0.12/0.19 % Problem : Vampire---4.8_32368 : TPTP v0.0.0. Released v0.0.0. 0.12/0.20 % Command : run_E %s %d THM 0.20/0.41 % Computer : n025.cluster.edu 0.20/0.41 % Model : x86_64 x86_64 0.20/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.20/0.41 % Memory : 8042.1875MB 0.20/0.41 % OS : Linux 3.10.0-693.el7.x86_64 0.20/0.41 % CPULimit : 1440 0.20/0.41 % WCLimit : 180 0.20/0.41 % DateTime : Mon Jul 3 13:08:53 EDT 2023 0.20/0.41 % CPUTime : 0.41/0.62 Running higher-order theorem provingRunning: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368 0.41/0.62 # Version: 3.1pre001-ho 41.33/5.87 # Preprocessing class: HSLMSLSSLLLCHFA. 41.33/5.87 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 41.33/5.87 # Starting ehoh_best5 with 180s (1) cores 41.33/5.87 # Starting almost_fo_3_lam with 180s (1) cores 41.33/5.87 # Starting new_bool_5 with 180s (1) cores 41.33/5.87 # Starting pre_casc_3 with 180s (1) cores 41.33/5.87 # Starting ho_unfolding_8 with 180s (1) cores 41.33/5.87 # Starting new_ho_10_cnf2 with 180s (1) cores 41.33/5.87 # Starting new_bool_3 with 180s (1) cores 41.33/5.87 # Starting new_ho_5 with 180s (1) cores 41.33/5.87 # new_ho_10_cnf2 with pid 32552 completed with status 0 41.33/5.87 # Result found by new_ho_10_cnf2 41.33/5.87 # Preprocessing class: HSLMSLSSLLLCHFA. 41.33/5.87 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 41.33/5.87 # Starting ehoh_best5 with 180s (1) cores 41.33/5.87 # Starting almost_fo_3_lam with 180s (1) cores 41.33/5.87 # Starting new_bool_5 with 180s (1) cores 41.33/5.87 # Starting pre_casc_3 with 180s (1) cores 41.33/5.87 # Starting ho_unfolding_8 with 180s (1) cores 41.33/5.87 # Starting new_ho_10_cnf2 with 180s (1) cores 41.33/5.87 # No SInE strategy applied 41.33/5.87 # Search class: HGHSM-SMLM32-MHFMMSBN 41.33/5.87 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 41.33/5.87 # Starting sh3 with 98s (1) cores 41.33/5.87 # sh3 with pid 32563 completed with status 0 41.33/5.87 # Result found by sh3 41.33/5.87 # Preprocessing class: HSLMSLSSLLLCHFA. 41.33/5.87 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 41.33/5.87 # Starting ehoh_best5 with 180s (1) cores 41.33/5.87 # Starting almost_fo_3_lam with 180s (1) cores 41.33/5.87 # Starting new_bool_5 with 180s (1) cores 41.33/5.87 # Starting pre_casc_3 with 180s (1) cores 41.33/5.87 # Starting ho_unfolding_8 with 180s (1) cores 41.33/5.87 # Starting new_ho_10_cnf2 with 180s (1) cores 41.33/5.87 # No SInE strategy applied 41.33/5.87 # Search class: HGHSM-SMLM32-MHFMMSBN 41.33/5.87 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 41.33/5.87 # Starting sh3 with 98s (1) cores 41.33/5.87 # Preprocessing time : 0.025 s 41.33/5.87 # Presaturation interreduction done 41.33/5.87 # SatCheck found unsatisfiable ground set 41.33/5.87 41.33/5.87 # Proof found! 41.33/5.87 # SZS status Theorem 41.33/5.87 # SZS output start CNFRefutation 41.33/5.87 thf(decl_22, type, in: $i > $i > $o). 41.33/5.87 thf(decl_23, type, exu: ($i > $o) > $o). 41.33/5.87 thf(decl_24, type, setextAx: $o). 41.33/5.87 thf(decl_25, type, emptyset: $i). 41.33/5.87 thf(decl_26, type, emptysetAx: $o). 41.33/5.87 thf(decl_27, type, setadjoin: $i > $i > $i). 41.33/5.87 thf(decl_28, type, setadjoinAx: $o). 41.33/5.87 thf(decl_29, type, powerset: $i > $i). 41.33/5.87 thf(decl_30, type, powersetAx: $o). 41.33/5.87 thf(decl_31, type, setunion: $i > $i). 41.33/5.87 thf(decl_32, type, setunionAx: $o). 41.33/5.87 thf(decl_33, type, omega: $i). 41.33/5.87 thf(decl_34, type, omega0Ax: $o). 41.33/5.87 thf(decl_35, type, omegaSAx: $o). 41.33/5.87 thf(decl_36, type, omegaIndAx: $o). 41.33/5.87 thf(decl_37, type, replAx: $o). 41.33/5.87 thf(decl_38, type, foundationAx: $o). 41.33/5.87 thf(decl_39, type, wellorderingAx: $o). 41.33/5.87 thf(decl_40, type, descr: ($i > $o) > $i). 41.33/5.87 thf(decl_41, type, descrp: $o). 41.33/5.87 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_43, type, dsetconstrI: $o). 41.33/5.87 thf(decl_44, type, dsetconstrEL: $o). 41.33/5.87 thf(decl_45, type, dsetconstrER: $o). 41.33/5.87 thf(decl_46, type, exuE1: $o). 41.33/5.87 thf(decl_47, type, prop2set: $o > $i). 41.33/5.87 thf(decl_48, type, prop2setE: $o). 41.33/5.87 thf(decl_49, type, emptysetE: $o). 41.33/5.87 thf(decl_50, type, emptysetimpfalse: $o). 41.33/5.87 thf(decl_51, type, notinemptyset: $o). 41.33/5.87 thf(decl_52, type, exuE3e: $o). 41.33/5.87 thf(decl_53, type, setext: $o). 41.33/5.87 thf(decl_54, type, emptyI: $o). 41.33/5.87 thf(decl_55, type, noeltsimpempty: $o). 41.33/5.87 thf(decl_56, type, setbeta: $o). 41.33/5.87 thf(decl_57, type, nonempty: $i > $o). 41.33/5.87 thf(decl_58, type, nonemptyE1: $o). 41.33/5.87 thf(decl_59, type, nonemptyI: $o). 41.33/5.87 thf(decl_60, type, nonemptyI1: $o). 41.33/5.87 thf(decl_61, type, setadjoinIL: $o). 41.33/5.87 thf(decl_62, type, emptyinunitempty: $o). 41.33/5.87 thf(decl_63, type, setadjoinIR: $o). 41.33/5.87 thf(decl_64, type, setadjoinE: $o). 41.33/5.87 thf(decl_65, type, setadjoinOr: $o). 41.33/5.87 thf(decl_66, type, setoftrueEq: $o). 41.33/5.87 thf(decl_67, type, powersetI: $o). 41.33/5.87 thf(decl_68, type, emptyinPowerset: $o). 41.33/5.87 thf(decl_69, type, emptyInPowerset: $o). 41.33/5.87 thf(decl_70, type, powersetE: $o). 41.33/5.87 thf(decl_71, type, setunionI: $o). 41.33/5.87 thf(decl_72, type, setunionE: $o). 41.33/5.87 thf(decl_73, type, subPowSU: $o). 41.33/5.87 thf(decl_74, type, exuE2: $o). 41.33/5.87 thf(decl_75, type, nonemptyImpWitness: $o). 41.33/5.87 thf(decl_76, type, uniqinunit: $o). 41.33/5.87 thf(decl_77, type, notinsingleton: $o). 41.33/5.87 thf(decl_78, type, eqinunit: $o). 41.33/5.87 thf(decl_79, type, singletonsswitch: $o). 41.33/5.87 thf(decl_80, type, upairsetE: $o). 41.33/5.87 thf(decl_81, type, upairsetIL: $o). 41.33/5.87 thf(decl_82, type, upairsetIR: $o). 41.33/5.87 thf(decl_83, type, emptyE1: $o). 41.33/5.87 thf(decl_84, type, vacuousDall: $o). 41.33/5.87 thf(decl_85, type, quantDeMorgan1: $o). 41.33/5.87 thf(decl_86, type, quantDeMorgan2: $o). 41.33/5.87 thf(decl_87, type, quantDeMorgan3: $o). 41.33/5.87 thf(decl_88, type, quantDeMorgan4: $o). 41.33/5.87 thf(decl_89, type, prop2setI: $o). 41.33/5.87 thf(decl_90, type, set2prop: $i > $o). 41.33/5.87 thf(decl_91, type, prop2set2propI: $o). 41.33/5.87 thf(decl_92, type, notdexE: $o). 41.33/5.87 thf(decl_93, type, notdallE: $o). 41.33/5.87 thf(decl_94, type, exuI1: $o). 41.33/5.87 thf(decl_95, type, exuI3: $o). 41.33/5.87 thf(decl_96, type, exuI2: $o). 41.33/5.87 thf(decl_97, type, inCongP: $o). 41.33/5.87 thf(decl_98, type, in__Cong: $o). 41.33/5.87 thf(decl_99, type, exuE3u: $o). 41.33/5.87 thf(decl_100, type, exu__Cong: $o). 41.33/5.87 thf(decl_101, type, emptyset__Cong: $o). 41.33/5.87 thf(decl_102, type, setadjoin__Cong: $o). 41.33/5.87 thf(decl_103, type, powerset__Cong: $o). 41.33/5.87 thf(decl_104, type, setunion__Cong: $o). 41.33/5.87 thf(decl_105, type, omega__Cong: $o). 41.33/5.87 thf(decl_106, type, exuEu: $o). 41.33/5.87 thf(decl_107, type, descr__Cong: $o). 41.33/5.87 thf(decl_108, type, dsetconstr__Cong: $o). 41.33/5.87 thf(decl_109, type, subset: $i > $i > $o). 41.33/5.87 thf(decl_112, type, subsetI1: $o). 41.33/5.87 thf(decl_113, type, eqimpsubset2: $o). 41.33/5.87 thf(decl_114, type, eqimpsubset1: $o). 41.33/5.87 thf(decl_115, type, subsetI2: $o). 41.33/5.87 thf(decl_116, type, emptysetsubset: $o). 41.33/5.87 thf(decl_117, type, subsetE: $o). 41.33/5.87 thf(decl_118, type, subsetE2: $o). 41.33/5.87 thf(decl_119, type, notsubsetI: $o). 41.33/5.87 thf(decl_120, type, notequalI1: $o). 41.33/5.87 thf(decl_121, type, notequalI2: $o). 41.33/5.87 thf(decl_122, type, subsetRefl: $o). 41.33/5.87 thf(decl_123, type, subsetTrans: $o). 41.33/5.87 thf(decl_124, type, setadjoinSub: $o). 41.33/5.87 thf(decl_125, type, setadjoinSub2: $o). 41.33/5.87 thf(decl_126, type, subset2powerset: $o). 41.33/5.87 thf(decl_127, type, setextsub: $o). 41.33/5.87 thf(decl_128, type, subsetemptysetimpeq: $o). 41.33/5.87 thf(decl_129, type, powersetI1: $o). 41.33/5.87 thf(decl_130, type, powersetE1: $o). 41.33/5.87 thf(decl_131, type, inPowerset: $o). 41.33/5.87 thf(decl_132, type, powersetsubset: $o). 41.33/5.87 thf(decl_133, type, sepInPowerset: $o). 41.33/5.87 thf(decl_134, type, sepSubset: $o). 41.33/5.87 thf(decl_135, type, binunion: $i > $i > $i). 41.33/5.87 thf(decl_136, type, binunionIL: $o). 41.33/5.87 thf(decl_137, type, upairset2IR: $o). 41.33/5.87 thf(decl_138, type, binunionIR: $o). 41.33/5.87 thf(decl_139, type, binunionEcases: $o). 41.33/5.87 thf(decl_140, type, binunionE: $o). 41.33/5.87 thf(decl_141, type, binunionLsub: $o). 41.33/5.87 thf(decl_142, type, binunionRsub: $o). 41.33/5.87 thf(decl_143, type, binintersect: $i > $i > $i). 41.33/5.87 thf(decl_144, type, binintersectI: $o). 41.33/5.87 thf(decl_145, type, binintersectSubset5: $o). 41.33/5.87 thf(decl_146, type, binintersectEL: $o). 41.33/5.87 thf(decl_147, type, binintersectLsub: $o). 41.33/5.87 thf(decl_148, type, binintersectSubset2: $o). 41.33/5.87 thf(decl_149, type, binintersectSubset3: $o). 41.33/5.87 thf(decl_150, type, binintersectER: $o). 41.33/5.87 thf(decl_151, type, disjointsetsI1: $o). 41.33/5.87 thf(decl_152, type, binintersectRsub: $o). 41.33/5.87 thf(decl_153, type, binintersectSubset4: $o). 41.33/5.87 thf(decl_154, type, binintersectSubset1: $o). 41.33/5.87 thf(decl_155, type, bs114d: $o). 41.33/5.87 thf(decl_157, type, setminus: $i > $i > $i). 41.33/5.87 thf(decl_158, type, setminusI: $o). 41.33/5.87 thf(decl_159, type, setminusEL: $o). 41.33/5.87 thf(decl_160, type, setminusER: $o). 41.33/5.87 thf(decl_161, type, setminusSubset2: $o). 41.33/5.87 thf(decl_162, type, setminusERneg: $o). 41.33/5.87 thf(decl_163, type, setminusELneg: $o). 41.33/5.87 thf(decl_164, type, setminusILneg: $o). 41.33/5.87 thf(decl_165, type, setminusIRneg: $o). 41.33/5.87 thf(decl_166, type, setminusLsub: $o). 41.33/5.87 thf(decl_167, type, setminusSubset1: $o). 41.33/5.87 thf(decl_168, type, symdiff: $i > $i > $i). 41.33/5.87 thf(decl_169, type, symdiffE: $o). 41.33/5.87 thf(decl_170, type, symdiffI1: $o). 41.33/5.87 thf(decl_171, type, symdiffI2: $o). 41.33/5.87 thf(decl_172, type, symdiffIneg1: $o). 41.33/5.87 thf(decl_173, type, symdiffIneg2: $o). 41.33/5.87 thf(decl_174, type, iskpair: $i > $o). 41.33/5.87 thf(decl_175, type, secondinupair: $o). 41.33/5.87 thf(decl_176, type, setukpairIL: $o). 41.33/5.87 thf(decl_177, type, setukpairIR: $o). 41.33/5.87 thf(decl_178, type, kpairiskpair: $o). 41.33/5.87 thf(decl_179, type, kpair: $i > $i > $i). 41.33/5.87 thf(decl_180, type, kpairp: $o). 41.33/5.87 thf(decl_181, type, cartprod: $i > $i > $i). 41.33/5.87 thf(decl_182, type, singletonsubset: $o). 41.33/5.87 thf(decl_183, type, singletoninpowerset: $o). 41.33/5.87 thf(decl_184, type, singletoninpowunion: $o). 41.33/5.87 thf(decl_185, type, upairset2E: $o). 41.33/5.87 thf(decl_186, type, upairsubunion: $o). 41.33/5.87 thf(decl_187, type, upairinpowunion: $o). 41.33/5.87 thf(decl_188, type, ubforcartprodlem1: $o). 41.33/5.87 thf(decl_189, type, ubforcartprodlem2: $o). 41.33/5.87 thf(decl_190, type, ubforcartprodlem3: $o). 41.33/5.87 thf(decl_191, type, cartprodpairin: $o). 41.33/5.87 thf(decl_192, type, cartprodmempair1: $o). 41.33/5.87 thf(decl_193, type, cartprodmempair: $o). 41.33/5.87 thf(decl_194, type, setunionE2: $o). 41.33/5.87 thf(decl_195, type, setunionsingleton1: $o). 41.33/5.87 thf(decl_196, type, setunionsingleton2: $o). 41.33/5.87 thf(decl_197, type, setunionsingleton: $o). 41.33/5.87 thf(decl_198, type, singleton: $i > $o). 41.33/5.87 thf(decl_199, type, singletonprop: $o). 41.33/5.87 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 41.33/5.87 thf(decl_201, type, ex1E1: $o). 41.33/5.87 thf(decl_202, type, ex1I: $o). 41.33/5.87 thf(decl_203, type, ex1I2: $o). 41.33/5.87 thf(decl_204, type, singletonsuniq: $o). 41.33/5.87 thf(decl_209, type, setukpairinjL1: $o). 41.33/5.87 thf(decl_210, type, kfstsingleton: $o). 41.33/5.87 thf(decl_211, type, theprop: $o). 41.33/5.87 thf(decl_212, type, kfst: $i > $i). 41.33/5.87 thf(decl_213, type, kfstpairEq: $o). 41.33/5.87 thf(decl_214, type, cartprodfstin: $o). 41.33/5.87 thf(decl_215, type, setukpairinjL2: $o). 41.33/5.87 thf(decl_216, type, setukpairinjL: $o). 41.33/5.87 thf(decl_217, type, setukpairinjR11: $o). 41.33/5.87 thf(decl_218, type, setukpairinjR12: $o). 41.33/5.87 thf(decl_219, type, setukpairinjR1: $o). 41.33/5.87 thf(decl_220, type, upairequniteq: $o). 41.33/5.87 thf(decl_221, type, setukpairinjR2: $o). 41.33/5.87 thf(decl_222, type, setukpairinjR: $o). 41.33/5.87 thf(decl_223, type, ksndsingleton: $o). 41.33/5.87 thf(decl_224, type, ksnd: $i > $i). 41.33/5.87 thf(decl_225, type, ksndpairEq: $o). 41.33/5.87 thf(decl_226, type, kpairsurjEq: $o). 41.33/5.87 thf(decl_227, type, cartprodsndin: $o). 41.33/5.87 thf(decl_228, type, cartprodpairmemEL: $o). 41.33/5.87 thf(decl_229, type, cartprodpairmemER: $o). 41.33/5.87 thf(decl_230, type, cartprodmempaircEq: $o). 41.33/5.87 thf(decl_231, type, cartprodfstpairEq: $o). 41.33/5.87 thf(decl_232, type, cartprodsndpairEq: $o). 41.33/5.87 thf(decl_233, type, cartprodpairsurjEq: $o). 41.33/5.87 thf(decl_234, type, breln: $i > $i > $i > $o). 41.33/5.87 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 41.33/5.87 thf(decl_236, type, dpsetconstrI: $o). 41.33/5.87 thf(decl_237, type, dpsetconstrSub: $o). 41.33/5.87 thf(decl_238, type, setOfPairsIsBReln: $o). 41.33/5.87 thf(decl_239, type, dpsetconstrERa: $o). 41.33/5.87 thf(decl_240, type, dpsetconstrEL1: $o). 41.33/5.87 thf(decl_241, type, dpsetconstrEL2: $o). 41.33/5.87 thf(decl_242, type, dpsetconstrER: $o). 41.33/5.87 thf(decl_243, type, func: $i > $i > $i > $o). 41.33/5.87 thf(decl_244, type, funcSet: $i > $i > $i). 41.33/5.87 thf(decl_245, type, funcImageSingleton: $o). 41.33/5.87 thf(decl_246, type, apProp: $o). 41.33/5.87 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 41.33/5.87 thf(decl_248, type, app: $o). 41.33/5.87 thf(decl_249, type, infuncsetfunc: $o). 41.33/5.87 thf(decl_250, type, ap2p: $o). 41.33/5.87 thf(decl_251, type, funcinfuncset: $o). 41.33/5.87 thf(decl_252, type, lamProp: $o). 41.33/5.87 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 41.33/5.87 thf(decl_254, type, lamp: $o). 41.33/5.87 thf(decl_255, type, lam2p: $o). 41.33/5.87 thf(decl_256, type, brelnall1: $o). 41.33/5.87 thf(decl_257, type, brelnall2: $o). 41.33/5.87 thf(decl_258, type, ex1E2: $o). 41.33/5.87 thf(decl_259, type, funcGraphProp1: $o). 41.33/5.87 thf(decl_260, type, funcGraphProp3: $o). 41.33/5.87 thf(decl_261, type, funcGraphProp2: $o). 41.33/5.87 thf(decl_262, type, funcextLem: $o). 41.33/5.87 thf(decl_263, type, funcGraphProp4: $o). 41.33/5.87 thf(decl_264, type, subbreln: $o). 41.33/5.87 thf(decl_265, type, eqbreln: $o). 41.33/5.87 thf(decl_266, type, funcext: $o). 41.33/5.87 thf(decl_267, type, funcext2: $o). 41.33/5.87 thf(decl_268, type, ap2apEq1: $o). 41.33/5.87 thf(decl_269, type, ap2apEq2: $o). 41.33/5.87 thf(decl_270, type, beta1: $o). 41.33/5.87 thf(decl_271, type, eta1: $o). 41.33/5.87 thf(decl_272, type, lam2lamEq: $o). 41.33/5.87 thf(decl_273, type, beta2: $o). 41.33/5.87 thf(decl_274, type, eta2: $o). 41.33/5.87 thf(decl_275, type, iffalseProp1: $o). 41.33/5.87 thf(decl_276, type, iffalseProp2: $o). 41.33/5.87 thf(decl_277, type, iftrueProp1: $o). 41.33/5.87 thf(decl_278, type, iftrueProp2: $o). 41.33/5.87 thf(decl_279, type, ifSingleton: $o). 41.33/5.87 thf(decl_280, type, if: $i > $o > $i > $i > $i). 41.33/5.87 thf(decl_281, type, ifp: $o). 41.33/5.87 thf(decl_282, type, theeq: $o). 41.33/5.87 thf(decl_283, type, iftrue: $o). 41.33/5.87 thf(decl_284, type, iffalse: $o). 41.33/5.87 thf(decl_285, type, iftrueorfalse: $o). 41.33/5.87 thf(decl_286, type, binintersectT_lem: $o). 41.33/5.87 thf(decl_287, type, binunionT_lem: $o). 41.33/5.87 thf(decl_288, type, powersetT_lem: $o). 41.33/5.87 thf(decl_289, type, setminusT_lem: $o). 41.33/5.87 thf(decl_290, type, complementT_lem: $o). 41.33/5.87 thf(decl_291, type, setextT: $o). 41.33/5.87 thf(decl_292, type, subsetTI: $o). 41.33/5.87 thf(decl_293, type, powersetTI1: $o). 41.33/5.87 thf(decl_294, type, powersetTE1: $o). 41.33/5.87 thf(decl_295, type, complementTI1: $o). 41.33/5.87 thf(decl_296, type, complementTE1: $o). 41.33/5.87 thf(decl_297, type, binintersectTELcontra: $o). 41.33/5.87 thf(decl_298, type, binintersectTERcontra: $o). 41.33/5.87 thf(decl_299, type, contrasubsetT: $o). 41.33/5.87 thf(decl_300, type, contrasubsetT1: $o). 41.33/5.87 thf(decl_301, type, contrasubsetT2: $o). 41.33/5.87 thf(decl_302, type, contrasubsetT3: $o). 41.33/5.87 thf(decl_303, type, doubleComplementI1: $o). 41.33/5.87 thf(decl_304, type, doubleComplementE1: $o). 41.33/5.87 thf(decl_305, type, doubleComplementSub1: $o). 41.33/5.87 thf(decl_306, type, doubleComplementSub2: $o). 41.33/5.87 thf(decl_307, type, doubleComplementEq: $o). 41.33/5.87 thf(decl_308, type, complementTnotintersectT: $o). 41.33/5.87 thf(decl_309, type, complementImpComplementIntersect: $o). 41.33/5.87 thf(decl_310, type, complementSubsetComplementIntersect: $o). 41.33/5.87 thf(decl_311, type, complementInPowersetComplementIntersect: $o). 41.33/5.87 thf(decl_312, type, contraSubsetComplement: $o). 41.33/5.87 thf(decl_313, type, complementTcontraSubset: $o). 41.33/5.87 thf(decl_314, type, binunionTILcontra: $o). 41.33/5.87 thf(decl_315, type, binunionTIRcontra: $o). 41.33/5.87 thf(decl_316, type, inIntersectImpInUnion: $o). 41.33/5.87 thf(decl_317, type, inIntersectImpInUnion2: $o). 41.33/5.87 thf(decl_318, type, inIntersectImpInIntersectUnions: $o). 41.33/5.87 thf(decl_319, type, intersectInPowersetIntersectUnions: $o). 41.33/5.87 thf(decl_320, type, inComplementUnionImpNotIn1: $o). 41.33/5.87 thf(decl_321, type, inComplementUnionImpInComplement1: $o). 41.33/5.87 thf(decl_322, type, binunionTE: $o). 41.33/5.87 thf(decl_323, type, binunionTEcontra: $o). 41.33/5.87 thf(decl_324, type, demorgan2a1: $o). 41.33/5.87 thf(decl_325, type, complementUnionInPowersetComplement: $o). 41.33/5.87 thf(decl_326, type, demorgan2a2: $o). 41.33/5.87 thf(decl_327, type, demorgan1a: $o). 41.33/5.87 thf(decl_328, type, demorgan1b: $o). 41.33/5.87 thf(decl_329, type, demorgan1: $o). 41.33/5.87 thf(decl_330, type, demorgan2a: $o). 41.33/5.87 thf(decl_331, type, demorgan2b2: $o). 41.33/5.87 thf(decl_332, type, demorgan2b: $o). 41.33/5.87 thf(decl_333, type, demorgan2: $o). 41.33/5.87 thf(decl_334, type, woz13rule0: $o). 41.33/5.87 thf(decl_335, type, woz13rule1: $o). 41.33/5.87 thf(decl_336, type, woz13rule2: $o). 41.33/5.87 thf(decl_337, type, woz13rule3: $o). 41.33/5.87 thf(decl_338, type, woz13rule4: $o). 41.33/5.87 thf(decl_339, type, woz1_1: $o). 41.33/5.87 thf(decl_340, type, woz1_2: $o). 41.33/5.87 thf(decl_341, type, woz1_3: $o). 41.33/5.87 thf(decl_342, type, woz1_4: $o). 41.33/5.87 thf(decl_343, type, woz1_5: $o). 41.33/5.87 thf(decl_344, type, breln1: $i > $i > $o). 41.33/5.87 thf(decl_345, type, breln1all2: $o). 41.33/5.87 thf(decl_346, type, breln1Set: $i > $i). 41.33/5.87 thf(decl_347, type, breln1SetBreln1: $o). 41.33/5.87 thf(decl_353, type, reflwellordering: $i > $i > $o). 41.33/5.87 thf(decl_354, type, choice2fnsingleton: $o). 41.33/5.87 thf(decl_355, type, setOfPairsIsBReln1: $o). 41.33/5.87 thf(decl_356, type, breln1all1: $o). 41.33/5.87 thf(decl_357, type, subbreln1: $o). 41.33/5.87 thf(decl_358, type, eqbreln1: $o). 41.33/5.87 thf(decl_359, type, breln1invset: $i > $i > $i). 41.33/5.87 thf(decl_360, type, breln1invprop: $o). 41.33/5.87 thf(decl_361, type, breln1invI: $o). 41.33/5.87 thf(decl_362, type, breln1invE: $o). 41.33/5.87 thf(decl_363, type, breln1compset: $i > $i > $i > $i). 41.33/5.87 thf(decl_364, type, breln1compprop: $o). 41.33/5.87 thf(decl_365, type, breln1compI: $o). 41.33/5.87 thf(decl_366, type, breln1compE: $o). 41.33/5.87 thf(decl_367, type, breln1compEex: $o). 41.33/5.87 thf(decl_368, type, breln1unionprop: $o). 41.33/5.87 thf(decl_369, type, breln1unionIL: $o). 41.33/5.87 thf(decl_370, type, breln1unionIR: $o). 41.33/5.87 thf(decl_371, type, breln1unionI: $o). 41.33/5.87 thf(decl_372, type, breln1unionE: $o). 41.33/5.87 thf(decl_373, type, breln1unionEcases: $o). 41.33/5.87 thf(decl_374, type, breln1unionCommutes: $o). 41.33/5.87 thf(decl_375, type, woz2Ex: $o). 41.33/5.87 thf(decl_376, type, woz2W: $o). 41.33/5.87 thf(decl_377, type, woz2A: $o). 41.33/5.87 thf(decl_378, type, woz2B: $o). 41.33/5.87 thf(decl_379, type, image1Ex: $o). 41.33/5.87 thf(decl_380, type, image1Ex1: $o). 41.33/5.87 thf(decl_381, type, image1: $i > ($i > $i) > $i). 41.33/5.87 thf(decl_382, type, image1Equiv: $o). 41.33/5.87 thf(decl_383, type, image1E: $o). 41.33/5.87 thf(decl_384, type, image1I: $o). 41.33/5.87 thf(decl_385, type, injective: $i > $i > $i > $o). 41.33/5.87 thf(decl_386, type, injFuncSet: $i > $i > $i). 41.33/5.87 thf(decl_387, type, injFuncInInjFuncSet: $o). 41.33/5.87 thf(decl_388, type, injFuncSetFuncIn: $o). 41.33/5.87 thf(decl_389, type, injFuncSetFuncInj: $o). 41.33/5.87 thf(decl_390, type, surjective: $i > $i > $i > $o). 41.33/5.87 thf(decl_391, type, surjFuncSet: $i > $i > $i). 41.33/5.87 thf(decl_392, type, surjFuncSetFuncIn: $o). 41.33/5.87 thf(decl_393, type, surjFuncSetFuncSurj: $o). 41.33/5.87 thf(decl_394, type, leftInvIsSurj: $o). 41.33/5.87 thf(decl_395, type, surjCantorThm: $o). 41.33/5.87 thf(decl_396, type, foundation2: $o). 41.33/5.87 thf(decl_397, type, notinself: $o). 41.33/5.87 thf(decl_398, type, notinself2: $o). 41.33/5.87 thf(decl_399, type, omegaS: $i > $i). 41.33/5.87 thf(decl_400, type, omegaSp: $o). 41.33/5.87 thf(decl_401, type, omegaSclos: $o). 41.33/5.87 thf(decl_402, type, peano0notS: $o). 41.33/5.87 thf(decl_406, type, peanoSinj: $o). 41.33/5.87 thf(decl_408, type, transitiveset: $i > $o). 41.33/5.87 thf(decl_409, type, transitivesetOp1: $o). 41.33/5.87 thf(decl_410, type, binintTransitive: $o). 41.33/5.87 thf(decl_411, type, transitivesetOp2: $o). 41.33/5.87 thf(decl_412, type, setunionTransitive: $o). 41.33/5.87 thf(decl_413, type, stricttotalorderedByIn: $i > $o). 41.33/5.87 thf(decl_414, type, wellorderedByIn: $i > $o). 41.33/5.87 thf(decl_415, type, ordinal: $i > $o). 41.33/5.87 thf(decl_417, type, ordinalMinLem1: $o). 41.33/5.87 thf(decl_418, type, ordinalTransSet: $o). 41.33/5.87 thf(decl_419, type, ordinalTransSet1: $o). 41.33/5.87 thf(decl_420, type, epred1_0: $o). 41.33/5.87 thf(decl_421, type, epred2_1: $i > $o). 41.33/5.87 thf(decl_422, type, epred3_1: $i > $o). 41.33/5.87 thf(decl_423, type, epred4_1: $i > $o). 41.33/5.87 thf(decl_424, type, epred5_1: $i > $o). 41.33/5.87 thf(decl_425, type, epred6_1: $i > $o). 41.33/5.87 thf(decl_426, type, esk1_2: $i > $i > $i). 41.33/5.87 thf(decl_427, type, esk2_2: $i > $i > $i). 41.33/5.87 thf(decl_428, type, esk3_2: $i > $i > $i). 41.33/5.87 thf(decl_429, type, esk4_1: $i > $i). 41.33/5.87 thf(decl_430, type, esk5_2: ($i > $i > $o) > $i > $i). 41.33/5.87 thf(decl_431, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 41.33/5.87 thf(decl_432, type, esk7_2: ($i > $i > $o) > $i > $i). 41.33/5.87 thf(decl_433, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 41.33/5.87 thf(decl_434, type, esk9_1: $i > $i). 41.33/5.87 thf(decl_435, type, esk10_2: ($i > $o) > $i > $i). 41.33/5.87 thf(decl_436, type, esk11_2: ($i > $o) > $i > $i). 41.33/5.87 thf(decl_437, type, esk12_1: ($i > $o) > $i). 41.33/5.87 thf(decl_438, type, esk13_2: ($i > $o) > $i > $i). 41.33/5.87 thf(decl_439, type, esk14_1: ($i > $o) > $i). 41.33/5.87 thf(decl_440, type, esk15_2: $i > $i > $i). 41.33/5.87 thf(decl_441, type, esk16_2: $i > $i > $i). 41.33/5.87 thf(decl_442, type, esk17_1: $i > $i). 41.33/5.87 thf(decl_443, type, esk18_1: $i > $i). 41.33/5.87 thf(decl_444, type, esk19_1: $i > $i). 41.33/5.87 thf(decl_445, type, esk20_2: $i > $i > $i). 41.33/5.87 thf(decl_446, type, esk21_3: $i > $i > $o > $i). 41.33/5.87 thf(decl_447, type, esk22_2: ($i > $o) > $i > $i). 41.33/5.87 thf(decl_448, type, esk23_1: ($i > $o) > $i). 41.33/5.87 thf(decl_449, type, esk24_1: $i > $i). 41.33/5.87 thf(decl_450, type, esk25_2: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_451, type, esk26_2: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_452, type, esk27_2: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_453, type, esk28_2: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_454, type, esk29_2: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_455, type, esk30_2: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_456, type, esk31_2: ($i > $o) > $i > $i). 41.33/5.87 thf(decl_457, type, esk32_1: ($i > $o) > $i). 41.33/5.87 thf(decl_458, type, esk33_1: ($i > $o) > $i). 41.33/5.87 thf(decl_459, type, esk34_1: ($i > $o) > $i). 41.33/5.87 thf(decl_460, type, esk35_1: ($i > $o) > $i). 41.33/5.87 thf(decl_461, type, esk36_2: ($i > $o) > $i > $i). 41.33/5.87 thf(decl_462, type, esk37_1: ($i > $o) > $i). 41.33/5.87 thf(decl_463, type, esk38_2: ($i > $o) > $i > $i). 41.33/5.87 thf(decl_464, type, esk39_2: ($i > $o) > ($i > $o) > $i). 41.33/5.87 thf(decl_465, type, esk40_2: ($i > $o) > ($i > $o) > $i). 41.33/5.87 thf(decl_466, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 41.33/5.87 thf(decl_467, type, esk42_2: ($i > $o) > ($i > $o) > $i). 41.33/5.87 thf(decl_468, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 41.33/5.87 thf(decl_469, type, esk44_2: ($i > $o) > ($i > $o) > $i). 41.33/5.87 thf(decl_470, type, esk45_2: ($i > $o) > $i > $i). 41.33/5.87 thf(decl_471, type, esk46_2: ($i > $o) > ($i > $o) > $i). 41.33/5.87 thf(decl_472, type, esk47_2: ($i > $o) > ($i > $o) > $i). 41.33/5.87 thf(decl_473, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 41.33/5.87 thf(decl_474, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 41.33/5.87 thf(decl_475, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 41.33/5.87 thf(decl_476, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 41.33/5.87 thf(decl_477, type, esk52_2: $i > $i > $i). 41.33/5.87 thf(decl_478, type, esk53_2: $i > $i > $i). 41.33/5.87 thf(decl_479, type, esk54_2: $i > $i > $i). 41.33/5.87 thf(decl_480, type, esk55_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_481, type, esk56_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_482, type, esk57_2: $i > $i > $i). 41.33/5.87 thf(decl_483, type, esk58_2: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_484, type, esk59_2: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_485, type, esk60_2: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_486, type, esk61_3: $i > ($i > $o) > $i > $i). 41.33/5.87 thf(decl_487, type, esk62_2: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_488, type, esk63_2: $i > ($i > $o) > $i). 41.33/5.87 thf(decl_489, type, esk64_3: $i > $i > ($i > $i) > $i). 41.33/5.87 thf(decl_490, type, esk65_3: $i > $i > ($i > $i) > $i). 41.33/5.87 thf(decl_491, type, esk66_3: $i > $i > ($i > $i) > $i). 41.33/5.87 thf(decl_492, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 41.33/5.87 thf(decl_493, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 41.33/5.87 thf(decl_494, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 41.33/5.87 thf(decl_495, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 41.33/5.87 thf(decl_496, type, esk71_4: $i > $i > $i > $i > $i). 41.33/5.87 thf(decl_497, type, esk72_4: $i > $i > $i > $i > $i). 41.33/5.87 thf(decl_498, type, esk73_4: $i > $i > $i > $i > $i). 41.33/5.87 thf(decl_499, type, esk74_4: $i > $i > $i > $i > $i). 41.33/5.87 thf(decl_500, type, esk75_4: $i > $i > $i > $i > $i). 41.33/5.87 thf(decl_501, type, esk76_4: $i > $i > $i > $i > $i). 41.33/5.87 thf(decl_502, type, esk77_4: $i > $i > $i > $i > $i). 41.33/5.87 thf(decl_503, type, esk78_4: $i > $i > $i > $i > $i). 41.33/5.87 thf(decl_504, type, esk79_4: $i > $i > $i > $i > $i). 41.33/5.87 thf(decl_505, type, esk80_3: $i > $i > ($i > $i) > $i). 41.33/5.87 thf(decl_506, type, esk81_3: $i > $i > ($i > $i) > $i). 41.33/5.87 thf(decl_507, type, esk82_3: $i > $i > ($i > $i) > $i). 41.33/5.87 thf(decl_508, type, esk83_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_509, type, esk84_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_510, type, esk85_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_511, type, esk86_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_512, type, esk87_3: $i > $i > ($i > $o) > $i). 41.33/5.87 thf(decl_513, type, esk88_3: $i > $i > ($i > $o) > $i). 41.33/5.87 thf(decl_514, type, esk89_3: $i > $i > ($i > $i > $o) > $i). 41.33/5.87 thf(decl_515, type, esk90_3: $i > $i > ($i > $o) > $i). 41.33/5.87 thf(decl_516, type, esk91_3: $i > $i > ($i > $o) > $i). 41.33/5.87 thf(decl_517, type, esk92_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_518, type, esk93_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_519, type, esk94_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_520, type, esk95_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_521, type, esk96_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_522, type, esk97_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_523, type, esk98_5: $i > $i > $i > $i > $i > $i). 41.33/5.87 thf(decl_524, type, esk99_6: $i > $i > $i > $i > $i > $o > $i). 41.33/5.87 thf(decl_525, type, esk100_2: $i > ($i > $i) > $i). 41.33/5.87 thf(decl_526, type, esk101_3: $i > ($i > $i) > $i > $i). 41.33/5.87 thf(decl_527, type, esk102_2: $i > ($i > $i) > $i). 41.33/5.87 thf(decl_528, type, esk103_3: $i > ($i > $i) > $i > $i). 41.33/5.87 thf(decl_529, type, esk104_3: $i > ($i > $i) > $i > $i). 41.33/5.87 thf(decl_530, type, esk105_3: $i > ($i > $i) > $i > $i). 41.33/5.87 thf(decl_531, type, esk106_3: $i > ($i > $i) > $i > $i). 41.33/5.87 thf(decl_532, type, esk107_3: $i > ($i > $i) > $i > $i). 41.33/5.87 thf(decl_533, type, esk108_3: $i > $i > ($i > $i) > $i). 41.33/5.87 thf(decl_534, type, esk109_4: $i > $i > ($i > $i) > $i > $i). 41.33/5.87 thf(decl_535, type, esk110_1: $i > $i). 41.33/5.87 thf(decl_536, type, esk111_1: $i > $i). 41.33/5.87 thf(decl_537, type, esk112_1: $i > $i). 41.33/5.87 thf(decl_538, type, esk113_2: $i > $i > $i). 41.33/5.87 thf(decl_539, type, esk114_1: $i > $i). 41.33/5.87 thf(decl_540, type, esk115_1: $i > $i). 41.33/5.87 thf(decl_541, type, esk116_1: $i > $i). 41.33/5.87 thf(decl_542, type, esk117_1: $i > $i). 41.33/5.87 thf(decl_543, type, esk118_1: $i > $i). 41.33/5.87 thf(decl_544, type, esk119_1: $i > $i). 41.33/5.87 thf(decl_545, type, esk120_2: $i > $i > $i). 41.33/5.87 thf(decl_546, type, esk121_2: $i > $i > $i). 41.33/5.87 thf(decl_547, type, esk122_2: $i > $i > $i). 41.33/5.87 thf(decl_548, type, esk123_2: $i > $i > $i). 41.33/5.87 thf(decl_549, type, esk124_3: $i > $i > $i > $i). 41.33/5.87 thf(decl_550, type, esk125_1: $i > $i). 41.33/5.87 thf(decl_551, type, esk126_1: $i > $i). 41.33/5.87 thf(decl_552, type, esk127_1: $i > $i). 41.33/5.87 thf(decl_553, type, esk128_2: $i > $i > $i). 41.33/5.87 thf(decl_554, type, esk129_1: $i > $i). 41.33/5.87 thf(decl_555, type, esk130_1: $i > $i). 41.33/5.87 thf(decl_556, type, esk131_1: $i > $i). 41.33/5.87 thf(decl_557, type, esk132_2: $i > $i > $i). 41.33/5.87 thf(decl_558, type, esk133_0: $i). 41.33/5.87 thf(decl_559, type, esk134_0: $i). 41.33/5.87 thf(decl_585, type, esk160_2: $i > $i > $i). 41.33/5.87 thf(wellorderedByIn, axiom, ((wellorderedByIn)=(^[X4:$i]:(((stricttotalorderedByIn @ X4)&![X21:$i]:(((in @ X21 @ (powerset @ X4))=>((nonempty @ X21)=>?[X2:$i]:(((in @ X2 @ X21)&![X48:$i]:(((in @ X48 @ X21)=>(((X2)=(X48))|(in @ X2 @ X48))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', wellorderedByIn)). 41.33/5.87 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', nonempty)). 41.33/5.87 thf(stricttotalorderedByIn, axiom, ((stricttotalorderedByIn)=(^[X4:$i]:(((![X2:$i]:(((in @ X2 @ X4)=>![X21:$i]:(((in @ X21 @ X4)=>![X48:$i]:(((in @ X48 @ X4)=>(((in @ X2 @ X21)&(in @ X21 @ X48))=>(in @ X2 @ X48))))))))&![X21:$i]:(((in @ X21 @ X4)=>![X48:$i]:(((in @ X48 @ X4)=>((((X21)=(X48))|(in @ X21 @ X48))|(in @ X48 @ X21)))))))&![X21:$i]:(((in @ X21 @ X4)=>~((in @ X21 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', stricttotalorderedByIn)). 41.33/5.87 thf(ordinal, axiom, ((ordinal)=(^[X2:$i]:(((transitiveset @ X2)&(wellorderedByIn @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ordinal)). 41.33/5.87 thf(transitiveset, axiom, ((transitiveset)=(^[X4:$i]:(![X21:$i]:(((in @ X21 @ X4)=>(subset @ X21 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', transitiveset)). 41.33/5.87 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', replAx)). 41.33/5.87 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', exu)). 41.33/5.87 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', descrp)). 41.33/5.87 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', exuE1)). 41.33/5.87 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', exuE3e)). 41.33/5.87 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', nonemptyI)). 41.33/5.87 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', exuE2)). 41.33/5.87 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', exuI1)). 41.33/5.87 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', exuI3)). 41.33/5.87 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', exuI2)). 41.33/5.87 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', exuE3u)). 41.33/5.87 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', exu__Cong)). 41.33/5.87 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', exuEu)). 41.33/5.87 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', descr__Cong)). 41.33/5.87 thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', image1Ex1)). 41.33/5.87 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', dsetconstrI)). 41.33/5.87 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', dsetconstrEL)). 41.33/5.87 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', dsetconstrER)). 41.33/5.87 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setbeta)). 41.33/5.87 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', nonemptyE1)). 41.33/5.87 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', nonemptyI1)). 41.33/5.87 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setoftrueEq)). 41.33/5.87 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', nonemptyImpWitness)). 41.33/5.87 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', emptyE1)). 41.33/5.87 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', dsetconstr__Cong)). 41.33/5.87 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', sepInPowerset)). 41.33/5.87 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', sepSubset)). 41.33/5.87 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', singletonprop)). 41.33/5.87 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ex1E1)). 41.33/5.87 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ex1I)). 41.33/5.87 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ex1I2)). 41.33/5.87 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', kfstsingleton)). 41.33/5.87 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ksndsingleton)). 41.33/5.87 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', dpsetconstrI)). 41.33/5.87 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', dpsetconstrSub)). 41.33/5.87 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setOfPairsIsBReln)). 41.33/5.87 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', dpsetconstrERa)). 41.33/5.87 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', dpsetconstrEL1)). 41.33/5.87 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', dpsetconstrEL2)). 41.33/5.87 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', dpsetconstrER)). 41.33/5.87 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', funcImageSingleton)). 41.33/5.87 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', apProp)). 41.33/5.87 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', lamProp)). 41.33/5.87 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', lamp)). 41.33/5.87 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', lam2p)). 41.33/5.87 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ex1E2)). 41.33/5.87 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', beta1)). 41.33/5.87 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', eta1)). 41.33/5.87 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', lam2lamEq)). 41.33/5.87 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', beta2)). 41.33/5.87 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', eta2)). 41.33/5.87 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', iffalseProp1)). 41.33/5.87 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', iffalseProp2)). 41.33/5.87 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', iftrueProp1)). 41.33/5.87 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', iftrueProp2)). 41.33/5.87 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ifSingleton)). 41.33/5.87 thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:(((X52 @ X2 @ X3)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ X3 @ X14) @ X33))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', choice2fnsingleton)). 41.33/5.87 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setOfPairsIsBReln1)). 41.33/5.87 thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', image1Equiv)). 41.33/5.87 thf(image1E, axiom, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', image1E)). 41.33/5.87 thf(image1I, axiom, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X61 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', image1I)). 41.33/5.87 thf(foundation2, axiom, ((foundation2)<=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', foundation2)). 41.33/5.87 thf(transitivesetOp1, axiom, ((transitivesetOp1)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', transitivesetOp1)). 41.33/5.87 thf(binintTransitive, axiom, ((binintTransitive)<=>![X21:$i]:(((transitiveset @ X21)=>![X48:$i]:(((transitiveset @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintTransitive)). 41.33/5.87 thf(transitivesetOp2, axiom, ((transitivesetOp2)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i, X2:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', transitivesetOp2)). 41.33/5.87 thf(setunionTransitive, axiom, ((setunionTransitive)<=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(transitiveset @ X2)))=>(transitiveset @ (setunion @ X21))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setunionTransitive)). 41.33/5.87 thf(ordinalMinLem1, axiom, ((ordinalMinLem1)<=>![X21:$i]:(((ordinal @ X21)=>![X48:$i]:(((ordinal @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ordinalMinLem1)). 41.33/5.87 thf(ordinalTransSet, axiom, ((ordinalTransSet)<=>![X21:$i]:(((ordinal @ X21)=>![X2:$i, X4:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ordinalTransSet)). 41.33/5.87 thf(ordinalTransSet1, axiom, ((ordinalTransSet1)<=>![X21:$i]:(((ordinal @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ordinalTransSet1)). 41.33/5.87 thf(setunionOrdinalLem1, conjecture, ((setextAx)=>((((powersetAx)=>(((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((((exuE1)=>((prop2setE)=>((emptysetE)=>(((notinemptyset)=>((exuE3e)=>(((emptyI)=>((((nonemptyE1)=>(((nonemptyI1)=>(((((setadjoinE)=>((((powersetI)=>(((((((((nonemptyImpWitness)=>((uniqinunit)=>(((((upairsetE)=>((((emptyE1)=>(((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>((notdexE)=>((((exuI3)=>((exuI2)=>((inCongP)=>((((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>(((((((eqimpsubset2)=>(((subsetI2)=>((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>((((subsetRefl)=>((subsetTrans)=>(((setadjoinSub2)=>((subset2powerset)=>((((((inPowerset)=>(((((binunionIL)=>(((((binunionE)=>((binunionLsub)=>((((((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>(((disjointsetsI1)=>((binintersectRsub)=>(((binintersectSubset1)=>((bs114d)=>((setminusI)=>(((((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>(((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((((((((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((((((((setunionsingleton)=>((((ex1I)=>((ex1I2)=>((singletonsuniq)=>((((theprop)=>((kfstpairEq)=>((cartprodfstin)=>(((((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>(((setukpairinjR)=>(((ksndpairEq)=>((kpairsurjEq)=>(((((cartprodmempaircEq)=>(((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>(((dpsetconstrEL1)=>(((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>(((((((((brelnall1)=>(((ex1E2)=>(((funcGraphProp3)=>((funcGraphProp2)=>((((((funcext)=>((((ap2apEq2)=>((beta1)=>(((((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((((((theeq)=>(((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((((complementT_lem)=>((setextT)=>(((((complementTI1)=>(((binintersectTELcontra)=>((binintersectTERcontra)=>(((((contrasubsetT3)=>((((((doubleComplementEq)=>(((complementImpComplementIntersect)=>(((complementInPowersetComplementIntersect)=>(((((binunionTIRcontra)=>((((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>(((inComplementUnionImpInComplement1)=>((((demorgan2a1)=>(((demorgan2a2)=>((demorgan1a)=>(((((demorgan2b2)=>((((woz13rule0)=>(((woz13rule2)=>((((((woz1_3)=>((woz1_4)=>(((breln1all2)=>((breln1SetBreln1)=>(((((subbreln1)=>(((breln1invprop)=>((breln1invI)=>((breln1invE)=>((breln1compprop)=>((breln1compI)=>((breln1compE)=>((((breln1unionIL)=>((((breln1unionE)=>((breln1unionEcases)=>((((woz2W)=>(((woz2B)=>(((image1Ex1)=>((image1Equiv)=>((image1E)=>((image1I)=>((((((((((notinself)=>((notinself2)=>((omegaSp)=>(((((transitivesetOp1)=>(((transitivesetOp2)=>(((ordinalMinLem1)=>(((ordinalTransSet1)=>![X21:$i]:((![X2:$i]:(((ordinal @ X2)<=(in @ X2 @ X21)))=>(transitiveset @ (setunion @ X21)))))<=(ordinalTransSet)))<=(setunionTransitive)))<=(binintTransitive)))<=(peanoSinj))<=(peano0notS))<=(omegaSclos)))))<=(foundation2))<=(surjCantorThm))<=(leftInvIsSurj))<=(surjFuncSetFuncSurj))<=(surjFuncSetFuncIn))<=(injFuncSetFuncInj))<=(injFuncSetFuncIn))<=(injFuncInInjFuncSet))))))<=(image1Ex)))<=(woz2A)))<=(woz2Ex))<=(breln1unionCommutes))))<=(breln1unionI))<=(breln1unionIR)))<=(breln1unionprop))<=(breln1compEex))))))))<=(eqbreln1)))<=(breln1all1))<=(setOfPairsIsBReln1))<=(choice2fnsingleton))))<=(woz1_5))))<=(woz1_2))<=(woz1_1))<=(woz13rule4))<=(woz13rule3)))<=(woz13rule1)))<=(demorgan2))<=(demorgan2b)))<=(demorgan2a))<=(demorgan1))<=(demorgan1b))))<=(complementUnionInPowersetComplement)))<=(binunionTEcontra))<=(binunionTE)))<=(inComplementUnionImpNotIn1))))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion)))<=(binunionTILcontra))<=(complementTcontraSubset))<=(contraSubsetComplement)))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT)))<=(doubleComplementSub2))<=(doubleComplementSub1))<=(doubleComplementE1))<=(doubleComplementI1)))<=(contrasubsetT2))<=(contrasubsetT1))<=(contrasubsetT))))<=(complementTE1)))<=(powersetTE1))<=(powersetTI1))<=(subsetTI))))<=(setminusT_lem))<=(powersetT_lem))))))<=(iftrue)))<=(ifp))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1)))))<=(beta2))<=(lam2lamEq))<=(eta1))))<=(ap2apEq1))<=(funcext2)))<=(eqbreln))<=(subbreln))<=(funcGraphProp4))<=(funcextLem))))<=(funcGraphProp1)))<=(brelnall2)))<=(lam2p))<=(lamp))<=(lamProp))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc))<=(app)))))<=(dpsetconstrEL2)))<=(dpsetconstrERa)))))))<=(cartprodfstpairEq)))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin))))<=(ksndsingleton)))<=(setukpairinjR2)))))<=(setukpairinjR11))<=(setukpairinjL))<=(setukpairinjL2)))))<=(kfstsingleton))<=(setukpairinjL1)))))<=(ex1E1))<=(singletonprop)))<=(setunionsingleton2))<=(setunionsingleton1))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin)))))))<=(upairset2E))<=(singletoninpowunion))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp))<=(kpairiskpair)))))<=(symdiffIneg2))<=(symdiffIneg1)))))<=(setminusSubset1)))))<=(setminusELneg)))<=(setminusSubset2))<=(setminusER))<=(setminusEL)))))<=(binintersectSubset4))))<=(binintersectER)))))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))))<=(binunionEcases))<=(binunionIR))<=(upairset2IR)))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))))<=(setadjoinSub))))<=(notequalI2))<=(notequalI1))))<=(subsetE))))<=(eqimpsubset1)))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu))<=(omega__Cong)))))))<=(exuE3u))<=(in__Cong)))))<=(exuI1))<=(notdallE)))))<=(quantDeMorgan4)))))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL)))<=(singletonsswitch))<=(eqinunit))<=(notinsingleton))))<=(exuE2))<=(subPowSU))<=(setunionE))<=(setunionI))<=(powersetE))<=(emptyInPowerset))<=(emptyinPowerset)))<=(setoftrueEq))<=(setadjoinOr)))<=(setadjoinIR))<=(emptyinunitempty))<=(setadjoinIL)))<=(nonemptyI)))<=(setbeta))<=(noeltsimpempty)))<=(setext))))<=(emptysetimpfalse)))))<=(dsetconstrER))<=(dsetconstrEL)))))<=(foundationAx))<=(replAx)))))<=(setunionAx)))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setunionOrdinalLem1)). 41.33/5.87 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setextAx)). 41.33/5.87 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', emptysetAx)). 41.33/5.87 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setadjoinAx)). 41.33/5.87 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', powersetAx)). 41.33/5.87 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setunionAx)). 41.33/5.87 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', omega0Ax)). 41.33/5.87 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', omegaSAx)). 41.33/5.87 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', omegaIndAx)). 41.33/5.87 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', foundationAx)). 41.33/5.87 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', wellorderingAx)). 41.33/5.87 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', prop2setE)). 41.33/5.87 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', emptysetE)). 41.33/5.87 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', emptysetimpfalse)). 41.33/5.87 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', notinemptyset)). 41.33/5.87 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setext)). 41.33/5.87 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', emptyI)). 41.33/5.87 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', noeltsimpempty)). 41.33/5.87 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setadjoinIL)). 41.33/5.87 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', emptyinunitempty)). 41.33/5.87 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setadjoinIR)). 41.33/5.87 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setadjoinE)). 41.33/5.87 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setadjoinOr)). 41.33/5.87 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', powersetI)). 41.33/5.87 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', emptyinPowerset)). 41.33/5.87 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', emptyInPowerset)). 41.33/5.87 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', powersetE)). 41.33/5.87 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setunionI)). 41.33/5.87 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setunionE)). 41.33/5.87 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subPowSU)). 41.33/5.87 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', uniqinunit)). 41.33/5.87 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', notinsingleton)). 41.33/5.87 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', eqinunit)). 41.33/5.87 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', singletonsswitch)). 41.33/5.87 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', upairsetE)). 41.33/5.87 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', upairsetIL)). 41.33/5.87 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', upairsetIR)). 41.33/5.87 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', vacuousDall)). 41.33/5.87 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', quantDeMorgan1)). 41.33/5.87 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', quantDeMorgan2)). 41.33/5.87 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', quantDeMorgan3)). 41.33/5.87 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', quantDeMorgan4)). 41.33/5.87 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', prop2setI)). 41.33/5.87 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', prop2set2propI)). 41.33/5.87 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', notdexE)). 41.33/5.87 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', notdallE)). 41.33/5.87 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', inCongP)). 41.33/5.87 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', in__Cong)). 41.33/5.87 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', emptyset__Cong)). 41.33/5.87 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setadjoin__Cong)). 41.33/5.87 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', powerset__Cong)). 41.33/5.87 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setunion__Cong)). 41.33/5.87 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', omega__Cong)). 41.33/5.87 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subsetI1)). 41.33/5.87 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', eqimpsubset2)). 41.33/5.87 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', eqimpsubset1)). 41.33/5.87 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subsetI2)). 41.33/5.87 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', emptysetsubset)). 41.33/5.87 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subsetE)). 41.33/5.87 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subsetE2)). 41.33/5.87 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', notsubsetI)). 41.33/5.87 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', notequalI1)). 41.33/5.87 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', notequalI2)). 41.33/5.87 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subsetRefl)). 41.33/5.87 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subsetTrans)). 41.33/5.87 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setadjoinSub)). 41.33/5.87 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setadjoinSub2)). 41.33/5.87 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subset2powerset)). 41.33/5.87 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setextsub)). 41.33/5.87 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subsetemptysetimpeq)). 41.33/5.87 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', powersetI1)). 41.33/5.87 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', powersetE1)). 41.33/5.87 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', inPowerset)). 41.33/5.87 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', powersetsubset)). 41.33/5.87 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binunionIL)). 41.33/5.87 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', upairset2IR)). 41.33/5.87 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binunionIR)). 41.33/5.87 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binunionEcases)). 41.33/5.87 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binunionE)). 41.33/5.87 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binunionLsub)). 41.33/5.87 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binunionRsub)). 41.33/5.87 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectI)). 41.33/5.87 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectSubset5)). 41.33/5.87 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectEL)). 41.33/5.87 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectLsub)). 41.33/5.87 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectSubset2)). 41.33/5.87 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectSubset3)). 41.33/5.87 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectER)). 41.33/5.87 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', disjointsetsI1)). 41.33/5.87 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectRsub)). 41.33/5.87 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectSubset4)). 41.33/5.87 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectSubset1)). 41.33/5.87 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', bs114d)). 41.33/5.87 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setminusI)). 41.33/5.87 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setminusEL)). 41.33/5.87 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setminusER)). 41.33/5.87 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setminusSubset2)). 41.33/5.87 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setminusERneg)). 41.33/5.87 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setminusELneg)). 41.33/5.87 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setminusILneg)). 41.33/5.87 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setminusIRneg)). 41.33/5.87 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setminusLsub)). 41.33/5.87 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setminusSubset1)). 41.33/5.87 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', symdiffE)). 41.33/5.87 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', symdiffI1)). 41.33/5.87 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', symdiffI2)). 41.33/5.87 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', symdiffIneg1)). 41.33/5.87 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', symdiffIneg2)). 41.33/5.87 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', secondinupair)). 41.33/5.87 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setukpairIL)). 41.33/5.87 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setukpairIR)). 41.33/5.87 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', kpairiskpair)). 41.33/5.87 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', kpairp)). 41.33/5.87 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', singletonsubset)). 41.33/5.87 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', singletoninpowerset)). 41.33/5.87 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', singletoninpowunion)). 41.33/5.87 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', upairset2E)). 41.33/5.87 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', upairsubunion)). 41.33/5.87 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', upairinpowunion)). 41.33/5.87 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ubforcartprodlem1)). 41.33/5.87 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ubforcartprodlem2)). 41.33/5.87 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ubforcartprodlem3)). 41.33/5.87 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', cartprodpairin)). 41.33/5.87 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', cartprodmempair1)). 41.33/5.87 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', cartprodmempair)). 41.33/5.87 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setunionE2)). 41.33/5.87 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setunionsingleton1)). 41.33/5.87 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setunionsingleton2)). 41.33/5.87 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setunionsingleton)). 41.33/5.87 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', singletonsuniq)). 41.33/5.87 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setukpairinjL1)). 41.33/5.87 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', theprop)). 41.33/5.87 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', kfstpairEq)). 41.33/5.87 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', cartprodfstin)). 41.33/5.87 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setukpairinjL2)). 41.33/5.87 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setukpairinjL)). 41.33/5.87 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setukpairinjR11)). 41.33/5.87 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setukpairinjR12)). 41.33/5.87 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setukpairinjR1)). 41.33/5.87 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', upairequniteq)). 41.33/5.87 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setukpairinjR2)). 41.33/5.87 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setukpairinjR)). 41.33/5.87 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ksndpairEq)). 41.33/5.87 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', kpairsurjEq)). 41.33/5.87 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', cartprodsndin)). 41.33/5.87 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', cartprodpairmemEL)). 41.33/5.87 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', cartprodpairmemER)). 41.33/5.87 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', cartprodmempaircEq)). 41.33/5.87 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', cartprodfstpairEq)). 41.33/5.87 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', cartprodsndpairEq)). 41.33/5.87 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', cartprodpairsurjEq)). 41.33/5.87 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', app)). 41.33/5.87 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', infuncsetfunc)). 41.33/5.87 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ap2p)). 41.33/5.87 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', funcinfuncset)). 41.33/5.87 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', brelnall1)). 41.33/5.87 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', brelnall2)). 41.33/5.87 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', funcGraphProp1)). 41.33/5.87 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', funcGraphProp3)). 41.33/5.87 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', funcGraphProp2)). 41.33/5.87 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', funcextLem)). 41.33/5.87 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', funcGraphProp4)). 41.33/5.87 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subbreln)). 41.33/5.87 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', eqbreln)). 41.33/5.87 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', funcext)). 41.33/5.87 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', funcext2)). 41.33/5.87 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ap2apEq1)). 41.33/5.87 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ap2apEq2)). 41.33/5.87 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', ifp)). 41.33/5.87 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', theeq)). 41.33/5.87 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', iftrue)). 41.33/5.87 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', iffalse)). 41.33/5.87 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', iftrueorfalse)). 41.33/5.87 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectT_lem)). 41.33/5.87 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binunionT_lem)). 41.33/5.87 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', powersetT_lem)). 41.33/5.87 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setminusT_lem)). 41.33/5.87 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', complementT_lem)). 41.33/5.87 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', setextT)). 41.33/5.87 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subsetTI)). 41.33/5.87 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', powersetTI1)). 41.33/5.87 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', powersetTE1)). 41.33/5.87 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', complementTI1)). 41.33/5.87 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', complementTE1)). 41.33/5.87 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectTELcontra)). 41.33/5.87 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binintersectTERcontra)). 41.33/5.87 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', contrasubsetT)). 41.33/5.87 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', contrasubsetT1)). 41.33/5.87 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', contrasubsetT2)). 41.33/5.87 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', contrasubsetT3)). 41.33/5.87 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', doubleComplementI1)). 41.33/5.87 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', doubleComplementE1)). 41.33/5.87 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', doubleComplementSub1)). 41.33/5.87 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', doubleComplementSub2)). 41.33/5.87 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', doubleComplementEq)). 41.33/5.87 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', complementTnotintersectT)). 41.33/5.87 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', complementImpComplementIntersect)). 41.33/5.87 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', complementSubsetComplementIntersect)). 41.33/5.87 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', complementInPowersetComplementIntersect)). 41.33/5.87 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', contraSubsetComplement)). 41.33/5.87 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', complementTcontraSubset)). 41.33/5.87 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binunionTILcontra)). 41.33/5.87 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binunionTIRcontra)). 41.33/5.87 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', inIntersectImpInUnion)). 41.33/5.87 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', inIntersectImpInUnion2)). 41.33/5.87 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', inIntersectImpInIntersectUnions)). 41.33/5.87 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', intersectInPowersetIntersectUnions)). 41.33/5.87 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', inComplementUnionImpNotIn1)). 41.33/5.87 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', inComplementUnionImpInComplement1)). 41.33/5.87 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binunionTE)). 41.33/5.87 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', binunionTEcontra)). 41.33/5.87 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', demorgan2a1)). 41.33/5.87 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', complementUnionInPowersetComplement)). 41.33/5.87 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', demorgan2a2)). 41.33/5.87 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', demorgan1a)). 41.33/5.87 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', demorgan1b)). 41.33/5.87 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', demorgan1)). 41.33/5.87 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', demorgan2a)). 41.33/5.87 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', demorgan2b2)). 41.33/5.87 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', demorgan2b)). 41.33/5.87 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', demorgan2)). 41.33/5.87 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz13rule0)). 41.33/5.87 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz13rule1)). 41.33/5.87 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz13rule2)). 41.33/5.87 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz13rule3)). 41.33/5.87 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz13rule4)). 41.33/5.87 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz1_1)). 41.33/5.87 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz1_2)). 41.33/5.87 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz1_3)). 41.33/5.87 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz1_4)). 41.33/5.87 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz1_5)). 41.33/5.87 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1all2)). 41.33/5.87 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1SetBreln1)). 41.33/5.87 thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1all1)). 41.33/5.87 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', subbreln1)). 41.33/5.87 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', eqbreln1)). 41.33/5.87 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1invprop)). 41.33/5.87 thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1invI)). 41.33/5.87 thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1invE)). 41.33/5.87 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1compprop)). 41.33/5.87 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1compI)). 41.33/5.87 thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1compE)). 41.33/5.87 thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1compEex)). 41.33/5.87 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1unionprop)). 41.33/5.87 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1unionIL)). 41.33/5.87 thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1unionIR)). 41.33/5.87 thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1unionI)). 41.33/5.87 thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1unionE)). 41.33/5.87 thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1unionEcases)). 41.33/5.87 thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', breln1unionCommutes)). 41.33/5.87 thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz2Ex)). 41.33/5.87 thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz2W)). 41.33/5.87 thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz2A)). 41.33/5.87 thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', woz2B)). 41.33/5.87 thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', image1Ex)). 41.33/5.87 thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', injFuncInInjFuncSet)). 41.33/5.87 thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', injFuncSetFuncIn)). 41.33/5.87 thf(injFuncSetFuncInj, axiom, ((injFuncSetFuncInj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', injFuncSetFuncInj)). 41.33/5.87 thf(surjFuncSetFuncIn, axiom, ((surjFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', surjFuncSetFuncIn)). 41.33/5.87 thf(surjFuncSetFuncSurj, axiom, ((surjFuncSetFuncSurj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X2 @ X3))=>(surjective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', surjFuncSetFuncSurj)). 41.33/5.87 thf(leftInvIsSurj, axiom, ((leftInvIsSurj)<=>![X4:$i, X5:$i, X62:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X62 @ X2) @ X5)))=>![X34:$i]:(((in @ X34 @ (funcSet @ X5 @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X5 @ X4 @ X34 @ (X62 @ X2))=(X2))))=>(surjective @ X5 @ X4 @ X34))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', leftInvIsSurj)). 41.33/5.87 thf(surjCantorThm, axiom, ((surjCantorThm)<=>![X4:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ (powerset @ X4)))=>~((surjective @ X4 @ (powerset @ X4) @ X29))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', surjCantorThm)). 41.33/5.87 thf(notinself, axiom, ((notinself)<=>![X4:$i]:(~((in @ X4 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', notinself)). 41.33/5.87 thf(notinself2, axiom, ((notinself2)<=>![X4:$i, X5:$i]:(((in @ X4 @ X5)=>~((in @ X5 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', notinself2)). 41.33/5.87 thf(omegaSp, axiom, ((omegaSp)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (omegaS @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', omegaSp)). 41.33/5.87 thf(omegaSclos, axiom, ((omegaSclos)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', omegaSclos)). 41.33/5.87 thf(peano0notS, axiom, ((peano0notS)<=>![X2:$i]:(((in @ X2 @ omega)=>((omegaS @ X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', peano0notS)). 41.33/5.87 thf(peanoSinj, axiom, ((peanoSinj)<=>![X2:$i]:(((in @ X2 @ omega)=>![X3:$i]:(((in @ X3 @ omega)=>(((omegaS @ X2)=(omegaS @ X3))=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.iO7IE6tqRh/Vampire---4.8_32368', peanoSinj)). 41.33/5.87 thf(c_0_342, plain, ((wellorderedByIn)=(^[Z0/* 8 */:$i]:(((((![X1189:$i]:(((in @ X1189 @ Z0)=>![X1190:$i]:(((in @ X1190 @ Z0)=>![X1191:$i]:(((in @ X1191 @ Z0)=>(((in @ X1189 @ X1190)&(in @ X1190 @ X1191))=>(in @ X1189 @ X1191))))))))&![X1192:$i]:(((in @ X1192 @ Z0)=>![X1193:$i]:(((in @ X1193 @ Z0)=>((((X1192)=(X1193))|(in @ X1192 @ X1193))|(in @ X1193 @ X1192)))))))&![X1194:$i]:(((in @ X1194 @ Z0)=>~((in @ X1194 @ X1194))))))&![X21:$i]:(((in @ X21 @ (powerset @ Z0))=>((((X21)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X21)&![X48:$i]:(((in @ X48 @ X21)=>(((X2)=(X48))|(in @ X2 @ X48))))))))))))), inference(fof_simplification,[status(thm)],[wellorderedByIn])). 41.33/5.87 thf(c_0_343, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 41.33/5.87 thf(c_0_344, plain, ((stricttotalorderedByIn)=(^[Z0/* 8 */:$i]:(((![X2:$i]:(((in @ X2 @ Z0)=>![X21:$i]:(((in @ X21 @ Z0)=>![X48:$i]:(((in @ X48 @ Z0)=>(((in @ X2 @ X21)&(in @ X21 @ X48))=>(in @ X2 @ X48))))))))&![X21:$i]:(((in @ X21 @ Z0)=>![X48:$i]:(((in @ X48 @ Z0)=>((((X21)=(X48))|(in @ X21 @ X48))|(in @ X48 @ X21)))))))&![X21:$i]:(((in @ X21 @ Z0)=>~((in @ X21 @ X21)))))))), inference(fof_simplification,[status(thm)],[stricttotalorderedByIn])). 41.33/5.87 thf(c_0_345, plain, ((ordinal)=(^[Z0/* 8 */:$i]:(((![X1195:$i]:(((in @ X1195 @ Z0)=>(subset @ X1195 @ Z0))))&(((((![X1196:$i]:(((in @ X1196 @ Z0)=>![X1197:$i]:(((in @ X1197 @ Z0)=>![X1198:$i]:(((in @ X1198 @ Z0)=>(((in @ X1196 @ X1197)&(in @ X1197 @ X1198))=>(in @ X1196 @ X1198))))))))&![X1199:$i]:(((in @ X1199 @ Z0)=>![X1200:$i]:(((in @ X1200 @ Z0)=>((((X1199)=(X1200))|(in @ X1199 @ X1200))|(in @ X1200 @ X1199)))))))&![X1201:$i]:(((in @ X1201 @ Z0)=>~((in @ X1201 @ X1201))))))&![X1202:$i]:(((in @ X1202 @ (powerset @ Z0))=>((((X1202)!=(emptyset)))=>?[X1203:$i]:(((in @ X1203 @ X1202)&![X1204:$i]:(((in @ X1204 @ X1202)=>(((X1203)=(X1204))|(in @ X1203 @ X1204))))))))))))))), inference(fof_simplification,[status(thm)],[ordinal])). 41.33/5.87 thf(c_0_346, plain, ((transitiveset)=(^[Z0/* 6 */:$i]:(![X21:$i]:(((in @ X21 @ Z0)=>(subset @ X21 @ Z0)))))), inference(fof_simplification,[status(thm)],[transitiveset])). 41.33/5.87 thf(c_0_347, plain, ((wellorderedByIn)=(^[Z0/* 8 */:$i]:(((((![X1189:$i]:(((in @ X1189 @ Z0)=>![X1190:$i]:(((in @ X1190 @ Z0)=>![X1191:$i]:(((in @ X1191 @ Z0)=>(((in @ X1189 @ X1190)&(in @ X1190 @ X1191))=>(in @ X1189 @ X1191))))))))&![X1192:$i]:(((in @ X1192 @ Z0)=>![X1193:$i]:(((in @ X1193 @ Z0)=>((((X1192)=(X1193))|(in @ X1192 @ X1193))|(in @ X1193 @ X1192)))))))&![X1194:$i]:(((in @ X1194 @ Z0)=>~((in @ X1194 @ X1194))))))&![X21:$i]:(((in @ X21 @ (powerset @ Z0))=>((((X21)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X21)&![X48:$i]:(((in @ X48 @ X21)=>(((X2)=(X48))|(in @ X2 @ X48))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_342, c_0_343]), c_0_344])). 41.33/5.87 thf(c_0_348, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 41.33/5.87 thf(c_0_349, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 41.33/5.87 thf(c_0_350, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 41.33/5.87 thf(c_0_351, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 41.33/5.87 thf(c_0_352, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 41.33/5.87 thf(c_0_353, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 41.33/5.87 thf(c_0_354, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 41.33/5.87 thf(c_0_355, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 41.33/5.87 thf(c_0_356, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 41.33/5.87 thf(c_0_357, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 41.33/5.87 thf(c_0_358, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 41.33/5.87 thf(c_0_359, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 41.33/5.87 thf(c_0_360, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 41.33/5.87 thf(c_0_361, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 41.33/5.87 thf(c_0_362, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0/* 6 */:$i]:(![X2:$i]:(((in @ X2 @ Z0)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])). 41.33/5.87 thf(c_0_363, plain, ((ordinal)=(^[Z0/* 8 */:$i]:(((![X1195:$i]:(((in @ X1195 @ Z0)=>(subset @ X1195 @ Z0))))&(((((![X1196:$i]:(((in @ X1196 @ Z0)=>![X1197:$i]:(((in @ X1197 @ Z0)=>![X1198:$i]:(((in @ X1198 @ Z0)=>(((in @ X1196 @ X1197)&(in @ X1197 @ X1198))=>(in @ X1196 @ X1198))))))))&![X1199:$i]:(((in @ X1199 @ Z0)=>![X1200:$i]:(((in @ X1200 @ Z0)=>((((X1199)=(X1200))|(in @ X1199 @ X1200))|(in @ X1200 @ X1199)))))))&![X1201:$i]:(((in @ X1201 @ Z0)=>~((in @ X1201 @ X1201))))))&![X1202:$i]:(((in @ X1202 @ (powerset @ Z0))=>((((X1202)!=(emptyset)))=>?[X1203:$i]:(((in @ X1203 @ X1202)&![X1204:$i]:(((in @ X1204 @ X1202)=>(((X1203)=(X1204))|(in @ X1203 @ X1204))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_345, c_0_346]), c_0_347])). 41.33/5.87 thf(c_0_364, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1152:$i]:((((X6 @ X2 @ X1152))&![X1153:$i]:((((X6 @ X2 @ X1153))=>((X1152)=(X1153)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_348, c_0_349])). 41.33/5.87 thf(c_0_365, plain, ((descrp)=(![X1:$i > $o]:(((?[X1154:$i]:((((X1 @ X1154))&![X1155:$i]:((((X1 @ X1155))=>((X1154)=(X1155)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_350, c_0_349])). 41.33/5.87 thf(c_0_366, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 41.33/5.87 thf(c_0_367, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 41.33/5.87 thf(c_0_368, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 41.33/5.87 thf(c_0_369, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1156:$i]:((((X1 @ X1156))&![X1157:$i]:((((X1 @ X1157))=>((X1156)=(X1157)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_351, c_0_349])). 41.33/5.87 thf(c_0_370, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1158:$i]:((((X1 @ X1158))&![X1159:$i]:((((X1 @ X1159))=>((X1158)=(X1159)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_352, c_0_349])). 41.33/5.87 thf(c_0_371, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 41.33/5.87 thf(c_0_372, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_343])). 41.33/5.87 thf(c_0_373, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_353, c_0_343])). 41.33/5.87 thf(c_0_374, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_343])). 41.33/5.87 thf(c_0_375, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 41.33/5.87 thf(c_0_376, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1160:$i]:((((X1 @ X1160))&![X1161:$i]:((((X1 @ X1161))=>((X1160)=(X1161)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_354, c_0_349])). 41.33/5.87 thf(c_0_377, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_343])). 41.33/5.87 thf(c_0_378, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 41.33/5.87 thf(c_0_379, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1162:$i]:((((X1 @ X1162))&![X1163:$i]:((((X1 @ X1163))=>((X1162)=(X1163))))))))))), inference(apply_def,[status(thm)],[c_0_355, c_0_349])). 41.33/5.87 thf(c_0_380, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1164:$i]:((((X1 @ X1164))&![X1165:$i]:((((X1 @ X1165))=>((X1164)=(X1165)))))))))))), inference(apply_def,[status(thm)],[c_0_356, c_0_349])). 41.33/5.87 thf(c_0_381, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1166:$i]:((((X1 @ X1166))&![X1167:$i]:((((X1 @ X1167))=>((X1166)=(X1167))))))))))), inference(apply_def,[status(thm)],[c_0_357, c_0_349])). 41.33/5.87 thf(c_0_382, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1168:$i]:((((X1 @ X1168))&![X1169:$i]:((((X1 @ X1169))=>((X1168)=(X1169)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_358, c_0_349])). 41.33/5.87 thf(c_0_383, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1170:$i]:((((X1 @ X1170))&![X1171:$i]:((((X1 @ X1171))=>((X1170)=(X1171)))))))<=>(?[X1172:$i]:((((X17 @ X1172))&![X1173:$i]:((((X17 @ X1173))=>((X1172)=(X1173)))))))))))), inference(apply_def,[status(thm)],[c_0_359, c_0_349])). 41.33/5.87 thf(c_0_384, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1174:$i]:((((X1 @ X1174))&![X1175:$i]:((((X1 @ X1175))=>((X1174)=(X1175)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_360, c_0_349])). 41.33/5.87 thf(c_0_385, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1176:$i]:((((X1 @ X1176))&![X1177:$i]:((((X1 @ X1177))=>((X1176)=(X1177)))))))=>((?[X1178:$i]:((((X17 @ X1178))&![X1179:$i]:((((X17 @ X1179))=>((X1178)=(X1179)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_361, c_0_349])). 41.33/5.87 thf(c_0_386, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 41.33/5.87 thf(c_0_387, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 41.33/5.87 thf(c_0_388, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 41.33/5.87 thf(c_0_389, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 41.33/5.87 thf(c_0_390, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 41.33/5.87 thf(c_0_391, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 41.33/5.87 thf(c_0_392, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 41.33/5.87 thf(c_0_393, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 41.33/5.87 thf(c_0_394, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 41.33/5.87 thf(c_0_395, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 41.33/5.87 thf(c_0_396, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 41.33/5.87 thf(c_0_397, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 41.33/5.87 thf(c_0_398, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 41.33/5.87 thf(c_0_399, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 41.33/5.87 thf(c_0_400, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 41.33/5.87 thf(c_0_401, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 41.33/5.87 thf(c_0_402, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 41.33/5.87 thf(c_0_403, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 41.33/5.87 thf(c_0_404, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 41.33/5.87 thf(c_0_405, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 41.33/5.87 thf(c_0_406, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 41.33/5.87 thf(c_0_407, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 41.33/5.87 thf(c_0_408, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 41.33/5.87 thf(c_0_409, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 41.33/5.87 thf(c_0_410, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 41.33/5.87 thf(c_0_411, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 41.33/5.87 thf(c_0_412, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 41.33/5.87 thf(c_0_413, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 41.33/5.87 thf(c_0_414, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 41.33/5.87 thf(c_0_415, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 41.33/5.87 thf(c_0_416, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 41.33/5.87 thf(c_0_417, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 41.33/5.87 thf(c_0_418, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 8 */:$i]:(((X52 @ X2 @ Z0)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ Z0 @ X14) @ X33))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])). 41.33/5.87 thf(c_0_419, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])). 41.33/5.87 thf(c_0_420, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1180:$i]:(((![X2:$i]:(((in @ X2 @ X1180)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))&![X1181:$i]:(((![X2:$i]:(((in @ X2 @ X1181)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))=>((X1180)=(X1181)))))))))), inference(apply_def,[status(thm)],[c_0_362, c_0_349])). 41.33/5.87 thf(c_0_421, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])). 41.33/5.87 thf(c_0_422, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])). 41.33/5.87 thf(c_0_423, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])). 41.33/5.87 thf(c_0_424, axiom, ((foundation2)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset)))))))), inference(apply_def,[status(thm)],[foundation2, c_0_343])). 41.33/5.87 thf(c_0_425, axiom, ((transitivesetOp1)=(![X21:$i]:(((![X1182:$i]:(((in @ X1182 @ X21)=>(subset @ X1182 @ X21))))=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21))))))), inference(apply_def,[status(thm)],[transitivesetOp1, c_0_346])). 41.33/5.87 thf(c_0_426, axiom, ((binintTransitive)=(![X21:$i]:(((![X1183:$i]:(((in @ X1183 @ X21)=>(subset @ X1183 @ X21))))=>![X48:$i]:(((![X1184:$i]:(((in @ X1184 @ X48)=>(subset @ X1184 @ X48))))=>(![X1185:$i]:(((in @ X1185 @ (binintersect @ X21 @ X48))=>(subset @ X1185 @ (binintersect @ X21 @ X48))))))))))), inference(apply_def,[status(thm)],[binintTransitive, c_0_346])). 41.33/5.87 thf(c_0_427, axiom, ((transitivesetOp2)=(![X21:$i]:(((![X1186:$i]:(((in @ X1186 @ X21)=>(subset @ X1186 @ X21))))=>![X4:$i, X2:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21)))))))), inference(apply_def,[status(thm)],[transitivesetOp2, c_0_346])). 41.33/5.87 thf(c_0_428, axiom, ((setunionTransitive)=(![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(![X1187:$i]:(((in @ X1187 @ X2)=>(subset @ X1187 @ X2))))))=>(![X1188:$i]:(((in @ X1188 @ (setunion @ X21))=>(subset @ X1188 @ (setunion @ X21))))))))), inference(apply_def,[status(thm)],[setunionTransitive, c_0_346])). 41.33/5.87 thf(c_0_429, axiom, ((ordinalMinLem1)=(![X21:$i]:(((((![X1205:$i]:(((in @ X1205 @ X21)=>(subset @ X1205 @ X21))))&(((((![X1206:$i]:(((in @ X1206 @ X21)=>![X1207:$i]:(((in @ X1207 @ X21)=>![X1208:$i]:(((in @ X1208 @ X21)=>(((in @ X1206 @ X1207)&(in @ X1207 @ X1208))=>(in @ X1206 @ X1208))))))))&![X1209:$i]:(((in @ X1209 @ X21)=>![X1210:$i]:(((in @ X1210 @ X21)=>((((X1209)=(X1210))|(in @ X1209 @ X1210))|(in @ X1210 @ X1209)))))))&![X1211:$i]:(((in @ X1211 @ X21)=>~((in @ X1211 @ X1211))))))&![X1212:$i]:(((in @ X1212 @ (powerset @ X21))=>((((X1212)!=(emptyset)))=>?[X1213:$i]:(((in @ X1213 @ X1212)&![X1214:$i]:(((in @ X1214 @ X1212)=>(((X1213)=(X1214))|(in @ X1213 @ X1214)))))))))))))=>![X48:$i]:(((((![X1215:$i]:(((in @ X1215 @ X48)=>(subset @ X1215 @ X48))))&(((((![X1216:$i]:(((in @ X1216 @ X48)=>![X1217:$i]:(((in @ X1217 @ X48)=>![X1218:$i]:(((in @ X1218 @ X48)=>(((in @ X1216 @ X1217)&(in @ X1217 @ X1218))=>(in @ X1216 @ X1218))))))))&![X1219:$i]:(((in @ X1219 @ X48)=>![X1220:$i]:(((in @ X1220 @ X48)=>((((X1219)=(X1220))|(in @ X1219 @ X1220))|(in @ X1220 @ X1219)))))))&![X1221:$i]:(((in @ X1221 @ X48)=>~((in @ X1221 @ X1221))))))&![X1222:$i]:(((in @ X1222 @ (powerset @ X48))=>((((X1222)!=(emptyset)))=>?[X1223:$i]:(((in @ X1223 @ X1222)&![X1224:$i]:(((in @ X1224 @ X1222)=>(((X1223)=(X1224))|(in @ X1223 @ X1224)))))))))))))=>(![X1225:$i]:(((in @ X1225 @ (binintersect @ X21 @ X48))=>(subset @ X1225 @ (binintersect @ X21 @ X48))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ordinalMinLem1, c_0_346]), c_0_363])). 41.33/5.87 thf(c_0_430, axiom, ((ordinalTransSet)=(![X21:$i]:(((((![X1226:$i]:(((in @ X1226 @ X21)=>(subset @ X1226 @ X21))))&(((((![X1227:$i]:(((in @ X1227 @ X21)=>![X1228:$i]:(((in @ X1228 @ X21)=>![X1229:$i]:(((in @ X1229 @ X21)=>(((in @ X1227 @ X1228)&(in @ X1228 @ X1229))=>(in @ X1227 @ X1229))))))))&![X1230:$i]:(((in @ X1230 @ X21)=>![X1231:$i]:(((in @ X1231 @ X21)=>((((X1230)=(X1231))|(in @ X1230 @ X1231))|(in @ X1231 @ X1230)))))))&![X1232:$i]:(((in @ X1232 @ X21)=>~((in @ X1232 @ X1232))))))&![X1233:$i]:(((in @ X1233 @ (powerset @ X21))=>((((X1233)!=(emptyset)))=>?[X1234:$i]:(((in @ X1234 @ X1233)&![X1235:$i]:(((in @ X1235 @ X1233)=>(((X1234)=(X1235))|(in @ X1234 @ X1235)))))))))))))=>![X2:$i, X4:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21)))))))), inference(apply_def,[status(thm)],[ordinalTransSet, c_0_363])). 41.33/5.87 thf(c_0_431, axiom, ((ordinalTransSet1)=(![X21:$i]:(((((![X1236:$i]:(((in @ X1236 @ X21)=>(subset @ X1236 @ X21))))&(((((![X1237:$i]:(((in @ X1237 @ X21)=>![X1238:$i]:(((in @ X1238 @ X21)=>![X1239:$i]:(((in @ X1239 @ X21)=>(((in @ X1237 @ X1238)&(in @ X1238 @ X1239))=>(in @ X1237 @ X1239))))))))&![X1240:$i]:(((in @ X1240 @ X21)=>![X1241:$i]:(((in @ X1241 @ X21)=>((((X1240)=(X1241))|(in @ X1240 @ X1241))|(in @ X1241 @ X1240)))))))&![X1242:$i]:(((in @ X1242 @ X21)=>~((in @ X1242 @ X1242))))))&![X1243:$i]:(((in @ X1243 @ (powerset @ X21))=>((((X1243)!=(emptyset)))=>?[X1244:$i]:(((in @ X1244 @ X1243)&![X1245:$i]:(((in @ X1245 @ X1243)=>(((X1244)=(X1245))|(in @ X1244 @ X1245)))))))))))))=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21))))))), inference(apply_def,[status(thm)],[ordinalTransSet1, c_0_363])). 41.33/5.87 thf(c_0_432, plain, ((epred1_0)<=>![X1256:$i]:(?[X1257:$i]:((((![X1258:$i]:(((in @ X1258 @ X1257)=>![X1259:$i]:(((in @ X1259 @ X1258)=>(in @ X1259 @ X1256)))))&![X1260:$i, X1261:$i]:((((in @ X1260 @ X1256)&(in @ X1261 @ X1256))=>(![X1262:$i]:(((in @ X1262 @ X1257)=>((in @ X1260 @ X1262)<=>(in @ X1261 @ X1262))))=>((X1260)=(X1261))))))&![X1263:$i, X1264:$i]:((((in @ X1263 @ X1257)&(in @ X1264 @ X1257))=>(![X1265:$i]:(((in @ X1265 @ X1263)=>(in @ X1265 @ X1264)))|![X1266:$i]:(((in @ X1266 @ X1264)=>(in @ X1266 @ X1263)))))))&![X1267:$i]:(((![X1268:$i]:(((in @ X1268 @ X1267)=>(in @ X1268 @ X1256)))&?[X1269:$i]:((in @ X1269 @ X1267)))=>?[X1270:$i, X1271:$i]:(((((in @ X1270 @ X1257)&(in @ X1271 @ X1267))&~(?[X1272:$i]:(((in @ X1272 @ X1270)&(in @ X1272 @ X1267)))))&![X1273:$i]:(((in @ X1273 @ X1257)=>(![X1274:$i]:(((in @ X1274 @ X1273)=>(in @ X1274 @ X1270)))|(in @ X1271 @ X1273)))))))))))), introduced(definition)). 41.33/5.87 thf(c_0_433, plain, ![X1768:$i]:(((epred2_1 @ X1768)<=>(![X1770:$i]:(((in @ X1770 @ X1768)=>![X1771:$i]:(((in @ X1771 @ X1768)=>![X1772:$i]:(((in @ X1772 @ X1768)=>(((in @ X1770 @ X1771)&(in @ X1771 @ X1772))=>(in @ X1770 @ X1772))))))))&![X1773:$i]:(((in @ X1773 @ X1768)=>![X1774:$i]:(((in @ X1774 @ X1768)=>(((X1773)=(X1774))|(in @ X1773 @ X1774)|(in @ X1774 @ X1773))))))))), introduced(definition)). 41.33/5.87 thf(c_0_434, plain, ![X1779:$i]:(((epred3_1 @ X1779)<=>(![X1781:$i]:(((in @ X1781 @ X1779)=>![X1782:$i]:(((in @ X1782 @ X1779)=>![X1783:$i]:(((in @ X1783 @ X1779)=>(((in @ X1781 @ X1782)&(in @ X1782 @ X1783))=>(in @ X1781 @ X1783))))))))&![X1784:$i]:(((in @ X1784 @ X1779)=>![X1785:$i]:(((in @ X1785 @ X1779)=>(((X1784)=(X1785))|(in @ X1784 @ X1785)|(in @ X1785 @ X1784))))))))), introduced(definition)). 41.33/5.87 thf(c_0_435, plain, ![X1814:$i]:(((epred4_1 @ X1814)<=>(![X1816:$i]:(((in @ X1816 @ X1814)=>![X1817:$i]:(((in @ X1817 @ X1814)=>![X1818:$i]:(((in @ X1818 @ X1814)=>(((in @ X1816 @ X1817)&(in @ X1817 @ X1818))=>(in @ X1816 @ X1818))))))))&![X1819:$i]:(((in @ X1819 @ X1814)=>![X1820:$i]:(((in @ X1820 @ X1814)=>(((X1819)=(X1820))|(in @ X1819 @ X1820)|(in @ X1820 @ X1819))))))))), introduced(definition)). 41.33/5.87 thf(c_0_436, plain, ![X1791:$i]:(((epred5_1 @ X1791)<=>(![X1793:$i]:(((in @ X1793 @ X1791)=>![X1794:$i]:(((in @ X1794 @ X1791)=>![X1795:$i]:(((in @ X1795 @ X1791)=>(((in @ X1793 @ X1794)&(in @ X1794 @ X1795))=>(in @ X1793 @ X1795))))))))&![X1796:$i]:(((in @ X1796 @ X1791)=>![X1797:$i]:(((in @ X1797 @ X1791)=>(((X1796)=(X1797))|(in @ X1796 @ X1797)|(in @ X1797 @ X1796))))))))), introduced(definition)). 41.33/5.87 thf(c_0_437, plain, ![X2:$i]:(((epred6_1 @ X2)<=>(![X1803:$i]:(((in @ X1803 @ X2)=>(subset @ X1803 @ X2)))&(((![X1804:$i]:(((in @ X1804 @ X2)=>![X1805:$i]:(((in @ X1805 @ X2)=>![X1806:$i]:(((in @ X1806 @ X2)=>(((in @ X1804 @ X1805)&(in @ X1805 @ X1806))=>(in @ X1804 @ X1806))))))))&![X1807:$i]:(((in @ X1807 @ X2)=>![X1808:$i]:(((in @ X1808 @ X2)=>(((X1807)=(X1808))|(in @ X1807 @ X1808)|(in @ X1808 @ X1807)))))))&![X1809:$i]:(((in @ X1809 @ X2)=>~(in @ X1809 @ X1809))))&![X1810:$i]:(((in @ X1810 @ (powerset @ X2))=>(((X1810)!=(emptyset))=>?[X1811:$i]:(((in @ X1811 @ X1810)&![X1812:$i]:(((in @ X1812 @ X1810)=>(((X1811)=(X1812))|(in @ X1811 @ X1812))))))))))))), introduced(definition)). 41.33/5.87 thf(c_0_438, negated_conjecture, ~((![X1246:$i, X1247:$i]:((![X1248:$i]:(((in @ X1248 @ X1246)<=>(in @ X1248 @ X1247)))=>((X1246)=(X1247))))=>(![X2426:$i]:(~(in @ X2426 @ emptyset))=>(![X2423:$i, X2424:$i, X2425:$i]:(((in @ X2425 @ (setadjoin @ X2423 @ X2424))<=>(((X2425)=(X2423))|(in @ X2425 @ X2424))))=>(![X1249:$i, X1250:$i]:(((in @ X1250 @ (powerset @ X1249))<=>![X1251:$i]:(((in @ X1251 @ X1250)=>(in @ X1251 @ X1249)))))=>(![X2420:$i, X2421:$i]:(((in @ X2421 @ (setunion @ X2420))<=>?[X2422:$i]:(((in @ X2421 @ X2422)&(in @ X2422 @ X2420)))))=>((in @ emptyset @ omega)=>(![X1252:$i]:(((in @ X1252 @ omega)=>(in @ (setadjoin @ X1252 @ X1252) @ omega)))=>(![X1253:$i]:((((in @ emptyset @ X1253)&![X1254:$i]:((((in @ X1254 @ omega)&(in @ X1254 @ X1253))=>(in @ (setadjoin @ X1254 @ X1254) @ X1253))))=>![X1255:$i]:(((in @ X1255 @ omega)=>(in @ X1255 @ X1253)))))=>(![X2412:$i > $i > $o, X2413:$i]:((![X2414:$i]:(((in @ X2414 @ X2413)=>?[X2415:$i]:(((X2412 @ X2414 @ X2415)&![X2416:$i]:(((X2412 @ X2414 @ X2416)=>((X2415)=(X2416))))))))=>?[X2417:$i]:(![X2418:$i]:(((in @ X2418 @ X2417)<=>?[X2419:$i]:(((in @ X2419 @ X2413)&(X2412 @ X2419 @ X2418))))))))=>(![X2408:$i]:((?[X2409:$i]:((in @ X2409 @ X2408))=>?[X2410:$i]:(((in @ X2410 @ X2408)&~(?[X2411:$i]:(((in @ X2411 @ X2410)&(in @ X2411 @ X2408))))))))=>((epred1_0)=>(![X1275:$i > $o]:((?[X1276:$i]:(((X1275 @ X1276)&![X1277:$i]:(((X1275 @ X1277)=>((X1276)=(X1277))))))=>(X1275 @ (descr @ (^[Z0/* 3 */:$i]:((X1275 @ Z0)))))))=>(![X1278:$i, X1279:$i > $o, X1280:$i]:(((in @ X1280 @ X1278)=>((X1279 @ X1280)=>(in @ X1280 @ (dsetconstr @ X1278 @ (^[Z0/* 3 */:$i]:((X1279 @ Z0))))))))=>(![X2405:$i, X2406:$i > $o, X2407:$i]:(((in @ X2407 @ (dsetconstr @ X2405 @ (^[Z0/* 3 */:$i]:((X2406 @ Z0)))))=>(in @ X2407 @ X2405)))=>(![X2402:$i, X2403:$i > $o, X2404:$i]:(((in @ X2404 @ (dsetconstr @ X2402 @ (^[Z0/* 3 */:$i]:((X2403 @ Z0)))))=>(X2403 @ X2404)))=>(![X1281:$i > $o]:((?[X1282:$i]:(((X1281 @ X1282)&![X1283:$i]:(((X1281 @ X1283)=>((X1282)=(X1283))))))=>?[X1284:$i]:(((X1281 @ X1284)&![X1285:$i]:(((X1281 @ X1285)=>((X1284)=(X1285))))))))=>(![X1286:$o, X1287:$i]:(((in @ X1287 @ (prop2set @ ((X1286))))=>(X1286)))=>(![X1288:$i]:(((in @ X1288 @ emptyset)=>![X1289:$o]:((X1289))))=>(![X2401:$i]:(~(in @ X2401 @ emptyset))=>(![X1290:$i]:(~(in @ X1290 @ emptyset))=>(![X1291:$i > $o]:((?[X1292:$i]:(((X1291 @ X1292)&![X1293:$i]:(((X1291 @ X1293)=>((X1292)=(X1293))))))=>?[X1294:$i]:((X1291 @ X1294))))=>(![X2397:$i, X2398:$i]:((![X2399:$i]:(((in @ X2399 @ X2397)=>(in @ X2399 @ X2398)))=>(![X2400:$i]:(((in @ X2400 @ X2398)=>(in @ X2400 @ X2397)))=>((X2397)=(X2398)))))=>(![X1295:$i]:((![X1296:$i]:(~(in @ X1296 @ X1295))=>((X1295)=(emptyset))))=>(![X2395:$i]:((![X2396:$i]:(~(in @ X2396 @ X2395))=>((X2395)=(emptyset))))=>(![X2392:$i, X2393:$i > $o, X2394:$i]:(((in @ X2394 @ X2392)=>((in @ X2394 @ (dsetconstr @ X2392 @ (^[Z0/* 3 */:$i]:((X2393 @ Z0)))))<=>(X2393 @ X2394))))=>(![X1297:$i]:((((X1297)!=(emptyset))=>?[X1298:$i]:((in @ X1298 @ X1297))))=>(![X2389:$i, X2390:$i > $o, X2391:$i]:(((in @ X2391 @ X2389)=>((X2390 @ X2391)=>((dsetconstr @ X2389 @ (^[Z0/* 3 */:$i]:((X2390 @ Z0))))!=(emptyset)))))=>(![X1299:$i]:((?[X1300:$i]:((in @ X1300 @ X1299))=>((X1299)!=(emptyset))))=>(![X2387:$i, X2388:$i]:((in @ X2387 @ (setadjoin @ X2387 @ X2388)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X2384:$i, X2385:$i, X2386:$i]:(((in @ X2386 @ X2385)=>(in @ X2386 @ (setadjoin @ X2384 @ X2385))))=>(![X1301:$i, X1302:$i, X1303:$i]:(((in @ X1303 @ (setadjoin @ X1301 @ X1302))=>![X1304:$o]:(((((X1303)=(X1301))=>(X1304))=>(((in @ X1303 @ X1302)=>(X1304))=>(X1304))))))=>(![X2381:$i, X2382:$i, X2383:$i]:(((in @ X2383 @ (setadjoin @ X2381 @ X2382))=>(((X2383)=(X2381))|(in @ X2383 @ X2382))))=>(![X2380:$i]:(((dsetconstr @ X2380 @ (^[Z0/* 3 */:$i]:(($true))))=(X2380)))=>(![X1305:$i, X1306:$i]:((![X1307:$i]:(((in @ X1307 @ X1306)=>(in @ X1307 @ X1305)))=>(in @ X1306 @ (powerset @ X1305))))=>(![X2379:$i]:((in @ emptyset @ (powerset @ X2379)))=>(![X2378:$i]:((in @ emptyset @ (powerset @ X2378)))=>(![X2375:$i, X2376:$i, X2377:$i]:(((in @ X2376 @ (powerset @ X2375))=>((in @ X2377 @ X2376)=>(in @ X2377 @ X2375))))=>(![X2372:$i, X2373:$i, X2374:$i]:(((in @ X2373 @ X2374)=>((in @ X2374 @ X2372)=>(in @ X2373 @ (setunion @ X2372)))))=>(![X2368:$i, X2369:$i]:(((in @ X2369 @ (setunion @ X2368))=>![X2370:$o]:((![X2371:$i]:(((in @ X2369 @ X2371)=>((in @ X2371 @ X2368)=>(X2370))))=>(X2370)))))=>(![X2366:$i, X2367:$i]:(((in @ X2367 @ X2366)=>(in @ X2367 @ (powerset @ (setunion @ X2366)))))=>(![X2361:$i > $o]:((?[X2362:$i]:(((X2361 @ X2362)&![X2363:$i]:(((X2361 @ X2363)=>((X2362)=(X2363))))))=>?[X2364:$i]:(![X2365:$i]:(((X2361 @ X2365)<=>((X2365)=(X2364)))))))=>(![X1308:$i]:((((X1308)!=(emptyset))=>?[X1309:$i]:((in @ X1309 @ X1308))))=>(![X1310:$i, X1311:$i]:(((in @ X1310 @ 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_364]), foundationAx]), wellorderingAx]), c_0_365]), c_0_366]), c_0_367]), c_0_368]), c_0_369]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_370]), setext]), emptyI]), noeltsimpempty]), c_0_371]), c_0_372]), c_0_373]), c_0_374]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_375]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_376]), c_0_377]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_378]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_379]), c_0_380]), c_0_381]), inCongP]), in__Cong]), c_0_382]), c_0_383]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_384]), c_0_385]), c_0_386]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_387]), c_0_388]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_389]), c_0_390]), c_0_391]), c_0_392]), singletonsuniq]), setukpairinjL1]), c_0_393]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_394]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_395]), c_0_396]), c_0_397]), c_0_398]), c_0_399]), c_0_400]), c_0_401]), c_0_402]), c_0_403]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_404]), c_0_405]), c_0_406]), brelnall1]), brelnall2]), c_0_407]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), subbreln]), eqbreln]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_408]), c_0_409]), c_0_410]), c_0_411]), c_0_412]), c_0_413]), c_0_414]), c_0_415]), c_0_416]), c_0_417]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3]), woz1_4]), woz1_5]), breln1all2]), breln1SetBreln1]), c_0_418]), c_0_419]), breln1all1]), subbreln1]), eqbreln1]), breln1invprop]), breln1invI]), breln1invE]), breln1compprop]), breln1compI]), breln1compE]), breln1compEex]), breln1unionprop]), breln1unionIL]), breln1unionIR]), breln1unionI]), breln1unionE]), breln1unionEcases]), breln1unionCommutes]), woz2Ex]), woz2W]), woz2A]), woz2B]), image1Ex]), c_0_420]), c_0_421]), c_0_422]), c_0_423]), injFuncInInjFuncSet]), injFuncSetFuncIn]), injFuncSetFuncInj]), surjFuncSetFuncIn]), surjFuncSetFuncSurj]), leftInvIsSurj]), surjCantorThm]), c_0_424]), notinself]), notinself2]), omegaSp]), omegaSclos]), peano0notS]), peanoSinj]), c_0_346]), c_0_425]), c_0_426]), c_0_427]), c_0_428]), c_0_363]), c_0_429]), c_0_430]), c_0_431])])]), c_0_432]), c_0_433]), c_0_434]), c_0_435]), c_0_436]), c_0_437])). 41.33/5.87 thf(c_0_439, negated_conjecture, ![X2427:$i, X2428:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2440:$i, X2441:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2449:$i, X2450:$i > $i > $o, X2451:$i, X2453:$i, X2456:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2463:$i, X2464:$i > $o, X2465:$i, X2467:$i, X2468:$i > $o, X2469:$i, X2470:$i, X2471:$i > $o, X2472:$i, X2473:$i, X2474:$i > $o, X2475:$i, X2476:$i > $o, X2477:$i, X2480:$i, X2481:$o, X2482:$i, X2483:$i, X2484:$o, X2485:$i, X2486:$i, X2487:$i > $o, X2488:$i, X2491:$i, X2492:$i, X2495:$i, X2497:$i, X2499:$i, X2500:$i > $o, X2501:$i, X2502:$i, X2504:$i, X2505:$i > $o, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$o, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$o, X2537:$i, X2538:$i, X2539:$i > $o, X2540:$i, X2543:$i, X2544:$i, X2545:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i > $o, X2564:$i, X2565:$i > $o, X2566:$i, X2567:$i, X2568:$i > $o, X2569:$i, X2571:$i, X2572:$i > $o, X2574:$i, X2575:$i, X2576:$i > $o, X2578:$i, X2579:$i, X2580:$i > $o, X2581:$i, X2583:$o, X2584:$o, X2585:$i, X2586:$i > $o, X2588:$i, X2589:$i, X2590:$i > $o, X2591:$i, X2593:$i > $o, X2594:$i, X2597:$i, X2598:$i > $o, X2599:$i, X2603:$i, X2604:$i > $o, X2605:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i > $o, X2618:$i, X2620:$i, X2621:$i, X2622:$i > $o, X2623:$i > $o, X2626:$i, X2629:$i, X2630:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i > $o, X2643:$i, X2645:$i, X2646:$i, X2647:$i > $o, X2648:$i > $o, X2651:$i, X2653:$i, X2655:$i, X2656:$i, X2657:$i > $o, X2658:$i > $o, X2661:$i, X2662:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i > $o, X2709:$i, X2710:$i > $o, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$o, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$o, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2856:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i > $o, X2865:$i, X2866:$i, X2867:$i > $o, X2869:$i, X2870:$i > $o, X2871:$i, X2873:$i, X2874:$i > $o, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$i, X2885:$i, X2886:$i, X2887:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2901:$i, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i > $i > $o, X2950:$i, X2951:$i, X2952:$i, X2953:$i, X2954:$i > $i > $o, X2955:$i, X2956:$i, X2957:$i > $i > $o, X2958:$i, X2959:$i, X2960:$i > $i > $o, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i > $i > $o, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i > $i > $o, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i > $i > $o, X2976:$i, X2977:$i, X2978:$i, X2979:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3002:$i > $i, X3004:$i, X3005:$i, X3006:$i > $i, X3008:$i, X3009:$i, X3010:$i > $i, X3012:$i, X3013:$i, X3014:$i, X3015:$i > $o, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i > $o, X3025:$i, X3026:$i, X3027:$i > $o, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i, X3037:$i, X3038:$i, X3039:$i, X3040:$i, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3069:$i, X3070:$i, X3071:$i, X3072:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3079:$i, X3080:$i, X3081:$i, X3082:$i, X3083:$i, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i > $i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$i > $i, X3099:$i, X3100:$i, X3101:$i > $i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$o, X3109:$i, X3110:$i, X3111:$i, X3112:$o, X3113:$i, X3114:$i, X3115:$i, X3116:$o, X3117:$i, X3118:$i, X3119:$i, X3120:$o, X3121:$i, X3122:$i, X3123:$i, X3124:$o, X3125:$i, X3126:$i, X3127:$i, X3128:$o, X3129:$i, X3130:$i, X3131:$i, X3132:$i, X3133:$i, X3134:$o, X3135:$i, X3136:$i, X3137:$i, X3138:$o, X3139:$i, X3140:$i, X3141:$i, X3142:$o, X3143:$i, X3144:$i, X3145:$i, X3146:$i, X3147:$i, X3148:$i, X3149:$i, X3150:$i, X3151:$i, X3152:$i, X3153:$i, X3154:$i, X3155:$i, X3156:$i, X3157:$i, X3158:$i, X3159:$i, X3160:$i, X3163:$i, X3164:$i, X3165:$i, X3167:$i, X3168:$i, X3169:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i, X3176:$i, X3177:$i, X3178:$i, X3179:$i, X3180:$i, X3181:$i, X3182:$i, X3183:$i, X3184:$i, X3185:$i, X3186:$i, X3187:$i, X3188:$i, X3189:$i, X3190:$i, X3191:$i, X3192:$i, X3193:$i, X3194:$i, X3195:$i, X3196:$i, X3197:$i, X3198:$i, X3199:$i, X3200:$i, X3201:$i, X3202:$i, X3203:$i, X3204:$i, X3205:$i, X3206:$i, X3207:$i, X3208:$i, X3209:$i, X3210:$i, X3211:$i, X3212:$i, X3213:$i, X3214:$i, X3215:$i, X3216:$i, X3217:$i, X3218:$i, X3219:$i, X3220:$i, X3221:$i, X3222:$i, X3223:$i, X3224:$i, X3225:$i, X3226:$i, X3227:$i, X3228:$i, X3229:$i, X3230:$i, X3231:$i, X3232:$i, X3233:$i, X3234:$i, X3235:$i, X3236:$i, X3237:$i, X3238:$i, X3239:$i, X3240:$i, X3241:$i, X3242:$i, X3243:$i, X3244:$i, X3245:$i, X3246:$i, X3247:$i, X3248:$i, X3249:$i, X3250:$i, X3251:$i, X3252:$i, X3253:$i, X3254:$i, X3255:$i, X3256:$i, X3257:$i, X3258:$i, X3259:$i, X3260:$i, X3261:$i, X3262:$i, X3263:$i, X3264:$i, X3265:$i, X3266:$i, X3267:$i, X3268:$i, X3269:$i, X3270:$i, X3271:$i, X3272:$i, X3273:$i, X3274:$o, X3275:$i, X3276:$i, X3277:$i, X3278:$i, X3279:$i, X3280:$i, X3281:$i, X3282:$i, X3283:$i, X3284:$i, X3285:$i, X3286:$i, X3287:$i, X3288:$i, X3289:$i, X3290:$i, X3291:$i, X3292:$i, X3293:$i, X3294:$i, X3295:$i, X3296:$i, X3297:$i, X3298:$i, X3299:$i, X3300:$i, X3301:$i, X3302:$i, X3303:$i, X3304:$i, X3305:$i, X3306:$i, X3307:$i, X3308:$i, X3309:$i, X3310:$i, X3311:$i, X3312:$i, X3313:$i, X3314:$i, X3315:$i, X3316:$i, X3317:$i, X3318:$i, X3319:$i, X3320:$i, X3321:$i, X3322:$i, X3323:$i, X3324:$i, X3325:$i, X3326:$i, X3327:$i, X3328:$i, X3329:$i, X3330:$i, X3331:$i, X3332:$i, X3333:$i, X3334:$i, X3335:$i, X3336:$i, X3337:$i, X3338:$i, X3339:$i, X3340:$i, X3341:$i, X3342:$i, X3343:$i, X3344:$i, X3345:$i, X3346:$i, X3347:$i, X3348:$i, X3349:$i, X3350:$i, X3351:$i, X3352:$i, X3353:$i, X3354:$i, X3355:$i, X3356:$i, X3357:$i, X3358:$i > $o, X3361:$i, X3362:$i, X3363:$i, X3364:$i, X3365:$i, X3366:$i > $i > $o, X3368:$i, X3369:$i, X3370:$i, X3371:$i, X3372:$i > $i > $o, X3373:$i, X3374:$i, X3375:$i > $o, X3378:$i, X3379:$i, X3380:$i, X3381:$i, X3384:$i, X3385:$i, X3386:$i, X3391:$i, X3392:$i, X3393:$i, X3394:$i, X3395:$i, X3396:$i, X3397:$i, X3398:$i, X3399:$i, X3400:$i, X3401:$i, X3402:$i, X3403:$i, X3404:$i, X3405:$i, X3406:$i, X3407:$i, X3408:$i, X3409:$i, X3410:$i, X3411:$i, X3412:$i, X3413:$i, X3414:$i, X3416:$i, X3417:$i, X3418:$i, X3419:$i, X3420:$i, X3421:$o, X3423:$i, X3424:$i, X3425:$i, X3426:$i, X3427:$i, X3428:$i, X3429:$i, X3430:$i, X3431:$i, X3432:$i, X3433:$i, X3434:$i, X3435:$i, X3436:$i, X3437:$i, X3438:$i, X3439:$i, X3440:$i, X3441:$i, X3442:$i, X3443:$i, X3444:$i, X3445:$i, X3446:$i, X3447:$i, X3448:$i, X3449:$i, X3450:$i, X3451:$o, X3452:$i, X3453:$i, 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X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((esk131_1 @ X3572)!=(emptyset))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(((in @ (esk132_2 @ X3572 @ X3576) @ (esk131_1 @ X3572))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((X3576)!=(esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(~(in @ X3576 @ (esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))))))&(((in @ (esk131_1 @ X3572) @ (powerset @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((esk131_1 @ X3572)!=(emptyset))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(((in @ (esk132_2 @ X3572 @ X3576) @ (esk131_1 @ X3572))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((X3576)!=(esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(~(in @ X3576 @ (esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572))))))))&((((in @ (esk131_1 @ X3572) @ (powerset @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((esk131_1 @ X3572)!=(emptyset))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(((in @ (esk132_2 @ X3572 @ X3576) @ (esk131_1 @ X3572))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((X3576)!=(esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(~(in @ X3576 @ (esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))))))&(((in @ (esk131_1 @ X3572) @ (powerset @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((esk131_1 @ X3572)!=(emptyset))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(((in @ (esk132_2 @ X3572 @ X3576) @ (esk131_1 @ X3572))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((X3576)!=(esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(~(in @ X3576 @ (esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))))))))&((~(in @ X3580 @ esk133_0)|(epred6_1 @ X3580))&((in @ esk134_0 @ (setunion @ esk133_0))&~(subset @ esk134_0 @ (setunion @ esk133_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_438])])])])])])). 41.33/5.88 thf(c_0_440, plain, ![X2:$i]:(((epred6_1 @ X2)=>(![X1803:$i]:(((in @ X1803 @ X2)=>(subset @ X1803 @ X2)))&(((![X1804:$i]:(((in @ X1804 @ X2)=>![X1805:$i]:(((in @ X1805 @ X2)=>![X1806:$i]:(((in @ X1806 @ X2)=>(((in @ X1804 @ X1805)&(in @ X1805 @ X1806))=>(in @ X1804 @ X1806))))))))&![X1807:$i]:(((in @ X1807 @ X2)=>![X1808:$i]:(((in @ X1808 @ X2)=>(((X1807)=(X1808))|(in @ X1807 @ X1808)|(in @ X1808 @ X1807)))))))&![X1809:$i]:(((in @ X1809 @ X2)=>~(in @ X1809 @ X1809))))&![X1810:$i]:(((in @ X1810 @ (powerset @ X2))=>(((X1810)!=(emptyset))=>?[X1811:$i]:(((in @ X1811 @ X1810)&![X1812:$i]:(((in @ X1812 @ X1810)=>(((X1811)=(X1812))|(in @ X1811 @ X1812))))))))))))), inference(split_equiv,[status(thm)],[c_0_437])). 41.33/5.88 thf(c_0_441, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk115_1 @ X2) @ X2)|(subset @ X3 @ (setunion @ X2))|~((in @ X3 @ (setunion @ X2))))), inference(split_conjunct,[status(thm)],[c_0_439])). 41.33/5.88 thf(c_0_442, negated_conjecture, (in @ esk134_0 @ (setunion @ esk133_0)), inference(split_conjunct,[status(thm)],[c_0_439])). 41.33/5.88 thf(c_0_443, negated_conjecture, ~((subset @ esk134_0 @ (setunion @ esk133_0))), inference(split_conjunct,[status(thm)],[c_0_439])). 41.33/5.88 thf(c_0_444, plain, ![X3625:$i, X3626:$i, X3627:$i, X3628:$i, X3629:$i, X3630:$i, X3631:$i, X3632:$i, X3633:$i, X3635:$i]:(((~(in @ X3626 @ X3625)|(subset @ X3626 @ X3625)|~(epred6_1 @ X3625))&((((~(in @ X3627 @ X3625)|(~(in @ X3628 @ X3625)|(~(in @ X3629 @ X3625)|(~(in @ X3627 @ X3628)|~(in @ X3628 @ X3629)|(in @ X3627 @ X3629))))|~(epred6_1 @ X3625))&(~(in @ X3630 @ X3625)|(~(in @ X3631 @ X3625)|(((X3630)=(X3631))|(in @ X3630 @ X3631)|(in @ X3631 @ X3630)))|~(epred6_1 @ X3625)))&(~(in @ X3632 @ X3625)|~(in @ X3632 @ X3632)|~(epred6_1 @ X3625)))&(((in @ (esk160_2 @ X3625 @ X3633) @ X3633)|((X3633)=(emptyset))|~(in @ X3633 @ (powerset @ X3625))|~(epred6_1 @ X3625))&(~(in @ X3635 @ X3633)|(((esk160_2 @ X3625 @ X3633)=(X3635))|(in @ (esk160_2 @ X3625 @ X3633) @ X3635))|((X3633)=(emptyset))|~(in @ X3633 @ (powerset @ X3625))|~(epred6_1 @ X3625)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_440])])])])])). 41.33/5.88 thf(c_0_445, negated_conjecture, ![X2:$i]:(((epred6_1 @ X2)|~((in @ X2 @ esk133_0)))), inference(split_conjunct,[status(thm)],[c_0_439])). 41.33/5.88 thf(c_0_446, negated_conjecture, (in @ (esk115_1 @ esk133_0) @ esk133_0), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_441, c_0_442]), c_0_443])). 41.33/5.88 thf(c_0_447, plain, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ X3))|~((epred6_1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_444])). 41.33/5.88 thf(c_0_448, negated_conjecture, (epred6_1 @ (esk115_1 @ esk133_0)), inference(spm,[status(thm)],[c_0_445, c_0_446])). 41.33/5.88 thf(c_0_449, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk116_1 @ X2) @ (esk115_1 @ X2))|(subset @ X3 @ (setunion @ X2))|~((in @ X3 @ (setunion @ X2))))), inference(split_conjunct,[status(thm)],[c_0_439])). 41.33/5.88 thf(c_0_450, negated_conjecture, ![X3:$i, X2:$i]:(((subset @ X3 @ (setunion @ X2))|~((subset @ (esk116_1 @ X2) @ (esk115_1 @ X2)))|~((in @ X3 @ (setunion @ X2))))), inference(split_conjunct,[status(thm)],[c_0_439])). 41.33/5.88 thf(c_0_451, plain, ![X2:$i]:(((subset @ X2 @ (esk115_1 @ esk133_0))|~((in @ X2 @ (esk115_1 @ esk133_0))))), inference(spm,[status(thm)],[c_0_447, c_0_448])). 41.33/5.88 thf(c_0_452, negated_conjecture, (in @ (esk116_1 @ esk133_0) @ (esk115_1 @ esk133_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_449, c_0_442]), c_0_443])). 41.33/5.88 thf(c_0_453, negated_conjecture, ![X2:$i]:(((subset @ X2 @ (setunion @ esk133_0))|~((in @ X2 @ (setunion @ esk133_0))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_450, c_0_451]), c_0_452])])). 41.33/5.88 thf(c_0_454, plain, ($false), inference(cdclpropres,[status(thm)],[c_0_453, c_0_443, c_0_442]), ['proof']). 41.33/5.88 # SZS output end CNFRefutation 41.33/5.88 # Parsed axioms : 740 41.33/5.88 # Removed by relevancy pruning/SinE : 0 41.33/5.88 # Initial clauses : 1558 41.33/5.88 # Removed in clause preprocessing : 434 41.33/5.88 # Initial clauses in saturation : 1124 41.33/5.88 # Processed clauses : 11586 41.33/5.88 # ...of these trivial : 140 41.33/5.88 # ...subsumed : 6446 41.33/5.88 # ...remaining for further processing : 5000 41.33/5.88 # Other redundant clauses eliminated : 139 41.33/5.88 # Clauses deleted for lack of memory : 0 41.33/5.88 # Backward-subsumed : 510 41.33/5.88 # Backward-rewritten : 31 41.33/5.88 # Generated clauses : 189558 41.33/5.88 # ...of the previous two non-redundant : 185759 41.33/5.88 # ...aggressively subsumed : 0 41.33/5.88 # Contextual simplify-reflections : 55 41.33/5.88 # Paramodulations : 189149 41.33/5.88 # Factorizations : 2 41.33/5.88 # NegExts : 228 41.33/5.88 # Equation resolutions : 147 41.33/5.88 # Total rewrite steps : 8161 41.33/5.88 # Propositional unsat checks : 1 41.33/5.88 # Propositional check models : 0 41.33/5.88 # Propositional check unsatisfiable : 1 41.33/5.88 # Propositional clauses : 179198 41.33/5.88 # Propositional clauses after purity: 4362 41.33/5.88 # Propositional unsat core size : 3 41.33/5.88 # Propositional preprocessing time : 0.000 41.33/5.88 # Propositional encoding time : 0.492 41.33/5.88 # Propositional solver time : 0.025 41.33/5.88 # Success case prop preproc time : 0.000 41.33/5.88 # Success case prop encoding time : 0.492 41.33/5.88 # Success case prop solver time : 0.025 41.33/5.88 # Current number of processed clauses : 3699 41.33/5.88 # Positive orientable unit clauses : 144 41.33/5.88 # Positive unorientable unit clauses: 0 41.33/5.88 # Negative unit clauses : 654 41.33/5.88 # Non-unit-clauses : 2901 41.33/5.88 # Current number of unprocessed clauses: 175499 41.33/5.88 # ...number of literals in the above : 706626 41.33/5.88 # Current number of archived formulas : 0 41.33/5.88 # Current number of archived clauses : 1279 41.33/5.88 # Clause-clause subsumption calls (NU) : 2105688 41.33/5.88 # Rec. Clause-clause subsumption calls : 495888 41.33/5.88 # Non-unit clause-clause subsumptions : 3742 41.33/5.88 # Unit Clause-clause subsumption calls : 138540 41.33/5.88 # Rewrite failures with RHS unbound : 0 41.33/5.88 # BW rewrite match attempts : 73 41.33/5.88 # BW rewrite match successes : 24 41.33/5.88 # Condensation attempts : 0 41.33/5.88 # Condensation successes : 0 41.33/5.88 # Termbank termtop insertions : 7656013 41.33/5.88 41.33/5.88 # ------------------------------------------------- 41.33/5.88 # User time : 5.058 s 41.33/5.88 # System time : 0.161 s 41.33/5.88 # Total time : 5.218 s 41.33/5.88 # Maximum resident set size: 11976 pages 42.31/5.98 42.31/5.98 # ------------------------------------------------- 42.31/5.98 # User time : 5.080 s 42.31/5.98 # System time : 0.164 s 42.31/5.98 # Total time : 5.244 s 42.31/5.98 # Maximum resident set size: 3148 pages 42.31/5.98 % E---3.1 exiting 42.31/5.99 EOF