0.09/0.14	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.09/0.14	% Command    : run_E %s %d THM
0.14/0.36	% Computer : n025.cluster.edu
0.14/0.36	% Model    : x86_64 x86_64
0.14/0.36	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.36	% Memory   : 8042.1875MB
0.14/0.36	% OS       : Linux 3.10.0-693.el7.x86_64
0.14/0.36	% CPULimit   : 1440
0.14/0.36	% WCLimit    : 180
0.14/0.36	% DateTime   : Thu Jul  4 07:33:24 EDT 2024
0.14/0.36	% CPUTime    : 
0.23/0.53	Running higher-order theorem proving
0.43/0.60	Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p
0.46/0.83	# Version: 3.2.0-ho
0.46/0.83	# Preprocessing class: HSLMSLSSLLLCHSA.
0.46/0.83	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
0.46/0.83	# Starting ho_unfolding_5 with 720s (4) cores
0.46/0.83	# Starting pre_casc_3 with 180s (1) cores
0.46/0.83	# Starting new_ho_10_cnf2 with 180s (1) cores
0.46/0.83	# Starting full_lambda_10 with 180s (1) cores
0.46/0.83	# Starting ehoh_best_nonlift_rwall with 180s (1) cores
0.46/0.83	# ehoh_best_nonlift_rwall with pid 16418 completed with status 0
0.46/0.83	# Result found by ehoh_best_nonlift_rwall
0.46/0.83	# Preprocessing class: HSLMSLSSLLLCHSA.
0.46/0.83	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
0.46/0.83	# Starting ho_unfolding_5 with 720s (4) cores
0.46/0.83	# Starting pre_casc_3 with 180s (1) cores
0.46/0.83	# Starting new_ho_10_cnf2 with 180s (1) cores
0.46/0.83	# Starting full_lambda_10 with 180s (1) cores
0.46/0.83	# Starting ehoh_best_nonlift_rwall with 180s (1) cores
0.46/0.83	# No SInE strategy applied
0.46/0.83	# Search class: HGHSM-FSLM32-DHSMMSBN
0.46/0.83	# partial match(1): HGHSM-FSLM32-MHSMMSBN
0.46/0.83	# Scheduled 12 strats onto 1 cores with 180 seconds (180 total)
0.46/0.83	# Starting full_lambda_5 with 15s (1) cores
0.46/0.83	# full_lambda_5 with pid 16419 completed with status 0
0.46/0.83	# Result found by full_lambda_5
0.46/0.83	# Preprocessing class: HSLMSLSSLLLCHSA.
0.46/0.83	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
0.46/0.83	# Starting ho_unfolding_5 with 720s (4) cores
0.46/0.83	# Starting pre_casc_3 with 180s (1) cores
0.46/0.83	# Starting new_ho_10_cnf2 with 180s (1) cores
0.46/0.83	# Starting full_lambda_10 with 180s (1) cores
0.46/0.83	# Starting ehoh_best_nonlift_rwall with 180s (1) cores
0.46/0.83	# No SInE strategy applied
0.46/0.83	# Search class: HGHSM-FSLM32-DHSMMSBN
0.46/0.83	# partial match(1): HGHSM-FSLM32-MHSMMSBN
0.46/0.83	# Scheduled 12 strats onto 1 cores with 180 seconds (180 total)
0.46/0.83	# Starting full_lambda_5 with 15s (1) cores
0.46/0.83	# Preprocessing time       : 0.007 s
0.46/0.83	# Presaturation interreduction done
0.46/0.83	
0.46/0.83	# Proof found!
0.46/0.83	# SZS status Theorem
0.46/0.83	# SZS output start CNFRefutation
0.46/0.83	thf(decl_22, type, in: $i > $i > $o).
0.46/0.83	thf(decl_23, type, exu: ($i > $o) > $o).
0.46/0.83	thf(decl_24, type, setextAx: $o).
0.46/0.83	thf(decl_25, type, emptyset: $i).
0.46/0.83	thf(decl_26, type, emptysetAx: $o).
0.46/0.83	thf(decl_27, type, setadjoin: $i > $i > $i).
0.46/0.83	thf(decl_28, type, setadjoinAx: $o).
0.46/0.83	thf(decl_29, type, powerset: $i > $i).
0.46/0.83	thf(decl_30, type, powersetAx: $o).
0.46/0.83	thf(decl_31, type, setunion: $i > $i).
0.46/0.83	thf(decl_32, type, setunionAx: $o).
0.46/0.83	thf(decl_33, type, omega: $i).
0.46/0.83	thf(decl_34, type, omega0Ax: $o).
0.46/0.83	thf(decl_35, type, omegaSAx: $o).
0.46/0.83	thf(decl_36, type, omegaIndAx: $o).
0.46/0.83	thf(decl_37, type, replAx: $o).
0.46/0.83	thf(decl_38, type, foundationAx: $o).
0.46/0.83	thf(decl_39, type, wellorderingAx: $o).
0.46/0.83	thf(decl_40, type, descr: ($i > $o) > $i).
0.46/0.83	thf(decl_41, type, descrp: $o).
0.46/0.83	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_43, type, dsetconstrI: $o).
0.46/0.83	thf(decl_44, type, dsetconstrEL: $o).
0.46/0.83	thf(decl_45, type, dsetconstrER: $o).
0.46/0.83	thf(decl_46, type, exuE1: $o).
0.46/0.83	thf(decl_47, type, prop2set: $o > $i).
0.46/0.83	thf(decl_48, type, prop2setE: $o).
0.46/0.83	thf(decl_49, type, emptysetE: $o).
0.46/0.83	thf(decl_50, type, emptysetimpfalse: $o).
0.46/0.83	thf(decl_51, type, notinemptyset: $o).
0.46/0.83	thf(decl_52, type, exuE3e: $o).
0.46/0.83	thf(decl_53, type, setext: $o).
0.46/0.83	thf(decl_54, type, emptyI: $o).
0.46/0.83	thf(decl_55, type, noeltsimpempty: $o).
0.46/0.83	thf(decl_56, type, setbeta: $o).
0.46/0.83	thf(decl_57, type, nonempty: $i > $o).
0.46/0.83	thf(decl_58, type, nonemptyE1: $o).
0.46/0.83	thf(decl_59, type, nonemptyI: $o).
0.46/0.83	thf(decl_60, type, nonemptyI1: $o).
0.46/0.83	thf(decl_61, type, setadjoinIL: $o).
0.46/0.83	thf(decl_62, type, emptyinunitempty: $o).
0.46/0.83	thf(decl_63, type, setadjoinIR: $o).
0.46/0.83	thf(decl_64, type, setadjoinE: $o).
0.46/0.83	thf(decl_65, type, setadjoinOr: $o).
0.46/0.83	thf(decl_66, type, setoftrueEq: $o).
0.46/0.83	thf(decl_67, type, powersetI: $o).
0.46/0.83	thf(decl_68, type, emptyinPowerset: $o).
0.46/0.83	thf(decl_69, type, emptyInPowerset: $o).
0.46/0.83	thf(decl_70, type, powersetE: $o).
0.46/0.83	thf(decl_71, type, setunionI: $o).
0.46/0.83	thf(decl_72, type, setunionE: $o).
0.46/0.83	thf(decl_73, type, subPowSU: $o).
0.46/0.83	thf(decl_74, type, exuE2: $o).
0.46/0.83	thf(decl_75, type, nonemptyImpWitness: $o).
0.46/0.83	thf(decl_76, type, uniqinunit: $o).
0.46/0.83	thf(decl_77, type, notinsingleton: $o).
0.46/0.83	thf(decl_78, type, eqinunit: $o).
0.46/0.83	thf(decl_79, type, singletonsswitch: $o).
0.46/0.83	thf(decl_80, type, upairsetE: $o).
0.46/0.83	thf(decl_81, type, upairsetIL: $o).
0.46/0.83	thf(decl_82, type, upairsetIR: $o).
0.46/0.83	thf(decl_83, type, emptyE1: $o).
0.46/0.83	thf(decl_84, type, vacuousDall: $o).
0.46/0.83	thf(decl_85, type, quantDeMorgan1: $o).
0.46/0.83	thf(decl_86, type, quantDeMorgan2: $o).
0.46/0.83	thf(decl_87, type, quantDeMorgan3: $o).
0.46/0.83	thf(decl_88, type, quantDeMorgan4: $o).
0.46/0.83	thf(decl_89, type, prop2setI: $o).
0.46/0.83	thf(decl_90, type, set2prop: $i > $o).
0.46/0.83	thf(decl_91, type, prop2set2propI: $o).
0.46/0.83	thf(decl_92, type, notdexE: $o).
0.46/0.83	thf(decl_93, type, notdallE: $o).
0.46/0.83	thf(decl_94, type, exuI1: $o).
0.46/0.83	thf(decl_95, type, exuI3: $o).
0.46/0.83	thf(decl_96, type, exuI2: $o).
0.46/0.83	thf(decl_97, type, inCongP: $o).
0.46/0.83	thf(decl_98, type, in__Cong: $o).
0.46/0.83	thf(decl_99, type, exuE3u: $o).
0.46/0.83	thf(decl_100, type, exu__Cong: $o).
0.46/0.83	thf(decl_101, type, emptyset__Cong: $o).
0.46/0.83	thf(decl_102, type, setadjoin__Cong: $o).
0.46/0.83	thf(decl_103, type, powerset__Cong: $o).
0.46/0.83	thf(decl_104, type, setunion__Cong: $o).
0.46/0.83	thf(decl_105, type, omega__Cong: $o).
0.46/0.83	thf(decl_106, type, exuEu: $o).
0.46/0.83	thf(decl_107, type, descr__Cong: $o).
0.46/0.83	thf(decl_108, type, dsetconstr__Cong: $o).
0.46/0.83	thf(decl_109, type, subset: $i > $i > $o).
0.46/0.83	thf(decl_112, type, subsetI1: $o).
0.46/0.83	thf(decl_113, type, eqimpsubset2: $o).
0.46/0.83	thf(decl_114, type, eqimpsubset1: $o).
0.46/0.83	thf(decl_115, type, subsetI2: $o).
0.46/0.83	thf(decl_116, type, emptysetsubset: $o).
0.46/0.83	thf(decl_117, type, subsetE: $o).
0.46/0.83	thf(decl_118, type, subsetE2: $o).
0.46/0.83	thf(decl_119, type, notsubsetI: $o).
0.46/0.83	thf(decl_120, type, notequalI1: $o).
0.46/0.83	thf(decl_121, type, notequalI2: $o).
0.46/0.83	thf(decl_122, type, subsetRefl: $o).
0.46/0.83	thf(decl_123, type, subsetTrans: $o).
0.46/0.83	thf(decl_124, type, setadjoinSub: $o).
0.46/0.83	thf(decl_125, type, setadjoinSub2: $o).
0.46/0.83	thf(decl_126, type, subset2powerset: $o).
0.46/0.83	thf(decl_127, type, setextsub: $o).
0.46/0.83	thf(decl_128, type, subsetemptysetimpeq: $o).
0.46/0.83	thf(decl_129, type, powersetI1: $o).
0.46/0.83	thf(decl_130, type, powersetE1: $o).
0.46/0.83	thf(decl_131, type, inPowerset: $o).
0.46/0.83	thf(decl_132, type, powersetsubset: $o).
0.46/0.83	thf(decl_133, type, sepInPowerset: $o).
0.46/0.83	thf(decl_134, type, sepSubset: $o).
0.46/0.83	thf(decl_135, type, binunion: $i > $i > $i).
0.46/0.83	thf(decl_136, type, binunionIL: $o).
0.46/0.83	thf(decl_137, type, upairset2IR: $o).
0.46/0.83	thf(decl_138, type, binunionIR: $o).
0.46/0.83	thf(decl_139, type, binunionEcases: $o).
0.46/0.83	thf(decl_140, type, binunionE: $o).
0.46/0.83	thf(decl_141, type, binunionLsub: $o).
0.46/0.83	thf(decl_142, type, binunionRsub: $o).
0.46/0.83	thf(decl_143, type, binintersect: $i > $i > $i).
0.46/0.83	thf(decl_144, type, binintersectI: $o).
0.46/0.83	thf(decl_145, type, binintersectSubset5: $o).
0.46/0.83	thf(decl_146, type, binintersectEL: $o).
0.46/0.83	thf(decl_147, type, binintersectLsub: $o).
0.46/0.83	thf(decl_148, type, binintersectSubset2: $o).
0.46/0.83	thf(decl_149, type, binintersectSubset3: $o).
0.46/0.83	thf(decl_150, type, binintersectER: $o).
0.46/0.83	thf(decl_151, type, disjointsetsI1: $o).
0.46/0.83	thf(decl_152, type, binintersectRsub: $o).
0.46/0.83	thf(decl_153, type, binintersectSubset4: $o).
0.46/0.83	thf(decl_154, type, binintersectSubset1: $o).
0.46/0.83	thf(decl_155, type, bs114d: $o).
0.46/0.83	thf(decl_157, type, setminus: $i > $i > $i).
0.46/0.83	thf(decl_158, type, setminusI: $o).
0.46/0.83	thf(decl_159, type, setminusEL: $o).
0.46/0.83	thf(decl_160, type, setminusER: $o).
0.46/0.83	thf(decl_161, type, setminusSubset2: $o).
0.46/0.83	thf(decl_162, type, setminusERneg: $o).
0.46/0.83	thf(decl_163, type, setminusELneg: $o).
0.46/0.83	thf(decl_164, type, setminusILneg: $o).
0.46/0.83	thf(decl_165, type, setminusIRneg: $o).
0.46/0.83	thf(decl_166, type, setminusLsub: $o).
0.46/0.83	thf(decl_167, type, setminusSubset1: $o).
0.46/0.83	thf(decl_168, type, symdiff: $i > $i > $i).
0.46/0.83	thf(decl_169, type, symdiffE: $o).
0.46/0.83	thf(decl_170, type, symdiffI1: $o).
0.46/0.83	thf(decl_171, type, symdiffI2: $o).
0.46/0.83	thf(decl_172, type, symdiffIneg1: $o).
0.46/0.83	thf(decl_173, type, symdiffIneg2: $o).
0.46/0.83	thf(decl_174, type, iskpair: $i > $o).
0.46/0.83	thf(decl_175, type, secondinupair: $o).
0.46/0.83	thf(decl_176, type, setukpairIL: $o).
0.46/0.83	thf(decl_177, type, setukpairIR: $o).
0.46/0.83	thf(decl_178, type, kpairiskpair: $o).
0.46/0.83	thf(decl_179, type, kpair: $i > $i > $i).
0.46/0.83	thf(decl_180, type, kpairp: $o).
0.46/0.83	thf(decl_181, type, cartprod: $i > $i > $i).
0.46/0.83	thf(decl_182, type, singletonsubset: $o).
0.46/0.83	thf(decl_183, type, singletoninpowerset: $o).
0.46/0.83	thf(decl_184, type, singletoninpowunion: $o).
0.46/0.83	thf(decl_185, type, upairset2E: $o).
0.46/0.83	thf(decl_186, type, upairsubunion: $o).
0.46/0.83	thf(decl_187, type, upairinpowunion: $o).
0.46/0.83	thf(decl_188, type, ubforcartprodlem1: $o).
0.46/0.83	thf(decl_189, type, ubforcartprodlem2: $o).
0.46/0.83	thf(decl_190, type, ubforcartprodlem3: $o).
0.46/0.83	thf(decl_191, type, cartprodpairin: $o).
0.46/0.83	thf(decl_192, type, cartprodmempair1: $o).
0.46/0.83	thf(decl_193, type, cartprodmempair: $o).
0.46/0.83	thf(decl_194, type, setunionE2: $o).
0.46/0.83	thf(decl_195, type, setunionsingleton1: $o).
0.46/0.83	thf(decl_196, type, setunionsingleton2: $o).
0.46/0.83	thf(decl_197, type, setunionsingleton: $o).
0.46/0.83	thf(decl_198, type, singleton: $i > $o).
0.46/0.83	thf(decl_199, type, singletonprop: $o).
0.46/0.83	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
0.46/0.83	thf(decl_201, type, ex1E1: $o).
0.46/0.83	thf(decl_202, type, ex1I: $o).
0.46/0.83	thf(decl_203, type, ex1I2: $o).
0.46/0.83	thf(decl_204, type, singletonsuniq: $o).
0.46/0.83	thf(decl_209, type, setukpairinjL1: $o).
0.46/0.83	thf(decl_210, type, kfstsingleton: $o).
0.46/0.83	thf(decl_211, type, theprop: $o).
0.46/0.83	thf(decl_212, type, kfst: $i > $i).
0.46/0.83	thf(decl_213, type, kfstpairEq: $o).
0.46/0.83	thf(decl_214, type, cartprodfstin: $o).
0.46/0.83	thf(decl_215, type, setukpairinjL2: $o).
0.46/0.83	thf(decl_216, type, setukpairinjL: $o).
0.46/0.83	thf(decl_217, type, setukpairinjR11: $o).
0.46/0.83	thf(decl_218, type, setukpairinjR12: $o).
0.46/0.83	thf(decl_219, type, setukpairinjR1: $o).
0.46/0.83	thf(decl_220, type, upairequniteq: $o).
0.46/0.83	thf(decl_221, type, setukpairinjR2: $o).
0.46/0.83	thf(decl_222, type, setukpairinjR: $o).
0.46/0.83	thf(decl_223, type, ksndsingleton: $o).
0.46/0.83	thf(decl_224, type, ksnd: $i > $i).
0.46/0.83	thf(decl_225, type, ksndpairEq: $o).
0.46/0.83	thf(decl_226, type, kpairsurjEq: $o).
0.46/0.83	thf(decl_227, type, cartprodsndin: $o).
0.46/0.83	thf(decl_228, type, cartprodpairmemEL: $o).
0.46/0.83	thf(decl_229, type, cartprodpairmemER: $o).
0.46/0.83	thf(decl_230, type, cartprodmempaircEq: $o).
0.46/0.83	thf(decl_231, type, cartprodfstpairEq: $o).
0.46/0.83	thf(decl_232, type, cartprodsndpairEq: $o).
0.46/0.83	thf(decl_233, type, cartprodpairsurjEq: $o).
0.46/0.83	thf(decl_234, type, breln: $i > $i > $i > $o).
0.46/0.83	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
0.46/0.83	thf(decl_236, type, dpsetconstrI: $o).
0.46/0.83	thf(decl_237, type, dpsetconstrSub: $o).
0.46/0.83	thf(decl_238, type, setOfPairsIsBReln: $o).
0.46/0.83	thf(decl_239, type, dpsetconstrERa: $o).
0.46/0.83	thf(decl_240, type, dpsetconstrEL1: $o).
0.46/0.83	thf(decl_241, type, dpsetconstrEL2: $o).
0.46/0.83	thf(decl_242, type, dpsetconstrER: $o).
0.46/0.83	thf(decl_243, type, func: $i > $i > $i > $o).
0.46/0.83	thf(decl_244, type, funcSet: $i > $i > $i).
0.46/0.83	thf(decl_245, type, funcImageSingleton: $o).
0.46/0.83	thf(decl_246, type, apProp: $o).
0.46/0.83	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
0.46/0.83	thf(decl_248, type, app: $o).
0.46/0.83	thf(decl_249, type, infuncsetfunc: $o).
0.46/0.83	thf(decl_250, type, ap2p: $o).
0.46/0.83	thf(decl_251, type, funcinfuncset: $o).
0.46/0.83	thf(decl_252, type, lamProp: $o).
0.46/0.83	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
0.46/0.83	thf(decl_254, type, lamp: $o).
0.46/0.83	thf(decl_255, type, lam2p: $o).
0.46/0.83	thf(decl_256, type, brelnall1: $o).
0.46/0.83	thf(decl_257, type, brelnall2: $o).
0.46/0.83	thf(decl_258, type, ex1E2: $o).
0.46/0.83	thf(decl_259, type, funcGraphProp1: $o).
0.46/0.83	thf(decl_260, type, funcGraphProp3: $o).
0.46/0.83	thf(decl_261, type, funcGraphProp2: $o).
0.46/0.83	thf(decl_262, type, funcextLem: $o).
0.46/0.83	thf(decl_263, type, funcGraphProp4: $o).
0.46/0.83	thf(decl_264, type, subbreln: $o).
0.46/0.83	thf(decl_265, type, eqbreln: $o).
0.46/0.83	thf(decl_266, type, funcext: $o).
0.46/0.83	thf(decl_267, type, funcext2: $o).
0.46/0.83	thf(decl_268, type, ap2apEq1: $o).
0.46/0.83	thf(decl_269, type, ap2apEq2: $o).
0.46/0.83	thf(decl_270, type, beta1: $o).
0.46/0.83	thf(decl_271, type, eta1: $o).
0.46/0.83	thf(decl_272, type, lam2lamEq: $o).
0.46/0.83	thf(decl_273, type, beta2: $o).
0.46/0.83	thf(decl_274, type, eta2: $o).
0.46/0.83	thf(decl_275, type, iffalseProp1: $o).
0.46/0.83	thf(decl_276, type, iffalseProp2: $o).
0.46/0.83	thf(decl_277, type, iftrueProp1: $o).
0.46/0.83	thf(decl_278, type, iftrueProp2: $o).
0.46/0.83	thf(decl_279, type, ifSingleton: $o).
0.46/0.83	thf(decl_280, type, if: $i > $o > $i > $i > $i).
0.46/0.83	thf(decl_281, type, ifp: $o).
0.46/0.83	thf(decl_282, type, theeq: $o).
0.46/0.83	thf(decl_283, type, iftrue: $o).
0.46/0.83	thf(decl_284, type, iffalse: $o).
0.46/0.83	thf(decl_285, type, iftrueorfalse: $o).
0.46/0.83	thf(decl_286, type, binintersectT_lem: $o).
0.46/0.83	thf(decl_287, type, binunionT_lem: $o).
0.46/0.83	thf(decl_288, type, powersetT_lem: $o).
0.46/0.83	thf(decl_289, type, setminusT_lem: $o).
0.46/0.83	thf(decl_290, type, complementT_lem: $o).
0.46/0.83	thf(decl_291, type, setextT: $o).
0.46/0.83	thf(decl_292, type, subsetTI: $o).
0.46/0.83	thf(decl_293, type, powersetTI1: $o).
0.46/0.83	thf(decl_294, type, powersetTE1: $o).
0.46/0.83	thf(decl_295, type, complementTI1: $o).
0.46/0.83	thf(decl_296, type, complementTE1: $o).
0.46/0.83	thf(decl_297, type, binintersectTELcontra: $o).
0.46/0.83	thf(decl_298, type, binintersectTERcontra: $o).
0.46/0.83	thf(decl_299, type, contrasubsetT: $o).
0.46/0.83	thf(decl_300, type, contrasubsetT1: $o).
0.46/0.83	thf(decl_301, type, contrasubsetT2: $o).
0.46/0.83	thf(decl_302, type, contrasubsetT3: $o).
0.46/0.83	thf(decl_303, type, doubleComplementI1: $o).
0.46/0.83	thf(decl_304, type, doubleComplementE1: $o).
0.46/0.83	thf(decl_305, type, doubleComplementSub1: $o).
0.46/0.83	thf(decl_306, type, doubleComplementSub2: $o).
0.46/0.83	thf(decl_307, type, doubleComplementEq: $o).
0.46/0.83	thf(decl_308, type, complementTnotintersectT: $o).
0.46/0.83	thf(decl_309, type, complementImpComplementIntersect: $o).
0.46/0.83	thf(decl_310, type, complementSubsetComplementIntersect: $o).
0.46/0.83	thf(decl_311, type, complementInPowersetComplementIntersect: $o).
0.46/0.83	thf(decl_312, type, contraSubsetComplement: $o).
0.46/0.83	thf(decl_313, type, complementTcontraSubset: $o).
0.46/0.83	thf(decl_314, type, binunionTILcontra: $o).
0.46/0.83	thf(decl_315, type, binunionTIRcontra: $o).
0.46/0.83	thf(decl_316, type, inIntersectImpInUnion: $o).
0.46/0.83	thf(decl_317, type, inIntersectImpInUnion2: $o).
0.46/0.83	thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
0.46/0.83	thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
0.46/0.83	thf(decl_320, type, inComplementUnionImpNotIn1: $o).
0.46/0.83	thf(decl_321, type, inComplementUnionImpInComplement1: $o).
0.46/0.83	thf(decl_322, type, binunionTE: $o).
0.46/0.83	thf(decl_323, type, binunionTEcontra: $o).
0.46/0.83	thf(decl_324, type, demorgan2a1: $o).
0.46/0.83	thf(decl_325, type, complementUnionInPowersetComplement: $o).
0.46/0.83	thf(decl_326, type, demorgan2a2: $o).
0.46/0.83	thf(decl_327, type, demorgan1a: $o).
0.46/0.83	thf(decl_328, type, demorgan1b: $o).
0.46/0.83	thf(decl_329, type, demorgan1: $o).
0.46/0.83	thf(decl_330, type, demorgan2a: $o).
0.46/0.83	thf(decl_331, type, demorgan2b2: $o).
0.46/0.83	thf(decl_332, type, demorgan2b: $o).
0.46/0.83	thf(decl_333, type, demorgan2: $o).
0.46/0.83	thf(decl_334, type, woz13rule0: $o).
0.46/0.83	thf(decl_335, type, woz13rule1: $o).
0.46/0.83	thf(decl_336, type, woz13rule2: $o).
0.46/0.83	thf(decl_337, type, woz13rule3: $o).
0.46/0.83	thf(decl_338, type, woz13rule4: $o).
0.46/0.83	thf(decl_339, type, woz1_1: $o).
0.46/0.83	thf(decl_340, type, woz1_2: $o).
0.46/0.83	thf(decl_341, type, woz1_3: $o).
0.46/0.83	thf(decl_342, type, woz1_4: $o).
0.46/0.83	thf(decl_343, type, woz1_5: $o).
0.46/0.83	thf(decl_344, type, breln1: $i > $i > $o).
0.46/0.83	thf(decl_345, type, breln1all2: $o).
0.46/0.83	thf(decl_346, type, breln1Set: $i > $i).
0.46/0.83	thf(decl_347, type, breln1SetBreln1: $o).
0.46/0.83	thf(decl_353, type, reflwellordering: $i > $i > $o).
0.46/0.83	thf(decl_354, type, choice2fnsingleton: $o).
0.46/0.83	thf(decl_355, type, setOfPairsIsBReln1: $o).
0.46/0.83	thf(decl_356, type, epred1_0: $o).
0.46/0.83	thf(decl_357, type, esk1_2: $i > $i > $i).
0.46/0.83	thf(decl_358, type, esk2_2: $i > $i > $i).
0.46/0.83	thf(decl_359, type, esk3_2: $i > $i > $i).
0.46/0.83	thf(decl_360, type, esk4_1: $i > $i).
0.46/0.83	thf(decl_361, type, esk5_2: ($i > $i > $o) > $i > $i).
0.46/0.83	thf(decl_362, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
0.46/0.83	thf(decl_363, type, esk7_2: ($i > $i > $o) > $i > $i).
0.46/0.83	thf(decl_364, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
0.46/0.83	thf(decl_365, type, esk9_1: $i > $i).
0.46/0.83	thf(decl_366, type, esk10_2: ($i > $o) > $i > $i).
0.46/0.83	thf(decl_367, type, esk11_2: ($i > $o) > $i > $i).
0.46/0.83	thf(decl_368, type, esk12_1: ($i > $o) > $i).
0.46/0.83	thf(decl_369, type, esk13_2: ($i > $o) > $i > $i).
0.46/0.83	thf(decl_370, type, esk14_1: ($i > $o) > $i).
0.46/0.83	thf(decl_371, type, esk15_2: $i > $i > $i).
0.46/0.83	thf(decl_372, type, esk16_2: $i > $i > $i).
0.46/0.83	thf(decl_373, type, esk17_1: $i > $i).
0.46/0.83	thf(decl_374, type, esk18_1: $i > $i).
0.46/0.83	thf(decl_375, type, esk19_1: $i > $i).
0.46/0.83	thf(decl_376, type, esk20_2: $i > $i > $i).
0.46/0.83	thf(decl_377, type, esk21_3: $i > $i > $o > $i).
0.46/0.83	thf(decl_378, type, esk22_2: ($i > $o) > $i > $i).
0.46/0.83	thf(decl_379, type, esk23_1: ($i > $o) > $i).
0.46/0.83	thf(decl_380, type, esk24_1: $i > $i).
0.46/0.83	thf(decl_381, type, esk25_2: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_382, type, esk26_2: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_383, type, esk27_2: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_384, type, esk28_2: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_385, type, esk29_2: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_386, type, esk30_2: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_387, type, esk31_2: ($i > $o) > $i > $i).
0.46/0.83	thf(decl_388, type, esk32_1: ($i > $o) > $i).
0.46/0.83	thf(decl_389, type, esk33_1: ($i > $o) > $i).
0.46/0.83	thf(decl_390, type, esk34_1: ($i > $o) > $i).
0.46/0.83	thf(decl_391, type, esk35_1: ($i > $o) > $i).
0.46/0.83	thf(decl_392, type, esk36_2: ($i > $o) > $i > $i).
0.46/0.83	thf(decl_393, type, esk37_1: ($i > $o) > $i).
0.46/0.83	thf(decl_394, type, esk38_2: ($i > $o) > $i > $i).
0.46/0.83	thf(decl_395, type, esk39_2: ($i > $o) > ($i > $o) > $i).
0.46/0.83	thf(decl_396, type, esk40_2: ($i > $o) > ($i > $o) > $i).
0.46/0.83	thf(decl_397, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
0.46/0.83	thf(decl_398, type, esk42_2: ($i > $o) > ($i > $o) > $i).
0.46/0.83	thf(decl_399, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
0.46/0.83	thf(decl_400, type, esk44_2: ($i > $o) > ($i > $o) > $i).
0.46/0.83	thf(decl_401, type, esk45_2: ($i > $o) > $i > $i).
0.46/0.83	thf(decl_402, type, esk46_2: ($i > $o) > ($i > $o) > $i).
0.46/0.83	thf(decl_403, type, esk47_2: ($i > $o) > ($i > $o) > $i).
0.46/0.83	thf(decl_404, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
0.46/0.83	thf(decl_405, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
0.46/0.83	thf(decl_406, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.46/0.83	thf(decl_407, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.46/0.83	thf(decl_408, type, esk52_2: $i > $i > $i).
0.46/0.83	thf(decl_409, type, esk53_2: $i > $i > $i).
0.46/0.83	thf(decl_410, type, esk54_2: $i > $i > $i).
0.46/0.83	thf(decl_411, type, esk55_3: $i > $i > $i > $i).
0.46/0.83	thf(decl_412, type, esk56_3: $i > $i > $i > $i).
0.46/0.83	thf(decl_413, type, esk57_2: $i > $i > $i).
0.46/0.83	thf(decl_414, type, esk58_2: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_415, type, esk59_2: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_416, type, esk60_2: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_417, type, esk61_3: $i > ($i > $o) > $i > $i).
0.46/0.83	thf(decl_418, type, esk62_2: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_419, type, esk63_2: $i > ($i > $o) > $i).
0.46/0.83	thf(decl_420, type, esk64_3: $i > $i > ($i > $i) > $i).
0.46/0.83	thf(decl_421, type, esk65_3: $i > $i > ($i > $i) > $i).
0.46/0.83	thf(decl_422, type, esk66_3: $i > $i > ($i > $i) > $i).
0.46/0.83	thf(decl_423, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
0.46/0.83	thf(decl_424, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
0.46/0.83	thf(decl_425, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
0.46/0.83	thf(decl_426, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
0.46/0.83	thf(decl_427, type, esk71_4: $i > $i > $i > $i > $i).
0.46/0.83	thf(decl_428, type, esk72_4: $i > $i > $i > $i > $i).
0.46/0.83	thf(decl_429, type, esk73_4: $i > $i > $i > $i > $i).
0.46/0.83	thf(decl_430, type, esk74_4: $i > $i > $i > $i > $i).
0.46/0.83	thf(decl_431, type, esk75_4: $i > $i > $i > $i > $i).
0.46/0.83	thf(decl_432, type, esk76_4: $i > $i > $i > $i > $i).
0.46/0.83	thf(decl_433, type, esk77_4: $i > $i > $i > $i > $i).
0.46/0.83	thf(decl_434, type, esk78_4: $i > $i > $i > $i > $i).
0.46/0.83	thf(decl_435, type, esk79_4: $i > $i > $i > $i > $i).
0.46/0.83	thf(decl_436, type, esk80_3: $i > $i > ($i > $i) > $i).
0.46/0.83	thf(decl_437, type, esk81_3: $i > $i > ($i > $i) > $i).
0.46/0.83	thf(decl_438, type, esk82_3: $i > $i > ($i > $i) > $i).
0.46/0.83	thf(decl_439, type, esk83_3: $i > $i > $i > $i).
0.46/0.83	thf(decl_440, type, esk84_3: $i > $i > $i > $i).
0.46/0.83	thf(decl_441, type, esk85_3: $i > $i > $i > $i).
0.46/0.83	thf(decl_442, type, esk86_3: $i > $i > $i > $i).
0.46/0.83	thf(decl_443, type, esk87_3: $i > $i > ($i > $o) > $i).
0.46/0.83	thf(decl_444, type, esk88_3: $i > $i > ($i > $o) > $i).
0.46/0.83	thf(decl_445, type, esk89_3: $i > $i > ($i > $i > $o) > $i).
0.46/0.83	thf(decl_446, type, esk90_0: $i).
0.46/0.83	thf(decl_447, type, esk91_0: $i).
0.46/0.83	thf(decl_448, type, epred2_0: $i > $o).
0.46/0.83	thf(decl_449, type, esk92_0: $i).
0.46/0.83	thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', breln1)).
0.46/0.83	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', breln)).
0.46/0.83	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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', replAx)).
0.46/0.83	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', exu)).
0.46/0.83	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', descrp)).
0.46/0.83	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', exuE1)).
0.46/0.83	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', exuE3e)).
0.46/0.83	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', nonempty)).
0.46/0.83	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', nonemptyI)).
0.46/0.83	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', exuE2)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', exuI1)).
0.46/0.83	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', exuI3)).
0.46/0.83	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', exuI2)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', exuE3u)).
0.46/0.83	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', exu__Cong)).
0.46/0.83	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', exuEu)).
0.46/0.83	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', descr__Cong)).
0.46/0.83	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setOfPairsIsBReln)).
0.46/0.83	thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setOfPairsIsBReln1)).
0.46/0.83	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', dsetconstrI)).
0.46/0.83	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', dsetconstrEL)).
0.46/0.83	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', dsetconstrER)).
0.46/0.83	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setbeta)).
0.46/0.83	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', nonemptyE1)).
0.46/0.83	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', nonemptyI1)).
0.46/0.83	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setoftrueEq)).
0.46/0.83	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', nonemptyImpWitness)).
0.46/0.83	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.3nOKDTCzDP/E---3.1_16336.p', emptyE1)).
0.46/0.83	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', dsetconstr__Cong)).
0.46/0.83	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', sepInPowerset)).
0.46/0.83	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', sepSubset)).
0.46/0.83	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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', singletonprop)).
0.46/0.83	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ex1E1)).
0.46/0.83	thf(ex1I, axiom, ((ex1I)<=>![X4:$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.3nOKDTCzDP/E---3.1_16336.p', ex1I)).
0.46/0.83	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ex1I2)).
0.46/0.83	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', kfstsingleton)).
0.46/0.83	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ksndsingleton)).
0.46/0.83	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', dpsetconstrI)).
0.46/0.83	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', dpsetconstrSub)).
0.46/0.83	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', dpsetconstrERa)).
0.46/0.83	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', dpsetconstrEL1)).
0.46/0.83	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', dpsetconstrEL2)).
0.46/0.83	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', dpsetconstrER)).
0.46/0.83	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.3nOKDTCzDP/E---3.1_16336.p', funcImageSingleton)).
0.46/0.83	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', apProp)).
0.46/0.83	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.3nOKDTCzDP/E---3.1_16336.p', lamProp)).
0.46/0.83	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', lamp)).
0.46/0.83	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', lam2p)).
0.46/0.83	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.3nOKDTCzDP/E---3.1_16336.p', brelnall1)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', brelnall2)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', ex1E2)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', subbreln)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', eqbreln)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', beta1)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', eta1)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', lam2lamEq)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', beta2)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', eta2)).
0.46/0.83	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', iffalseProp1)).
0.46/0.83	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.3nOKDTCzDP/E---3.1_16336.p', iffalseProp2)).
0.46/0.83	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', iftrueProp1)).
0.46/0.83	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', iftrueProp2)).
0.46/0.83	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ifSingleton)).
0.46/0.83	thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', breln1all2)).
0.46/0.83	thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', breln1SetBreln1)).
0.46/0.83	thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:(((X52 @ X2 @ X3)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ X3 @ X14) @ X33))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', choice2fnsingleton)).
0.46/0.83	thf(breln1all1, conjecture, (((emptysetAx)=>((setadjoinAx)=>(((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((((foundationAx)=>((wellorderingAx)=>((((((((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>(((setext)=>((emptyI)=>((noeltsimpempty)=>(((nonemptyE1)=>(((((((setadjoinE)=>((((powersetI)=>((((powersetE)=>((((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((((upairsetE)=>(((upairsetIR)=>((emptyE1)=>(((quantDeMorgan1)=>((quantDeMorgan2)=>(((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>(((exuI1)=>((exuI3)=>(((inCongP)=>((in__Cong)=>((exuE3u)=>(((emptyset__Cong)=>((setadjoin__Cong)=>((((omega__Cong)=>((exuEu)=>((((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((((subset2powerset)=>((setextsub)=>(((powersetI1)=>((((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((((binunionEcases)=>(((binunionLsub)=>(((binintersectI)=>(((binintersectEL)=>((binintersectLsub)=>(((binintersectSubset3)=>(((((binintersectSubset4)=>(((bs114d)=>((setminusI)=>(((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>(((setminusLsub)=>(((symdiffE)=>(((symdiffI2)=>((symdiffIneg1)=>(((((setukpairIR)=>(((kpairp)=>((singletonsubset)=>(((((((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>(((setunionsingleton2)=>(((singletonprop)=>((ex1E1)=>(((((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>(((cartprodfstin)=>((setukpairinjL2)=>(((setukpairinjR11)=>(((((setukpairinjR2)=>((setukpairinjR)=>(((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((((cartprodsndpairEq)=>(((((setOfPairsIsBReln)=>((((dpsetconstrEL2)=>((dpsetconstrER)=>((((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>(((lamp)=>(((((ex1E2)=>((funcGraphProp1)=>(((funcGraphProp2)=>(((funcGraphProp4)=>((((funcext)=>((funcext2)=>(((ap2apEq2)=>(((eta1)=>((lam2lamEq)=>(((eta2)=>((iffalseProp1)=>(((iftrueProp1)=>((((((iftrue)=>(((iftrueorfalse)=>((((powersetT_lem)=>(((((((powersetTE1)=>((((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>(((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>(((((complementSubsetComplementIntersect)=>(((contraSubsetComplement)=>((((binunionTIRcontra)=>((((((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>(((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>(((demorgan1a)=>(((demorgan1)=>((demorgan2a)=>(((((woz13rule0)=>((((((woz1_1)=>((((woz1_4)=>((((((setOfPairsIsBReln1)=>![X4:$i, X33:$i]:((![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))<=![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:((((X1 @ (kpair @ X2 @ X3))<=(in @ (kpair @ X2 @ X3) @ X33))<=(in @ X3 @ X4)))))))<=(breln1 @ X4 @ X33))))<=(choice2fnsingleton))<=(breln1SetBreln1))<=(breln1all2))<=(woz1_5)))<=(woz1_3))<=(woz1_2)))<=(woz13rule4))<=(woz13rule3))<=(woz13rule2))<=(woz13rule1)))<=(demorgan2))<=(demorgan2b))<=(demorgan2b2))))<=(demorgan1b)))<=(demorgan2a2)))))<=(binunionTE))))<=(intersectInPowersetIntersectUnions))<=(inIntersectImpInIntersectUnions))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion)))<=(binunionTILcontra))<=(complementTcontraSubset)))<=(complementInPowersetComplementIntersect)))<=(complementImpComplementIntersect))<=(complementTnotintersectT))<=(doubleComplementEq))))))))<=(contrasubsetT1)))))<=(complementTE1))<=(complementTI1)))<=(powersetTI1))<=(subsetTI))<=(setextT))<=(complementT_lem))<=(setminusT_lem)))<=(binunionT_lem))<=(binintersectT_lem)))<=(iffalse)))<=(theeq))<=(ifp))<=(ifSingleton))<=(iftrueProp2)))<=(iffalseProp2))))<=(beta2))))<=(beta1)))<=(ap2apEq1))))<=(eqbreln))<=(subbreln)))<=(funcextLem)))<=(funcGraphProp3))))<=(brelnall2))<=(brelnall1))<=(lam2p)))<=(lamProp))))))<=(apProp))<=(funcImageSingleton))))<=(dpsetconstrEL1))<=(dpsetconstrERa)))<=(dpsetconstrSub))<=(dpsetconstrI))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))<=(cartprodmempaircEq)))))))<=(ksndsingleton))))<=(upairequniteq))<=(setukpairinjR1))<=(setukpairinjR12)))<=(setukpairinjL))))<=(kfstpairEq)))))<=(singletonsuniq))<=(ex1I2))<=(ex1I))))<=(setunionsingleton)))<=(setunionsingleton1)))))))<=(ubforcartprodlem2)))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion))<=(singletoninpowerset))))<=(kpairiskpair)))<=(setukpairIL))<=(secondinupair))<=(symdiffIneg2))))<=(symdiffI1)))<=(setminusSubset1)))<=(setminusIRneg)))))))<=(setminusEL))))<=(binintersectSubset1)))<=(binintersectRsub))<=(disjointsetsI1))<=(binintersectER)))<=(binintersectSubset2))))<=(binintersectSubset5)))<=(binunionRsub)))<=(binunionE)))<=(binunionIR))<=(upairset2IR))))))<=(inPowerset))<=(powersetE1)))<=(subsetemptysetimpeq))))<=(setadjoinSub2))<=(setadjoinSub))))))<=(notsubsetI))<=(subsetE2))))))))<=(dsetconstr__Cong))<=(descr__Cong))))<=(setunion__Cong))<=(powerset__Cong))))<=(exu__Cong)))))<=(exuI2))))<=(notdallE)))<=(prop2set2propI))))<=(quantDeMorgan3))))<=(vacuousDall))))<=(upairsetIL)))<=(singletonsswitch))<=(eqinunit)))))))<=(setunionE))<=(setunionI)))<=(emptyInPowerset))<=(emptyinPowerset)))<=(setoftrueEq))<=(setadjoinOr)))<=(setadjoinIR))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI)))<=(setbeta)))))<=(exuE3e)))))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))))<=(replAx))<=(omegaIndAx)))))<=(powersetAx))))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', breln1all1)).
0.46/0.83	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setextAx)).
0.46/0.83	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', emptysetAx)).
0.46/0.83	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setadjoinAx)).
0.46/0.83	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', powersetAx)).
0.46/0.83	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setunionAx)).
0.46/0.83	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', omega0Ax)).
0.46/0.83	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', omegaSAx)).
0.46/0.83	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', omegaIndAx)).
0.46/0.83	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', foundationAx)).
0.46/0.83	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.3nOKDTCzDP/E---3.1_16336.p', wellorderingAx)).
0.46/0.83	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', prop2setE)).
0.46/0.83	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', emptysetE)).
0.46/0.83	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', emptysetimpfalse)).
0.46/0.83	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', notinemptyset)).
0.46/0.83	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setext)).
0.46/0.83	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', emptyI)).
0.46/0.83	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', noeltsimpempty)).
0.46/0.83	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setadjoinIL)).
0.46/0.83	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', emptyinunitempty)).
0.46/0.83	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setadjoinIR)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', setadjoinE)).
0.46/0.83	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setadjoinOr)).
0.46/0.83	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', powersetI)).
0.46/0.83	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', emptyinPowerset)).
0.46/0.83	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', emptyInPowerset)).
0.46/0.83	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', powersetE)).
0.46/0.83	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setunionI)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', setunionE)).
0.46/0.83	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', subPowSU)).
0.46/0.83	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', uniqinunit)).
0.46/0.83	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', notinsingleton)).
0.46/0.83	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', eqinunit)).
0.46/0.83	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', singletonsswitch)).
0.46/0.83	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', upairsetE)).
0.46/0.83	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', upairsetIL)).
0.46/0.83	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', upairsetIR)).
0.46/0.83	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', vacuousDall)).
0.46/0.83	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', quantDeMorgan1)).
0.46/0.83	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', quantDeMorgan2)).
0.46/0.83	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', quantDeMorgan3)).
0.46/0.83	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', quantDeMorgan4)).
0.46/0.83	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', prop2setI)).
0.46/0.83	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', prop2set2propI)).
0.46/0.83	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', notdexE)).
0.46/0.83	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', notdallE)).
0.46/0.83	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', inCongP)).
0.46/0.83	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', in__Cong)).
0.46/0.83	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', emptyset__Cong)).
0.46/0.83	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setadjoin__Cong)).
0.46/0.83	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', powerset__Cong)).
0.46/0.83	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setunion__Cong)).
0.46/0.83	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', omega__Cong)).
0.46/0.83	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', subsetI1)).
0.46/0.83	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', eqimpsubset2)).
0.46/0.83	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', eqimpsubset1)).
0.46/0.83	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', subsetI2)).
0.46/0.83	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', emptysetsubset)).
0.46/0.83	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', subsetE)).
0.46/0.83	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', subsetE2)).
0.46/0.83	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', notsubsetI)).
0.46/0.83	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', notequalI1)).
0.46/0.83	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', notequalI2)).
0.46/0.83	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', subsetRefl)).
0.46/0.83	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', subsetTrans)).
0.46/0.83	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setadjoinSub)).
0.46/0.83	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setadjoinSub2)).
0.46/0.83	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', subset2powerset)).
0.46/0.83	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setextsub)).
0.46/0.83	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', subsetemptysetimpeq)).
0.46/0.83	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', powersetI1)).
0.46/0.83	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', powersetE1)).
0.46/0.83	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', inPowerset)).
0.46/0.83	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', powersetsubset)).
0.46/0.83	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binunionIL)).
0.46/0.83	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', upairset2IR)).
0.46/0.83	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binunionIR)).
0.46/0.83	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binunionEcases)).
0.46/0.83	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binunionE)).
0.46/0.83	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binunionLsub)).
0.46/0.83	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binunionRsub)).
0.46/0.83	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectI)).
0.46/0.83	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectSubset5)).
0.46/0.83	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectEL)).
0.46/0.83	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectLsub)).
0.46/0.83	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectSubset2)).
0.46/0.83	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectSubset3)).
0.46/0.83	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectER)).
0.46/0.83	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', disjointsetsI1)).
0.46/0.83	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectRsub)).
0.46/0.83	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectSubset4)).
0.46/0.83	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectSubset1)).
0.46/0.83	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', bs114d)).
0.46/0.83	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setminusI)).
0.46/0.83	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setminusEL)).
0.46/0.83	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setminusER)).
0.46/0.83	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setminusSubset2)).
0.46/0.83	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setminusERneg)).
0.46/0.83	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setminusELneg)).
0.46/0.83	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setminusILneg)).
0.46/0.83	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setminusIRneg)).
0.46/0.83	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setminusLsub)).
0.46/0.83	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setminusSubset1)).
0.46/0.83	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', symdiffE)).
0.46/0.83	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', symdiffI1)).
0.46/0.83	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', symdiffI2)).
0.46/0.83	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', symdiffIneg1)).
0.46/0.83	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', symdiffIneg2)).
0.46/0.83	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', secondinupair)).
0.46/0.83	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setukpairIL)).
0.46/0.83	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setukpairIR)).
0.46/0.83	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', kpairiskpair)).
0.46/0.83	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', kpairp)).
0.46/0.83	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', singletonsubset)).
0.46/0.83	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', singletoninpowerset)).
0.46/0.83	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', singletoninpowunion)).
0.46/0.83	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', upairset2E)).
0.46/0.83	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', upairsubunion)).
0.46/0.83	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', upairinpowunion)).
0.46/0.83	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ubforcartprodlem1)).
0.46/0.83	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ubforcartprodlem2)).
0.46/0.83	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ubforcartprodlem3)).
0.46/0.83	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', cartprodpairin)).
0.46/0.83	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.3nOKDTCzDP/E---3.1_16336.p', cartprodmempair1)).
0.46/0.83	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', cartprodmempair)).
0.46/0.83	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setunionE2)).
0.46/0.83	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setunionsingleton1)).
0.46/0.83	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setunionsingleton2)).
0.46/0.83	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setunionsingleton)).
0.46/0.83	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', singletonsuniq)).
0.46/0.83	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.3nOKDTCzDP/E---3.1_16336.p', setukpairinjL1)).
0.46/0.83	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', theprop)).
0.46/0.83	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', kfstpairEq)).
0.46/0.83	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', cartprodfstin)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', setukpairinjL2)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', setukpairinjL)).
0.46/0.83	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setukpairinjR11)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', setukpairinjR12)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', setukpairinjR1)).
0.46/0.83	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', upairequniteq)).
0.46/0.83	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setukpairinjR2)).
0.46/0.83	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setukpairinjR)).
0.46/0.83	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ksndpairEq)).
0.46/0.83	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', kpairsurjEq)).
0.46/0.83	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', cartprodsndin)).
0.46/0.83	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', cartprodpairmemEL)).
0.46/0.83	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', cartprodpairmemER)).
0.46/0.83	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', cartprodmempaircEq)).
0.46/0.83	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', cartprodfstpairEq)).
0.46/0.83	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', cartprodsndpairEq)).
0.46/0.83	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', cartprodpairsurjEq)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', app)).
0.46/0.83	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', infuncsetfunc)).
0.46/0.83	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ap2p)).
0.46/0.83	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', funcinfuncset)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', funcGraphProp1)).
0.46/0.83	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.3nOKDTCzDP/E---3.1_16336.p', funcGraphProp3)).
0.46/0.83	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', funcGraphProp2)).
0.46/0.83	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.3nOKDTCzDP/E---3.1_16336.p', funcextLem)).
0.46/0.83	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', funcGraphProp4)).
0.46/0.83	thf(funcext, axiom, ((funcext)<=>![X4:$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.3nOKDTCzDP/E---3.1_16336.p', funcext)).
0.46/0.83	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', funcext2)).
0.46/0.83	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ap2apEq1)).
0.46/0.83	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ap2apEq2)).
0.46/0.83	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', ifp)).
0.46/0.83	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', theeq)).
0.46/0.83	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', iftrue)).
0.46/0.83	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', iffalse)).
0.46/0.83	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', iftrueorfalse)).
0.46/0.83	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectT_lem)).
0.46/0.83	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binunionT_lem)).
0.46/0.83	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', powersetT_lem)).
0.46/0.83	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setminusT_lem)).
0.46/0.83	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', complementT_lem)).
0.46/0.83	thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', setextT)).
0.46/0.83	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', subsetTI)).
0.46/0.83	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', powersetTI1)).
0.46/0.83	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', powersetTE1)).
0.46/0.83	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', complementTI1)).
0.46/0.83	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', complementTE1)).
0.46/0.83	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectTELcontra)).
0.46/0.83	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binintersectTERcontra)).
0.46/0.83	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', contrasubsetT)).
0.46/0.83	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', contrasubsetT1)).
0.46/0.83	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', contrasubsetT2)).
0.46/0.83	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', contrasubsetT3)).
0.46/0.83	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', doubleComplementI1)).
0.46/0.83	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', doubleComplementE1)).
0.46/0.83	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', doubleComplementSub1)).
0.46/0.83	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', doubleComplementSub2)).
0.46/0.83	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', doubleComplementEq)).
0.46/0.83	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', complementTnotintersectT)).
0.46/0.83	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', complementImpComplementIntersect)).
0.46/0.83	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', complementSubsetComplementIntersect)).
0.46/0.83	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', complementInPowersetComplementIntersect)).
0.46/0.83	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', contraSubsetComplement)).
0.46/0.83	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', complementTcontraSubset)).
0.46/0.83	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binunionTILcontra)).
0.46/0.83	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binunionTIRcontra)).
0.46/0.83	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', inIntersectImpInUnion)).
0.46/0.83	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', inIntersectImpInUnion2)).
0.46/0.83	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', inIntersectImpInIntersectUnions)).
0.46/0.83	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', intersectInPowersetIntersectUnions)).
0.46/0.83	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', inComplementUnionImpNotIn1)).
0.46/0.83	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', inComplementUnionImpInComplement1)).
0.46/0.83	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binunionTE)).
0.46/0.83	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', binunionTEcontra)).
0.46/0.83	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', demorgan2a1)).
0.46/0.83	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', complementUnionInPowersetComplement)).
0.46/0.83	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', demorgan2a2)).
0.46/0.83	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', demorgan1a)).
0.46/0.83	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', demorgan1b)).
0.46/0.83	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', demorgan1)).
0.46/0.83	thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', demorgan2a)).
0.46/0.83	thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', demorgan2b2)).
0.46/0.83	thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', demorgan2b)).
0.46/0.83	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', demorgan2)).
0.46/0.83	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', woz13rule0)).
0.46/0.83	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', woz13rule1)).
0.46/0.83	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', woz13rule2)).
0.46/0.83	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', woz13rule3)).
0.46/0.83	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', woz13rule4)).
0.46/0.83	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', woz1_1)).
0.46/0.83	thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', woz1_2)).
0.46/0.83	thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', woz1_3)).
0.46/0.83	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', woz1_4)).
0.46/0.83	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.3nOKDTCzDP/E---3.1_16336.p', woz1_5)).
0.46/0.83	thf(c_0_293, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
0.46/0.83	thf(c_0_294, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
0.46/0.83	thf(c_0_295, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
0.46/0.83	thf(c_0_296, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
0.46/0.83	thf(c_0_297, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
0.46/0.83	thf(c_0_298, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
0.46/0.83	thf(c_0_299, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
0.46/0.83	thf(c_0_300, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
0.46/0.83	thf(c_0_301, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
0.46/0.83	thf(c_0_302, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
0.46/0.83	thf(c_0_303, 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])).
0.46/0.83	thf(c_0_304, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
0.46/0.83	thf(c_0_305, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
0.46/0.83	thf(c_0_306, 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])).
0.46/0.83	thf(c_0_307, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
0.46/0.83	thf(c_0_308, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
0.46/0.83	thf(c_0_309, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
0.46/0.83	thf(c_0_310, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
0.46/0.83	thf(c_0_311, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_293, c_0_294])).
0.46/0.83	thf(c_0_312, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
0.46/0.83	thf(c_0_313, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X984:$i]:((((X6 @ X2 @ X984))&![X985:$i]:((((X6 @ X2 @ X985))=>((X984)=(X985)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_295, c_0_296])).
0.46/0.83	thf(c_0_314, plain, ((descrp)=(![X1:$i > $o]:(((?[X986:$i]:((((X1 @ X986))&![X987:$i]:((((X1 @ X987))=>((X986)=(X987)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_297, c_0_296])).
0.46/0.83	thf(c_0_315, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
0.46/0.83	thf(c_0_316, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
0.46/0.83	thf(c_0_317, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
0.46/0.83	thf(c_0_318, plain, ((exuE1)=(![X1:$i > $o]:(((?[X988:$i]:((((X1 @ X988))&![X989:$i]:((((X1 @ X989))=>((X988)=(X989)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_298, c_0_296])).
0.46/0.83	thf(c_0_319, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X990:$i]:((((X1 @ X990))&![X991:$i]:((((X1 @ X991))=>((X990)=(X991)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_299, c_0_296])).
0.46/0.83	thf(c_0_320, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
0.46/0.83	thf(c_0_321, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_300])).
0.46/0.83	thf(c_0_322, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_301, c_0_300])).
0.46/0.83	thf(c_0_323, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_300])).
0.46/0.83	thf(c_0_324, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
0.46/0.83	thf(c_0_325, plain, ((exuE2)=(![X1:$i > $o]:(((?[X992:$i]:((((X1 @ X992))&![X993:$i]:((((X1 @ X993))=>((X992)=(X993)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_302, c_0_296])).
0.46/0.83	thf(c_0_326, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_300])).
0.46/0.83	thf(c_0_327, 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])).
0.46/0.83	thf(c_0_328, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X994:$i]:((((X1 @ X994))&![X995:$i]:((((X1 @ X995))=>((X994)=(X995))))))))))), inference(apply_def,[status(thm)],[c_0_303, c_0_296])).
0.46/0.83	thf(c_0_329, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X996:$i]:((((X1 @ X996))&![X997:$i]:((((X1 @ X997))=>((X996)=(X997)))))))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_296])).
0.46/0.83	thf(c_0_330, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X998:$i]:((((X1 @ X998))&![X999:$i]:((((X1 @ X999))=>((X998)=(X999))))))))))), inference(apply_def,[status(thm)],[c_0_305, c_0_296])).
0.46/0.83	thf(c_0_331, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1000:$i]:((((X1 @ X1000))&![X1001:$i]:((((X1 @ X1001))=>((X1000)=(X1001)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_306, c_0_296])).
0.46/0.83	thf(c_0_332, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1002:$i]:((((X1 @ X1002))&![X1003:$i]:((((X1 @ X1003))=>((X1002)=(X1003)))))))<=>(?[X1004:$i]:((((X17 @ X1004))&![X1005:$i]:((((X17 @ X1005))=>((X1004)=(X1005)))))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_296])).
0.46/0.83	thf(c_0_333, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1006:$i]:((((X1 @ X1006))&![X1007:$i]:((((X1 @ X1007))=>((X1006)=(X1007)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_308, c_0_296])).
0.46/0.83	thf(c_0_334, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1008:$i]:((((X1 @ X1008))&![X1009:$i]:((((X1 @ X1009))=>((X1008)=(X1009)))))))=>((?[X1010:$i]:((((X17 @ X1010))&![X1011:$i]:((((X17 @ X1011))=>((X1010)=(X1011)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_309, c_0_296])).
0.46/0.83	thf(c_0_335, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
0.46/0.83	thf(c_0_336, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
0.46/0.83	thf(c_0_337, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
0.46/0.83	thf(c_0_338, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
0.46/0.83	thf(c_0_339, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
0.46/0.83	thf(c_0_340, plain, ((ex1I)<=>![X4:$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])).
0.46/0.83	thf(c_0_341, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
0.46/0.83	thf(c_0_342, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
0.46/0.83	thf(c_0_343, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
0.46/0.83	thf(c_0_344, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
0.46/0.83	thf(c_0_345, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
0.46/0.83	thf(c_0_346, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_310, c_0_294])).
0.46/0.83	thf(c_0_347, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
0.46/0.83	thf(c_0_348, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
0.46/0.83	thf(c_0_349, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
0.46/0.83	thf(c_0_350, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
0.46/0.83	thf(c_0_351, plain, ((funcImageSingleton)<=>![X4:$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])).
0.46/0.83	thf(c_0_352, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
0.46/0.83	thf(c_0_353, plain, ((lamProp)<=>![X4:$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])).
0.46/0.83	thf(c_0_354, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
0.46/0.83	thf(c_0_355, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
0.46/0.83	thf(c_0_356, axiom, ((brelnall1)=(![X4:$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_294])).
0.46/0.83	thf(c_0_357, 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_294])).
0.46/0.83	thf(c_0_358, 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])).
0.46/0.83	thf(c_0_359, 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_294])).
0.46/0.83	thf(c_0_360, 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_294])).
0.46/0.83	thf(c_0_361, 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])).
0.46/0.83	thf(c_0_362, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
0.46/0.83	thf(c_0_363, 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])).
0.46/0.83	thf(c_0_364, 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])).
0.46/0.83	thf(c_0_365, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
0.46/0.83	thf(c_0_366, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
0.46/0.83	thf(c_0_367, plain, ((iffalseProp2)<=>![X4:$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])).
0.46/0.83	thf(c_0_368, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
0.46/0.83	thf(c_0_369, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
0.46/0.83	thf(c_0_370, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
0.46/0.83	thf(c_0_371, axiom, ((breln1all2)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[breln1all2, c_0_311])).
0.46/0.83	thf(c_0_372, axiom, ((breln1SetBreln1)=(![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>((subset @ X33 @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[breln1SetBreln1, c_0_311])).
0.46/0.83	thf(c_0_373, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 8 */:$i]:(((X52 @ X2 @ Z0)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ Z0 @ X14) @ X33))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])).
0.46/0.83	thf(c_0_374, plain, ((setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X4)))))), inference(apply_def,[status(thm)],[c_0_312, c_0_311])).
0.46/0.83	thf(c_0_375, plain, ((epred1_0)<=>![X1024:$i]:(?[X1025:$i]:((((![X1026:$i]:(((in @ X1026 @ X1025)=>![X1027:$i]:(((in @ X1027 @ X1026)=>(in @ X1027 @ X1024)))))&![X1028:$i, X1029:$i]:((((in @ X1028 @ X1024)&(in @ X1029 @ X1024))=>(![X1030:$i]:(((in @ X1030 @ X1025)=>((in @ X1028 @ X1030)<=>(in @ X1029 @ X1030))))=>((X1028)=(X1029))))))&![X1031:$i, X1032:$i]:((((in @ X1031 @ X1025)&(in @ X1032 @ X1025))=>(![X1033:$i]:(((in @ X1033 @ X1031)=>(in @ X1033 @ X1032)))|![X1034:$i]:(((in @ X1034 @ X1032)=>(in @ X1034 @ X1031)))))))&![X1035:$i]:(((![X1036:$i]:(((in @ X1036 @ X1035)=>(in @ X1036 @ X1024)))&?[X1037:$i]:((in @ X1037 @ X1035)))=>?[X1038:$i, X1039:$i]:(((((in @ X1038 @ X1025)&(in @ X1039 @ X1035))&~(?[X1040:$i]:(((in @ X1040 @ X1038)&(in @ X1040 @ X1035)))))&![X1041:$i]:(((in @ X1041 @ X1025)=>(![X1042:$i]:(((in @ X1042 @ X1041)=>(in @ X1042 @ X1038)))|(in @ X1039 @ X1041)))))))))))), introduced(definition)).
0.46/0.83	thf(c_0_376, negated_conjecture, ~((![X1962:$i, X1963:$i]:((![X1964:$i]:(((in @ X1964 @ X1962)<=>(in @ X1964 @ X1963)))=>((X1962)=(X1963))))=>(![X1012:$i]:(~(in @ X1012 @ emptyset))=>(![X1013:$i, X1014:$i, X1015:$i]:(((in @ X1015 @ (setadjoin @ X1013 @ X1014))<=>(((X1015)=(X1013))|(in @ X1015 @ X1014))))=>(![X1959:$i, X1960:$i]:(((in @ X1960 @ (powerset @ X1959))<=>![X1961:$i]:(((in @ X1961 @ X1960)=>(in @ X1961 @ X1959)))))=>(![X1016:$i, X1017:$i]:(((in @ X1017 @ (setunion @ X1016))<=>?[X1018:$i]:(((in @ X1017 @ X1018)&(in @ X1018 @ X1016)))))=>((in @ emptyset @ omega)=>(![X1019:$i]:(((in @ X1019 @ omega)=>(in @ (setadjoin @ X1019 @ X1019) @ omega)))=>(![X1956:$i]:((((in @ emptyset @ X1956)&![X1957:$i]:((((in @ X1957 @ omega)&(in @ X1957 @ X1956))=>(in @ (setadjoin @ X1957 @ X1957) @ X1956))))=>![X1958:$i]:(((in @ X1958 @ omega)=>(in @ X1958 @ X1956)))))=>(![X1948:$i > $i > $o, X1949:$i]:((![X1950:$i]:(((in @ X1950 @ X1949)=>?[X1951:$i]:(((X1948 @ X1950 @ X1951)&![X1952:$i]:(((X1948 @ X1950 @ X1952)=>((X1951)=(X1952))))))))=>?[X1953:$i]:(![X1954:$i]:(((in @ X1954 @ X1953)<=>?[X1955:$i]:(((in @ X1955 @ X1949)&(X1948 @ X1955 @ X1954))))))))=>(![X1020:$i]:((?[X1021:$i]:((in @ X1021 @ X1020))=>?[X1022:$i]:(((in @ X1022 @ X1020)&~(?[X1023:$i]:(((in @ X1023 @ X1022)&(in @ X1023 @ X1020))))))))=>((epred1_0)=>(![X1945:$i > $o]:((?[X1946:$i]:(((X1945 @ X1946)&![X1947:$i]:(((X1945 @ X1947)=>((X1946)=(X1947))))))=>(X1945 @ (descr @ (^[Z0/* 17 */:$i]:(X1945 @ Z0))))))=>(![X1942:$i, X1943:$i > $o, X1944:$i]:(((in @ X1944 @ X1942)=>((X1943 @ X1944)=>(in @ X1944 @ (dsetconstr @ X1942 @ X1943)))))=>(![X1939:$i, X1940:$i > $o, X1941:$i]:(((in @ X1941 @ (dsetconstr @ X1939 @ X1940))=>(in @ X1941 @ X1939)))=>(![X1936:$i, X1937:$i > $o, X1938:$i]:(((in @ X1938 @ (dsetconstr @ X1936 @ X1937))=>(X1937 @ X1938)))=>(![X1931:$i > $o]:((?[X1932:$i]:(((X1931 @ X1932)&![X1933:$i]:(((X1931 @ X1933)=>((X1932)=(X1933))))))=>?[X1934:$i]:(((X1931 @ X1934)&![X1935:$i]:(((X1931 @ X1935)=>((X1934)=(X1935))))))))=>(![X1929:$o, X1930:$i]:(((in @ X1930 @ (prop2set @ ((X1929))))=>(X1929)))=>(![X1043:$i]:(((in @ X1043 @ emptyset)=>![X1044:$o]:((X1044))))=>(![X1045:$i]:(((in @ X1045 @ emptyset)=>~($true)))=>(![X1046:$i]:(~(in @ X1046 @ emptyset))=>(![X1925:$i > $o]:((?[X1926:$i]:(((X1925 @ X1926)&![X1927:$i]:(((X1925 @ X1927)=>((X1926)=(X1927))))))=>?[X1928:$i]:((X1925 @ X1928))))=>(![X1047:$i, X1048:$i]:((![X1049:$i]:(((in @ X1049 @ X1047)=>(in @ X1049 @ X1048)))=>(![X1050:$i]:(((in @ X1050 @ X1048)=>(in @ X1050 @ X1047)))=>((X1047)=(X1048)))))=>(![X1051:$i]:((![X1052:$i]:(~(in @ X1052 @ X1051))=>((X1051)=(emptyset))))=>(![X1053:$i]:((![X1054:$i]:(~(in @ X1054 @ X1053))=>((X1053)=(emptyset))))=>(![X1922:$i, X1923:$i > $o, X1924:$i]:(((in @ X1924 @ X1922)=>((in @ X1924 @ (dsetconstr @ X1922 @ X1923))<=>(X1923 @ X1924))))=>(![X1055:$i]:((((X1055)!=(emptyset))=>?[X1056:$i]:((in @ X1056 @ X1055))))=>(![X1919:$i, X1920:$i > $o, X1921:$i]:(((in @ X1921 @ X1919)=>((X1920 @ X1921)=>((dsetconstr @ X1919 @ X1920)!=(emptyset)))))=>(![X1917:$i]:((?[X1918:$i]:((in @ X1918 @ X1917))=>((X1917)!=(emptyset))))=>(![X1915:$i, X1916:$i]:((in @ X1915 @ (setadjoin @ X1915 @ X1916)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1912:$i, X1913:$i, X1914:$i]:(((in @ X1914 @ X1913)=>(in @ X1914 @ (setadjoin @ X1912 @ X1913))))=>(![X1057:$i, X1058:$i, X1059:$i]:(((in @ X1059 @ (setadjoin @ X1057 @ X1058))=>![X1060:$o]:(((((X1059)=(X1057))=>(X1060))=>(((in @ X1059 @ X1058)=>(X1060))=>(X1060))))))=>(![X1909:$i, X1910:$i, X1911:$i]:(((in @ X1911 @ (setadjoin @ X1909 @ X1910))=>(((X1911)=(X1909))|(in @ X1911 @ X1910))))=>(![X1908:$i]:(((dsetconstr @ X1908 @ (^[Z0/* 1 */:$i]:($true)))=(X1908)))=>(![X1061:$i, X1062:$i]:((![X1063:$i]:(((in @ X1063 @ X1062)=>(in @ X1063 @ X1061)))=>(in @ X1062 @ (powerset @ X1061))))=>(![X1907:$i]:((in @ emptyset @ (powerset @ X1907)))=>(![X1906:$i]:((in @ emptyset @ (powerset @ X1906)))=>(![X1064:$i, X1065:$i, X1066:$i]:(((in @ X1065 @ (powerset @ X1064))=>((in @ X1066 @ X1065)=>(in @ X1066 @ X1064))))=>(![X1903:$i, X1904:$i, X1905:$i]:(((in @ X1904 @ X1905)=>((in @ X1905 @ X1903)=>(in @ X1904 @ (setunion @ X1903)))))=>(![X1899:$i, X1900:$i]:(((in @ X1900 @ (setunion @ X1899))=>![X1901:$o]:((![X1902:$i]:(((in @ X1900 @ X1902)=>((in @ X1902 @ X1899)=>(X1901))))=>(X1901)))))=>(![X1067:$i, X1068:$i]:(((in @ X1068 @ X1067)=>(in @ X1068 @ (powerset @ (setunion @ X1067)))))=>(![X1069:$i > $o]:((?[X1070:$i]:(((X1069 @ X1070)&![X1071:$i]:(((X1069 @ X1071)=>((X1070)=(X1071))))))=>?[X1072:$i]:(![X1073:$i]:(((X1069 @ X1073)<=>((X1073)=(X1072)))))))=>(![X1074:$i]:((((X1074)!=(emptyset))=>?[X1075:$i]:(((in @ X1075 @ X1074)&$true))))=>(![X1076:$i, X1077:$i]:(((in @ X1076 @ (setadjoin @ X1077 @ emptyset))=>((X1076)=(X1077))))=>(![X1078:$i, X1079:$i]:((((X1078)!=(X1079))=>~(in @ X1079 @ (setadjoin @ X1078 @ emptyset))))=>(![X1897:$i, X1898:$i]:((((X1897)=(X1898))=>(in @ X1897 @ (setadjoin @ X1898 @ emptyset))))=>(![X1895:$i, X1896:$i]:(((in @ X1895 @ (setadjoin @ X1896 @ emptyset))=>(in @ X1896 @ (setadjoin @ X1895 @ emptyset))))=>(![X1080:$i, X1081:$i, X1082:$i]:(((in @ X1082 @ (setadjoin @ X1080 @ (setadjoin @ X1081 @ emptyset)))=>(((X1082)=(X1080))|((X1082)=(X1081)))))=>(![X1893:$i, X1894:$i]:((in @ X1893 @ (setadjoin @ X1893 @ (setadjoin @ X1894 @ emptyset))))=>(![X1083:$i, X1084:$i]:((in @ X1084 @ (setadjoin @ X1083 @ (setadjoin @ X1084 @ emptyset))))=>(![X1085:$i, X1086:$i > $o]:((?[X1087:$i]:(((in @ X1087 @ X1085)&(X1086 @ X1087)))=>(((dsetconstr @ X1085 @ X1086)=(emptyset))=>~($true))))=>(![X1891:$i > $o, X1892:$i]:(((in @ X1892 @ emptyset)=>(X1891 @ X1892)))=>(![X1088:$i, X1089:$i > $o]:((~(![X1090:$i]:(((in @ X1090 @ X1088)=>(X1089 @ X1090))))=>?[X1091:$i]:(((in @ X1091 @ X1088)&~((X1089 @ X1091))))))=>(![X1092:$i, X1093:$i > $o]:((![X1094:$i]:(((in @ X1094 @ X1092)=>~((X1093 @ X1094))))=>~(?[X1095:$i]:(((in @ X1095 @ X1092)&(X1093 @ 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y_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[breln1all1]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_313]), foundationAx]), wellorderingAx]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), c_0_318]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_319]), setext]), emptyI]), noeltsimpempty]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_324]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_325]), c_0_326]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_327]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_328]), c_0_329]), c_0_330]), inCongP]), in__Cong]), c_0_331]), c_0_332]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_333]), c_0_334]), c_0_335]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_336]), c_0_337]), 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_338]), c_0_339]), c_0_340]), c_0_341]), singletonsuniq]), setukpairinjL1]), c_0_342]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_343]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), c_0_348]), c_0_349]), c_0_350]), c_0_351]), c_0_352]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_353]), c_0_354]), c_0_355]), c_0_356]), c_0_357]), c_0_358]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_359]), c_0_360]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_361]), c_0_362]), c_0_363]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), c_0_368]), c_0_369]), c_0_370]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3]), woz1_4]), woz1_5]), c_0_311]), c_0_371]), c_0_372]), c_0_373]), c_0_374])])]), c_0_375])).
0.46/0.83	thf(c_0_377, negated_conjecture, ![X1965:$i, X1966:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1978:$i, X1979:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1987:$i, X1988:$i > $i > $o, X1989:$i, X1991:$i, X1994:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2001:$i, X2002:$i > $o, X2003:$i, X2005:$i, X2006:$i > $o, X2007:$i, X2008:$i, X2009:$i > $o, X2010:$i, X2011:$i, X2012:$i > $o, X2013:$i, X2014:$i > $o, X2015:$i, X2018:$i, X2019:$o, X2020:$i, X2021:$i, X2022:$o, X2023:$i, X2024:$i, X2025:$i > $o, X2026:$i, X2029:$i, X2030:$i, X2033:$i, X2035:$i, X2037:$i, X2038:$i > $o, X2039:$i, X2040:$i, X2042:$i, X2043:$i > $o, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$o, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$o, X2075:$i, X2076:$i, X2077:$i > $o, X2078:$i, X2081:$i, X2082:$i, X2083:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i > $o, X2102:$i, X2103:$i > $o, X2104:$i, X2105:$i, X2106:$i > $o, X2107:$i, X2109:$i, X2110:$i > $o, X2112:$i, X2113:$i, X2114:$i > $o, X2116:$i, X2117:$i, X2118:$i > $o, X2119:$i, X2121:$o, X2122:$o, X2123:$i, X2124:$i > $o, X2126:$i, X2127:$i, X2128:$i > $o, X2129:$i, X2131:$i > $o, X2132:$i, X2135:$i, X2136:$i > $o, X2137:$i, X2141:$i, X2142:$i > $o, X2143:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i > $o, X2156:$i, X2158:$i, X2159:$i, X2160:$i > $o, X2161:$i > $o, X2164:$i, X2167:$i, X2168:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i > $o, X2181:$i, X2183:$i, X2184:$i, X2185:$i > $o, X2186:$i > $o, X2189:$i, X2191:$i, X2193:$i, X2194:$i, X2195:$i > $o, X2196:$i > $o, X2199:$i, X2200:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i > $o, X2247:$i, X2248:$i > $o, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$o, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$o, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i > 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X2501:$i, X2502:$i, X2503:$i > $i > $o, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i > $i > $o, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i > $i > $o, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i > $i, X2542:$i, X2543:$i, X2544:$i > $i, X2546:$i, X2547:$i, X2548:$i > $i, X2550:$i, X2551:$i, X2552:$i, X2553:$i > $o, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i > $o, X2563:$i, X2564:$i, X2565:$i > $o, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2607:$i, X2608:$i, 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X2703)|~(in @ X2703 @ (powerset @ X2701))|~(in @ X2702 @ (powerset @ X2701)))&(~(in @ (esk85_3 @ X2701 @ X2702 @ X2703) @ X2703)|(subset @ X2702 @ X2703)|~(in @ X2703 @ (powerset @ X2701))|~(in @ X2702 @ (powerset @ X2701)))))&((((in @ (esk86_3 @ X2705 @ X2706 @ X2707) @ X2705)|(in @ X2706 @ (powerset @ X2707))|~(in @ X2707 @ (powerset @ X2705))|~(in @ X2706 @ (powerset @ X2705)))&(((in @ (esk86_3 @ X2705 @ X2706 @ X2707) @ X2706)|(in @ X2706 @ (powerset @ X2707))|~(in @ X2707 @ (powerset @ X2705))|~(in @ X2706 @ (powerset @ X2705)))&(~(in @ (esk86_3 @ X2705 @ X2706 @ X2707) @ X2707)|(in @ X2706 @ (powerset @ X2707))|~(in @ X2707 @ (powerset @ X2705))|~(in @ X2706 @ (powerset @ X2705)))))&((~(in @ X2710 @ (powerset @ X2709))|(~(in @ X2711 @ (powerset @ X2709))|(~(in @ X2712 @ X2709)|(~(in @ X2710 @ (powerset @ X2711))|(~(in @ X2712 @ X2710)|(in @ X2712 @ X2711))))))&((~(in @ X2714 @ (powerset @ X2713))|(~(in @ X2715 @ X2713)|(~(in @ X2715 @ X2714)|~(in @ X2715 @ (setminus @ X2713 @ X2714)))))&((~(in @ X2717 @ (powerset @ X2716))|(~(in @ X2718 @ X2716)|((in @ X2718 @ (setminus @ X2716 @ X2717))|(in @ X2718 @ X2717))))&((~(in @ X2720 @ (powerset @ X2719))|(~(in @ X2721 @ (powerset @ X2719))|(~(in @ X2722 @ X2719)|((in @ X2722 @ X2720)|~(in @ X2722 @ (binintersect @ X2720 @ X2721))))))&((~(in @ X2724 @ (powerset @ X2723))|(~(in @ X2725 @ (powerset @ X2723))|(~(in @ X2726 @ X2723)|((in @ X2726 @ X2725)|~(in @ X2726 @ (binintersect @ X2724 @ X2725))))))&((~(in @ X2728 @ (powerset @ X2727))|(~(in @ X2729 @ (powerset @ X2727))|(~(in @ X2730 @ X2727)|(~(subset @ X2728 @ (setminus @ X2727 @ X2729))|(~(in @ X2730 @ X2729)|~(in @ X2730 @ X2728))))))&((~(in @ X2732 @ (powerset @ X2731))|(~(in @ X2733 @ (powerset @ X2731))|(~(in @ X2734 @ X2731)|(~(subset @ X2732 @ X2733)|((in @ X2734 @ X2733)|~(in @ X2734 @ X2732))))))&((~(in @ X2736 @ (powerset @ X2735))|(~(in @ X2737 @ (powerset @ X2735))|(~(subset @ X2736 @ X2737)|(subset @ (setminus @ X2735 @ X2737) @ (setminus @ X2735 @ X2736)))))&((~(in @ X2739 @ (powerset @ X2738))|(~(in @ X2740 @ (powerset @ X2738))|(~(subset @ (setminus @ X2738 @ X2740) @ (setminus @ X2738 @ X2739))|(subset @ X2739 @ X2740))))&((~(in @ X2742 @ (powerset @ X2741))|(~(in @ X2743 @ X2741)|(~(in @ X2743 @ X2742)|(in @ X2743 @ (setminus @ X2741 @ (setminus @ X2741 @ X2742))))))&((~(in @ X2745 @ (powerset @ X2744))|(~(in @ X2746 @ X2744)|(~(in @ X2746 @ (setminus @ X2744 @ (setminus @ X2744 @ X2745)))|(in @ X2746 @ X2745))))&((~(in @ X2748 @ (powerset @ X2747))|(subset @ X2748 @ (setminus @ X2747 @ (setminus @ X2747 @ X2748))))&((~(in @ X2750 @ (powerset @ X2749))|(subset @ (setminus @ X2749 @ (setminus @ X2749 @ X2750)) @ X2750))&((~(in @ X2752 @ (powerset @ X2751))|((X2752)=(setminus @ X2751 @ (setminus @ X2751 @ X2752))))&((~(in @ X2754 @ (powerset @ X2753))|(~(in @ X2755 @ (powerset @ X2753))|(~(in @ X2756 @ X2753)|(~(in @ X2756 @ (setminus @ X2753 @ X2754))|~(in @ X2756 @ (binintersect @ X2754 @ X2755))))))&((~(in @ X2758 @ (powerset @ X2757))|(~(in @ X2759 @ (powerset @ X2757))|(~(in @ X2760 @ X2757)|(~(in @ X2760 @ (setminus @ X2757 @ X2758))|(in @ X2760 @ (setminus @ X2757 @ (binintersect @ X2758 @ X2759)))))))&((~(in @ X2762 @ (powerset @ X2761))|(~(in @ X2763 @ (powerset @ X2761))|(subset @ (setminus @ X2761 @ X2762) @ (setminus @ X2761 @ (binintersect @ X2762 @ X2763)))))&((~(in @ X2765 @ (powerset @ X2764))|(~(in @ X2766 @ (powerset @ X2764))|(in @ (setminus @ X2764 @ X2765) @ (powerset @ (setminus @ X2764 @ (binintersect @ X2765 @ X2766))))))&((~(in @ X2768 @ (powerset @ X2767))|(~(in @ X2769 @ (powerset @ X2767))|(~(subset @ X2768 @ (setminus @ X2767 @ X2769))|(~(in @ X2770 @ X2767)|(~(in @ X2770 @ X2769)|(in @ X2770 @ (setminus @ X2767 @ X2768)))))))&((~(in @ X2772 @ (powerset @ X2771))|(~(in @ X2773 @ (powerset @ X2771))|(~(subset @ X2772 @ (setminus @ X2771 @ X2773))|(subset @ X2773 @ (setminus @ X2771 @ X2772)))))&((~(in @ X2775 @ (powerset @ X2774))|(~(in @ X2776 @ (powerset @ X2774))|(~(in @ X2777 @ X2774)|((in @ X2777 @ (binunion @ X2775 @ X2776))|~(in @ X2777 @ X2775)))))&((~(in @ X2779 @ (powerset @ X2778))|(~(in @ X2780 @ (powerset @ X2778))|(~(in @ X2781 @ X2778)|((in @ X2781 @ (binunion @ X2779 @ X2780))|~(in @ X2781 @ X2780)))))&((~(in @ X2783 @ (powerset @ X2782))|(~(in @ X2784 @ (powerset @ X2782))|(~(in @ X2785 @ (powerset @ X2782))|(~(in @ X2786 @ X2782)|(~(in @ X2786 @ (binintersect @ X2783 @ X2784))|(in @ X2786 @ (binunion @ X2783 @ X2785)))))))&((~(in @ X2788 @ (powerset @ X2787))|(~(in @ X2789 @ (powerset @ X2787))|(~(in @ X2790 @ (powerset @ X2787))|(~(in @ X2791 @ X2787)|(~(in @ X2791 @ (binintersect @ X2788 @ X2789))|(in @ X2791 @ (binunion @ X2789 @ X2790)))))))&((~(in @ X2793 @ (powerset @ X2792))|(~(in @ X2794 @ (powerset @ X2792))|(~(in @ X2795 @ (powerset @ X2792))|(~(in @ X2796 @ X2792)|(~(in @ X2796 @ (binintersect @ X2793 @ X2794))|(in @ X2796 @ (binintersect @ (binunion @ X2793 @ X2795) @ (binunion @ X2794 @ X2795))))))))&((~(in @ X2798 @ (powerset @ X2797))|(~(in @ X2799 @ (powerset @ X2797))|(~(in @ X2800 @ (powerset @ X2797))|(in @ (binintersect @ X2798 @ X2799) @ (powerset @ (binintersect @ (binunion @ X2798 @ X2800) @ (binunion @ X2799 @ X2800)))))))&((~(in @ X2802 @ (powerset @ X2801))|(~(in @ X2803 @ (powerset @ X2801))|(~(in @ X2804 @ X2801)|(~(in @ X2804 @ (setminus @ X2801 @ (binunion @ X2802 @ X2803)))|~(in @ X2804 @ X2802)))))&((~(in @ X2806 @ (powerset @ X2805))|(~(in @ X2807 @ (powerset @ X2805))|(~(in @ X2808 @ X2805)|(~(in @ X2808 @ (setminus @ X2805 @ (binunion @ X2806 @ X2807)))|(in @ X2808 @ (setminus @ X2805 @ X2806))))))&(((((in @ X2813 @ X2811)|(X2812)|(in @ X2813 @ X2810)|~(in @ X2813 @ (binunion @ X2810 @ X2811))|~(in @ X2813 @ X2809)|~(in @ X2811 @ (powerset @ X2809))|~(in @ X2810 @ (powerset @ X2809)))&(~(X2812)|(X2812)|(in @ X2813 @ X2810)|~(in @ X2813 @ (binunion @ X2810 @ X2811))|~(in @ X2813 @ X2809)|~(in @ X2811 @ (powerset @ X2809))|~(in @ X2810 @ (powerset @ X2809))))&(((in @ X2813 @ X2811)|(X2812)|~(X2812)|~(in @ X2813 @ (binunion @ X2810 @ X2811))|~(in @ X2813 @ X2809)|~(in @ X2811 @ (powerset @ X2809))|~(in @ X2810 @ (powerset @ X2809)))&(~(X2812)|(X2812)|~(X2812)|~(in @ X2813 @ (binunion @ X2810 @ X2811))|~(in @ X2813 @ X2809)|~(in @ X2811 @ (powerset @ X2809))|~(in @ X2810 @ (powerset @ X2809)))))&((~(in @ X2815 @ (powerset @ X2814))|(~(in @ X2816 @ (powerset @ X2814))|(~(in @ X2817 @ X2814)|((in @ X2817 @ X2815)|((in @ X2817 @ X2816)|~(in @ X2817 @ (binunion @ X2815 @ X2816)))))))&((~(in @ X2819 @ (powerset @ X2818))|(~(in @ X2820 @ (powerset @ X2818))|(~(in @ X2821 @ X2818)|(~(in @ X2821 @ (setminus @ X2818 @ (binunion @ X2819 @ X2820)))|(in @ X2821 @ (setminus @ X2818 @ X2819))))))&((~(in @ X2823 @ (powerset @ X2822))|(~(in @ X2824 @ (powerset @ X2822))|(in @ (setminus @ X2822 @ (binunion @ X2823 @ X2824)) @ (powerset @ (setminus @ X2822 @ X2823)))))&((~(in @ X2826 @ (powerset @ X2825))|(~(in @ X2827 @ (powerset @ X2825))|(~(in @ X2828 @ X2825)|(~(in @ X2828 @ (setminus @ X2825 @ (binunion @ X2826 @ X2827)))|(in @ X2828 @ (setminus @ X2825 @ X2827))))))&((~(in @ X2830 @ (powerset @ X2829))|(~(in @ X2831 @ (powerset @ X2829))|(~(in @ X2832 @ X2829)|(~(in @ X2832 @ (setminus @ X2829 @ (binintersect @ X2830 @ X2831)))|(in @ X2832 @ (binunion @ (setminus @ X2829 @ X2830) @ (setminus @ X2829 @ X2831)))))))&((~(in @ X2834 @ (powerset @ X2833))|(~(in @ X2835 @ (powerset @ X2833))|(~(in @ X2836 @ X2833)|(~(in @ X2836 @ (binunion @ (setminus @ X2833 @ X2834) @ (setminus @ X2833 @ X2835)))|(in @ X2836 @ (setminus @ X2833 @ (binintersect @ X2834 @ X2835)))))))&((~(in @ X2838 @ (powerset @ X2837))|(~(in @ X2839 @ (powerset @ X2837))|((setminus @ X2837 @ (binintersect @ X2838 @ X2839))=(binunion @ (setminus @ X2837 @ X2838) @ (setminus @ X2837 @ X2839)))))&((~(in @ X2841 @ (powerset @ X2840))|(~(in @ X2842 @ (powerset @ X2840))|(~(in @ X2843 @ X2840)|(~(in @ X2843 @ (setminus @ X2840 @ (binunion @ X2841 @ X2842)))|(in @ X2843 @ (binintersect @ (setminus @ X2840 @ X2841) @ (setminus @ X2840 @ X2842)))))))&((~(in @ X2845 @ (powerset @ X2844))|(~(in @ X2846 @ (powerset @ X2844))|(~(in @ X2847 @ X2844)|(~(in @ X2847 @ (setminus @ X2844 @ X2845))|(~(in @ X2847 @ (setminus @ X2844 @ X2846))|(in @ X2847 @ (setminus @ X2844 @ (binunion @ X2845 @ X2846))))))))&((~(in @ X2849 @ (powerset @ X2848))|(~(in @ X2850 @ (powerset @ X2848))|(~(in @ X2851 @ X2848)|(~(in @ X2851 @ (binintersect @ (setminus @ X2848 @ X2849) @ (setminus @ X2848 @ X2850)))|(in @ X2851 @ (setminus @ X2848 @ (binunion @ X2849 @ X2850)))))))&((~(in @ X2853 @ (powerset @ X2852))|(~(in @ X2854 @ (powerset @ X2852))|((setminus @ X2852 @ (binunion @ X2853 @ X2854))=(binintersect @ (setminus @ X2852 @ X2853) @ (setminus @ X2852 @ X2854)))))&((~(in @ X2856 @ (powerset @ X2855))|(~(in @ X2857 @ (powerset @ X2855))|(~(in @ X2858 @ (binintersect @ X2856 @ X2857))|(in @ X2858 @ X2855))))&((~(in @ X2860 @ (powerset @ X2859))|(~(in @ X2861 @ (powerset @ X2859))|(~(in @ X2862 @ (powerset @ X2859))|(~(subset @ X2860 @ X2862)|(subset @ (binintersect @ X2860 @ X2861) @ X2862)))))&((~(in @ X2864 @ (powerset @ X2863))|(~(in @ X2865 @ (powerset @ X2863))|(~(in @ X2866 @ (powerset @ X2863))|(~(subset @ X2865 @ X2866)|(subset @ (binintersect @ X2864 @ X2865) @ X2866)))))&((~(in @ X2868 @ (powerset @ X2867))|(~(in @ X2869 @ (powerset @ X2867))|(~(in @ X2870 @ (powerset @ X2867))|(~(subset @ X2868 @ X2869)|(~(subset @ X2868 @ X2870)|(subset @ X2868 @ (binintersect @ X2869 @ X2870)))))))&((~(in @ X2872 @ (powerset @ X2871))|(~(in @ X2873 @ (powerset @ X2871))|(~(in @ X2874 @ (powerset @ X2871))|(~(in @ X2875 @ (powerset @ X2871))|(~(subset @ X2872 @ X2874)|(~(subset @ X2873 @ X2875)|(subset @ (binintersect @ X2872 @ X2873) @ (binintersect @ X2874 @ X2875))))))))&((~(in @ X2877 @ (powerset @ X2876))|(~(in @ X2878 @ (powerset @ X2876))|(in @ (setminus @ X2876 @ X2877) @ (powerset @ (setminus @ X2876 @ (binintersect @ X2877 @ X2878))))))&((~(in @ X2880 @ (powerset @ X2879))|(~(in @ X2881 @ (powerset @ X2879))|(~(in @ X2882 @ (powerset @ X2879))|(~(in @ X2883 @ (powerset @ X2879))|((setminus @ X2879 @ (binintersect @ (binunion @ X2880 @ X2881) @ (binunion @ X2882 @ X2883)))=(binunion @ (binintersect @ (setminus @ X2879 @ X2880) @ (setminus @ X2879 @ X2881)) @ (binintersect @ (setminus @ X2879 @ X2882) @ (setminus @ X2879 @ X2883))))))))&((~(in @ X2885 @ (powerset @ X2884))|(~(in @ X2886 @ (powerset @ X2884))|(~(in @ X2887 @ (powerset @ X2884))|(in @ (binintersect @ X2885 @ X2886) @ (powerset @ (binintersect @ (binunion @ X2885 @ X2887) @ (binunion @ X2886 @ X2887)))))))&((~(in @ X2889 @ (powerset @ X2888))|(~(in @ X2890 @ (powerset @ X2888))|(~(subset @ X2889 @ (setminus @ X2888 @ X2890))|(subset @ X2890 @ (setminus @ X2888 @ X2889)))))&((~(in @ X2892 @ (powerset @ X2891))|(~(in @ X2893 @ (powerset @ X2891))|(in @ (setminus @ X2891 @ (binunion @ X2892 @ X2893)) @ (powerset @ (setminus @ X2891 @ X2892)))))&((((in @ (esk87_3 @ X2894 @ X2895 @ X2896) @ X2894)|(~(in @ X2899 @ X2895)|(X2896 @ X2899))|~(subset @ X2895 @ (cartprod @ X2894 @ X2894)))&(((in @ (esk88_3 @ X2894 @ X2895 @ X2896) @ X2894)|(~(in @ X2899 @ X2895)|(X2896 @ X2899))|~(subset @ X2895 @ (cartprod @ X2894 @ X2894)))&(((in @ (kpair @ (esk87_3 @ X2894 @ X2895 @ X2896) @ (esk88_3 @ X2894 @ X2895 @ X2896)) @ X2895)|(~(in @ X2899 @ X2895)|(X2896 @ X2899))|~(subset @ X2895 @ (cartprod @ X2894 @ X2894)))&(~(X2896 @ (kpair @ (esk87_3 @ X2894 @ X2895 @ X2896) @ (esk88_3 @ X2894 @ X2895 @ X2896)))|(~(in @ X2899 @ X2895)|(X2896 @ X2899))|~(subset @ X2895 @ (cartprod @ X2894 @ X2894))))))&((~(in @ X2901 @ (breln1Set @ X2900))|(subset @ X2901 @ (cartprod @ X2900 @ X2900)))&((((in @ (esk89_3 @ X2902 @ X2903 @ X2904) @ X2902)|(~(in @ X2907 @ (breln1Set @ X2903))|(~(reflwellordering @ X2903 @ X2907)|(~(in @ X2908 @ X2902)|(singleton @ (dsetconstr @ X2903 @ (^[Z0/* 8 */:$i]:((X2904 @ X2908 @ Z0&![X1487:$i]:(((in @ X1487 @ X2903)=>(X2904 @ X2908 @ X1487=>(in @ (kpair @ Z0 @ X1487) @ X2907)))))))))))))&(~(in @ X2906 @ X2903)|~(X2904 @ (esk89_3 @ X2902 @ X2903 @ X2904) @ X2906)|(~(in @ X2907 @ (breln1Set @ X2903))|(~(reflwellordering @ X2903 @ X2907)|(~(in @ X2908 @ X2902)|(singleton @ (dsetconstr @ X2903 @ (^[Z0/* 8 */:$i]:((X2904 @ X2908 @ Z0&![X1487:$i]:(((in @ X1487 @ X2903)=>(X2904 @ X2908 @ X1487=>(in @ (kpair @ Z0 @ X1487) @ X2907))))))))))))))&((subset @ (dpsetconstr @ X2909 @ X2909 @ X2910) @ (cartprod @ X2909 @ X2909))&((subset @ esk91_0 @ (cartprod @ esk90_0 @ esk90_0))&((~(in @ X2914 @ esk90_0)|(~(in @ X2915 @ esk90_0)|(~(in @ (kpair @ X2914 @ X2915) @ esk91_0)|(epred2_0 @ (kpair @ X2914 @ X2915)))))&((in @ esk92_0 @ esk91_0)&~(epred2_0 @ esk92_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_376])])])])])])])).
0.46/0.83	thf(c_0_378, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_377])).
0.46/0.83	thf(c_0_379, negated_conjecture, (subset @ esk91_0 @ (cartprod @ esk90_0 @ esk90_0)), inference(split_conjunct,[status(thm)],[c_0_377])).
0.46/0.83	thf(c_0_380, negated_conjecture, ![X2:$i]:(((in @ X2 @ (cartprod @ esk90_0 @ esk90_0))|~((in @ X2 @ esk91_0)))), inference(spm,[status(thm)],[c_0_378, c_0_379])).
0.46/0.83	thf(c_0_381, negated_conjecture, (in @ esk92_0 @ esk91_0), inference(split_conjunct,[status(thm)],[c_0_377])).
0.46/0.83	thf(c_0_382, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((kpair @ (kfst @ X2) @ (ksnd @ X2))=(X2))|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_377])).
0.46/0.83	thf(c_0_383, negated_conjecture, (in @ esk92_0 @ (cartprod @ esk90_0 @ esk90_0)), inference(spm,[status(thm)],[c_0_380, c_0_381])).
0.46/0.83	thf(c_0_384, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (ksnd @ X2) @ X4)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_377])).
0.46/0.83	thf(c_0_385, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (kfst @ X2) @ X3)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_377])).
0.46/0.83	thf(c_0_386, negated_conjecture, ![X2:$i, X3:$i]:(((epred2_0 @ (kpair @ X2 @ X3))|~((in @ X2 @ esk90_0))|~((in @ X3 @ esk90_0))|~((in @ (kpair @ X2 @ X3) @ esk91_0)))), inference(split_conjunct,[status(thm)],[c_0_377])).
0.46/0.83	thf(c_0_387, negated_conjecture, ((kpair @ (kfst @ esk92_0) @ (ksnd @ esk92_0))=(esk92_0)), inference(spm,[status(thm)],[c_0_382, c_0_383])).
0.46/0.83	thf(c_0_388, negated_conjecture, (in @ (ksnd @ esk92_0) @ esk90_0), inference(spm,[status(thm)],[c_0_384, c_0_383])).
0.46/0.83	thf(c_0_389, negated_conjecture, (in @ (kfst @ esk92_0) @ esk90_0), inference(spm,[status(thm)],[c_0_385, c_0_383])).
0.46/0.83	thf(c_0_390, negated_conjecture, ~((epred2_0 @ esk92_0)), inference(split_conjunct,[status(thm)],[c_0_377])).
0.46/0.83	thf(c_0_391, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_386, c_0_387]), c_0_381]), c_0_388]), c_0_389])]), c_0_390]), ['proof']).
0.46/0.83	# SZS output end CNFRefutation
0.46/0.83	# Parsed axioms                        : 627
0.46/0.83	# Removed by relevancy pruning/SinE    : 0
0.46/0.83	# Initial clauses                      : 814
0.46/0.83	# Removed in clause preprocessing      : 366
0.46/0.83	# Initial clauses in saturation        : 448
0.46/0.83	# Processed clauses                    : 722
0.46/0.83	# ...of these trivial                  : 13
0.46/0.83	# ...subsumed                          : 84
0.46/0.83	# ...remaining for further processing  : 625
0.46/0.83	# Other redundant clauses eliminated   : 25
0.46/0.83	# Clauses deleted for lack of memory   : 0
0.46/0.83	# Backward-subsumed                    : 2
0.46/0.83	# Backward-rewritten                   : 3
0.46/0.83	# Generated clauses                    : 1751
0.46/0.83	# ...of the previous two non-redundant : 1585
0.46/0.83	# ...aggressively subsumed             : 0
0.46/0.83	# Contextual simplify-reflections      : 15
0.46/0.83	# Paramodulations                      : 1722
0.46/0.83	# Factorizations                       : 0
0.46/0.83	# NegExts                              : 0
0.46/0.83	# Equation resolutions                 : 28
0.46/0.83	# Disequality decompositions           : 0
0.46/0.83	# Total rewrite steps                  : 166
0.46/0.83	# ...of those cached                   : 106
0.46/0.83	# Propositional unsat checks           : 0
0.46/0.83	#    Propositional check models        : 0
0.46/0.83	#    Propositional check unsatisfiable : 0
0.46/0.83	#    Propositional clauses             : 0
0.46/0.83	#    Propositional clauses after purity: 0
0.46/0.83	#    Propositional unsat core size     : 0
0.46/0.83	#    Propositional preprocessing time  : 0.000
0.46/0.83	#    Propositional encoding time       : 0.000
0.46/0.83	#    Propositional solver time         : 0.000
0.46/0.83	#    Success case prop preproc time    : 0.000
0.46/0.83	#    Success case prop encoding time   : 0.000
0.46/0.83	#    Success case prop solver time     : 0.000
0.46/0.83	# Current number of processed clauses  : 219
0.46/0.83	#    Positive orientable unit clauses  : 54
0.46/0.83	#    Positive unorientable unit clauses: 0
0.46/0.83	#    Negative unit clauses             : 2
0.46/0.83	#    Non-unit-clauses                  : 163
0.46/0.83	# Current number of unprocessed clauses: 1696
0.46/0.83	# ...number of literals in the above   : 4733
0.46/0.83	# Current number of archived formulas  : 0
0.46/0.83	# Current number of archived clauses   : 391
0.46/0.83	# Clause-clause subsumption calls (NU) : 38591
0.46/0.83	# Rec. Clause-clause subsumption calls : 12808
0.46/0.83	# Non-unit clause-clause subsumptions  : 85
0.46/0.83	# Unit Clause-clause subsumption calls : 48
0.46/0.83	# Rewrite failures with RHS unbound    : 0
0.46/0.83	# BW rewrite match attempts            : 16
0.46/0.83	# BW rewrite match successes           : 3
0.46/0.83	# Condensation attempts                : 0
0.46/0.83	# Condensation successes               : 0
0.46/0.83	# Termbank termtop insertions          : 121521
0.46/0.83	# Search garbage collected termcells   : 31256
0.46/0.83	
0.46/0.83	# -------------------------------------------------
0.46/0.83	# User time                : 0.181 s
0.46/0.83	# System time              : 0.012 s
0.46/0.83	# Total time               : 0.192 s
0.46/0.83	# Maximum resident set size: 9320 pages
0.46/0.83	
0.46/0.83	# -------------------------------------------------
0.46/0.83	# User time                : 0.197 s
0.46/0.83	# System time              : 0.016 s
0.46/0.83	# Total time               : 0.213 s
0.46/0.83	# Maximum resident set size: 2744 pages
0.46/0.83	% E---3.1 exiting
0.46/0.83	% E exiting
0.46/0.83	EOF