0.17/0.17 % Problem : Vampire---4.8_29375 : TPTP v0.0.0. Released v0.0.0. 0.19/0.18 % Command : run_E %s %d THM 0.19/0.39 % Computer : n001.cluster.edu 0.19/0.39 % Model : x86_64 x86_64 0.19/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.19/0.39 % Memory : 8042.1875MB 0.19/0.39 % OS : Linux 3.10.0-693.el7.x86_64 0.19/0.39 % CPULimit : 1440 0.19/0.39 % WCLimit : 180 0.19/0.39 % DateTime : Mon Jul 3 13:40:30 EDT 2023 0.19/0.39 % CPUTime : 0.36/0.58 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.JnWl4ZueJ5/Vampire---4.8_29375 0.36/0.58 # Version: 3.1pre001-ho 0.43/0.95 # Preprocessing class: HSLMSLSSLLLCHFA. 0.43/0.95 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.43/0.95 # Starting ehoh_best5 with 180s (1) cores 0.43/0.95 # Starting almost_fo_3_lam with 180s (1) cores 0.43/0.95 # Starting new_bool_5 with 180s (1) cores 0.43/0.95 # Starting pre_casc_3 with 180s (1) cores 0.43/0.95 # Starting ho_unfolding_8 with 180s (1) cores 0.43/0.95 # Starting new_ho_10_cnf2 with 180s (1) cores 0.43/0.95 # Starting new_bool_3 with 180s (1) cores 0.43/0.95 # Starting new_ho_5 with 180s (1) cores 0.43/0.95 # new_bool_5 with pid 29555 completed with status 0 0.43/0.95 # Result found by new_bool_5 0.43/0.95 # Preprocessing class: HSLMSLSSLLLCHFA. 0.43/0.95 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.43/0.95 # Starting ehoh_best5 with 180s (1) cores 0.43/0.95 # Starting almost_fo_3_lam with 180s (1) cores 0.43/0.95 # Starting new_bool_5 with 180s (1) cores 0.43/0.95 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.43/0.95 # Search class: HGHSM-FSLM32-MHFMMSBN 0.43/0.95 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 0.43/0.95 # Starting ho_unfolding_8 with 33s (1) cores 0.43/0.95 # ho_unfolding_8 with pid 29563 completed with status 0 0.43/0.95 # Result found by ho_unfolding_8 0.43/0.95 # Preprocessing class: HSLMSLSSLLLCHFA. 0.43/0.95 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.43/0.95 # Starting ehoh_best5 with 180s (1) cores 0.43/0.95 # Starting almost_fo_3_lam with 180s (1) cores 0.43/0.95 # Starting new_bool_5 with 180s (1) cores 0.43/0.95 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.43/0.95 # Search class: HGHSM-FSLM32-MHFMMSBN 0.43/0.95 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 0.43/0.95 # Starting ho_unfolding_8 with 33s (1) cores 0.43/0.95 # Preprocessing time : 0.067 s 0.43/0.95 # Presaturation interreduction done 0.43/0.95 0.43/0.95 # Proof found! 0.43/0.95 # SZS status Theorem 0.43/0.95 # SZS output start CNFRefutation 0.43/0.95 thf(decl_22, type, in: $i > $i > $o). 0.43/0.95 thf(decl_23, type, exu: ($i > $o) > $o). 0.43/0.95 thf(decl_24, type, setextAx: $o). 0.43/0.95 thf(decl_25, type, emptyset: $i). 0.43/0.95 thf(decl_26, type, emptysetAx: $o). 0.43/0.95 thf(decl_27, type, setadjoin: $i > $i > $i). 0.43/0.95 thf(decl_28, type, setadjoinAx: $o). 0.43/0.95 thf(decl_29, type, powerset: $i > $i). 0.43/0.95 thf(decl_30, type, powersetAx: $o). 0.43/0.95 thf(decl_31, type, setunion: $i > $i). 0.43/0.95 thf(decl_32, type, setunionAx: $o). 0.43/0.95 thf(decl_33, type, omega: $i). 0.43/0.95 thf(decl_34, type, omega0Ax: $o). 0.43/0.95 thf(decl_35, type, omegaSAx: $o). 0.43/0.95 thf(decl_36, type, omegaIndAx: $o). 0.43/0.95 thf(decl_37, type, replAx: $o). 0.43/0.95 thf(decl_38, type, foundationAx: $o). 0.43/0.95 thf(decl_39, type, wellorderingAx: $o). 0.43/0.95 thf(decl_40, type, descr: ($i > $o) > $i). 0.43/0.95 thf(decl_41, type, descrp: $o). 0.43/0.95 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_43, type, dsetconstrI: $o). 0.43/0.95 thf(decl_44, type, dsetconstrEL: $o). 0.43/0.95 thf(decl_45, type, dsetconstrER: $o). 0.43/0.95 thf(decl_46, type, exuE1: $o). 0.43/0.95 thf(decl_47, type, prop2set: $o > $i). 0.43/0.95 thf(decl_48, type, prop2setE: $o). 0.43/0.95 thf(decl_49, type, emptysetE: $o). 0.43/0.95 thf(decl_50, type, emptysetimpfalse: $o). 0.43/0.95 thf(decl_51, type, notinemptyset: $o). 0.43/0.95 thf(decl_52, type, exuE3e: $o). 0.43/0.95 thf(decl_53, type, setext: $o). 0.43/0.95 thf(decl_54, type, emptyI: $o). 0.43/0.95 thf(decl_55, type, noeltsimpempty: $o). 0.43/0.95 thf(decl_56, type, setbeta: $o). 0.43/0.95 thf(decl_57, type, nonempty: $i > $o). 0.43/0.95 thf(decl_58, type, nonemptyE1: $o). 0.43/0.95 thf(decl_59, type, nonemptyI: $o). 0.43/0.95 thf(decl_60, type, nonemptyI1: $o). 0.43/0.95 thf(decl_61, type, setadjoinIL: $o). 0.43/0.95 thf(decl_62, type, emptyinunitempty: $o). 0.43/0.95 thf(decl_63, type, setadjoinIR: $o). 0.43/0.95 thf(decl_64, type, setadjoinE: $o). 0.43/0.95 thf(decl_65, type, setadjoinOr: $o). 0.43/0.95 thf(decl_66, type, setoftrueEq: $o). 0.43/0.95 thf(decl_67, type, powersetI: $o). 0.43/0.95 thf(decl_68, type, emptyinPowerset: $o). 0.43/0.95 thf(decl_69, type, emptyInPowerset: $o). 0.43/0.95 thf(decl_70, type, powersetE: $o). 0.43/0.95 thf(decl_71, type, setunionI: $o). 0.43/0.95 thf(decl_72, type, setunionE: $o). 0.43/0.95 thf(decl_73, type, subPowSU: $o). 0.43/0.95 thf(decl_74, type, exuE2: $o). 0.43/0.95 thf(decl_75, type, nonemptyImpWitness: $o). 0.43/0.95 thf(decl_76, type, uniqinunit: $o). 0.43/0.95 thf(decl_77, type, notinsingleton: $o). 0.43/0.95 thf(decl_78, type, eqinunit: $o). 0.43/0.95 thf(decl_79, type, singletonsswitch: $o). 0.43/0.95 thf(decl_80, type, upairsetE: $o). 0.43/0.95 thf(decl_81, type, upairsetIL: $o). 0.43/0.95 thf(decl_82, type, upairsetIR: $o). 0.43/0.95 thf(decl_83, type, emptyE1: $o). 0.43/0.95 thf(decl_84, type, vacuousDall: $o). 0.43/0.95 thf(decl_85, type, quantDeMorgan1: $o). 0.43/0.95 thf(decl_86, type, quantDeMorgan2: $o). 0.43/0.95 thf(decl_87, type, quantDeMorgan3: $o). 0.43/0.95 thf(decl_88, type, quantDeMorgan4: $o). 0.43/0.95 thf(decl_89, type, prop2setI: $o). 0.43/0.95 thf(decl_91, type, prop2set2propI: $o). 0.43/0.95 thf(decl_92, type, notdexE: $o). 0.43/0.95 thf(decl_93, type, notdallE: $o). 0.43/0.95 thf(decl_94, type, exuI1: $o). 0.43/0.95 thf(decl_95, type, exuI3: $o). 0.43/0.95 thf(decl_96, type, exuI2: $o). 0.43/0.95 thf(decl_97, type, inCongP: $o). 0.43/0.95 thf(decl_98, type, in__Cong: $o). 0.43/0.95 thf(decl_99, type, exuE3u: $o). 0.43/0.95 thf(decl_100, type, exu__Cong: $o). 0.43/0.95 thf(decl_101, type, emptyset__Cong: $o). 0.43/0.95 thf(decl_102, type, setadjoin__Cong: $o). 0.43/0.95 thf(decl_103, type, powerset__Cong: $o). 0.43/0.95 thf(decl_104, type, setunion__Cong: $o). 0.43/0.95 thf(decl_105, type, omega__Cong: $o). 0.43/0.95 thf(decl_106, type, exuEu: $o). 0.43/0.95 thf(decl_107, type, descr__Cong: $o). 0.43/0.95 thf(decl_108, type, dsetconstr__Cong: $o). 0.43/0.95 thf(decl_109, type, subset: $i > $i > $o). 0.43/0.95 thf(decl_112, type, subsetI1: $o). 0.43/0.95 thf(decl_113, type, eqimpsubset2: $o). 0.43/0.95 thf(decl_114, type, eqimpsubset1: $o). 0.43/0.95 thf(decl_115, type, subsetI2: $o). 0.43/0.95 thf(decl_116, type, emptysetsubset: $o). 0.43/0.95 thf(decl_117, type, subsetE: $o). 0.43/0.95 thf(decl_118, type, subsetE2: $o). 0.43/0.95 thf(decl_119, type, notsubsetI: $o). 0.43/0.95 thf(decl_120, type, notequalI1: $o). 0.43/0.95 thf(decl_121, type, notequalI2: $o). 0.43/0.95 thf(decl_122, type, subsetRefl: $o). 0.43/0.95 thf(decl_123, type, subsetTrans: $o). 0.43/0.95 thf(decl_124, type, setadjoinSub: $o). 0.43/0.95 thf(decl_125, type, setadjoinSub2: $o). 0.43/0.95 thf(decl_126, type, subset2powerset: $o). 0.43/0.95 thf(decl_127, type, setextsub: $o). 0.43/0.95 thf(decl_128, type, subsetemptysetimpeq: $o). 0.43/0.95 thf(decl_129, type, powersetI1: $o). 0.43/0.95 thf(decl_130, type, powersetE1: $o). 0.43/0.95 thf(decl_131, type, inPowerset: $o). 0.43/0.95 thf(decl_132, type, powersetsubset: $o). 0.43/0.95 thf(decl_133, type, sepInPowerset: $o). 0.43/0.95 thf(decl_134, type, sepSubset: $o). 0.43/0.95 thf(decl_135, type, binunion: $i > $i > $i). 0.43/0.95 thf(decl_136, type, binunionIL: $o). 0.43/0.95 thf(decl_137, type, upairset2IR: $o). 0.43/0.95 thf(decl_138, type, binunionIR: $o). 0.43/0.95 thf(decl_139, type, binunionEcases: $o). 0.43/0.95 thf(decl_140, type, binunionE: $o). 0.43/0.95 thf(decl_141, type, binunionLsub: $o). 0.43/0.95 thf(decl_142, type, binunionRsub: $o). 0.43/0.95 thf(decl_143, type, binintersect: $i > $i > $i). 0.43/0.95 thf(decl_144, type, binintersectI: $o). 0.43/0.95 thf(decl_145, type, binintersectSubset5: $o). 0.43/0.95 thf(decl_146, type, binintersectEL: $o). 0.43/0.95 thf(decl_147, type, binintersectLsub: $o). 0.43/0.95 thf(decl_148, type, binintersectSubset2: $o). 0.43/0.95 thf(decl_149, type, binintersectSubset3: $o). 0.43/0.95 thf(decl_150, type, binintersectER: $o). 0.43/0.95 thf(decl_151, type, disjointsetsI1: $o). 0.43/0.95 thf(decl_152, type, binintersectRsub: $o). 0.43/0.95 thf(decl_153, type, binintersectSubset4: $o). 0.43/0.95 thf(decl_154, type, binintersectSubset1: $o). 0.43/0.95 thf(decl_155, type, bs114d: $o). 0.43/0.95 thf(decl_157, type, setminus: $i > $i > $i). 0.43/0.95 thf(decl_158, type, setminusI: $o). 0.43/0.95 thf(decl_159, type, setminusEL: $o). 0.43/0.95 thf(decl_160, type, setminusER: $o). 0.43/0.95 thf(decl_161, type, setminusSubset2: $o). 0.43/0.95 thf(decl_162, type, setminusERneg: $o). 0.43/0.95 thf(decl_163, type, setminusELneg: $o). 0.43/0.95 thf(decl_164, type, setminusILneg: $o). 0.43/0.95 thf(decl_165, type, setminusIRneg: $o). 0.43/0.95 thf(decl_166, type, setminusLsub: $o). 0.43/0.95 thf(decl_167, type, setminusSubset1: $o). 0.43/0.95 thf(decl_168, type, symdiff: $i > $i > $i). 0.43/0.95 thf(decl_169, type, symdiffE: $o). 0.43/0.95 thf(decl_170, type, symdiffI1: $o). 0.43/0.95 thf(decl_171, type, symdiffI2: $o). 0.43/0.95 thf(decl_172, type, symdiffIneg1: $o). 0.43/0.95 thf(decl_173, type, symdiffIneg2: $o). 0.43/0.95 thf(decl_174, type, iskpair: $i > $o). 0.43/0.95 thf(decl_175, type, secondinupair: $o). 0.43/0.95 thf(decl_176, type, setukpairIL: $o). 0.43/0.95 thf(decl_177, type, setukpairIR: $o). 0.43/0.95 thf(decl_178, type, kpairiskpair: $o). 0.43/0.95 thf(decl_179, type, kpair: $i > $i > $i). 0.43/0.95 thf(decl_180, type, kpairp: $o). 0.43/0.95 thf(decl_181, type, cartprod: $i > $i > $i). 0.43/0.95 thf(decl_182, type, singletonsubset: $o). 0.43/0.95 thf(decl_183, type, singletoninpowerset: $o). 0.43/0.95 thf(decl_184, type, singletoninpowunion: $o). 0.43/0.95 thf(decl_185, type, upairset2E: $o). 0.43/0.95 thf(decl_186, type, upairsubunion: $o). 0.43/0.95 thf(decl_187, type, upairinpowunion: $o). 0.43/0.95 thf(decl_188, type, ubforcartprodlem1: $o). 0.43/0.95 thf(decl_189, type, ubforcartprodlem2: $o). 0.43/0.95 thf(decl_190, type, ubforcartprodlem3: $o). 0.43/0.95 thf(decl_191, type, cartprodpairin: $o). 0.43/0.95 thf(decl_192, type, cartprodmempair1: $o). 0.43/0.95 thf(decl_193, type, cartprodmempair: $o). 0.43/0.95 thf(decl_194, type, setunionE2: $o). 0.43/0.95 thf(decl_195, type, setunionsingleton1: $o). 0.43/0.95 thf(decl_196, type, setunionsingleton2: $o). 0.43/0.95 thf(decl_197, type, setunionsingleton: $o). 0.43/0.95 thf(decl_198, type, singleton: $i > $o). 0.43/0.95 thf(decl_199, type, singletonprop: $o). 0.43/0.95 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 0.43/0.95 thf(decl_201, type, ex1E1: $o). 0.43/0.95 thf(decl_202, type, ex1I: $o). 0.43/0.95 thf(decl_203, type, ex1I2: $o). 0.43/0.95 thf(decl_204, type, singletonsuniq: $o). 0.43/0.95 thf(decl_209, type, setukpairinjL1: $o). 0.43/0.95 thf(decl_210, type, kfstsingleton: $o). 0.43/0.95 thf(decl_211, type, theprop: $o). 0.43/0.95 thf(decl_212, type, kfst: $i > $i). 0.43/0.95 thf(decl_213, type, kfstpairEq: $o). 0.43/0.95 thf(decl_214, type, cartprodfstin: $o). 0.43/0.95 thf(decl_215, type, setukpairinjL2: $o). 0.43/0.95 thf(decl_216, type, setukpairinjL: $o). 0.43/0.95 thf(decl_217, type, setukpairinjR11: $o). 0.43/0.95 thf(decl_218, type, setukpairinjR12: $o). 0.43/0.95 thf(decl_219, type, setukpairinjR1: $o). 0.43/0.95 thf(decl_220, type, upairequniteq: $o). 0.43/0.95 thf(decl_221, type, setukpairinjR2: $o). 0.43/0.95 thf(decl_222, type, setukpairinjR: $o). 0.43/0.95 thf(decl_223, type, ksndsingleton: $o). 0.43/0.95 thf(decl_224, type, ksnd: $i > $i). 0.43/0.95 thf(decl_225, type, ksndpairEq: $o). 0.43/0.95 thf(decl_226, type, kpairsurjEq: $o). 0.43/0.95 thf(decl_227, type, cartprodsndin: $o). 0.43/0.95 thf(decl_228, type, cartprodpairmemEL: $o). 0.43/0.95 thf(decl_229, type, cartprodpairmemER: $o). 0.43/0.95 thf(decl_230, type, cartprodmempaircEq: $o). 0.43/0.95 thf(decl_231, type, cartprodfstpairEq: $o). 0.43/0.95 thf(decl_232, type, cartprodsndpairEq: $o). 0.43/0.95 thf(decl_233, type, cartprodpairsurjEq: $o). 0.43/0.95 thf(decl_234, type, breln: $i > $i > $i > $o). 0.43/0.95 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.43/0.95 thf(decl_236, type, dpsetconstrI: $o). 0.43/0.95 thf(decl_237, type, dpsetconstrSub: $o). 0.43/0.95 thf(decl_238, type, setOfPairsIsBReln: $o). 0.43/0.95 thf(decl_239, type, dpsetconstrERa: $o). 0.43/0.95 thf(decl_240, type, dpsetconstrEL1: $o). 0.43/0.95 thf(decl_241, type, dpsetconstrEL2: $o). 0.43/0.95 thf(decl_242, type, dpsetconstrER: $o). 0.43/0.95 thf(decl_243, type, func: $i > $i > $i > $o). 0.43/0.95 thf(decl_244, type, funcSet: $i > $i > $i). 0.43/0.95 thf(decl_245, type, funcImageSingleton: $o). 0.43/0.95 thf(decl_246, type, apProp: $o). 0.43/0.95 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 0.43/0.95 thf(decl_248, type, app: $o). 0.43/0.95 thf(decl_249, type, infuncsetfunc: $o). 0.43/0.95 thf(decl_250, type, ap2p: $o). 0.43/0.95 thf(decl_251, type, funcinfuncset: $o). 0.43/0.95 thf(decl_252, type, lamProp: $o). 0.43/0.95 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 0.43/0.95 thf(decl_254, type, lamp: $o). 0.43/0.95 thf(decl_255, type, lam2p: $o). 0.43/0.95 thf(decl_256, type, brelnall1: $o). 0.43/0.95 thf(decl_257, type, brelnall2: $o). 0.43/0.95 thf(decl_258, type, ex1E2: $o). 0.43/0.95 thf(decl_259, type, funcGraphProp1: $o). 0.43/0.95 thf(decl_260, type, funcGraphProp3: $o). 0.43/0.95 thf(decl_261, type, funcGraphProp2: $o). 0.43/0.95 thf(decl_262, type, funcextLem: $o). 0.43/0.95 thf(decl_263, type, funcGraphProp4: $o). 0.43/0.95 thf(decl_264, type, subbreln: $o). 0.43/0.95 thf(decl_265, type, eqbreln: $o). 0.43/0.95 thf(decl_266, type, funcext: $o). 0.43/0.95 thf(decl_267, type, funcext2: $o). 0.43/0.95 thf(decl_268, type, ap2apEq1: $o). 0.43/0.95 thf(decl_269, type, ap2apEq2: $o). 0.43/0.95 thf(decl_270, type, beta1: $o). 0.43/0.95 thf(decl_271, type, eta1: $o). 0.43/0.95 thf(decl_272, type, lam2lamEq: $o). 0.43/0.95 thf(decl_273, type, beta2: $o). 0.43/0.95 thf(decl_274, type, eta2: $o). 0.43/0.95 thf(decl_275, type, iffalseProp1: $o). 0.43/0.95 thf(decl_276, type, iffalseProp2: $o). 0.43/0.95 thf(decl_277, type, iftrueProp1: $o). 0.43/0.95 thf(decl_278, type, iftrueProp2: $o). 0.43/0.95 thf(decl_279, type, ifSingleton: $o). 0.43/0.95 thf(decl_280, type, if: $i > $o > $i > $i > $i). 0.43/0.95 thf(decl_281, type, ifp: $o). 0.43/0.95 thf(decl_282, type, theeq: $o). 0.43/0.95 thf(decl_283, type, iftrue: $o). 0.43/0.95 thf(decl_284, type, iffalse: $o). 0.43/0.95 thf(decl_285, type, iftrueorfalse: $o). 0.43/0.95 thf(decl_286, type, binintersectT_lem: $o). 0.43/0.95 thf(decl_287, type, binunionT_lem: $o). 0.43/0.95 thf(decl_288, type, powersetT_lem: $o). 0.43/0.95 thf(decl_289, type, setminusT_lem: $o). 0.43/0.95 thf(decl_290, type, complementT_lem: $o). 0.43/0.95 thf(decl_291, type, setextT: $o). 0.43/0.95 thf(decl_292, type, subsetTI: $o). 0.43/0.95 thf(decl_293, type, powersetTI1: $o). 0.43/0.95 thf(decl_294, type, powersetTE1: $o). 0.43/0.95 thf(decl_295, type, complementTI1: $o). 0.43/0.95 thf(decl_296, type, complementTE1: $o). 0.43/0.95 thf(decl_297, type, binintersectTELcontra: $o). 0.43/0.95 thf(decl_298, type, binintersectTERcontra: $o). 0.43/0.95 thf(decl_299, type, contrasubsetT: $o). 0.43/0.95 thf(decl_300, type, contrasubsetT1: $o). 0.43/0.95 thf(decl_301, type, contrasubsetT2: $o). 0.43/0.95 thf(decl_302, type, contrasubsetT3: $o). 0.43/0.95 thf(decl_303, type, doubleComplementI1: $o). 0.43/0.95 thf(decl_304, type, doubleComplementE1: $o). 0.43/0.95 thf(decl_305, type, doubleComplementSub1: $o). 0.43/0.95 thf(decl_306, type, doubleComplementSub2: $o). 0.43/0.95 thf(decl_307, type, doubleComplementEq: $o). 0.43/0.95 thf(decl_308, type, complementTnotintersectT: $o). 0.43/0.95 thf(decl_309, type, complementImpComplementIntersect: $o). 0.43/0.95 thf(decl_310, type, complementSubsetComplementIntersect: $o). 0.43/0.95 thf(decl_311, type, complementInPowersetComplementIntersect: $o). 0.43/0.95 thf(decl_312, type, contraSubsetComplement: $o). 0.43/0.95 thf(decl_313, type, complementTcontraSubset: $o). 0.43/0.95 thf(decl_314, type, binunionTILcontra: $o). 0.43/0.95 thf(decl_315, type, binunionTIRcontra: $o). 0.43/0.95 thf(decl_316, type, inIntersectImpInUnion: $o). 0.43/0.95 thf(decl_317, type, inIntersectImpInUnion2: $o). 0.43/0.95 thf(decl_318, type, inIntersectImpInIntersectUnions: $o). 0.43/0.95 thf(decl_319, type, intersectInPowersetIntersectUnions: $o). 0.43/0.95 thf(decl_320, type, inComplementUnionImpNotIn1: $o). 0.43/0.95 thf(decl_321, type, inComplementUnionImpInComplement1: $o). 0.43/0.95 thf(decl_322, type, binunionTE: $o). 0.43/0.95 thf(decl_323, type, binunionTEcontra: $o). 0.43/0.95 thf(decl_324, type, demorgan2a1: $o). 0.43/0.95 thf(decl_325, type, complementUnionInPowersetComplement: $o). 0.43/0.95 thf(decl_326, type, demorgan2a2: $o). 0.43/0.95 thf(decl_327, type, epred1_0: $o). 0.43/0.95 thf(decl_328, type, esk1_2: $i > $i > $i). 0.43/0.95 thf(decl_329, type, esk2_2: $i > $i > $i). 0.43/0.95 thf(decl_330, type, esk3_2: $i > $i > $i). 0.43/0.95 thf(decl_331, type, esk4_1: $i > $i). 0.43/0.95 thf(decl_332, type, esk5_2: ($i > $i > $o) > $i > $i). 0.43/0.95 thf(decl_333, type, esk6_2: ($i > $i > $o) > $i > $i). 0.43/0.95 thf(decl_334, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 0.43/0.95 thf(decl_335, type, esk8_1: $i > $i). 0.43/0.95 thf(decl_336, type, esk9_1: ($i > $o) > $i). 0.43/0.95 thf(decl_337, type, esk10_1: ($i > $o) > $i). 0.43/0.95 thf(decl_338, type, esk11_2: $i > $i > $i). 0.43/0.95 thf(decl_339, type, esk12_2: $i > $i > $i). 0.43/0.95 thf(decl_340, type, esk13_1: $i > $i). 0.43/0.95 thf(decl_341, type, esk14_1: $i > $i). 0.43/0.95 thf(decl_342, type, esk15_1: $i > $i). 0.43/0.95 thf(decl_343, type, esk16_2: $i > $i > $i). 0.43/0.95 thf(decl_344, type, esk17_3: $i > $i > $o > $i). 0.43/0.95 thf(decl_345, type, esk18_1: ($i > $o) > $i). 0.43/0.95 thf(decl_346, type, esk19_1: $i > $i). 0.43/0.95 thf(decl_347, type, esk20_2: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_348, type, esk21_2: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_349, type, esk22_2: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_350, type, esk23_2: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_351, type, esk24_2: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_352, type, esk25_2: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_353, type, esk26_2: ($i > $o) > $i > $i). 0.43/0.95 thf(decl_354, type, esk27_1: ($i > $o) > $i). 0.43/0.95 thf(decl_355, type, esk28_1: ($i > $o) > $i). 0.43/0.95 thf(decl_356, type, esk29_2: ($i > $o) > $i > $i). 0.43/0.95 thf(decl_357, type, esk30_2: ($i > $o) > ($i > $o) > $i). 0.43/0.95 thf(decl_358, type, esk31_2: ($i > $o) > ($i > $o) > $i). 0.43/0.95 thf(decl_359, type, esk32_2: ($i > $o) > ($i > $o) > $i). 0.43/0.95 thf(decl_360, type, esk33_2: ($i > $o) > ($i > $o) > $i). 0.43/0.95 thf(decl_361, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.43/0.95 thf(decl_362, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.43/0.95 thf(decl_363, type, esk36_2: $i > $i > $i). 0.43/0.95 thf(decl_364, type, esk37_2: $i > $i > $i). 0.43/0.95 thf(decl_365, type, esk38_2: $i > $i > $i). 0.43/0.95 thf(decl_366, type, esk39_3: $i > $i > $i > $i). 0.43/0.95 thf(decl_367, type, esk40_3: $i > $i > $i > $i). 0.43/0.95 thf(decl_368, type, esk41_2: $i > $i > $i). 0.43/0.95 thf(decl_369, type, esk42_2: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_370, type, esk43_2: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_371, type, esk44_2: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_372, type, esk45_3: $i > ($i > $o) > $i > $i). 0.43/0.95 thf(decl_373, type, esk46_2: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_374, type, esk47_2: $i > ($i > $o) > $i). 0.43/0.95 thf(decl_375, type, esk48_3: $i > $i > ($i > $i) > $i). 0.43/0.95 thf(decl_376, type, esk49_3: $i > $i > ($i > $i) > $i). 0.43/0.95 thf(decl_377, type, esk50_3: $i > $i > ($i > $i) > $i). 0.43/0.95 thf(decl_378, type, esk51_4: $i > $i > $i > ($i > $o) > $i). 0.43/0.95 thf(decl_379, type, esk52_4: $i > $i > $i > ($i > $o) > $i). 0.43/0.95 thf(decl_380, type, esk53_4: $i > $i > $i > ($i > $o) > $i). 0.43/0.95 thf(decl_381, type, esk54_4: $i > $i > $i > ($i > $o) > $i). 0.43/0.95 thf(decl_382, type, esk55_4: $i > $i > $i > $i > $i). 0.43/0.95 thf(decl_383, type, esk56_4: $i > $i > $i > $i > $i). 0.43/0.95 thf(decl_384, type, esk57_4: $i > $i > $i > $i > $i). 0.43/0.95 thf(decl_385, type, esk58_4: $i > $i > $i > $i > $i). 0.43/0.95 thf(decl_386, type, esk59_4: $i > $i > $i > $i > $i). 0.43/0.95 thf(decl_387, type, esk60_4: $i > $i > $i > $i > $i). 0.43/0.95 thf(decl_388, type, esk61_4: $i > $i > $i > $i > $i). 0.43/0.95 thf(decl_389, type, esk62_4: $i > $i > $i > $i > $i). 0.43/0.95 thf(decl_390, type, esk63_4: $i > $i > $i > $i > $i). 0.43/0.95 thf(decl_391, type, esk64_3: $i > $i > ($i > $i) > $i). 0.43/0.95 thf(decl_392, type, esk65_3: $i > $i > ($i > $i) > $i). 0.43/0.95 thf(decl_393, type, esk66_3: $i > $i > ($i > $i) > $i). 0.43/0.95 thf(decl_394, type, esk67_3: $i > $i > $i > $i). 0.43/0.95 thf(decl_395, type, esk68_3: $i > $i > $i > $i). 0.43/0.95 thf(decl_396, type, esk69_3: $i > $i > $i > $i). 0.43/0.95 thf(decl_397, type, esk70_3: $i > $i > $i > $i). 0.43/0.95 thf(decl_398, type, esk71_0: $i). 0.43/0.95 thf(decl_399, type, esk72_0: $i). 0.43/0.95 thf(decl_400, type, esk73_0: $i). 0.43/0.95 thf(decl_401, type, esk74_0: $i). 0.43/0.95 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', descr__Cong)). 0.43/0.95 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', exu__Cong)). 0.43/0.95 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', exuI1)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', ksndsingleton)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', exuE2)). 0.43/0.95 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setbeta)). 0.43/0.95 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', dpsetconstrSub)). 0.43/0.95 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', exuE3e)). 0.43/0.95 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setOfPairsIsBReln)). 0.43/0.95 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', dpsetconstrERa)). 0.43/0.95 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', dsetconstrEL)). 0.43/0.95 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', dsetconstrI)). 0.43/0.95 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', dpsetconstrEL1)). 0.43/0.95 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', dpsetconstrER)). 0.43/0.95 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', lamProp)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', ex1E2)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', beta1)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', lam2lamEq)). 0.43/0.95 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', iffalseProp2)). 0.43/0.95 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', iftrueProp2)). 0.43/0.95 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', ifSingleton)). 0.43/0.95 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', ex1I)). 0.43/0.95 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', iftrueProp1)). 0.43/0.95 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', iffalseProp1)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', eta2)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', beta2)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', eta1)). 0.43/0.95 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', lam2p)). 0.43/0.95 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', lamp)). 0.43/0.95 thf(apProp, axiom, ((apProp)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', apProp)). 0.43/0.95 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', funcImageSingleton)). 0.43/0.95 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', dpsetconstrEL2)). 0.43/0.95 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', dpsetconstrI)). 0.43/0.95 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', kfstsingleton)). 0.43/0.95 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', ex1I2)). 0.43/0.95 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', ex1E1)). 0.43/0.95 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', singletonprop)). 0.43/0.95 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', sepSubset)). 0.43/0.95 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', sepInPowerset)). 0.43/0.95 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', dsetconstr__Cong)). 0.43/0.95 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', exuEu)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', exuE3u)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', exuI2)). 0.43/0.95 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', exuI3)). 0.43/0.95 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', emptyE1)). 0.43/0.95 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setoftrueEq)). 0.43/0.95 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', nonemptyI)). 0.43/0.95 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', exuE1)). 0.43/0.95 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', dsetconstrER)). 0.43/0.95 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', descrp)). 0.43/0.95 thf(replAx, axiom, ((replAx)<=>![X6:$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.JnWl4ZueJ5/Vampire---4.8_29375', replAx)). 0.43/0.95 thf(demorgan1a, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>(((((omegaSAx)=>((omegaIndAx)=>((replAx)=>((((descrp)=>((((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>(((((setext)=>((((((nonemptyI)=>((nonemptyI1)=>(((((((setoftrueEq)=>(((emptyinPowerset)=>(((((setunionE)=>((((nonemptyImpWitness)=>((((eqinunit)=>((((((emptyE1)=>((vacuousDall)=>((((quantDeMorgan3)=>(((prop2setI)=>((((notdallE)=>(((exuI3)=>((exuI2)=>((((exuE3u)=>(((((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>(((dsetconstr__Cong)=>((((eqimpsubset1)=>(((((subsetE2)=>(((notequalI1)=>((((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>(((subsetemptysetimpeq)=>(((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((((((binunionEcases)=>((binunionE)=>(((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((((((binintersectRsub)=>((binintersectSubset4)=>(((((setminusEL)=>(((((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((((((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((((((((upairset2E)=>(((upairinpowunion)=>(((((((cartprodmempair)=>((((((((ex1I)=>((((((theprop)=>((kfstpairEq)=>(((((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>(((setukpairinjR2)=>(((ksndsingleton)=>((((cartprodsndin)=>((cartprodpairmemEL)=>((((cartprodfstpairEq)=>(((cartprodpairsurjEq)=>(((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>(((dpsetconstrER)=>((((((((lamProp)=>((((brelnall1)=>(((ex1E2)=>((funcGraphProp1)=>(((funcGraphProp2)=>(((funcGraphProp4)=>((((funcext)=>(((((beta1)=>(((lam2lamEq)=>(((((iffalseProp2)=>(((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>(((complementT_lem)=>(((((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>(((((((doubleComplementI1)=>(((doubleComplementSub1)=>((doubleComplementSub2)=>(((complementTnotintersectT)=>((((complementInPowersetComplementIntersect)=>(((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>(((inComplementUnionImpNotIn1)=>((((binunionTEcontra)=>(((![X4:$i, X21:$i]:((![X48:$i]:((![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))<=(in @ X48 @ (powerset @ X4))))<=(in @ X21 @ (powerset @ X4))))<=(demorgan2a2))<=(complementUnionInPowersetComplement))<=(demorgan2a1)))<=(binunionTE))<=(inComplementUnionImpInComplement1)))<=(intersectInPowersetIntersectUnions))))))))<=(contraSubsetComplement)))<=(complementSubsetComplementIntersect))<=(complementImpComplementIntersect)))<=(doubleComplementEq))))<=(doubleComplementE1)))<=(contrasubsetT3))<=(contrasubsetT2))<=(contrasubsetT1))<=(contrasubsetT))<=(binintersectTERcontra))))))<=(powersetTI1))<=(subsetTI))<=(setextT)))<=(setminusT_lem))))))))))))<=(iftrueProp1)))<=(iffalseProp1))<=(eta2))<=(beta2)))<=(eta1)))<=(ap2apEq2))<=(ap2apEq1))<=(funcext2)))<=(eqbreln))<=(subbreln)))<=(funcextLem)))<=(funcGraphProp3))))<=(brelnall2)))<=(lam2p))<=(lamp)))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc))<=(app))<=(apProp))<=(funcImageSingleton)))<=(dpsetconstrEL2))))))<=(dpsetconstrI)))<=(cartprodsndpairEq)))<=(cartprodmempaircEq))<=(cartprodpairmemER))))<=(kpairsurjEq))<=(ksndpairEq)))<=(setukpairinjR)))<=(upairequniteq)))))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin))))<=(kfstsingleton))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2)))<=(ex1E1))<=(singletonprop))<=(setunionsingleton))<=(setunionsingleton2))<=(setunionsingleton1))<=(setunionE2)))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2))<=(ubforcartprodlem1)))<=(upairsubunion)))<=(singletoninpowunion))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR)))))))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1))<=(setminusLsub)))))<=(setminusERneg))<=(setminusSubset2))<=(setminusER)))<=(setminusI))<=(bs114d))<=(binintersectSubset1))))<=(disjointsetsI1))<=(binintersectER))<=(binintersectSubset3))<=(binintersectSubset2)))))))<=(binunionLsub))))<=(binunionIR))<=(upairset2IR))<=(binunionIL))<=(sepSubset))))))<=(powersetI1)))<=(setextsub))))))<=(subsetRefl))<=(notequalI2)))<=(notsubsetI)))<=(subsetE))<=(emptysetsubset))<=(subsetI2)))<=(eqimpsubset2))<=(subsetI1)))<=(descr__Cong))))))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong))<=(inCongP))))<=(exuI1)))<=(notdexE))<=(prop2set2propI)))<=(quantDeMorgan4)))<=(quantDeMorgan2))<=(quantDeMorgan1))))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch)))<=(notinsingleton))<=(uniqinunit)))<=(exuE2))<=(subPowSU)))<=(setunionI))<=(powersetE))<=(emptyInPowerset)))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty))<=(setadjoinIL))))<=(nonemptyE1))<=(setbeta))<=(noeltsimpempty))<=(emptyI)))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse))))))<=(dsetconstrEL))<=(dsetconstrI)))<=(wellorderingAx))<=(foundationAx)))))<=(omega0Ax))<=(setunionAx))<=(powersetAx))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', demorgan1a)). 0.43/0.95 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setukpairIL)). 0.43/0.95 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', subPowSU)). 0.43/0.95 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', powersetAx)). 0.43/0.95 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', subsetI2)). 0.43/0.95 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', secondinupair)). 0.43/0.95 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', eqimpsubset2)). 0.43/0.95 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', subsetI1)). 0.43/0.95 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', theprop)). 0.43/0.95 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setadjoin__Cong)). 0.43/0.95 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', kfstpairEq)). 0.43/0.95 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', emptyset__Cong)). 0.43/0.95 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', in__Cong)). 0.43/0.95 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setukpairinjR11)). 0.43/0.95 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', inCongP)). 0.43/0.95 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setukpairinjR12)). 0.43/0.95 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', notdexE)). 0.43/0.95 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', quantDeMorgan4)). 0.43/0.95 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', quantDeMorgan2)). 0.43/0.95 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setukpairinjR1)). 0.43/0.95 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', quantDeMorgan1)). 0.43/0.95 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', upairsetIR)). 0.43/0.95 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', upairsetIL)). 0.43/0.95 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setukpairinjR2)). 0.43/0.95 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', upairsetE)). 0.43/0.95 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', singletonsswitch)). 0.43/0.95 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', notinsingleton)). 0.43/0.95 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', uniqinunit)). 0.43/0.95 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', funcext)). 0.43/0.95 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setunionI)). 0.43/0.95 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', cartprodsndin)). 0.43/0.95 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', powersetE)). 0.43/0.95 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', emptyInPowerset)). 0.43/0.95 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', powersetI)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', cartprodpairmemEL)). 0.43/0.95 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setadjoinOr)). 0.43/0.95 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setadjoinE)). 0.43/0.95 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', cartprodfstpairEq)). 0.43/0.95 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setadjoinIR)). 0.43/0.95 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', emptyinunitempty)). 0.43/0.95 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setadjoinIL)). 0.43/0.95 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', cartprodpairsurjEq)). 0.43/0.95 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', nonemptyE1)). 0.43/0.95 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', noeltsimpempty)). 0.43/0.95 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', emptyI)). 0.43/0.95 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', notinemptyset)). 0.43/0.95 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', emptysetimpfalse)). 0.43/0.95 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', wellorderingAx)). 0.43/0.95 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', foundationAx)). 0.43/0.95 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', omega0Ax)). 0.43/0.95 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setunionAx)). 0.43/0.95 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', upairset2E)). 0.43/0.95 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', brelnall1)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', funcGraphProp1)). 0.43/0.95 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', funcGraphProp2)). 0.43/0.95 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', funcGraphProp4)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', demorgan2a2)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', ifp)). 0.43/0.95 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', theeq)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', iftrue)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', upairinpowunion)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', iffalse)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', iftrueorfalse)). 0.43/0.95 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectT_lem)). 0.43/0.95 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', binunionT_lem)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', powersetT_lem)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', complementT_lem)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', powersetTE1)). 0.43/0.95 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', complementTI1)). 0.43/0.95 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', complementTE1)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', binintersectTELcontra)). 0.43/0.95 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', cartprodmempair)). 0.43/0.95 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', doubleComplementI1)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', doubleComplementSub1)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', doubleComplementSub2)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', complementTnotintersectT)). 0.43/0.95 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', complementInPowersetComplementIntersect)). 0.43/0.95 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', complementTcontraSubset)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', binunionTILcontra)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', binunionTIRcontra)). 0.43/0.95 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', inIntersectImpInUnion)). 0.43/0.95 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', inIntersectImpInUnion2)). 0.43/0.95 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', inIntersectImpInIntersectUnions)). 0.43/0.95 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', inComplementUnionImpNotIn1)). 0.43/0.95 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binunionTEcontra)). 0.43/0.95 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', notequalI2)). 0.43/0.95 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', notsubsetI)). 0.43/0.95 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', subsetE)). 0.43/0.95 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', emptysetsubset)). 0.43/0.95 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', complementUnionInPowersetComplement)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', demorgan2a1)). 0.43/0.95 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binunionTE)). 0.43/0.95 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', inComplementUnionImpInComplement1)). 0.43/0.95 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', intersectInPowersetIntersectUnions)). 0.43/0.95 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', contraSubsetComplement)). 0.43/0.95 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', complementSubsetComplementIntersect)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', complementImpComplementIntersect)). 0.43/0.95 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', doubleComplementEq)). 0.43/0.95 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', doubleComplementE1)). 0.43/0.95 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', contrasubsetT3)). 0.43/0.95 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', contrasubsetT2)). 0.43/0.95 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', contrasubsetT1)). 0.43/0.95 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', contrasubsetT)). 0.43/0.95 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectTERcontra)). 0.43/0.95 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', powersetTI1)). 0.43/0.95 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', subsetTI)). 0.43/0.95 thf(setextT, axiom, ((setextT)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', setextT)). 0.43/0.95 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setminusT_lem)). 0.43/0.95 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', ap2apEq2)). 0.43/0.95 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', ap2apEq1)). 0.43/0.95 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', funcext2)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', eqbreln)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', subbreln)). 0.43/0.95 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', funcextLem)). 0.43/0.95 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', funcGraphProp3)). 0.43/0.95 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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.JnWl4ZueJ5/Vampire---4.8_29375', brelnall2)). 0.43/0.95 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', funcinfuncset)). 0.43/0.95 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', ap2p)). 0.43/0.95 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', infuncsetfunc)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', app)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', cartprodsndpairEq)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', cartprodmempaircEq)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', cartprodpairmemER)). 0.43/0.95 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', kpairsurjEq)). 0.43/0.95 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', ksndpairEq)). 0.43/0.95 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setukpairinjR)). 0.43/0.95 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', upairequniteq)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', setukpairinjL)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', setukpairinjL2)). 0.43/0.95 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', cartprodfstin)). 0.43/0.95 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.JnWl4ZueJ5/Vampire---4.8_29375', setukpairinjL1)). 0.43/0.95 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', singletonsuniq)). 0.43/0.95 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setunionsingleton)). 0.43/0.95 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setunionsingleton2)). 0.43/0.95 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setunionsingleton1)). 0.43/0.95 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setunionE2)). 0.43/0.95 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', cartprodmempair1)). 0.43/0.95 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', cartprodpairin)). 0.43/0.95 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', ubforcartprodlem3)). 0.43/0.95 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', ubforcartprodlem2)). 0.43/0.95 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', ubforcartprodlem1)). 0.43/0.95 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', upairsubunion)). 0.43/0.95 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', singletoninpowunion)). 0.43/0.95 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', singletoninpowerset)). 0.43/0.95 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', singletonsubset)). 0.43/0.95 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', kpairp)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', kpairiskpair)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', setukpairIR)). 0.43/0.95 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', symdiffI1)). 0.43/0.95 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', symdiffE)). 0.43/0.95 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setminusSubset1)). 0.43/0.95 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setminusLsub)). 0.43/0.95 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setminusERneg)). 0.43/0.95 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setminusSubset2)). 0.43/0.95 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setminusER)). 0.43/0.95 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setminusI)). 0.43/0.95 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', bs114d)). 0.43/0.95 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectSubset1)). 0.43/0.95 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', disjointsetsI1)). 0.43/0.95 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectER)). 0.43/0.95 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectSubset3)). 0.43/0.95 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectSubset2)). 0.43/0.95 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binunionLsub)). 0.43/0.95 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binunionIR)). 0.43/0.95 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', upairset2IR)). 0.43/0.95 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binunionIL)). 0.43/0.95 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', powersetI1)). 0.43/0.95 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setextsub)). 0.43/0.95 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', subsetRefl)). 0.43/0.95 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', symdiffIneg2)). 0.43/0.95 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', symdiffIneg1)). 0.43/0.95 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', symdiffI2)). 0.43/0.95 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setminusIRneg)). 0.43/0.95 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setminusILneg)). 0.43/0.95 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setminusELneg)). 0.43/0.95 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setminusEL)). 0.43/0.95 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectSubset4)). 0.43/0.95 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectRsub)). 0.43/0.95 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectLsub)). 0.43/0.95 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectEL)). 0.43/0.95 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectSubset5)). 0.43/0.95 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binintersectI)). 0.43/0.95 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binunionRsub)). 0.43/0.95 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binunionE)). 0.43/0.95 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', binunionEcases)). 0.43/0.95 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', powersetsubset)). 0.43/0.95 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', inPowerset)). 0.43/0.95 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', powersetE1)). 0.43/0.95 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', subsetemptysetimpeq)). 0.43/0.95 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', subset2powerset)). 0.43/0.95 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setadjoinSub2)). 0.43/0.95 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setadjoinSub)). 0.43/0.95 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', subsetTrans)). 0.43/0.95 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', notequalI1)). 0.43/0.95 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', subsetE2)). 0.43/0.95 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', eqimpsubset1)). 0.43/0.95 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', omega__Cong)). 0.43/0.95 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setunion__Cong)). 0.43/0.95 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', powerset__Cong)). 0.43/0.95 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', notdallE)). 0.43/0.95 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', prop2setI)). 0.43/0.95 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', quantDeMorgan3)). 0.43/0.95 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', vacuousDall)). 0.43/0.95 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', eqinunit)). 0.43/0.95 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', nonemptyImpWitness)). 0.43/0.95 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setunionE)). 0.43/0.95 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', emptyinPowerset)). 0.43/0.95 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', nonemptyI1)). 0.43/0.95 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.JnWl4ZueJ5/Vampire---4.8_29375', setext)). 0.43/0.95 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', emptysetE)). 0.43/0.95 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', prop2setE)). 0.43/0.95 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', omegaIndAx)). 0.43/0.95 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', omegaSAx)). 0.43/0.95 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setadjoinAx)). 0.43/0.95 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', emptysetAx)). 0.43/0.95 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.JnWl4ZueJ5/Vampire---4.8_29375', setextAx)). 0.43/0.95 thf(c_0_267, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.43/0.95 thf(c_0_268, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.43/0.95 thf(c_0_269, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.43/0.95 thf(c_0_270, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 0.43/0.95 thf(c_0_271, 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])). 0.43/0.95 thf(c_0_272, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.43/0.95 thf(c_0_273, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 0.43/0.95 thf(c_0_274, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.43/0.95 thf(c_0_275, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 0.43/0.95 thf(c_0_276, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 0.43/0.95 thf(c_0_277, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.43/0.95 thf(c_0_278, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.43/0.95 thf(c_0_279, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 0.43/0.95 thf(c_0_280, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 0.43/0.95 thf(c_0_281, plain, ((lamProp)<=>![X4:$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])). 0.43/0.95 thf(c_0_282, 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])). 0.43/0.95 thf(c_0_283, 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])). 0.43/0.95 thf(c_0_284, 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])). 0.43/0.95 thf(c_0_285, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 0.43/0.95 thf(c_0_286, plain, ((iftrueProp2)<=>![X4:$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])). 0.43/0.95 thf(c_0_287, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 0.43/0.95 thf(c_0_288, plain, ((ex1I)<=>![X4:$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])). 0.43/0.95 thf(c_0_289, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 0.43/0.95 thf(c_0_290, plain, ((iffalseProp1)<=>![X4:$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])). 0.43/0.95 thf(c_0_291, 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])). 0.43/0.95 thf(c_0_292, 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])). 0.43/0.95 thf(c_0_293, 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])). 0.43/0.95 thf(c_0_294, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 0.43/0.95 thf(c_0_295, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 0.43/0.95 thf(c_0_296, plain, ((apProp)<=>![X4:$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])). 0.43/0.95 thf(c_0_297, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 0.43/0.95 thf(c_0_298, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 0.43/0.95 thf(c_0_299, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 0.43/0.95 thf(c_0_300, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 0.43/0.95 thf(c_0_301, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.43/0.95 thf(c_0_302, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.43/0.95 thf(c_0_303, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.43/0.95 thf(c_0_304, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.43/0.95 thf(c_0_305, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.43/0.95 thf(c_0_306, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.43/0.95 thf(c_0_307, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.43/0.95 thf(c_0_308, 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])). 0.43/0.95 thf(c_0_309, 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])). 0.43/0.95 thf(c_0_310, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.43/0.95 thf(c_0_311, plain, ((emptyE1)<=>![X4:$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])). 0.43/0.95 thf(c_0_312, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.43/0.95 thf(c_0_313, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.43/0.95 thf(c_0_314, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.43/0.95 thf(c_0_315, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.43/0.95 thf(c_0_316, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.43/0.95 thf(c_0_317, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.43/0.95 thf(c_0_318, plain, ((epred1_0)<=>![X1708:$i]:(?[X1709:$i]:((((![X1710:$i]:(((in @ X1710 @ X1709)=>![X1711:$i]:(((in @ X1711 @ X1710)=>(in @ X1711 @ X1708)))))&![X1712:$i, X1713:$i]:((((in @ X1712 @ X1708)&(in @ X1713 @ X1708))=>(![X1714:$i]:(((in @ X1714 @ X1709)=>((in @ X1712 @ X1714)<=>(in @ X1713 @ X1714))))=>((X1712)=(X1713))))))&![X1715:$i, X1716:$i]:((((in @ X1715 @ X1709)&(in @ X1716 @ X1709))=>(![X1717:$i]:(((in @ X1717 @ X1715)=>(in @ X1717 @ X1716)))|![X1718:$i]:(((in @ X1718 @ X1716)=>(in @ X1718 @ X1715)))))))&![X1719:$i]:(((![X1720:$i]:(((in @ X1720 @ X1719)=>(in @ X1720 @ X1708)))&?[X1721:$i]:((in @ X1721 @ X1719)))=>?[X1722:$i, X1723:$i]:(((((in @ X1722 @ X1709)&(in @ X1723 @ X1719))&~(?[X1724:$i]:(((in @ X1724 @ X1722)&(in @ X1724 @ X1719)))))&![X1725:$i]:(((in @ X1725 @ X1709)=>(![X1726:$i]:(((in @ X1726 @ X1725)=>(in @ X1726 @ X1722)))|(in @ X1723 @ X1725)))))))))))), introduced(definition)). 0.43/0.95 thf(c_0_319, negated_conjecture, ~((![X896:$i, X897:$i]:((![X898:$i]:(((in @ X898 @ X896)<=>(in @ X898 @ X897)))=>((X896)=(X897))))=>(![X899:$i]:(~(in @ X899 @ emptyset))=>(![X900:$i, X901:$i, X902:$i]:(((in @ X902 @ (setadjoin @ X900 @ X901))<=>(((X902)=(X900))|(in @ X902 @ X901))))=>(![X1734:$i, X1735:$i]:(((in @ X1735 @ (powerset @ X1734))<=>![X1736:$i]:(((in @ X1736 @ X1735)=>(in @ X1736 @ X1734)))))=>(![X1731:$i, X1732:$i]:(((in @ X1732 @ (setunion @ X1731))<=>?[X1733:$i]:(((in @ X1732 @ X1733)&(in @ X1733 @ X1731)))))=>((in @ emptyset @ omega)=>(![X903:$i]:(((in @ X903 @ omega)=>(in @ (setadjoin @ X903 @ X903) @ omega)))=>(![X904:$i]:((((in @ emptyset @ X904)&![X905:$i]:((((in @ X905 @ omega)&(in @ X905 @ X904))=>(in @ (setadjoin @ X905 @ X905) @ X904))))=>![X906:$i]:(((in @ X906 @ omega)=>(in @ X906 @ X904)))))=>(![X907:$i > $i > $o, X908:$i]:((![X909:$i]:(((in @ X909 @ X908)=>(exu @ (^[Z0/* 3 */:$i]:((X907 @ X909 @ Z0))))))=>?[X910:$i]:(![X911:$i]:(((in @ X911 @ X910)<=>?[X912:$i]:(((in @ X912 @ X908)&(X907 @ X912 @ X911))))))))=>(![X1727:$i]:((?[X1728:$i]:((in @ X1728 @ X1727))=>?[X1729:$i]:(((in @ X1729 @ X1727)&~(?[X1730:$i]:(((in @ X1730 @ X1729)&(in @ X1730 @ X1727))))))))=>((epred1_0)=>(![X913:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X913 @ Z0))))=>(X913 @ (descr @ (^[Z0/* 3 */:$i]:((X913 @ Z0)))))))=>(![X1705:$i, X1706:$i > $o, X1707:$i]:(((in @ X1707 @ X1705)=>((X1706 @ X1707)=>(in @ X1707 @ (dsetconstr @ X1705 @ (^[Z0/* 3 */:$i]:((X1706 @ Z0))))))))=>(![X1702:$i, X1703:$i > $o, X1704:$i]:(((in @ X1704 @ (dsetconstr @ X1702 @ (^[Z0/* 3 */:$i]:((X1703 @ Z0)))))=>(in @ X1704 @ X1702)))=>(![X914:$i, X915:$i > $o, X916:$i]:(((in @ X916 @ (dsetconstr @ X914 @ (^[Z0/* 3 */:$i]:((X915 @ Z0)))))=>(X915 @ X916)))=>(![X917:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X917 @ Z0))))=>?[X918:$i]:(((X917 @ X918)&![X919:$i]:(((X917 @ X919)=>((X918)=(X919))))))))=>(![X920:$o, X921:$i]:(((in @ X921 @ (prop2set @ ((X920))))=>(X920)))=>(![X922:$i]:(((in @ X922 @ emptyset)=>![X923:$o]:((X923))))=>(![X1701:$i]:(~(in @ X1701 @ emptyset))=>(![X1700:$i]:(~(in @ X1700 @ emptyset))=>(![X1698:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1698 @ Z0))))=>?[X1699:$i]:((X1698 @ X1699))))=>(![X924:$i, X925:$i]:((![X926:$i]:(((in @ X926 @ X924)=>(in @ X926 @ X925)))=>(![X927:$i]:(((in @ X927 @ X925)=>(in @ X927 @ X924)))=>((X924)=(X925)))))=>(![X1696:$i]:((![X1697:$i]:(~(in @ X1697 @ X1696))=>((X1696)=(emptyset))))=>(![X1694:$i]:((![X1695:$i]:(~(in @ X1695 @ X1694))=>((X1694)=(emptyset))))=>(![X1691:$i, X1692:$i > $o, X1693:$i]:(((in @ X1693 @ X1691)=>((in @ X1693 @ (dsetconstr @ X1691 @ (^[Z0/* 3 */:$i]:((X1692 @ Z0)))))<=>(X1692 @ X1693))))=>(![X1689:$i]:(((nonempty @ X1689)=>?[X1690:$i]:((in @ X1690 @ X1689))))=>(![X928:$i, X929:$i > $o, X930:$i]:(((in @ X930 @ X928)=>((X929 @ X930)=>(nonempty @ (dsetconstr @ X928 @ (^[Z0/* 3 */:$i]:((X929 @ Z0))))))))=>(![X931:$i]:((?[X932:$i]:((in @ X932 @ X931))=>(nonempty @ X931)))=>(![X1687:$i, X1688:$i]:((in @ X1687 @ (setadjoin @ X1687 @ X1688)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1684:$i, X1685:$i, X1686:$i]:(((in @ X1686 @ X1685)=>(in @ X1686 @ (setadjoin @ X1684 @ X1685))))=>(![X1680:$i, X1681:$i, X1682:$i]:(((in @ X1682 @ (setadjoin @ X1680 @ X1681))=>![X1683:$o]:(((((X1682)=(X1680))=>(X1683))=>(((in @ X1682 @ X1681)=>(X1683))=>(X1683))))))=>(![X1677:$i, X1678:$i, X1679:$i]:(((in @ X1679 @ (setadjoin @ X1677 @ X1678))=>(((X1679)=(X1677))|(in @ X1679 @ X1678))))=>(![X933:$i]:(((dsetconstr @ X933 @ (^[Z0/* 3 */:$i]:(($true))))=(X933)))=>(![X1674:$i, X1675:$i]:((![X1676:$i]:(((in @ X1676 @ X1675)=>(in @ X1676 @ X1674)))=>(in @ X1675 @ (powerset @ X1674))))=>(![X934:$i]:((in @ emptyset @ (powerset @ X934)))=>(![X1673:$i]:((in @ emptyset @ (powerset @ X1673)))=>(![X1670:$i, X1671:$i, X1672:$i]:(((in @ X1671 @ (powerset @ X1670))=>((in @ X1672 @ X1671)=>(in @ X1672 @ X1670))))=>(![X1667:$i, X1668:$i, X1669:$i]:(((in @ X1668 @ X1669)=>((in @ X1669 @ X1667)=>(in @ X1668 @ (setunion @ X1667)))))=>(![X935:$i, X936:$i]:(((in @ X936 @ (setunion @ X935))=>![X937:$o]:((![X938:$i]:(((in @ X936 @ X938)=>((in @ X938 @ X935)=>(X937))))=>(X937)))))=>(![X1665:$i, X1666:$i]:(((in @ X1666 @ X1665)=>(in @ X1666 @ (powerset @ (setunion @ X1665)))))=>(![X1662:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1662 @ Z0))))=>?[X1663:$i]:(![X1664:$i]:(((X1662 @ X1664)<=>((X1664)=(X1663)))))))=>(![X939:$i]:(((nonempty @ X939)=>?[X940:$i]:((in @ X940 @ X939))))=>(![X1660:$i, X1661:$i]:(((in @ X1660 @ (setadjoin @ X1661 @ emptyset))=>((X1660)=(X1661))))=>(![X1658:$i, X1659:$i]:((((X1658)!=(X1659))=>~(in @ X1659 @ (setadjoin @ X1658 @ emptyset))))=>(![X941:$i, X942:$i]:((((X941)=(X942))=>(in @ X941 @ (setadjoin @ X942 @ emptyset))))=>(![X1656:$i, X1657:$i]:(((in @ X1656 @ (setadjoin @ X1657 @ emptyset))=>(in @ X1657 @ (setadjoin @ X1656 @ emptyset))))=>(![X1653:$i, X1654:$i, X1655:$i]:(((in @ X1655 @ (setadjoin @ X1653 @ (setadjoin @ X1654 @ emptyset)))=>(((X1655)=(X1653))|((X1655)=(X1654)))))=>(![X1651:$i, X1652:$i]:((in @ X1651 @ (setadjoin @ X1651 @ (setadjoin @ X1652 @ emptyset))))=>(![X1649:$i, X1650:$i]:((in @ X1650 @ (setadjoin @ X1649 @ (setadjoin @ X1650 @ emptyset))))=>(![X943:$i, X944:$i > $o]:((?[X945:$i]:(((in @ X945 @ X943)&(X944 @ X945)))=>((dsetconstr @ X943 @ (^[Z0/* 3 */:$i]:((X944 @ Z0))))!=(emptyset))))=>(![X946:$i > $o, X947:$i]:(((in @ X947 @ emptyset)=>(X946 @ X947)))=>(![X1645:$i, X1646:$i > $o]:((~(![X1647:$i]:(((in @ X1647 @ X1645)=>(X1646 @ X1647))))=>?[X1648:$i]:(((in @ X1648 @ X1645)&~(X1646 @ X1648)))))=>(![X1641:$i, X1642:$i > $o]:((![X1643:$i]:(((in @ X1643 @ X1641)=>~(X1642 @ X1643)))=>~(?[X1644:$i]:(((in @ X1644 @ X1641)&(X1642 @ X1644))))))=>(![X948:$i, X949:$i > $o]:((~(?[X950:$i]:(((in @ X950 @ X948)&(X949 @ X950))))=>![X951:$i]:(((in @ X951 @ X948)=>~(X949 @ X951)))))=>(![X1637:$i, X1638:$i > $o]:((?[X1639:$i]:(((in @ X1639 @ X1637)&~(X1638 @ X1639)))=>~(![X1640:$i]:(((in @ X1640 @ X1637)=>(X1638 @ X1640))))))=>(![X952:$o]:(((X952)=>(in @ emptyset @ (prop2set @ ((X952))))))=>((prop2set2propI)=>(![X1633:$i, X1634:$i > $o]:((~(?[X1635:$i]:(((in @ X1635 @ X1633)&(X1634 @ X1635))))=>![X1636:$i]:(((in @ X1636 @ X1633)=>~(X1634 @ X1636)))))=>(![X953:$i, X954:$i > $o]:((~(![X955:$i]:(((in @ X955 @ X953)=>(X954 @ X955))))=>?[X956:$i]:(((in @ X956 @ X953)&~(X954 @ X956)))))=>(![X1630:$i > $o]:((?[X1631:$i]:(((X1630 @ X1631)&![X1632:$i]:(((X1630 @ X1632)=>((X1631)=(X1632))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1630 @ Z0))))))=>(![X957:$i > $o]:((?[X958:$i]:((X957 @ X958))=>(![X959:$i, X960:$i]:(((X957 @ X959)=>((X957 @ X960)=>((X959)=(X960)))))=>(exu @ (^[Z0/* 3 */:$i]:((X957 @ Z0)))))))=>(![X961:$i > $o]:((?[X962:$i]:(![X963:$i]:(((X961 @ X963)<=>((X963)=(X962)))))=>(exu @ (^[Z0/* 3 */:$i]:((X961 @ Z0))))))=>(![X1626:$i, X1627:$i]:((((X1626)=(X1627))=>![X1628:$i, X1629:$i]:((((X1628)=(X1629))=>((in @ X1628 @ X1626)=>(in @ X1629 @ X1627))))))=>(![X1622:$i, X1623:$i]:((((X1622)=(X1623))=>![X1624:$i, X1625:$i]:((((X1624)=(X1625))=>((in @ X1624 @ X1622)<=>(in @ X1625 @ X1623))))))=>(![X964:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X964 @ Z0))))=>![X965:$i, X966:$i]:(((X964 @ X965)=>((X964 @ X966)=>((X965)=(X966)))))))=>(![X1618:$i > $o, X1619:$i > $o]:((![X1620:$i, X1621:$i]:((((X1620)=(X1621))=>((X1618 @ X1620)<=>(X1619 @ X1621))))=>((exu @ (^[Z0/* 3 */:$i]:((X1618 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X1619 @ Z0)))))))=>(((emptyset)=(emptyset))=>(![X1614:$i, X1615:$i]:((((X1614)=(X1615))=>![X1616:$i, X1617:$i]:((((X1616)=(X1617))=>((setadjoin @ X1614 @ X1616)=(setadjoin @ X1615 @ X1617))))))=>(![X967:$i, X968:$i]:((((X967)=(X968))=>((powerset @ X967)=(powerset @ X968))))=>(![X969:$i, X970:$i]:((((X969)=(X970))=>((setunion @ X969)=(setunion @ X970))))=>(((omega)=(omega))=>(![X971:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X971 @ Z0))))=>![X972:$i, X973:$i]:(((X971 @ X972)=>((X971 @ X973)=>((X972)=(X973)))))))=>(![X1610:$i > $o, X1611:$i > $o]:((![X1612:$i, X1613:$i]:((((X1612)=(X1613))=>((X1610 @ X1612)<=>(X1611 @ X1613))))=>((exu @ (^[Z0/* 3 */:$i]:((X1610 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X1611 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1610 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1611 @ Z0)))))))))=>(![X974:$i, X975:$i]:((((X974)=(X975))=>![X976:$i > $o, X977:$i > $o]:((![X978:$i]:(((in @ X978 @ X974)=>![X979:$i]:(((in @ X979 @ X975)=>(((X978)=(X979))=>((X976 @ X978)<=>(X977 @ X979)))))))=>((dsetconstr @ X974 @ (^[Z0/* 3 */:$i]:((X976 @ Z0))))=(dsetconstr @ X975 @ (^[Z0/* 3 */:$i]:((X977 @ Z0)))))))))=>(![X1607:$i, X1608:$i]:((![X1609:$i]:(((in @ X1609 @ X1607)=>(in @ X1609 @ X1608)))=>(subset @ X1607 @ X1608)))=>(![X1605:$i, X1606:$i]:((((X1605)=(X1606))=>(subset @ X1606 @ X1605)))=>(![X980:$i, X981:$i]:((((X980)=(X981))=>(subset @ X980 @ X981)))=>(![X1602:$i, X1603:$i]:((![X1604:$i]:(((in @ X1604 @ X1602)=>(in @ X1604 @ X1603)))=>(subset @ X1602 @ X1603)))=>(![X1601:$i]:((subset @ emptyset @ X1601))=>(![X1598:$i, X1599:$i, X1600:$i]:(((subset @ X1598 @ X1599)=>((in @ X1600 @ X1598)=>(in @ X1600 @ X1599))))=>(![X982:$i, X983:$i, X984:$i]:(((subset @ X982 @ X983)=>(~(in @ X984 @ X983)=>~(in @ X984 @ X982))))=>(![X1595:$i, X1596:$i, X1597:$i]:(((in @ X1597 @ X1595)=>(~(in @ X1597 @ X1596)=>~(subset @ X1595 @ X1596))))=>(![X985:$i, X986:$i]:((~(subset @ X985 @ X986)=>((X985)!=(X986))))=>(![X1592:$i, X1593:$i, X1594:$i]:(((in @ X1594 @ X1592)=>(~(in @ X1594 @ X1593)=>((X1592)!=(X1593)))))=>(![X1591:$i]:((subset @ X1591 @ X1591))=>(![X987:$i, X988:$i, X989:$i]:(((subset @ X987 @ X988)=>((subset @ X988 @ X989)=>(subset @ X987 @ X989))))=>(![X990:$i, X991:$i]:((subset @ X991 @ (setadjoin @ X990 @ X991)))=>(![X992:$i, X993:$i, X994:$i]:(((subset @ X992 @ X994)=>(subset @ X992 @ (setadjoin @ X993 @ X994))))=>(![X995:$i, X996:$i]:(((subset @ X995 @ X996)=>(in @ X995 @ (powerset @ X996))))=>(![X1589:$i, X1590:$i]:(((subset @ X1589 @ X1590)=>((subset @ X1590 @ X1589)=>((X1589)=(X1590)))))=>(![X997:$i]:(((subset @ X997 @ emptyset)=>((X997)=(emptyset))))=>(![X1587:$i, X1588:$i]:(((subset @ X1588 @ X1587)=>(in @ X1588 @ (powerset @ X1587))))=>(![X998:$i, X999:$i]:(((in @ X999 @ (powerset @ X998))=>(subset @ X999 @ X998)))=>(![X1000:$i]:((in @ X1000 @ (powerset @ X1000)))=>(![X1001:$i, X1002:$i]:(((subset @ X1001 @ X1002)=>(subset @ (powerset @ X1001) @ (powerset @ X1002))))=>(![X1003:$i, X1004:$i > $o]:((in @ (dsetconstr @ X1003 @ (^[Z0/* 3 */:$i]:((X1004 @ Z0)))) @ (powerset @ X1003)))=>(![X1585:$i, X1586:$i > $o]:((subset @ (dsetconstr @ X1585 @ (^[Z0/* 3 */:$i]:((X1586 @ Z0)))) @ X1585))=>(![X1582:$i, X1583:$i, X1584:$i]:(((in @ X1584 @ X1582)=>(in @ X1584 @ (binunion @ X1582 @ X1583))))=>(![X1580:$i, X1581:$i]:((in @ X1581 @ (setadjoin @ X1580 @ (setadjoin @ X1581 @ emptyset))))=>(![X1577:$i, X1578:$i, X1579:$i]:(((in @ X1579 @ X1578)=>(in @ X1579 @ (binunion @ X1577 @ X1578))))=>(![X1005:$i, X1006:$i, X1007:$i, X1008:$o]:(((in @ X1007 @ (binunion @ X1005 @ X1006))=>(((in @ X1007 @ X1005)=>(X1008))=>(((in @ X1007 @ X1006)=>(X1008))=>(X1008)))))=>(![X1009:$i, X1010:$i, X1011:$i]:(((in @ X1011 @ (binunion @ X1009 @ X1010))=>((in @ X1011 @ X1009)|(in @ X1011 @ X1010))))=>(![X1575:$i, X1576:$i]:((subset @ X1575 @ (binunion @ X1575 @ X1576)))=>(![X1012:$i, X1013:$i]:((subset @ X1013 @ (binunion @ X1012 @ X1013)))=>(![X1014:$i, X1015:$i, X1016:$i]:(((in @ X1016 @ X1014)=>((in @ X1016 @ X1015)=>(in @ X1016 @ (binintersect @ X1014 @ X1015)))))=>(![X1017:$i, X1018:$i, X1019:$i]:(((subset @ X1019 @ X1017)=>((subset @ X1019 @ X1018)=>(subset @ X1019 @ (binintersect @ X1017 @ X1018)))))=>(![X1020:$i, X1021:$i, X1022:$i]:(((in @ X1022 @ (binintersect @ X1020 @ X1021))=>(in @ X1022 @ X1020)))=>(![X1023:$i, X1024:$i]:((subset @ (binintersect @ X1023 @ X1024) @ X1023))=>(![X1573:$i, X1574:$i]:(((subset @ X1573 @ X1574)=>((binintersect @ X1573 @ X1574)=(X1573))))=>(![X1571:$i, X1572:$i]:((((binintersect @ X1571 @ X1572)=(X1572))=>(subset @ X1572 @ X1571)))=>(![X1568:$i, X1569:$i, X1570:$i]:(((in @ X1570 @ (binintersect @ X1568 @ X1569))=>(in @ X1570 @ X1569)))=>(![X1565:$i, X1566:$i]:((~(?[X1567:$i]:(((in @ X1567 @ X1565)&(in @ X1567 @ X1566))))=>((binintersect @ X1565 @ X1566)=(emptyset))))=>(![X1025:$i, X1026:$i]:((subset @ 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setukpairIL]), subPowSU]), powersetAx]), subsetI2]), secondinupair]), eqimpsubset2]), subsetI1]), theprop]), c_0_267]), setadjoin__Cong]), kfstpairEq]), emptyset__Cong]), c_0_268]), in__Cong]), setukpairinjR11]), inCongP]), c_0_269]), setukpairinjR12]), notdexE]), quantDeMorgan4]), quantDeMorgan2]), setukpairinjR1]), quantDeMorgan1]), upairsetIR]), upairsetIL]), setukpairinjR2]), upairsetE]), singletonsswitch]), notinsingleton]), c_0_270]), uniqinunit]), c_0_271]), funcext]), setunionI]), cartprodsndin]), powersetE]), emptyInPowerset]), powersetI]), cartprodpairmemEL]), setadjoinOr]), setadjoinE]), cartprodfstpairEq]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), cartprodpairsurjEq]), nonemptyE1]), c_0_272]), c_0_273]), noeltsimpempty]), emptyI]), c_0_274]), c_0_275]), notinemptyset]), emptysetimpfalse]), c_0_276]), c_0_277]), c_0_278]), wellorderingAx]), c_0_279]), foundationAx]), omega0Ax]), c_0_280]), setunionAx]), upairset2E]), c_0_281]), brelnall1]), c_0_282]), funcGraphProp1]), funcGraphProp2]), funcGraphProp4]), demorgan2a2]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), ifp]), theeq]), iftrue]), upairinpowunion]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), complementT_lem]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), cartprodmempair]), doubleComplementI1]), doubleComplementSub1]), doubleComplementSub2]), complementTnotintersectT]), complementInPowersetComplementIntersect]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), inComplementUnionImpNotIn1]), binunionTEcontra]), notequalI2]), notsubsetI]), subsetE]), emptysetsubset]), complementUnionInPowersetComplement]), demorgan2a1]), binunionTE]), inComplementUnionImpInComplement1]), intersectInPowersetIntersectUnions]), contraSubsetComplement]), complementSubsetComplementIntersect]), complementImpComplementIntersect]), doubleComplementEq]), doubleComplementE1]), contrasubsetT3]), contrasubsetT2]), contrasubsetT1]), contrasubsetT]), binintersectTERcontra]), powersetTI1]), subsetTI]), setextT]), setminusT_lem]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), ap2apEq2]), ap2apEq1]), funcext2]), eqbreln]), subbreln]), funcextLem]), funcGraphProp3]), brelnall2]), c_0_294]), c_0_295]), funcinfuncset]), ap2p]), infuncsetfunc]), app]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), cartprodsndpairEq]), cartprodmempaircEq]), cartprodpairmemER]), kpairsurjEq]), ksndpairEq]), setukpairinjR]), upairequniteq]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), c_0_300]), setukpairinjL1]), singletonsuniq]), c_0_301]), c_0_302]), c_0_303]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairsubunion]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusERneg]), setminusSubset2]), setminusER]), setminusI]), bs114d]), binintersectSubset1]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binunionLsub]), binunionIR]), upairset2IR]), binunionIL]), c_0_304]), powersetI1]), setextsub]), subsetRefl]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusEL]), binintersectSubset4]), binintersectRsub]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionE]), binunionEcases]), c_0_305]), powersetsubset]), inPowerset]), powersetE1]), subsetemptysetimpeq]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), notequalI1]), subsetE2]), eqimpsubset1]), c_0_306]), c_0_307]), omega__Cong]), setunion__Cong]), powerset__Cong]), c_0_308]), c_0_309]), c_0_310]), notdallE]), prop2setI]), quantDeMorgan3]), vacuousDall]), c_0_311]), eqinunit]), nonemptyImpWitness]), setunionE]), emptyinPowerset]), c_0_312]), nonemptyI1]), c_0_313]), setext]), emptysetE]), prop2setE]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), omegaIndAx]), omegaSAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_318])). 0.43/0.95 thf(c_0_320, negated_conjecture, ![X1737:$i, X1738:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1750:$i, X1751:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1759:$i, X1760:$i > $i > $o, X1761:$i, X1764:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1771:$i, X1772:$i > $o, X1773:$i, X1774:$i > $o, X1775:$i, X1776:$i, X1777:$i > $o, X1778:$i, X1779:$i, X1780:$i > $o, X1781:$i, X1782:$i > $o, X1784:$i, X1785:$o, X1786:$i, X1787:$i, X1788:$o, X1789:$i, X1790:$i, X1791:$i > $o, X1793:$i, X1794:$i, X1797:$i, X1799:$i, X1801:$i, X1802:$i > $o, X1803:$i, X1804:$i, X1806:$i, X1807:$i > $o, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$o, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$o, X1839:$i, X1840:$i, X1841:$i > $o, X1843:$i, X1844:$i, X1845:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i > $o, X1864:$i, X1865:$i > $o, X1866:$i, X1867:$i, X1868:$i > $o, X1869:$i, X1871:$i, X1872:$i > $o, X1874:$i, X1875:$i, X1876:$i > $o, X1878:$i, X1879:$i, X1880:$i > $o, X1881:$i, X1883:$o, X1884:$i, X1885:$i > $o, X1887:$i, X1888:$i, X1889:$i > $o, X1890:$i, X1892:$i > $o, X1893:$i, X1895:$i > $o, X1896:$i, X1899:$i > $o, X1900:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i > $o, X1911:$i, X1912:$i, X1913:$i > $o, X1914:$i > $o, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i > $o, X1926:$i, X1927:$i, X1928:$i > $o, X1929:$i > $o, X1932:$i, X1933:$i, X1934:$i > $o, X1935:$i > $o, X1938:$i, X1939:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i > $o, X1986:$i, X1987:$i > $o, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$o, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$o, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i > $o, X2142:$i, X2143:$i, X2144:$i > $o, X2146:$i, X2147:$i > $o, X2148:$i, X2150:$i, X2151:$i > $o, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i > $i > $o, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i > $i > $o, X2232:$i, X2233:$i, X2234:$i > $i > $o, X2235:$i, X2236:$i, X2237:$i > $i > $o, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i > $i > $o, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i > $i > $o, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i > $i > $o, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i > $i, X2281:$i, X2282:$i, X2283:$i > $i, X2285:$i, X2286:$i, X2287:$i > $i, X2289:$i, X2290:$i, X2291:$i, X2292:$i > $o, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i > $o, X2302:$i, X2303:$i, X2304:$i > $o, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, 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@ (powerset @ X2430))|(~(in @ X2432 @ (powerset @ X2430))|(in @ (setminus @ X2431 @ X2432) @ (powerset @ X2430))))&((~(in @ X2434 @ (powerset @ X2433))|(in @ (setminus @ X2433 @ X2434) @ (powerset @ X2433)))&(((((in @ (esk68_3 @ X2435 @ X2436 @ X2437) @ X2435)|((X2436)=(X2437))|(in @ (esk67_3 @ X2435 @ X2436 @ X2437) @ X2435)|~(in @ X2437 @ (powerset @ X2435))|~(in @ X2436 @ (powerset @ X2435)))&(((in @ (esk68_3 @ X2435 @ X2436 @ X2437) @ X2437)|((X2436)=(X2437))|(in @ (esk67_3 @ X2435 @ X2436 @ X2437) @ X2435)|~(in @ X2437 @ (powerset @ X2435))|~(in @ X2436 @ (powerset @ X2435)))&(~(in @ (esk68_3 @ X2435 @ X2436 @ X2437) @ X2436)|((X2436)=(X2437))|(in @ (esk67_3 @ X2435 @ X2436 @ X2437) @ X2435)|~(in @ X2437 @ (powerset @ X2435))|~(in @ X2436 @ (powerset @ X2435)))))&((((in @ (esk68_3 @ X2435 @ X2436 @ X2437) @ X2435)|((X2436)=(X2437))|(in @ (esk67_3 @ X2435 @ X2436 @ X2437) @ X2436)|~(in @ X2437 @ (powerset @ X2435))|~(in @ X2436 @ (powerset @ X2435)))&(((in @ (esk68_3 @ X2435 @ X2436 @ X2437) @ X2437)|((X2436)=(X2437))|(in @ (esk67_3 @ X2435 @ X2436 @ X2437) @ X2436)|~(in @ X2437 @ (powerset @ X2435))|~(in @ X2436 @ (powerset @ X2435)))&(~(in @ (esk68_3 @ X2435 @ X2436 @ X2437) @ X2436)|((X2436)=(X2437))|(in @ (esk67_3 @ X2435 @ X2436 @ X2437) @ X2436)|~(in @ X2437 @ (powerset @ X2435))|~(in @ X2436 @ (powerset @ X2435)))))&(((in @ (esk68_3 @ X2435 @ X2436 @ X2437) @ X2435)|((X2436)=(X2437))|~(in @ (esk67_3 @ X2435 @ X2436 @ X2437) @ X2437)|~(in @ X2437 @ (powerset @ X2435))|~(in @ X2436 @ (powerset @ X2435)))&(((in @ (esk68_3 @ X2435 @ X2436 @ X2437) @ X2437)|((X2436)=(X2437))|~(in @ (esk67_3 @ X2435 @ X2436 @ X2437) @ X2437)|~(in @ X2437 @ (powerset @ X2435))|~(in @ X2436 @ (powerset @ X2435)))&(~(in @ (esk68_3 @ X2435 @ X2436 @ X2437) @ X2436)|((X2436)=(X2437))|~(in @ (esk67_3 @ X2435 @ X2436 @ X2437) @ X2437)|~(in @ X2437 @ (powerset @ X2435))|~(in @ X2436 @ (powerset @ X2435)))))))&((((in @ (esk69_3 @ X2440 @ X2441 @ X2442) @ X2440)|(subset @ X2441 @ X2442)|~(in @ X2442 @ (powerset @ X2440))|~(in @ X2441 @ (powerset @ X2440)))&(((in @ (esk69_3 @ X2440 @ X2441 @ X2442) @ X2441)|(subset @ X2441 @ X2442)|~(in @ X2442 @ (powerset @ X2440))|~(in @ X2441 @ (powerset @ X2440)))&(~(in @ (esk69_3 @ X2440 @ X2441 @ X2442) @ X2442)|(subset @ X2441 @ X2442)|~(in @ X2442 @ (powerset @ X2440))|~(in @ X2441 @ (powerset @ X2440)))))&((((in @ (esk70_3 @ X2444 @ X2445 @ X2446) @ X2444)|(in @ X2445 @ (powerset @ X2446))|~(in @ X2446 @ (powerset @ X2444))|~(in @ X2445 @ (powerset @ X2444)))&(((in @ (esk70_3 @ X2444 @ X2445 @ X2446) @ X2445)|(in @ X2445 @ (powerset @ X2446))|~(in @ X2446 @ (powerset @ X2444))|~(in @ X2445 @ (powerset @ X2444)))&(~(in @ (esk70_3 @ X2444 @ X2445 @ X2446) @ X2446)|(in @ X2445 @ (powerset @ X2446))|~(in @ X2446 @ (powerset @ X2444))|~(in @ X2445 @ (powerset @ X2444)))))&((~(in @ X2449 @ (powerset @ X2448))|(~(in @ X2450 @ (powerset @ X2448))|(~(in @ X2451 @ X2448)|(~(in @ X2449 @ (powerset @ X2450))|(~(in @ X2451 @ X2449)|(in @ X2451 @ X2450))))))&((~(in @ X2453 @ (powerset @ X2452))|(~(in @ X2454 @ X2452)|(~(in @ X2454 @ X2453)|~(in @ X2454 @ (setminus @ X2452 @ X2453)))))&((~(in @ X2456 @ (powerset @ X2455))|(~(in @ X2457 @ X2455)|((in @ X2457 @ (setminus @ X2455 @ X2456))|(in @ X2457 @ X2456))))&((~(in @ X2459 @ (powerset @ X2458))|(~(in @ X2460 @ (powerset @ X2458))|(~(in @ X2461 @ X2458)|((in @ X2461 @ X2459)|~(in @ X2461 @ (binintersect @ X2459 @ X2460))))))&((~(in @ X2463 @ (powerset @ X2462))|(~(in @ X2464 @ (powerset @ X2462))|(~(in @ X2465 @ X2462)|((in @ X2465 @ X2464)|~(in @ X2465 @ (binintersect @ X2463 @ X2464))))))&((~(in @ X2467 @ (powerset @ X2466))|(~(in @ X2468 @ (powerset @ X2466))|(~(in @ X2469 @ X2466)|(~(subset @ X2467 @ (setminus @ X2466 @ X2468))|(~(in @ X2469 @ X2468)|~(in @ X2469 @ X2467))))))&((~(in @ X2471 @ (powerset @ X2470))|(~(in @ X2472 @ (powerset @ X2470))|(~(in @ X2473 @ X2470)|(~(subset @ X2471 @ X2472)|((in @ X2473 @ X2472)|~(in @ X2473 @ X2471))))))&((~(in @ X2475 @ (powerset @ X2474))|(~(in @ X2476 @ (powerset @ X2474))|(~(subset @ X2475 @ X2476)|(subset @ (setminus @ X2474 @ X2476) @ (setminus @ X2474 @ X2475)))))&((~(in @ X2478 @ (powerset @ X2477))|(~(in @ X2479 @ (powerset @ X2477))|(~(subset @ (setminus @ X2477 @ X2479) @ (setminus @ X2477 @ X2478))|(subset @ X2478 @ X2479))))&((~(in @ X2481 @ (powerset @ X2480))|(~(in @ X2482 @ X2480)|(~(in @ X2482 @ X2481)|(in @ X2482 @ (setminus @ X2480 @ (setminus @ X2480 @ X2481))))))&((~(in @ X2484 @ (powerset @ X2483))|(~(in @ X2485 @ X2483)|(~(in @ X2485 @ (setminus @ X2483 @ (setminus @ X2483 @ X2484)))|(in @ X2485 @ X2484))))&((~(in @ X2487 @ (powerset @ X2486))|(subset @ X2487 @ (setminus @ X2486 @ (setminus @ X2486 @ X2487))))&((~(in @ X2489 @ (powerset @ X2488))|(subset @ (setminus @ X2488 @ (setminus @ X2488 @ X2489)) @ X2489))&((~(in @ X2491 @ (powerset @ X2490))|((X2491)=(setminus @ X2490 @ (setminus @ X2490 @ X2491))))&((~(in @ X2493 @ (powerset @ X2492))|(~(in @ X2494 @ (powerset @ X2492))|(~(in @ X2495 @ X2492)|(~(in @ X2495 @ (setminus @ X2492 @ X2493))|~(in @ X2495 @ (binintersect @ X2493 @ X2494))))))&((~(in @ X2497 @ (powerset @ X2496))|(~(in @ X2498 @ (powerset @ X2496))|(~(in @ X2499 @ X2496)|(~(in @ X2499 @ (setminus @ X2496 @ X2497))|(in @ X2499 @ (setminus @ X2496 @ (binintersect @ X2497 @ X2498)))))))&((~(in @ X2501 @ (powerset @ X2500))|(~(in @ X2502 @ (powerset @ X2500))|(subset @ (setminus @ X2500 @ X2501) @ (setminus @ X2500 @ (binintersect @ X2501 @ X2502)))))&((~(in @ X2504 @ (powerset @ X2503))|(~(in @ X2505 @ (powerset @ X2503))|(in @ (setminus @ X2503 @ X2504) @ (powerset @ (setminus @ X2503 @ (binintersect @ X2504 @ X2505))))))&((~(in @ X2507 @ (powerset @ X2506))|(~(in @ X2508 @ (powerset @ X2506))|(~(subset @ X2507 @ (setminus @ X2506 @ X2508))|(~(in @ X2509 @ X2506)|(~(in @ X2509 @ X2508)|(in @ X2509 @ (setminus @ X2506 @ X2507)))))))&((~(in @ X2511 @ (powerset @ X2510))|(~(in @ X2512 @ (powerset @ X2510))|(~(subset @ X2511 @ (setminus @ X2510 @ X2512))|(subset @ X2512 @ (setminus @ X2510 @ X2511)))))&((~(in @ X2514 @ (powerset @ X2513))|(~(in @ X2515 @ (powerset @ X2513))|(~(in @ X2516 @ X2513)|((in @ X2516 @ (binunion @ X2514 @ X2515))|~(in @ X2516 @ X2514)))))&((~(in @ X2518 @ (powerset @ X2517))|(~(in @ X2519 @ (powerset @ X2517))|(~(in @ X2520 @ X2517)|((in @ X2520 @ (binunion @ X2518 @ X2519))|~(in @ X2520 @ X2519)))))&((~(in @ X2522 @ (powerset @ X2521))|(~(in @ X2523 @ (powerset @ X2521))|(~(in @ X2524 @ (powerset @ X2521))|(~(in @ X2525 @ X2521)|(~(in @ X2525 @ (binintersect @ X2522 @ X2523))|(in @ X2525 @ (binunion @ X2522 @ X2524)))))))&((~(in @ X2527 @ (powerset @ X2526))|(~(in @ X2528 @ (powerset @ X2526))|(~(in @ X2529 @ (powerset @ X2526))|(~(in @ X2530 @ X2526)|(~(in @ X2530 @ (binintersect @ X2527 @ X2528))|(in @ X2530 @ (binunion @ X2528 @ X2529)))))))&((~(in @ X2532 @ (powerset @ X2531))|(~(in @ X2533 @ (powerset @ X2531))|(~(in @ X2534 @ (powerset @ X2531))|(~(in @ X2535 @ X2531)|(~(in @ X2535 @ (binintersect @ X2532 @ X2533))|(in @ X2535 @ (binintersect @ (binunion @ X2532 @ X2534) @ (binunion @ X2533 @ X2534))))))))&((~(in @ X2537 @ (powerset @ X2536))|(~(in @ X2538 @ (powerset @ X2536))|(~(in @ X2539 @ (powerset @ X2536))|(in @ (binintersect @ X2537 @ X2538) @ (powerset @ (binintersect @ (binunion @ X2537 @ X2539) @ (binunion @ X2538 @ X2539)))))))&((~(in @ X2541 @ (powerset @ X2540))|(~(in @ X2542 @ (powerset @ X2540))|(~(in @ X2543 @ X2540)|(~(in @ X2543 @ (setminus @ X2540 @ (binunion @ X2541 @ X2542)))|~(in @ X2543 @ X2541)))))&((~(in @ X2545 @ (powerset @ X2544))|(~(in @ X2546 @ (powerset @ X2544))|(~(in @ X2547 @ X2544)|(~(in @ X2547 @ (setminus @ X2544 @ (binunion @ X2545 @ X2546)))|(in @ X2547 @ (setminus @ X2544 @ X2545))))))&(((((in @ X2552 @ X2550)|(X2551)|(in @ X2552 @ X2549)|~(in @ X2552 @ (binunion @ X2549 @ X2550))|~(in @ X2552 @ X2548)|~(in @ X2550 @ (powerset @ X2548))|~(in @ X2549 @ (powerset @ X2548)))&(~(X2551)|(X2551)|(in @ X2552 @ X2549)|~(in @ X2552 @ (binunion @ X2549 @ X2550))|~(in @ X2552 @ X2548)|~(in @ X2550 @ (powerset @ X2548))|~(in @ X2549 @ (powerset @ X2548))))&(((in @ X2552 @ X2550)|(X2551)|~(X2551)|~(in @ X2552 @ (binunion @ X2549 @ X2550))|~(in @ X2552 @ X2548)|~(in @ X2550 @ (powerset @ X2548))|~(in @ X2549 @ (powerset @ X2548)))&(~(X2551)|(X2551)|~(X2551)|~(in @ X2552 @ (binunion @ X2549 @ X2550))|~(in @ X2552 @ X2548)|~(in @ X2550 @ (powerset @ X2548))|~(in @ X2549 @ (powerset @ X2548)))))&((~(in @ X2554 @ (powerset @ X2553))|(~(in @ X2555 @ (powerset @ X2553))|(~(in @ X2556 @ X2553)|((in @ X2556 @ X2554)|((in @ X2556 @ X2555)|~(in @ X2556 @ (binunion @ X2554 @ X2555)))))))&((~(in @ X2558 @ (powerset @ X2557))|(~(in @ X2559 @ (powerset @ X2557))|(~(in @ X2560 @ X2557)|(~(in @ X2560 @ (setminus @ X2557 @ (binunion @ X2558 @ X2559)))|(in @ X2560 @ (setminus @ X2557 @ X2558))))))&((~(in @ X2562 @ (powerset @ X2561))|(~(in @ X2563 @ (powerset @ X2561))|(in @ (setminus @ X2561 @ (binunion @ X2562 @ X2563)) @ (powerset @ (setminus @ X2561 @ X2562)))))&((~(in @ X2565 @ (powerset @ X2564))|(~(in @ X2566 @ (powerset @ X2564))|(~(in @ X2567 @ X2564)|(~(in @ X2567 @ (setminus @ X2564 @ (binunion @ X2565 @ X2566)))|(in @ X2567 @ (setminus @ X2564 @ X2566))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ esk71_0)&((in @ esk74_0 @ (setminus @ esk71_0 @ (binintersect @ esk72_0 @ esk73_0)))&~(in @ esk74_0 @ (binunion @ (setminus @ esk71_0 @ esk72_0) @ (setminus @ esk71_0 @ esk73_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_319])])])])])])). 0.43/0.95 thf(c_0_321, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_320])). 0.43/0.95 thf(c_0_322, negated_conjecture, (in @ esk74_0 @ (setminus @ esk71_0 @ (binintersect @ esk72_0 @ esk73_0))), inference(split_conjunct,[status(thm)],[c_0_320])). 0.43/0.95 thf(c_0_323, negated_conjecture, ~((in @ esk74_0 @ (binunion @ (setminus @ esk71_0 @ esk72_0) @ (setminus @ esk71_0 @ esk73_0)))), inference(split_conjunct,[status(thm)],[c_0_320])). 0.43/0.95 thf(c_0_324, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X4 @ X3))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_320])). 0.43/0.95 thf(c_0_325, negated_conjecture, ~((in @ esk74_0 @ (binintersect @ esk72_0 @ esk73_0))), inference(spm,[status(thm)],[c_0_321, c_0_322])). 0.43/0.95 thf(c_0_326, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ (binintersect @ X3 @ X4))|~((in @ X2 @ X3))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_320])). 0.43/0.95 thf(c_0_327, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ esk73_0))), inference(spm,[status(thm)],[c_0_323, c_0_324])). 0.43/0.95 thf(c_0_328, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_320])). 0.43/0.95 thf(c_0_329, negated_conjecture, (in @ esk74_0 @ esk71_0), inference(split_conjunct,[status(thm)],[c_0_320])). 0.43/0.95 thf(c_0_330, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_320])). 0.43/0.95 thf(c_0_331, negated_conjecture, (~((in @ esk74_0 @ esk73_0))|~((in @ esk74_0 @ esk72_0))), inference(spm,[status(thm)],[c_0_325, c_0_326])). 0.43/0.95 thf(c_0_332, negated_conjecture, (in @ esk74_0 @ esk73_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_327, c_0_328]), c_0_329])])). 0.43/0.95 thf(c_0_333, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ esk72_0))), inference(spm,[status(thm)],[c_0_323, c_0_330])). 0.43/0.95 thf(c_0_334, negated_conjecture, ~((in @ esk74_0 @ esk72_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_331, c_0_332])])). 0.43/0.95 thf(c_0_335, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333, c_0_328]), c_0_329])]), c_0_334]), ['proof']). 0.43/0.95 # SZS output end CNFRefutation 0.43/0.95 # Parsed axioms : 577 0.43/0.95 # Removed by relevancy pruning/SinE : 310 0.43/0.95 # Initial clauses : 426 0.43/0.95 # Removed in clause preprocessing : 32 0.43/0.95 # Initial clauses in saturation : 394 0.43/0.95 # Processed clauses : 810 0.43/0.95 # ...of these trivial : 11 0.43/0.95 # ...subsumed : 54 0.43/0.95 # ...remaining for further processing : 744 0.43/0.95 # Other redundant clauses eliminated : 54 0.43/0.95 # Clauses deleted for lack of memory : 0 0.43/0.95 # Backward-subsumed : 2 0.43/0.95 # Backward-rewritten : 7 0.43/0.95 # Generated clauses : 8260 0.43/0.95 # ...of the previous two non-redundant : 8017 0.43/0.95 # ...aggressively subsumed : 0 0.43/0.95 # Contextual simplify-reflections : 8 0.43/0.95 # Paramodulations : 8171 0.43/0.95 # Factorizations : 2 0.43/0.95 # NegExts : 0 0.43/0.95 # Equation resolutions : 61 0.43/0.95 # Total rewrite steps : 214 0.43/0.95 # Propositional unsat checks : 0 0.43/0.95 # Propositional check models : 0 0.43/0.95 # Propositional check unsatisfiable : 0 0.43/0.95 # Propositional clauses : 0 0.43/0.95 # Propositional clauses after purity: 0 0.43/0.95 # Propositional unsat core size : 0 0.43/0.95 # Propositional preprocessing time : 0.000 0.43/0.95 # Propositional encoding time : 0.000 0.43/0.95 # Propositional solver time : 0.000 0.43/0.95 # Success case prop preproc time : 0.000 0.43/0.95 # Success case prop encoding time : 0.000 0.43/0.95 # Success case prop solver time : 0.000 0.43/0.95 # Current number of processed clauses : 376 0.43/0.95 # Positive orientable unit clauses : 49 0.43/0.95 # Positive unorientable unit clauses: 0 0.43/0.95 # Negative unit clauses : 13 0.43/0.95 # Non-unit-clauses : 314 0.43/0.95 # Current number of unprocessed clauses: 7931 0.43/0.95 # ...number of literals in the above : 33590 0.43/0.95 # Current number of archived formulas : 0 0.43/0.95 # Current number of archived clauses : 352 0.43/0.95 # Clause-clause subsumption calls (NU) : 66640 0.43/0.95 # Rec. Clause-clause subsumption calls : 28659 0.43/0.95 # Non-unit clause-clause subsumptions : 47 0.43/0.95 # Unit Clause-clause subsumption calls : 1390 0.43/0.95 # Rewrite failures with RHS unbound : 0 0.43/0.95 # BW rewrite match attempts : 36 0.43/0.95 # BW rewrite match successes : 5 0.43/0.95 # Condensation attempts : 0 0.43/0.95 # Condensation successes : 0 0.43/0.95 # Termbank termtop insertions : 211644 0.43/0.95 0.43/0.95 # ------------------------------------------------- 0.43/0.95 # User time : 0.330 s 0.43/0.95 # System time : 0.024 s 0.43/0.95 # Total time : 0.354 s 0.43/0.95 # Maximum resident set size: 8284 pages 0.43/0.98 0.43/0.98 # ------------------------------------------------- 0.43/0.98 # User time : 0.345 s 0.43/0.98 # System time : 0.028 s 0.43/0.98 # Total time : 0.373 s 0.43/0.98 # Maximum resident set size: 2744 pages 0.43/0.98 % E---3.1 exiting 0.43/0.98 EOF