925))=>((in @ X927 @ X926)=>(in @ X927 @ X925))))=>(![X1630:$i, X1631:$i, X1632:$i]:(((in @ X1631 @ X1632)=>((in @ X1632 @ X1630)=>(in @ X1631 @ (setunion @ X1630)))))=>(![X1626:$i, X1627:$i]:(((in @ X1627 @ (setunion @ X1626))=>![X1628:$o]:((![X1629:$i]:(((in @ X1627 @ X1629)=>((in @ X1629 @ X1626)=>(X1628))))=>(X1628)))))=>(![X1624:$i, X1625:$i]:(((in @ X1625 @ X1624)=>(in @ X1625 @ (powerset @ (setunion @ X1624)))))=>(![X1619:$i > $o]:((?[X1620:$i]:(((X1619 @ X1620)&![X1621:$i]:(((X1619 @ X1621)=>((X1620)=(X1621))))))=>?[X1622:$i]:(![X1623:$i]:(((X1619 @ X1623)<=>((X1623)=(X1622)))))))=>(![X1617:$i]:((((X1617)!=(emptyset))=>?[X1618:$i]:(((in @ X1618 @ X1617)&$true))))=>(![X1615:$i, X1616:$i]:(((in @ X1615 @ (setadjoin @ X1616 @ emptyset))=>((X1615)=(X1616))))=>(![X928:$i, X929:$i]:((((X928)!=(X929))=>~(in @ X929 @ (setadjoin @ X928 @ emptyset))))=>(![X1613:$i, X1614:$i]:((((X1613)=(X1614))=>(in @ X1613 @ (setadjoin @ X1614 @ emptyset))))=>(![X930:$i, X931:$i]:(((in @ X930 @ (setadjoin @ X931 @ emptyset))=>(in @ X931 @ (setadjoin @ X930 @ emptyset))))=>(![X932:$i, X933:$i, X934:$i]:(((in @ X934 @ (setadjoin @ X932 @ (setadjoin @ X933 @ emptyset)))=>(((X934)=(X932))|((X934)=(X933)))))=>(![X1611:$i, X1612:$i]:((in @ X1611 @ (setadjoin @ X1611 @ (setadjoin @ X1612 @ emptyset))))=>(![X935:$i, X936:$i]:((in @ X936 @ (setadjoin @ X935 @ (setadjoin @ X936 @ emptyset))))=>(![X937:$i, X938:$i > $o]:((?[X939:$i]:(((in @ X939 @ X937)&(X938 @ X939)))=>(((dsetconstr @ X937 @ X938)=(emptyset))=>~($true))))=>(![X1609:$i > $o, X1610:$i]:(((in @ X1610 @ emptyset)=>(X1609 @ X1610)))=>(![X940:$i, X941:$i > $o]:((~(![X942:$i]:(((in @ X942 @ X940)=>(X941 @ X942))))=>?[X943:$i]:(((in @ X943 @ X940)&~((X941 @ X943))))))=>(![X944:$i, X945:$i > $o]:((![X946:$i]:(((in @ X946 @ X944)=>~((X945 @ X946))))=>~(?[X947:$i]:(((in @ X947 @ X944)&(X945 @ X947))))))=>(![X1605:$i, X1606:$i > $o]:((~(?[X1607:$i]:(((in @ X1607 @ X1605)&(X1606 @ X1607))))=>![X1608:$i]:(((in @ X1608 @ X1605)=>~((X1606 @ X1608))))))=>(![X948:$i, X949:$i > $o]:((?[X950:$i]:(((in @ X950 @ X948)&~((X949 @ X950))))=>~(![X951:$i]:(((in @ X951 @ X948)=>(X949 @ X951))))))=>(![X952:$o]:(((X952)=>(in @ emptyset @ (prop2set @ ((X952))))))=>(![X953:$o]:(((X953)=>(set2prop @ (prop2set @ ((X953))))))=>(![X1601:$i, X1602:$i > $o]:((~(?[X1603:$i]:(((in @ X1603 @ X1601)&(X1602 @ X1603))))=>![X1604:$i]:(((in @ X1604 @ X1601)=>~((X1602 @ X1604))))))=>(![X1597:$i, X1598:$i > $o]:((~(![X1599:$i]:(((in @ X1599 @ X1597)=>(X1598 @ X1599))))=>?[X1600:$i]:(((in @ X1600 @ X1597)&~((X1598 @ X1600))))))=>(![X954:$i > $o]:((?[X955:$i]:(((X954 @ X955)&![X956:$i]:(((X954 @ X956)=>((X955)=(X956))))))=>?[X957:$i]:(((X954 @ X957)&![X958:$i]:(((X954 @ X958)=>((X957)=(X958))))))))=>(![X959:$i > $o]:((?[X960:$i]:((X959 @ X960))=>(![X961:$i, X962:$i]:(((X959 @ X961)=>((X959 @ X962)=>((X961)=(X962)))))=>?[X963:$i]:(((X959 @ X963)&![X964:$i]:(((X959 @ X964)=>((X963)=(X964)))))))))=>(![X965:$i > $o]:((?[X966:$i]:(![X967:$i]:(((X965 @ X967)<=>((X967)=(X966)))))=>?[X968:$i]:(((X965 @ X968)&![X969:$i]:(((X965 @ X969)=>((X968)=(X969))))))))=>(![X970:$i, X971:$i]:((((X970)=(X971))=>![X972:$i, X973:$i]:((((X972)=(X973))=>((in @ X972 @ X970)=>(in @ X973 @ X971))))))=>(![X1593:$i, X1594:$i]:((((X1593)=(X1594))=>![X1595:$i, X1596:$i]:((((X1595)=(X1596))=>((in @ X1595 @ X1593)<=>(in @ X1596 @ X1594))))))=>(![X974:$i > $o]:((?[X975:$i]:(((X974 @ X975)&![X976:$i]:(((X974 @ X976)=>((X975)=(X976))))))=>![X977:$i, X978:$i]:(((X974 @ X977)=>((X974 @ X978)=>((X977)=(X978)))))))=>(![X979:$i > $o, X980:$i > $o]:((![X981:$i, X982:$i]:((((X981)=(X982))=>((X979 @ X981)<=>(X980 @ X982))))=>(?[X983:$i]:(((X979 @ X983)&![X984:$i]:(((X979 @ X984)=>((X983)=(X984))))))<=>?[X985:$i]:(((X980 @ X985)&![X986:$i]:(((X980 @ X986)=>((X985)=(X986)))))))))=>(((emptyset)=(emptyset))=>(![X1589:$i, X1590:$i]:((((X1589)=(X1590))=>![X1591:$i, X1592:$i]:((((X1591)=(X1592))=>((setadjoin @ X1589 @ X1591)=(setadjoin @ X1590 @ X1592))))))=>(![X987:$i, X988:$i]:((((X987)=(X988))=>((powerset @ X987)=(powerset @ X988))))=>(![X989:$i, X990:$i]:((((X989)=(X990))=>((setunion @ X989)=(setunion @ X990))))=>(((omega)=(omega))=>(![X991:$i > $o]:((?[X992:$i]:(((X991 @ X992)&![X993:$i]:(((X991 @ X993)=>((X992)=(X993))))))=>![X994:$i, X995:$i]:(((X991 @ X994)=>((X991 @ X995)=>((X994)=(X995)))))))=>(![X996:$i > $o, X997:$i > $o]:((![X998:$i, X999:$i]:((((X998)=(X999))=>((X996 @ X998)<=>(X997 @ X999))))=>(?[X1000:$i]:(((X996 @ X1000)&![X1001:$i]:(((X996 @ X1001)=>((X1000)=(X1001))))))=>(?[X1002:$i]:(((X997 @ X1002)&![X1003:$i]:(((X997 @ X1003)=>((X1002)=(X1003))))))=>((descr @ X996)=(descr @ X997))))))=>(![X1583:$i, X1584:$i]:((((X1583)=(X1584))=>![X1585:$i > $o, X1586:$i > $o]:((![X1587:$i]:(((in @ X1587 @ X1583)=>![X1588:$i]:(((in @ X1588 @ X1584)=>(((X1587)=(X1588))=>((X1585 @ X1587)<=>(X1586 @ X1588)))))))=>((dsetconstr @ X1583 @ X1585)=(dsetconstr @ X1584 @ X1586))))))=>(![X1004:$i, X1005:$i]:((![X1006:$i]:(((in @ X1006 @ X1004)=>(in @ X1006 @ X1005)))=>(subset @ X1004 @ X1005)))=>(![X1007:$i, X1008:$i]:((((X1007)=(X1008))=>(subset @ X1008 @ X1007)))=>(![X1009:$i, X1010:$i]:((((X1009)=(X1010))=>(subset @ X1009 @ X1010)))=>(![X1011:$i, X1012:$i]:((![X1013:$i]:(((in @ X1013 @ X1011)=>(in @ X1013 @ X1012)))=>(subset @ X1011 @ X1012)))=>(![X1014:$i]:((subset @ emptyset @ X1014))=>(![X1015:$i, X1016:$i, X1017:$i]:(((subset @ X1015 @ X1016)=>((in @ X1017 @ X1015)=>(in @ X1017 @ X1016))))=>(![X1018:$i, X1019:$i, X1020:$i]:(((subset @ X1018 @ X1019)=>(~(in @ X1020 @ X1019)=>~(in @ X1020 @ X1018))))=>(![X1580:$i, X1581:$i, X1582:$i]:(((in @ X1582 @ X1580)=>(~(in @ X1582 @ X1581)=>~(subset @ X1580 @ X1581))))=>(![X1578:$i, X1579:$i]:((~(subset @ X1578 @ X1579)=>((X1578)!=(X1579))))=>(![X1575:$i, X1576:$i, X1577:$i]:(((in @ X1577 @ X1575)=>(~(in @ X1577 @ X1576)=>((X1575)!=(X1576)))))=>(![X1574:$i]:((subset @ X1574 @ X1574))=>(![X1571:$i, X1572:$i, X1573:$i]:(((subset @ X1571 @ X1572)=>((subset @ X1572 @ X1573)=>(subset @ X1571 @ X1573))))=>(![X1569:$i, X1570:$i]:((subset @ X1570 @ (setadjoin @ X1569 @ X1570)))=>(![X1021:$i, X1022:$i, X1023:$i]:(((subset @ X1021 @ X1023)=>(subset @ X1021 @ (setadjoin @ X1022 @ X1023))))=>(![X1567:$i, X1568:$i]:(((subset @ X1567 @ X1568)=>(in @ X1567 @ (powerset @ X1568))))=>(![X1024:$i, X1025:$i]:(((subset @ X1024 @ X1025)=>((subset @ X1025 @ X1024)=>((X1024)=(X1025)))))=>(![X1026:$i]:(((subset @ X1026 @ emptyset)=>((X1026)=(emptyset))))=>(![X1565:$i, X1566:$i]:(((subset @ X1566 @ X1565)=>(in @ X1566 @ (powerset @ X1565))))=>(![X1027:$i, X1028:$i]:(((in @ X1028 @ (powerset @ X1027))=>(subset @ X1028 @ X1027)))=>(![X1029:$i]:((in @ X1029 @ (powerset @ X1029)))=>(![X1563:$i, X1564:$i]:(((subset @ X1563 @ X1564)=>(subset @ (powerset @ X1563) @ (powerset @ X1564))))=>(![X1561:$i, X1562:$i > $o]:((in @ (dsetconstr @ X1561 @ X1562) @ (powerset @ X1561)))=>(![X1030:$i, X1031:$i > $o]:((subset @ (dsetconstr @ X1030 @ X1031) @ X1030))=>(![X1558:$i, X1559:$i, X1560:$i]:(((in @ X1560 @ X1558)=>(in @ X1560 @ (binunion @ X1558 @ X1559))))=>(![X1556:$i, X1557:$i]:((in @ X1557 @ (setadjoin @ X1556 @ (setadjoin @ X1557 @ emptyset))))=>(![X1553:$i, X1554:$i, X1555:$i]:(((in @ X1555 @ X1554)=>(in @ X1555 @ (binunion @ X1553 @ X1554))))=>(![X1032:$i, X1033:$i, X1034:$i, X1035:$o]:(((in @ X1034 @ (binunion @ X1032 @ X1033))=>(((in @ X1034 @ X1032)=>(X1035))=>(((in @ X1034 @ X1033)=>(X1035))=>(X1035)))))=>(![X1550:$i, X1551:$i, X1552:$i]:(((in @ X1552 @ (binunion @ X1550 @ X1551))=>((in @ X1552 @ X1550)|(in @ X1552 @ X1551))))=>(![X1036:$i, X1037:$i]:((subset @ X1036 @ (binunion @ X1036 @ X1037)))=>(![X1038:$i, X1039:$i]:((subset @ X1039 @ (binunion @ X1038 @ X1039)))=>(![X1040:$i, X1041:$i, X1042:$i]:(((in @ X1042 @ X1040)=>((in @ X1042 @ X1041)=>(in @ X1042 @ (binintersect @ X1040 @ X1041)))))=>(![X1043:$i, X1044:$i, X1045:$i]:(((subset @ X1045 @ X1043)=>((subset @ X1045 @ X1044)=>(subset @ X1045 @ (binintersect @ X1043 @ X1044)))))=>(![X1046:$i, X1047:$i, X1048:$i]:(((in @ X1048 @ (binintersect @ X1046 @ X1047))=>(in @ X1048 @ X1046)))=>(![X1049:$i, X1050:$i]:((subset @ (binintersect @ X1049 @ X1050) @ X1049))=>(![X1051:$i, X1052:$i]:(((subset @ X1051 @ X1052)=>((binintersect @ X1051 @ X1052)=(X1051))))=>(![X1053:$i, X1054:$i]:((((binintersect @ X1053 @ X1054)=(X1054))=>(subset @ X1054 @ X1053)))=>(![X1055:$i, X1056:$i, X1057:$i]:(((in @ X1057 @ (binintersect @ X1055 @ X1056))=>(in @ X1057 @ X1056)))=>(![X1058:$i, X1059:$i]:((~(?[X1060:$i]:(((in @ X1060 @ X1058)&(in @ X1060 @ X1059))))=>((binintersect @ X1058 @ X1059)=(emptyset))))=>(![X1061:$i, X1062:$i]:((subset @ (binintersect @ X1061 @ X1062) @ X1062))=>(![X1063:$i, X1064:$i]:(((subset @ X1064 @ X1063)=>((binintersect @ X1063 @ X1064)=(X1064))))=>(![X1065:$i, X1066:$i]:((((binintersect @ X1065 @ X1066)=(X1065))=>(subset @ X1065 @ X1066)))=>(![X1547:$i, X1548:$i, X1549:$i]:(((binintersect @ X1547 @ (binunion @ X1548 @ X1549))=(binunion @ (binintersect @ X1547 @ X1548) @ (binintersect @ X1547 @ 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_282]), foundationAx]), wellorderingAx]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_288]), setext]), emptyI]), noeltsimpempty]), c_0_289]), c_0_290]), c_0_291]), c_0_292]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_293]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_294]), c_0_295]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_296]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_297]), c_0_298]), c_0_299]), inCongP]), in__Cong]), c_0_300]), c_0_301]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_302]), c_0_303]), c_0_304]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_305]), c_0_306]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_307]), c_0_308]), c_0_309]), c_0_310]), singletonsuniq]), setukpairinjL1]), c_0_311]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_312]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), c_0_318]), c_0_319]), c_0_320]), c_0_321]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_322]), c_0_323]), c_0_324]), c_0_325]), c_0_326]), c_0_327]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_328]), c_0_329]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_330]), c_0_331]), c_0_332]), c_0_333]), c_0_334]), c_0_335]), c_0_336]), c_0_337]), c_0_338]), c_0_339]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra])])]), c_0_340])).
2.13/180.04	thf(c_0_342, negated_conjecture, ![X1691:$i, X1692:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1704:$i, X1705:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1713:$i, X1714:$i > $i > $o, X1715:$i, X1717:$i, X1720:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1727:$i, X1728:$i > $o, X1729:$i, X1731:$i, X1732:$i > $o, X1733:$i, X1734:$i, X1735:$i > $o, X1736:$i, X1737:$i, X1738:$i > $o, X1739:$i, X1740:$i > $o, X1741:$i, X1744:$i, X1745:$o, X1746:$i, X1747:$i, X1748:$o, X1749:$i, X1750:$i, X1751:$i > $o, X1752:$i, X1755:$i, X1756:$i, X1759:$i, X1761:$i, X1763:$i, X1764:$i > $o, X1765:$i, X1766:$i, X1768:$i, X1769:$i > $o, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$o, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$o, X1801:$i, X1802:$i, X1803:$i > $o, X1804:$i, X1807:$i, X1808:$i, X1809:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i > $o, X1828:$i, X1829:$i > $o, X1830:$i, X1831:$i, X1832:$i > $o, X1833:$i, X1835:$i, X1836:$i > $o, X1838:$i, X1839:$i, X1840:$i > $o, X1842:$i, X1843:$i, X1844:$i > $o, X1845:$i, X1847:$o, X1848:$o, X1849:$i, X1850:$i > $o, X1852:$i, X1853:$i, X1854:$i > $o, X1855:$i, X1857:$i > $o, X1858:$i, X1861:$i, X1862:$i > $o, X1863:$i, X1867:$i, X1868:$i > $o, X1869:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i > $o, X1882:$i, X1884:$i, X1885:$i, X1886:$i > $o, X1887:$i > $o, X1890:$i, X1893:$i, X1894:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i > $o, X1907:$i, X1909:$i, X1910:$i, X1911:$i > $o, X1912:$i > $o, X1915:$i, X1917:$i, X1919:$i, X1920:$i, X1921:$i > $o, X1922:$i > $o, X1925:$i, X1926:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i > $o, X1973:$i, X1974:$i > $o, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$o, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$o, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i > $o, X2129:$i, X2130:$i, X2131:$i > $o, X2133:$i, X2134:$i > $o, X2135:$i, X2137:$i, X2138:$i > $o, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i > $i > $o, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i > $i > $o, X2219:$i, X2220:$i, X2221:$i > $i > $o, X2222:$i, X2223:$i, X2224:$i > $i > $o, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i > $i > $o, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i > $i > $o, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i > $i > $o, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i > $i, X2268:$i, X2269:$i, X2270:$i > $i, X2272:$i, X2273:$i, X2274:$i > $i, X2276:$i, X2277:$i, X2278:$i, X2279:$i > $o, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i > $o, X2289:$i, X2290:$i, X2291:$i > $o, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i > $i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i > $i, X2363:$i, X2364:$i, X2365:$i > $i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$o, X2373:$i, X2374:$i, X2375:$i, X2376:$o, X2377:$i, X2378:$i, X2379:$i, X2380:$o, X2381:$i, X2382:$i, X2383:$i, X2384:$o, X2385:$i, X2386:$i, X2387:$i, X2388:$o, X2389:$i, X2390:$i, X2391:$i, X2392:$o, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$o, X2399:$i, X2400:$i, X2401:$i, X2402:$o, X2403:$i, X2404:$i, X2405:$i, X2406:$o, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2427:$i, X2428:$i, X2429:$i, X2431:$i, X2432:$i, X2433:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, 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@ X2325 @ X2326 @ X2327 @ X2328)) @ X2328)|~(subset @ X2328 @ (cartprod @ X2325 @ X2326))|~(subset @ X2327 @ (cartprod @ X2325 @ X2326)))&(((in @ (kpair @ (esk76_4 @ X2325 @ X2326 @ X2327 @ X2328) @ (esk77_4 @ X2325 @ X2326 @ X2327 @ X2328)) @ X2328)|((X2327)=(X2328))|~(in @ (kpair @ (esk74_4 @ X2325 @ X2326 @ X2327 @ X2328) @ (esk75_4 @ X2325 @ X2326 @ X2327 @ X2328)) @ X2328)|~(subset @ X2328 @ (cartprod @ X2325 @ X2326))|~(subset @ X2327 @ (cartprod @ X2325 @ X2326)))&(~(in @ (kpair @ (esk76_4 @ X2325 @ X2326 @ X2327 @ X2328) @ (esk77_4 @ X2325 @ X2326 @ X2327 @ X2328)) @ X2327)|((X2327)=(X2328))|~(in @ (kpair @ (esk74_4 @ X2325 @ X2326 @ X2327 @ X2328) @ (esk75_4 @ X2325 @ X2326 @ X2327 @ X2328)) @ X2328)|~(subset @ X2328 @ (cartprod @ X2325 @ X2326))|~(subset @ X2327 @ (cartprod @ X2325 @ X2326)))))))))&((((in @ (esk78_4 @ X2333 @ X2334 @ X2335 @ X2336) @ X2333)|((X2335)=(X2336))|~(func @ X2333 @ X2334 @ X2336)|~(func @ X2333 @ X2334 @ X2335))&(((ap @ X2333 @ X2334 @ X2335 @ (esk78_4 @ X2333 @ X2334 @ X2335 @ X2336))!=(ap @ X2333 @ X2334 @ X2336 @ (esk78_4 @ X2333 @ X2334 @ X2335 @ X2336)))|((X2335)=(X2336))|~(func @ X2333 @ X2334 @ X2336)|~(func @ X2333 @ X2334 @ X2335)))&((((in @ (esk79_4 @ X2338 @ X2339 @ X2340 @ X2341) @ X2338)|((X2340)=(X2341))|~(in @ X2341 @ (funcSet @ X2338 @ X2339))|~(in @ X2340 @ (funcSet @ X2338 @ X2339)))&(((ap @ X2338 @ X2339 @ X2340 @ (esk79_4 @ X2338 @ X2339 @ X2340 @ X2341))!=(ap @ X2338 @ X2339 @ X2341 @ (esk79_4 @ X2338 @ X2339 @ X2340 @ X2341)))|((X2340)=(X2341))|~(in @ X2341 @ (funcSet @ X2338 @ X2339))|~(in @ X2340 @ (funcSet @ X2338 @ X2339))))&((~(in @ X2345 @ (funcSet @ X2343 @ X2344))|(~(in @ X2346 @ X2343)|((ap @ X2343 @ X2344 @ X2345 @ X2346)=(ap @ X2343 @ X2344 @ X2345 @ X2346))))&((~(func @ X2347 @ X2348 @ X2349)|(~(in @ X2350 @ X2347)|((ap @ X2347 @ X2348 @ X2349 @ X2350)=(ap @ X2347 @ X2348 @ X2349 @ X2350))))&((((in @ (esk80_3 @ X2351 @ X2352 @ X2353) @ X2351)|(~(in @ X2355 @ X2351)|((ap @ X2351 @ X2352 @ (lam @ X2351 @ X2352 @ X2353) @ X2355)=(X2353 @ X2355))))&(~(in @ (X2353 @ (esk80_3 @ X2351 @ X2352 @ X2353)) @ X2352)|(~(in @ X2355 @ X2351)|((ap @ X2351 @ X2352 @ (lam @ X2351 @ X2352 @ X2353) @ X2355)=(X2353 @ X2355)))))&((~(func @ X2356 @ X2357 @ X2358)|((lam @ X2356 @ X2357 @ (ap @ X2356 @ X2357 @ X2358))=(X2358)))&((((in @ (esk81_3 @ X2359 @ X2360 @ X2361) @ X2359)|((lam @ X2359 @ X2360 @ X2361)=(lam @ X2359 @ X2360 @ X2361)))&(~(in @ (X2361 @ (esk81_3 @ X2359 @ X2360 @ X2361)) @ X2360)|((lam @ X2359 @ X2360 @ X2361)=(lam @ X2359 @ X2360 @ X2361))))&((((in @ (esk82_3 @ X2363 @ X2364 @ X2365) @ X2363)|(~(in @ X2367 @ X2363)|((ap @ X2363 @ X2364 @ (lam @ X2363 @ X2364 @ X2365) @ X2367)=(X2365 @ X2367))))&(~(in @ (X2365 @ (esk82_3 @ X2363 @ X2364 @ X2365)) @ X2364)|(~(in @ X2367 @ X2363)|((ap @ X2363 @ X2364 @ (lam @ X2363 @ X2364 @ X2365) @ X2367)=(X2365 @ X2367)))))&((~(in @ X2370 @ (funcSet @ X2368 @ X2369))|((lam @ X2368 @ X2369 @ (ap @ X2368 @ X2369 @ X2370))=(X2370)))&((~(in @ X2373 @ X2371)|(~(in @ X2374 @ X2371)|((X2372)|(in @ X2374 @ (dsetconstr @ X2371 @ (^[Z0/* 9 */:$i]:((((X2372)&((Z0)=(X2373)))|(~((X2372))&((Z0)=(X2374)))))))))))&((~(in @ X2377 @ X2375)|(~(in @ X2378 @ X2375)|((X2376)|((dsetconstr @ X2375 @ (^[Z0/* 9 */:$i]:((((X2376)&((Z0)=(X2377)))|(~((X2376))&((Z0)=(X2378)))))))=(setadjoin @ X2378 @ emptyset)))))&((~(in @ X2381 @ X2379)|(~(in @ X2382 @ X2379)|(~(X2380)|(in @ X2381 @ (dsetconstr @ X2379 @ (^[Z0/* 9 */:$i]:((((X2380)&((Z0)=(X2381)))|(~((X2380))&((Z0)=(X2382)))))))))))&((~(in @ X2385 @ X2383)|(~(in @ X2386 @ X2383)|(~(X2384)|((dsetconstr @ X2383 @ (^[Z0/* 9 */:$i]:((((X2384)&((Z0)=(X2385)))|(~((X2384))&((Z0)=(X2386)))))))=(setadjoin @ X2385 @ emptyset)))))&((~(in @ X2389 @ X2387)|(~(in @ X2390 @ X2387)|(singleton @ (dsetconstr @ X2387 @ (^[Z0/* 9 */:$i]:((((X2388)&((Z0)=(X2389)))|(~((X2388))&((Z0)=(X2390))))))))))&((~(in @ X2393 @ X2391)|(~(in @ X2394 @ X2391)|(in @ (if @ X2391 @ ((X2392)) @ X2393 @ X2394) @ X2391)))&((~(singleton @ X2395)|(~(in @ X2396 @ X2395)|((setunion @ X2395)=(X2396))))&((~(in @ X2399 @ X2397)|(~(in @ X2400 @ X2397)|(~(X2398)|((if @ X2397 @ ((X2398)) @ X2399 @ X2400)=(X2399)))))&((~(in @ X2403 @ X2401)|(~(in @ X2404 @ X2401)|((X2402)|((if @ X2401 @ ((X2402)) @ X2403 @ X2404)=(X2404)))))&((~(in @ X2407 @ X2405)|(~(in @ X2408 @ X2405)|(in @ (if @ X2405 @ ((X2406)) @ X2407 @ X2408) @ (setadjoin @ X2407 @ (setadjoin @ X2408 @ emptyset)))))&((~(in @ X2410 @ (powerset @ X2409))|(~(in @ X2411 @ (powerset @ X2409))|(in @ (binintersect @ X2410 @ X2411) @ (powerset @ X2409))))&((~(in @ X2413 @ (powerset @ X2412))|(~(in @ X2414 @ (powerset @ X2412))|(in @ (binunion @ X2413 @ X2414) @ (powerset @ X2412))))&((~(in @ X2416 @ (powerset @ X2415))|(in @ (powerset @ X2416) @ (powerset @ (powerset @ X2415))))&((~(in @ X2418 @ (powerset @ X2417))|(~(in @ X2419 @ (powerset @ X2417))|(in @ (setminus @ X2418 @ X2419) @ (powerset @ X2417))))&((~(in @ X2421 @ (powerset @ X2420))|(in @ (setminus @ X2420 @ X2421) @ (powerset @ X2420)))&(((((in @ (esk84_3 @ X2422 @ X2423 @ X2424) @ X2422)|((X2423)=(X2424))|(in @ (esk83_3 @ X2422 @ X2423 @ X2424) @ X2422)|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))&(((in @ (esk84_3 @ X2422 @ X2423 @ X2424) @ X2424)|((X2423)=(X2424))|(in @ (esk83_3 @ X2422 @ X2423 @ X2424) @ X2422)|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))&(~(in @ (esk84_3 @ X2422 @ X2423 @ X2424) @ X2423)|((X2423)=(X2424))|(in @ (esk83_3 @ X2422 @ X2423 @ X2424) @ X2422)|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))))&((((in @ (esk84_3 @ X2422 @ X2423 @ X2424) @ X2422)|((X2423)=(X2424))|(in @ (esk83_3 @ X2422 @ X2423 @ X2424) @ X2423)|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))&(((in @ (esk84_3 @ X2422 @ X2423 @ X2424) @ X2424)|((X2423)=(X2424))|(in @ (esk83_3 @ X2422 @ X2423 @ X2424) @ X2423)|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))&(~(in @ (esk84_3 @ X2422 @ X2423 @ X2424) @ X2423)|((X2423)=(X2424))|(in @ (esk83_3 @ X2422 @ X2423 @ X2424) @ X2423)|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))))&(((in @ (esk84_3 @ X2422 @ X2423 @ X2424) @ X2422)|((X2423)=(X2424))|~(in @ (esk83_3 @ X2422 @ X2423 @ X2424) @ X2424)|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))&(((in @ (esk84_3 @ X2422 @ X2423 @ X2424) @ X2424)|((X2423)=(X2424))|~(in @ (esk83_3 @ X2422 @ X2423 @ X2424) @ X2424)|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))&(~(in @ (esk84_3 @ X2422 @ X2423 @ X2424) @ X2423)|((X2423)=(X2424))|~(in @ (esk83_3 @ X2422 @ X2423 @ X2424) @ X2424)|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))))))&((((in @ (esk85_3 @ X2427 @ X2428 @ X2429) @ X2427)|(subset @ X2428 @ X2429)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))&(((in @ (esk85_3 @ X2427 @ X2428 @ X2429) @ X2428)|(subset @ X2428 @ X2429)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))&(~(in @ (esk85_3 @ X2427 @ X2428 @ X2429) @ X2429)|(subset @ X2428 @ X2429)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))))&((((in @ (esk86_3 @ X2431 @ X2432 @ X2433) @ X2431)|(in @ X2432 @ (powerset @ X2433))|~(in @ X2433 @ (powerset @ X2431))|~(in @ X2432 @ (powerset @ X2431)))&(((in @ (esk86_3 @ X2431 @ X2432 @ X2433) @ X2432)|(in @ X2432 @ (powerset @ X2433))|~(in @ X2433 @ (powerset @ X2431))|~(in @ X2432 @ (powerset @ X2431)))&(~(in @ (esk86_3 @ X2431 @ X2432 @ X2433) @ X2433)|(in @ X2432 @ (powerset @ X2433))|~(in @ X2433 @ (powerset @ X2431))|~(in @ X2432 @ (powerset @ X2431)))))&((~(in @ X2436 @ (powerset @ X2435))|(~(in @ X2437 @ (powerset @ X2435))|(~(in @ X2438 @ X2435)|(~(in @ X2436 @ (powerset @ X2437))|(~(in @ X2438 @ X2436)|(in @ X2438 @ X2437))))))&((~(in @ X2440 @ (powerset @ X2439))|(~(in @ X2441 @ X2439)|(~(in @ X2441 @ X2440)|~(in @ X2441 @ (setminus @ X2439 @ X2440)))))&((~(in @ X2443 @ (powerset @ X2442))|(~(in @ X2444 @ X2442)|((in @ X2444 @ (setminus @ X2442 @ X2443))|(in @ X2444 @ X2443))))&((~(in @ X2446 @ (powerset @ X2445))|(~(in @ X2447 @ (powerset @ X2445))|(~(in @ X2448 @ X2445)|((in @ X2448 @ X2446)|~(in @ X2448 @ (binintersect @ X2446 @ X2447))))))&((~(in @ X2450 @ (powerset @ X2449))|(~(in @ X2451 @ (powerset @ X2449))|(~(in @ X2452 @ X2449)|((in @ X2452 @ X2451)|~(in @ X2452 @ (binintersect @ X2450 @ X2451))))))&((~(in @ X2454 @ (powerset @ X2453))|(~(in @ X2455 @ (powerset @ X2453))|(~(in @ X2456 @ X2453)|(~(subset @ X2454 @ (setminus @ X2453 @ X2455))|(~(in @ X2456 @ X2455)|~(in @ X2456 @ X2454))))))&((~(in @ X2458 @ (powerset @ X2457))|(~(in @ X2459 @ (powerset @ X2457))|(~(in @ X2460 @ X2457)|(~(subset @ X2458 @ X2459)|((in @ X2460 @ X2459)|~(in @ X2460 @ X2458))))))&((~(in @ X2462 @ (powerset @ X2461))|(~(in @ X2463 @ (powerset @ X2461))|(~(subset @ X2462 @ X2463)|(subset @ (setminus @ X2461 @ X2463) @ (setminus @ X2461 @ X2462)))))&((~(in @ X2465 @ (powerset @ X2464))|(~(in @ X2466 @ (powerset @ X2464))|(~(subset @ (setminus @ X2464 @ X2466) @ (setminus @ X2464 @ X2465))|(subset @ X2465 @ X2466))))&((~(in @ X2468 @ (powerset @ X2467))|(~(in @ X2469 @ X2467)|(~(in @ X2469 @ X2468)|(in @ X2469 @ (setminus @ X2467 @ (setminus @ X2467 @ X2468))))))&((~(in @ X2471 @ (powerset @ X2470))|(~(in @ X2472 @ X2470)|(~(in @ X2472 @ (setminus @ X2470 @ (setminus @ X2470 @ X2471)))|(in @ X2472 @ X2471))))&((~(in @ X2474 @ (powerset @ X2473))|(subset @ X2474 @ (setminus @ X2473 @ (setminus @ X2473 @ X2474))))&((~(in @ X2476 @ (powerset @ X2475))|(subset @ (setminus @ X2475 @ (setminus @ X2475 @ X2476)) @ X2476))&((~(in @ X2478 @ (powerset @ X2477))|((X2478)=(setminus @ X2477 @ (setminus @ X2477 @ X2478))))&((~(in @ X2480 @ (powerset @ X2479))|(~(in @ X2481 @ (powerset @ X2479))|(~(in @ X2482 @ X2479)|(~(in @ X2482 @ (setminus @ X2479 @ X2480))|~(in @ X2482 @ (binintersect @ X2480 @ X2481))))))&((~(in @ X2484 @ (powerset @ X2483))|(~(in @ X2485 @ (powerset @ X2483))|(~(in @ X2486 @ X2483)|(~(in @ X2486 @ (setminus @ X2483 @ X2484))|(in @ X2486 @ (setminus @ X2483 @ (binintersect @ X2484 @ X2485)))))))&((~(in @ X2488 @ (powerset @ X2487))|(~(in @ X2489 @ (powerset @ X2487))|(subset @ (setminus @ X2487 @ X2488) @ (setminus @ X2487 @ (binintersect @ X2488 @ X2489)))))&((~(in @ X2491 @ (powerset @ X2490))|(~(in @ X2492 @ (powerset @ X2490))|(in @ (setminus @ X2490 @ X2491) @ (powerset @ (setminus @ X2490 @ (binintersect @ X2491 @ X2492))))))&((~(in @ X2494 @ (powerset @ X2493))|(~(in @ X2495 @ (powerset @ X2493))|(~(subset @ X2494 @ (setminus @ X2493 @ X2495))|(~(in @ X2496 @ X2493)|(~(in @ X2496 @ X2495)|(in @ X2496 @ (setminus @ X2493 @ X2494)))))))&((~(in @ X2498 @ (powerset @ X2497))|(~(in @ X2499 @ (powerset @ X2497))|(~(subset @ X2498 @ (setminus @ X2497 @ X2499))|(subset @ X2499 @ (setminus @ X2497 @ X2498)))))&((~(in @ X2501 @ (powerset @ X2500))|(~(in @ X2502 @ (powerset @ X2500))|(~(in @ X2503 @ X2500)|((in @ X2503 @ (binunion @ X2501 @ X2502))|~(in @ X2503 @ X2501)))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((in @ esk90_0 @ esk87_0)&(~(in @ esk90_0 @ (binunion @ esk88_0 @ esk89_0))&(in @ esk90_0 @ esk89_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_341])])])])])])])).
2.13/180.04	thf(c_0_343, negated_conjecture, ~((in @ esk90_0 @ (binunion @ esk88_0 @ esk89_0))), inference(split_conjunct,[status(thm)],[c_0_342])).
2.13/180.04	thf(c_0_344, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X4 @ X3))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_342])).
2.13/180.04	thf(c_0_345, negated_conjecture, (in @ esk90_0 @ esk89_0), inference(split_conjunct,[status(thm)],[c_0_342])).
2.13/180.04	thf(c_0_346, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_343, c_0_344]), c_0_345])]), ['proof']).
2.13/180.04	# SZS output end CNFRefutation
2.13/180.04	# Parsed axioms                        : 553
2.13/180.04	# Removed by relevancy pruning/SinE    : 0
2.13/180.04	# Initial clauses                      : 734
2.13/180.04	# Removed in clause preprocessing      : 322
2.13/180.04	# Initial clauses in saturation        : 412
2.13/180.04	# Processed clauses                    : 526
2.13/180.04	# ...of these trivial                  : 10
2.13/180.04	# ...subsumed                          : 34
2.13/180.04	# ...remaining for further processing  : 482
2.13/180.04	# Other redundant clauses eliminated   : 24
2.13/180.04	# Clauses deleted for lack of memory   : 0
2.13/180.04	# Backward-subsumed                    : 2
2.13/180.04	# Backward-rewritten                   : 1
2.13/180.04	# Generated clauses                    : 575
2.13/180.04	# ...of the previous two non-redundant : 503
2.13/180.04	# ...aggressively subsumed             : 0
2.13/180.04	# Contextual simplify-reflections      : 6
2.13/180.04	# Paramodulations                      : 543
2.13/180.04	# Factorizations                       : 0
2.13/180.04	# NegExts                              : 0
2.13/180.04	# Equation resolutions                 : 29
2.13/180.04	# Disequality decompositions           : 0
2.13/180.04	# Total rewrite steps                  : 88
2.13/180.04	# ...of those cached                   : 58
2.13/180.04	# Propositional unsat checks           : 0
2.13/180.04	#    Propositional check models        : 0
2.13/180.04	#    Propositional check unsatisfiable : 0
2.13/180.04	#    Propositional clauses             : 0
2.13/180.04	#    Propositional clauses after purity: 0
2.13/180.04	#    Propositional unsat core size     : 0
2.13/180.04	#    Propositional preprocessing time  : 0.000
2.13/180.04	#    Propositional encoding time       : 0.000
2.13/180.04	#    Propositional solver time         : 0.000
2.13/180.04	#    Success case prop preproc time    : 0.000
2.13/180.04	#    Success case prop encoding time   : 0.000
2.13/180.04	#    Success case prop solver time     : 0.000
2.13/180.04	# Current number of processed clauses  : 104
2.13/180.04	#    Positive orientable unit clauses  : 33
2.13/180.04	#    Positive unorientable unit clauses: 0
2.13/180.04	#    Negative unit clauses             : 3
2.13/180.04	#    Non-unit-clauses                  : 68
2.13/180.04	# Current number of unprocessed clauses: 747
2.13/180.04	# ...number of literals in the above   : 2134
2.13/180.04	# Current number of archived formulas  : 0
2.13/180.04	# Current number of archived clauses   : 363
2.13/180.04	# Clause-clause subsumption calls (NU) : 25370
2.13/180.04	# Rec. Clause-clause subsumption calls : 8525
2.13/180.04	# Non-unit clause-clause subsumptions  : 37
2.13/180.04	# Unit Clause-clause subsumption calls : 73
2.13/180.04	# Rewrite failures with RHS unbound    : 0
2.13/180.04	# BW rewrite match attempts            : 26
2.13/180.04	# BW rewrite match successes           : 1
2.13/180.04	# Condensation attempts                : 0
2.13/180.04	# Condensation successes               : 0
2.13/180.04	# Termbank termtop insertions          : 84360
2.13/180.04	# Search garbage collected termcells   : 26560
2.13/180.04	
2.13/180.04	# -------------------------------------------------
2.13/180.04	# User time                : 0.203 s
2.13/180.04	# System time              : 0.024 s
2.13/180.04	# Total time               : 0.227 s
2.13/180.04	# Maximum resident set size: 8196 pages
2.13/180.04	
2.13/180.04	# -------------------------------------------------
2.13/180.04	# User time                : 0.218 s
2.13/180.04	# System time              : 0.028 s
2.13/180.04	# Total time               : 0.246 s
2.13/180.04	# Maximum resident set size: 2744 pages
2.13/180.04	% E---3.1 exiting
2.13/180.04	% E exiting
2.13/180.04	EOF