0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.11/0.33	% Computer : n025.cluster.edu
0.11/0.33	% Model    : x86_64 x86_64
0.11/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory   : 8042.1875MB
0.11/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit   : 1920
0.11/0.33	% WCLimit    : 240
0.11/0.33	% DateTime   : Wed Jul 30 04:29:04 EDT 2025
0.11/0.34	% CPUTime    : 
0.18/0.46	Running higher-order theorem proving
0.18/0.49	Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p
0.62/0.67	# Version: 3.0.0-ho
0.62/0.67	# Preprocessing class: HSLMSLSSLLLCHSA.
0.62/0.67	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
0.62/0.67	# Starting ho_unfolding_5 with 960s (4) cores
0.62/0.67	# Starting pre_casc_3 with 240s (1) cores
0.62/0.67	# Starting new_ho_10_cnf2 with 240s (1) cores
0.62/0.67	# Starting full_lambda_10 with 240s (1) cores
0.62/0.67	# Starting ehoh_best_nonlift_rwall with 240s (1) cores
0.62/0.67	# ho_unfolding_5 with pid 11091 completed with status 0
0.62/0.67	# Result found by ho_unfolding_5
0.62/0.67	# Preprocessing class: HSLMSLSSLLLCHSA.
0.62/0.67	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
0.62/0.67	# Starting ho_unfolding_5 with 960s (4) cores
0.62/0.67	# No SInE strategy applied
0.62/0.67	# Search class: HGHSM-FSLM32-MHSMMSBN
0.62/0.67	# Scheduled 12 strats onto 4 cores with 960 seconds (960 total)
0.62/0.67	# Starting full_lambda_5 with 79s (1) cores
0.62/0.67	# Starting ho_unfolding_5 with 97s (1) cores
0.62/0.67	# Starting pre_casc_4 with 79s (1) cores
0.62/0.67	# Starting pre_casc_3 with 79s (1) cores
0.62/0.67	# pre_casc_4 with pid 11098 completed with status 0
0.62/0.67	# Result found by pre_casc_4
0.62/0.67	# Preprocessing class: HSLMSLSSLLLCHSA.
0.62/0.67	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
0.62/0.67	# Starting ho_unfolding_5 with 960s (4) cores
0.62/0.67	# No SInE strategy applied
0.62/0.67	# Search class: HGHSM-FSLM32-MHSMMSBN
0.62/0.67	# Scheduled 12 strats onto 4 cores with 960 seconds (960 total)
0.62/0.67	# Starting full_lambda_5 with 79s (1) cores
0.62/0.67	# Starting ho_unfolding_5 with 97s (1) cores
0.62/0.67	# Starting pre_casc_4 with 79s (1) cores
0.62/0.67	# Preprocessing time       : 0.007 s
0.62/0.67	# Presaturation interreduction done
0.62/0.67	
0.62/0.67	# Proof found!
0.62/0.67	# SZS status Theorem
0.62/0.67	# SZS output start CNFRefutation
0.62/0.67	thf(decl_23, type, in: $i > $i > $o).
0.62/0.67	thf(decl_24, type, exu: ($i > $o) > $o).
0.62/0.67	thf(decl_25, type, setextAx: $o).
0.62/0.67	thf(decl_26, type, emptyset: $i).
0.62/0.67	thf(decl_27, type, emptysetAx: $o).
0.62/0.67	thf(decl_28, type, setadjoin: $i > $i > $i).
0.62/0.67	thf(decl_29, type, setadjoinAx: $o).
0.62/0.67	thf(decl_30, type, powerset: $i > $i).
0.62/0.67	thf(decl_31, type, powersetAx: $o).
0.62/0.67	thf(decl_32, type, setunion: $i > $i).
0.62/0.67	thf(decl_33, type, setunionAx: $o).
0.62/0.67	thf(decl_34, type, omega: $i).
0.62/0.67	thf(decl_35, type, omega0Ax: $o).
0.62/0.67	thf(decl_36, type, omegaSAx: $o).
0.62/0.67	thf(decl_37, type, omegaIndAx: $o).
0.62/0.67	thf(decl_38, type, replAx: $o).
0.62/0.67	thf(decl_39, type, foundationAx: $o).
0.62/0.67	thf(decl_40, type, wellorderingAx: $o).
0.62/0.67	thf(decl_41, type, descr: ($i > $o) > $i).
0.62/0.67	thf(decl_42, type, descrp: $o).
0.62/0.67	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_44, type, dsetconstrI: $o).
0.62/0.67	thf(decl_45, type, dsetconstrEL: $o).
0.62/0.67	thf(decl_46, type, dsetconstrER: $o).
0.62/0.67	thf(decl_47, type, exuE1: $o).
0.62/0.67	thf(decl_48, type, prop2set: $o > $i).
0.62/0.67	thf(decl_49, type, prop2setE: $o).
0.62/0.67	thf(decl_50, type, emptysetE: $o).
0.62/0.67	thf(decl_51, type, emptysetimpfalse: $o).
0.62/0.67	thf(decl_52, type, notinemptyset: $o).
0.62/0.67	thf(decl_53, type, exuE3e: $o).
0.62/0.67	thf(decl_54, type, setext: $o).
0.62/0.67	thf(decl_55, type, emptyI: $o).
0.62/0.67	thf(decl_56, type, noeltsimpempty: $o).
0.62/0.67	thf(decl_57, type, setbeta: $o).
0.62/0.67	thf(decl_58, type, nonempty: $i > $o).
0.62/0.67	thf(decl_59, type, nonemptyE1: $o).
0.62/0.67	thf(decl_60, type, nonemptyI: $o).
0.62/0.67	thf(decl_61, type, nonemptyI1: $o).
0.62/0.67	thf(decl_62, type, setadjoinIL: $o).
0.62/0.67	thf(decl_63, type, emptyinunitempty: $o).
0.62/0.67	thf(decl_64, type, setadjoinIR: $o).
0.62/0.67	thf(decl_65, type, setadjoinE: $o).
0.62/0.67	thf(decl_66, type, setadjoinOr: $o).
0.62/0.67	thf(decl_67, type, setoftrueEq: $o).
0.62/0.67	thf(decl_68, type, powersetI: $o).
0.62/0.67	thf(decl_69, type, emptyinPowerset: $o).
0.62/0.67	thf(decl_70, type, emptyInPowerset: $o).
0.62/0.67	thf(decl_71, type, powersetE: $o).
0.62/0.67	thf(decl_72, type, setunionI: $o).
0.62/0.67	thf(decl_73, type, setunionE: $o).
0.62/0.67	thf(decl_74, type, subPowSU: $o).
0.62/0.67	thf(decl_75, type, exuE2: $o).
0.62/0.67	thf(decl_76, type, nonemptyImpWitness: $o).
0.62/0.67	thf(decl_77, type, uniqinunit: $o).
0.62/0.67	thf(decl_78, type, notinsingleton: $o).
0.62/0.67	thf(decl_79, type, eqinunit: $o).
0.62/0.67	thf(decl_80, type, singletonsswitch: $o).
0.62/0.67	thf(decl_81, type, upairsetE: $o).
0.62/0.67	thf(decl_82, type, upairsetIL: $o).
0.62/0.67	thf(decl_83, type, upairsetIR: $o).
0.62/0.67	thf(decl_84, type, emptyE1: $o).
0.62/0.67	thf(decl_85, type, vacuousDall: $o).
0.62/0.67	thf(decl_86, type, quantDeMorgan1: $o).
0.62/0.67	thf(decl_87, type, quantDeMorgan2: $o).
0.62/0.67	thf(decl_88, type, quantDeMorgan3: $o).
0.62/0.67	thf(decl_89, type, quantDeMorgan4: $o).
0.62/0.67	thf(decl_90, type, prop2setI: $o).
0.62/0.67	thf(decl_91, type, set2prop: $i > $o).
0.62/0.67	thf(decl_92, type, prop2set2propI: $o).
0.62/0.67	thf(decl_93, type, notdexE: $o).
0.62/0.67	thf(decl_94, type, notdallE: $o).
0.62/0.67	thf(decl_95, type, exuI1: $o).
0.62/0.67	thf(decl_96, type, exuI3: $o).
0.62/0.67	thf(decl_97, type, exuI2: $o).
0.62/0.67	thf(decl_98, type, inCongP: $o).
0.62/0.67	thf(decl_99, type, in__Cong: $o).
0.62/0.67	thf(decl_100, type, exuE3u: $o).
0.62/0.67	thf(decl_101, type, exu__Cong: $o).
0.62/0.67	thf(decl_102, type, emptyset__Cong: $o).
0.62/0.67	thf(decl_103, type, setadjoin__Cong: $o).
0.62/0.67	thf(decl_104, type, powerset__Cong: $o).
0.62/0.67	thf(decl_105, type, setunion__Cong: $o).
0.62/0.67	thf(decl_106, type, omega__Cong: $o).
0.62/0.67	thf(decl_107, type, exuEu: $o).
0.62/0.67	thf(decl_108, type, descr__Cong: $o).
0.62/0.67	thf(decl_109, type, dsetconstr__Cong: $o).
0.62/0.67	thf(decl_110, type, subset: $i > $i > $o).
0.62/0.67	thf(decl_113, type, subsetI1: $o).
0.62/0.67	thf(decl_114, type, eqimpsubset2: $o).
0.62/0.67	thf(decl_115, type, eqimpsubset1: $o).
0.62/0.67	thf(decl_116, type, subsetI2: $o).
0.62/0.67	thf(decl_117, type, emptysetsubset: $o).
0.62/0.67	thf(decl_118, type, subsetE: $o).
0.62/0.67	thf(decl_119, type, subsetE2: $o).
0.62/0.67	thf(decl_120, type, notsubsetI: $o).
0.62/0.67	thf(decl_121, type, notequalI1: $o).
0.62/0.67	thf(decl_122, type, notequalI2: $o).
0.62/0.67	thf(decl_123, type, subsetRefl: $o).
0.62/0.67	thf(decl_124, type, subsetTrans: $o).
0.62/0.67	thf(decl_125, type, setadjoinSub: $o).
0.62/0.67	thf(decl_126, type, setadjoinSub2: $o).
0.62/0.67	thf(decl_127, type, subset2powerset: $o).
0.62/0.67	thf(decl_128, type, setextsub: $o).
0.62/0.67	thf(decl_129, type, subsetemptysetimpeq: $o).
0.62/0.67	thf(decl_130, type, powersetI1: $o).
0.62/0.67	thf(decl_131, type, powersetE1: $o).
0.62/0.67	thf(decl_132, type, inPowerset: $o).
0.62/0.67	thf(decl_133, type, powersetsubset: $o).
0.62/0.67	thf(decl_134, type, sepInPowerset: $o).
0.62/0.67	thf(decl_135, type, sepSubset: $o).
0.62/0.67	thf(decl_136, type, binunion: $i > $i > $i).
0.62/0.67	thf(decl_137, type, binunionIL: $o).
0.62/0.67	thf(decl_138, type, upairset2IR: $o).
0.62/0.67	thf(decl_139, type, binunionIR: $o).
0.62/0.67	thf(decl_140, type, binunionEcases: $o).
0.62/0.67	thf(decl_141, type, binunionE: $o).
0.62/0.67	thf(decl_142, type, binunionLsub: $o).
0.62/0.67	thf(decl_143, type, binunionRsub: $o).
0.62/0.67	thf(decl_144, type, binintersect: $i > $i > $i).
0.62/0.67	thf(decl_145, type, binintersectI: $o).
0.62/0.67	thf(decl_146, type, binintersectSubset5: $o).
0.62/0.67	thf(decl_147, type, binintersectEL: $o).
0.62/0.67	thf(decl_148, type, binintersectLsub: $o).
0.62/0.67	thf(decl_149, type, binintersectSubset2: $o).
0.62/0.67	thf(decl_150, type, binintersectSubset3: $o).
0.62/0.67	thf(decl_151, type, binintersectER: $o).
0.62/0.67	thf(decl_152, type, disjointsetsI1: $o).
0.62/0.67	thf(decl_153, type, binintersectRsub: $o).
0.62/0.67	thf(decl_154, type, binintersectSubset4: $o).
0.62/0.67	thf(decl_155, type, binintersectSubset1: $o).
0.62/0.67	thf(decl_156, type, bs114d: $o).
0.62/0.67	thf(decl_158, type, setminus: $i > $i > $i).
0.62/0.67	thf(decl_159, type, setminusI: $o).
0.62/0.67	thf(decl_160, type, setminusEL: $o).
0.62/0.67	thf(decl_161, type, setminusER: $o).
0.62/0.67	thf(decl_162, type, setminusSubset2: $o).
0.62/0.67	thf(decl_163, type, setminusERneg: $o).
0.62/0.67	thf(decl_164, type, setminusELneg: $o).
0.62/0.67	thf(decl_165, type, setminusILneg: $o).
0.62/0.67	thf(decl_166, type, setminusIRneg: $o).
0.62/0.67	thf(decl_167, type, setminusLsub: $o).
0.62/0.67	thf(decl_168, type, setminusSubset1: $o).
0.62/0.67	thf(decl_169, type, symdiff: $i > $i > $i).
0.62/0.67	thf(decl_170, type, symdiffE: $o).
0.62/0.67	thf(decl_171, type, symdiffI1: $o).
0.62/0.67	thf(decl_172, type, symdiffI2: $o).
0.62/0.67	thf(decl_173, type, symdiffIneg1: $o).
0.62/0.67	thf(decl_174, type, symdiffIneg2: $o).
0.62/0.67	thf(decl_175, type, iskpair: $i > $o).
0.62/0.67	thf(decl_176, type, secondinupair: $o).
0.62/0.67	thf(decl_177, type, setukpairIL: $o).
0.62/0.67	thf(decl_178, type, setukpairIR: $o).
0.62/0.67	thf(decl_179, type, kpairiskpair: $o).
0.62/0.67	thf(decl_180, type, kpair: $i > $i > $i).
0.62/0.67	thf(decl_181, type, kpairp: $o).
0.62/0.67	thf(decl_182, type, cartprod: $i > $i > $i).
0.62/0.67	thf(decl_183, type, singletonsubset: $o).
0.62/0.67	thf(decl_184, type, singletoninpowerset: $o).
0.62/0.67	thf(decl_185, type, singletoninpowunion: $o).
0.62/0.67	thf(decl_186, type, upairset2E: $o).
0.62/0.67	thf(decl_187, type, upairsubunion: $o).
0.62/0.67	thf(decl_188, type, upairinpowunion: $o).
0.62/0.67	thf(decl_189, type, ubforcartprodlem1: $o).
0.62/0.67	thf(decl_190, type, ubforcartprodlem2: $o).
0.62/0.67	thf(decl_191, type, ubforcartprodlem3: $o).
0.62/0.67	thf(decl_192, type, cartprodpairin: $o).
0.62/0.67	thf(decl_193, type, cartprodmempair1: $o).
0.62/0.67	thf(decl_194, type, cartprodmempair: $o).
0.62/0.67	thf(decl_195, type, setunionE2: $o).
0.62/0.67	thf(decl_196, type, setunionsingleton1: $o).
0.62/0.67	thf(decl_197, type, setunionsingleton2: $o).
0.62/0.67	thf(decl_198, type, setunionsingleton: $o).
0.62/0.67	thf(decl_199, type, singleton: $i > $o).
0.62/0.67	thf(decl_200, type, singletonprop: $o).
0.62/0.67	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
0.62/0.67	thf(decl_202, type, ex1E1: $o).
0.62/0.67	thf(decl_203, type, ex1I: $o).
0.62/0.67	thf(decl_204, type, ex1I2: $o).
0.62/0.67	thf(decl_205, type, singletonsuniq: $o).
0.62/0.67	thf(decl_210, type, setukpairinjL1: $o).
0.62/0.67	thf(decl_211, type, kfstsingleton: $o).
0.62/0.67	thf(decl_212, type, theprop: $o).
0.62/0.67	thf(decl_213, type, kfst: $i > $i).
0.62/0.67	thf(decl_214, type, kfstpairEq: $o).
0.62/0.67	thf(decl_215, type, cartprodfstin: $o).
0.62/0.67	thf(decl_216, type, setukpairinjL2: $o).
0.62/0.67	thf(decl_217, type, setukpairinjL: $o).
0.62/0.67	thf(decl_218, type, setukpairinjR11: $o).
0.62/0.67	thf(decl_219, type, setukpairinjR12: $o).
0.62/0.67	thf(decl_220, type, setukpairinjR1: $o).
0.62/0.67	thf(decl_221, type, upairequniteq: $o).
0.62/0.67	thf(decl_222, type, setukpairinjR2: $o).
0.62/0.67	thf(decl_223, type, setukpairinjR: $o).
0.62/0.67	thf(decl_224, type, ksndsingleton: $o).
0.62/0.67	thf(decl_225, type, ksnd: $i > $i).
0.62/0.67	thf(decl_226, type, ksndpairEq: $o).
0.62/0.67	thf(decl_227, type, kpairsurjEq: $o).
0.62/0.67	thf(decl_228, type, cartprodsndin: $o).
0.62/0.67	thf(decl_229, type, cartprodpairmemEL: $o).
0.62/0.67	thf(decl_230, type, cartprodpairmemER: $o).
0.62/0.67	thf(decl_231, type, cartprodmempaircEq: $o).
0.62/0.67	thf(decl_232, type, cartprodfstpairEq: $o).
0.62/0.67	thf(decl_233, type, cartprodsndpairEq: $o).
0.62/0.67	thf(decl_234, type, cartprodpairsurjEq: $o).
0.62/0.67	thf(decl_235, type, breln: $i > $i > $i > $o).
0.62/0.67	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
0.62/0.67	thf(decl_237, type, dpsetconstrI: $o).
0.62/0.67	thf(decl_238, type, dpsetconstrSub: $o).
0.62/0.67	thf(decl_239, type, setOfPairsIsBReln: $o).
0.62/0.67	thf(decl_240, type, dpsetconstrERa: $o).
0.62/0.67	thf(decl_241, type, dpsetconstrEL1: $o).
0.62/0.67	thf(decl_242, type, dpsetconstrEL2: $o).
0.62/0.67	thf(decl_243, type, dpsetconstrER: $o).
0.62/0.67	thf(decl_244, type, func: $i > $i > $i > $o).
0.62/0.67	thf(decl_245, type, funcSet: $i > $i > $i).
0.62/0.67	thf(decl_246, type, funcImageSingleton: $o).
0.62/0.67	thf(decl_247, type, apProp: $o).
0.62/0.67	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
0.62/0.67	thf(decl_249, type, app: $o).
0.62/0.67	thf(decl_250, type, infuncsetfunc: $o).
0.62/0.67	thf(decl_251, type, ap2p: $o).
0.62/0.67	thf(decl_252, type, funcinfuncset: $o).
0.62/0.67	thf(decl_253, type, lamProp: $o).
0.62/0.67	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
0.62/0.67	thf(decl_255, type, lamp: $o).
0.62/0.67	thf(decl_256, type, lam2p: $o).
0.62/0.67	thf(decl_257, type, brelnall1: $o).
0.62/0.67	thf(decl_258, type, brelnall2: $o).
0.62/0.67	thf(decl_259, type, ex1E2: $o).
0.62/0.67	thf(decl_260, type, funcGraphProp1: $o).
0.62/0.67	thf(decl_261, type, funcGraphProp3: $o).
0.62/0.67	thf(decl_262, type, funcGraphProp2: $o).
0.62/0.67	thf(decl_263, type, funcextLem: $o).
0.62/0.67	thf(decl_264, type, funcGraphProp4: $o).
0.62/0.67	thf(decl_265, type, subbreln: $o).
0.62/0.67	thf(decl_266, type, eqbreln: $o).
0.62/0.67	thf(decl_267, type, funcext: $o).
0.62/0.67	thf(decl_268, type, funcext2: $o).
0.62/0.67	thf(decl_269, type, ap2apEq1: $o).
0.62/0.67	thf(decl_270, type, ap2apEq2: $o).
0.62/0.67	thf(decl_271, type, beta1: $o).
0.62/0.67	thf(decl_272, type, eta1: $o).
0.62/0.67	thf(decl_273, type, lam2lamEq: $o).
0.62/0.67	thf(decl_274, type, beta2: $o).
0.62/0.67	thf(decl_275, type, eta2: $o).
0.62/0.67	thf(decl_276, type, iffalseProp1: $o).
0.62/0.67	thf(decl_277, type, iffalseProp2: $o).
0.62/0.67	thf(decl_278, type, epred1_0: $o).
0.62/0.67	thf(decl_279, type, esk1_2: $i > $i > $i).
0.62/0.67	thf(decl_280, type, esk2_2: $i > $i > $i).
0.62/0.67	thf(decl_281, type, esk3_2: $i > $i > $i).
0.62/0.67	thf(decl_282, type, esk4_1: $i > $i).
0.62/0.67	thf(decl_283, type, esk5_2: ($i > $i > $o) > $i > $i).
0.62/0.67	thf(decl_284, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
0.62/0.67	thf(decl_285, type, esk7_2: ($i > $i > $o) > $i > $i).
0.62/0.67	thf(decl_286, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
0.62/0.67	thf(decl_287, type, esk9_1: $i > $i).
0.62/0.67	thf(decl_288, type, esk10_2: ($i > $o) > $i > $i).
0.62/0.67	thf(decl_289, type, esk11_2: ($i > $o) > $i > $i).
0.62/0.67	thf(decl_290, type, esk12_1: ($i > $o) > $i).
0.62/0.67	thf(decl_291, type, esk13_2: ($i > $o) > $i > $i).
0.62/0.67	thf(decl_292, type, esk14_1: ($i > $o) > $i).
0.62/0.67	thf(decl_293, type, esk15_2: $i > $i > $i).
0.62/0.67	thf(decl_294, type, esk16_2: $i > $i > $i).
0.62/0.67	thf(decl_295, type, esk17_1: $i > $i).
0.62/0.67	thf(decl_296, type, esk18_1: $i > $i).
0.62/0.67	thf(decl_297, type, esk19_1: $i > $i).
0.62/0.67	thf(decl_298, type, esk20_2: $i > $i > $i).
0.62/0.67	thf(decl_299, type, esk21_3: $i > $i > $o > $i).
0.62/0.67	thf(decl_300, type, esk22_2: ($i > $o) > $i > $i).
0.62/0.67	thf(decl_301, type, esk23_1: ($i > $o) > $i).
0.62/0.67	thf(decl_302, type, esk24_1: $i > $i).
0.62/0.67	thf(decl_303, type, esk25_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_304, type, esk26_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_305, type, esk27_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_306, type, esk28_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_307, type, esk29_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_308, type, esk30_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_309, type, esk31_2: ($i > $o) > $i > $i).
0.62/0.67	thf(decl_310, type, esk32_1: ($i > $o) > $i).
0.62/0.67	thf(decl_311, type, esk33_1: ($i > $o) > $i).
0.62/0.67	thf(decl_312, type, esk34_1: ($i > $o) > $i).
0.62/0.67	thf(decl_313, type, esk35_1: ($i > $o) > $i).
0.62/0.67	thf(decl_314, type, esk36_2: ($i > $o) > $i > $i).
0.62/0.67	thf(decl_315, type, esk37_1: ($i > $o) > $i).
0.62/0.67	thf(decl_316, type, esk38_2: ($i > $o) > $i > $i).
0.62/0.67	thf(decl_317, type, esk39_2: ($i > $o) > ($i > $o) > $i).
0.62/0.67	thf(decl_318, type, esk40_2: ($i > $o) > ($i > $o) > $i).
0.62/0.67	thf(decl_319, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
0.62/0.67	thf(decl_320, type, esk42_2: ($i > $o) > ($i > $o) > $i).
0.62/0.67	thf(decl_321, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
0.62/0.67	thf(decl_322, type, esk44_2: ($i > $o) > ($i > $o) > $i).
0.62/0.67	thf(decl_323, type, esk45_2: ($i > $o) > $i > $i).
0.62/0.67	thf(decl_324, type, esk46_2: ($i > $o) > ($i > $o) > $i).
0.62/0.67	thf(decl_325, type, esk47_2: ($i > $o) > ($i > $o) > $i).
0.62/0.67	thf(decl_326, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
0.62/0.67	thf(decl_327, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
0.62/0.67	thf(decl_328, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.62/0.67	thf(decl_329, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.62/0.67	thf(decl_330, type, esk52_2: $i > $i > $i).
0.62/0.67	thf(decl_331, type, esk53_2: $i > $i > $i).
0.62/0.67	thf(decl_332, type, esk54_2: $i > $i > $i).
0.62/0.67	thf(decl_333, type, esk55_3: $i > $i > $i > $i).
0.62/0.67	thf(decl_334, type, esk56_3: $i > $i > $i > $i).
0.62/0.67	thf(decl_335, type, esk57_2: $i > $i > $i).
0.62/0.67	thf(decl_336, type, esk58_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_337, type, esk59_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_338, type, esk60_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_339, type, esk61_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_340, type, esk62_3: $i > ($i > $o) > $i > $i).
0.62/0.67	thf(decl_341, type, esk63_3: $i > ($i > $o) > $i > $i).
0.62/0.67	thf(decl_342, type, esk64_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_343, type, esk65_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_344, type, esk66_2: $i > ($i > $o) > $i).
0.62/0.67	thf(decl_345, type, esk67_1: $i > $i).
0.62/0.67	thf(decl_346, type, esk68_1: $i > $i).
0.62/0.67	thf(decl_347, type, esk69_4: $i > $i > $i > $i > $i).
0.62/0.67	thf(decl_348, type, esk70_3: $i > $i > ($i > $i) > $i).
0.62/0.67	thf(decl_349, type, esk71_3: $i > $i > ($i > $i) > $i).
0.62/0.67	thf(decl_350, type, esk72_3: $i > $i > ($i > $i) > $i).
0.62/0.67	thf(decl_351, type, esk73_4: $i > $i > $i > ($i > $o) > $i).
0.62/0.67	thf(decl_352, type, esk74_4: $i > $i > $i > ($i > $o) > $i).
0.62/0.67	thf(decl_353, type, esk75_4: $i > $i > $i > ($i > $o) > $i).
0.62/0.67	thf(decl_354, type, esk76_4: $i > $i > $i > ($i > $o) > $i).
0.62/0.67	thf(decl_355, type, esk77_4: $i > $i > $i > $i > $i).
0.62/0.67	thf(decl_356, type, esk78_4: $i > $i > $i > $i > $i).
0.62/0.67	thf(decl_357, type, esk79_4: $i > $i > $i > $i > $i).
0.62/0.67	thf(decl_358, type, esk80_4: $i > $i > $i > $i > $i).
0.62/0.67	thf(decl_359, type, esk81_4: $i > $i > $i > $i > $i).
0.62/0.67	thf(decl_360, type, esk82_4: $i > $i > $i > $i > $i).
0.62/0.67	thf(decl_361, type, esk83_4: $i > $i > $i > $i > $i).
0.62/0.67	thf(decl_362, type, esk84_4: $i > $i > $i > $i > $i).
0.62/0.67	thf(decl_363, type, esk85_4: $i > $i > $i > $i > $i).
0.62/0.67	thf(decl_364, type, esk86_3: $i > $i > ($i > $i) > $i).
0.62/0.67	thf(decl_365, type, esk87_3: $i > $i > ($i > $i) > $i).
0.62/0.67	thf(decl_366, type, esk88_3: $i > $i > ($i > $i) > $i).
0.62/0.67	thf(decl_367, type, esk89_0: $i).
0.62/0.67	thf(decl_368, type, epred2_0: $o).
0.62/0.67	thf(decl_369, type, esk90_0: $i).
0.62/0.67	thf(decl_370, type, esk91_0: $i).
0.62/0.67	thf(decl_376, type, epred3_0: $i > $o).
0.62/0.67	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', ex1)).
0.62/0.67	thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', singleton)).
0.62/0.67	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', replAx)).
0.62/0.67	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', exu)).
0.62/0.67	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', descrp)).
0.62/0.67	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', exuE1)).
0.62/0.67	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', exuE3e)).
0.62/0.67	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', nonempty)).
0.62/0.67	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', nonemptyI)).
0.62/0.67	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', exuE2)).
0.62/0.67	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', exuI1)).
0.62/0.67	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', exuI3)).
0.62/0.67	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', exuI2)).
0.62/0.67	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', exuE3u)).
0.62/0.67	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', exu__Cong)).
0.62/0.67	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', exuEu)).
0.62/0.67	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', descr__Cong)).
0.62/0.67	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', singletonprop)).
0.62/0.67	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', ex1E1)).
0.62/0.67	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', ex1I)).
0.62/0.67	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', ex1I2)).
0.62/0.67	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', kfstsingleton)).
0.62/0.67	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', ksndsingleton)).
0.62/0.67	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setOfPairsIsBReln)).
0.62/0.67	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', breln)).
0.62/0.67	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', funcImageSingleton)).
0.62/0.67	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.9vlwmE1uFM/E---3.1_11012.p', ex1E2)).
0.62/0.67	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', dsetconstrI)).
0.62/0.67	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', dsetconstrEL)).
0.62/0.67	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', dsetconstrER)).
0.62/0.67	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setbeta)).
0.62/0.67	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', nonemptyE1)).
0.62/0.67	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', nonemptyI1)).
0.62/0.67	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setoftrueEq)).
0.62/0.67	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', nonemptyImpWitness)).
0.62/0.67	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', emptyE1)).
0.62/0.67	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', dsetconstr__Cong)).
0.62/0.67	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', sepInPowerset)).
0.62/0.67	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', sepSubset)).
0.62/0.67	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', theprop)).
0.62/0.67	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', dpsetconstrI)).
0.62/0.67	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', dpsetconstrSub)).
0.62/0.67	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', dpsetconstrERa)).
0.62/0.67	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', dpsetconstrEL1)).
0.62/0.67	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', dpsetconstrEL2)).
0.62/0.67	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', dpsetconstrER)).
0.62/0.67	thf(apProp, axiom, ((apProp)<=>![X4:$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.9vlwmE1uFM/E---3.1_11012.p', apProp)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', lamProp)).
0.62/0.67	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', lamp)).
0.62/0.67	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', lam2p)).
0.62/0.67	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.9vlwmE1uFM/E---3.1_11012.p', brelnall1)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', brelnall2)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', subbreln)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', eqbreln)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', beta1)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', eta1)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', lam2lamEq)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', beta2)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', eta2)).
0.62/0.67	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', iffalseProp1)).
0.62/0.67	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.9vlwmE1uFM/E---3.1_11012.p', iffalseProp2)).
0.62/0.67	thf(iftrueProp1, conjecture, (((emptysetAx)=>(((((omega0Ax)=>(((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>(((dsetconstrI)=>((((((((((((((nonemptyE1)=>(((nonemptyI1)=>(((emptyinunitempty)=>(((setadjoinE)=>((setadjoinOr)=>(((((emptyInPowerset)=>(((setunionI)=>((setunionE)=>((((nonemptyImpWitness)=>(((notinsingleton)=>((eqinunit)=>(((upairsetE)=>(((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>(((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>(((((exuI1)=>((exuI3)=>((exuI2)=>(((in__Cong)=>((exuE3u)=>(((emptyset__Cong)=>((setadjoin__Cong)=>(((setunion__Cong)=>((omega__Cong)=>(((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>(((((subsetE)=>(((notsubsetI)=>(((notequalI2)=>((((((((subsetemptysetimpeq)=>(((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>(((binunionE)=>(((binunionRsub)=>(((binintersectSubset5)=>(((binintersectLsub)=>((binintersectSubset2)=>((((((binintersectSubset4)=>(((bs114d)=>(((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>(((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>(((((setukpairIR)=>(((kpairp)=>((singletonsubset)=>(((((upairsubunion)=>((upairinpowunion)=>(((((((((setunionsingleton1)=>(((setunionsingleton)=>(((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>(((((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((((((((((cartprodsndin)=>((((cartprodmempaircEq)=>(((cartprodsndpairEq)=>((((dpsetconstrSub)=>((((dpsetconstrEL1)=>((dpsetconstrEL2)=>(((((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>(((((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>(((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((((![X4:$i, X41:$o, X2:$i]:((![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:(((((X14)=(X2))&(X41))|(((X14)=(X3))&~((X41)))))))))))<=(in @ X2 @ X4)))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))<=(beta2))))))))<=(funcext))))))<=(funcGraphProp2))<=(funcGraphProp3))<=(funcGraphProp1))))))<=(lamp))<=(lamProp))))))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER))))<=(dpsetconstrERa))<=(setOfPairsIsBReln)))<=(dpsetconstrI))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq)))<=(cartprodpairmemER))<=(cartprodpairmemEL)))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1))<=(setukpairinjR12))))))<=(kfstpairEq))<=(theprop))<=(kfstsingleton)))))))<=(singletonprop)))<=(setunionsingleton2)))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2))<=(ubforcartprodlem1))))<=(upairset2E))<=(singletoninpowunion))<=(singletoninpowerset))))<=(kpairiskpair)))<=(setukpairIL))<=(secondinupair))<=(symdiffIneg2)))))))))<=(setminusILneg)))))))<=(setminusI)))<=(binintersectSubset1)))<=(binintersectRsub))<=(disjointsetsI1))<=(binintersectER))<=(binintersectSubset3))))<=(binintersectEL)))<=(binintersectI)))<=(binunionLsub)))<=(binunionEcases))))))))))<=(powersetI1)))<=(setextsub))<=(subset2powerset))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1)))<=(subsetE2)))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1))))))<=(exuEu))))<=(powerset__Cong))))<=(exu__Cong))))<=(inCongP)))))<=(notdallE))<=(notdexE))<=(prop2set2propI)))))<=(quantDeMorgan2))))))<=(upairsetIL)))<=(singletonsswitch))))<=(uniqinunit)))<=(exuE2))<=(subPowSU))))<=(powersetE)))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq))))<=(setadjoinIR)))<=(setadjoinIL)))<=(nonemptyI)))<=(setbeta))<=(noeltsimpempty))<=(emptyI))<=(setext))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp))))))<=(omegaSAx)))<=(setunionAx))<=(powersetAx))<=(setadjoinAx)))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', iftrueProp1)).
0.62/0.67	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setextAx)).
0.62/0.67	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', emptysetAx)).
0.62/0.67	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setadjoinAx)).
0.62/0.67	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', powersetAx)).
0.62/0.67	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setunionAx)).
0.62/0.67	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', omega0Ax)).
0.62/0.67	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', omegaSAx)).
0.62/0.67	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', omegaIndAx)).
0.62/0.67	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', foundationAx)).
0.62/0.67	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', wellorderingAx)).
0.62/0.67	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', prop2setE)).
0.62/0.67	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', emptysetE)).
0.62/0.67	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', emptysetimpfalse)).
0.62/0.67	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', notinemptyset)).
0.62/0.67	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setext)).
0.62/0.67	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', emptyI)).
0.62/0.67	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', noeltsimpempty)).
0.62/0.67	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setadjoinIL)).
0.62/0.67	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', emptyinunitempty)).
0.62/0.67	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setadjoinIR)).
0.62/0.67	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setadjoinE)).
0.62/0.67	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setadjoinOr)).
0.62/0.67	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', powersetI)).
0.62/0.67	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', emptyinPowerset)).
0.62/0.67	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', emptyInPowerset)).
0.62/0.67	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', powersetE)).
0.62/0.67	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setunionI)).
0.62/0.67	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setunionE)).
0.62/0.67	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', subPowSU)).
0.62/0.67	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', uniqinunit)).
0.62/0.67	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', notinsingleton)).
0.62/0.67	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', eqinunit)).
0.62/0.67	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', singletonsswitch)).
0.62/0.67	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', upairsetE)).
0.62/0.67	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', upairsetIL)).
0.62/0.67	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', upairsetIR)).
0.62/0.67	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', vacuousDall)).
0.62/0.67	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', quantDeMorgan1)).
0.62/0.67	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', quantDeMorgan2)).
0.62/0.67	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', quantDeMorgan3)).
0.62/0.67	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', quantDeMorgan4)).
0.62/0.67	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', prop2setI)).
0.62/0.67	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', prop2set2propI)).
0.62/0.67	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', notdexE)).
0.62/0.67	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', notdallE)).
0.62/0.67	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', inCongP)).
0.62/0.67	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', in__Cong)).
0.62/0.67	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', emptyset__Cong)).
0.62/0.67	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setadjoin__Cong)).
0.62/0.67	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', powerset__Cong)).
0.62/0.67	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setunion__Cong)).
0.62/0.67	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', omega__Cong)).
0.62/0.67	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', subsetI1)).
0.62/0.67	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', eqimpsubset2)).
0.62/0.67	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', eqimpsubset1)).
0.62/0.67	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', subsetI2)).
0.62/0.67	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', emptysetsubset)).
0.62/0.67	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', subsetE)).
0.62/0.67	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', subsetE2)).
0.62/0.67	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', notsubsetI)).
0.62/0.67	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', notequalI1)).
0.62/0.67	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', notequalI2)).
0.62/0.67	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', subsetRefl)).
0.62/0.67	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', subsetTrans)).
0.62/0.67	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setadjoinSub)).
0.62/0.67	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setadjoinSub2)).
0.62/0.67	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', subset2powerset)).
0.62/0.67	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setextsub)).
0.62/0.67	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', subsetemptysetimpeq)).
0.62/0.67	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', powersetI1)).
0.62/0.67	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', powersetE1)).
0.62/0.67	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', inPowerset)).
0.62/0.67	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', powersetsubset)).
0.62/0.67	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binunionIL)).
0.62/0.67	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', upairset2IR)).
0.62/0.67	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binunionIR)).
0.62/0.67	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binunionEcases)).
0.62/0.67	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binunionE)).
0.62/0.67	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binunionLsub)).
0.62/0.67	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binunionRsub)).
0.62/0.67	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binintersectI)).
0.62/0.67	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binintersectSubset5)).
0.62/0.67	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binintersectEL)).
0.62/0.67	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binintersectLsub)).
0.62/0.67	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binintersectSubset2)).
0.62/0.67	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binintersectSubset3)).
0.62/0.67	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binintersectER)).
0.62/0.67	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', disjointsetsI1)).
0.62/0.67	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binintersectRsub)).
0.62/0.67	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binintersectSubset4)).
0.62/0.67	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', binintersectSubset1)).
0.62/0.67	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', bs114d)).
0.62/0.67	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setminusI)).
0.62/0.67	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setminusEL)).
0.62/0.67	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setminusER)).
0.62/0.67	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setminusSubset2)).
0.62/0.67	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setminusERneg)).
0.62/0.67	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setminusELneg)).
0.62/0.67	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setminusILneg)).
0.62/0.67	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setminusIRneg)).
0.62/0.67	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setminusLsub)).
0.62/0.67	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setminusSubset1)).
0.62/0.67	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', symdiffE)).
0.62/0.67	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', symdiffI1)).
0.62/0.67	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', symdiffI2)).
0.62/0.67	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', symdiffIneg1)).
0.62/0.67	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', symdiffIneg2)).
0.62/0.67	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', secondinupair)).
0.62/0.67	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setukpairIL)).
0.62/0.67	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setukpairIR)).
0.62/0.67	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', kpairiskpair)).
0.62/0.67	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', kpairp)).
0.62/0.67	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', singletonsubset)).
0.62/0.67	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', singletoninpowerset)).
0.62/0.67	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', singletoninpowunion)).
0.62/0.67	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', upairset2E)).
0.62/0.67	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', upairsubunion)).
0.62/0.67	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', upairinpowunion)).
0.62/0.67	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', ubforcartprodlem1)).
0.62/0.67	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', ubforcartprodlem2)).
0.62/0.67	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', ubforcartprodlem3)).
0.62/0.67	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', cartprodpairin)).
0.62/0.67	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', cartprodmempair1)).
0.62/0.67	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', cartprodmempair)).
0.62/0.67	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setunionE2)).
0.62/0.67	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setunionsingleton1)).
0.62/0.67	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setunionsingleton2)).
0.62/0.67	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setunionsingleton)).
0.62/0.67	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', singletonsuniq)).
0.62/0.67	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setukpairinjL1)).
0.62/0.67	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', kfstpairEq)).
0.62/0.67	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', cartprodfstin)).
0.62/0.67	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setukpairinjL2)).
0.62/0.67	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setukpairinjL)).
0.62/0.67	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setukpairinjR11)).
0.62/0.67	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setukpairinjR12)).
0.62/0.67	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setukpairinjR1)).
0.62/0.67	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', upairequniteq)).
0.62/0.67	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setukpairinjR2)).
0.62/0.67	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', setukpairinjR)).
0.62/0.67	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', ksndpairEq)).
0.62/0.67	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', kpairsurjEq)).
0.62/0.67	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', cartprodsndin)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', cartprodpairmemEL)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', cartprodpairmemER)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', cartprodmempaircEq)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', cartprodfstpairEq)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', cartprodsndpairEq)).
0.62/0.67	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', cartprodpairsurjEq)).
0.62/0.67	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', app)).
0.62/0.67	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', infuncsetfunc)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', ap2p)).
0.62/0.67	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', funcinfuncset)).
0.62/0.67	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', funcGraphProp1)).
0.62/0.67	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', funcGraphProp3)).
0.62/0.67	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.9vlwmE1uFM/E---3.1_11012.p', funcGraphProp2)).
0.62/0.67	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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', funcextLem)).
0.62/0.67	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.9vlwmE1uFM/E---3.1_11012.p', funcGraphProp4)).
0.62/0.67	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.9vlwmE1uFM/E---3.1_11012.p', funcext)).
0.62/0.67	thf(funcext2, axiom, ((funcext2)<=>![X4:$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.9vlwmE1uFM/E---3.1_11012.p', funcext2)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', ap2apEq1)).
0.62/0.67	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.9vlwmE1uFM/E---3.1_11012.p', ap2apEq2)).
0.62/0.67	thf(c_0_224, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X741:$i]:(((in @ X741 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X741 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
0.62/0.67	thf(c_0_225, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
0.62/0.67	thf(c_0_226, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
0.62/0.67	thf(c_0_227, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
0.62/0.67	thf(c_0_228, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
0.62/0.67	thf(c_0_229, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
0.62/0.67	thf(c_0_230, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
0.62/0.67	thf(c_0_231, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
0.62/0.67	thf(c_0_232, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
0.62/0.67	thf(c_0_233, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
0.62/0.67	thf(c_0_234, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
0.62/0.67	thf(c_0_235, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
0.62/0.67	thf(c_0_236, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
0.62/0.67	thf(c_0_237, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
0.62/0.67	thf(c_0_238, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
0.62/0.67	thf(c_0_239, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
0.62/0.67	thf(c_0_240, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
0.62/0.67	thf(c_0_241, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
0.62/0.67	thf(c_0_242, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
0.62/0.67	thf(c_0_243, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X741:$i]:(((in @ X741 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X741 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_224, c_0_225])).
0.62/0.67	thf(c_0_244, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
0.62/0.67	thf(c_0_245, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
0.62/0.67	thf(c_0_246, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
0.62/0.67	thf(c_0_247, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
0.62/0.67	thf(c_0_248, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
0.62/0.67	thf(c_0_249, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
0.62/0.67	thf(c_0_250, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
0.62/0.67	thf(c_0_251, plain, ((ex1E2)<=>![X4:$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])).
0.62/0.67	thf(c_0_252, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X712:$i]:((((X6 @ X2 @ X712))&![X713:$i]:((((X6 @ X2 @ X713))=>((X712)=(X713)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_227])).
0.62/0.67	thf(c_0_253, plain, ((descrp)=(![X1:$i > $o]:(((?[X714:$i]:((((X1 @ X714))&![X715:$i]:((((X1 @ X715))=>((X714)=(X715)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_227])).
0.62/0.67	thf(c_0_254, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
0.62/0.67	thf(c_0_255, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
0.62/0.67	thf(c_0_256, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
0.62/0.67	thf(c_0_257, plain, ((exuE1)=(![X1:$i > $o]:(((?[X716:$i]:((((X1 @ X716))&![X717:$i]:((((X1 @ X717))=>((X716)=(X717)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_229, c_0_227])).
0.62/0.67	thf(c_0_258, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X718:$i]:((((X1 @ X718))&![X719:$i]:((((X1 @ X719))=>((X718)=(X719)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_230, c_0_227])).
0.62/0.67	thf(c_0_259, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
0.62/0.67	thf(c_0_260, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_231])).
0.62/0.67	thf(c_0_261, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_231])).
0.62/0.67	thf(c_0_262, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_231])).
0.62/0.67	thf(c_0_263, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
0.62/0.67	thf(c_0_264, plain, ((exuE2)=(![X1:$i > $o]:(((?[X720:$i]:((((X1 @ X720))&![X721:$i]:((((X1 @ X721))=>((X720)=(X721)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_227])).
0.62/0.67	thf(c_0_265, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_231])).
0.62/0.67	thf(c_0_266, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
0.62/0.67	thf(c_0_267, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X722:$i]:((((X1 @ X722))&![X723:$i]:((((X1 @ X723))=>((X722)=(X723))))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_227])).
0.62/0.67	thf(c_0_268, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X724:$i]:((((X1 @ X724))&![X725:$i]:((((X1 @ X725))=>((X724)=(X725)))))))))))), inference(apply_def,[status(thm)],[c_0_235, c_0_227])).
0.62/0.67	thf(c_0_269, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X726:$i]:((((X1 @ X726))&![X727:$i]:((((X1 @ X727))=>((X726)=(X727))))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_227])).
0.62/0.67	thf(c_0_270, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X728:$i]:((((X1 @ X728))&![X729:$i]:((((X1 @ X729))=>((X728)=(X729)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_227])).
0.62/0.67	thf(c_0_271, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X730:$i]:((((X1 @ X730))&![X731:$i]:((((X1 @ X731))=>((X730)=(X731)))))))<=>(?[X732:$i]:((((X17 @ X732))&![X733:$i]:((((X17 @ X733))=>((X732)=(X733)))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_227])).
0.62/0.67	thf(c_0_272, plain, ((exuEu)=(![X1:$i > $o]:(((?[X734:$i]:((((X1 @ X734))&![X735:$i]:((((X1 @ X735))=>((X734)=(X735)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_227])).
0.62/0.67	thf(c_0_273, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X736:$i]:((((X1 @ X736))&![X737:$i]:((((X1 @ X737))=>((X736)=(X737)))))))=>((?[X738:$i]:((((X17 @ X738))&![X739:$i]:((((X17 @ X739))=>((X738)=(X739)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_227])).
0.62/0.67	thf(c_0_274, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
0.62/0.67	thf(c_0_275, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
0.62/0.67	thf(c_0_276, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
0.62/0.67	thf(c_0_277, 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)))=>(?[X740:$i]:(((in @ X740 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X740 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_225])).
0.62/0.67	thf(c_0_278, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X742:$i]:(((in @ X742 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X742 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_243])).
0.62/0.67	thf(c_0_279, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X743:$i]:(((in @ X743 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X743 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_243])).
0.62/0.67	thf(c_0_280, 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)))=>(?[X744:$i]:(((in @ X744 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X744 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_243])).
0.62/0.67	thf(c_0_281, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X745:$i]:(((in @ X745 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X745 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_225])).
0.62/0.67	thf(c_0_282, axiom, ((theprop)=(![X21:$i]:(((?[X746:$i]:(((in @ X746 @ X21)&((X21)=(setadjoin @ X746 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_225])).
0.62/0.67	thf(c_0_283, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X747:$i]:(((in @ X747 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X747 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_247, c_0_225])).
0.62/0.67	thf(c_0_284, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
0.62/0.67	thf(c_0_285, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
0.62/0.67	thf(c_0_286, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_248, c_0_249])).
0.62/0.67	thf(c_0_287, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
0.62/0.67	thf(c_0_288, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
0.62/0.67	thf(c_0_289, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
0.62/0.67	thf(c_0_290, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
0.62/0.67	thf(c_0_291, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(?[X748:$i]:(((in @ X748 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X748 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_250, c_0_225])).
0.62/0.67	thf(c_0_292, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
0.62/0.67	thf(c_0_293, plain, ((lamProp)<=>![X4:$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])).
0.62/0.67	thf(c_0_294, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
0.62/0.67	thf(c_0_295, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
0.62/0.67	thf(c_0_296, axiom, ((brelnall1)=(![X4:$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_249])).
0.62/0.67	thf(c_0_297, 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_249])).
0.62/0.67	thf(c_0_298, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((?[X749:$i]:(((in @ X749 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X749 @ emptyset)))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_251, c_0_243])).
0.62/0.67	thf(c_0_299, 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_249])).
0.62/0.67	thf(c_0_300, 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_249])).
0.62/0.67	thf(c_0_301, 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])).
0.62/0.67	thf(c_0_302, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
0.62/0.67	thf(c_0_303, 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])).
0.62/0.67	thf(c_0_304, 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])).
0.62/0.67	thf(c_0_305, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
0.62/0.67	thf(c_0_306, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
0.62/0.67	thf(c_0_307, plain, ((iffalseProp2)<=>![X4:$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])).
0.62/0.67	thf(c_0_308, plain, ((epred1_0)<=>![X766:$i]:(?[X767:$i]:((((![X768:$i]:(((in @ X768 @ X767)=>![X769:$i]:(((in @ X769 @ X768)=>(in @ X769 @ X766)))))&![X770:$i, X771:$i]:((((in @ X770 @ X766)&(in @ X771 @ X766))=>(![X772:$i]:(((in @ X772 @ X767)=>((in @ X770 @ X772)<=>(in @ X771 @ X772))))=>((X770)=(X771))))))&![X773:$i, X774:$i]:((((in @ X773 @ X767)&(in @ X774 @ X767))=>(![X775:$i]:(((in @ X775 @ X773)=>(in @ X775 @ X774)))|![X776:$i]:(((in @ X776 @ X774)=>(in @ X776 @ X773)))))))&![X777:$i]:(((![X778:$i]:(((in @ X778 @ X777)=>(in @ X778 @ X766)))&?[X779:$i]:((in @ X779 @ X777)))=>?[X780:$i, X781:$i]:(((((in @ X780 @ X767)&(in @ X781 @ X777))&~(?[X782:$i]:(((in @ X782 @ X780)&(in @ X782 @ X777)))))&![X783:$i]:(((in @ X783 @ X767)=>(![X784:$i]:(((in @ X784 @ X783)=>(in @ X784 @ X780)))|(in @ X781 @ X783)))))))))))), introduced(definition)).
0.62/0.67	thf(c_0_309, negated_conjecture, ~((![X1450:$i, X1451:$i]:((![X1452:$i]:(((in @ X1452 @ X1450)<=>(in @ X1452 @ X1451)))=>((X1450)=(X1451))))=>(![X750:$i]:(~(in @ X750 @ emptyset))=>(![X1447:$i, X1448:$i, X1449:$i]:(((in @ X1449 @ (setadjoin @ X1447 @ X1448))<=>(((X1449)=(X1447))|(in @ X1449 @ X1448))))=>(![X1444:$i, X1445:$i]:(((in @ X1445 @ (powerset @ X1444))<=>![X1446:$i]:(((in @ X1446 @ X1445)=>(in @ X1446 @ X1444)))))=>(![X1441:$i, X1442:$i]:(((in @ X1442 @ (setunion @ X1441))<=>?[X1443:$i]:(((in @ X1442 @ X1443)&(in @ X1443 @ X1441)))))=>((in @ emptyset @ omega)=>(![X1440:$i]:(((in @ X1440 @ omega)=>(in @ (setadjoin @ X1440 @ X1440) @ omega)))=>(![X751:$i]:((((in @ emptyset @ X751)&![X752:$i]:((((in @ X752 @ omega)&(in @ X752 @ X751))=>(in @ (setadjoin @ X752 @ X752) @ X751))))=>![X753:$i]:(((in @ X753 @ omega)=>(in @ X753 @ X751)))))=>(![X754:$i > $i > $o, X755:$i]:((![X756:$i]:(((in @ X756 @ X755)=>?[X757:$i]:(((X754 @ X756 @ X757)&![X758:$i]:(((X754 @ X756 @ X758)=>((X757)=(X758))))))))=>?[X759:$i]:(![X760:$i]:(((in @ X760 @ X759)<=>?[X761:$i]:(((in @ X761 @ X755)&(X754 @ X761 @ X760))))))))=>(![X762:$i]:((?[X763:$i]:((in @ X763 @ X762))=>?[X764:$i]:(((in @ X764 @ X762)&~(?[X765:$i]:(((in @ X765 @ X764)&(in @ X765 @ X762))))))))=>((epred1_0)=>(![X1437:$i > $o]:((?[X1438:$i]:(((X1437 @ X1438)&![X1439:$i]:(((X1437 @ X1439)=>((X1438)=(X1439))))))=>(X1437 @ (descr @ (^[Z0/* 17 */:$i]:(X1437 @ Z0))))))=>(![X785:$i, X786:$i > $o, X787:$i]:(((in @ X787 @ X785)=>((X786 @ X787)=>(in @ X787 @ (dsetconstr @ X785 @ X786)))))=>(![X1434:$i, X1435:$i > $o, X1436:$i]:(((in @ X1436 @ (dsetconstr @ X1434 @ X1435))=>(in @ X1436 @ X1434)))=>(![X1431:$i, X1432:$i > $o, X1433:$i]:(((in @ X1433 @ (dsetconstr @ X1431 @ X1432))=>(X1432 @ X1433)))=>(![X1426:$i > $o]:((?[X1427:$i]:(((X1426 @ X1427)&![X1428:$i]:(((X1426 @ X1428)=>((X1427)=(X1428))))))=>?[X1429:$i]:(((X1426 @ X1429)&![X1430:$i]:(((X1426 @ X1430)=>((X1429)=(X1430))))))))=>(![X1424:$o, X1425:$i]:(((in @ X1425 @ (prop2set @ ((X1424))))=>(X1424)))=>(![X1422:$i]:(((in @ X1422 @ emptyset)=>![X1423:$o]:((X1423))))=>(![X1421:$i]:(((in @ X1421 @ emptyset)=>~($true)))=>(![X1420:$i]:(~(in @ X1420 @ emptyset))=>(![X1416:$i > $o]:((?[X1417:$i]:(((X1416 @ X1417)&![X1418:$i]:(((X1416 @ X1418)=>((X1417)=(X1418))))))=>?[X1419:$i]:((X1416 @ X1419))))=>(![X1412:$i, X1413:$i]:((![X1414:$i]:(((in @ X1414 @ X1412)=>(in @ X1414 @ X1413)))=>(![X1415:$i]:(((in @ X1415 @ X1413)=>(in @ X1415 @ X1412)))=>((X1412)=(X1413)))))=>(![X1410:$i]:((![X1411:$i]:(~(in @ X1411 @ X1410))=>((X1410)=(emptyset))))=>(![X1408:$i]:((![X1409:$i]:(~(in @ X1409 @ X1408))=>((X1408)=(emptyset))))=>(![X1405:$i, X1406:$i > $o, X1407:$i]:(((in @ X1407 @ X1405)=>((in @ X1407 @ (dsetconstr @ X1405 @ X1406))<=>(X1406 @ X1407))))=>(![X788:$i]:((((X788)!=(emptyset))=>?[X789:$i]:((in @ X789 @ X788))))=>(![X1402:$i, X1403:$i > $o, X1404:$i]:(((in @ X1404 @ X1402)=>((X1403 @ X1404)=>((dsetconstr @ X1402 @ X1403)!=(emptyset)))))=>(![X790:$i]:((?[X791:$i]:((in @ X791 @ X790))=>((X790)!=(emptyset))))=>(![X1400:$i, X1401:$i]:((in @ X1400 @ (setadjoin @ X1400 @ X1401)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1397:$i, X1398:$i, X1399:$i]:(((in @ X1399 @ X1398)=>(in @ X1399 @ (setadjoin @ X1397 @ X1398))))=>(![X792:$i, X793:$i, X794:$i]:(((in @ X794 @ (setadjoin @ X792 @ X793))=>![X795:$o]:(((((X794)=(X792))=>(X795))=>(((in @ X794 @ X793)=>(X795))=>(X795))))))=>(![X796:$i, X797:$i, X798:$i]:(((in @ X798 @ (setadjoin @ X796 @ X797))=>(((X798)=(X796))|(in @ X798 @ X797))))=>(![X1396:$i]:(((dsetconstr @ X1396 @ (^[Z0/* 1 */:$i]:($true)))=(X1396)))=>(![X1393:$i, X1394:$i]:((![X1395:$i]:(((in @ X1395 @ X1394)=>(in @ X1395 @ X1393)))=>(in @ X1394 @ (powerset @ X1393))))=>(![X1392:$i]:((in @ emptyset @ (powerset @ X1392)))=>(![X799:$i]:((in @ emptyset @ (powerset @ X799)))=>(![X1389:$i, X1390:$i, X1391:$i]:(((in @ X1390 @ (powerset @ X1389))=>((in @ X1391 @ X1390)=>(in @ X1391 @ X1389))))=>(![X800:$i, X801:$i, X802:$i]:(((in @ X801 @ X802)=>((in @ X802 @ X800)=>(in @ X801 @ (setunion @ X800)))))=>(![X803:$i, X804:$i]:(((in @ X804 @ (setunion @ X803))=>![X805:$o]:((![X806:$i]:(((in @ X804 @ X806)=>((in @ X806 @ X803)=>(X805))))=>(X805)))))=>(![X1387:$i, X1388:$i]:(((in @ X1388 @ X1387)=>(in @ X1388 @ (powerset @ (setunion @ X1387)))))=>(![X1382:$i > $o]:((?[X1383:$i]:(((X1382 @ X1383)&![X1384:$i]:(((X1382 @ X1384)=>((X1383)=(X1384))))))=>?[X1385:$i]:(![X1386:$i]:(((X1382 @ X1386)<=>((X1386)=(X1385)))))))=>(![X807:$i]:((((X807)!=(emptyset))=>?[X808:$i]:(((in @ X808 @ X807)&$true))))=>(![X1380:$i, X1381:$i]:(((in @ X1380 @ (setadjoin @ X1381 @ emptyset))=>((X1380)=(X1381))))=>(![X809:$i, X810:$i]:((((X809)!=(X810))=>~(in @ X810 @ (setadjoin @ X809 @ emptyset))))=>(![X811:$i, X812:$i]:((((X811)=(X812))=>(in @ X811 @ (setadjoin @ X812 @ emptyset))))=>(![X1378:$i, X1379:$i]:(((in @ X1378 @ (setadjoin @ X1379 @ emptyset))=>(in @ X1379 @ (setadjoin @ X1378 @ emptyset))))=>(![X813:$i, X814:$i, X815:$i]:(((in @ X815 @ (setadjoin @ X813 @ (setadjoin @ X814 @ emptyset)))=>(((X815)=(X813))|((X815)=(X814)))))=>(![X1376:$i, X1377:$i]:((in @ X1376 @ (setadjoin @ X1376 @ (setadjoin @ X1377 @ emptyset))))=>(![X816:$i, X817:$i]:((in @ X817 @ (setadjoin @ X816 @ (setadjoin @ X817 @ emptyset))))=>(![X818:$i, X819:$i > $o]:((?[X820:$i]:(((in @ X820 @ X818)&(X819 @ X820)))=>(((dsetconstr @ X818 @ X819)=(emptyset))=>~($true))))=>(![X821:$i > $o, X822:$i]:(((in @ X822 @ emptyset)=>(X821 @ X822)))=>(![X823:$i, X824:$i > $o]:((~(![X825:$i]:(((in @ X825 @ X823)=>(X824 @ X825))))=>?[X826:$i]:(((in @ X826 @ X823)&~((X824 @ X826))))))=>(![X1372:$i, X1373:$i > $o]:((![X1374:$i]:(((in @ X1374 @ X1372)=>~((X1373 @ X1374))))=>~(?[X1375:$i]:(((in @ X1375 @ X1372)&(X1373 @ X1375))))))=>(![X827:$i, X828:$i > $o]:((~(?[X829:$i]:(((in @ X829 @ X827)&(X828 @ X829))))=>![X830:$i]:(((in @ X830 @ X827)=>~((X828 @ X830))))))=>(![X831:$i, X832:$i > $o]:((?[X833:$i]:(((in @ X833 @ X831)&~((X832 @ X833))))=>~(![X834:$i]:(((in @ X834 @ X831)=>(X832 @ X834))))))=>(![X835:$o]:(((X835)=>(in @ emptyset @ (prop2set @ ((X835))))))=>(![X1371:$o]:(((X1371)=>(set2prop @ (prop2set @ ((X1371))))))=>(![X1367:$i, X1368:$i > $o]:((~(?[X1369:$i]:(((in @ X1369 @ X1367)&(X1368 @ X1369))))=>![X1370:$i]:(((in @ X1370 @ X1367)=>~((X1368 @ X1370))))))=>(![X1363:$i, X1364:$i > $o]:((~(![X1365:$i]:(((in @ X1365 @ X1363)=>(X1364 @ X1365))))=>?[X1366:$i]:(((in @ X1366 @ X1363)&~((X1364 @ X1366))))))=>(![X836:$i > $o]:((?[X837:$i]:(((X836 @ X837)&![X838:$i]:(((X836 @ X838)=>((X837)=(X838))))))=>?[X839:$i]:(((X836 @ X839)&![X840:$i]:(((X836 @ X840)=>((X839)=(X840))))))))=>(![X841:$i > $o]:((?[X842:$i]:((X841 @ X842))=>(![X843:$i, X844:$i]:(((X841 @ X843)=>((X841 @ X844)=>((X843)=(X844)))))=>?[X845:$i]:(((X841 @ X845)&![X846:$i]:(((X841 @ X846)=>((X845)=(X846)))))))))=>(![X847:$i > $o]:((?[X848:$i]:(![X849:$i]:(((X847 @ X849)<=>((X849)=(X848)))))=>?[X850:$i]:(((X847 @ X850)&![X851:$i]:(((X847 @ X851)=>((X850)=(X851))))))))=>(![X1359:$i, X1360:$i]:((((X1359)=(X1360))=>![X1361:$i, X1362:$i]:((((X1361)=(X1362))=>((in @ X1361 @ X1359)=>(in @ X1362 @ X1360))))))=>(![X852:$i, X853:$i]:((((X852)=(X853))=>![X854:$i, X855:$i]:((((X854)=(X855))=>((in @ X854 @ X852)<=>(in @ X855 @ X853))))))=>(![X856:$i > $o]:((?[X857:$i]:(((X856 @ X857)&![X858:$i]:(((X856 @ X858)=>((X857)=(X858))))))=>![X859:$i, X860:$i]:(((X856 @ X859)=>((X856 @ X860)=>((X859)=(X860)))))))=>(![X1351:$i > $o, X1352:$i > $o]:((![X1353:$i, X1354:$i]:((((X1353)=(X1354))=>((X1351 @ X1353)<=>(X1352 @ X1354))))=>(?[X1355:$i]:(((X1351 @ X1355)&![X1356:$i]:(((X1351 @ X1356)=>((X1355)=(X1356))))))<=>?[X1357:$i]:(((X1352 @ X1357)&![X1358:$i]:(((X1352 @ X1358)=>((X1357)=(X1358)))))))))=>(((emptyset)=(emptyset))=>(![X861:$i, X862:$i]:((((X861)=(X862))=>![X863:$i, X864:$i]:((((X863)=(X864))=>((setadjoin @ X861 @ X863)=(setadjoin @ X862 @ X864))))))=>(![X1349:$i, X1350:$i]:((((X1349)=(X1350))=>((powerset @ X1349)=(powerset @ X1350))))=>(![X865:$i, X866:$i]:((((X865)=(X866))=>((setunion @ X865)=(setunion @ X866))))=>(((omega)=(omega))=>(![X1344:$i > $o]:((?[X1345:$i]:(((X1344 @ X1345)&![X1346:$i]:(((X1344 @ X1346)=>((X1345)=(X1346))))))=>![X1347:$i, X1348:$i]:(((X1344 @ X1347)=>((X1344 @ X1348)=>((X1347)=(X1348)))))))=>(![X867:$i > $o, X868:$i > $o]:((![X869:$i, X870:$i]:((((X869)=(X870))=>((X867 @ X869)<=>(X868 @ X870))))=>(?[X871:$i]:(((X867 @ X871)&![X872:$i]:(((X867 @ X872)=>((X871)=(X872))))))=>(?[X873:$i]:(((X868 @ X873)&![X874:$i]:(((X868 @ X874)=>((X873)=(X874))))))=>((descr @ X867)=(descr @ X868))))))=>(![X875:$i, X876:$i]:((((X875)=(X876))=>![X877:$i > $o, X878:$i > $o]:((![X879:$i]:(((in @ X879 @ X875)=>![X880:$i]:(((in @ X880 @ X876)=>(((X879)=(X880))=>((X877 @ X879)<=>(X878 @ X880)))))))=>((dsetconstr @ X875 @ X877)=(dsetconstr @ X876 @ X878))))))=>(![X881:$i, X882:$i]:((![X883:$i]:(((in @ X883 @ X881)=>(in @ X883 @ X882)))=>(subset @ X881 @ X882)))=>(![X884:$i, X885:$i]:((((X884)=(X885))=>(subset @ X885 @ X884)))=>(![X1342:$i, X1343:$i]:((((X1342)=(X1343))=>(subset @ X1342 @ X1343)))=>(![X1339:$i, X1340:$i]:((![X1341:$i]:(((in @ X1341 @ X1339)=>(in @ X1341 @ X1340)))=>(subset @ X1339 @ X1340)))=>(![X1338:$i]:((subset @ emptyset @ X1338))=>(![X886:$i, X887:$i, X888:$i]:(((subset @ X886 @ X887)=>((in @ X888 @ X886)=>(in @ X888 @ X887))))=>(![X1335:$i, X1336:$i, X1337:$i]:(((subset @ X1335 @ X1336)=>(~(in @ X1337 @ X1336)=>~(in @ X1337 @ X1335))))=>(![X889:$i, X890:$i, X891:$i]:(((in @ X891 @ X889)=>(~(in @ X891 @ X890)=>~(subset @ X889 @ X890))))=>(![X1333:$i, X1334:$i]:((~(subset @ X1333 @ X1334)=>((X1333)!=(X1334))))=>(![X892:$i, X893:$i, X894:$i]:(((in @ X894 @ X892)=>(~(in @ X894 @ X893)=>((X892)!=(X893)))))=>(![X1332:$i]:((subset @ X1332 @ X1332))=>(![X1329:$i, X1330:$i, X1331:$i]:(((subset @ X1329 @ X1330)=>((subset @ X1330 @ X1331)=>(subset @ X1329 @ X1331))))=>(![X1327:$i, X1328:$i]:((subset @ X1328 @ (setadjoin @ X1327 @ X1328)))=>(![X1324:$i, X1325:$i, X1326:$i]:(((subset @ X1324 @ X1326)=>(subset @ X1324 @ (setadjoin @ X1325 @ X1326))))=>(![X1322:$i, X1323:$i]:(((subset @ X1322 @ X1323)=>(in @ X1322 @ (powerset @ X1323))))=>(![X1320:$i, X1321:$i]:(((subset @ X1320 @ X1321)=>((subset @ X1321 @ X1320)=>((X1320)=(X1321)))))=>(![X895:$i]:(((subset @ X895 @ emptyset)=>((X895)=(emptyset))))=>(![X1318:$i, X1319:$i]:(((subset @ X1319 @ X1318)=>(in @ X1319 @ (powerset @ X1318))))=>(![X896:$i, X897:$i]:(((in @ X897 @ (powerset @ X896))=>(subset @ X897 @ X896)))=>(![X898:$i]:((in @ X898 @ (powerset @ X898)))=>(![X899:$i, X900:$i]:(((subset @ X899 @ X900)=>(subset @ (powerset @ X899) @ (powerset @ X900))))=>(![X901:$i, X902:$i > $o]:((in @ (dsetconstr @ X901 @ X902) @ (powerset @ X901)))=>(![X903:$i, X904:$i > $o]:((subset @ (dsetconstr @ X903 @ X904) @ X903))=>(![X905:$i, X906:$i, X907:$i]:(((in @ X907 @ X905)=>(in @ X907 @ (binunion @ X905 @ X906))))=>(![X908:$i, X909:$i]:((in @ X909 @ (setadjoin @ X908 @ (setadjoin @ X909 @ emptyset))))=>(![X910:$i, X911:$i, X912:$i]:(((in @ X912 @ X911)=>(in @ X912 @ (binunion @ X910 @ X911))))=>(![X1314:$i, X1315:$i, X1316:$i, X1317:$o]:(((in @ X1316 @ (binunion @ X1314 @ X1315))=>(((in @ X1316 @ X1314)=>(X1317))=>(((in @ X1316 @ X1315)=>(X1317))=>(X1317)))))=>(![X913:$i, X914:$i, X915:$i]:(((in @ X915 @ (binunion @ X913 @ X914))=>((in @ X915 @ X913)|(in @ X915 @ X914))))=>(![X1312:$i, X1313:$i]:((subset @ X1312 @ (binunion @ X1312 @ X1313)))=>(![X916:$i, X917:$i]:((subset @ X917 @ (binunion @ X916 @ X917)))=>(![X1309:$i, X1310:$i, X1311:$i]:(((in @ X1311 @ X1309)=>((in @ X1311 @ X1310)=>(in @ X1311 @ (binintersect @ X1309 @ X1310)))))=>(![X918:$i, X919:$i, X920:$i]:(((subset @ X920 @ X918)=>((subset @ X920 @ X919)=>(subset @ X920 @ (binintersect @ X918 @ X919)))))=>(![X1306:$i, X1307:$i, X1308:$i]:(((in @ X1308 @ (binintersect @ X1306 @ X1307))=>(in @ X1308 @ X1306)))=>(![X921:$i, X922:$i]:((subset @ (binintersect @ X921 @ X922) @ X921))=>(![X923:$i, X924:$i]:(((subset @ X923 @ X924)=>((binintersect @ X923 @ X924)=(X923))))=>(![X1304:$i, X1305:$i]:((((binintersect @ X1304 @ X1305)=(X1305))=>(subset @ X1305 @ X1304)))=>(![X1301:$i, X1302:$i, X1303:$i]:(((in @ X1303 @ (binintersect @ X1301 @ X1302))=>(in @ X1303 @ X1302)))=>(![X1298:$i, X1299:$i]:((~(?[X1300:$i]:(((in @ X1300 @ X1298)&(in @ X1300 @ X1299))))=>((binintersect @ X1298 @ X1299)=(emptyset))))=>(![X1296:$i, X1297:$i]:((subset @ (binintersect @ X1296 @ X1297) @ X1297))=>(![X925:$i, X926:$i]:(((subset @ X926 @ X925)=>((binintersect @ X925 @ X926)=(X926))))=>(![X1294:$i, X1295:$i]:((((binintersect @ X1294 @ X1295)=(X1294))=>(subset @ X1294 @ X1295)))=>(![X927:$i, X928:$i, X929:$i]:(((binintersect @ X927 @ (binunion @ X928 @ X929))=(binunion @ (binintersect @ X927 @ X928) @ (binintersect @ X927 @ X929))))=>(![X1291:$i, X1292:$i, X1293:$i]:(((in @ X1293 @ X1291)=>(~(in @ X1293 @ X1292)=>(in @ X1293 @ (setminus @ X1291 @ X1292)))))=>(![X930:$i, X931:$i, X932:$i]:(((in @ X932 @ (setminus @ X930 @ X931))=>(in @ X932 @ X930)))=>(![X933:$i, X934:$i, X935:$i]:(((in @ X935 @ (setminus @ X933 @ X934))=>~(in @ X935 @ X934)))=>(![X936:$i, X937:$i]:(((subset @ X936 @ X937)=>((setminus @ X936 @ X937)=(emptyset))))=>(![X938:$i, X939:$i, X940:$i]:((~(in @ X940 @ (setminus @ X938 @ X939))=>((in @ X940 @ X938)=>(in @ X940 @ X939))))=>(![X941:$i, X942:$i, X943:$i]:((~(in @ X943 @ (setminus @ X941 @ X942))=>(~(in @ X943 @ X942)=>~(in @ X943 @ X941))))=>(![X1288:$i, X1289:$i, X1290:$i]:((~(in @ X1290 @ X1288)=>~(in @ X1290 @ (setminus @ X1288 @ X1289))))=>(![X944:$i, X945:$i, X946:$i]:(((in @ X946 @ X945)=>~(in @ X946 @ (setminus @ X944 @ X945))))=>(![X947:$i, X948:$i]:((subset @ (setminus @ X947 @ X948) @ X947))=>(![X949:$i, X950:$i]:((((setminus @ X949 @ X950)=(emptyset))=>(subset @ X949 @ X950)))=>(![X951:$i, X952:$i, X953:$i]:(((in @ X953 @ (symdiff @ X951 @ X952))=>![X954:$o]:((((in @ X953 @ X951)=>(~(in @ X953 @ X952)=>(X954)))=>((~(in @ X953 @ 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X1123))))=>(![X1136:$i, X1137:$i, X1138:$i > $i]:((![X1139:$i]:(((in @ X1139 @ X1136)=>(in @ (X1138 @ X1139) @ X1137)))=>![X1140:$i]:(((in @ X1140 @ X1136)=>((ap @ X1136 @ X1137 @ (lam @ X1136 @ X1137 @ X1138) @ X1140)=(X1138 @ X1140))))))=>(![X1133:$i, X1134:$i, X1135:$i]:(((in @ X1135 @ (funcSet @ X1133 @ X1134))=>((lam @ X1133 @ X1134 @ (ap @ X1133 @ X1134 @ X1135))=(X1135))))=>(![X1129:$i, X1130:$o, X1131:$i]:(((in @ X1131 @ X1129)=>![X1132:$i]:(((in @ X1132 @ X1129)=>(~(X1130)=>(in @ X1132 @ (dsetconstr @ X1129 @ (^[Z0/* 9 */:$i]:((((X1130)&((Z0)=(X1131)))|(~((X1130))&((Z0)=(X1132)))))))))))))=>(![X1125:$i, X1126:$o, X1127:$i]:(((in @ X1127 @ X1125)=>![X1128:$i]:(((in @ X1128 @ X1125)=>(~(X1126)=>((dsetconstr @ X1125 @ (^[Z0/* 9 */:$i]:((((X1126)&((Z0)=(X1127)))|(~((X1126))&((Z0)=(X1128)))))))=(setadjoin @ X1128 @ emptyset)))))))=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:(((((Z0)=(X2))&(X41))|(((Z0)=(X3))&~((X41)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[iftrueProp1])]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_252]), foundationAx]), wellorderingAx]), c_0_253]), c_0_254]), c_0_255]), c_0_256]), c_0_257]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_258]), setext]), emptyI]), noeltsimpempty]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_263]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_264]), c_0_265]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_266]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_267]), c_0_268]), c_0_269]), inCongP]), in__Cong]), c_0_270]), c_0_271]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_272]), c_0_273]), c_0_274]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_275]), c_0_276]), 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_277]), c_0_278]), c_0_279]), c_0_280]), singletonsuniq]), setukpairinjL1]), c_0_281]), c_0_282]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_283]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), c_0_292]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), c_0_297]), c_0_298]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_299]), c_0_300]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), c_0_306]), c_0_307])])]), c_0_308])).
0.62/0.67	thf(c_0_310, negated_conjecture, ![X1453:$i, X1454:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1466:$i, X1467:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1475:$i, X1476:$i > $i > $o, X1477:$i, X1479:$i, X1482:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1489:$i, X1490:$i > $o, X1491:$i, X1493:$i, X1494:$i > $o, X1495:$i, X1496:$i, X1497:$i > $o, X1498:$i, X1499:$i, X1500:$i > $o, X1501:$i, X1502:$i > $o, X1503:$i, X1506:$i, X1507:$o, X1508:$i, X1509:$i, X1510:$o, X1511:$i, X1512:$i, X1513:$i > $o, X1514:$i, X1517:$i, X1518:$i, X1521:$i, X1523:$i, X1525:$i, X1526:$i > $o, X1527:$i, X1528:$i, X1530:$i, X1531:$i > $o, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$o, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$o, X1563:$i, X1564:$i, X1565:$i > $o, X1566:$i, X1569:$i, X1570:$i, X1571:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i > $o, X1590:$i, X1591:$i > $o, X1592:$i, X1593:$i, X1594:$i > $o, X1595:$i, X1597:$i, X1598:$i > $o, X1600:$i, X1601:$i, X1602:$i > $o, X1604:$i, X1605:$i, X1606:$i > $o, X1607:$i, X1609:$o, X1610:$o, X1611:$i, X1612:$i > $o, X1614:$i, X1615:$i, X1616:$i > $o, X1617:$i, X1619:$i > $o, X1620:$i, X1623:$i, X1624:$i > $o, X1625:$i, X1629:$i, X1630:$i > $o, X1631:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i > $o, X1644:$i, X1646:$i, X1647:$i, X1648:$i > $o, X1649:$i > $o, X1652:$i, X1655:$i, X1656:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i > $o, X1669:$i, X1671:$i, X1672:$i, X1673:$i > $o, X1674:$i > $o, X1677:$i, X1679:$i, X1681:$i, X1682:$i, X1683:$i > $o, X1684:$i > $o, X1687:$i, X1688:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i > $o, X1735:$i, X1736:$i > $o, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$o, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$o, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i > $o, X1891:$i, X1893:$i, X1894:$i > $o, X1895:$i, X1897:$i, X1898:$i > $o, X1899:$i, X1902:$i, X1903:$i > $o, X1906:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$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:$i, X1951:$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:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i > $i > $o, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i > $i > $o, X1988:$i, X1989:$i, X1990:$i > $i > $o, X1991:$i, X1992:$i, X1993:$i > $i > $o, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i > $i > $o, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i > $i > $o, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i > $i > $o, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2016:$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 > $i, X2038:$i, X2039:$i, X2040:$i > $i, X2042:$i, X2043:$i, X2044:$i > $i, X2046:$i, X2047:$i, X2048:$i, X2049:$i > $o, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i > $o, X2059:$i, X2060:$i, X2061:$i > $o, X2062:$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:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i > $i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i > $i, X2134:$i, X2135:$i, X2136:$i > $i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$o, X2144:$i, X2145:$i, X2146:$i, X2147:$o, X2148:$i, X2149:$i]:((((~(in @ (esk1_2 @ X1453 @ X1454) @ X1453)|~(in @ (esk1_2 @ X1453 @ X1454) @ X1454)|((X1453)=(X1454)))&((in @ (esk1_2 @ X1453 @ X1454) @ X1453)|(in @ (esk1_2 @ X1453 @ X1454) @ X1454)|((X1453)=(X1454))))&(~(in @ X1456 @ emptyset)&(((~(in @ X1459 @ (setadjoin @ X1457 @ X1458))|(((X1459)=(X1457))|(in @ X1459 @ X1458)))&((((X1459)!=(X1457))|(in @ X1459 @ (setadjoin @ X1457 @ X1458)))&(~(in @ X1459 @ X1458)|(in @ X1459 @ (setadjoin @ X1457 @ X1458)))))&(((~(in @ X1461 @ (powerset @ X1460))|(~(in @ X1462 @ X1461)|(in @ X1462 @ X1460)))&(((in @ (esk2_2 @ X1463 @ 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(cartprod @ X2046 @ X2047)))&(((in @ (kpair @ (esk73_4 @ X2046 @ X2047 @ X2048 @ X2049) @ (esk74_4 @ X2046 @ X2047 @ X2048 @ X2049)) @ X2048)|(~(in @ X2052 @ X2048)|(X2049 @ X2052))|~(subset @ X2048 @ (cartprod @ X2046 @ X2047)))&(~(X2049 @ (kpair @ (esk73_4 @ X2046 @ X2047 @ X2048 @ X2049) @ (esk74_4 @ X2046 @ X2047 @ X2048 @ X2049)))|(~(in @ X2052 @ X2048)|(X2049 @ X2052))|~(subset @ X2048 @ (cartprod @ X2046 @ X2047))))))&((((in @ (esk75_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2053)|(~(in @ X2059 @ X2055)|(X2056 @ X2059))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (esk76_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2054)|(~(in @ X2059 @ X2055)|(X2056 @ X2059))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (kpair @ (esk75_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk76_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2055)|(~(in @ X2059 @ X2055)|(X2056 @ X2059))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(~(X2056 @ (kpair @ (esk75_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk76_4 @ X2053 @ X2054 @ X2055 @ X2056)))|(~(in @ X2059 @ X2055)|(X2056 @ X2059))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054))))))&((~(in @ X2062 @ (dsetconstr @ X2060 @ X2061))|((dsetconstr @ X2060 @ X2061)!=(setadjoin @ X2062 @ emptyset))|(~(in @ X2063 @ X2060)|(~(in @ X2064 @ X2060)|(~(X2061 @ X2063)|(~(X2061 @ X2064)|((X2063)=(X2064)))))))&((~(func @ X2065 @ X2066 @ X2067)|(~(in @ X2068 @ X2065)|(in @ (kpair @ X2068 @ (ap @ X2065 @ X2066 @ X2067 @ X2068)) @ X2067)))&((~(in @ X2071 @ (funcSet @ X2069 @ X2070))|(~(in @ X2072 @ X2069)|(in @ (kpair @ X2072 @ (ap @ X2069 @ X2070 @ X2071 @ X2072)) @ X2071)))&((~(func @ X2073 @ X2074 @ X2075)|(~(in @ X2076 @ X2073)|(~(in @ X2077 @ X2074)|(~(in @ (kpair @ X2076 @ X2077) @ X2075)|((ap @ X2073 @ X2074 @ X2075 @ X2076)=(X2077))))))&((((in @ (esk77_4 @ X2078 @ X2079 @ X2080 @ X2081) @ X2078)|(~(in @ X2083 @ X2078)|(~(in @ X2084 @ X2079)|(~(in @ (kpair @ X2083 @ X2084) @ X2081)|(in @ (kpair @ X2083 @ X2084) @ X2080))))|~(func @ X2078 @ X2079 @ X2081)|~(func @ X2078 @ X2079 @ X2080))&(((ap @ X2078 @ X2079 @ X2080 @ (esk77_4 @ X2078 @ X2079 @ X2080 @ X2081))!=(ap @ X2078 @ X2079 @ X2081 @ (esk77_4 @ X2078 @ X2079 @ X2080 @ X2081)))|(~(in @ X2083 @ X2078)|(~(in @ X2084 @ X2079)|(~(in @ (kpair @ X2083 @ X2084) @ X2081)|(in @ (kpair @ X2083 @ X2084) @ X2080))))|~(func @ X2078 @ X2079 @ X2081)|~(func @ X2078 @ X2079 @ X2080)))&((~(in @ X2087 @ (funcSet @ X2085 @ X2086))|(~(in @ X2088 @ X2085)|(~(in @ X2089 @ X2086)|(~(in @ (kpair @ X2088 @ X2089) @ X2087)|((ap @ X2085 @ X2086 @ X2087 @ X2088)=(X2089))))))&((((in @ (esk78_4 @ X2090 @ X2091 @ X2092 @ X2093) @ X2090)|(subset @ X2092 @ X2093)|~(subset @ X2093 @ (cartprod @ X2090 @ X2091))|~(subset @ X2092 @ (cartprod @ X2090 @ X2091)))&(((in @ (esk79_4 @ X2090 @ X2091 @ X2092 @ X2093) @ X2091)|(subset @ X2092 @ X2093)|~(subset @ X2093 @ (cartprod @ X2090 @ X2091))|~(subset @ X2092 @ (cartprod @ X2090 @ X2091)))&(((in @ (kpair @ (esk78_4 @ X2090 @ X2091 @ X2092 @ X2093) @ (esk79_4 @ X2090 @ X2091 @ X2092 @ X2093)) @ X2092)|(subset @ X2092 @ X2093)|~(subset @ X2093 @ (cartprod @ X2090 @ X2091))|~(subset @ X2092 @ (cartprod @ X2090 @ X2091)))&(~(in @ (kpair @ (esk78_4 @ X2090 @ X2091 @ X2092 @ X2093) @ (esk79_4 @ X2090 @ X2091 @ X2092 @ X2093)) @ X2093)|(subset @ X2092 @ X2093)|~(subset @ X2093 @ (cartprod @ X2090 @ X2091))|~(subset @ X2092 @ (cartprod @ X2090 @ X2091))))))&(((((in @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|((X2098)=(X2099))|(in @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|((X2098)=(X2099))|(in @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|((X2098)=(X2099))|(in @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(~(in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|((X2098)=(X2099))|(in @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097))))))&((((in @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|((X2098)=(X2099))|(in @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|((X2098)=(X2099))|(in @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|((X2098)=(X2099))|(in @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(~(in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|((X2098)=(X2099))|(in @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097))))))&((((in @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|((X2098)=(X2099))|(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|((X2098)=(X2099))|(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|((X2098)=(X2099))|(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(~(in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|((X2098)=(X2099))|(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097))))))&(((in @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2096)|((X2098)=(X2099))|~(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099) @ X2097)|((X2098)=(X2099))|~(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(((in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|((X2098)=(X2099))|~(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))&(~(in @ (kpair @ (esk82_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk83_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2098)|((X2098)=(X2099))|~(in @ (kpair @ (esk80_4 @ X2096 @ X2097 @ X2098 @ X2099) @ (esk81_4 @ X2096 @ X2097 @ X2098 @ X2099)) @ X2099)|~(subset @ X2099 @ (cartprod @ X2096 @ X2097))|~(subset @ X2098 @ (cartprod @ X2096 @ X2097)))))))))&((((in @ (esk84_4 @ X2104 @ X2105 @ X2106 @ X2107) @ X2104)|((X2106)=(X2107))|~(func @ X2104 @ X2105 @ X2107)|~(func @ X2104 @ X2105 @ X2106))&(((ap @ X2104 @ X2105 @ X2106 @ (esk84_4 @ X2104 @ X2105 @ X2106 @ X2107))!=(ap @ X2104 @ X2105 @ X2107 @ (esk84_4 @ X2104 @ X2105 @ X2106 @ X2107)))|((X2106)=(X2107))|~(func @ X2104 @ X2105 @ X2107)|~(func @ X2104 @ X2105 @ X2106)))&((((in @ (esk85_4 @ X2109 @ X2110 @ X2111 @ X2112) @ X2109)|((X2111)=(X2112))|~(in @ X2112 @ (funcSet @ X2109 @ X2110))|~(in @ X2111 @ (funcSet @ X2109 @ X2110)))&(((ap @ X2109 @ X2110 @ X2111 @ (esk85_4 @ X2109 @ X2110 @ X2111 @ X2112))!=(ap @ X2109 @ X2110 @ X2112 @ (esk85_4 @ X2109 @ X2110 @ X2111 @ X2112)))|((X2111)=(X2112))|~(in @ X2112 @ (funcSet @ X2109 @ X2110))|~(in @ X2111 @ (funcSet @ X2109 @ X2110))))&((~(in @ X2116 @ (funcSet @ X2114 @ X2115))|(~(in @ X2117 @ X2114)|((ap @ X2114 @ X2115 @ X2116 @ X2117)=(ap @ X2114 @ X2115 @ X2116 @ X2117))))&((~(func @ X2118 @ X2119 @ X2120)|(~(in @ X2121 @ X2118)|((ap @ X2118 @ X2119 @ X2120 @ X2121)=(ap @ X2118 @ X2119 @ X2120 @ X2121))))&((((in @ (esk86_3 @ X2122 @ X2123 @ X2124) @ X2122)|(~(in @ X2126 @ X2122)|((ap @ X2122 @ X2123 @ (lam @ X2122 @ X2123 @ X2124) @ X2126)=(X2124 @ X2126))))&(~(in @ (X2124 @ (esk86_3 @ X2122 @ X2123 @ X2124)) @ X2123)|(~(in @ X2126 @ X2122)|((ap @ X2122 @ X2123 @ (lam @ X2122 @ X2123 @ X2124) @ X2126)=(X2124 @ X2126)))))&((~(func @ X2127 @ X2128 @ X2129)|((lam @ X2127 @ X2128 @ (ap @ X2127 @ X2128 @ X2129))=(X2129)))&((((in @ (esk87_3 @ X2130 @ X2131 @ X2132) @ X2130)|((lam @ X2130 @ X2131 @ X2132)=(lam @ X2130 @ X2131 @ X2132)))&(~(in @ (X2132 @ (esk87_3 @ X2130 @ X2131 @ X2132)) @ X2131)|((lam @ X2130 @ X2131 @ X2132)=(lam @ X2130 @ X2131 @ X2132))))&((((in @ (esk88_3 @ X2134 @ X2135 @ X2136) @ X2134)|(~(in @ X2138 @ X2134)|((ap @ X2134 @ X2135 @ (lam @ X2134 @ X2135 @ X2136) @ X2138)=(X2136 @ X2138))))&(~(in @ (X2136 @ (esk88_3 @ X2134 @ X2135 @ X2136)) @ X2135)|(~(in @ X2138 @ X2134)|((ap @ X2134 @ X2135 @ (lam @ X2134 @ X2135 @ X2136) @ X2138)=(X2136 @ X2138)))))&((~(in @ X2141 @ (funcSet @ X2139 @ X2140))|((lam @ X2139 @ X2140 @ (ap @ X2139 @ X2140 @ X2141))=(X2141)))&((~(in @ X2144 @ X2142)|(~(in @ X2145 @ X2142)|((X2143)|(in @ X2145 @ (dsetconstr @ X2142 @ (^[Z0/* 9 */:$i]:((((X2143)&((Z0)=(X2144)))|(~((X2143))&((Z0)=(X2145)))))))))))&((~(in @ X2148 @ X2146)|(~(in @ X2149 @ X2146)|((X2147)|((dsetconstr @ X2146 @ (^[Z0/* 9 */:$i]:((((X2147)&((Z0)=(X2148)))|(~((X2147))&((Z0)=(X2149)))))))=(setadjoin @ X2149 @ emptyset)))))&((in @ esk90_0 @ esk89_0)&((in @ esk91_0 @ esk89_0)&((epred2_0)&~(in @ esk90_0 @ (dsetconstr @ esk89_0 @ (^[Z0/* 9 */:$i]:(((((Z0)=(esk90_0))&(epred2_0))|(((Z0)=(esk91_0))&~((epred2_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_309])])])])])])])).
0.62/0.67	thf(c_0_311, plain, ![X2173:$i]:(((epred3_0 @ X2173)<=>((((X2173)=(esk90_0))&(epred2_0))|(((X2173)=(esk91_0))&~((epred2_0)))))), introduced(definition)).
0.62/0.67	thf(c_0_312, plain, ![X2186:$i]:(((((((X2186)=(esk91_0))|((X2186)=(esk90_0))|~(epred3_0 @ X2186))&(~(epred2_0)|((X2186)=(esk90_0))|~(epred3_0 @ X2186)))&((((X2186)=(esk91_0))|(epred2_0)|~(epred3_0 @ X2186))&(~(epred2_0)|(epred2_0)|~(epred3_0 @ X2186))))&((((X2186)!=(esk90_0))|~(epred2_0)|(epred3_0 @ X2186))&(((X2186)!=(esk91_0))|(epred2_0)|(epred3_0 @ X2186))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])])).
0.62/0.67	thf(c_0_313, negated_conjecture, ~((((in @ esk90_0 @ (dsetconstr @ esk89_0 @ epred3_0)))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_310]), c_0_311])).
0.62/0.67	thf(c_0_314, plain, ![X2:$i]:(((epred3_0 @ X2)|((X2)!=(esk90_0))|~((epred2_0)))), inference(split_conjunct,[status(thm)],[c_0_312])).
0.62/0.67	thf(c_0_315, negated_conjecture, (epred2_0), inference(split_conjunct,[status(thm)],[c_0_310])).
0.62/0.67	thf(c_0_316, negated_conjecture, ~((in @ esk90_0 @ (dsetconstr @ esk89_0 @ epred3_0))), inference(cn,[status(thm)],[c_0_313])).
0.62/0.67	thf(c_0_317, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_310])).
0.62/0.67	thf(c_0_318, negated_conjecture, (in @ esk90_0 @ esk89_0), inference(split_conjunct,[status(thm)],[c_0_310])).
0.62/0.67	thf(c_0_319, plain, (epred3_0 @ esk90_0), inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_314, c_0_315])])])).
0.62/0.67	thf(c_0_320, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316, c_0_317]), c_0_318]), c_0_319])]), ['proof']).
0.62/0.67	# SZS output end CNFRefutation
0.62/0.67	# Parsed axioms                        : 479
0.62/0.67	# Removed by relevancy pruning/SinE    : 0
0.62/0.67	# Initial clauses                      : 683
0.62/0.67	# Removed in clause preprocessing      : 291
0.62/0.67	# Initial clauses in saturation        : 392
0.62/0.67	# Processed clauses                    : 647
0.62/0.67	# ...of these trivial                  : 14
0.62/0.67	# ...subsumed                          : 66
0.62/0.67	# ...remaining for further processing  : 567
0.62/0.67	# Other redundant clauses eliminated   : 27
0.62/0.67	# Clauses deleted for lack of memory   : 0
0.62/0.67	# Backward-subsumed                    : 0
0.62/0.67	# Backward-rewritten                   : 5
0.62/0.67	# Generated clauses                    : 1377
0.62/0.67	# ...of the previous two non-redundant : 1243
0.62/0.67	# ...aggressively subsumed             : 0
0.62/0.67	# Contextual simplify-reflections      : 1
0.62/0.67	# Paramodulations                      : 1324
0.62/0.67	# Factorizations                       : 0
0.62/0.67	# NegExts                              : 10
0.62/0.67	# Equation resolutions                 : 30
0.62/0.67	# Disequality decompositions           : 0
0.62/0.67	# Total rewrite steps                  : 161
0.62/0.67	# ...of those cached                   : 103
0.62/0.67	# Propositional unsat checks           : 0
0.62/0.67	#    Propositional check models        : 0
0.62/0.67	#    Propositional check unsatisfiable : 0
0.62/0.67	#    Propositional clauses             : 0
0.62/0.67	#    Propositional clauses after purity: 0
0.62/0.67	#    Propositional unsat core size     : 0
0.62/0.67	#    Propositional preprocessing time  : 0.000
0.62/0.67	#    Propositional encoding time       : 0.000
0.62/0.67	#    Propositional solver time         : 0.000
0.62/0.67	#    Success case prop preproc time    : 0.000
0.62/0.67	#    Success case prop encoding time   : 0.000
0.62/0.67	#    Success case prop solver time     : 0.000
0.62/0.67	# Current number of processed clauses  : 200
0.62/0.67	#    Positive orientable unit clauses  : 52
0.62/0.67	#    Positive unorientable unit clauses: 0
0.62/0.67	#    Negative unit clauses             : 4
0.62/0.67	#    Non-unit-clauses                  : 144
0.62/0.67	# Current number of unprocessed clauses: 1325
0.62/0.67	# ...number of literals in the above   : 3603
0.62/0.67	# Current number of archived formulas  : 0
0.62/0.67	# Current number of archived clauses   : 351
0.62/0.67	# Clause-clause subsumption calls (NU) : 20233
0.62/0.67	# Rec. Clause-clause subsumption calls : 7788
0.62/0.67	# Non-unit clause-clause subsumptions  : 42
0.62/0.67	# Unit Clause-clause subsumption calls : 182
0.62/0.67	# Rewrite failures with RHS unbound    : 0
0.62/0.67	# BW rewrite match attempts            : 27
0.62/0.67	# BW rewrite match successes           : 3
0.62/0.67	# Condensation attempts                : 0
0.62/0.67	# Condensation successes               : 0
0.62/0.67	# Termbank termtop insertions          : 88501
0.62/0.67	# Search garbage collected termcells   : 23281
0.62/0.67	
0.62/0.67	# -------------------------------------------------
0.62/0.67	# User time                : 0.131 s
0.62/0.67	# System time              : 0.010 s
0.62/0.67	# Total time               : 0.141 s
0.62/0.67	# Maximum resident set size: 7348 pages
0.62/0.67	
0.62/0.67	# -------------------------------------------------
0.62/0.67	# User time                : 0.385 s
0.62/0.67	# System time              : 0.029 s
0.62/0.67	# Total time               : 0.414 s
0.62/0.67	# Maximum resident set size: 2348 pages
0.62/0.67	% E exiting
0.62/0.67	% E exiting
0.62/0.67	EOF