0.03/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : run_E %s %d THM
0.10/0.32	% Computer : n022.cluster.edu
0.10/0.32	% Model    : x86_64 x86_64
0.10/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.32	% Memory   : 8042.1875MB
0.10/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.10/0.32	% CPULimit   : 960
0.10/0.32	% WCLimit    : 120
0.10/0.32	% DateTime   : Tue Aug  9 04:45:16 EDT 2022
0.10/0.33	% CPUTime    : 
0.18/0.49	Running higher-order on 8 cores theorem proving
0.18/0.49	Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=120 /export/starexec/sandbox2/benchmark/theBenchmark.p
0.18/0.49	# Version: 3.0pre003-ho
3.07/1.16	# Preprocessing class: HSLMSLSSLLLCHFA.
3.07/1.16	# Scheduled 8 strats onto 8 cores with 120 seconds (960 total)
3.07/1.16	# Starting ehoh_best5 with 120s (1) cores
3.07/1.16	# Starting almost_fo_3_lam with 120s (1) cores
3.07/1.16	# Starting new_bool_5 with 120s (1) cores
3.07/1.16	# Starting pre_casc_3 with 120s (1) cores
3.07/1.16	# Starting ho_unfolding_8 with 120s (1) cores
3.07/1.16	# Starting new_ho_10_cnf2 with 120s (1) cores
3.07/1.16	# Starting new_bool_3 with 120s (1) cores
3.07/1.16	# Starting new_ho_5 with 120s (1) cores
3.07/1.16	# pre_casc_3 with pid 10061 completed with status 0
3.07/1.16	# Result found by pre_casc_3
3.07/1.16	# Preprocessing class: HSLMSLSSLLLCHFA.
3.07/1.16	# Scheduled 8 strats onto 8 cores with 120 seconds (960 total)
3.07/1.16	# Starting ehoh_best5 with 120s (1) cores
3.07/1.16	# Starting almost_fo_3_lam with 120s (1) cores
3.07/1.16	# Starting new_bool_5 with 120s (1) cores
3.07/1.16	# Starting pre_casc_3 with 120s (1) cores
3.07/1.16	# SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
3.07/1.16	# ...ProofStateSinE()=279/591
3.07/1.16	# Search class: HGHSM-FSLM32-MHFMMSBN
3.07/1.16	# Scheduled 9 strats onto 1 cores with 120 seconds (120 total)
3.07/1.16	# Starting ho_unfolding_8 with 25s (1) cores
3.07/1.16	# ho_unfolding_8 with pid 10067 completed with status 0
3.07/1.16	# Result found by ho_unfolding_8
3.07/1.16	# Preprocessing class: HSLMSLSSLLLCHFA.
3.07/1.16	# Scheduled 8 strats onto 8 cores with 120 seconds (960 total)
3.07/1.16	# Starting ehoh_best5 with 120s (1) cores
3.07/1.16	# Starting almost_fo_3_lam with 120s (1) cores
3.07/1.16	# Starting new_bool_5 with 120s (1) cores
3.07/1.16	# Starting pre_casc_3 with 120s (1) cores
3.07/1.16	# SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
3.07/1.16	# ...ProofStateSinE()=279/591
3.07/1.16	# Search class: HGHSM-FSLM32-MHFMMSBN
3.07/1.16	# Scheduled 9 strats onto 1 cores with 120 seconds (120 total)
3.07/1.16	# Starting ho_unfolding_8 with 25s (1) cores
3.07/1.16	# Preprocessing time       : 0.074 s
3.07/1.16	# Presaturation interreduction done
3.07/1.16	
3.07/1.16	# Proof found!
3.07/1.16	# SZS status Theorem
3.07/1.16	# SZS output start CNFRefutation
3.07/1.16	thf(decl_22, type, in: $i > $i > $o).
3.07/1.16	thf(decl_23, type, exu: ($i > $o) > $o).
3.07/1.16	thf(decl_24, type, setextAx: $o).
3.07/1.16	thf(decl_25, type, emptyset: $i).
3.07/1.16	thf(decl_26, type, emptysetAx: $o).
3.07/1.16	thf(decl_27, type, setadjoin: $i > $i > $i).
3.07/1.16	thf(decl_28, type, setadjoinAx: $o).
3.07/1.16	thf(decl_29, type, powerset: $i > $i).
3.07/1.16	thf(decl_30, type, powersetAx: $o).
3.07/1.16	thf(decl_31, type, setunion: $i > $i).
3.07/1.16	thf(decl_32, type, setunionAx: $o).
3.07/1.16	thf(decl_33, type, omega: $i).
3.07/1.16	thf(decl_34, type, omega0Ax: $o).
3.07/1.16	thf(decl_35, type, omegaSAx: $o).
3.07/1.16	thf(decl_36, type, omegaIndAx: $o).
3.07/1.16	thf(decl_37, type, replAx: $o).
3.07/1.16	thf(decl_38, type, foundationAx: $o).
3.07/1.16	thf(decl_39, type, wellorderingAx: $o).
3.07/1.16	thf(decl_40, type, descr: ($i > $o) > $i).
3.07/1.16	thf(decl_41, type, descrp: $o).
3.07/1.16	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_43, type, dsetconstrI: $o).
3.07/1.16	thf(decl_44, type, dsetconstrEL: $o).
3.07/1.16	thf(decl_45, type, dsetconstrER: $o).
3.07/1.16	thf(decl_46, type, exuE1: $o).
3.07/1.16	thf(decl_47, type, prop2set: $o > $i).
3.07/1.16	thf(decl_48, type, prop2setE: $o).
3.07/1.16	thf(decl_49, type, emptysetE: $o).
3.07/1.16	thf(decl_50, type, emptysetimpfalse: $o).
3.07/1.16	thf(decl_51, type, notinemptyset: $o).
3.07/1.16	thf(decl_52, type, exuE3e: $o).
3.07/1.16	thf(decl_53, type, setext: $o).
3.07/1.16	thf(decl_54, type, emptyI: $o).
3.07/1.16	thf(decl_55, type, noeltsimpempty: $o).
3.07/1.16	thf(decl_56, type, setbeta: $o).
3.07/1.16	thf(decl_57, type, nonempty: $i > $o).
3.07/1.16	thf(decl_58, type, nonemptyE1: $o).
3.07/1.16	thf(decl_59, type, nonemptyI: $o).
3.07/1.16	thf(decl_60, type, nonemptyI1: $o).
3.07/1.16	thf(decl_61, type, setadjoinIL: $o).
3.07/1.16	thf(decl_62, type, emptyinunitempty: $o).
3.07/1.16	thf(decl_63, type, setadjoinIR: $o).
3.07/1.16	thf(decl_64, type, setadjoinE: $o).
3.07/1.16	thf(decl_65, type, setadjoinOr: $o).
3.07/1.16	thf(decl_66, type, setoftrueEq: $o).
3.07/1.16	thf(decl_67, type, powersetI: $o).
3.07/1.16	thf(decl_68, type, emptyinPowerset: $o).
3.07/1.16	thf(decl_69, type, emptyInPowerset: $o).
3.07/1.16	thf(decl_70, type, powersetE: $o).
3.07/1.16	thf(decl_71, type, setunionI: $o).
3.07/1.16	thf(decl_72, type, setunionE: $o).
3.07/1.16	thf(decl_73, type, subPowSU: $o).
3.07/1.16	thf(decl_74, type, exuE2: $o).
3.07/1.16	thf(decl_75, type, nonemptyImpWitness: $o).
3.07/1.16	thf(decl_76, type, uniqinunit: $o).
3.07/1.16	thf(decl_77, type, notinsingleton: $o).
3.07/1.16	thf(decl_78, type, eqinunit: $o).
3.07/1.16	thf(decl_79, type, singletonsswitch: $o).
3.07/1.16	thf(decl_80, type, upairsetE: $o).
3.07/1.16	thf(decl_81, type, upairsetIL: $o).
3.07/1.16	thf(decl_82, type, upairsetIR: $o).
3.07/1.16	thf(decl_83, type, emptyE1: $o).
3.07/1.16	thf(decl_84, type, vacuousDall: $o).
3.07/1.16	thf(decl_85, type, quantDeMorgan1: $o).
3.07/1.16	thf(decl_86, type, quantDeMorgan2: $o).
3.07/1.16	thf(decl_87, type, quantDeMorgan3: $o).
3.07/1.16	thf(decl_88, type, quantDeMorgan4: $o).
3.07/1.16	thf(decl_89, type, prop2setI: $o).
3.07/1.16	thf(decl_90, type, set2prop: $i > $o).
3.07/1.16	thf(decl_91, type, prop2set2propI: $o).
3.07/1.16	thf(decl_92, type, notdexE: $o).
3.07/1.16	thf(decl_93, type, notdallE: $o).
3.07/1.16	thf(decl_94, type, exuI1: $o).
3.07/1.16	thf(decl_95, type, exuI3: $o).
3.07/1.16	thf(decl_96, type, exuI2: $o).
3.07/1.16	thf(decl_97, type, inCongP: $o).
3.07/1.16	thf(decl_98, type, in__Cong: $o).
3.07/1.16	thf(decl_99, type, exuE3u: $o).
3.07/1.16	thf(decl_100, type, exu__Cong: $o).
3.07/1.16	thf(decl_101, type, emptyset__Cong: $o).
3.07/1.16	thf(decl_102, type, setadjoin__Cong: $o).
3.07/1.16	thf(decl_103, type, powerset__Cong: $o).
3.07/1.16	thf(decl_104, type, setunion__Cong: $o).
3.07/1.16	thf(decl_105, type, omega__Cong: $o).
3.07/1.16	thf(decl_106, type, exuEu: $o).
3.07/1.16	thf(decl_107, type, descr__Cong: $o).
3.07/1.16	thf(decl_108, type, dsetconstr__Cong: $o).
3.07/1.16	thf(decl_109, type, subset: $i > $i > $o).
3.07/1.16	thf(decl_110, type, disjoint: $i > $i > $o).
3.07/1.16	thf(decl_111, type, setsmeet: $i > $i > $o).
3.07/1.16	thf(decl_112, type, subsetI1: $o).
3.07/1.16	thf(decl_113, type, eqimpsubset2: $o).
3.07/1.16	thf(decl_114, type, eqimpsubset1: $o).
3.07/1.16	thf(decl_115, type, subsetI2: $o).
3.07/1.16	thf(decl_116, type, emptysetsubset: $o).
3.07/1.16	thf(decl_117, type, subsetE: $o).
3.07/1.16	thf(decl_118, type, subsetE2: $o).
3.07/1.16	thf(decl_119, type, notsubsetI: $o).
3.07/1.16	thf(decl_120, type, notequalI1: $o).
3.07/1.16	thf(decl_121, type, notequalI2: $o).
3.07/1.16	thf(decl_122, type, subsetRefl: $o).
3.07/1.16	thf(decl_123, type, subsetTrans: $o).
3.07/1.16	thf(decl_124, type, setadjoinSub: $o).
3.07/1.16	thf(decl_125, type, setadjoinSub2: $o).
3.07/1.16	thf(decl_126, type, subset2powerset: $o).
3.07/1.16	thf(decl_127, type, setextsub: $o).
3.07/1.16	thf(decl_128, type, subsetemptysetimpeq: $o).
3.07/1.16	thf(decl_129, type, powersetI1: $o).
3.07/1.16	thf(decl_130, type, powersetE1: $o).
3.07/1.16	thf(decl_131, type, inPowerset: $o).
3.07/1.16	thf(decl_132, type, powersetsubset: $o).
3.07/1.16	thf(decl_133, type, sepInPowerset: $o).
3.07/1.16	thf(decl_134, type, sepSubset: $o).
3.07/1.16	thf(decl_135, type, binunion: $i > $i > $i).
3.07/1.16	thf(decl_136, type, binunionIL: $o).
3.07/1.16	thf(decl_137, type, upairset2IR: $o).
3.07/1.16	thf(decl_138, type, binunionIR: $o).
3.07/1.16	thf(decl_139, type, binunionEcases: $o).
3.07/1.16	thf(decl_140, type, binunionE: $o).
3.07/1.16	thf(decl_141, type, binunionLsub: $o).
3.07/1.16	thf(decl_142, type, binunionRsub: $o).
3.07/1.16	thf(decl_143, type, binintersect: $i > $i > $i).
3.07/1.16	thf(decl_144, type, binintersectI: $o).
3.07/1.16	thf(decl_145, type, binintersectSubset5: $o).
3.07/1.16	thf(decl_146, type, binintersectEL: $o).
3.07/1.16	thf(decl_147, type, binintersectLsub: $o).
3.07/1.16	thf(decl_148, type, binintersectSubset2: $o).
3.07/1.16	thf(decl_149, type, binintersectSubset3: $o).
3.07/1.16	thf(decl_150, type, binintersectER: $o).
3.07/1.16	thf(decl_151, type, disjointsetsI1: $o).
3.07/1.16	thf(decl_152, type, binintersectRsub: $o).
3.07/1.16	thf(decl_153, type, binintersectSubset4: $o).
3.07/1.16	thf(decl_154, type, binintersectSubset1: $o).
3.07/1.16	thf(decl_155, type, bs114d: $o).
3.07/1.16	thf(decl_156, type, regular: $i > $o).
3.07/1.16	thf(decl_157, type, setminus: $i > $i > $i).
3.07/1.16	thf(decl_158, type, setminusI: $o).
3.07/1.16	thf(decl_159, type, setminusEL: $o).
3.07/1.16	thf(decl_160, type, setminusER: $o).
3.07/1.16	thf(decl_161, type, setminusSubset2: $o).
3.07/1.16	thf(decl_162, type, setminusERneg: $o).
3.07/1.16	thf(decl_163, type, setminusELneg: $o).
3.07/1.16	thf(decl_164, type, setminusILneg: $o).
3.07/1.16	thf(decl_165, type, setminusIRneg: $o).
3.07/1.16	thf(decl_166, type, setminusLsub: $o).
3.07/1.16	thf(decl_167, type, setminusSubset1: $o).
3.07/1.16	thf(decl_168, type, symdiff: $i > $i > $i).
3.07/1.16	thf(decl_169, type, symdiffE: $o).
3.07/1.16	thf(decl_170, type, symdiffI1: $o).
3.07/1.16	thf(decl_171, type, symdiffI2: $o).
3.07/1.16	thf(decl_172, type, symdiffIneg1: $o).
3.07/1.16	thf(decl_173, type, symdiffIneg2: $o).
3.07/1.16	thf(decl_174, type, iskpair: $i > $o).
3.07/1.16	thf(decl_175, type, secondinupair: $o).
3.07/1.16	thf(decl_176, type, setukpairIL: $o).
3.07/1.16	thf(decl_177, type, setukpairIR: $o).
3.07/1.16	thf(decl_178, type, kpairiskpair: $o).
3.07/1.16	thf(decl_179, type, kpair: $i > $i > $i).
3.07/1.16	thf(decl_180, type, kpairp: $o).
3.07/1.16	thf(decl_181, type, cartprod: $i > $i > $i).
3.07/1.16	thf(decl_182, type, singletonsubset: $o).
3.07/1.16	thf(decl_183, type, singletoninpowerset: $o).
3.07/1.16	thf(decl_184, type, singletoninpowunion: $o).
3.07/1.16	thf(decl_185, type, upairset2E: $o).
3.07/1.16	thf(decl_186, type, upairsubunion: $o).
3.07/1.16	thf(decl_187, type, upairinpowunion: $o).
3.07/1.16	thf(decl_188, type, ubforcartprodlem1: $o).
3.07/1.16	thf(decl_189, type, ubforcartprodlem2: $o).
3.07/1.16	thf(decl_190, type, ubforcartprodlem3: $o).
3.07/1.16	thf(decl_191, type, cartprodpairin: $o).
3.07/1.16	thf(decl_192, type, cartprodmempair1: $o).
3.07/1.16	thf(decl_193, type, cartprodmempair: $o).
3.07/1.16	thf(decl_194, type, setunionE2: $o).
3.07/1.16	thf(decl_195, type, setunionsingleton1: $o).
3.07/1.16	thf(decl_196, type, setunionsingleton2: $o).
3.07/1.16	thf(decl_197, type, setunionsingleton: $o).
3.07/1.16	thf(decl_198, type, singleton: $i > $o).
3.07/1.16	thf(decl_199, type, singletonprop: $o).
3.07/1.16	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
3.07/1.16	thf(decl_201, type, ex1E1: $o).
3.07/1.16	thf(decl_202, type, ex1I: $o).
3.07/1.16	thf(decl_203, type, ex1I2: $o).
3.07/1.16	thf(decl_204, type, singletonsuniq: $o).
3.07/1.16	thf(decl_205, type, atmost1p: $i > $o).
3.07/1.16	thf(decl_206, type, atleast2p: $i > $o).
3.07/1.16	thf(decl_207, type, atmost2p: $i > $o).
3.07/1.16	thf(decl_208, type, upairsetp: $i > $o).
3.07/1.16	thf(decl_209, type, setukpairinjL1: $o).
3.07/1.16	thf(decl_210, type, kfstsingleton: $o).
3.07/1.16	thf(decl_211, type, theprop: $o).
3.07/1.16	thf(decl_212, type, kfst: $i > $i).
3.07/1.16	thf(decl_213, type, kfstpairEq: $o).
3.07/1.16	thf(decl_214, type, cartprodfstin: $o).
3.07/1.16	thf(decl_215, type, setukpairinjL2: $o).
3.07/1.16	thf(decl_216, type, setukpairinjL: $o).
3.07/1.16	thf(decl_217, type, setukpairinjR11: $o).
3.07/1.16	thf(decl_218, type, setukpairinjR12: $o).
3.07/1.16	thf(decl_219, type, setukpairinjR1: $o).
3.07/1.16	thf(decl_220, type, upairequniteq: $o).
3.07/1.16	thf(decl_221, type, setukpairinjR2: $o).
3.07/1.16	thf(decl_222, type, setukpairinjR: $o).
3.07/1.16	thf(decl_223, type, ksndsingleton: $o).
3.07/1.16	thf(decl_224, type, ksnd: $i > $i).
3.07/1.16	thf(decl_225, type, ksndpairEq: $o).
3.07/1.16	thf(decl_226, type, kpairsurjEq: $o).
3.07/1.16	thf(decl_227, type, cartprodsndin: $o).
3.07/1.16	thf(decl_228, type, cartprodpairmemEL: $o).
3.07/1.16	thf(decl_229, type, cartprodpairmemER: $o).
3.07/1.16	thf(decl_230, type, cartprodmempaircEq: $o).
3.07/1.16	thf(decl_231, type, cartprodfstpairEq: $o).
3.07/1.16	thf(decl_232, type, cartprodsndpairEq: $o).
3.07/1.16	thf(decl_233, type, cartprodpairsurjEq: $o).
3.07/1.16	thf(decl_234, type, breln: $i > $i > $i > $o).
3.07/1.16	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
3.07/1.16	thf(decl_236, type, dpsetconstrI: $o).
3.07/1.16	thf(decl_237, type, dpsetconstrSub: $o).
3.07/1.16	thf(decl_238, type, setOfPairsIsBReln: $o).
3.07/1.16	thf(decl_239, type, dpsetconstrERa: $o).
3.07/1.16	thf(decl_240, type, dpsetconstrEL1: $o).
3.07/1.16	thf(decl_241, type, dpsetconstrEL2: $o).
3.07/1.16	thf(decl_242, type, dpsetconstrER: $o).
3.07/1.16	thf(decl_243, type, func: $i > $i > $i > $o).
3.07/1.16	thf(decl_244, type, funcSet: $i > $i > $i).
3.07/1.16	thf(decl_245, type, funcImageSingleton: $o).
3.07/1.16	thf(decl_246, type, apProp: $o).
3.07/1.16	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
3.07/1.16	thf(decl_248, type, app: $o).
3.07/1.16	thf(decl_249, type, infuncsetfunc: $o).
3.07/1.16	thf(decl_250, type, ap2p: $o).
3.07/1.16	thf(decl_251, type, funcinfuncset: $o).
3.07/1.16	thf(decl_252, type, lamProp: $o).
3.07/1.16	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
3.07/1.16	thf(decl_254, type, lamp: $o).
3.07/1.16	thf(decl_255, type, lam2p: $o).
3.07/1.16	thf(decl_256, type, brelnall1: $o).
3.07/1.16	thf(decl_257, type, brelnall2: $o).
3.07/1.16	thf(decl_258, type, ex1E2: $o).
3.07/1.16	thf(decl_259, type, funcGraphProp1: $o).
3.07/1.16	thf(decl_260, type, funcGraphProp3: $o).
3.07/1.16	thf(decl_261, type, funcGraphProp2: $o).
3.07/1.16	thf(decl_262, type, funcextLem: $o).
3.07/1.16	thf(decl_263, type, funcGraphProp4: $o).
3.07/1.16	thf(decl_264, type, subbreln: $o).
3.07/1.16	thf(decl_265, type, eqbreln: $o).
3.07/1.16	thf(decl_266, type, funcext: $o).
3.07/1.16	thf(decl_267, type, funcext2: $o).
3.07/1.16	thf(decl_268, type, ap2apEq1: $o).
3.07/1.16	thf(decl_269, type, ap2apEq2: $o).
3.07/1.16	thf(decl_270, type, beta1: $o).
3.07/1.16	thf(decl_271, type, eta1: $o).
3.07/1.16	thf(decl_272, type, lam2lamEq: $o).
3.07/1.16	thf(decl_273, type, beta2: $o).
3.07/1.16	thf(decl_274, type, eta2: $o).
3.07/1.16	thf(decl_275, type, iffalseProp1: $o).
3.07/1.16	thf(decl_276, type, iffalseProp2: $o).
3.07/1.16	thf(decl_277, type, iftrueProp1: $o).
3.07/1.16	thf(decl_278, type, iftrueProp2: $o).
3.07/1.16	thf(decl_279, type, ifSingleton: $o).
3.07/1.16	thf(decl_280, type, if: $i > $o > $i > $i > $i).
3.07/1.16	thf(decl_281, type, ifp: $o).
3.07/1.16	thf(decl_282, type, theeq: $o).
3.07/1.16	thf(decl_283, type, iftrue: $o).
3.07/1.16	thf(decl_284, type, iffalse: $o).
3.07/1.16	thf(decl_285, type, iftrueorfalse: $o).
3.07/1.16	thf(decl_286, type, binintersectT_lem: $o).
3.07/1.16	thf(decl_287, type, binunionT_lem: $o).
3.07/1.16	thf(decl_288, type, powersetT_lem: $o).
3.07/1.16	thf(decl_289, type, setminusT_lem: $o).
3.07/1.16	thf(decl_290, type, complementT_lem: $o).
3.07/1.16	thf(decl_291, type, setextT: $o).
3.07/1.16	thf(decl_292, type, subsetTI: $o).
3.07/1.16	thf(decl_293, type, powersetTI1: $o).
3.07/1.16	thf(decl_294, type, powersetTE1: $o).
3.07/1.16	thf(decl_295, type, complementTI1: $o).
3.07/1.16	thf(decl_296, type, complementTE1: $o).
3.07/1.16	thf(decl_297, type, binintersectTELcontra: $o).
3.07/1.16	thf(decl_298, type, binintersectTERcontra: $o).
3.07/1.16	thf(decl_299, type, contrasubsetT: $o).
3.07/1.16	thf(decl_300, type, contrasubsetT1: $o).
3.07/1.16	thf(decl_301, type, contrasubsetT2: $o).
3.07/1.16	thf(decl_302, type, contrasubsetT3: $o).
3.07/1.16	thf(decl_303, type, doubleComplementI1: $o).
3.07/1.16	thf(decl_304, type, doubleComplementE1: $o).
3.07/1.16	thf(decl_305, type, doubleComplementSub1: $o).
3.07/1.16	thf(decl_306, type, doubleComplementSub2: $o).
3.07/1.16	thf(decl_307, type, doubleComplementEq: $o).
3.07/1.16	thf(decl_308, type, complementTnotintersectT: $o).
3.07/1.16	thf(decl_309, type, complementImpComplementIntersect: $o).
3.07/1.16	thf(decl_310, type, complementSubsetComplementIntersect: $o).
3.07/1.16	thf(decl_311, type, complementInPowersetComplementIntersect: $o).
3.07/1.16	thf(decl_312, type, contraSubsetComplement: $o).
3.07/1.16	thf(decl_313, type, complementTcontraSubset: $o).
3.07/1.16	thf(decl_314, type, binunionTILcontra: $o).
3.07/1.16	thf(decl_315, type, binunionTIRcontra: $o).
3.07/1.16	thf(decl_316, type, inIntersectImpInUnion: $o).
3.07/1.16	thf(decl_317, type, inIntersectImpInUnion2: $o).
3.07/1.16	thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
3.07/1.16	thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
3.07/1.16	thf(decl_320, type, inComplementUnionImpNotIn1: $o).
3.07/1.16	thf(decl_321, type, inComplementUnionImpInComplement1: $o).
3.07/1.16	thf(decl_322, type, binunionTE: $o).
3.07/1.16	thf(decl_323, type, binunionTEcontra: $o).
3.07/1.16	thf(decl_324, type, demorgan2a1: $o).
3.07/1.16	thf(decl_325, type, complementUnionInPowersetComplement: $o).
3.07/1.16	thf(decl_326, type, demorgan2a2: $o).
3.07/1.16	thf(decl_327, type, demorgan1a: $o).
3.07/1.16	thf(decl_328, type, demorgan1b: $o).
3.07/1.16	thf(decl_329, type, demorgan1: $o).
3.07/1.16	thf(decl_330, type, demorgan2a: $o).
3.07/1.16	thf(decl_331, type, demorgan2b2: $o).
3.07/1.16	thf(decl_332, type, demorgan2b: $o).
3.07/1.16	thf(decl_333, type, demorgan2: $o).
3.07/1.16	thf(decl_334, type, epred1_0: $o).
3.07/1.16	thf(decl_335, type, esk1_2: $i > $i > $i).
3.07/1.16	thf(decl_336, type, esk2_2: $i > $i > $i).
3.07/1.16	thf(decl_337, type, esk3_2: $i > $i > $i).
3.07/1.16	thf(decl_338, type, esk4_1: $i > $i).
3.07/1.16	thf(decl_339, type, esk5_2: ($i > $i > $o) > $i > $i).
3.07/1.16	thf(decl_340, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
3.07/1.16	thf(decl_341, type, esk7_2: ($i > $i > $o) > $i > $i).
3.07/1.16	thf(decl_342, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
3.07/1.16	thf(decl_343, type, esk9_1: $i > $i).
3.07/1.16	thf(decl_344, type, esk10_2: ($i > $o) > $i > $i).
3.07/1.16	thf(decl_345, type, esk11_2: ($i > $o) > $i > $i).
3.07/1.16	thf(decl_346, type, esk12_1: ($i > $o) > $i).
3.07/1.16	thf(decl_347, type, esk13_2: ($i > $o) > $i > $i).
3.07/1.16	thf(decl_348, type, esk14_1: ($i > $o) > $i).
3.07/1.16	thf(decl_349, type, esk15_2: $i > $i > $i).
3.07/1.16	thf(decl_350, type, esk16_2: $i > $i > $i).
3.07/1.16	thf(decl_351, type, esk17_1: $i > $i).
3.07/1.16	thf(decl_352, type, esk18_1: $i > $i).
3.07/1.16	thf(decl_353, type, esk19_1: $i > $i).
3.07/1.16	thf(decl_354, type, esk20_2: $i > $i > $i).
3.07/1.16	thf(decl_355, type, esk21_3: $i > $i > $o > $i).
3.07/1.16	thf(decl_356, type, esk22_2: ($i > $o) > $i > $i).
3.07/1.16	thf(decl_357, type, esk23_1: ($i > $o) > $i).
3.07/1.16	thf(decl_358, type, esk24_1: $i > $i).
3.07/1.16	thf(decl_359, type, esk25_2: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_360, type, esk26_2: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_361, type, esk27_2: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_362, type, esk28_2: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_363, type, esk29_2: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_364, type, esk30_2: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_365, type, esk31_2: ($i > $o) > $i > $i).
3.07/1.16	thf(decl_366, type, esk32_1: ($i > $o) > $i).
3.07/1.16	thf(decl_367, type, esk33_1: ($i > $o) > $i).
3.07/1.16	thf(decl_368, type, esk34_1: ($i > $o) > $i).
3.07/1.16	thf(decl_369, type, esk35_1: ($i > $o) > $i).
3.07/1.16	thf(decl_370, type, esk36_2: ($i > $o) > $i > $i).
3.07/1.16	thf(decl_371, type, esk37_1: ($i > $o) > $i).
3.07/1.16	thf(decl_372, type, esk38_2: ($i > $o) > $i > $i).
3.07/1.16	thf(decl_373, type, esk39_2: ($i > $o) > ($i > $o) > $i).
3.07/1.16	thf(decl_374, type, esk40_2: ($i > $o) > ($i > $o) > $i).
3.07/1.16	thf(decl_375, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
3.07/1.16	thf(decl_376, type, esk42_2: ($i > $o) > ($i > $o) > $i).
3.07/1.16	thf(decl_377, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
3.07/1.16	thf(decl_378, type, esk44_2: ($i > $o) > ($i > $o) > $i).
3.07/1.16	thf(decl_379, type, esk45_2: ($i > $o) > $i > $i).
3.07/1.16	thf(decl_380, type, esk46_2: ($i > $o) > ($i > $o) > $i).
3.07/1.16	thf(decl_381, type, esk47_2: ($i > $o) > ($i > $o) > $i).
3.07/1.16	thf(decl_382, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
3.07/1.16	thf(decl_383, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
3.07/1.16	thf(decl_384, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
3.07/1.16	thf(decl_385, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
3.07/1.16	thf(decl_386, type, esk52_2: $i > $i > $i).
3.07/1.16	thf(decl_387, type, esk53_2: $i > $i > $i).
3.07/1.16	thf(decl_388, type, esk54_2: $i > $i > $i).
3.07/1.16	thf(decl_389, type, esk55_3: $i > $i > $i > $i).
3.07/1.16	thf(decl_390, type, esk56_3: $i > $i > $i > $i).
3.07/1.16	thf(decl_391, type, esk57_2: $i > $i > $i).
3.07/1.16	thf(decl_392, type, esk58_2: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_393, type, esk59_2: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_394, type, esk60_2: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_395, type, esk61_3: $i > ($i > $o) > $i > $i).
3.07/1.16	thf(decl_396, type, esk62_2: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_397, type, esk63_2: $i > ($i > $o) > $i).
3.07/1.16	thf(decl_398, type, esk64_3: $i > $i > ($i > $i) > $i).
3.07/1.16	thf(decl_399, type, esk65_3: $i > $i > ($i > $i) > $i).
3.07/1.16	thf(decl_400, type, esk66_3: $i > $i > ($i > $i) > $i).
3.07/1.16	thf(decl_401, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
3.07/1.16	thf(decl_402, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
3.07/1.16	thf(decl_403, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
3.07/1.16	thf(decl_404, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
3.07/1.16	thf(decl_405, type, esk71_4: $i > $i > $i > $i > $i).
3.07/1.16	thf(decl_406, type, esk72_4: $i > $i > $i > $i > $i).
3.07/1.16	thf(decl_407, type, esk73_4: $i > $i > $i > $i > $i).
3.07/1.16	thf(decl_408, type, esk74_4: $i > $i > $i > $i > $i).
3.07/1.16	thf(decl_409, type, esk75_4: $i > $i > $i > $i > $i).
3.07/1.16	thf(decl_410, type, esk76_4: $i > $i > $i > $i > $i).
3.07/1.16	thf(decl_411, type, esk77_4: $i > $i > $i > $i > $i).
3.07/1.16	thf(decl_412, type, esk78_4: $i > $i > $i > $i > $i).
3.07/1.16	thf(decl_413, type, esk79_4: $i > $i > $i > $i > $i).
3.07/1.16	thf(decl_414, type, esk80_3: $i > $i > ($i > $i) > $i).
3.07/1.16	thf(decl_415, type, esk81_3: $i > $i > ($i > $i) > $i).
3.07/1.16	thf(decl_416, type, esk82_3: $i > $i > ($i > $i) > $i).
3.07/1.16	thf(decl_417, type, esk83_3: $i > $i > $i > $i).
3.07/1.16	thf(decl_418, type, esk84_3: $i > $i > $i > $i).
3.07/1.16	thf(decl_419, type, esk85_3: $i > $i > $i > $i).
3.07/1.16	thf(decl_420, type, esk86_3: $i > $i > $i > $i).
3.07/1.16	thf(decl_421, type, esk87_0: $i).
3.07/1.16	thf(decl_422, type, esk88_0: $i).
3.07/1.16	thf(decl_423, type, esk89_0: $i).
3.07/1.16	thf(decl_424, type, esk90_0: $i).
3.07/1.16	thf(decl_425, type, esk91_1: $i > $i).
3.07/1.16	thf(decl_426, type, esk92_3: $i > $i > $i > $i).
3.07/1.16	thf(decl_427, type, esk93_2: $i > $i > $i).
3.07/1.16	thf(decl_428, type, esk94_2: $i > $i > $i).
3.07/1.16	thf(decl_429, type, esk95_2: $i > $i > $i).
3.07/1.16	thf(decl_430, type, epred2_3: $i > $o > $i > $i > $o).
3.07/1.16	thf(decl_431, type, epred3_2: $i > $i > $i > $o).
3.07/1.16	thf(decl_432, type, epred4_1: ($i > $i) > $i > $i > $o).
3.07/1.16	thf(decl_433, type, epred5_2: $i > $i > $i > $o).
3.07/1.16	thf(decl_434, type, epred6_1: $i > $i > $o).
3.07/1.16	thf(decl_435, type, epred7_1: $i > $i > $o).
3.07/1.16	thf(decl_436, type, epred8_0: $i > $o).
3.07/1.16	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln)).
3.07/1.16	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI2)).
3.07/1.16	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu)).
3.07/1.16	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonempty)).
3.07/1.16	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI)).
3.07/1.16	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE1)).
3.07/1.16	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descrp)).
3.07/1.16	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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/benchmark/theBenchmark.p', ex1E2)).
3.07/1.16	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1)).
3.07/1.16	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setOfPairsIsBReln)).
3.07/1.16	thf(ex1I, axiom, ((ex1I)<=>![X4:$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/benchmark/theBenchmark.p', ex1I)).
3.07/1.16	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1I2)).
3.07/1.16	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1E1)).
3.07/1.16	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descr__Cong)).
3.07/1.16	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuEu)).
3.07/1.16	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu__Cong)).
3.07/1.16	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE3u)).
3.07/1.16	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI3)).
3.07/1.16	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI1)).
3.07/1.16	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE2)).
3.07/1.16	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE3e)).
3.07/1.16	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', replAx)).
3.07/1.16	thf(lamProp, axiom, ((lamProp)<=>![X4:$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/benchmark/theBenchmark.p', lamProp)).
3.07/1.16	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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', lam2p)).
3.07/1.16	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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/benchmark/theBenchmark.p', brelnall2)).
3.07/1.16	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/benchmark/theBenchmark.p', subbreln)).
3.07/1.16	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/benchmark/theBenchmark.p', eqbreln)).
3.07/1.16	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/benchmark/theBenchmark.p', lam2lamEq)).
3.07/1.16	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iftrueProp1)).
3.07/1.16	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI1)).
3.07/1.16	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setbeta)).
3.07/1.16	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrER)).
3.07/1.16	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrI)).
3.07/1.16	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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/benchmark/theBenchmark.p', ifSingleton)).
3.07/1.16	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndsingleton)).
3.07/1.16	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iftrueProp2)).
3.07/1.16	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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/benchmark/theBenchmark.p', iffalseProp2)).
3.07/1.16	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iffalseProp1)).
3.07/1.16	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eta2)).
3.07/1.16	thf(beta2, axiom, ((beta2)<=>![X4:$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/benchmark/theBenchmark.p', beta2)).
3.07/1.16	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/benchmark/theBenchmark.p', eta1)).
3.07/1.16	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/benchmark/theBenchmark.p', beta1)).
3.07/1.16	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/benchmark/theBenchmark.p', brelnall1)).
3.07/1.16	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', lamp)).
3.07/1.16	thf(apProp, axiom, ((apProp)<=>![X4:$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/benchmark/theBenchmark.p', apProp)).
3.07/1.16	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcImageSingleton)).
3.07/1.16	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrER)).
3.07/1.16	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrSub)).
3.07/1.16	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrI)).
3.07/1.16	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstsingleton)).
3.07/1.16	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrERa)).
3.07/1.16	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrEL1)).
3.07/1.16	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrEL2)).
3.07/1.16	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonprop)).
3.07/1.16	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepSubset)).
3.07/1.16	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepInPowerset)).
3.07/1.16	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstr__Cong)).
3.07/1.16	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyE1)).
3.07/1.16	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyImpWitness)).
3.07/1.16	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setoftrueEq)).
3.07/1.16	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyE1)).
3.07/1.16	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/benchmark/theBenchmark.p', dsetconstrEL)).
3.07/1.16	thf(woz13rule0, conjecture, (((emptysetAx)=>((setadjoinAx)=>(((setunionAx)=>(((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((((dsetconstrEL)=>((((prop2setE)=>((emptysetE)=>((((exuE3e)=>((setext)=>(((noeltsimpempty)=>(((nonemptyE1)=>((((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>(((powersetE)=>((setunionI)=>((((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>(((singletonsswitch)=>(((((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>(((quantDeMorgan4)=>((prop2setI)=>((((notdallE)=>((exuI1)=>((exuI3)=>(((inCongP)=>(((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>(((powerset__Cong)=>((((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>(((eqimpsubset2)=>(((((subsetE)=>((((notequalI1)=>((notequalI2)=>((((((((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>(((sepInPowerset)=>((sepSubset)=>(((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((((binunionRsub)=>(((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>(((binintersectSubset3)=>((binintersectER)=>((((((bs114d)=>((setminusI)=>((setminusEL)=>(((setminusSubset2)=>(((setminusELneg)=>((((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((((secondinupair)=>((setukpairIL)=>(((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>(((upairinpowunion)=>((ubforcartprodlem1)=>((((cartprodpairin)=>((cartprodmempair1)=>((((((setunionsingleton)=>((singletonprop)=>((ex1E1)=>(((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>(((theprop)=>(((cartprodfstin)=>((setukpairinjL2)=>(((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>(((setukpairinjR)=>((ksndsingleton)=>((((((cartprodpairmemER)=>((((cartprodsndpairEq)=>((cartprodpairsurjEq)=>(((((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((((((infuncsetfunc)=>((ap2p)=>(((lamProp)=>(((lam2p)=>(((brelnall2)=>((((((funcextLem)=>(((subbreln)=>((eqbreln)=>((funcext)=>(((((((lam2lamEq)=>((((((iftrueProp1)=>(((((theeq)=>((iftrue)=>((((((((complementT_lem)=>(((subsetTI)=>(((powersetTE1)=>((((binintersectTELcontra)=>(((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>(((((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((((binunionTIRcontra)=>(((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((((binunionTE)=>(((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>(((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((((demorgan2)=>![X4:$i, X21:$i]:((![X48:$i]:((![X2:$i]:(((in @ X2 @ X4)<=(in @ X2 @ (binintersect @ X21 @ X48))))<=(in @ X48 @ (powerset @ X4))))<=(in @ X21 @ (powerset @ X4)))))<=(demorgan2b))<=(demorgan2b2)))))<=(demorgan1a)))))<=(binunionTEcontra)))<=(inComplementUnionImpInComplement1))<=(inComplementUnionImpNotIn1)))))<=(inIntersectImpInUnion)))<=(binunionTILcontra))<=(complementTcontraSubset))))))))<=(doubleComplementSub2))<=(doubleComplementSub1))<=(doubleComplementE1)))))))<=(binintersectTERcontra)))<=(complementTE1))<=(complementTI1)))<=(powersetTI1)))<=(setextT)))<=(setminusT_lem))<=(powersetT_lem))<=(binunionT_lem))<=(binintersectT_lem))<=(iftrueorfalse))<=(iffalse))))<=(ifp))<=(ifSingleton))<=(iftrueProp2)))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))<=(beta2)))<=(eta1))<=(beta1))<=(ap2apEq2))<=(ap2apEq1))<=(funcext2)))))<=(funcGraphProp4)))<=(funcGraphProp2))<=(funcGraphProp3))<=(funcGraphProp1))<=(ex1E2)))<=(brelnall1)))<=(lamp)))<=(funcinfuncset))))<=(app))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER)))))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI))))<=(cartprodfstpairEq))<=(cartprodmempaircEq)))<=(cartprodpairmemEL))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))))<=(setukpairinjR2))))))<=(setukpairinjL))))<=(kfstpairEq)))<=(kfstsingleton)))))<=(ex1I)))))<=(setunionsingleton2))<=(setunionsingleton1))<=(setunionE2))<=(cartprodmempair))))<=(ubforcartprodlem3))<=(ubforcartprodlem2))))<=(upairsubunion))))))))<=(setukpairIR))))<=(symdiffIneg2))<=(symdiffIneg1)))))))<=(setminusIRneg))<=(setminusILneg)))<=(setminusERneg)))<=(setminusER)))))<=(binintersectSubset1))<=(binintersectSubset4))<=(binintersectRsub))<=(disjointsetsI1))))<=(binintersectSubset2)))))<=(binintersectI)))<=(binunionLsub))<=(binunionE)))))<=(binunionIL))))<=(powersetsubset)))<=(powersetE1))))<=(setextsub))<=(subset2powerset))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl))))<=(notsubsetI))<=(subsetE2)))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1)))<=(subsetI1)))))<=(omega__Cong))<=(setunion__Cong)))<=(setadjoin__Cong)))))<=(in__Cong)))<=(exuI2)))))<=(notdexE))<=(prop2set2propI))))<=(quantDeMorgan3))))))<=(upairsetIR))<=(upairsetIL))<=(upairsetE)))<=(eqinunit))))))<=(subPowSU))<=(setunionE))))<=(emptyInPowerset))))))))))<=(nonemptyI1))<=(nonemptyI)))<=(setbeta)))<=(emptyI))))<=(notinemptyset))<=(emptysetimpfalse))))<=(exuE1))<=(dsetconstrER)))<=(dsetconstrI))<=(descrp)))))))<=(omega0Ax)))<=(powersetAx))))<=(setextAx)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz13rule0)).
3.07/1.16	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE)).
3.07/1.16	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyInPowerset)).
3.07/1.16	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextAx)).
3.07/1.16	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetRefl)).
3.07/1.16	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notsubsetI)).
3.07/1.16	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE2)).
3.07/1.16	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetsubset)).
3.07/1.16	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI2)).
3.07/1.16	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset1)).
3.07/1.16	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI1)).
3.07/1.16	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega__Cong)).
3.07/1.16	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunion__Cong)).
3.07/1.16	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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/benchmark/theBenchmark.p', funcextLem)).
3.07/1.16	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/benchmark/theBenchmark.p', setadjoin__Cong)).
3.07/1.16	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/benchmark/theBenchmark.p', in__Cong)).
3.07/1.16	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdexE)).
3.07/1.16	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2set2propI)).
3.07/1.16	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcext)).
3.07/1.16	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan3)).
3.07/1.16	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIR)).
3.07/1.16	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIL)).
3.07/1.16	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetE)).
3.07/1.16	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqinunit)).
3.07/1.16	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subPowSU)).
3.07/1.16	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/benchmark/theBenchmark.p', binunionTIRcontra)).
3.07/1.16	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', theeq)).
3.07/1.16	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/benchmark/theBenchmark.p', iftrue)).
3.07/1.16	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyI)).
3.07/1.16	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinemptyset)).
3.07/1.16	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementT_lem)).
3.07/1.16	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetimpfalse)).
3.07/1.16	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetTI)).
3.07/1.16	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega0Ax)).
3.07/1.16	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetTE1)).
3.07/1.16	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetAx)).
3.07/1.16	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/benchmark/theBenchmark.p', binintersectTELcontra)).
3.07/1.16	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/benchmark/theBenchmark.p', contrasubsetT)).
3.07/1.16	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/benchmark/theBenchmark.p', contrasubsetT1)).
3.07/1.16	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', contrasubsetT2)).
3.07/1.16	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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/benchmark/theBenchmark.p', contrasubsetT3)).
3.07/1.16	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementI1)).
3.07/1.16	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementEq)).
3.07/1.16	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementTnotintersectT)).
3.07/1.16	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementImpComplementIntersect)).
3.07/1.16	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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/benchmark/theBenchmark.p', complementSubsetComplementIntersect)).
3.07/1.16	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementInPowersetComplementIntersect)).
3.07/1.16	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', contraSubsetComplement)).
3.07/1.16	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ifp)).
3.07/1.16	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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/benchmark/theBenchmark.p', inIntersectImpInUnion2)).
3.07/1.16	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inIntersectImpInIntersectUnions)).
3.07/1.16	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', intersectInPowersetIntersectUnions)).
3.07/1.16	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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/benchmark/theBenchmark.p', binunionTE)).
3.07/1.16	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/benchmark/theBenchmark.p', demorgan2a1)).
3.07/1.16	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementUnionInPowersetComplement)).
3.07/1.16	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2a2)).
3.07/1.16	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan1b)).
3.07/1.16	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$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/benchmark/theBenchmark.p', demorgan1)).
3.07/1.16	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/benchmark/theBenchmark.p', demorgan2a)).
3.07/1.16	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2)).
3.07/1.16	thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2b)).
3.07/1.16	thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2b2)).
3.07/1.16	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan1a)).
3.07/1.16	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionTEcontra)).
3.07/1.16	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inComplementUnionImpInComplement1)).
3.07/1.16	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inComplementUnionImpNotIn1)).
3.07/1.16	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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/benchmark/theBenchmark.p', inIntersectImpInUnion)).
3.07/1.16	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/benchmark/theBenchmark.p', binunionTILcontra)).
3.07/1.16	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementTcontraSubset)).
3.07/1.16	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementSub2)).
3.07/1.16	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR1)).
3.07/1.16	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementSub1)).
3.07/1.16	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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/benchmark/theBenchmark.p', doubleComplementE1)).
3.07/1.16	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/benchmark/theBenchmark.p', binintersectTERcontra)).
3.07/1.16	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementTE1)).
3.07/1.16	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementTI1)).
3.07/1.16	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/benchmark/theBenchmark.p', powersetTI1)).
3.07/1.16	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextT)).
3.07/1.16	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusT_lem)).
3.07/1.16	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairequniteq)).
3.07/1.16	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetT_lem)).
3.07/1.16	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR)).
3.07/1.16	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionT_lem)).
3.07/1.16	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectT_lem)).
3.07/1.16	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iftrueorfalse)).
3.07/1.16	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iffalse)).
3.07/1.16	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE1)).
3.07/1.16	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ap2apEq2)).
3.07/1.16	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ap2apEq1)).
3.07/1.16	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairmemER)).
3.07/1.16	thf(funcext2, axiom, ((funcext2)<=>![X4:$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/benchmark/theBenchmark.p', funcext2)).
3.07/1.16	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcGraphProp4)).
3.07/1.16	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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/benchmark/theBenchmark.p', funcGraphProp2)).
3.07/1.16	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/benchmark/theBenchmark.p', funcGraphProp3)).
3.07/1.16	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/benchmark/theBenchmark.p', funcGraphProp1)).
3.07/1.16	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcinfuncset)).
3.07/1.16	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', app)).
3.07/1.16	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodfstpairEq)).
3.07/1.16	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempaircEq)).
3.07/1.16	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairmemEL)).
3.07/1.16	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodsndin)).
3.07/1.16	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairsurjEq)).
3.07/1.16	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndpairEq)).
3.07/1.16	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR2)).
3.07/1.16	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL)).
3.07/1.16	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstpairEq)).
3.07/1.16	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton2)).
3.07/1.16	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton1)).
3.07/1.16	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE2)).
3.07/1.16	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempair)).
3.07/1.16	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem3)).
3.07/1.16	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem2)).
3.07/1.16	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsubunion)).
3.07/1.16	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairIR)).
3.07/1.16	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg2)).
3.07/1.16	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg1)).
3.07/1.16	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusIRneg)).
3.07/1.16	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusILneg)).
3.07/1.16	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusERneg)).
3.07/1.16	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusER)).
3.07/1.16	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset1)).
3.07/1.16	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset4)).
3.07/1.16	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectRsub)).
3.07/1.16	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodsndpairEq)).
3.07/1.16	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', disjointsetsI1)).
3.07/1.16	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset2)).
3.07/1.16	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectI)).
3.07/1.16	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionLsub)).
3.07/1.16	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairsurjEq)).
3.07/1.16	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionE)).
3.07/1.16	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIL)).
3.07/1.16	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetsubset)).
3.07/1.16	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', infuncsetfunc)).
3.07/1.16	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ap2p)).
3.07/1.16	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextsub)).
3.07/1.16	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subset2powerset)).
3.07/1.16	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub2)).
3.07/1.16	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub)).
3.07/1.16	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetTrans)).
3.07/1.16	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR12)).
3.07/1.16	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR11)).
3.07/1.16	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL2)).
3.07/1.16	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodfstin)).
3.07/1.16	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', theprop)).
3.07/1.16	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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/benchmark/theBenchmark.p', setukpairinjL1)).
3.07/1.16	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsuniq)).
3.07/1.16	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton)).
3.07/1.16	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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/benchmark/theBenchmark.p', cartprodmempair1)).
3.07/1.16	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/benchmark/theBenchmark.p', cartprodpairin)).
3.07/1.16	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/benchmark/theBenchmark.p', ubforcartprodlem1)).
3.07/1.16	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/benchmark/theBenchmark.p', upairinpowunion)).
3.07/1.16	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2E)).
3.07/1.16	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowunion)).
3.07/1.16	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowerset)).
3.07/1.16	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsubset)).
3.07/1.16	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairp)).
3.07/1.16	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairiskpair)).
3.07/1.16	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/benchmark/theBenchmark.p', setukpairIL)).
3.07/1.16	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', secondinupair)).
3.07/1.16	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI2)).
3.07/1.16	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI1)).
3.07/1.16	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/benchmark/theBenchmark.p', symdiffE)).
3.07/1.16	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset1)).
3.07/1.16	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusLsub)).
3.07/1.16	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusELneg)).
3.07/1.16	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset2)).
3.07/1.16	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusEL)).
3.07/1.16	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusI)).
3.07/1.16	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', bs114d)).
3.07/1.16	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectER)).
3.07/1.16	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset3)).
3.07/1.16	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectLsub)).
3.07/1.16	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectEL)).
3.07/1.16	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset5)).
3.07/1.16	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionRsub)).
3.07/1.16	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionEcases)).
3.07/1.16	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIR)).
3.07/1.16	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2IR)).
3.07/1.16	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inPowerset)).
3.07/1.16	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI1)).
3.07/1.16	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetemptysetimpeq)).
3.07/1.16	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI2)).
3.07/1.16	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI1)).
3.07/1.16	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE)).
3.07/1.16	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset2)).
3.07/1.16	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powerset__Cong)).
3.07/1.16	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyset__Cong)).
3.07/1.16	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/benchmark/theBenchmark.p', inCongP)).
3.07/1.16	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdallE)).
3.07/1.16	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setI)).
3.07/1.16	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan4)).
3.07/1.16	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan2)).
3.07/1.16	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan1)).
3.07/1.16	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', vacuousDall)).
3.07/1.16	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsswitch)).
3.07/1.16	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinsingleton)).
3.07/1.16	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', uniqinunit)).
3.07/1.16	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionI)).
3.07/1.16	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE)).
3.07/1.16	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinPowerset)).
3.07/1.16	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI)).
3.07/1.16	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinOr)).
3.07/1.16	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinE)).
3.07/1.16	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIR)).
3.07/1.16	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinunitempty)).
3.07/1.16	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIL)).
3.07/1.16	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', noeltsimpempty)).
3.07/1.16	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/benchmark/theBenchmark.p', setext)).
3.07/1.16	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetE)).
3.07/1.16	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setE)).
3.07/1.16	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', wellorderingAx)).
3.07/1.16	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', foundationAx)).
3.07/1.16	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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/benchmark/theBenchmark.p', omegaIndAx)).
3.07/1.16	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaSAx)).
3.07/1.16	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionAx)).
3.07/1.16	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinAx)).
3.07/1.16	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetAx)).
3.07/1.16	thf(c_0_279, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
3.07/1.16	thf(c_0_280, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
3.07/1.16	thf(c_0_281, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
3.07/1.16	thf(c_0_282, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
3.07/1.16	thf(c_0_283, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
3.07/1.16	thf(c_0_284, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
3.07/1.16	thf(c_0_285, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
3.07/1.16	thf(c_0_286, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$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])).
3.07/1.16	thf(c_0_287, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
3.07/1.16	thf(c_0_288, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
3.07/1.16	thf(c_0_289, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
3.07/1.16	thf(c_0_290, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
3.07/1.16	thf(c_0_291, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
3.07/1.16	thf(c_0_292, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
3.07/1.16	thf(c_0_293, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
3.07/1.16	thf(c_0_294, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
3.07/1.16	thf(c_0_295, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
3.07/1.16	thf(c_0_296, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
3.07/1.16	thf(c_0_297, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
3.07/1.16	thf(c_0_298, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
3.07/1.16	thf(c_0_299, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
3.07/1.16	thf(c_0_300, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
3.07/1.16	thf(c_0_301, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
3.07/1.16	thf(c_0_302, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
3.07/1.16	thf(c_0_303, axiom, ((brelnall2)=(![X4:$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_279])).
3.07/1.16	thf(c_0_304, 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_279])).
3.07/1.16	thf(c_0_305, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X937:$i]:((((X1 @ X937))&![X938:$i]:((((X1 @ X938))=>((X937)=(X938))))))))))), inference(apply_def,[status(thm)],[c_0_280, c_0_281])).
3.07/1.16	thf(c_0_306, axiom, ((eqbreln)=(![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_279])).
3.07/1.16	thf(c_0_307, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
3.07/1.16	thf(c_0_308, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
3.07/1.16	thf(c_0_309, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_282])).
3.07/1.16	thf(c_0_310, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_283, c_0_282])).
3.07/1.16	thf(c_0_311, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
3.07/1.16	thf(c_0_312, plain, ((exuE1)=(![X1:$i > $o]:(((?[X927:$i]:((((X1 @ X927))&![X928:$i]:((((X1 @ X928))=>((X927)=(X928)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_284, c_0_281])).
3.07/1.16	thf(c_0_313, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
3.07/1.16	thf(c_0_314, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
3.07/1.16	thf(c_0_315, plain, ((descrp)=(![X1:$i > $o]:(((?[X925:$i]:((((X1 @ X925))&![X926:$i]:((((X1 @ X926))=>((X925)=(X926)))))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_285, c_0_281])).
3.07/1.16	thf(c_0_316, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
3.07/1.16	thf(c_0_317, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
3.07/1.16	thf(c_0_318, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
3.07/1.16	thf(c_0_319, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
3.07/1.16	thf(c_0_320, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
3.07/1.16	thf(c_0_321, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
3.07/1.16	thf(c_0_322, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
3.07/1.16	thf(c_0_323, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
3.07/1.16	thf(c_0_324, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
3.07/1.16	thf(c_0_325, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_286, c_0_287])).
3.07/1.16	thf(c_0_326, 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_279])).
3.07/1.16	thf(c_0_327, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
3.07/1.16	thf(c_0_328, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
3.07/1.16	thf(c_0_329, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
3.07/1.16	thf(c_0_330, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
3.07/1.16	thf(c_0_331, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_288, c_0_279])).
3.07/1.16	thf(c_0_332, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
3.07/1.16	thf(c_0_333, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
3.07/1.16	thf(c_0_334, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
3.07/1.16	thf(c_0_335, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))))))), inference(apply_def,[status(thm)],[c_0_289, c_0_287])).
3.07/1.16	thf(c_0_336, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
3.07/1.16	thf(c_0_337, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
3.07/1.16	thf(c_0_338, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
3.07/1.16	thf(c_0_339, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))), inference(apply_def,[status(thm)],[c_0_290, c_0_287])).
3.07/1.16	thf(c_0_340, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_291, c_0_287])).
3.07/1.16	thf(c_0_341, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
3.07/1.16	thf(c_0_342, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
3.07/1.16	thf(c_0_343, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
3.07/1.16	thf(c_0_344, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
3.07/1.16	thf(c_0_345, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X947:$i]:((((X1 @ X947))&![X948:$i]:((((X1 @ X948))=>((X947)=(X948)))))))=>((?[X949:$i]:((((X17 @ X949))&![X950:$i]:((((X17 @ X950))=>((X949)=(X950)))))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_292, c_0_281])).
3.07/1.16	thf(c_0_346, plain, ((exuEu)=(![X1:$i > $o]:(((?[X945:$i]:((((X1 @ X945))&![X946:$i]:((((X1 @ X946))=>((X945)=(X946)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_293, c_0_281])).
3.07/1.16	thf(c_0_347, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X941:$i]:((((X1 @ X941))&![X942:$i]:((((X1 @ X942))=>((X941)=(X942)))))))<=>(?[X943:$i]:((((X17 @ X943))&![X944:$i]:((((X17 @ X944))=>((X943)=(X944)))))))))))), inference(apply_def,[status(thm)],[c_0_294, c_0_281])).
3.07/1.16	thf(c_0_348, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X939:$i]:((((X1 @ X939))&![X940:$i]:((((X1 @ X940))=>((X939)=(X940)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_295, c_0_281])).
3.07/1.16	thf(c_0_349, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X935:$i]:((((X1 @ X935))&![X936:$i]:((((X1 @ X936))=>((X935)=(X936)))))))))))), inference(apply_def,[status(thm)],[c_0_296, c_0_281])).
3.07/1.16	thf(c_0_350, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X933:$i]:((((X1 @ X933))&![X934:$i]:((((X1 @ X934))=>((X933)=(X934))))))))))), inference(apply_def,[status(thm)],[c_0_297, c_0_281])).
3.07/1.16	thf(c_0_351, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
3.07/1.16	thf(c_0_352, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_282])).
3.07/1.16	thf(c_0_353, plain, ((exuE2)=(![X1:$i > $o]:(((?[X931:$i]:((((X1 @ X931))&![X932:$i]:((((X1 @ X932))=>((X931)=(X932)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_298, c_0_281])).
3.07/1.16	thf(c_0_354, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
3.07/1.16	thf(c_0_355, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_282])).
3.07/1.16	thf(c_0_356, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X929:$i]:((((X1 @ X929))&![X930:$i]:((((X1 @ X930))=>((X929)=(X930)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_299, c_0_281])).
3.07/1.16	thf(c_0_357, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
3.07/1.16	thf(c_0_358, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X923:$i]:((((X6 @ X2 @ X923))&![X924:$i]:((((X6 @ X2 @ X924))=>((X923)=(X924)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_300, c_0_281])).
3.07/1.16	thf(c_0_359, plain, ((epred1_0)<=>![X974:$i]:(?[X975:$i]:((((![X976:$i]:(((in @ X976 @ X975)=>![X977:$i]:(((in @ X977 @ X976)=>(in @ X977 @ X974)))))&![X978:$i, X979:$i]:((((in @ X978 @ X974)&(in @ X979 @ X974))=>(![X980:$i]:(((in @ X980 @ X975)=>((in @ X978 @ X980)<=>(in @ X979 @ X980))))=>((X978)=(X979))))))&![X981:$i, X982:$i]:((((in @ X981 @ X975)&(in @ X982 @ X975))=>(![X983:$i]:(((in @ X983 @ X981)=>(in @ X983 @ X982)))|![X984:$i]:(((in @ X984 @ X982)=>(in @ X984 @ X981)))))))&![X985:$i]:(((![X986:$i]:(((in @ X986 @ X985)=>(in @ X986 @ X974)))&?[X987:$i]:((in @ X987 @ X985)))=>?[X988:$i, X989:$i]:(((((in @ X988 @ X975)&(in @ X989 @ X985))&~(?[X990:$i]:(((in @ X990 @ X988)&(in @ X990 @ X985)))))&![X991:$i]:(((in @ X991 @ X975)=>(![X992:$i]:(((in @ X992 @ X991)=>(in @ X992 @ X988)))|(in @ X989 @ X991)))))))))))), introduced(definition)).
3.07/1.16	thf(c_0_360, negated_conjecture, ~((![X1844:$i, X1845:$i]:((![X1846:$i]:(((in @ X1846 @ X1844)<=>(in @ X1846 @ X1845)))=>((X1844)=(X1845))))=>(![X951:$i]:(~(in @ X951 @ emptyset))=>(![X952:$i, X953:$i, X954:$i]:(((in @ X954 @ (setadjoin @ X952 @ X953))<=>(((X954)=(X952))|(in @ X954 @ X953))))=>(![X1841:$i, X1842:$i]:(((in @ X1842 @ (powerset @ X1841))<=>![X1843:$i]:(((in @ X1843 @ X1842)=>(in @ X1843 @ X1841)))))=>(![X955:$i, X956:$i]:(((in @ X956 @ (setunion @ X955))<=>?[X957:$i]:(((in @ X956 @ X957)&(in @ X957 @ X955)))))=>((in @ emptyset @ omega)=>(![X958:$i]:(((in @ X958 @ omega)=>(in @ (setadjoin @ X958 @ X958) @ omega)))=>(![X959:$i]:((((in @ emptyset @ X959)&![X960:$i]:((((in @ X960 @ omega)&(in @ X960 @ X959))=>(in @ (setadjoin @ X960 @ X960) @ X959))))=>![X961:$i]:(((in @ X961 @ omega)=>(in @ X961 @ X959)))))=>(![X962:$i > $i > $o, X963:$i]:((![X964:$i]:(((in @ X964 @ X963)=>?[X965:$i]:(((X962 @ X964 @ X965)&![X966:$i]:(((X962 @ X964 @ X966)=>((X965)=(X966))))))))=>?[X967:$i]:(![X968:$i]:(((in @ X968 @ X967)<=>?[X969:$i]:(((in @ X969 @ X963)&(X962 @ X969 @ X968))))))))=>(![X970:$i]:((?[X971:$i]:((in @ X971 @ X970))=>?[X972:$i]:(((in @ X972 @ X970)&~(?[X973:$i]:(((in @ X973 @ X972)&(in @ X973 @ X970))))))))=>((epred1_0)=>(![X1838:$i > $o]:((?[X1839:$i]:(((X1838 @ X1839)&![X1840:$i]:(((X1838 @ X1840)=>((X1839)=(X1840))))))=>(X1838 @ (descr @ (^[Z0:$i]:((X1838 @ Z0)))))))=>(![X1835:$i, X1836:$i > $o, X1837:$i]:(((in @ X1837 @ X1835)=>((X1836 @ X1837)=>(in @ X1837 @ (dsetconstr @ X1835 @ (^[Z0:$i]:((X1836 @ Z0))))))))=>(![X993:$i, X994:$i > $o, X995:$i]:(((in @ X995 @ (dsetconstr @ X993 @ (^[Z0:$i]:((X994 @ Z0)))))=>(in @ X995 @ X993)))=>(![X1832:$i, X1833:$i > $o, X1834:$i]:(((in @ X1834 @ (dsetconstr @ X1832 @ (^[Z0:$i]:((X1833 @ Z0)))))=>(X1833 @ X1834)))=>(![X1827:$i > $o]:((?[X1828:$i]:(((X1827 @ X1828)&![X1829:$i]:(((X1827 @ X1829)=>((X1828)=(X1829))))))=>?[X1830:$i]:(((X1827 @ X1830)&![X1831:$i]:(((X1827 @ X1831)=>((X1830)=(X1831))))))))=>(![X996:$o, X997:$i]:(((in @ X997 @ (prop2set @ ((X996))))=>(X996)))=>(![X998:$i]:(((in @ X998 @ emptyset)=>![X999:$o]:((X999))))=>(![X1826:$i]:(~(in @ X1826 @ emptyset))=>(![X1825:$i]:(~(in @ X1825 @ emptyset))=>(![X1000:$i > $o]:((?[X1001:$i]:(((X1000 @ X1001)&![X1002:$i]:(((X1000 @ X1002)=>((X1001)=(X1002))))))=>?[X1003:$i]:((X1000 @ X1003))))=>(![X1004:$i, X1005:$i]:((![X1006:$i]:(((in @ X1006 @ X1004)=>(in @ X1006 @ X1005)))=>(![X1007:$i]:(((in @ X1007 @ X1005)=>(in @ X1007 @ X1004)))=>((X1004)=(X1005)))))=>(![X1823:$i]:((![X1824:$i]:(~(in @ X1824 @ X1823))=>((X1823)=(emptyset))))=>(![X1008:$i]:((![X1009:$i]:(~(in @ X1009 @ X1008))=>((X1008)=(emptyset))))=>(![X1820:$i, X1821:$i > $o, X1822:$i]:(((in @ X1822 @ X1820)=>((in @ X1822 @ (dsetconstr @ X1820 @ (^[Z0:$i]:((X1821 @ Z0)))))<=>(X1821 @ X1822))))=>(![X1010:$i]:((((X1010)!=(emptyset))=>?[X1011:$i]:((in @ X1011 @ X1010))))=>(![X1817:$i, X1818:$i > $o, X1819:$i]:(((in @ X1819 @ X1817)=>((X1818 @ X1819)=>((dsetconstr @ X1817 @ (^[Z0:$i]:((X1818 @ Z0))))!=(emptyset)))))=>(![X1815:$i]:((?[X1816:$i]:((in @ X1816 @ X1815))=>((X1815)!=(emptyset))))=>(![X1012:$i, X1013:$i]:((in @ X1012 @ (setadjoin @ X1012 @ X1013)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1014:$i, X1015:$i, X1016:$i]:(((in @ X1016 @ X1015)=>(in @ X1016 @ (setadjoin @ X1014 @ X1015))))=>(![X1017:$i, X1018:$i, X1019:$i]:(((in @ X1019 @ (setadjoin @ X1017 @ X1018))=>![X1020:$o]:(((((X1019)=(X1017))=>(X1020))=>(((in @ X1019 @ X1018)=>(X1020))=>(X1020))))))=>(![X1021:$i, X1022:$i, X1023:$i]:(((in @ X1023 @ (setadjoin @ X1021 @ X1022))=>(((X1023)=(X1021))|(in @ X1023 @ X1022))))=>(![X1024:$i]:(((dsetconstr @ X1024 @ (^[Z0:$i]:(($true))))=(X1024)))=>(![X1025:$i, X1026:$i]:((![X1027:$i]:(((in @ X1027 @ X1026)=>(in @ X1027 @ X1025)))=>(in @ X1026 @ (powerset @ X1025))))=>(![X1028:$i]:((in @ emptyset @ (powerset @ X1028)))=>(![X1814:$i]:((in @ emptyset @ (powerset @ X1814)))=>(![X1029:$i, X1030:$i, X1031:$i]:(((in @ X1030 @ (powerset @ X1029))=>((in @ X1031 @ X1030)=>(in @ X1031 @ X1029))))=>(![X1032:$i, X1033:$i, X1034:$i]:(((in @ X1033 @ X1034)=>((in @ X1034 @ X1032)=>(in @ X1033 @ (setunion @ X1032)))))=>(![X1810:$i, X1811:$i]:(((in @ X1811 @ (setunion @ X1810))=>![X1812:$o]:((![X1813:$i]:(((in @ X1811 @ X1813)=>((in @ X1813 @ X1810)=>(X1812))))=>(X1812)))))=>(![X1808:$i, X1809:$i]:(((in @ X1809 @ X1808)=>(in @ X1809 @ (powerset @ (setunion @ X1808)))))=>(![X1035:$i > $o]:((?[X1036:$i]:(((X1035 @ X1036)&![X1037:$i]:(((X1035 @ X1037)=>((X1036)=(X1037))))))=>?[X1038:$i]:(![X1039:$i]:(((X1035 @ X1039)<=>((X1039)=(X1038)))))))=>(![X1040:$i]:((((X1040)!=(emptyset))=>?[X1041:$i]:((in @ X1041 @ X1040))))=>(![X1042:$i, X1043:$i]:(((in @ X1042 @ (setadjoin @ X1043 @ emptyset))=>((X1042)=(X1043))))=>(![X1044:$i, X1045:$i]:((((X1044)!=(X1045))=>~(in @ X1045 @ (setadjoin @ X1044 @ emptyset))))=>(![X1806:$i, X1807:$i]:((((X1806)=(X1807))=>(in @ X1806 @ (setadjoin @ X1807 @ emptyset))))=>(![X1046:$i, X1047:$i]:(((in @ X1046 @ (setadjoin @ X1047 @ emptyset))=>(in @ X1047 @ (setadjoin @ X1046 @ emptyset))))=>(![X1803:$i, X1804:$i, X1805:$i]:(((in @ X1805 @ (setadjoin @ X1803 @ (setadjoin @ X1804 @ emptyset)))=>(((X1805)=(X1803))|((X1805)=(X1804)))))=>(![X1801:$i, X1802:$i]:((in @ X1801 @ (setadjoin @ X1801 @ (setadjoin @ X1802 @ emptyset))))=>(![X1799:$i, X1800:$i]:((in @ X1800 @ (setadjoin @ X1799 @ (setadjoin @ X1800 @ emptyset))))=>(![X1048:$i, X1049:$i > $o]:((?[X1050:$i]:(((in @ X1050 @ X1048)&(X1049 @ X1050)))=>((dsetconstr @ X1048 @ (^[Z0:$i]:((X1049 @ Z0))))!=(emptyset))))=>(![X1051:$i > $o, X1052:$i]:(((in @ X1052 @ emptyset)=>(X1051 @ X1052)))=>(![X1053:$i, X1054:$i > $o]:((~(![X1055:$i]:(((in @ X1055 @ X1053)=>(X1054 @ X1055))))=>?[X1056:$i]:(((in @ X1056 @ X1053)&~(X1054 @ X1056)))))=>(![X1057:$i, X1058:$i > $o]:((![X1059:$i]:(((in @ X1059 @ X1057)=>~(X1058 @ X1059)))=>~(?[X1060:$i]:(((in @ X1060 @ X1057)&(X1058 @ X1060))))))=>(![X1795:$i, X1796:$i > $o]:((~(?[X1797:$i]:(((in @ X1797 @ X1795)&(X1796 @ X1797))))=>![X1798:$i]:(((in @ X1798 @ X1795)=>~(X1796 @ X1798)))))=>(![X1061:$i, X1062:$i > $o]:((?[X1063:$i]:(((in @ X1063 @ X1061)&~(X1062 @ X1063)))=>~(![X1064:$i]:(((in @ X1064 @ X1061)=>(X1062 @ X1064))))))=>(![X1065:$o]:(((X1065)=>(in @ emptyset @ (prop2set @ ((X1065))))))=>(![X1794:$o]:(((X1794)=>(set2prop @ (prop2set @ ((X1794))))))=>(![X1790:$i, X1791:$i > $o]:((~(?[X1792:$i]:(((in @ X1792 @ X1790)&(X1791 @ X1792))))=>![X1793:$i]:(((in @ X1793 @ X1790)=>~(X1791 @ X1793)))))=>(![X1066:$i, X1067:$i > $o]:((~(![X1068:$i]:(((in @ X1068 @ X1066)=>(X1067 @ X1068))))=>?[X1069:$i]:(((in @ X1069 @ X1066)&~(X1067 @ X1069)))))=>(![X1070:$i > $o]:((?[X1071:$i]:(((X1070 @ X1071)&![X1072:$i]:(((X1070 @ X1072)=>((X1071)=(X1072))))))=>?[X1073:$i]:(((X1070 @ X1073)&![X1074:$i]:(((X1070 @ X1074)=>((X1073)=(X1074))))))))=>(![X1075:$i > $o]:((?[X1076:$i]:((X1075 @ X1076))=>(![X1077:$i, X1078:$i]:(((X1075 @ X1077)=>((X1075 @ X1078)=>((X1077)=(X1078)))))=>?[X1079:$i]:(((X1075 @ X1079)&![X1080:$i]:(((X1075 @ X1080)=>((X1079)=(X1080)))))))))=>(![X1785:$i > $o]:((?[X1786:$i]:(![X1787:$i]:(((X1785 @ X1787)<=>((X1787)=(X1786)))))=>?[X1788:$i]:(((X1785 @ X1788)&![X1789:$i]:(((X1785 @ X1789)=>((X1788)=(X1789))))))))=>(![X1081:$i, X1082:$i]:((((X1081)=(X1082))=>![X1083:$i, X1084:$i]:((((X1083)=(X1084))=>((in @ X1083 @ X1081)=>(in @ X1084 @ X1082))))))=>(![X1781:$i, X1782:$i]:((((X1781)=(X1782))=>![X1783:$i, X1784:$i]:((((X1783)=(X1784))=>((in @ X1783 @ X1781)<=>(in @ X1784 @ X1782))))))=>(![X1085:$i > $o]:((?[X1086:$i]:(((X1085 @ X1086)&![X1087:$i]:(((X1085 @ X1087)=>((X1086)=(X1087))))))=>![X1088:$i, X1089:$i]:(((X1085 @ X1088)=>((X1085 @ X1089)=>((X1088)=(X1089)))))))=>(![X1090:$i > $o, X1091:$i > $o]:((![X1092:$i, X1093:$i]:((((X1092)=(X1093))=>((X1090 @ X1092)<=>(X1091 @ X1093))))=>(?[X1094:$i]:(((X1090 @ X1094)&![X1095:$i]:(((X1090 @ X1095)=>((X1094)=(X1095))))))<=>?[X1096:$i]:(((X1091 @ X1096)&![X1097:$i]:(((X1091 @ X1097)=>((X1096)=(X1097)))))))))=>(((emptyset)=(emptyset))=>(![X1777:$i, X1778:$i]:((((X1777)=(X1778))=>![X1779:$i, X1780:$i]:((((X1779)=(X1780))=>((setadjoin @ X1777 @ X1779)=(setadjoin @ X1778 @ X1780))))))=>(![X1098:$i, X1099:$i]:((((X1098)=(X1099))=>((powerset @ X1098)=(powerset @ X1099))))=>(![X1775:$i, X1776:$i]:((((X1775)=(X1776))=>((setunion @ X1775)=(setunion @ X1776))))=>(((omega)=(omega))=>(![X1100:$i > $o]:((?[X1101:$i]:(((X1100 @ X1101)&![X1102:$i]:(((X1100 @ X1102)=>((X1101)=(X1102))))))=>![X1103:$i, X1104:$i]:(((X1100 @ X1103)=>((X1100 @ X1104)=>((X1103)=(X1104)))))))=>(![X1105:$i > $o, X1106:$i > $o]:((![X1107:$i, X1108:$i]:((((X1107)=(X1108))=>((X1105 @ X1107)<=>(X1106 @ X1108))))=>(?[X1109:$i]:(((X1105 @ X1109)&![X1110:$i]:(((X1105 @ X1110)=>((X1109)=(X1110))))))=>(?[X1111:$i]:(((X1106 @ X1111)&![X1112:$i]:(((X1106 @ X1112)=>((X1111)=(X1112))))))=>((descr @ (^[Z0:$i]:((X1105 @ Z0))))=(descr @ (^[Z0:$i]:((X1106 @ Z0)))))))))=>(![X1113:$i, X1114:$i]:((((X1113)=(X1114))=>![X1115:$i > $o, X1116:$i > $o]:((![X1117:$i]:(((in @ X1117 @ X1113)=>![X1118:$i]:(((in @ X1118 @ X1114)=>(((X1117)=(X1118))=>((X1115 @ X1117)<=>(X1116 @ X1118)))))))=>((dsetconstr @ X1113 @ (^[Z0:$i]:((X1115 @ Z0))))=(dsetconstr @ X1114 @ (^[Z0:$i]:((X1116 @ Z0)))))))))=>(![X1772:$i, X1773:$i]:((![X1774:$i]:(((in @ X1774 @ X1772)=>(in @ X1774 @ X1773)))=>(subset @ X1772 @ X1773)))=>(![X1119:$i, X1120:$i]:((((X1119)=(X1120))=>(subset @ X1120 @ X1119)))=>(![X1770:$i, X1771:$i]:((((X1770)=(X1771))=>(subset @ X1770 @ X1771)))=>(![X1767:$i, X1768:$i]:((![X1769:$i]:(((in @ X1769 @ X1767)=>(in @ X1769 @ X1768)))=>(subset @ X1767 @ X1768)))=>(![X1766:$i]:((subset @ emptyset @ X1766))=>(![X1121:$i, X1122:$i, X1123:$i]:(((subset @ X1121 @ X1122)=>((in @ X1123 @ X1121)=>(in @ X1123 @ X1122))))=>(![X1763:$i, X1764:$i, X1765:$i]:(((subset @ X1763 @ X1764)=>(~(in @ X1765 @ X1764)=>~(in @ X1765 @ X1763))))=>(![X1760:$i, X1761:$i, X1762:$i]:(((in @ X1762 @ X1760)=>(~(in @ X1762 @ X1761)=>~(subset @ X1760 @ X1761))))=>(![X1124:$i, X1125:$i]:((~(subset @ X1124 @ X1125)=>((X1124)!=(X1125))))=>(![X1126:$i, X1127:$i, X1128:$i]:(((in @ X1128 @ X1126)=>(~(in @ X1128 @ X1127)=>((X1126)!=(X1127)))))=>(![X1759:$i]:((subset @ X1759 @ X1759))=>(![X1756:$i, X1757:$i, X1758:$i]:(((subset @ X1756 @ X1757)=>((subset @ X1757 @ X1758)=>(subset @ X1756 @ X1758))))=>(![X1754:$i, X1755:$i]:((subset @ X1755 @ (setadjoin @ X1754 @ X1755)))=>(![X1751:$i, X1752:$i, X1753:$i]:(((subset @ X1751 @ X1753)=>(subset @ X1751 @ (setadjoin @ X1752 @ X1753))))=>(![X1749:$i, X1750:$i]:(((subset @ X1749 @ X1750)=>(in @ X1749 @ (powerset @ X1750))))=>(![X1747:$i, X1748:$i]:(((subset @ X1747 @ X1748)=>((subset @ X1748 @ X1747)=>((X1747)=(X1748)))))=>(![X1129:$i]:(((subset @ X1129 @ emptyset)=>((X1129)=(emptyset))))=>(![X1130:$i, X1131:$i]:(((subset @ X1131 @ X1130)=>(in @ X1131 @ (powerset @ X1130))))=>(![X1745:$i, X1746:$i]:(((in @ X1746 @ (powerset @ X1745))=>(subset @ X1746 @ X1745)))=>(![X1132:$i]:((in @ X1132 @ (powerset @ X1132)))=>(![X1743:$i, X1744:$i]:(((subset @ X1743 @ X1744)=>(subset @ (powerset @ X1743) @ (powerset @ X1744))))=>(![X1133:$i, X1134:$i > $o]:((in @ (dsetconstr @ X1133 @ (^[Z0:$i]:((X1134 @ Z0)))) @ (powerset @ X1133)))=>(![X1135:$i, X1136:$i > $o]:((subset @ (dsetconstr @ X1135 @ (^[Z0:$i]:((X1136 @ Z0)))) @ X1135))=>(![X1740:$i, X1741:$i, X1742:$i]:(((in @ X1742 @ X1740)=>(in @ X1742 @ (binunion @ X1740 @ X1741))))=>(![X1137:$i, X1138:$i]:((in @ X1138 @ (setadjoin @ X1137 @ (setadjoin @ X1138 @ emptyset))))=>(![X1139:$i, X1140:$i, X1141:$i]:(((in @ X1141 @ X1140)=>(in @ X1141 @ (binunion @ X1139 @ X1140))))=>(![X1142:$i, X1143:$i, X1144:$i, X1145:$o]:(((in @ X1144 @ (binunion @ X1142 @ X1143))=>(((in @ X1144 @ X1142)=>(X1145))=>(((in @ X1144 @ X1143)=>(X1145))=>(X1145)))))=>(![X1737:$i, X1738:$i, X1739:$i]:(((in @ X1739 @ (binunion @ X1737 @ X1738))=>((in @ X1739 @ X1737)|(in @ X1739 @ X1738))))=>(![X1735:$i, X1736:$i]:((subset @ X1735 @ (binunion @ X1735 @ X1736)))=>(![X1146:$i, X1147:$i]:((subset @ X1147 @ (binunion @ X1146 @ X1147)))=>(![X1732:$i, X1733:$i, X1734:$i]:(((in @ X1734 @ X1732)=>((in @ X1734 @ X1733)=>(in @ X1734 @ (binintersect @ X1732 @ X1733)))))=>(![X1148:$i, X1149:$i, X1150:$i]:(((subset @ X1150 @ X1148)=>((subset @ X1150 @ X1149)=>(subset @ X1150 @ (binintersect @ X1148 @ X1149)))))=>(![X1151:$i, X1152:$i, X1153:$i]:(((in @ X1153 @ (binintersect @ X1151 @ X1152))=>(in @ X1153 @ X1151)))=>(![X1154:$i, X1155:$i]:((subset @ (binintersect @ X1154 @ X1155) @ X1154))=>(![X1730:$i, X1731:$i]:(((subset @ X1730 @ X1731)=>((binintersect @ X1730 @ X1731)=(X1730))))=>(![X1156:$i, X1157:$i]:((((binintersect @ X1156 @ X1157)=(X1157))=>(subset @ X1157 @ X1156)))=>(![X1158:$i, X1159:$i, X1160:$i]:(((in @ X1160 @ (binintersect @ X1158 @ X1159))=>(in @ X1160 @ X1159)))=>(![X1727:$i, X1728:$i]:((~(?[X1729:$i]:(((in @ X1729 @ X1727)&(in @ X1729 @ X1728))))=>((binintersect @ X1727 @ X1728)=(emptyset))))=>(![X1725:$i, X1726:$i]:((subset @ (binintersect @ X1725 @ X1726) @ X1726))=>(![X1723:$i, X1724:$i]:(((subset @ X1724 @ X1723)=>((binintersect @ X1723 @ X1724)=(X1724))))=>(![X1721:$i, X1722:$i]:((((binintersect @ X1721 @ X1722)=(X1721))=>(subset @ X1721 @ X1722)))=>(![X1161:$i, X1162:$i, X1163:$i]:(((binintersect @ X1161 @ (binunion @ X1162 @ X1163))=(binunion @ (binintersect @ X1161 @ X1162) @ (binintersect @ X1161 @ X1163))))=>(![X1164:$i, X1165:$i, X1166:$i]:(((in @ X1166 @ X1164)=>(~(in @ X1166 @ X1165)=>(in @ X1166 @ (setminus @ X1164 @ X1165)))))=>(![X1167:$i, X1168:$i, X1169:$i]:(((in @ X1169 @ (setminus @ X1167 @ X1168))=>(in @ X1169 @ X1167)))=>(![X1718:$i, X1719:$i, X1720:$i]:(((in @ X1720 @ (setminus @ X1718 @ X1719))=>~(in @ X1720 @ X1719)))=>(![X1170:$i, X1171:$i]:(((subset @ X1170 @ X1171)=>((setminus @ X1170 @ X1171)=(emptyset))))=>(![X1715:$i, X1716:$i, X1717:$i]:((~(in @ X1717 @ (setminus @ X1715 @ X1716))=>((in @ X1717 @ X1715)=>(in @ X1717 @ X1716))))=>(![X1172:$i, X1173:$i, X1174:$i]:((~(in @ X1174 @ (setminus @ X1172 @ X1173))=>(~(in @ X1174 @ X1173)=>~(in @ X1174 @ X1172))))=>(![X1712:$i, X1713:$i, X1714:$i]:((~(in @ X1714 @ X1712)=>~(in @ X1714 @ (setminus @ X1712 @ X1713))))=>(![X1709:$i, X1710:$i, X1711:$i]:(((in @ X1711 @ X1710)=>~(in @ X1711 @ (setminus @ X1709 @ X1710))))=>(![X1175:$i, X1176:$i]:((subset @ (setminus @ X1175 @ X1176) @ X1175))=>(![X1177:$i, X1178:$i]:((((setminus @ X1177 @ X1178)=(emptyset))=>(subset @ X1177 @ X1178)))=>(![X1179:$i, X1180:$i, X1181:$i]:(((in @ X1181 @ (symdiff @ X1179 @ X1180))=>![X1182:$o]:((((in @ X1181 @ X1179)=>(~(in @ X1181 @ X1180)=>(X1182)))=>((~(in @ X1181 @ X1179)=>((in @ X1181 @ X1180)=>(X1182)))=>(X1182))))))=>(![X1183:$i, X1184:$i, X1185:$i]:(((in @ X1185 @ X1183)=>(~(in @ X1185 @ X1184)=>(in @ X1185 @ (symdiff @ X1183 @ X1184)))))=>(![X1186:$i, X1187:$i, X1188:$i]:((~(in @ X1188 @ X1186)=>((in @ X1188 @ X1187)=>(in @ X1188 @ (symdiff @ X1186 @ X1187)))))=>(![X1706:$i, 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[woz13rule0]), setunionE]), emptyInPowerset]), setextAx]), subsetRefl]), notsubsetI]), subsetE2]), c_0_301]), emptysetsubset]), subsetI2]), c_0_302]), eqimpsubset1]), subsetI1]), c_0_303]), omega__Cong]), setunion__Cong]), funcextLem]), setadjoin__Cong]), in__Cong]), c_0_304]), c_0_305]), notdexE]), c_0_306]), prop2set2propI]), funcext]), quantDeMorgan3]), upairsetIR]), upairsetIL]), c_0_307]), upairsetE]), eqinunit]), subPowSU]), c_0_308]), binunionTIRcontra]), c_0_309]), theeq]), c_0_310]), c_0_311]), iftrue]), emptyI]), notinemptyset]), complementT_lem]), emptysetimpfalse]), c_0_312]), c_0_313]), c_0_314]), subsetTI]), c_0_315]), omega0Ax]), powersetTE1]), powersetAx]), binintersectTELcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), ifp]), c_0_316]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), binunionTE]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2]), demorgan2b]), demorgan2b2]), demorgan1a]), binunionTEcontra]), inComplementUnionImpInComplement1]), inComplementUnionImpNotIn1]), inIntersectImpInUnion]), binunionTILcontra]), complementTcontraSubset]), doubleComplementSub2]), setukpairinjR1]), doubleComplementSub1]), doubleComplementE1]), binintersectTERcontra]), complementTE1]), complementTI1]), powersetTI1]), setextT]), setminusT_lem]), upairequniteq]), powersetT_lem]), setukpairinjR]), binunionT_lem]), c_0_317]), binintersectT_lem]), iftrueorfalse]), iffalse]), powersetE1]), c_0_318]), c_0_319]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), c_0_324]), ap2apEq2]), ap2apEq1]), cartprodpairmemER]), funcext2]), funcGraphProp4]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), c_0_325]), c_0_326]), c_0_327]), funcinfuncset]), app]), c_0_328]), c_0_329]), c_0_330]), c_0_331]), c_0_332]), c_0_333]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), setukpairinjR2]), setukpairinjL]), kfstpairEq]), c_0_334]), c_0_335]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair]), ubforcartprodlem3]), ubforcartprodlem2]), upairsubunion]), setukpairIR]), symdiffIneg2]), symdiffIneg1]), setminusIRneg]), setminusILneg]), setminusERneg]), setminusER]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), cartprodsndpairEq]), disjointsetsI1]), binintersectSubset2]), binintersectI]), binunionLsub]), cartprodpairsurjEq]), c_0_336]), binunionE]), c_0_337]), c_0_338]), binunionIL]), powersetsubset]), infuncsetfunc]), ap2p]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), setukpairinjR12]), setukpairinjR11]), setukpairinjL2]), cartprodfstin]), theprop]), setukpairinjL1]), singletonsuniq]), c_0_339]), c_0_340]), c_0_341]), setunionsingleton]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem1]), upairinpowunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIL]), secondinupair]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusELneg]), setminusSubset2]), setminusEL]), setminusI]), bs114d]), binintersectER]), binintersectSubset3]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binunionRsub]), binunionEcases]), binunionIR]), upairset2IR]), c_0_342]), c_0_343]), inPowerset]), powersetI1]), subsetemptysetimpeq]), notequalI2]), notequalI1]), subsetE]), eqimpsubset2]), c_0_344]), c_0_345]), c_0_346]), powerset__Cong]), emptyset__Cong]), c_0_347]), c_0_348]), inCongP]), c_0_349]), c_0_350]), notdallE]), prop2setI]), quantDeMorgan4]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_351]), singletonsswitch]), notinsingleton]), uniqinunit]), c_0_352]), c_0_353]), setunionI]), powersetE]), emptyinPowerset]), powersetI]), c_0_354]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_355]), noeltsimpempty]), setext]), c_0_356]), emptysetE]), prop2setE]), c_0_357]), wellorderingAx]), foundationAx]), c_0_358]), omegaIndAx]), omegaSAx]), setunionAx]), setadjoinAx]), emptysetAx])])]), c_0_359])).
3.07/1.16	thf(c_0_361, negated_conjecture, ![X1847:$i, X1848:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1860:$i, X1861:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1869:$i, X1870:$i > $i > $o, X1871:$i, X1873:$i, X1876:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1883:$i, X1884:$i > $o, X1885:$i, X1887:$i, X1888:$i > $o, X1889:$i, X1890:$i, X1891:$i > $o, X1892:$i, X1893:$i, X1894:$i > $o, X1895:$i, X1896:$i > $o, X1897:$i, X1900:$i, X1901:$o, X1902:$i, X1903:$i, X1904:$o, X1905:$i, X1906:$i, X1907:$i > $o, X1908:$i, X1911:$i, X1912:$i, X1915:$i, X1917:$i, X1919:$i, X1920:$i > $o, X1921:$i, X1922:$i, X1924:$i, X1925:$i > $o, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$o, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$o, X1957:$i, X1958:$i, X1959:$i > $o, X1960:$i, X1963:$i, X1964:$i, X1965:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i > $o, X1984:$i, X1985:$i > $o, X1986:$i, X1987:$i, X1988:$i > $o, X1989:$i, X1991:$i, X1992:$i > $o, X1994:$i, X1995:$i, X1996:$i > $o, X1998:$i, X1999:$i, X2000:$i > $o, X2001:$i, X2003:$o, X2004:$o, X2005:$i, X2006:$i > $o, X2008:$i, X2009:$i, X2010:$i > $o, X2011:$i, X2013:$i > $o, X2014:$i, X2017:$i, X2018:$i > $o, X2019:$i, X2023:$i, X2024:$i > $o, X2025:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i > $o, X2038:$i, X2040:$i, X2041:$i, X2042:$i > $o, X2043:$i > $o, X2046:$i, X2049:$i, X2050:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i > $o, X2063:$i, X2065:$i, X2066:$i, X2067:$i > $o, X2068:$i > $o, X2071:$i, X2073:$i, X2075:$i, X2076:$i, X2077:$i > $o, X2078:$i > $o, X2081:$i, X2082:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i > $o, X2129:$i, X2130:$i > $o, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$o, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$o, 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, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i > 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@ X2584 @ X2585)|~(in @ X2585 @ (powerset @ X2583))|~(in @ X2584 @ (powerset @ X2583)))&(~(in @ (esk85_3 @ X2583 @ X2584 @ X2585) @ X2585)|(subset @ X2584 @ X2585)|~(in @ X2585 @ (powerset @ X2583))|~(in @ X2584 @ (powerset @ X2583)))))&((((in @ (esk86_3 @ X2587 @ X2588 @ X2589) @ X2587)|(in @ X2588 @ (powerset @ X2589))|~(in @ X2589 @ (powerset @ X2587))|~(in @ X2588 @ (powerset @ X2587)))&(((in @ (esk86_3 @ X2587 @ X2588 @ X2589) @ X2588)|(in @ X2588 @ (powerset @ X2589))|~(in @ X2589 @ (powerset @ X2587))|~(in @ X2588 @ (powerset @ X2587)))&(~(in @ (esk86_3 @ X2587 @ X2588 @ X2589) @ X2589)|(in @ X2588 @ (powerset @ X2589))|~(in @ X2589 @ (powerset @ X2587))|~(in @ X2588 @ (powerset @ X2587)))))&((~(in @ X2592 @ (powerset @ X2591))|(~(in @ X2593 @ (powerset @ X2591))|(~(in @ X2594 @ X2591)|(~(in @ X2592 @ (powerset @ X2593))|(~(in @ X2594 @ X2592)|(in @ X2594 @ X2593))))))&((~(in @ X2596 @ (powerset @ X2595))|(~(in @ X2597 @ X2595)|(~(in @ X2597 @ X2596)|~(in @ X2597 @ (setminus @ X2595 @ X2596)))))&((~(in @ X2599 @ (powerset @ X2598))|(~(in @ X2600 @ X2598)|((in @ X2600 @ (setminus @ X2598 @ X2599))|(in @ X2600 @ X2599))))&((~(in @ X2602 @ (powerset @ X2601))|(~(in @ X2603 @ (powerset @ X2601))|(~(in @ X2604 @ X2601)|((in @ X2604 @ X2602)|~(in @ X2604 @ (binintersect @ X2602 @ X2603))))))&((~(in @ X2606 @ (powerset @ X2605))|(~(in @ X2607 @ (powerset @ X2605))|(~(in @ X2608 @ X2605)|((in @ X2608 @ X2607)|~(in @ X2608 @ (binintersect @ X2606 @ X2607))))))&((~(in @ X2610 @ (powerset @ X2609))|(~(in @ X2611 @ (powerset @ X2609))|(~(in @ X2612 @ X2609)|(~(subset @ X2610 @ (setminus @ X2609 @ X2611))|(~(in @ X2612 @ X2611)|~(in @ X2612 @ X2610))))))&((~(in @ X2614 @ (powerset @ X2613))|(~(in @ X2615 @ (powerset @ X2613))|(~(in @ X2616 @ X2613)|(~(subset @ X2614 @ X2615)|((in @ X2616 @ X2615)|~(in @ X2616 @ X2614))))))&((~(in @ X2618 @ (powerset @ X2617))|(~(in @ X2619 @ (powerset @ X2617))|(~(subset @ X2618 @ X2619)|(subset @ (setminus @ X2617 @ X2619) @ (setminus @ X2617 @ X2618)))))&((~(in @ X2621 @ (powerset @ X2620))|(~(in @ X2622 @ (powerset @ X2620))|(~(subset @ (setminus @ X2620 @ X2622) @ (setminus @ X2620 @ X2621))|(subset @ X2621 @ X2622))))&((~(in @ X2624 @ (powerset @ X2623))|(~(in @ X2625 @ X2623)|(~(in @ X2625 @ X2624)|(in @ X2625 @ (setminus @ X2623 @ (setminus @ X2623 @ X2624))))))&((~(in @ X2627 @ (powerset @ X2626))|(~(in @ X2628 @ X2626)|(~(in @ X2628 @ (setminus @ X2626 @ (setminus @ X2626 @ X2627)))|(in @ X2628 @ X2627))))&((~(in @ X2630 @ (powerset @ X2629))|(subset @ X2630 @ (setminus @ X2629 @ (setminus @ X2629 @ X2630))))&((~(in @ X2632 @ (powerset @ X2631))|(subset @ (setminus @ X2631 @ (setminus @ X2631 @ X2632)) @ X2632))&((~(in @ X2634 @ (powerset @ X2633))|((X2634)=(setminus @ X2633 @ (setminus @ X2633 @ X2634))))&((~(in @ X2636 @ (powerset @ X2635))|(~(in @ X2637 @ (powerset @ X2635))|(~(in @ X2638 @ X2635)|(~(in @ X2638 @ (setminus @ X2635 @ X2636))|~(in @ X2638 @ (binintersect @ X2636 @ X2637))))))&((~(in @ X2640 @ (powerset @ X2639))|(~(in @ X2641 @ (powerset @ X2639))|(~(in @ X2642 @ X2639)|(~(in @ X2642 @ (setminus @ X2639 @ X2640))|(in @ X2642 @ (setminus @ X2639 @ (binintersect @ X2640 @ X2641)))))))&((~(in @ X2644 @ (powerset @ X2643))|(~(in @ X2645 @ (powerset @ X2643))|(subset @ (setminus @ X2643 @ X2644) @ (setminus @ X2643 @ (binintersect @ X2644 @ X2645)))))&((~(in @ X2647 @ (powerset @ X2646))|(~(in @ X2648 @ (powerset @ X2646))|(in @ (setminus @ X2646 @ X2647) @ (powerset @ (setminus @ X2646 @ (binintersect @ X2647 @ X2648))))))&((~(in @ X2650 @ (powerset @ X2649))|(~(in @ X2651 @ (powerset @ X2649))|(~(subset @ X2650 @ (setminus @ X2649 @ X2651))|(~(in @ X2652 @ X2649)|(~(in @ X2652 @ X2651)|(in @ X2652 @ (setminus @ X2649 @ X2650)))))))&((~(in @ X2654 @ (powerset @ X2653))|(~(in @ X2655 @ (powerset @ X2653))|(~(subset @ X2654 @ (setminus @ X2653 @ X2655))|(subset @ X2655 @ (setminus @ X2653 @ X2654)))))&((~(in @ X2657 @ (powerset @ X2656))|(~(in @ X2658 @ (powerset @ X2656))|(~(in @ X2659 @ X2656)|((in @ X2659 @ (binunion @ X2657 @ X2658))|~(in @ X2659 @ X2657)))))&((~(in @ X2661 @ (powerset @ X2660))|(~(in @ X2662 @ (powerset @ X2660))|(~(in @ X2663 @ X2660)|((in @ X2663 @ (binunion @ X2661 @ X2662))|~(in @ X2663 @ X2662)))))&((~(in @ X2665 @ (powerset @ X2664))|(~(in @ X2666 @ (powerset @ X2664))|(~(in @ X2667 @ (powerset @ X2664))|(~(in @ X2668 @ X2664)|(~(in @ X2668 @ (binintersect @ X2665 @ X2666))|(in @ X2668 @ (binunion @ X2665 @ X2667)))))))&((~(in @ X2670 @ (powerset @ X2669))|(~(in @ X2671 @ (powerset @ X2669))|(~(in @ X2672 @ (powerset @ X2669))|(~(in @ X2673 @ X2669)|(~(in @ X2673 @ (binintersect @ X2670 @ X2671))|(in @ X2673 @ (binunion @ X2671 @ X2672)))))))&((~(in @ X2675 @ (powerset @ X2674))|(~(in @ X2676 @ (powerset @ X2674))|(~(in @ X2677 @ (powerset @ X2674))|(~(in @ X2678 @ X2674)|(~(in @ X2678 @ (binintersect @ X2675 @ X2676))|(in @ X2678 @ (binintersect @ (binunion @ X2675 @ X2677) @ (binunion @ X2676 @ X2677))))))))&((~(in @ X2680 @ (powerset @ X2679))|(~(in @ X2681 @ (powerset @ X2679))|(~(in @ X2682 @ (powerset @ X2679))|(in @ (binintersect @ X2680 @ X2681) @ (powerset @ (binintersect @ (binunion @ X2680 @ X2682) @ (binunion @ X2681 @ X2682)))))))&((~(in @ X2684 @ (powerset @ X2683))|(~(in @ X2685 @ (powerset @ X2683))|(~(in @ X2686 @ X2683)|(~(in @ X2686 @ (setminus @ X2683 @ (binunion @ X2684 @ X2685)))|~(in @ X2686 @ X2684)))))&((~(in @ X2688 @ (powerset @ X2687))|(~(in @ X2689 @ (powerset @ X2687))|(~(in @ X2690 @ X2687)|(~(in @ X2690 @ (setminus @ X2687 @ (binunion @ X2688 @ X2689)))|(in @ X2690 @ (setminus @ X2687 @ X2688))))))&(((((in @ X2695 @ X2693)|(X2694)|(in @ X2695 @ X2692)|~(in @ X2695 @ (binunion @ X2692 @ X2693))|~(in @ X2695 @ X2691)|~(in @ X2693 @ (powerset @ X2691))|~(in @ X2692 @ (powerset @ X2691)))&(~(X2694)|(X2694)|(in @ X2695 @ X2692)|~(in @ X2695 @ (binunion @ X2692 @ X2693))|~(in @ X2695 @ X2691)|~(in @ X2693 @ (powerset @ X2691))|~(in @ X2692 @ (powerset @ X2691))))&(((in @ X2695 @ X2693)|(X2694)|~(X2694)|~(in @ X2695 @ (binunion @ X2692 @ X2693))|~(in @ X2695 @ X2691)|~(in @ X2693 @ (powerset @ X2691))|~(in @ X2692 @ (powerset @ X2691)))&(~(X2694)|(X2694)|~(X2694)|~(in @ X2695 @ (binunion @ X2692 @ X2693))|~(in @ X2695 @ X2691)|~(in @ X2693 @ (powerset @ X2691))|~(in @ X2692 @ (powerset @ X2691)))))&((~(in @ X2697 @ (powerset @ X2696))|(~(in @ X2698 @ (powerset @ X2696))|(~(in @ X2699 @ X2696)|((in @ X2699 @ X2697)|((in @ X2699 @ X2698)|~(in @ X2699 @ (binunion @ X2697 @ X2698)))))))&((~(in @ X2701 @ (powerset @ X2700))|(~(in @ X2702 @ (powerset @ X2700))|(~(in @ X2703 @ X2700)|(~(in @ X2703 @ (setminus @ X2700 @ (binunion @ X2701 @ X2702)))|(in @ X2703 @ (setminus @ X2700 @ X2701))))))&((~(in @ X2705 @ (powerset @ X2704))|(~(in @ X2706 @ (powerset @ X2704))|(in @ (setminus @ X2704 @ (binunion @ X2705 @ X2706)) @ (powerset @ (setminus @ X2704 @ X2705)))))&((~(in @ X2708 @ (powerset @ X2707))|(~(in @ X2709 @ (powerset @ X2707))|(~(in @ X2710 @ X2707)|(~(in @ X2710 @ (setminus @ X2707 @ (binunion @ X2708 @ X2709)))|(in @ X2710 @ (setminus @ X2707 @ X2709))))))&((~(in @ X2712 @ (powerset @ X2711))|(~(in @ X2713 @ (powerset @ X2711))|(~(in @ X2714 @ X2711)|(~(in @ X2714 @ (setminus @ X2711 @ (binintersect @ X2712 @ X2713)))|(in @ X2714 @ (binunion @ (setminus @ X2711 @ X2712) @ (setminus @ X2711 @ X2713)))))))&((~(in @ X2716 @ (powerset @ X2715))|(~(in @ X2717 @ (powerset @ X2715))|(~(in @ X2718 @ X2715)|(~(in @ X2718 @ (binunion @ (setminus @ X2715 @ X2716) @ (setminus @ X2715 @ X2717)))|(in @ X2718 @ (setminus @ X2715 @ (binintersect @ X2716 @ X2717)))))))&((~(in @ X2720 @ (powerset @ X2719))|(~(in @ X2721 @ (powerset @ X2719))|((setminus @ X2719 @ (binintersect @ X2720 @ X2721))=(binunion @ (setminus @ X2719 @ X2720) @ (setminus @ X2719 @ X2721)))))&((~(in @ X2723 @ (powerset @ X2722))|(~(in @ X2724 @ (powerset @ X2722))|(~(in @ X2725 @ X2722)|(~(in @ X2725 @ (setminus @ X2722 @ (binunion @ X2723 @ X2724)))|(in @ X2725 @ (binintersect @ (setminus @ X2722 @ X2723) @ (setminus @ X2722 @ X2724)))))))&((~(in @ X2727 @ (powerset @ X2726))|(~(in @ X2728 @ (powerset @ X2726))|(~(in @ X2729 @ X2726)|(~(in @ X2729 @ (setminus @ X2726 @ X2727))|(~(in @ X2729 @ (setminus @ X2726 @ X2728))|(in @ X2729 @ (setminus @ X2726 @ (binunion @ X2727 @ X2728))))))))&((~(in @ X2731 @ (powerset @ X2730))|(~(in @ X2732 @ (powerset @ X2730))|(~(in @ X2733 @ X2730)|(~(in @ X2733 @ (binintersect @ (setminus @ X2730 @ X2731) @ (setminus @ X2730 @ X2732)))|(in @ X2733 @ (setminus @ X2730 @ (binunion @ X2731 @ X2732)))))))&((~(in @ X2735 @ (powerset @ X2734))|(~(in @ X2736 @ (powerset @ X2734))|((setminus @ X2734 @ (binunion @ X2735 @ X2736))=(binintersect @ (setminus @ X2734 @ X2735) @ (setminus @ X2734 @ X2736)))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((in @ esk90_0 @ (binintersect @ esk88_0 @ esk89_0))&~(in @ esk90_0 @ esk87_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[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_360])])])])])])).
3.07/1.16	thf(c_0_362, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_361])).
3.07/1.16	thf(c_0_363, negated_conjecture, (in @ esk89_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_361])).
3.07/1.16	thf(c_0_364, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X4)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_361])).
3.07/1.16	thf(c_0_365, negated_conjecture, (in @ esk90_0 @ (binintersect @ esk88_0 @ esk89_0)), inference(split_conjunct,[status(thm)],[c_0_361])).
3.07/1.16	thf(c_0_366, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk87_0)|~((in @ X2 @ esk89_0)))), inference(spm,[status(thm)],[c_0_362, c_0_363])).
3.07/1.16	thf(c_0_367, negated_conjecture, (in @ esk90_0 @ esk89_0), inference(spm,[status(thm)],[c_0_364, c_0_365])).
3.07/1.16	thf(c_0_368, negated_conjecture, ~((in @ esk90_0 @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_361])).
3.07/1.16	thf(c_0_369, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_366, c_0_367]), c_0_368]), ['proof']).
3.07/1.16	# SZS output end CNFRefutation
3.07/1.16	# Parsed axioms                        : 591
3.07/1.16	# Removed by relevancy pruning/SinE    : 312
3.07/1.16	# Initial clauses                      : 477
3.07/1.16	# Removed in clause preprocessing      : 32
3.07/1.16	# Initial clauses in saturation        : 445
3.07/1.16	# Processed clauses                    : 906
3.07/1.16	# ...of these trivial                  : 12
3.07/1.16	# ...subsumed                          : 56
3.07/1.16	# ...remaining for further processing  : 838
3.07/1.16	# Other redundant clauses eliminated   : 56
3.07/1.16	# Clauses deleted for lack of memory   : 0
3.07/1.16	# Backward-subsumed                    : 0
3.07/1.16	# Backward-rewritten                   : 4
3.07/1.16	# Generated clauses                    : 12371
3.07/1.16	# ...of the previous two non-redundant : 12043
3.07/1.16	# ...aggressively subsumed             : 0
3.07/1.16	# Contextual simplify-reflections      : 11
3.07/1.16	# Paramodulations                      : 12280
3.07/1.16	# Factorizations                       : 2
3.07/1.16	# NegExts                              : 0
3.07/1.16	# Equation resolutions                 : 63
3.07/1.16	# Propositional unsat checks           : 0
3.07/1.16	#    Propositional check models        : 0
3.07/1.16	#    Propositional check unsatisfiable : 0
3.07/1.16	#    Propositional clauses             : 0
3.07/1.16	#    Propositional clauses after purity: 0
3.07/1.16	#    Propositional unsat core size     : 0
3.07/1.16	#    Propositional preprocessing time  : 0.000
3.07/1.16	#    Propositional encoding time       : 0.000
3.07/1.16	#    Propositional solver time         : 0.000
3.07/1.16	#    Success case prop preproc time    : 0.000
3.07/1.16	#    Success case prop encoding time   : 0.000
3.07/1.16	#    Success case prop solver time     : 0.000
3.07/1.16	# Current number of processed clauses  : 424
3.07/1.16	#    Positive orientable unit clauses  : 44
3.07/1.16	#    Positive unorientable unit clauses: 0
3.07/1.16	#    Negative unit clauses             : 6
3.07/1.16	#    Non-unit-clauses                  : 374
3.07/1.16	# Current number of unprocessed clauses: 11961
3.07/1.16	# ...number of literals in the above   : 55015
3.07/1.16	# Current number of archived formulas  : 0
3.07/1.16	# Current number of archived clauses   : 396
3.07/1.16	# Clause-clause subsumption calls (NU) : 63380
3.07/1.16	# Rec. Clause-clause subsumption calls : 23146
3.07/1.16	# Non-unit clause-clause subsumptions  : 51
3.07/1.16	# Unit Clause-clause subsumption calls : 1480
3.07/1.16	# Rewrite failures with RHS unbound    : 0
3.07/1.16	# BW rewrite match attempts            : 33
3.07/1.16	# BW rewrite match successes           : 3
3.07/1.16	# Condensation attempts                : 0
3.07/1.16	# Condensation successes               : 0
3.07/1.16	# Termbank termtop insertions          : 317210
3.07/1.16	
3.07/1.16	# -------------------------------------------------
3.07/1.16	# User time                : 0.576 s
3.07/1.16	# System time              : 0.032 s
3.07/1.16	# Total time               : 0.608 s
3.07/1.16	# Maximum resident set size: 8988 pages
3.07/1.17	EOF