0.12/0.20 % Problem : Vampire---4.8_11301 : TPTP v0.0.0. Released v0.0.0. 0.12/0.21 % Command : run_E %s %d THM 0.22/0.42 % Computer : n024.cluster.edu 0.22/0.42 % Model : x86_64 x86_64 0.22/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.22/0.42 % Memory : 8042.1875MB 0.22/0.42 % OS : Linux 3.10.0-693.el7.x86_64 0.22/0.42 % CPULimit : 1440 0.22/0.42 % WCLimit : 180 0.22/0.42 % DateTime : Mon Jul 3 13:00:23 EDT 2023 0.22/0.42 % CPUTime : 0.49/0.64 Running higher-order theorem provingRunning: /export/starexec/sandbox/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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301 0.49/0.64 # Version: 3.1pre001-ho 0.51/1.04 # Preprocessing class: HSLMSLSSLLLCHFA. 0.51/1.04 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.51/1.04 # Starting ehoh_best5 with 180s (1) cores 0.51/1.04 # Starting almost_fo_3_lam with 180s (1) cores 0.51/1.04 # Starting new_bool_5 with 180s (1) cores 0.51/1.04 # Starting pre_casc_3 with 180s (1) cores 0.51/1.04 # Starting ho_unfolding_8 with 180s (1) cores 0.51/1.04 # Starting new_ho_10_cnf2 with 180s (1) cores 0.51/1.04 # Starting new_bool_3 with 180s (1) cores 0.51/1.04 # Starting new_ho_5 with 180s (1) cores 0.51/1.04 # new_bool_3 with pid 11724 completed with status 0 0.51/1.04 # Result found by new_bool_3 0.51/1.04 # Preprocessing class: HSLMSLSSLLLCHFA. 0.51/1.04 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.51/1.04 # Starting ehoh_best5 with 180s (1) cores 0.51/1.04 # Starting almost_fo_3_lam with 180s (1) cores 0.51/1.04 # Starting new_bool_5 with 180s (1) cores 0.51/1.04 # Starting pre_casc_3 with 180s (1) cores 0.51/1.04 # Starting ho_unfolding_8 with 180s (1) cores 0.51/1.04 # Starting new_ho_10_cnf2 with 180s (1) cores 0.51/1.04 # Starting new_bool_3 with 180s (1) cores 0.51/1.04 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.51/1.04 # Search class: HGHSM-FSLM32-MHFMMSBN 0.51/1.04 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 0.51/1.04 # Starting ho_unfolding_8 with 37s (1) cores 0.51/1.04 # ho_unfolding_8 with pid 11726 completed with status 0 0.51/1.04 # Result found by ho_unfolding_8 0.51/1.04 # Preprocessing class: HSLMSLSSLLLCHFA. 0.51/1.04 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.51/1.04 # Starting ehoh_best5 with 180s (1) cores 0.51/1.04 # Starting almost_fo_3_lam with 180s (1) cores 0.51/1.04 # Starting new_bool_5 with 180s (1) cores 0.51/1.04 # Starting pre_casc_3 with 180s (1) cores 0.51/1.04 # Starting ho_unfolding_8 with 180s (1) cores 0.51/1.04 # Starting new_ho_10_cnf2 with 180s (1) cores 0.51/1.04 # Starting new_bool_3 with 180s (1) cores 0.51/1.04 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.51/1.04 # Search class: HGHSM-FSLM32-MHFMMSBN 0.51/1.04 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 0.51/1.04 # Starting ho_unfolding_8 with 37s (1) cores 0.51/1.04 # Preprocessing time : 0.146 s 0.51/1.04 # Presaturation interreduction done 0.51/1.04 0.51/1.04 # Proof found! 0.51/1.04 # SZS status Theorem 0.51/1.04 # SZS output start CNFRefutation 0.51/1.04 thf(decl_22, type, in: $i > $i > $o). 0.51/1.04 thf(decl_23, type, exu: ($i > $o) > $o). 0.51/1.04 thf(decl_24, type, setextAx: $o). 0.51/1.04 thf(decl_25, type, emptyset: $i). 0.51/1.04 thf(decl_26, type, emptysetAx: $o). 0.51/1.04 thf(decl_27, type, setadjoin: $i > $i > $i). 0.51/1.04 thf(decl_28, type, setadjoinAx: $o). 0.51/1.04 thf(decl_29, type, powerset: $i > $i). 0.51/1.04 thf(decl_30, type, powersetAx: $o). 0.51/1.04 thf(decl_31, type, setunion: $i > $i). 0.51/1.04 thf(decl_32, type, setunionAx: $o). 0.51/1.04 thf(decl_33, type, omega: $i). 0.51/1.04 thf(decl_34, type, omega0Ax: $o). 0.51/1.04 thf(decl_35, type, omegaSAx: $o). 0.51/1.04 thf(decl_36, type, omegaIndAx: $o). 0.51/1.04 thf(decl_37, type, replAx: $o). 0.51/1.04 thf(decl_38, type, foundationAx: $o). 0.51/1.04 thf(decl_39, type, wellorderingAx: $o). 0.51/1.04 thf(decl_40, type, descr: ($i > $o) > $i). 0.51/1.04 thf(decl_41, type, descrp: $o). 0.51/1.04 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_43, type, dsetconstrI: $o). 0.51/1.04 thf(decl_44, type, dsetconstrEL: $o). 0.51/1.04 thf(decl_45, type, dsetconstrER: $o). 0.51/1.04 thf(decl_46, type, exuE1: $o). 0.51/1.04 thf(decl_47, type, prop2set: $o > $i). 0.51/1.04 thf(decl_48, type, prop2setE: $o). 0.51/1.04 thf(decl_49, type, emptysetE: $o). 0.51/1.04 thf(decl_50, type, emptysetimpfalse: $o). 0.51/1.04 thf(decl_51, type, notinemptyset: $o). 0.51/1.04 thf(decl_52, type, exuE3e: $o). 0.51/1.04 thf(decl_53, type, setext: $o). 0.51/1.04 thf(decl_54, type, emptyI: $o). 0.51/1.04 thf(decl_55, type, noeltsimpempty: $o). 0.51/1.04 thf(decl_56, type, setbeta: $o). 0.51/1.04 thf(decl_57, type, nonempty: $i > $o). 0.51/1.04 thf(decl_58, type, nonemptyE1: $o). 0.51/1.04 thf(decl_59, type, nonemptyI: $o). 0.51/1.04 thf(decl_60, type, nonemptyI1: $o). 0.51/1.04 thf(decl_61, type, setadjoinIL: $o). 0.51/1.04 thf(decl_62, type, emptyinunitempty: $o). 0.51/1.04 thf(decl_63, type, setadjoinIR: $o). 0.51/1.04 thf(decl_64, type, setadjoinE: $o). 0.51/1.04 thf(decl_65, type, setadjoinOr: $o). 0.51/1.04 thf(decl_66, type, setoftrueEq: $o). 0.51/1.04 thf(decl_67, type, powersetI: $o). 0.51/1.04 thf(decl_68, type, emptyinPowerset: $o). 0.51/1.04 thf(decl_69, type, emptyInPowerset: $o). 0.51/1.04 thf(decl_70, type, powersetE: $o). 0.51/1.04 thf(decl_71, type, setunionI: $o). 0.51/1.04 thf(decl_72, type, setunionE: $o). 0.51/1.04 thf(decl_73, type, subPowSU: $o). 0.51/1.04 thf(decl_74, type, exuE2: $o). 0.51/1.04 thf(decl_75, type, nonemptyImpWitness: $o). 0.51/1.04 thf(decl_76, type, uniqinunit: $o). 0.51/1.04 thf(decl_77, type, notinsingleton: $o). 0.51/1.04 thf(decl_78, type, eqinunit: $o). 0.51/1.04 thf(decl_79, type, singletonsswitch: $o). 0.51/1.04 thf(decl_80, type, upairsetE: $o). 0.51/1.04 thf(decl_81, type, upairsetIL: $o). 0.51/1.04 thf(decl_82, type, upairsetIR: $o). 0.51/1.04 thf(decl_83, type, emptyE1: $o). 0.51/1.04 thf(decl_84, type, vacuousDall: $o). 0.51/1.04 thf(decl_85, type, quantDeMorgan1: $o). 0.51/1.04 thf(decl_86, type, quantDeMorgan2: $o). 0.51/1.04 thf(decl_87, type, quantDeMorgan3: $o). 0.51/1.04 thf(decl_88, type, quantDeMorgan4: $o). 0.51/1.04 thf(decl_89, type, prop2setI: $o). 0.51/1.04 thf(decl_91, type, prop2set2propI: $o). 0.51/1.04 thf(decl_92, type, notdexE: $o). 0.51/1.04 thf(decl_93, type, notdallE: $o). 0.51/1.04 thf(decl_94, type, exuI1: $o). 0.51/1.04 thf(decl_95, type, exuI3: $o). 0.51/1.04 thf(decl_96, type, exuI2: $o). 0.51/1.04 thf(decl_97, type, inCongP: $o). 0.51/1.04 thf(decl_98, type, in__Cong: $o). 0.51/1.04 thf(decl_99, type, exuE3u: $o). 0.51/1.04 thf(decl_100, type, exu__Cong: $o). 0.51/1.04 thf(decl_101, type, emptyset__Cong: $o). 0.51/1.04 thf(decl_102, type, setadjoin__Cong: $o). 0.51/1.04 thf(decl_103, type, powerset__Cong: $o). 0.51/1.04 thf(decl_104, type, setunion__Cong: $o). 0.51/1.04 thf(decl_105, type, omega__Cong: $o). 0.51/1.04 thf(decl_106, type, exuEu: $o). 0.51/1.04 thf(decl_107, type, descr__Cong: $o). 0.51/1.04 thf(decl_108, type, dsetconstr__Cong: $o). 0.51/1.04 thf(decl_109, type, subset: $i > $i > $o). 0.51/1.04 thf(decl_112, type, subsetI1: $o). 0.51/1.04 thf(decl_113, type, eqimpsubset2: $o). 0.51/1.04 thf(decl_114, type, eqimpsubset1: $o). 0.51/1.04 thf(decl_115, type, subsetI2: $o). 0.51/1.04 thf(decl_116, type, emptysetsubset: $o). 0.51/1.04 thf(decl_117, type, subsetE: $o). 0.51/1.04 thf(decl_118, type, subsetE2: $o). 0.51/1.04 thf(decl_119, type, notsubsetI: $o). 0.51/1.04 thf(decl_120, type, notequalI1: $o). 0.51/1.04 thf(decl_121, type, notequalI2: $o). 0.51/1.04 thf(decl_122, type, subsetRefl: $o). 0.51/1.04 thf(decl_123, type, subsetTrans: $o). 0.51/1.04 thf(decl_124, type, setadjoinSub: $o). 0.51/1.04 thf(decl_125, type, setadjoinSub2: $o). 0.51/1.04 thf(decl_126, type, subset2powerset: $o). 0.51/1.04 thf(decl_127, type, setextsub: $o). 0.51/1.04 thf(decl_128, type, subsetemptysetimpeq: $o). 0.51/1.04 thf(decl_129, type, powersetI1: $o). 0.51/1.04 thf(decl_130, type, powersetE1: $o). 0.51/1.04 thf(decl_131, type, inPowerset: $o). 0.51/1.04 thf(decl_132, type, powersetsubset: $o). 0.51/1.04 thf(decl_133, type, sepInPowerset: $o). 0.51/1.04 thf(decl_134, type, sepSubset: $o). 0.51/1.04 thf(decl_135, type, binunion: $i > $i > $i). 0.51/1.04 thf(decl_136, type, binunionIL: $o). 0.51/1.04 thf(decl_137, type, upairset2IR: $o). 0.51/1.04 thf(decl_138, type, binunionIR: $o). 0.51/1.04 thf(decl_139, type, binunionEcases: $o). 0.51/1.04 thf(decl_140, type, binunionE: $o). 0.51/1.04 thf(decl_141, type, binunionLsub: $o). 0.51/1.04 thf(decl_142, type, binunionRsub: $o). 0.51/1.04 thf(decl_143, type, binintersect: $i > $i > $i). 0.51/1.04 thf(decl_144, type, binintersectI: $o). 0.51/1.04 thf(decl_145, type, binintersectSubset5: $o). 0.51/1.04 thf(decl_146, type, binintersectEL: $o). 0.51/1.04 thf(decl_147, type, binintersectLsub: $o). 0.51/1.04 thf(decl_148, type, binintersectSubset2: $o). 0.51/1.04 thf(decl_149, type, binintersectSubset3: $o). 0.51/1.04 thf(decl_150, type, binintersectER: $o). 0.51/1.04 thf(decl_151, type, disjointsetsI1: $o). 0.51/1.04 thf(decl_152, type, binintersectRsub: $o). 0.51/1.04 thf(decl_153, type, binintersectSubset4: $o). 0.51/1.04 thf(decl_154, type, binintersectSubset1: $o). 0.51/1.04 thf(decl_155, type, bs114d: $o). 0.51/1.04 thf(decl_157, type, setminus: $i > $i > $i). 0.51/1.04 thf(decl_158, type, setminusI: $o). 0.51/1.04 thf(decl_159, type, setminusEL: $o). 0.51/1.04 thf(decl_160, type, setminusER: $o). 0.51/1.04 thf(decl_161, type, setminusSubset2: $o). 0.51/1.04 thf(decl_162, type, setminusERneg: $o). 0.51/1.04 thf(decl_163, type, setminusELneg: $o). 0.51/1.04 thf(decl_164, type, setminusILneg: $o). 0.51/1.04 thf(decl_165, type, setminusIRneg: $o). 0.51/1.04 thf(decl_166, type, setminusLsub: $o). 0.51/1.04 thf(decl_167, type, setminusSubset1: $o). 0.51/1.04 thf(decl_168, type, symdiff: $i > $i > $i). 0.51/1.04 thf(decl_169, type, symdiffE: $o). 0.51/1.04 thf(decl_170, type, symdiffI1: $o). 0.51/1.04 thf(decl_171, type, symdiffI2: $o). 0.51/1.04 thf(decl_172, type, symdiffIneg1: $o). 0.51/1.04 thf(decl_173, type, symdiffIneg2: $o). 0.51/1.04 thf(decl_174, type, iskpair: $i > $o). 0.51/1.04 thf(decl_175, type, secondinupair: $o). 0.51/1.04 thf(decl_176, type, setukpairIL: $o). 0.51/1.04 thf(decl_177, type, setukpairIR: $o). 0.51/1.04 thf(decl_178, type, kpairiskpair: $o). 0.51/1.04 thf(decl_179, type, kpair: $i > $i > $i). 0.51/1.04 thf(decl_180, type, kpairp: $o). 0.51/1.04 thf(decl_181, type, cartprod: $i > $i > $i). 0.51/1.04 thf(decl_182, type, singletonsubset: $o). 0.51/1.04 thf(decl_183, type, singletoninpowerset: $o). 0.51/1.04 thf(decl_184, type, singletoninpowunion: $o). 0.51/1.04 thf(decl_185, type, upairset2E: $o). 0.51/1.04 thf(decl_186, type, upairsubunion: $o). 0.51/1.04 thf(decl_187, type, upairinpowunion: $o). 0.51/1.04 thf(decl_188, type, ubforcartprodlem1: $o). 0.51/1.04 thf(decl_189, type, ubforcartprodlem2: $o). 0.51/1.04 thf(decl_190, type, ubforcartprodlem3: $o). 0.51/1.04 thf(decl_191, type, cartprodpairin: $o). 0.51/1.04 thf(decl_192, type, cartprodmempair1: $o). 0.51/1.04 thf(decl_193, type, cartprodmempair: $o). 0.51/1.04 thf(decl_194, type, setunionE2: $o). 0.51/1.04 thf(decl_195, type, setunionsingleton1: $o). 0.51/1.04 thf(decl_196, type, setunionsingleton2: $o). 0.51/1.04 thf(decl_197, type, setunionsingleton: $o). 0.51/1.04 thf(decl_198, type, singleton: $i > $o). 0.51/1.04 thf(decl_199, type, singletonprop: $o). 0.51/1.04 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 0.51/1.04 thf(decl_201, type, ex1E1: $o). 0.51/1.04 thf(decl_202, type, ex1I: $o). 0.51/1.04 thf(decl_203, type, ex1I2: $o). 0.51/1.04 thf(decl_204, type, singletonsuniq: $o). 0.51/1.04 thf(decl_209, type, setukpairinjL1: $o). 0.51/1.04 thf(decl_210, type, kfstsingleton: $o). 0.51/1.04 thf(decl_211, type, theprop: $o). 0.51/1.04 thf(decl_212, type, kfst: $i > $i). 0.51/1.04 thf(decl_213, type, kfstpairEq: $o). 0.51/1.04 thf(decl_214, type, cartprodfstin: $o). 0.51/1.04 thf(decl_215, type, setukpairinjL2: $o). 0.51/1.04 thf(decl_216, type, setukpairinjL: $o). 0.51/1.04 thf(decl_217, type, setukpairinjR11: $o). 0.51/1.04 thf(decl_218, type, setukpairinjR12: $o). 0.51/1.04 thf(decl_219, type, setukpairinjR1: $o). 0.51/1.04 thf(decl_220, type, upairequniteq: $o). 0.51/1.04 thf(decl_221, type, setukpairinjR2: $o). 0.51/1.04 thf(decl_222, type, setukpairinjR: $o). 0.51/1.04 thf(decl_223, type, ksndsingleton: $o). 0.51/1.04 thf(decl_224, type, ksnd: $i > $i). 0.51/1.04 thf(decl_225, type, ksndpairEq: $o). 0.51/1.04 thf(decl_226, type, kpairsurjEq: $o). 0.51/1.04 thf(decl_227, type, cartprodsndin: $o). 0.51/1.04 thf(decl_228, type, cartprodpairmemEL: $o). 0.51/1.04 thf(decl_229, type, cartprodpairmemER: $o). 0.51/1.04 thf(decl_230, type, cartprodmempaircEq: $o). 0.51/1.04 thf(decl_231, type, cartprodfstpairEq: $o). 0.51/1.04 thf(decl_232, type, cartprodsndpairEq: $o). 0.51/1.04 thf(decl_233, type, cartprodpairsurjEq: $o). 0.51/1.04 thf(decl_234, type, breln: $i > $i > $i > $o). 0.51/1.04 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.51/1.04 thf(decl_236, type, dpsetconstrI: $o). 0.51/1.04 thf(decl_237, type, dpsetconstrSub: $o). 0.51/1.04 thf(decl_238, type, setOfPairsIsBReln: $o). 0.51/1.04 thf(decl_239, type, dpsetconstrERa: $o). 0.51/1.04 thf(decl_240, type, dpsetconstrEL1: $o). 0.51/1.04 thf(decl_241, type, dpsetconstrEL2: $o). 0.51/1.04 thf(decl_242, type, dpsetconstrER: $o). 0.51/1.04 thf(decl_243, type, func: $i > $i > $i > $o). 0.51/1.04 thf(decl_244, type, funcSet: $i > $i > $i). 0.51/1.04 thf(decl_245, type, funcImageSingleton: $o). 0.51/1.04 thf(decl_246, type, apProp: $o). 0.51/1.04 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 0.51/1.04 thf(decl_248, type, app: $o). 0.51/1.04 thf(decl_249, type, infuncsetfunc: $o). 0.51/1.04 thf(decl_250, type, ap2p: $o). 0.51/1.04 thf(decl_251, type, funcinfuncset: $o). 0.51/1.04 thf(decl_252, type, lamProp: $o). 0.51/1.04 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 0.51/1.04 thf(decl_254, type, lamp: $o). 0.51/1.04 thf(decl_255, type, lam2p: $o). 0.51/1.04 thf(decl_256, type, brelnall1: $o). 0.51/1.04 thf(decl_257, type, brelnall2: $o). 0.51/1.04 thf(decl_258, type, ex1E2: $o). 0.51/1.04 thf(decl_259, type, funcGraphProp1: $o). 0.51/1.04 thf(decl_260, type, funcGraphProp3: $o). 0.51/1.04 thf(decl_261, type, funcGraphProp2: $o). 0.51/1.04 thf(decl_262, type, funcextLem: $o). 0.51/1.04 thf(decl_263, type, funcGraphProp4: $o). 0.51/1.04 thf(decl_264, type, subbreln: $o). 0.51/1.04 thf(decl_265, type, eqbreln: $o). 0.51/1.04 thf(decl_266, type, funcext: $o). 0.51/1.04 thf(decl_267, type, funcext2: $o). 0.51/1.04 thf(decl_268, type, ap2apEq1: $o). 0.51/1.04 thf(decl_269, type, ap2apEq2: $o). 0.51/1.04 thf(decl_270, type, beta1: $o). 0.51/1.04 thf(decl_271, type, eta1: $o). 0.51/1.04 thf(decl_272, type, lam2lamEq: $o). 0.51/1.04 thf(decl_273, type, beta2: $o). 0.51/1.04 thf(decl_274, type, eta2: $o). 0.51/1.04 thf(decl_275, type, iffalseProp1: $o). 0.51/1.04 thf(decl_276, type, iffalseProp2: $o). 0.51/1.04 thf(decl_277, type, iftrueProp1: $o). 0.51/1.04 thf(decl_278, type, iftrueProp2: $o). 0.51/1.04 thf(decl_279, type, ifSingleton: $o). 0.51/1.04 thf(decl_280, type, if: $i > $o > $i > $i > $i). 0.51/1.04 thf(decl_281, type, ifp: $o). 0.51/1.04 thf(decl_282, type, theeq: $o). 0.51/1.04 thf(decl_283, type, iftrue: $o). 0.51/1.04 thf(decl_284, type, iffalse: $o). 0.51/1.04 thf(decl_285, type, iftrueorfalse: $o). 0.51/1.04 thf(decl_286, type, binintersectT_lem: $o). 0.51/1.04 thf(decl_287, type, binunionT_lem: $o). 0.51/1.04 thf(decl_288, type, powersetT_lem: $o). 0.51/1.04 thf(decl_289, type, setminusT_lem: $o). 0.51/1.04 thf(decl_290, type, complementT_lem: $o). 0.51/1.04 thf(decl_291, type, setextT: $o). 0.51/1.04 thf(decl_292, type, subsetTI: $o). 0.51/1.04 thf(decl_293, type, powersetTI1: $o). 0.51/1.04 thf(decl_294, type, powersetTE1: $o). 0.51/1.04 thf(decl_295, type, complementTI1: $o). 0.51/1.04 thf(decl_296, type, complementTE1: $o). 0.51/1.04 thf(decl_297, type, binintersectTELcontra: $o). 0.51/1.04 thf(decl_298, type, binintersectTERcontra: $o). 0.51/1.04 thf(decl_299, type, contrasubsetT: $o). 0.51/1.04 thf(decl_300, type, contrasubsetT1: $o). 0.51/1.04 thf(decl_301, type, contrasubsetT2: $o). 0.51/1.04 thf(decl_302, type, contrasubsetT3: $o). 0.51/1.04 thf(decl_303, type, doubleComplementI1: $o). 0.51/1.04 thf(decl_304, type, doubleComplementE1: $o). 0.51/1.04 thf(decl_305, type, doubleComplementSub1: $o). 0.51/1.04 thf(decl_306, type, doubleComplementSub2: $o). 0.51/1.04 thf(decl_307, type, doubleComplementEq: $o). 0.51/1.04 thf(decl_308, type, complementTnotintersectT: $o). 0.51/1.04 thf(decl_309, type, complementImpComplementIntersect: $o). 0.51/1.04 thf(decl_310, type, complementSubsetComplementIntersect: $o). 0.51/1.04 thf(decl_311, type, complementInPowersetComplementIntersect: $o). 0.51/1.04 thf(decl_312, type, contraSubsetComplement: $o). 0.51/1.04 thf(decl_313, type, complementTcontraSubset: $o). 0.51/1.04 thf(decl_314, type, binunionTILcontra: $o). 0.51/1.04 thf(decl_315, type, binunionTIRcontra: $o). 0.51/1.04 thf(decl_316, type, inIntersectImpInUnion: $o). 0.51/1.04 thf(decl_317, type, inIntersectImpInUnion2: $o). 0.51/1.04 thf(decl_318, type, inIntersectImpInIntersectUnions: $o). 0.51/1.04 thf(decl_319, type, intersectInPowersetIntersectUnions: $o). 0.51/1.04 thf(decl_320, type, inComplementUnionImpNotIn1: $o). 0.51/1.04 thf(decl_321, type, inComplementUnionImpInComplement1: $o). 0.51/1.04 thf(decl_322, type, binunionTE: $o). 0.51/1.04 thf(decl_323, type, binunionTEcontra: $o). 0.51/1.04 thf(decl_324, type, demorgan2a1: $o). 0.51/1.04 thf(decl_325, type, complementUnionInPowersetComplement: $o). 0.51/1.04 thf(decl_326, type, demorgan2a2: $o). 0.51/1.04 thf(decl_327, type, demorgan1a: $o). 0.51/1.04 thf(decl_328, type, demorgan1b: $o). 0.51/1.04 thf(decl_329, type, demorgan1: $o). 0.51/1.04 thf(decl_330, type, demorgan2a: $o). 0.51/1.04 thf(decl_331, type, demorgan2b2: $o). 0.51/1.04 thf(decl_332, type, demorgan2b: $o). 0.51/1.04 thf(decl_333, type, demorgan2: $o). 0.51/1.04 thf(decl_334, type, woz13rule0: $o). 0.51/1.04 thf(decl_335, type, woz13rule1: $o). 0.51/1.04 thf(decl_336, type, woz13rule2: $o). 0.51/1.04 thf(decl_337, type, woz13rule3: $o). 0.51/1.04 thf(decl_338, type, woz13rule4: $o). 0.51/1.04 thf(decl_339, type, woz1_1: $o). 0.51/1.04 thf(decl_340, type, woz1_2: $o). 0.51/1.04 thf(decl_341, type, woz1_3: $o). 0.51/1.04 thf(decl_342, type, woz1_4: $o). 0.51/1.04 thf(decl_343, type, woz1_5: $o). 0.51/1.04 thf(decl_344, type, breln1: $i > $i > $o). 0.51/1.04 thf(decl_345, type, breln1all2: $o). 0.51/1.04 thf(decl_346, type, breln1Set: $i > $i). 0.51/1.04 thf(decl_347, type, breln1SetBreln1: $o). 0.51/1.04 thf(decl_354, type, choice2fnsingleton: $o). 0.51/1.04 thf(decl_355, type, setOfPairsIsBReln1: $o). 0.51/1.04 thf(decl_356, type, breln1all1: $o). 0.51/1.04 thf(decl_357, type, subbreln1: $o). 0.51/1.04 thf(decl_358, type, eqbreln1: $o). 0.51/1.04 thf(decl_359, type, breln1invset: $i > $i > $i). 0.51/1.04 thf(decl_360, type, breln1invprop: $o). 0.51/1.04 thf(decl_361, type, breln1invI: $o). 0.51/1.04 thf(decl_362, type, breln1invE: $o). 0.51/1.04 thf(decl_363, type, breln1compset: $i > $i > $i > $i). 0.51/1.04 thf(decl_364, type, breln1compprop: $o). 0.51/1.04 thf(decl_365, type, breln1compI: $o). 0.51/1.04 thf(decl_366, type, breln1compE: $o). 0.51/1.04 thf(decl_367, type, breln1compEex: $o). 0.51/1.04 thf(decl_368, type, breln1unionprop: $o). 0.51/1.04 thf(decl_369, type, breln1unionIL: $o). 0.51/1.04 thf(decl_370, type, breln1unionIR: $o). 0.51/1.04 thf(decl_371, type, breln1unionI: $o). 0.51/1.04 thf(decl_372, type, breln1unionE: $o). 0.51/1.04 thf(decl_373, type, breln1unionEcases: $o). 0.51/1.04 thf(decl_374, type, breln1unionCommutes: $o). 0.51/1.04 thf(decl_375, type, woz2Ex: $o). 0.51/1.04 thf(decl_376, type, woz2W: $o). 0.51/1.04 thf(decl_377, type, woz2A: $o). 0.51/1.04 thf(decl_378, type, woz2B: $o). 0.51/1.04 thf(decl_379, type, image1Ex: $o). 0.51/1.04 thf(decl_380, type, image1Ex1: $o). 0.51/1.04 thf(decl_381, type, image1: $i > ($i > $i) > $i). 0.51/1.04 thf(decl_382, type, image1Equiv: $o). 0.51/1.04 thf(decl_383, type, image1E: $o). 0.51/1.04 thf(decl_384, type, image1I: $o). 0.51/1.04 thf(decl_385, type, injective: $i > $i > $i > $o). 0.51/1.04 thf(decl_386, type, injFuncSet: $i > $i > $i). 0.51/1.04 thf(decl_387, type, injFuncInInjFuncSet: $o). 0.51/1.04 thf(decl_388, type, epred1_0: $o). 0.51/1.04 thf(decl_389, type, esk1_2: $i > $i > $i). 0.51/1.04 thf(decl_390, type, esk2_2: $i > $i > $i). 0.51/1.04 thf(decl_391, type, esk3_2: $i > $i > $i). 0.51/1.04 thf(decl_392, type, esk4_1: $i > $i). 0.51/1.04 thf(decl_393, type, esk5_2: ($i > $i > $o) > $i > $i). 0.51/1.04 thf(decl_394, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.51/1.04 thf(decl_395, type, esk7_2: ($i > $i > $o) > $i > $i). 0.51/1.04 thf(decl_396, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.51/1.04 thf(decl_397, type, esk9_1: $i > $i). 0.51/1.04 thf(decl_398, type, esk10_2: ($i > $o) > $i > $i). 0.51/1.04 thf(decl_399, type, esk11_2: ($i > $o) > $i > $i). 0.51/1.04 thf(decl_400, type, esk12_1: ($i > $o) > $i). 0.51/1.04 thf(decl_401, type, esk13_2: ($i > $o) > $i > $i). 0.51/1.04 thf(decl_402, type, esk14_1: ($i > $o) > $i). 0.51/1.04 thf(decl_403, type, esk15_2: $i > $i > $i). 0.51/1.04 thf(decl_404, type, esk16_2: $i > $i > $i). 0.51/1.04 thf(decl_405, type, esk17_1: $i > $i). 0.51/1.04 thf(decl_406, type, esk18_1: $i > $i). 0.51/1.04 thf(decl_407, type, esk19_1: $i > $i). 0.51/1.04 thf(decl_408, type, esk20_2: $i > $i > $i). 0.51/1.04 thf(decl_409, type, esk21_3: $i > $i > $o > $i). 0.51/1.04 thf(decl_410, type, esk22_2: ($i > $o) > $i > $i). 0.51/1.04 thf(decl_411, type, esk23_1: ($i > $o) > $i). 0.51/1.04 thf(decl_412, type, esk24_1: $i > $i). 0.51/1.04 thf(decl_413, type, esk25_2: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_414, type, esk26_2: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_415, type, esk27_2: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_416, type, esk28_2: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_417, type, esk29_2: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_418, type, esk30_2: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_419, type, esk31_2: ($i > $o) > $i > $i). 0.51/1.04 thf(decl_420, type, esk32_1: ($i > $o) > $i). 0.51/1.04 thf(decl_421, type, esk33_1: ($i > $o) > $i). 0.51/1.04 thf(decl_422, type, esk34_1: ($i > $o) > $i). 0.51/1.04 thf(decl_423, type, esk35_1: ($i > $o) > $i). 0.51/1.04 thf(decl_424, type, esk36_2: ($i > $o) > $i > $i). 0.51/1.04 thf(decl_425, type, esk37_1: ($i > $o) > $i). 0.51/1.04 thf(decl_426, type, esk38_2: ($i > $o) > $i > $i). 0.51/1.04 thf(decl_427, type, esk39_2: ($i > $o) > ($i > $o) > $i). 0.51/1.04 thf(decl_428, type, esk40_2: ($i > $o) > ($i > $o) > $i). 0.51/1.04 thf(decl_429, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 0.51/1.04 thf(decl_430, type, esk42_2: ($i > $o) > ($i > $o) > $i). 0.51/1.04 thf(decl_431, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 0.51/1.04 thf(decl_432, type, esk44_2: ($i > $o) > ($i > $o) > $i). 0.51/1.04 thf(decl_433, type, esk45_2: ($i > $o) > $i > $i). 0.51/1.04 thf(decl_434, type, esk46_2: ($i > $o) > ($i > $o) > $i). 0.51/1.04 thf(decl_435, type, esk47_2: ($i > $o) > ($i > $o) > $i). 0.51/1.04 thf(decl_436, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 0.51/1.04 thf(decl_437, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 0.51/1.04 thf(decl_438, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.51/1.04 thf(decl_439, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.51/1.04 thf(decl_440, type, esk52_2: $i > $i > $i). 0.51/1.04 thf(decl_441, type, esk53_2: $i > $i > $i). 0.51/1.04 thf(decl_442, type, esk54_2: $i > $i > $i). 0.51/1.04 thf(decl_443, type, esk55_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_444, type, esk56_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_445, type, esk57_2: $i > $i > $i). 0.51/1.04 thf(decl_446, type, esk58_2: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_447, type, esk59_2: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_448, type, esk60_2: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_449, type, esk61_3: $i > ($i > $o) > $i > $i). 0.51/1.04 thf(decl_450, type, esk62_2: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_451, type, esk63_2: $i > ($i > $o) > $i). 0.51/1.04 thf(decl_452, type, esk64_3: $i > $i > ($i > $i) > $i). 0.51/1.04 thf(decl_453, type, esk65_3: $i > $i > ($i > $i) > $i). 0.51/1.04 thf(decl_454, type, esk66_3: $i > $i > ($i > $i) > $i). 0.51/1.04 thf(decl_455, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 0.51/1.04 thf(decl_456, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 0.51/1.04 thf(decl_457, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 0.51/1.04 thf(decl_458, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 0.51/1.04 thf(decl_459, type, esk71_4: $i > $i > $i > $i > $i). 0.51/1.04 thf(decl_460, type, esk72_4: $i > $i > $i > $i > $i). 0.51/1.04 thf(decl_461, type, esk73_4: $i > $i > $i > $i > $i). 0.51/1.04 thf(decl_462, type, esk74_4: $i > $i > $i > $i > $i). 0.51/1.04 thf(decl_463, type, esk75_4: $i > $i > $i > $i > $i). 0.51/1.04 thf(decl_464, type, esk76_4: $i > $i > $i > $i > $i). 0.51/1.04 thf(decl_465, type, esk77_4: $i > $i > $i > $i > $i). 0.51/1.04 thf(decl_466, type, esk78_4: $i > $i > $i > $i > $i). 0.51/1.04 thf(decl_467, type, esk79_4: $i > $i > $i > $i > $i). 0.51/1.04 thf(decl_468, type, esk80_3: $i > $i > ($i > $i) > $i). 0.51/1.04 thf(decl_469, type, esk81_3: $i > $i > ($i > $i) > $i). 0.51/1.04 thf(decl_470, type, esk82_3: $i > $i > ($i > $i) > $i). 0.51/1.04 thf(decl_471, type, esk83_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_472, type, esk84_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_473, type, esk85_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_474, type, esk86_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_475, type, esk87_3: $i > $i > ($i > $o) > $i). 0.51/1.04 thf(decl_476, type, esk88_3: $i > $i > ($i > $o) > $i). 0.51/1.04 thf(decl_477, type, esk89_3: $i > $i > ($i > $o) > $i). 0.51/1.04 thf(decl_478, type, esk90_3: $i > $i > ($i > $o) > $i). 0.51/1.04 thf(decl_479, type, esk91_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_480, type, esk92_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_481, type, esk93_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_482, type, esk94_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_483, type, esk95_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_484, type, esk96_3: $i > $i > $i > $i). 0.51/1.04 thf(decl_485, type, esk97_5: $i > $i > $i > $i > $i > $i). 0.51/1.04 thf(decl_486, type, esk98_6: $i > $i > $i > $i > $i > $o > $i). 0.51/1.04 thf(decl_487, type, esk99_2: $i > ($i > $i) > $i). 0.51/1.04 thf(decl_488, type, esk100_3: $i > ($i > $i) > $i > $i). 0.51/1.04 thf(decl_489, type, esk101_2: $i > ($i > $i) > $i). 0.51/1.04 thf(decl_490, type, esk102_3: $i > ($i > $i) > $i > $i). 0.51/1.04 thf(decl_491, type, esk103_3: $i > ($i > $i) > $i > $i). 0.51/1.04 thf(decl_492, type, esk104_3: $i > ($i > $i) > $i > $i). 0.51/1.04 thf(decl_493, type, esk105_3: $i > ($i > $i) > $i > $i). 0.51/1.04 thf(decl_494, type, esk106_3: $i > ($i > $i) > $i > $i). 0.51/1.04 thf(decl_495, type, esk107_0: $i). 0.51/1.04 thf(decl_496, type, esk108_0: $i). 0.51/1.04 thf(decl_497, type, esk109_0: $i). 0.51/1.04 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', exuEu)). 0.51/1.04 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', exu)). 0.51/1.04 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', exuE3u)). 0.51/1.04 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', exuI2)). 0.51/1.04 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', nonempty)). 0.51/1.04 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', exuE3e)). 0.51/1.04 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', replAx)). 0.51/1.04 thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', image1Ex1)). 0.51/1.04 thf(injFuncSet, axiom, ((injFuncSet)=(^[X4:$i, X5:$i]:(dsetconstr @ (funcSet @ X4 @ X5) @ (^[X29:$i]:((injective @ X4 @ X5 @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', injFuncSet)). 0.51/1.04 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', descr__Cong)). 0.51/1.04 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', exu__Cong)). 0.51/1.04 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', exuI3)). 0.51/1.04 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', exuI1)). 0.51/1.04 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', exuE2)). 0.51/1.04 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', nonemptyI)). 0.51/1.04 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', exuE1)). 0.51/1.04 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', descrp)). 0.51/1.04 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', singletonprop)). 0.51/1.04 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ex1I2)). 0.51/1.04 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', dpsetconstrI)). 0.51/1.04 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', nonemptyE1)). 0.51/1.04 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setOfPairsIsBReln)). 0.51/1.04 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', dsetconstrEL)). 0.51/1.04 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', dpsetconstrERa)). 0.51/1.04 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', dpsetconstrEL1)). 0.51/1.04 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', funcImageSingleton)). 0.51/1.04 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', apProp)). 0.51/1.04 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ex1E2)). 0.51/1.04 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', beta1)). 0.51/1.04 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', eta1)). 0.51/1.04 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', lam2lamEq)). 0.51/1.04 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', iffalseProp1)). 0.51/1.04 thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', image1Equiv)). 0.51/1.04 thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', injFuncInInjFuncSet)). 0.51/1.04 thf(image1I, axiom, ((image1I)<=>![X4:$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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', image1I)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', image1E)). 0.51/1.04 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setOfPairsIsBReln1)). 0.51/1.04 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ifSingleton)). 0.51/1.04 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', iftrueProp2)). 0.51/1.04 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', iftrueProp1)). 0.51/1.04 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', iffalseProp2)). 0.51/1.04 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', eta2)). 0.51/1.04 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', beta2)). 0.51/1.04 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', lam2p)). 0.51/1.04 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', lamp)). 0.51/1.04 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', lamProp)). 0.51/1.04 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', dpsetconstrER)). 0.51/1.04 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', dpsetconstrEL2)). 0.51/1.04 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', dpsetconstrSub)). 0.51/1.04 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ksndsingleton)). 0.51/1.04 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', kfstsingleton)). 0.51/1.04 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ex1I)). 0.51/1.04 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ex1E1)). 0.51/1.04 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', sepSubset)). 0.51/1.04 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', sepInPowerset)). 0.51/1.04 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', dsetconstr__Cong)). 0.51/1.04 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', emptyE1)). 0.51/1.04 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', nonemptyImpWitness)). 0.51/1.04 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setoftrueEq)). 0.51/1.04 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', nonemptyI1)). 0.51/1.04 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setbeta)). 0.51/1.04 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', dsetconstrER)). 0.51/1.04 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', dsetconstrI)). 0.51/1.04 thf(injFuncSetFuncIn, conjecture, ((setextAx)=>(((setadjoinAx)=>(((((omegaSAx)=>((omegaIndAx)=>((((wellorderingAx)=>((descrp)=>((dsetconstrI)=>(((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>(((notinemptyset)=>(((setext)=>((emptyI)=>(((setbeta)=>(((nonemptyI)=>((nonemptyI1)=>(((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((((emptyInPowerset)=>((powersetE)=>((setunionI)=>((((exuE2)=>((nonemptyImpWitness)=>((((eqinunit)=>((((((emptyE1)=>(((quantDeMorgan1)=>((((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>(((notdallE)=>((exuI1)=>((exuI3)=>((((in__Cong)=>(((exu__Cong)=>((((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>(((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>(((((((subsetE2)=>((notsubsetI)=>((notequalI1)=>(((subsetRefl)=>((subsetTrans)=>(((setadjoinSub2)=>((((((powersetE1)=>((inPowerset)=>(((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((((binunionEcases)=>((((((binintersectSubset5)=>(((binintersectLsub)=>((((((binintersectRsub)=>(((binintersectSubset1)=>((bs114d)=>(((setminusEL)=>(((setminusSubset2)=>(((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>(((((symdiffI2)=>(((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>(((upairinpowunion)=>(((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>(((setunionE2)=>(((setunionsingleton2)=>(((singletonprop)=>((((ex1I2)=>((singletonsuniq)=>((((theprop)=>((((setukpairinjL2)=>(((((setukpairinjR1)=>((((setukpairinjR)=>((((((((((((dpsetconstrI)=>(((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((((funcImageSingleton)=>((apProp)=>((app)=>((((funcinfuncset)=>(((((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>(((funcGraphProp2)=>(((funcGraphProp4)=>(((eqbreln)=>((funcext)=>((funcext2)=>(((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((((iffalseProp1)=>(((((((theeq)=>((iftrue)=>((((((((complementT_lem)=>((((powersetTI1)=>((((((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>(((((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>(((complementTnotintersectT)=>(((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((((binunionTIRcontra)=>(((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>(((((complementUnionInPowersetComplement)=>((((demorgan1b)=>(((demorgan2a)=>(((((((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((((((woz1_5)=>((breln1all2)=>(((((breln1all1)=>((subbreln1)=>(((breln1invprop)=>((breln1invI)=>(((breln1compprop)=>((breln1compI)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>(((breln1unionIR)=>((((((((woz2A)=>((((image1Ex1)=>((image1Equiv)=>(((![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))<=(in @ X29 @ (injFuncSet @ X4 @ X5))))<=(injFuncInInjFuncSet))<=(image1I))<=(image1E))))<=(image1Ex))<=(woz2B)))<=(woz2W))<=(woz2Ex))<=(breln1unionCommutes))<=(breln1unionEcases))<=(breln1unionE))<=(breln1unionI)))<=(breln1unionIL)))))))<=(breln1invE))))<=(eqbreln1))))<=(setOfPairsIsBReln1))<=(choice2fnsingleton))<=(breln1SetBreln1))))<=(woz1_4))<=(woz1_3))<=(woz1_2))<=(woz1_1)))))<=(woz13rule1))<=(woz13rule0))<=(demorgan2))<=(demorgan2b))<=(demorgan2b2)))<=(demorgan1)))<=(demorgan1a))<=(demorgan2a2)))<=(demorgan2a1))<=(binunionTEcontra))<=(binunionTE)))))))<=(inIntersectImpInUnion)))<=(binunionTILcontra))<=(complementTcontraSubset)))))<=(complementImpComplementIntersect)))<=(doubleComplementEq)))))<=(doubleComplementI1))<=(contrasubsetT3))<=(contrasubsetT2)))))<=(binintersectTELcontra))<=(complementTE1))<=(complementTI1))<=(powersetTE1)))<=(subsetTI))<=(setextT)))<=(setminusT_lem))<=(powersetT_lem))<=(binunionT_lem))<=(binintersectT_lem))<=(iftrueorfalse))<=(iffalse))))<=(ifp))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2)))<=(eta2))<=(beta2))))))<=(ap2apEq1)))))<=(subbreln)))<=(funcextLem)))<=(funcGraphProp3))))))<=(lam2p))<=(lamp))<=(lamProp)))<=(ap2p))<=(infuncsetfunc)))))<=(dpsetconstrER))<=(dpsetconstrEL2)))))<=(dpsetconstrSub)))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton)))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12))<=(setukpairinjR11))<=(setukpairinjL)))<=(cartprodfstin))<=(kfstpairEq)))<=(kfstsingleton))<=(setukpairinjL1))))<=(ex1I))<=(ex1E1)))<=(setunionsingleton)))<=(setunionsingleton1)))<=(cartprodmempair))))))<=(ubforcartprodlem1)))<=(upairsubunion)))))<=(singletonsubset))<=(kpairp)))))))<=(symdiffIneg1)))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1))))))<=(setminusERneg)))<=(setminusER)))<=(setminusI))))<=(binintersectSubset4)))<=(disjointsetsI1))<=(binintersectER))<=(binintersectSubset3))<=(binintersectSubset2)))<=(binintersectEL)))<=(binintersectI))<=(binunionRsub))<=(binunionLsub))<=(binunionE)))<=(binunionIR))<=(upairset2IR)))))<=(powersetsubset))))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset)))<=(setadjoinSub))))<=(notequalI2)))))<=(subsetE))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2)))))<=(exuEu)))))<=(setadjoin__Cong))<=(emptyset__Cong)))<=(exuE3u)))<=(inCongP))<=(exuI2)))))<=(notdexE)))))<=(quantDeMorgan3))<=(quantDeMorgan2)))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch)))<=(notinsingleton))<=(uniqinunit))))<=(subPowSU))<=(setunionE)))))<=(emptyinPowerset))<=(powersetI)))))))<=(setadjoinIL))))<=(nonemptyE1)))<=(noeltsimpempty))))<=(exuE3e)))<=(emptysetimpfalse))))))<=(dsetconstrEL)))))<=(foundationAx))<=(replAx))))<=(omega0Ax))<=(setunionAx))<=(powersetAx)))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', injFuncSetFuncIn)). 0.51/1.04 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', eqimpsubset2)). 0.51/1.04 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', emptysetAx)). 0.51/1.04 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectSubset3)). 0.51/1.04 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', secondinupair)). 0.51/1.04 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectSubset2)). 0.51/1.04 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectEL)). 0.51/1.04 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', upairinpowunion)). 0.51/1.04 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectI)). 0.51/1.04 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binunionRsub)). 0.51/1.04 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binunionLsub)). 0.51/1.04 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ubforcartprodlem2)). 0.51/1.04 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binunionE)). 0.51/1.04 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binunionIR)). 0.51/1.04 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ubforcartprodlem3)). 0.51/1.04 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', upairset2IR)). 0.51/1.04 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', powersetsubset)). 0.51/1.04 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', powersetI1)). 0.51/1.04 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', cartprodpairin)). 0.51/1.04 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subsetemptysetimpeq)). 0.51/1.04 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setextsub)). 0.51/1.04 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', cartprodmempair1)). 0.51/1.04 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subset2powerset)). 0.51/1.04 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setukpairIL)). 0.51/1.04 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setadjoinSub)). 0.51/1.04 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', notequalI2)). 0.51/1.04 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subsetE)). 0.51/1.04 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setunionE2)). 0.51/1.04 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', emptysetsubset)). 0.51/1.04 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subsetI2)). 0.51/1.04 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setunionsingleton2)). 0.51/1.04 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', eqimpsubset1)). 0.51/1.04 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', funcinfuncset)). 0.51/1.04 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setukpairIR)). 0.51/1.04 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setadjoin__Cong)). 0.51/1.04 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', emptyset__Cong)). 0.51/1.04 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', inCongP)). 0.51/1.04 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', notdexE)). 0.51/1.04 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', quantDeMorgan3)). 0.51/1.04 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', singletonsuniq)). 0.51/1.04 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', quantDeMorgan2)). 0.51/1.04 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', vacuousDall)). 0.51/1.04 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', theprop)). 0.51/1.04 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', upairsetIR)). 0.51/1.04 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', upairsetIL)). 0.51/1.04 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', upairsetE)). 0.51/1.04 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setukpairinjL2)). 0.51/1.04 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', singletonsswitch)). 0.51/1.04 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', notinsingleton)). 0.51/1.04 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setukpairinjR1)). 0.51/1.04 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', uniqinunit)). 0.51/1.04 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subPowSU)). 0.51/1.04 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setunionE)). 0.51/1.04 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setukpairinjR)). 0.51/1.04 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', emptyinPowerset)). 0.51/1.04 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', powersetI)). 0.51/1.04 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setadjoinIL)). 0.51/1.04 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', noeltsimpempty)). 0.51/1.04 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', emptysetimpfalse)). 0.51/1.04 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', foundationAx)). 0.51/1.04 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', omega0Ax)). 0.51/1.04 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setunionAx)). 0.51/1.04 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', powersetAx)). 0.51/1.04 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', app)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', intersectInPowersetIntersectUnions)). 0.51/1.04 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', brelnall1)). 0.51/1.04 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', brelnall2)). 0.51/1.04 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', funcGraphProp1)). 0.51/1.04 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', funcGraphProp2)). 0.51/1.04 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', funcGraphProp4)). 0.51/1.04 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', eqbreln)). 0.51/1.04 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', funcext)). 0.51/1.04 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', kpairiskpair)). 0.51/1.04 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', funcext2)). 0.51/1.04 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', singletoninpowerset)). 0.51/1.04 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ap2apEq2)). 0.51/1.04 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', theeq)). 0.51/1.04 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', iftrue)). 0.51/1.04 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', complementT_lem)). 0.51/1.04 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', powersetTI1)). 0.51/1.04 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectTERcontra)). 0.51/1.04 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', contrasubsetT)). 0.51/1.04 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', contrasubsetT1)). 0.51/1.04 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', doubleComplementE1)). 0.51/1.04 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', doubleComplementSub1)). 0.51/1.04 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', doubleComplementSub2)). 0.51/1.04 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', complementTnotintersectT)). 0.51/1.04 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', complementSubsetComplementIntersect)). 0.51/1.04 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', complementInPowersetComplementIntersect)). 0.51/1.04 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', contraSubsetComplement)). 0.51/1.04 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binunionTIRcontra)). 0.51/1.04 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', inIntersectImpInUnion2)). 0.51/1.04 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', inIntersectImpInIntersectUnions)). 0.51/1.04 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subsetTI)). 0.51/1.04 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setextT)). 0.51/1.04 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setminusT_lem)). 0.51/1.04 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', powersetT_lem)). 0.51/1.04 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binunionT_lem)). 0.51/1.04 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectT_lem)). 0.51/1.04 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', inComplementUnionImpNotIn1)). 0.51/1.04 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', inComplementUnionImpInComplement1)). 0.51/1.04 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', complementUnionInPowersetComplement)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', demorgan1b)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', demorgan2a)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz13rule2)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz13rule3)). 0.51/1.04 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:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz13rule4)). 0.51/1.04 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz1_5)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1all2)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1all1)). 0.51/1.04 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subbreln1)). 0.51/1.04 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1invprop)). 0.51/1.04 thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1invI)). 0.51/1.04 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1compprop)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1compI)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1compE)). 0.51/1.04 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:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1compEex)). 0.51/1.04 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1unionprop)). 0.51/1.04 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', singletoninpowunion)). 0.51/1.04 thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1unionIR)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz2A)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', image1Ex)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz2B)). 0.51/1.04 thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz2W)). 0.51/1.04 thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz2Ex)). 0.51/1.04 thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1unionCommutes)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1unionEcases)). 0.51/1.04 thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1unionE)). 0.51/1.04 thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1unionI)). 0.51/1.04 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1unionIL)). 0.51/1.04 thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1invE)). 0.51/1.04 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', eqbreln1)). 0.51/1.04 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', breln1SetBreln1)). 0.51/1.04 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz1_4)). 0.51/1.04 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz1_3)). 0.51/1.04 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz1_2)). 0.51/1.04 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz1_1)). 0.51/1.04 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz13rule1)). 0.51/1.04 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', woz13rule0)). 0.51/1.04 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', demorgan2)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', demorgan2b)). 0.51/1.04 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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', demorgan2b2)). 0.51/1.04 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', demorgan1)). 0.51/1.04 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', demorgan1a)). 0.51/1.04 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', demorgan2a2)). 0.51/1.04 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', demorgan2a1)). 0.51/1.04 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binunionTEcontra)). 0.51/1.04 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binunionTE)). 0.51/1.04 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', inIntersectImpInUnion)). 0.51/1.04 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binunionTILcontra)). 0.51/1.04 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', complementTcontraSubset)). 0.51/1.04 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', complementImpComplementIntersect)). 0.51/1.04 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', doubleComplementEq)). 0.51/1.04 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', doubleComplementI1)). 0.51/1.04 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', contrasubsetT3)). 0.51/1.04 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', contrasubsetT2)). 0.51/1.04 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectTELcontra)). 0.51/1.04 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', complementTE1)). 0.51/1.04 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', complementTI1)). 0.51/1.04 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', powersetTE1)). 0.51/1.04 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', iftrueorfalse)). 0.51/1.04 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', iffalse)). 0.51/1.04 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ifp)). 0.51/1.04 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ap2apEq1)). 0.51/1.04 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subbreln)). 0.51/1.04 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', funcextLem)). 0.51/1.04 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', funcGraphProp3)). 0.51/1.04 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ap2p)). 0.51/1.04 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', infuncsetfunc)). 0.51/1.04 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', cartprodpairsurjEq)). 0.51/1.04 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', cartprodsndpairEq)). 0.51/1.04 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', cartprodfstpairEq)). 0.51/1.04 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', cartprodmempaircEq)). 0.51/1.04 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', cartprodpairmemER)). 0.51/1.04 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', cartprodpairmemEL)). 0.51/1.04 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', cartprodsndin)). 0.51/1.04 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', kpairsurjEq)). 0.51/1.04 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ksndpairEq)). 0.51/1.04 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setukpairinjR2)). 0.51/1.04 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', upairequniteq)). 0.51/1.04 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setukpairinjR12)). 0.51/1.04 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setukpairinjR11)). 0.51/1.04 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setukpairinjL)). 0.51/1.04 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', cartprodfstin)). 0.51/1.04 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', kfstpairEq)). 0.51/1.04 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setukpairinjL1)). 0.51/1.04 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setunionsingleton)). 0.51/1.04 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setunionsingleton1)). 0.51/1.04 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', cartprodmempair)). 0.51/1.04 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', ubforcartprodlem1)). 0.51/1.04 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', upairsubunion)). 0.51/1.04 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', singletonsubset)). 0.51/1.04 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', kpairp)). 0.51/1.04 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', symdiffIneg1)). 0.51/1.04 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', symdiffI1)). 0.51/1.04 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', symdiffE)). 0.51/1.04 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setminusSubset1)). 0.51/1.04 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setminusERneg)). 0.51/1.04 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setminusER)). 0.51/1.04 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setminusI)). 0.51/1.04 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectSubset4)). 0.51/1.04 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', disjointsetsI1)). 0.51/1.04 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectER)). 0.51/1.04 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', upairset2E)). 0.51/1.04 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', symdiffIneg2)). 0.51/1.04 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', symdiffI2)). 0.51/1.04 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setminusLsub)). 0.51/1.04 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setminusIRneg)). 0.51/1.04 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setminusILneg)). 0.51/1.04 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setminusELneg)). 0.51/1.04 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setminusSubset2)). 0.51/1.04 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setminusEL)). 0.51/1.04 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', bs114d)). 0.51/1.04 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectSubset1)). 0.51/1.04 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectRsub)). 0.51/1.04 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectLsub)). 0.51/1.04 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binintersectSubset5)). 0.51/1.04 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binunionEcases)). 0.51/1.04 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', binunionIL)). 0.51/1.04 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', inPowerset)). 0.51/1.04 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', powersetE1)). 0.51/1.04 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setadjoinSub2)). 0.51/1.04 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subsetTrans)). 0.51/1.04 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subsetRefl)). 0.51/1.04 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', notequalI1)). 0.51/1.04 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', notsubsetI)). 0.51/1.04 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subsetE2)). 0.51/1.04 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', subsetI1)). 0.51/1.04 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', omega__Cong)). 0.51/1.04 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setunion__Cong)). 0.51/1.04 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', powerset__Cong)). 0.51/1.04 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', in__Cong)). 0.51/1.04 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', notdallE)). 0.51/1.04 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', prop2setI)). 0.51/1.04 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', quantDeMorgan4)). 0.51/1.04 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', quantDeMorgan1)). 0.51/1.04 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', eqinunit)). 0.51/1.04 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setunionI)). 0.51/1.04 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', powersetE)). 0.51/1.04 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', emptyInPowerset)). 0.51/1.04 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setadjoinOr)). 0.51/1.04 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setadjoinE)). 0.51/1.04 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setadjoinIR)). 0.51/1.04 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', emptyinunitempty)). 0.51/1.04 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', emptyI)). 0.51/1.04 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setext)). 0.51/1.04 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', notinemptyset)). 0.51/1.04 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', emptysetE)). 0.51/1.04 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', prop2setE)). 0.51/1.04 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', wellorderingAx)). 0.51/1.04 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', omegaIndAx)). 0.51/1.04 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', omegaSAx)). 0.51/1.04 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setadjoinAx)). 0.51/1.04 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.LlLII3FuHH/Vampire---4.8_11301', setextAx)). 0.51/1.04 thf(c_0_317, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.51/1.04 thf(c_0_318, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.51/1.04 thf(c_0_319, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.51/1.04 thf(c_0_320, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.51/1.04 thf(c_0_321, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.51/1.04 thf(c_0_322, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.51/1.04 thf(c_0_323, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.51/1.04 thf(c_0_324, plain, ((image1Ex1)<=>![X4:$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])). 0.51/1.04 thf(c_0_325, plain, ((injFuncSet)=(^[Z0/* 19 */:$i, Z1:$i]:(dsetconstr @ (funcSet @ Z0 @ Z1) @ (^[Z2/* 3 */:$i]:((injective @ Z0 @ Z1 @ Z2)))))), inference(fof_simplification,[status(thm)],[injFuncSet])). 0.51/1.04 thf(c_0_326, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.51/1.04 thf(c_0_327, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.51/1.04 thf(c_0_328, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.51/1.04 thf(c_0_329, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.51/1.04 thf(c_0_330, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.51/1.04 thf(c_0_331, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.51/1.04 thf(c_0_332, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.51/1.04 thf(c_0_333, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.51/1.04 thf(c_0_334, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1120:$i]:((((X1 @ X1120))&![X1121:$i]:((((X1 @ X1121))=>((X1120)=(X1121)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_317, c_0_318])). 0.51/1.04 thf(c_0_335, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.51/1.04 thf(c_0_336, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1114:$i]:((((X1 @ X1114))&![X1115:$i]:((((X1 @ X1115))=>((X1114)=(X1115)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_319, c_0_318])). 0.51/1.04 thf(c_0_337, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.51/1.04 thf(c_0_338, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1112:$i]:((((X1 @ X1112))&![X1113:$i]:((((X1 @ X1113))=>((X1112)=(X1113))))))))))), inference(apply_def,[status(thm)],[c_0_320, c_0_318])). 0.51/1.04 thf(c_0_339, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 0.51/1.04 thf(c_0_340, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_321])). 0.51/1.04 thf(c_0_341, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1104:$i]:((((X1 @ X1104))&![X1105:$i]:((((X1 @ X1105))=>((X1104)=(X1105)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_322, c_0_318])). 0.51/1.04 thf(c_0_342, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 0.51/1.04 thf(c_0_343, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.51/1.04 thf(c_0_344, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 0.51/1.04 thf(c_0_345, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1098:$i]:((((X6 @ X2 @ X1098))&![X1099:$i]:((((X6 @ X2 @ X1099))=>((X1098)=(X1099)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_323, c_0_318])). 0.51/1.04 thf(c_0_346, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 0.51/1.04 thf(c_0_347, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 0.51/1.04 thf(c_0_348, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 0.51/1.04 thf(c_0_349, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 0.51/1.04 thf(c_0_350, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 0.51/1.04 thf(c_0_351, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 0.51/1.04 thf(c_0_352, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 0.51/1.04 thf(c_0_353, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 0.51/1.04 thf(c_0_354, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1126:$i]:(((![X2:$i]:(((in @ X2 @ X1126)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))&![X1127:$i]:(((![X2:$i]:(((in @ X2 @ X1127)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))=>((X1126)=(X1127)))))))))), inference(apply_def,[status(thm)],[c_0_324, c_0_318])). 0.51/1.04 thf(c_0_355, plain, ((image1Equiv)<=>![X4:$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])). 0.51/1.04 thf(c_0_356, axiom, ((injFuncInInjFuncSet)=(![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (dsetconstr @ (funcSet @ X4 @ X5) @ (^[Z0/* 3 */:$i]:((injective @ X4 @ X5 @ Z0)))))))))), inference(apply_def,[status(thm)],[injFuncInInjFuncSet, c_0_325])). 0.51/1.04 thf(c_0_357, 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])). 0.51/1.04 thf(c_0_358, 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])). 0.51/1.04 thf(c_0_359, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])). 0.51/1.04 thf(c_0_360, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 0.51/1.04 thf(c_0_361, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 0.51/1.04 thf(c_0_362, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 0.51/1.04 thf(c_0_363, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 0.51/1.04 thf(c_0_364, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 0.51/1.04 thf(c_0_365, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 0.51/1.04 thf(c_0_366, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 0.51/1.04 thf(c_0_367, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 0.51/1.04 thf(c_0_368, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 0.51/1.04 thf(c_0_369, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 0.51/1.04 thf(c_0_370, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 0.51/1.04 thf(c_0_371, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 0.51/1.04 thf(c_0_372, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 0.51/1.04 thf(c_0_373, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 0.51/1.04 thf(c_0_374, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 0.51/1.04 thf(c_0_375, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.51/1.04 thf(c_0_376, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.51/1.04 thf(c_0_377, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.51/1.04 thf(c_0_378, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.51/1.04 thf(c_0_379, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1122:$i]:((((X1 @ X1122))&![X1123:$i]:((((X1 @ X1123))=>((X1122)=(X1123)))))))=>((?[X1124:$i]:((((X17 @ X1124))&![X1125:$i]:((((X17 @ X1125))=>((X1124)=(X1125)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_326, c_0_318])). 0.51/1.04 thf(c_0_380, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1116:$i]:((((X1 @ X1116))&![X1117:$i]:((((X1 @ X1117))=>((X1116)=(X1117)))))))<=>(?[X1118:$i]:((((X17 @ X1118))&![X1119:$i]:((((X17 @ X1119))=>((X1118)=(X1119)))))))))))), inference(apply_def,[status(thm)],[c_0_327, c_0_318])). 0.51/1.04 thf(c_0_381, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1110:$i]:((((X1 @ X1110))&![X1111:$i]:((((X1 @ X1111))=>((X1110)=(X1111)))))))))))), inference(apply_def,[status(thm)],[c_0_328, c_0_318])). 0.51/1.04 thf(c_0_382, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1108:$i]:((((X1 @ X1108))&![X1109:$i]:((((X1 @ X1109))=>((X1108)=(X1109))))))))))), inference(apply_def,[status(thm)],[c_0_329, c_0_318])). 0.51/1.04 thf(c_0_383, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 0.51/1.04 thf(c_0_384, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_321])). 0.51/1.04 thf(c_0_385, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1106:$i]:((((X1 @ X1106))&![X1107:$i]:((((X1 @ X1107))=>((X1106)=(X1107)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_330, c_0_318])). 0.51/1.04 thf(c_0_386, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.51/1.04 thf(c_0_387, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_321])). 0.51/1.04 thf(c_0_388, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_331, c_0_321])). 0.51/1.04 thf(c_0_389, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.51/1.04 thf(c_0_390, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1102:$i]:((((X1 @ X1102))&![X1103:$i]:((((X1 @ X1103))=>((X1102)=(X1103)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_332, c_0_318])). 0.51/1.04 thf(c_0_391, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.51/1.04 thf(c_0_392, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.51/1.04 thf(c_0_393, plain, ((descrp)=(![X1:$i > $o]:(((?[X1100:$i]:((((X1 @ X1100))&![X1101:$i]:((((X1 @ X1101))=>((X1100)=(X1101)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_333, c_0_318])). 0.51/1.04 thf(c_0_394, plain, ((epred1_0)<=>![X1138:$i]:(?[X1139:$i]:((((![X1140:$i]:(((in @ X1140 @ X1139)=>![X1141:$i]:(((in @ X1141 @ X1140)=>(in @ X1141 @ X1138)))))&![X1142:$i, X1143:$i]:((((in @ X1142 @ X1138)&(in @ X1143 @ X1138))=>(![X1144:$i]:(((in @ X1144 @ X1139)=>((in @ X1142 @ X1144)<=>(in @ X1143 @ X1144))))=>((X1142)=(X1143))))))&![X1145:$i, X1146:$i]:((((in @ X1145 @ X1139)&(in @ X1146 @ X1139))=>(![X1147:$i]:(((in @ X1147 @ X1145)=>(in @ X1147 @ X1146)))|![X1148:$i]:(((in @ X1148 @ X1146)=>(in @ X1148 @ X1145)))))))&![X1149:$i]:(((![X1150:$i]:(((in @ X1150 @ X1149)=>(in @ X1150 @ X1138)))&?[X1151:$i]:((in @ X1151 @ X1149)))=>?[X1152:$i, X1153:$i]:(((((in @ X1152 @ X1139)&(in @ X1153 @ X1149))&~(?[X1154:$i]:(((in @ X1154 @ X1152)&(in @ X1154 @ X1149)))))&![X1155:$i]:(((in @ X1155 @ X1139)=>(![X1156:$i]:(((in @ X1156 @ X1155)=>(in @ X1156 @ X1152)))|(in @ X1153 @ X1155)))))))))))), introduced(definition)). 0.51/1.04 thf(c_0_395, negated_conjecture, ~((![X1128:$i, X1129:$i]:((![X1130:$i]:(((in @ X1130 @ X1128)<=>(in @ X1130 @ X1129)))=>((X1128)=(X1129))))=>(![X2194:$i]:(~(in @ X2194 @ emptyset))=>(![X1131:$i, X1132:$i, X1133:$i]:(((in @ X1133 @ (setadjoin @ X1131 @ X1132))<=>(((X1133)=(X1131))|(in @ X1133 @ X1132))))=>(![X2191:$i, X2192:$i]:(((in @ X2192 @ (powerset @ X2191))<=>![X2193:$i]:(((in @ X2193 @ X2192)=>(in @ X2193 @ X2191)))))=>(![X2188:$i, X2189:$i]:(((in @ X2189 @ (setunion @ X2188))<=>?[X2190:$i]:(((in @ X2189 @ X2190)&(in @ X2190 @ X2188)))))=>((in @ emptyset @ omega)=>(![X1134:$i]:(((in @ X1134 @ omega)=>(in @ (setadjoin @ X1134 @ X1134) @ omega)))=>(![X1135:$i]:((((in @ emptyset @ X1135)&![X1136:$i]:((((in @ X1136 @ omega)&(in @ X1136 @ X1135))=>(in @ (setadjoin @ X1136 @ X1136) @ X1135))))=>![X1137:$i]:(((in @ X1137 @ omega)=>(in @ X1137 @ X1135)))))=>(![X2180:$i > $i > $o, X2181:$i]:((![X2182:$i]:(((in @ X2182 @ X2181)=>?[X2183:$i]:(((X2180 @ X2182 @ X2183)&![X2184:$i]:(((X2180 @ X2182 @ X2184)=>((X2183)=(X2184))))))))=>?[X2185:$i]:(![X2186:$i]:(((in @ X2186 @ X2185)<=>?[X2187:$i]:(((in @ X2187 @ X2181)&(X2180 @ X2187 @ X2186))))))))=>(![X2176:$i]:((?[X2177:$i]:((in @ X2177 @ X2176))=>?[X2178:$i]:(((in @ X2178 @ X2176)&~(?[X2179:$i]:(((in @ X2179 @ X2178)&(in @ X2179 @ X2176))))))))=>((epred1_0)=>(![X1157:$i > $o]:((?[X1158:$i]:(((X1157 @ X1158)&![X1159:$i]:(((X1157 @ X1159)=>((X1158)=(X1159))))))=>(X1157 @ (descr @ (^[Z0/* 3 */:$i]:((X1157 @ Z0)))))))=>(![X1160:$i, X1161:$i > $o, X1162:$i]:(((in @ X1162 @ X1160)=>((X1161 @ X1162)=>(in @ X1162 @ (dsetconstr @ X1160 @ (^[Z0/* 3 */:$i]:((X1161 @ Z0))))))))=>(![X2173:$i, X2174:$i > $o, X2175:$i]:(((in @ X2175 @ (dsetconstr @ X2173 @ (^[Z0/* 3 */:$i]:((X2174 @ Z0)))))=>(in @ X2175 @ X2173)))=>(![X1163:$i, X1164:$i > $o, X1165:$i]:(((in @ X1165 @ (dsetconstr @ X1163 @ (^[Z0/* 3 */:$i]:((X1164 @ Z0)))))=>(X1164 @ X1165)))=>(![X1166:$i > $o]:((?[X1167:$i]:(((X1166 @ X1167)&![X1168:$i]:(((X1166 @ X1168)=>((X1167)=(X1168))))))=>?[X1169:$i]:(((X1166 @ X1169)&![X1170:$i]:(((X1166 @ X1170)=>((X1169)=(X1170))))))))=>(![X1171:$o, X1172:$i]:(((in @ X1172 @ (prop2set @ ((X1171))))=>(X1171)))=>(![X1173:$i]:(((in @ X1173 @ emptyset)=>![X1174:$o]:((X1174))))=>(![X2172:$i]:(~(in @ X2172 @ emptyset))=>(![X1175:$i]:(~(in @ X1175 @ emptyset))=>(![X2168:$i > $o]:((?[X2169:$i]:(((X2168 @ X2169)&![X2170:$i]:(((X2168 @ X2170)=>((X2169)=(X2170))))))=>?[X2171:$i]:((X2168 @ X2171))))=>(![X1176:$i, X1177:$i]:((![X1178:$i]:(((in @ X1178 @ X1176)=>(in @ X1178 @ X1177)))=>(![X1179:$i]:(((in @ X1179 @ X1177)=>(in @ X1179 @ X1176)))=>((X1176)=(X1177)))))=>(![X1180:$i]:((![X1181:$i]:(~(in @ X1181 @ X1180))=>((X1180)=(emptyset))))=>(![X2166:$i]:((![X2167:$i]:(~(in @ X2167 @ X2166))=>((X2166)=(emptyset))))=>(![X1182:$i, X1183:$i > $o, X1184:$i]:(((in @ X1184 @ X1182)=>((in @ X1184 @ (dsetconstr @ X1182 @ (^[Z0/* 3 */:$i]:((X1183 @ Z0)))))<=>(X1183 @ X1184))))=>(![X2164:$i]:((((X2164)!=(emptyset))=>?[X2165:$i]:((in @ X2165 @ X2164))))=>(![X1185:$i, X1186:$i > $o, X1187:$i]:(((in @ X1187 @ X1185)=>((X1186 @ X1187)=>((dsetconstr @ X1185 @ (^[Z0/* 3 */:$i]:((X1186 @ Z0))))!=(emptyset)))))=>(![X1188:$i]:((?[X1189:$i]:((in @ X1189 @ X1188))=>((X1188)!=(emptyset))))=>(![X2162:$i, X2163:$i]:((in @ X2162 @ (setadjoin @ X2162 @ X2163)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1190:$i, X1191:$i, X1192:$i]:(((in @ X1192 @ X1191)=>(in @ X1192 @ (setadjoin @ X1190 @ X1191))))=>(![X1193:$i, X1194:$i, X1195:$i]:(((in @ X1195 @ (setadjoin @ X1193 @ X1194))=>![X1196:$o]:(((((X1195)=(X1193))=>(X1196))=>(((in @ X1195 @ X1194)=>(X1196))=>(X1196))))))=>(![X1197:$i, X1198:$i, X1199:$i]:(((in @ X1199 @ (setadjoin @ X1197 @ X1198))=>(((X1199)=(X1197))|(in @ X1199 @ X1198))))=>(![X1200:$i]:(((dsetconstr @ X1200 @ (^[Z0/* 3 */:$i]:(($true))))=(X1200)))=>(![X2159:$i, X2160:$i]:((![X2161:$i]:(((in @ X2161 @ X2160)=>(in @ X2161 @ X2159)))=>(in @ X2160 @ (powerset @ X2159))))=>(![X2158:$i]:((in @ emptyset @ (powerset @ X2158)))=>(![X1201:$i]:((in @ emptyset @ (powerset @ X1201)))=>(![X1202:$i, X1203:$i, X1204:$i]:(((in @ X1203 @ (powerset @ X1202))=>((in @ X1204 @ X1203)=>(in @ X1204 @ X1202))))=>(![X1205:$i, X1206:$i, X1207:$i]:(((in @ X1206 @ X1207)=>((in @ X1207 @ X1205)=>(in @ X1206 @ (setunion @ X1205)))))=>(![X2154:$i, X2155:$i]:(((in @ X2155 @ (setunion @ X2154))=>![X2156:$o]:((![X2157:$i]:(((in @ X2155 @ X2157)=>((in @ X2157 @ X2154)=>(X2156))))=>(X2156)))))=>(![X2152:$i, X2153:$i]:(((in @ X2153 @ X2152)=>(in @ X2153 @ (powerset @ (setunion @ X2152)))))=>(![X1208:$i > $o]:((?[X1209:$i]:(((X1208 @ X1209)&![X1210:$i]:(((X1208 @ X1210)=>((X1209)=(X1210))))))=>?[X1211:$i]:(![X1212:$i]:(((X1208 @ X1212)<=>((X1212)=(X1211)))))))=>(![X1213:$i]:((((X1213)!=(emptyset))=>?[X1214:$i]:((in @ X1214 @ X1213))))=>(![X2150:$i, X2151:$i]:(((in @ X2150 @ (setadjoin @ X2151 @ emptyset))=>((X2150)=(X2151))))=>(![X2148:$i, X2149:$i]:((((X2148)!=(X2149))=>~(in @ X2149 @ (setadjoin @ X2148 @ emptyset))))=>(![X1215:$i, X1216:$i]:((((X1215)=(X1216))=>(in @ X1215 @ (setadjoin @ X1216 @ emptyset))))=>(![X2146:$i, X2147:$i]:(((in @ X2146 @ (setadjoin @ X2147 @ emptyset))=>(in @ X2147 @ (setadjoin @ X2146 @ emptyset))))=>(![X2143:$i, X2144:$i, X2145:$i]:(((in @ X2145 @ (setadjoin @ X2143 @ (setadjoin @ X2144 @ emptyset)))=>(((X2145)=(X2143))|((X2145)=(X2144)))))=>(![X2141:$i, X2142:$i]:((in @ X2141 @ (setadjoin @ X2141 @ (setadjoin @ X2142 @ emptyset))))=>(![X2139:$i, X2140:$i]:((in @ X2140 @ (setadjoin @ X2139 @ (setadjoin @ X2140 @ emptyset))))=>(![X1217:$i, X1218:$i > $o]:((?[X1219:$i]:(((in @ X1219 @ X1217)&(X1218 @ X1219)))=>((dsetconstr @ X1217 @ (^[Z0/* 3 */:$i]:((X1218 @ Z0))))!=(emptyset))))=>(![X2137:$i > $o, X2138:$i]:(((in @ X2138 @ emptyset)=>(X2137 @ X2138)))=>(![X1220:$i, X1221:$i > $o]:((~(![X1222:$i]:(((in @ X1222 @ X1220)=>(X1221 @ X1222))))=>?[X1223:$i]:(((in @ X1223 @ X1220)&~(X1221 @ X1223)))))=>(![X2133:$i, X2134:$i > $o]:((![X2135:$i]:(((in @ X2135 @ X2133)=>~(X2134 @ X2135)))=>~(?[X2136:$i]:(((in @ X2136 @ X2133)&(X2134 @ X2136))))))=>(![X2129:$i, X2130:$i > $o]:((~(?[X2131:$i]:(((in @ X2131 @ X2129)&(X2130 @ X2131))))=>![X2132:$i]:(((in @ X2132 @ X2129)=>~(X2130 @ X2132)))))=>(![X1224:$i, X1225:$i > $o]:((?[X1226:$i]:(((in @ X1226 @ X1224)&~(X1225 @ X1226)))=>~(![X1227:$i]:(((in @ X1227 @ X1224)=>(X1225 @ X1227))))))=>(![X1228:$o]:(((X1228)=>(in @ emptyset @ (prop2set @ ((X1228))))))=>((prop2set2propI)=>(![X2125:$i, X2126:$i > $o]:((~(?[X2127:$i]:(((in @ X2127 @ X2125)&(X2126 @ X2127))))=>![X2128:$i]:(((in @ X2128 @ 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X2106:$i]:(((X2102 @ X2105)=>((X2102 @ X2106)=>((X2105)=(X2106)))))))=>(![X1260:$i > $o, X1261:$i > $o]:((![X1262:$i, X1263:$i]:((((X1262)=(X1263))=>((X1260 @ X1262)<=>(X1261 @ X1263))))=>(?[X1264:$i]:(((X1260 @ X1264)&![X1265:$i]:(((X1260 @ X1265)=>((X1264)=(X1265))))))=>(?[X1266:$i]:(((X1261 @ X1266)&![X1267:$i]:(((X1261 @ X1267)=>((X1266)=(X1267))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1260 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1261 @ Z0)))))))))=>(![X1268:$i, X1269:$i]:((((X1268)=(X1269))=>![X1270:$i > $o, X1271:$i > $o]:((![X1272:$i]:(((in @ X1272 @ X1268)=>![X1273:$i]:(((in @ X1273 @ X1269)=>(((X1272)=(X1273))=>((X1270 @ X1272)<=>(X1271 @ X1273)))))))=>((dsetconstr @ X1268 @ (^[Z0/* 3 */:$i]:((X1270 @ Z0))))=(dsetconstr @ X1269 @ (^[Z0/* 3 */:$i]:((X1271 @ Z0)))))))))=>(![X1274:$i, X1275:$i]:((![X1276:$i]:(((in @ X1276 @ X1274)=>(in @ X1276 @ X1275)))=>(subset @ X1274 @ X1275)))=>(![X2100:$i, X2101:$i]:((((X2100)=(X2101))=>(subset @ X2101 @ X2100)))=>(![X2098:$i, 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y_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[injFuncSetFuncIn]), eqimpsubset2]), emptysetAx]), binintersectSubset3]), secondinupair]), binintersectSubset2]), binintersectEL]), upairinpowunion]), binintersectI]), binunionRsub]), binunionLsub]), ubforcartprodlem2]), binunionE]), binunionIR]), ubforcartprodlem3]), upairset2IR]), powersetsubset]), powersetI1]), cartprodpairin]), subsetemptysetimpeq]), setextsub]), cartprodmempair1]), subset2powerset]), setukpairIL]), setadjoinSub]), notequalI2]), subsetE]), setunionE2]), emptysetsubset]), subsetI2]), setunionsingleton2]), eqimpsubset1]), funcinfuncset]), setukpairIR]), c_0_334]), setadjoin__Cong]), emptyset__Cong]), c_0_335]), c_0_336]), inCongP]), c_0_337]), c_0_338]), notdexE]), quantDeMorgan3]), singletonsuniq]), quantDeMorgan2]), vacuousDall]), theprop]), upairsetIR]), upairsetIL]), upairsetE]), setukpairinjL2]), singletonsswitch]), notinsingleton]), setukpairinjR1]), uniqinunit]), subPowSU]), setunionE]), setukpairinjR]), emptyinPowerset]), powersetI]), c_0_339]), setadjoinIL]), c_0_340]), noeltsimpempty]), c_0_341]), c_0_342]), emptysetimpfalse]), c_0_343]), c_0_344]), foundationAx]), c_0_345]), omega0Ax]), c_0_346]), setunionAx]), powersetAx]), c_0_347]), c_0_348]), app]), intersectInPowersetIntersectUnions]), brelnall1]), brelnall2]), c_0_349]), funcGraphProp1]), funcGraphProp2]), funcGraphProp4]), eqbreln]), funcext]), kpairiskpair]), funcext2]), singletoninpowerset]), ap2apEq2]), c_0_350]), c_0_351]), c_0_352]), c_0_353]), theeq]), iftrue]), complementT_lem]), powersetTI1]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), complementTnotintersectT]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), binunionTIRcontra]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), subsetTI]), setextT]), setminusT_lem]), powersetT_lem]), binunionT_lem]), binintersectT_lem]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), complementUnionInPowersetComplement]), demorgan1b]), demorgan2a]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_5]), breln1all2]), breln1all1]), subbreln1]), breln1invprop]), breln1invI]), breln1compprop]), breln1compI]), breln1compE]), breln1compEex]), breln1unionprop]), singletoninpowunion]), breln1unionIR]), woz2A]), c_0_354]), c_0_355]), c_0_325]), c_0_356]), c_0_357]), c_0_358]), image1Ex]), woz2B]), woz2W]), woz2Ex]), breln1unionCommutes]), breln1unionEcases]), breln1unionE]), breln1unionI]), breln1unionIL]), breln1invE]), eqbreln1]), c_0_359]), breln1SetBreln1]), woz1_4]), woz1_3]), woz1_2]), woz1_1]), woz13rule1]), woz13rule0]), demorgan2]), demorgan2b]), demorgan2b2]), demorgan1]), demorgan1a]), demorgan2a2]), demorgan2a1]), binunionTEcontra]), binunionTE]), inIntersectImpInUnion]), binunionTILcontra]), complementTcontraSubset]), complementImpComplementIntersect]), doubleComplementEq]), doubleComplementI1]), contrasubsetT3]), contrasubsetT2]), binintersectTELcontra]), complementTE1]), complementTI1]), powersetTE1]), iftrueorfalse]), iffalse]), ifp]), c_0_360]), c_0_361]), c_0_362]), c_0_363]), c_0_364]), c_0_365]), ap2apEq1]), subbreln]), funcextLem]), funcGraphProp3]), c_0_366]), c_0_367]), c_0_368]), ap2p]), infuncsetfunc]), c_0_369]), c_0_370]), c_0_371]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), c_0_372]), setukpairinjR2]), upairequniteq]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), cartprodfstin]), kfstpairEq]), c_0_373]), setukpairinjL1]), c_0_374]), c_0_375]), setunionsingleton]), setunionsingleton1]), cartprodmempair]), ubforcartprodlem1]), upairsubunion]), singletonsubset]), kpairp]), symdiffIneg1]), symdiffI1]), symdiffE]), setminusSubset1]), setminusERneg]), setminusER]), setminusI]), binintersectSubset4]), disjointsetsI1]), binintersectER]), upairset2E]), symdiffIneg2]), symdiffI2]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusSubset2]), setminusEL]), bs114d]), binintersectSubset1]), binintersectRsub]), binintersectLsub]), binintersectSubset5]), binunionEcases]), binunionIL]), c_0_376]), c_0_377]), inPowerset]), powersetE1]), setadjoinSub2]), subsetTrans]), subsetRefl]), notequalI1]), notsubsetI]), subsetE2]), subsetI1]), c_0_378]), c_0_379]), omega__Cong]), setunion__Cong]), powerset__Cong]), c_0_380]), in__Cong]), c_0_381]), c_0_382]), notdallE]), prop2setI]), quantDeMorgan4]), quantDeMorgan1]), c_0_383]), eqinunit]), c_0_384]), c_0_385]), setunionI]), powersetE]), emptyInPowerset]), c_0_386]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), c_0_387]), c_0_388]), c_0_389]), emptyI]), setext]), notinemptyset]), emptysetE]), prop2setE]), c_0_390]), c_0_391]), c_0_392]), c_0_393]), wellorderingAx]), omegaIndAx]), omegaSAx]), setadjoinAx]), setextAx])])]), c_0_394])). 0.51/1.04 thf(c_0_396, negated_conjecture, ![X2195:$i, X2196:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2208:$i, X2209:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2217:$i, X2218:$i > $i > $o, X2219:$i, X2221:$i, X2224:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2231:$i, X2232:$i > $o, X2233:$i, X2235:$i, X2236:$i > $o, X2237:$i, X2238:$i, X2239:$i > $o, X2240:$i, X2241:$i, X2242:$i > $o, X2243:$i, X2244:$i > $o, X2245:$i, X2248:$i, X2249:$o, X2250:$i, X2251:$i, X2252:$o, X2253:$i, X2254:$i, X2255:$i > $o, X2256:$i, X2259:$i, X2260:$i, X2263:$i, X2265:$i, X2267:$i, X2268:$i > $o, X2269:$i, X2270:$i, X2272:$i, X2273:$i > $o, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$o, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$o, X2305:$i, X2306:$i, X2307:$i > $o, X2308:$i, X2311:$i, X2312:$i, X2313:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i > $o, X2332:$i, X2333:$i > $o, X2334:$i, X2335:$i, X2336:$i > $o, X2337:$i, X2339:$i, X2340:$i > $o, X2342:$i, X2343:$i, X2344:$i > $o, X2346:$i, X2347:$i, X2348:$i > $o, X2349:$i, X2351:$o, X2352:$i, X2353:$i > $o, X2355:$i, X2356:$i, X2357:$i > $o, X2358:$i, X2360:$i > $o, X2361:$i, X2364:$i, X2365:$i > $o, X2366:$i, X2370:$i, X2371:$i > $o, X2372:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i > $o, X2385:$i, X2387:$i, X2388:$i, X2389:$i > $o, X2390:$i > $o, X2393:$i, X2396:$i, X2397:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i > $o, X2410:$i, X2412:$i, X2413:$i, X2414:$i > $o, X2415:$i > $o, X2418:$i, X2420:$i, X2422:$i, X2423:$i, X2424:$i > $o, X2425:$i > $o, X2428:$i, X2429:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i > $o, X2476:$i, X2477:$i > $o, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$o, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$o, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2623:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i > $o, X2632:$i, X2633:$i, X2634:$i > $o, X2636:$i, X2637:$i > $o, X2638:$i, X2640:$i, X2641:$i > $o, X2644:$i, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$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, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i > $i > $o, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i > $i > $o, X2722:$i, X2723:$i, X2724:$i > $i > $o, X2725:$i, X2726:$i, X2727:$i > $i > $o, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i > $i > $o, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i > $i > $o, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i > $i > $o, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$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 > $i, X2771:$i, X2772:$i, X2773:$i > $i, X2775:$i, X2776:$i, X2777:$i > $i, X2779:$i, X2780:$i, X2781:$i, X2782:$i > $o, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i > $o, X2792:$i, X2793:$i, X2794:$i > $o, X2795:$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, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2851:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2856:$i > $i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i, X2863:$i, X2864:$i > $i, X2866:$i, X2867:$i, X2868:$i > $i, X2870:$i, X2871:$i, X2872:$i, X2873:$i, X2874:$i, X2875:$o, X2876:$i, X2877:$i, X2878:$i, X2879:$o, X2880:$i, X2881:$i, X2882:$i, X2883:$o, X2884:$i, X2885:$i, X2886:$i, X2887:$o, X2888:$i, X2889:$i, X2890:$i, X2891:$o, X2892:$i, X2893:$i, X2894:$i, X2895:$o, X2896:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2901:$o, X2902:$i, X2903:$i, X2904:$i, X2905:$o, X2906:$i, X2907:$i, X2908:$i, X2909:$o, X2910:$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:$i, X2930:$i, X2931:$i, X2932:$i, X2934:$i, X2935:$i, X2936:$i, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$i, X2951:$i, X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i, X2976:$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, X3003:$i, X3004:$i, X3005:$i, X3006:$i, X3007:$i, X3008:$i, X3009:$i, X3010:$i, X3011:$i, X3012:$i, X3013:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i, X3023:$i, X3024:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$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:$o, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3047:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3059:$i, X3060:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i, X3068:$i, X3069:$i, X3070:$i, X3071:$i, X3072:$i, X3073:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i, X3079:$i, X3080:$i, X3081:$i, X3082:$i, X3083:$i, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i, X3090:$i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$i, X3115:$i, X3116:$i, X3117:$i, X3118:$i, X3119:$i, X3120:$i, X3121:$i, X3122:$i, X3123:$i, X3124:$i, X3125:$i > $o, X3128:$i, X3129:$i, X3130:$i, X3131:$i, X3132:$i > $i > $o, X3133:$i, X3134:$i, X3135:$i > $o, X3138:$i, X3139:$i, X3140:$i, X3141:$i, X3144:$i, X3145:$i, X3146:$i, X3151:$i, X3152:$i, X3153:$i, X3154:$i, X3155:$i, X3156:$i, X3157:$i, X3158:$i, X3159:$i, X3160:$i, X3161:$i, X3162:$i, X3163:$i, X3164:$i, X3165:$i, X3166:$i, X3167:$i, X3168:$i, X3169:$i, X3170:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3176:$i, X3177:$i, X3178:$i, X3179:$i, X3180:$i, X3181:$o, 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:$o, X3212:$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 > $i, X3231:$i, X3233:$i, X3234:$i, X3235:$i, X3236:$i > $i, X3238:$i, X3240:$i, X3241:$i, X3242:$i, X3244:$i, X3246:$i, X3247:$i > $i, X3248:$i, X3250:$i, X3251:$i > $i, X3252:$i, X3253:$i, X3254:$i, X3255:$i > $i, X3256:$i, X3258:$i, X3259:$i > $i, 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@ omega)&((~(in @ X2214 @ omega)|(in @ (setadjoin @ X2214 @ X2214) @ omega))&(((((in @ (esk4_1 @ X2215) @ omega)|~(in @ emptyset @ X2215)|(~(in @ X2217 @ omega)|(in @ X2217 @ X2215)))&((in @ (esk4_1 @ X2215) @ X2215)|~(in @ emptyset @ X2215)|(~(in @ X2217 @ omega)|(in @ X2217 @ X2215))))&(~(in @ (setadjoin @ (esk4_1 @ X2215) @ (esk4_1 @ X2215)) @ X2215)|~(in @ emptyset @ X2215)|(~(in @ X2217 @ omega)|(in @ X2217 @ X2215))))&((((((in @ (esk8_3 @ X2218 @ X2219 @ X2224) @ X2219)|~(in @ X2224 @ (esk7_2 @ X2218 @ X2219))|(in @ (esk5_2 @ X2218 @ X2219) @ X2219))&((X2218 @ (esk8_3 @ X2218 @ X2219 @ X2224) @ X2224)|~(in @ X2224 @ (esk7_2 @ X2218 @ X2219))|(in @ (esk5_2 @ X2218 @ X2219) @ X2219)))&(~(in @ X2227 @ X2219)|~(X2218 @ X2227 @ X2226)|(in @ X2226 @ (esk7_2 @ X2218 @ X2219))|(in @ (esk5_2 @ X2218 @ X2219) @ X2219)))&(((((in @ (esk8_3 @ X2218 @ X2219 @ X2224) @ X2219)|~(in @ X2224 @ (esk7_2 @ X2218 @ X2219))|((X2218 @ (esk5_2 @ X2218 @ X2219) @ (esk6_3 @ X2218 @ X2219 @ X2221))|~(X2218 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X3140)|(subset @ X3140 @ X3141)|~(breln1 @ X3139 @ X3141)|~(breln1 @ X3139 @ X3140))&(~(in @ (kpair @ (esk91_3 @ X3139 @ X3140 @ X3141) @ (esk92_3 @ X3139 @ X3140 @ X3141)) @ X3141)|(subset @ X3140 @ X3141)|~(breln1 @ X3139 @ X3141)|~(breln1 @ X3139 @ X3140)))))&(((((in @ (esk95_3 @ X3144 @ X3145 @ X3146) @ X3144)|((X3145)=(X3146))|(in @ (esk93_3 @ X3144 @ X3145 @ X3146) @ X3144)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(((in @ (esk96_3 @ X3144 @ X3145 @ X3146) @ X3144)|((X3145)=(X3146))|(in @ (esk93_3 @ X3144 @ X3145 @ X3146) @ X3144)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(((in @ (kpair @ (esk95_3 @ X3144 @ X3145 @ X3146) @ (esk96_3 @ X3144 @ X3145 @ X3146)) @ X3146)|((X3145)=(X3146))|(in @ (esk93_3 @ X3144 @ X3145 @ X3146) @ X3144)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(~(in @ (kpair @ (esk95_3 @ X3144 @ X3145 @ X3146) @ (esk96_3 @ X3144 @ X3145 @ X3146)) @ X3145)|((X3145)=(X3146))|(in @ (esk93_3 @ X3144 @ X3145 @ X3146) @ X3144)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145)))))&((((in @ (esk95_3 @ X3144 @ X3145 @ X3146) @ X3144)|((X3145)=(X3146))|(in @ (esk94_3 @ X3144 @ X3145 @ X3146) @ X3144)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(((in @ (esk96_3 @ X3144 @ X3145 @ X3146) @ X3144)|((X3145)=(X3146))|(in @ (esk94_3 @ X3144 @ X3145 @ X3146) @ X3144)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(((in @ (kpair @ (esk95_3 @ X3144 @ X3145 @ X3146) @ (esk96_3 @ X3144 @ X3145 @ X3146)) @ X3146)|((X3145)=(X3146))|(in @ (esk94_3 @ X3144 @ X3145 @ X3146) @ X3144)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(~(in @ (kpair @ (esk95_3 @ X3144 @ X3145 @ X3146) @ (esk96_3 @ X3144 @ X3145 @ X3146)) @ X3145)|((X3145)=(X3146))|(in @ (esk94_3 @ X3144 @ X3145 @ X3146) @ X3144)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145)))))&((((in @ (esk95_3 @ X3144 @ X3145 @ X3146) @ X3144)|((X3145)=(X3146))|(in @ (kpair @ (esk93_3 @ X3144 @ X3145 @ X3146) @ (esk94_3 @ X3144 @ X3145 @ X3146)) @ X3145)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(((in @ (esk96_3 @ X3144 @ X3145 @ X3146) @ X3144)|((X3145)=(X3146))|(in @ (kpair @ (esk93_3 @ X3144 @ X3145 @ X3146) @ (esk94_3 @ X3144 @ X3145 @ X3146)) @ X3145)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(((in @ (kpair @ (esk95_3 @ X3144 @ X3145 @ X3146) @ (esk96_3 @ X3144 @ X3145 @ X3146)) @ X3146)|((X3145)=(X3146))|(in @ (kpair @ (esk93_3 @ X3144 @ X3145 @ X3146) @ (esk94_3 @ X3144 @ X3145 @ X3146)) @ X3145)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(~(in @ (kpair @ (esk95_3 @ X3144 @ X3145 @ X3146) @ (esk96_3 @ X3144 @ X3145 @ X3146)) @ X3145)|((X3145)=(X3146))|(in @ (kpair @ (esk93_3 @ X3144 @ X3145 @ X3146) @ (esk94_3 @ X3144 @ X3145 @ X3146)) @ X3145)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145)))))&(((in @ (esk95_3 @ X3144 @ X3145 @ X3146) @ X3144)|((X3145)=(X3146))|~(in @ (kpair @ (esk93_3 @ X3144 @ X3145 @ X3146) @ (esk94_3 @ X3144 @ X3145 @ X3146)) @ X3146)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(((in @ (esk96_3 @ X3144 @ X3145 @ X3146) @ X3144)|((X3145)=(X3146))|~(in @ (kpair @ (esk93_3 @ X3144 @ X3145 @ X3146) @ (esk94_3 @ X3144 @ X3145 @ X3146)) @ X3146)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(((in @ (kpair @ (esk95_3 @ X3144 @ X3145 @ X3146) @ (esk96_3 @ X3144 @ X3145 @ X3146)) @ X3146)|((X3145)=(X3146))|~(in @ (kpair @ (esk93_3 @ X3144 @ X3145 @ X3146) @ (esk94_3 @ X3144 @ X3145 @ X3146)) @ X3146)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))&(~(in @ (kpair @ (esk95_3 @ X3144 @ X3145 @ X3146) @ (esk96_3 @ X3144 @ X3145 @ X3146)) @ X3145)|((X3145)=(X3146))|~(in @ (kpair @ (esk93_3 @ X3144 @ X3145 @ X3146) @ (esk94_3 @ X3144 @ X3145 @ X3146)) @ X3146)|~(breln1 @ X3144 @ X3146)|~(breln1 @ X3144 @ X3145))))))))&((~(breln1 @ X3151 @ X3152)|(breln1 @ X3151 @ (breln1invset @ X3151 @ X3152)))&((~(breln1 @ X3153 @ X3154)|(~(in @ X3155 @ X3153)|(~(in @ X3156 @ X3153)|(~(in @ (kpair @ X3155 @ X3156) @ X3154)|(in @ (kpair @ X3156 @ X3155) @ (breln1invset @ X3153 @ X3154))))))&((~(breln1 @ X3157 @ X3158)|(~(in @ X3159 @ X3157)|(~(in @ X3160 @ X3157)|(~(in @ (kpair @ X3160 @ X3159) @ (breln1invset @ X3157 @ X3158))|(in @ (kpair @ X3159 @ X3160) @ X3158)))))&((~(breln1 @ X3161 @ X3162)|(~(breln1 @ X3161 @ X3163)|(breln1 @ X3161 @ (breln1compset @ X3161 @ X3162 @ X3163))))&((~(breln1 @ X3164 @ X3165)|(~(breln1 @ X3164 @ X3166)|(~(in @ X3167 @ X3164)|(~(in @ X3168 @ X3164)|(~(in @ X3169 @ X3164)|(~(in @ (kpair @ X3167 @ X3169) @ X3165)|(~(in @ (kpair @ X3169 @ X3168) @ X3166)|(in @ (kpair @ X3167 @ X3168) @ (breln1compset @ X3164 @ X3165 @ X3166)))))))))&(((((in @ (esk97_5 @ X3170 @ X3171 @ X3172 @ X3173 @ X3174) @ X3170)|~(in @ (kpair @ X3173 @ X3174) @ (breln1compset @ X3170 @ X3171 @ X3172))|~(in @ X3174 @ X3170)|~(in @ X3173 @ X3170)|~(breln1 @ X3170 @ X3172)|~(breln1 @ X3170 @ X3171))&((in @ (kpair @ X3173 @ (esk97_5 @ X3170 @ X3171 @ X3172 @ X3173 @ X3174)) @ X3171)|~(in @ (kpair @ X3173 @ X3174) @ (breln1compset @ X3170 @ X3171 @ X3172))|~(in @ X3174 @ X3170)|~(in @ X3173 @ X3170)|~(breln1 @ X3170 @ X3172)|~(breln1 @ X3170 @ X3171)))&((in @ (kpair @ (esk97_5 @ X3170 @ X3171 @ X3172 @ X3173 @ X3174) @ X3174) @ X3172)|~(in @ (kpair @ X3173 @ X3174) @ (breln1compset @ X3170 @ X3171 @ X3172))|~(in @ X3174 @ X3170)|~(in @ X3173 @ X3170)|~(breln1 @ X3170 @ X3172)|~(breln1 @ X3170 @ X3171)))&((((in @ (esk98_6 @ X3176 @ X3177 @ X3178 @ X3179 @ X3180 @ X3181) @ X3176)|(X3181)|~(in @ (kpair @ X3179 @ X3180) @ (breln1compset @ X3176 @ X3177 @ X3178))|~(in @ X3180 @ X3176)|~(in @ X3179 @ X3176)|~(breln1 @ X3176 @ X3178)|~(breln1 @ X3176 @ X3177))&(((in @ (kpair @ X3179 @ (esk98_6 @ X3176 @ X3177 @ X3178 @ X3179 @ X3180 @ X3181)) @ X3177)|(X3181)|~(in @ (kpair @ X3179 @ X3180) @ (breln1compset @ X3176 @ X3177 @ X3178))|~(in @ X3180 @ X3176)|~(in @ X3179 @ X3176)|~(breln1 @ X3176 @ X3178)|~(breln1 @ X3176 @ X3177))&(((in @ (kpair @ (esk98_6 @ X3176 @ X3177 @ X3178 @ X3179 @ X3180 @ X3181) @ X3180) @ X3178)|(X3181)|~(in @ (kpair @ X3179 @ X3180) @ (breln1compset @ X3176 @ X3177 @ X3178))|~(in @ X3180 @ X3176)|~(in @ X3179 @ X3176)|~(breln1 @ X3176 @ X3178)|~(breln1 @ X3176 @ X3177))&(~(X3181)|(X3181)|~(in @ (kpair @ X3179 @ X3180) @ (breln1compset @ X3176 @ X3177 @ X3178))|~(in @ X3180 @ X3176)|~(in @ X3179 @ X3176)|~(breln1 @ X3176 @ X3178)|~(breln1 @ X3176 @ X3177)))))&((~(breln1 @ X3183 @ X3184)|(~(breln1 @ X3183 @ X3185)|(breln1 @ X3183 @ (binunion @ X3184 @ X3185))))&((~(breln1 @ X3186 @ X3187)|(~(breln1 @ X3186 @ X3188)|(~(in @ X3189 @ X3186)|(~(in @ X3190 @ X3186)|(~(in @ (kpair @ X3189 @ X3190) @ X3187)|(in @ (kpair @ X3189 @ X3190) @ (binunion @ X3187 @ X3188)))))))&((~(breln1 @ X3191 @ X3192)|(~(breln1 @ X3191 @ X3193)|(~(in @ X3194 @ X3191)|(~(in @ X3195 @ X3191)|(~(in @ (kpair @ X3194 @ X3195) @ X3193)|(in @ (kpair @ X3194 @ X3195) @ (binunion @ X3192 @ X3193)))))))&(((~(in @ (kpair @ X3199 @ X3200) @ X3197)|(in @ (kpair @ X3199 @ X3200) @ (binunion @ X3197 @ X3198))|~(in @ X3200 @ X3196)|~(in @ X3199 @ X3196)|~(breln1 @ X3196 @ X3198)|~(breln1 @ X3196 @ X3197))&(~(in @ (kpair @ X3199 @ X3200) @ X3198)|(in @ (kpair @ X3199 @ X3200) @ (binunion @ X3197 @ X3198))|~(in @ X3200 @ X3196)|~(in @ X3199 @ X3196)|~(breln1 @ X3196 @ X3198)|~(breln1 @ X3196 @ X3197)))&((~(breln1 @ X3201 @ X3202)|(~(breln1 @ X3201 @ X3203)|(~(in @ X3204 @ X3201)|(~(in @ X3205 @ X3201)|(~(in @ (kpair @ X3204 @ X3205) @ (binunion @ X3202 @ X3203))|((in @ (kpair @ X3204 @ X3205) @ X3202)|(in @ (kpair @ X3204 @ X3205) @ X3203)))))))&(((((in @ (kpair @ X3209 @ X3210) @ X3208)|(X3211)|(in @ (kpair @ X3209 @ X3210) @ X3207)|~(in @ (kpair @ X3209 @ X3210) @ (binunion @ X3207 @ X3208))|~(in @ X3210 @ X3206)|~(in @ X3209 @ X3206)|~(breln1 @ X3206 @ X3208)|~(breln1 @ X3206 @ X3207))&(~(X3211)|(X3211)|(in @ (kpair @ X3209 @ X3210) @ X3207)|~(in @ (kpair @ X3209 @ X3210) @ (binunion @ X3207 @ X3208))|~(in @ X3210 @ X3206)|~(in @ X3209 @ X3206)|~(breln1 @ X3206 @ X3208)|~(breln1 @ X3206 @ X3207)))&(((in @ (kpair @ X3209 @ X3210) @ X3208)|(X3211)|~(X3211)|~(in @ (kpair @ X3209 @ X3210) @ (binunion @ X3207 @ X3208))|~(in @ X3210 @ X3206)|~(in @ X3209 @ X3206)|~(breln1 @ X3206 @ X3208)|~(breln1 @ X3206 @ X3207))&(~(X3211)|(X3211)|~(X3211)|~(in @ (kpair @ X3209 @ X3210) @ (binunion @ X3207 @ X3208))|~(in @ X3210 @ X3206)|~(in @ X3209 @ X3206)|~(breln1 @ X3206 @ X3208)|~(breln1 @ X3206 @ X3207))))&((~(breln1 @ X3212 @ X3213)|(~(breln1 @ X3212 @ X3214)|((binunion @ X3213 @ X3214)=(binunion @ X3214 @ X3213))))&((~(breln1 @ X3215 @ X3216)|((X3216)=(breln1invset @ X3215 @ (breln1invset @ X3215 @ X3216))))&((~(breln1 @ X3217 @ X3218)|(~(breln1 @ X3217 @ X3219)|((breln1invset @ X3217 @ (breln1compset @ X3217 @ X3218 @ X3219))=(breln1compset @ X3217 @ (breln1invset @ X3217 @ X3219) @ (breln1invset @ X3217 @ X3218)))))&((~(breln1 @ X3220 @ X3221)|(~(breln1 @ X3220 @ X3222)|(~(breln1 @ X3220 @ X3223)|((breln1compset @ X3220 @ (binunion @ X3221 @ X3222) @ X3223)=(binunion @ (breln1compset @ X3220 @ X3221 @ X3223) @ (breln1compset @ X3220 @ X3222 @ X3223))))))&((~(breln1 @ X3224 @ X3225)|(~(breln1 @ X3224 @ X3226)|(~(breln1 @ X3224 @ X3227)|((breln1compset @ X3224 @ (binunion @ X3225 @ X3226) @ X3227)=(binunion @ (breln1invset @ X3224 @ (breln1compset @ X3224 @ (breln1invset @ X3224 @ X3227) @ (breln1invset @ X3224 @ X3226))) @ (breln1invset @ X3224 @ (breln1compset @ X3224 @ (breln1invset @ X3224 @ X3227) @ (breln1invset @ X3224 @ X3225))))))))&(((((in @ (esk100_3 @ X3228 @ X3229 @ X3231) @ X3228)|~(in @ X3231 @ (esk99_2 @ X3228 @ X3229)))&(((X3231)=(X3229 @ (esk100_3 @ X3228 @ X3229 @ X3231)))|~(in @ X3231 @ (esk99_2 @ X3228 @ X3229))))&(~(in @ X3234 @ X3228)|((X3233)!=(X3229 @ X3234))|(in @ X3233 @ (esk99_2 @ X3228 @ X3229))))&((((((in @ (esk102_3 @ X3235 @ X3236 @ X3238) @ X3235)|~(in @ X3238 @ (esk101_2 @ X3235 @ X3236)))&(((X3238)=(X3236 @ (esk102_3 @ X3235 @ X3236 @ X3238)))|~(in @ X3238 @ (esk101_2 @ X3235 @ X3236))))&(~(in @ X3241 @ X3235)|((X3240)!=(X3236 @ X3241))|(in @ X3240 @ (esk101_2 @ X3235 @ X3236))))&((~(in @ (esk103_3 @ X3235 @ X3236 @ X3242) @ X3242)|(~(in @ X3244 @ X3235)|((esk103_3 @ X3235 @ X3236 @ X3242)!=(X3236 @ X3244)))|((esk101_2 @ X3235 @ X3236)=(X3242)))&(((in @ (esk104_3 @ X3235 @ X3236 @ X3242) @ X3235)|(in @ (esk103_3 @ X3235 @ X3236 @ X3242) @ X3242)|((esk101_2 @ X3235 @ X3236)=(X3242)))&(((esk103_3 @ X3235 @ X3236 @ X3242)=(X3236 @ (esk104_3 @ X3235 @ X3236 @ X3242)))|(in @ (esk103_3 @ X3235 @ X3236 @ X3242) @ X3242)|((esk101_2 @ X3235 @ X3236)=(X3242))))))&(((((in @ (esk105_3 @ X3246 @ X3247 @ X3248) @ X3246)|~(in @ X3248 @ (image1 @ X3246 @ X3247)))&(((X3248)=(X3247 @ (esk105_3 @ X3246 @ X3247 @ X3248)))|~(in @ X3248 @ (image1 @ X3246 @ X3247))))&(~(in @ X3253 @ X3250)|((X3252)!=(X3251 @ X3253))|(in @ X3252 @ (image1 @ X3250 @ X3251))))&((((in @ (esk106_3 @ X3254 @ X3255 @ X3256) @ X3254)|~(in @ X3256 @ (image1 @ X3254 @ X3255)))&(((X3256)=(X3255 @ (esk106_3 @ X3254 @ X3255 @ X3256)))|~(in @ X3256 @ (image1 @ X3254 @ X3255))))&((~(in @ X3261 @ X3258)|((X3260)!=(X3259 @ X3261))|(in @ X3260 @ (image1 @ X3258 @ X3259)))&((~(in @ X3264 @ (funcSet @ X3262 @ X3263))|(~(injective @ X3262 @ X3263 @ X3264)|(in @ X3264 @ (dsetconstr @ (funcSet @ X3262 @ X3263) @ (^[Z0/* 3 */:$i]:((injective @ X3262 @ X3263 @ Z0)))))))&((in @ esk109_0 @ (dsetconstr @ (funcSet @ esk107_0 @ esk108_0) @ (^[Z0/* 3 */:$i]:((injective @ esk107_0 @ esk108_0 @ Z0)))))&~(in @ esk109_0 @ (funcSet @ esk107_0 @ esk108_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_395])])])])])])). 0.51/1.04 thf(c_0_397, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ X2 @ X3)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_396])). 0.51/1.04 thf(c_0_398, negated_conjecture, (in @ esk109_0 @ (dsetconstr @ (funcSet @ esk107_0 @ esk108_0) @ (injective @ esk107_0 @ esk108_0))), inference(split_conjunct,[status(thm)],[c_0_396])). 0.51/1.04 thf(c_0_399, negated_conjecture, ~((in @ esk109_0 @ (funcSet @ esk107_0 @ esk108_0))), inference(split_conjunct,[status(thm)],[c_0_396])). 0.51/1.04 thf(c_0_400, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_397, c_0_398]), c_0_399]), ['proof']). 0.51/1.04 # SZS output end CNFRefutation 0.51/1.04 # Parsed axioms : 685 0.51/1.04 # Removed by relevancy pruning/SinE : 368 0.51/1.04 # Initial clauses : 543 0.51/1.04 # Removed in clause preprocessing : 35 0.51/1.04 # Initial clauses in saturation : 508 0.51/1.04 # Processed clauses : 618 0.51/1.04 # ...of these trivial : 9 0.51/1.04 # ...subsumed : 51 0.51/1.04 # ...remaining for further processing : 558 0.51/1.04 # Other redundant clauses eliminated : 28 0.51/1.04 # Clauses deleted for lack of memory : 0 0.51/1.04 # Backward-subsumed : 2 0.51/1.04 # Backward-rewritten : 1 0.51/1.04 # Generated clauses : 382 0.51/1.04 # ...of the previous two non-redundant : 313 0.51/1.04 # ...aggressively subsumed : 0 0.51/1.04 # Contextual simplify-reflections : 14 0.51/1.04 # Paramodulations : 346 0.51/1.04 # Factorizations : 0 0.51/1.04 # NegExts : 0 0.51/1.04 # Equation resolutions : 33 0.51/1.04 # Total rewrite steps : 79 0.51/1.04 # Propositional unsat checks : 0 0.51/1.04 # Propositional check models : 0 0.51/1.04 # Propositional check unsatisfiable : 0 0.51/1.04 # Propositional clauses : 0 0.51/1.04 # Propositional clauses after purity: 0 0.51/1.04 # Propositional unsat core size : 0 0.51/1.04 # Propositional preprocessing time : 0.000 0.51/1.04 # Propositional encoding time : 0.000 0.51/1.04 # Propositional solver time : 0.000 0.51/1.04 # Success case prop preproc time : 0.000 0.51/1.04 # Success case prop encoding time : 0.000 0.51/1.04 # Success case prop solver time : 0.000 0.51/1.04 # Current number of processed clauses : 96 0.51/1.04 # Positive orientable unit clauses : 33 0.51/1.04 # Positive unorientable unit clauses: 0 0.51/1.04 # Negative unit clauses : 3 0.51/1.04 # Non-unit-clauses : 60 0.51/1.04 # Current number of unprocessed clauses: 643 0.51/1.04 # ...number of literals in the above : 2049 0.51/1.04 # Current number of archived formulas : 0 0.51/1.04 # Current number of archived clauses : 443 0.51/1.04 # Clause-clause subsumption calls (NU) : 55209 0.51/1.04 # Rec. Clause-clause subsumption calls : 15559 0.51/1.04 # Non-unit clause-clause subsumptions : 62 0.51/1.04 # Unit Clause-clause subsumption calls : 204 0.51/1.04 # Rewrite failures with RHS unbound : 0 0.51/1.04 # BW rewrite match attempts : 23 0.51/1.04 # BW rewrite match successes : 1 0.51/1.04 # Condensation attempts : 0 0.51/1.04 # Condensation successes : 0 0.51/1.04 # Termbank termtop insertions : 100338 0.51/1.04 0.51/1.04 # ------------------------------------------------- 0.51/1.04 # User time : 0.324 s 0.51/1.04 # System time : 0.035 s 0.51/1.04 # Total time : 0.359 s 0.51/1.04 # Maximum resident set size: 10244 pages 0.51/1.07 0.51/1.07 # ------------------------------------------------- 0.51/1.07 # User time : 0.351 s 0.51/1.07 # System time : 0.042 s 0.51/1.07 # Total time : 0.393 s 0.51/1.07 # Maximum resident set size: 2884 pages 0.51/1.07 % E---3.1 exiting 0.51/1.07 EOF