0.11/0.19 % Problem : Vampire---4.8_14217 : TPTP v0.0.0. Released v0.0.0. 0.11/0.20 % Command : run_E %s %d THM 0.19/0.41 % Computer : n009.cluster.edu 0.19/0.41 % Model : x86_64 x86_64 0.19/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.19/0.41 % Memory : 8042.1875MB 0.19/0.41 % OS : Linux 3.10.0-693.el7.x86_64 0.19/0.41 % CPULimit : 1440 0.19/0.41 % WCLimit : 180 0.19/0.41 % DateTime : Mon Jul 3 12:54:26 EDT 2023 0.19/0.41 % CPUTime : 0.37/0.61 Running higher-order theorem provingRunning: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217 0.37/0.61 # Version: 3.1pre001-ho 0.45/0.86 # Preprocessing class: HSLMSLSSLLLCHSA. 0.45/0.86 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 0.45/0.86 # Starting ho_unfolding_5 with 720s (4) cores 0.45/0.86 # Starting pre_casc_3 with 180s (1) cores 0.45/0.86 # Starting new_ho_10_cnf2 with 180s (1) cores 0.45/0.86 # Starting full_lambda_10 with 180s (1) cores 0.45/0.86 # Starting ehoh_best_nonlift_rwall with 180s (1) cores 0.45/0.86 # ho_unfolding_5 with pid 14397 completed with status 0 0.45/0.86 # Result found by ho_unfolding_5 0.45/0.86 # Preprocessing class: HSLMSLSSLLLCHSA. 0.45/0.86 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 0.45/0.86 # Starting ho_unfolding_5 with 720s (4) cores 0.45/0.86 # No SInE strategy applied 0.45/0.86 # Search class: HGHSM-FSLM32-MHSMMSBN 0.45/0.86 # Scheduled 12 strats onto 4 cores with 720 seconds (720 total) 0.45/0.86 # Starting full_lambda_5 with 59s (1) cores 0.45/0.86 # Starting ho_unfolding_5 with 73s (1) cores 0.45/0.86 # Starting pre_casc_4 with 59s (1) cores 0.45/0.86 # Starting pre_casc_3 with 59s (1) cores 0.45/0.86 # pre_casc_3 with pid 14405 completed with status 0 0.45/0.86 # Result found by pre_casc_3 0.45/0.86 # Preprocessing class: HSLMSLSSLLLCHSA. 0.45/0.86 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 0.45/0.86 # Starting ho_unfolding_5 with 720s (4) cores 0.45/0.86 # No SInE strategy applied 0.45/0.86 # Search class: HGHSM-FSLM32-MHSMMSBN 0.45/0.86 # Scheduled 12 strats onto 4 cores with 720 seconds (720 total) 0.45/0.86 # Starting full_lambda_5 with 59s (1) cores 0.45/0.86 # Starting ho_unfolding_5 with 73s (1) cores 0.45/0.86 # Starting pre_casc_4 with 59s (1) cores 0.45/0.86 # Starting pre_casc_3 with 59s (1) cores 0.45/0.86 # Preprocessing time : 0.012 s 0.45/0.86 # Presaturation interreduction done 0.45/0.86 0.45/0.86 # Proof found! 0.45/0.86 # SZS status Theorem 0.45/0.86 # SZS output start CNFRefutation 0.45/0.86 thf(decl_22, type, in: $i > $i > $o). 0.45/0.86 thf(decl_23, type, exu: ($i > $o) > $o). 0.45/0.86 thf(decl_24, type, setextAx: $o). 0.45/0.86 thf(decl_25, type, emptyset: $i). 0.45/0.86 thf(decl_26, type, emptysetAx: $o). 0.45/0.86 thf(decl_27, type, setadjoin: $i > $i > $i). 0.45/0.86 thf(decl_28, type, setadjoinAx: $o). 0.45/0.86 thf(decl_29, type, powerset: $i > $i). 0.45/0.86 thf(decl_30, type, powersetAx: $o). 0.45/0.86 thf(decl_31, type, setunion: $i > $i). 0.45/0.86 thf(decl_32, type, setunionAx: $o). 0.45/0.86 thf(decl_33, type, omega: $i). 0.45/0.86 thf(decl_34, type, omega0Ax: $o). 0.45/0.86 thf(decl_35, type, omegaSAx: $o). 0.45/0.86 thf(decl_36, type, omegaIndAx: $o). 0.45/0.86 thf(decl_37, type, replAx: $o). 0.45/0.86 thf(decl_38, type, foundationAx: $o). 0.45/0.86 thf(decl_39, type, wellorderingAx: $o). 0.45/0.86 thf(decl_40, type, descr: ($i > $o) > $i). 0.45/0.86 thf(decl_41, type, descrp: $o). 0.45/0.86 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_43, type, dsetconstrI: $o). 0.45/0.86 thf(decl_44, type, dsetconstrEL: $o). 0.45/0.86 thf(decl_45, type, dsetconstrER: $o). 0.45/0.86 thf(decl_46, type, exuE1: $o). 0.45/0.86 thf(decl_47, type, prop2set: $o > $i). 0.45/0.86 thf(decl_48, type, prop2setE: $o). 0.45/0.86 thf(decl_49, type, emptysetE: $o). 0.45/0.86 thf(decl_50, type, emptysetimpfalse: $o). 0.45/0.86 thf(decl_51, type, notinemptyset: $o). 0.45/0.86 thf(decl_52, type, exuE3e: $o). 0.45/0.86 thf(decl_53, type, setext: $o). 0.45/0.86 thf(decl_54, type, emptyI: $o). 0.45/0.86 thf(decl_55, type, noeltsimpempty: $o). 0.45/0.86 thf(decl_56, type, setbeta: $o). 0.45/0.86 thf(decl_57, type, nonempty: $i > $o). 0.45/0.86 thf(decl_58, type, nonemptyE1: $o). 0.45/0.86 thf(decl_59, type, nonemptyI: $o). 0.45/0.86 thf(decl_60, type, nonemptyI1: $o). 0.45/0.86 thf(decl_61, type, setadjoinIL: $o). 0.45/0.86 thf(decl_62, type, emptyinunitempty: $o). 0.45/0.86 thf(decl_63, type, setadjoinIR: $o). 0.45/0.86 thf(decl_64, type, setadjoinE: $o). 0.45/0.86 thf(decl_65, type, setadjoinOr: $o). 0.45/0.86 thf(decl_66, type, setoftrueEq: $o). 0.45/0.86 thf(decl_67, type, powersetI: $o). 0.45/0.86 thf(decl_68, type, emptyinPowerset: $o). 0.45/0.86 thf(decl_69, type, emptyInPowerset: $o). 0.45/0.86 thf(decl_70, type, powersetE: $o). 0.45/0.86 thf(decl_71, type, setunionI: $o). 0.45/0.86 thf(decl_72, type, setunionE: $o). 0.45/0.86 thf(decl_73, type, subPowSU: $o). 0.45/0.86 thf(decl_74, type, exuE2: $o). 0.45/0.86 thf(decl_75, type, nonemptyImpWitness: $o). 0.45/0.86 thf(decl_76, type, uniqinunit: $o). 0.45/0.86 thf(decl_77, type, notinsingleton: $o). 0.45/0.86 thf(decl_78, type, eqinunit: $o). 0.45/0.86 thf(decl_79, type, singletonsswitch: $o). 0.45/0.86 thf(decl_80, type, upairsetE: $o). 0.45/0.86 thf(decl_81, type, upairsetIL: $o). 0.45/0.86 thf(decl_82, type, upairsetIR: $o). 0.45/0.86 thf(decl_83, type, emptyE1: $o). 0.45/0.86 thf(decl_84, type, vacuousDall: $o). 0.45/0.86 thf(decl_85, type, quantDeMorgan1: $o). 0.45/0.86 thf(decl_86, type, quantDeMorgan2: $o). 0.45/0.86 thf(decl_87, type, quantDeMorgan3: $o). 0.45/0.86 thf(decl_88, type, quantDeMorgan4: $o). 0.45/0.86 thf(decl_89, type, prop2setI: $o). 0.45/0.86 thf(decl_90, type, set2prop: $i > $o). 0.45/0.86 thf(decl_91, type, prop2set2propI: $o). 0.45/0.86 thf(decl_92, type, notdexE: $o). 0.45/0.86 thf(decl_93, type, notdallE: $o). 0.45/0.86 thf(decl_94, type, exuI1: $o). 0.45/0.86 thf(decl_95, type, exuI3: $o). 0.45/0.86 thf(decl_96, type, exuI2: $o). 0.45/0.86 thf(decl_97, type, inCongP: $o). 0.45/0.86 thf(decl_98, type, in__Cong: $o). 0.45/0.86 thf(decl_99, type, exuE3u: $o). 0.45/0.86 thf(decl_100, type, exu__Cong: $o). 0.45/0.86 thf(decl_101, type, emptyset__Cong: $o). 0.45/0.86 thf(decl_102, type, setadjoin__Cong: $o). 0.45/0.86 thf(decl_103, type, powerset__Cong: $o). 0.45/0.86 thf(decl_104, type, setunion__Cong: $o). 0.45/0.86 thf(decl_105, type, omega__Cong: $o). 0.45/0.86 thf(decl_106, type, exuEu: $o). 0.45/0.86 thf(decl_107, type, descr__Cong: $o). 0.45/0.86 thf(decl_108, type, dsetconstr__Cong: $o). 0.45/0.86 thf(decl_109, type, subset: $i > $i > $o). 0.45/0.86 thf(decl_112, type, subsetI1: $o). 0.45/0.86 thf(decl_113, type, eqimpsubset2: $o). 0.45/0.86 thf(decl_114, type, eqimpsubset1: $o). 0.45/0.86 thf(decl_115, type, subsetI2: $o). 0.45/0.86 thf(decl_116, type, emptysetsubset: $o). 0.45/0.86 thf(decl_117, type, subsetE: $o). 0.45/0.86 thf(decl_118, type, subsetE2: $o). 0.45/0.86 thf(decl_119, type, notsubsetI: $o). 0.45/0.86 thf(decl_120, type, notequalI1: $o). 0.45/0.86 thf(decl_121, type, notequalI2: $o). 0.45/0.86 thf(decl_122, type, subsetRefl: $o). 0.45/0.86 thf(decl_123, type, subsetTrans: $o). 0.45/0.86 thf(decl_124, type, setadjoinSub: $o). 0.45/0.86 thf(decl_125, type, setadjoinSub2: $o). 0.45/0.86 thf(decl_126, type, subset2powerset: $o). 0.45/0.86 thf(decl_127, type, setextsub: $o). 0.45/0.86 thf(decl_128, type, subsetemptysetimpeq: $o). 0.45/0.86 thf(decl_129, type, powersetI1: $o). 0.45/0.86 thf(decl_130, type, powersetE1: $o). 0.45/0.86 thf(decl_131, type, inPowerset: $o). 0.45/0.86 thf(decl_132, type, powersetsubset: $o). 0.45/0.86 thf(decl_133, type, sepInPowerset: $o). 0.45/0.86 thf(decl_134, type, sepSubset: $o). 0.45/0.86 thf(decl_135, type, binunion: $i > $i > $i). 0.45/0.86 thf(decl_136, type, binunionIL: $o). 0.45/0.86 thf(decl_137, type, upairset2IR: $o). 0.45/0.86 thf(decl_138, type, binunionIR: $o). 0.45/0.86 thf(decl_139, type, binunionEcases: $o). 0.45/0.86 thf(decl_140, type, binunionE: $o). 0.45/0.86 thf(decl_141, type, binunionLsub: $o). 0.45/0.86 thf(decl_142, type, binunionRsub: $o). 0.45/0.86 thf(decl_143, type, binintersect: $i > $i > $i). 0.45/0.86 thf(decl_144, type, binintersectI: $o). 0.45/0.86 thf(decl_145, type, binintersectSubset5: $o). 0.45/0.86 thf(decl_146, type, binintersectEL: $o). 0.45/0.86 thf(decl_147, type, binintersectLsub: $o). 0.45/0.86 thf(decl_148, type, binintersectSubset2: $o). 0.45/0.86 thf(decl_149, type, binintersectSubset3: $o). 0.45/0.86 thf(decl_150, type, binintersectER: $o). 0.45/0.86 thf(decl_151, type, disjointsetsI1: $o). 0.45/0.86 thf(decl_152, type, binintersectRsub: $o). 0.45/0.86 thf(decl_153, type, binintersectSubset4: $o). 0.45/0.86 thf(decl_154, type, binintersectSubset1: $o). 0.45/0.86 thf(decl_155, type, bs114d: $o). 0.45/0.86 thf(decl_157, type, setminus: $i > $i > $i). 0.45/0.86 thf(decl_158, type, setminusI: $o). 0.45/0.86 thf(decl_159, type, setminusEL: $o). 0.45/0.86 thf(decl_160, type, setminusER: $o). 0.45/0.86 thf(decl_161, type, setminusSubset2: $o). 0.45/0.86 thf(decl_162, type, setminusERneg: $o). 0.45/0.86 thf(decl_163, type, setminusELneg: $o). 0.45/0.86 thf(decl_164, type, setminusILneg: $o). 0.45/0.86 thf(decl_165, type, setminusIRneg: $o). 0.45/0.86 thf(decl_166, type, setminusLsub: $o). 0.45/0.86 thf(decl_167, type, setminusSubset1: $o). 0.45/0.86 thf(decl_168, type, symdiff: $i > $i > $i). 0.45/0.86 thf(decl_169, type, symdiffE: $o). 0.45/0.86 thf(decl_170, type, symdiffI1: $o). 0.45/0.86 thf(decl_171, type, symdiffI2: $o). 0.45/0.86 thf(decl_172, type, symdiffIneg1: $o). 0.45/0.86 thf(decl_173, type, symdiffIneg2: $o). 0.45/0.86 thf(decl_174, type, iskpair: $i > $o). 0.45/0.86 thf(decl_175, type, secondinupair: $o). 0.45/0.86 thf(decl_176, type, setukpairIL: $o). 0.45/0.86 thf(decl_177, type, setukpairIR: $o). 0.45/0.86 thf(decl_178, type, kpairiskpair: $o). 0.45/0.86 thf(decl_179, type, kpair: $i > $i > $i). 0.45/0.86 thf(decl_180, type, kpairp: $o). 0.45/0.86 thf(decl_181, type, cartprod: $i > $i > $i). 0.45/0.86 thf(decl_182, type, singletonsubset: $o). 0.45/0.86 thf(decl_183, type, singletoninpowerset: $o). 0.45/0.86 thf(decl_184, type, singletoninpowunion: $o). 0.45/0.86 thf(decl_185, type, upairset2E: $o). 0.45/0.86 thf(decl_186, type, upairsubunion: $o). 0.45/0.86 thf(decl_187, type, upairinpowunion: $o). 0.45/0.86 thf(decl_188, type, ubforcartprodlem1: $o). 0.45/0.86 thf(decl_189, type, ubforcartprodlem2: $o). 0.45/0.86 thf(decl_190, type, ubforcartprodlem3: $o). 0.45/0.86 thf(decl_191, type, cartprodpairin: $o). 0.45/0.86 thf(decl_192, type, cartprodmempair1: $o). 0.45/0.86 thf(decl_193, type, cartprodmempair: $o). 0.45/0.86 thf(decl_194, type, setunionE2: $o). 0.45/0.86 thf(decl_195, type, setunionsingleton1: $o). 0.45/0.86 thf(decl_196, type, setunionsingleton2: $o). 0.45/0.86 thf(decl_197, type, setunionsingleton: $o). 0.45/0.86 thf(decl_198, type, singleton: $i > $o). 0.45/0.86 thf(decl_199, type, singletonprop: $o). 0.45/0.86 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 0.45/0.86 thf(decl_201, type, ex1E1: $o). 0.45/0.86 thf(decl_202, type, ex1I: $o). 0.45/0.86 thf(decl_203, type, ex1I2: $o). 0.45/0.86 thf(decl_204, type, singletonsuniq: $o). 0.45/0.86 thf(decl_209, type, setukpairinjL1: $o). 0.45/0.86 thf(decl_210, type, kfstsingleton: $o). 0.45/0.86 thf(decl_211, type, theprop: $o). 0.45/0.86 thf(decl_212, type, kfst: $i > $i). 0.45/0.86 thf(decl_213, type, kfstpairEq: $o). 0.45/0.86 thf(decl_214, type, cartprodfstin: $o). 0.45/0.86 thf(decl_215, type, setukpairinjL2: $o). 0.45/0.86 thf(decl_216, type, setukpairinjL: $o). 0.45/0.86 thf(decl_217, type, setukpairinjR11: $o). 0.45/0.86 thf(decl_218, type, setukpairinjR12: $o). 0.45/0.86 thf(decl_219, type, setukpairinjR1: $o). 0.45/0.86 thf(decl_220, type, upairequniteq: $o). 0.45/0.86 thf(decl_221, type, setukpairinjR2: $o). 0.45/0.86 thf(decl_222, type, setukpairinjR: $o). 0.45/0.86 thf(decl_223, type, ksndsingleton: $o). 0.45/0.86 thf(decl_224, type, ksnd: $i > $i). 0.45/0.86 thf(decl_225, type, ksndpairEq: $o). 0.45/0.86 thf(decl_226, type, kpairsurjEq: $o). 0.45/0.86 thf(decl_227, type, cartprodsndin: $o). 0.45/0.86 thf(decl_228, type, cartprodpairmemEL: $o). 0.45/0.86 thf(decl_229, type, cartprodpairmemER: $o). 0.45/0.86 thf(decl_230, type, cartprodmempaircEq: $o). 0.45/0.86 thf(decl_231, type, cartprodfstpairEq: $o). 0.45/0.86 thf(decl_232, type, cartprodsndpairEq: $o). 0.45/0.86 thf(decl_233, type, cartprodpairsurjEq: $o). 0.45/0.86 thf(decl_234, type, breln: $i > $i > $i > $o). 0.45/0.86 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.45/0.86 thf(decl_236, type, dpsetconstrI: $o). 0.45/0.86 thf(decl_237, type, dpsetconstrSub: $o). 0.45/0.86 thf(decl_238, type, setOfPairsIsBReln: $o). 0.45/0.86 thf(decl_239, type, dpsetconstrERa: $o). 0.45/0.86 thf(decl_240, type, dpsetconstrEL1: $o). 0.45/0.86 thf(decl_241, type, dpsetconstrEL2: $o). 0.45/0.86 thf(decl_242, type, dpsetconstrER: $o). 0.45/0.86 thf(decl_243, type, func: $i > $i > $i > $o). 0.45/0.86 thf(decl_244, type, funcSet: $i > $i > $i). 0.45/0.86 thf(decl_245, type, funcImageSingleton: $o). 0.45/0.86 thf(decl_246, type, apProp: $o). 0.45/0.86 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 0.45/0.86 thf(decl_248, type, app: $o). 0.45/0.86 thf(decl_249, type, infuncsetfunc: $o). 0.45/0.86 thf(decl_250, type, ap2p: $o). 0.45/0.86 thf(decl_251, type, funcinfuncset: $o). 0.45/0.86 thf(decl_252, type, lamProp: $o). 0.45/0.86 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 0.45/0.86 thf(decl_254, type, lamp: $o). 0.45/0.86 thf(decl_255, type, lam2p: $o). 0.45/0.86 thf(decl_256, type, brelnall1: $o). 0.45/0.86 thf(decl_257, type, brelnall2: $o). 0.45/0.86 thf(decl_258, type, ex1E2: $o). 0.45/0.86 thf(decl_259, type, funcGraphProp1: $o). 0.45/0.86 thf(decl_260, type, funcGraphProp3: $o). 0.45/0.86 thf(decl_261, type, funcGraphProp2: $o). 0.45/0.86 thf(decl_262, type, funcextLem: $o). 0.45/0.86 thf(decl_263, type, funcGraphProp4: $o). 0.45/0.86 thf(decl_264, type, subbreln: $o). 0.45/0.86 thf(decl_265, type, eqbreln: $o). 0.45/0.86 thf(decl_266, type, funcext: $o). 0.45/0.86 thf(decl_267, type, funcext2: $o). 0.45/0.86 thf(decl_268, type, ap2apEq1: $o). 0.45/0.86 thf(decl_269, type, ap2apEq2: $o). 0.45/0.86 thf(decl_270, type, beta1: $o). 0.45/0.86 thf(decl_271, type, eta1: $o). 0.45/0.86 thf(decl_272, type, lam2lamEq: $o). 0.45/0.86 thf(decl_273, type, beta2: $o). 0.45/0.86 thf(decl_274, type, eta2: $o). 0.45/0.86 thf(decl_275, type, iffalseProp1: $o). 0.45/0.86 thf(decl_276, type, iffalseProp2: $o). 0.45/0.86 thf(decl_277, type, iftrueProp1: $o). 0.45/0.86 thf(decl_278, type, iftrueProp2: $o). 0.45/0.86 thf(decl_279, type, ifSingleton: $o). 0.45/0.86 thf(decl_280, type, if: $i > $o > $i > $i > $i). 0.45/0.86 thf(decl_281, type, ifp: $o). 0.45/0.86 thf(decl_282, type, theeq: $o). 0.45/0.86 thf(decl_283, type, iftrue: $o). 0.45/0.86 thf(decl_284, type, iffalse: $o). 0.45/0.86 thf(decl_285, type, iftrueorfalse: $o). 0.45/0.86 thf(decl_286, type, binintersectT_lem: $o). 0.45/0.86 thf(decl_287, type, binunionT_lem: $o). 0.45/0.86 thf(decl_288, type, powersetT_lem: $o). 0.45/0.86 thf(decl_289, type, setminusT_lem: $o). 0.45/0.86 thf(decl_290, type, complementT_lem: $o). 0.45/0.86 thf(decl_291, type, setextT: $o). 0.45/0.86 thf(decl_292, type, subsetTI: $o). 0.45/0.86 thf(decl_293, type, powersetTI1: $o). 0.45/0.86 thf(decl_294, type, powersetTE1: $o). 0.45/0.86 thf(decl_295, type, complementTI1: $o). 0.45/0.86 thf(decl_296, type, complementTE1: $o). 0.45/0.86 thf(decl_297, type, binintersectTELcontra: $o). 0.45/0.86 thf(decl_298, type, binintersectTERcontra: $o). 0.45/0.86 thf(decl_299, type, contrasubsetT: $o). 0.45/0.86 thf(decl_300, type, contrasubsetT1: $o). 0.45/0.86 thf(decl_301, type, contrasubsetT2: $o). 0.45/0.86 thf(decl_302, type, contrasubsetT3: $o). 0.45/0.86 thf(decl_303, type, doubleComplementI1: $o). 0.45/0.86 thf(decl_304, type, doubleComplementE1: $o). 0.45/0.86 thf(decl_305, type, doubleComplementSub1: $o). 0.45/0.86 thf(decl_306, type, doubleComplementSub2: $o). 0.45/0.86 thf(decl_307, type, doubleComplementEq: $o). 0.45/0.86 thf(decl_308, type, complementTnotintersectT: $o). 0.45/0.86 thf(decl_309, type, complementImpComplementIntersect: $o). 0.45/0.86 thf(decl_310, type, complementSubsetComplementIntersect: $o). 0.45/0.86 thf(decl_311, type, complementInPowersetComplementIntersect: $o). 0.45/0.86 thf(decl_312, type, contraSubsetComplement: $o). 0.45/0.86 thf(decl_313, type, complementTcontraSubset: $o). 0.45/0.86 thf(decl_314, type, binunionTILcontra: $o). 0.45/0.86 thf(decl_315, type, binunionTIRcontra: $o). 0.45/0.86 thf(decl_316, type, inIntersectImpInUnion: $o). 0.45/0.86 thf(decl_317, type, inIntersectImpInUnion2: $o). 0.45/0.86 thf(decl_318, type, inIntersectImpInIntersectUnions: $o). 0.45/0.86 thf(decl_319, type, intersectInPowersetIntersectUnions: $o). 0.45/0.86 thf(decl_320, type, inComplementUnionImpNotIn1: $o). 0.45/0.86 thf(decl_321, type, inComplementUnionImpInComplement1: $o). 0.45/0.86 thf(decl_322, type, binunionTE: $o). 0.45/0.86 thf(decl_323, type, binunionTEcontra: $o). 0.45/0.86 thf(decl_324, type, demorgan2a1: $o). 0.45/0.86 thf(decl_325, type, complementUnionInPowersetComplement: $o). 0.45/0.86 thf(decl_326, type, demorgan2a2: $o). 0.45/0.86 thf(decl_327, type, demorgan1a: $o). 0.45/0.86 thf(decl_328, type, demorgan1b: $o). 0.45/0.86 thf(decl_329, type, demorgan1: $o). 0.45/0.86 thf(decl_330, type, demorgan2a: $o). 0.45/0.86 thf(decl_331, type, demorgan2b2: $o). 0.45/0.86 thf(decl_332, type, demorgan2b: $o). 0.45/0.86 thf(decl_333, type, demorgan2: $o). 0.45/0.86 thf(decl_334, type, woz13rule0: $o). 0.45/0.86 thf(decl_335, type, woz13rule1: $o). 0.45/0.86 thf(decl_336, type, woz13rule2: $o). 0.45/0.86 thf(decl_337, type, woz13rule3: $o). 0.45/0.86 thf(decl_338, type, woz13rule4: $o). 0.45/0.86 thf(decl_339, type, woz1_1: $o). 0.45/0.86 thf(decl_340, type, woz1_2: $o). 0.45/0.86 thf(decl_341, type, woz1_3: $o). 0.45/0.86 thf(decl_342, type, woz1_4: $o). 0.45/0.86 thf(decl_343, type, woz1_5: $o). 0.45/0.86 thf(decl_344, type, breln1: $i > $i > $o). 0.45/0.86 thf(decl_345, type, breln1all2: $o). 0.45/0.86 thf(decl_346, type, breln1Set: $i > $i). 0.45/0.86 thf(decl_347, type, breln1SetBreln1: $o). 0.45/0.86 thf(decl_353, type, reflwellordering: $i > $i > $o). 0.45/0.86 thf(decl_354, type, choice2fnsingleton: $o). 0.45/0.86 thf(decl_355, type, setOfPairsIsBReln1: $o). 0.45/0.86 thf(decl_356, type, breln1all1: $o). 0.45/0.86 thf(decl_357, type, subbreln1: $o). 0.45/0.86 thf(decl_358, type, eqbreln1: $o). 0.45/0.86 thf(decl_359, type, breln1invset: $i > $i > $i). 0.45/0.86 thf(decl_360, type, breln1invprop: $o). 0.45/0.86 thf(decl_361, type, breln1invI: $o). 0.45/0.86 thf(decl_362, type, breln1invE: $o). 0.45/0.86 thf(decl_363, type, breln1compset: $i > $i > $i > $i). 0.45/0.86 thf(decl_364, type, breln1compprop: $o). 0.45/0.86 thf(decl_365, type, breln1compI: $o). 0.45/0.86 thf(decl_366, type, breln1compE: $o). 0.45/0.86 thf(decl_367, type, breln1compEex: $o). 0.45/0.86 thf(decl_368, type, breln1unionprop: $o). 0.45/0.86 thf(decl_369, type, breln1unionIL: $o). 0.45/0.86 thf(decl_370, type, breln1unionIR: $o). 0.45/0.86 thf(decl_371, type, breln1unionI: $o). 0.45/0.86 thf(decl_372, type, breln1unionE: $o). 0.45/0.86 thf(decl_373, type, breln1unionEcases: $o). 0.45/0.86 thf(decl_374, type, breln1unionCommutes: $o). 0.45/0.86 thf(decl_375, type, woz2Ex: $o). 0.45/0.86 thf(decl_376, type, woz2W: $o). 0.45/0.86 thf(decl_377, type, woz2A: $o). 0.45/0.86 thf(decl_378, type, woz2B: $o). 0.45/0.86 thf(decl_379, type, image1Ex: $o). 0.45/0.86 thf(decl_380, type, image1Ex1: $o). 0.45/0.86 thf(decl_381, type, image1: $i > ($i > $i) > $i). 0.45/0.86 thf(decl_382, type, image1Equiv: $o). 0.45/0.86 thf(decl_383, type, epred1_0: $o). 0.45/0.86 thf(decl_384, type, esk1_2: $i > $i > $i). 0.45/0.86 thf(decl_385, type, esk2_2: $i > $i > $i). 0.45/0.86 thf(decl_386, type, esk3_2: $i > $i > $i). 0.45/0.86 thf(decl_387, type, esk4_1: $i > $i). 0.45/0.86 thf(decl_388, type, esk5_2: ($i > $i > $o) > $i > $i). 0.45/0.86 thf(decl_389, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.45/0.86 thf(decl_390, type, esk7_2: ($i > $i > $o) > $i > $i). 0.45/0.86 thf(decl_391, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.45/0.86 thf(decl_392, type, esk9_1: $i > $i). 0.45/0.86 thf(decl_393, type, esk10_2: ($i > $o) > $i > $i). 0.45/0.86 thf(decl_394, type, esk11_2: ($i > $o) > $i > $i). 0.45/0.86 thf(decl_395, type, esk12_1: ($i > $o) > $i). 0.45/0.86 thf(decl_396, type, esk13_2: ($i > $o) > $i > $i). 0.45/0.86 thf(decl_397, type, esk14_1: ($i > $o) > $i). 0.45/0.86 thf(decl_398, type, esk15_2: $i > $i > $i). 0.45/0.86 thf(decl_399, type, esk16_2: $i > $i > $i). 0.45/0.86 thf(decl_400, type, esk17_1: $i > $i). 0.45/0.86 thf(decl_401, type, esk18_1: $i > $i). 0.45/0.86 thf(decl_402, type, esk19_1: $i > $i). 0.45/0.86 thf(decl_403, type, esk20_2: $i > $i > $i). 0.45/0.86 thf(decl_404, type, esk21_3: $i > $i > $o > $i). 0.45/0.86 thf(decl_405, type, esk22_2: ($i > $o) > $i > $i). 0.45/0.86 thf(decl_406, type, esk23_1: ($i > $o) > $i). 0.45/0.86 thf(decl_407, type, esk24_1: $i > $i). 0.45/0.86 thf(decl_408, type, esk25_2: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_409, type, esk26_2: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_410, type, esk27_2: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_411, type, esk28_2: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_412, type, esk29_2: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_413, type, esk30_2: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_414, type, esk31_2: ($i > $o) > $i > $i). 0.45/0.86 thf(decl_415, type, esk32_1: ($i > $o) > $i). 0.45/0.86 thf(decl_416, type, esk33_1: ($i > $o) > $i). 0.45/0.86 thf(decl_417, type, esk34_1: ($i > $o) > $i). 0.45/0.86 thf(decl_418, type, esk35_1: ($i > $o) > $i). 0.45/0.86 thf(decl_419, type, esk36_2: ($i > $o) > $i > $i). 0.45/0.86 thf(decl_420, type, esk37_1: ($i > $o) > $i). 0.45/0.86 thf(decl_421, type, esk38_2: ($i > $o) > $i > $i). 0.45/0.86 thf(decl_422, type, esk39_2: ($i > $o) > ($i > $o) > $i). 0.45/0.86 thf(decl_423, type, esk40_2: ($i > $o) > ($i > $o) > $i). 0.45/0.86 thf(decl_424, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 0.45/0.86 thf(decl_425, type, esk42_2: ($i > $o) > ($i > $o) > $i). 0.45/0.86 thf(decl_426, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 0.45/0.86 thf(decl_427, type, esk44_2: ($i > $o) > ($i > $o) > $i). 0.45/0.86 thf(decl_428, type, esk45_2: ($i > $o) > $i > $i). 0.45/0.86 thf(decl_429, type, esk46_2: ($i > $o) > ($i > $o) > $i). 0.45/0.86 thf(decl_430, type, esk47_2: ($i > $o) > ($i > $o) > $i). 0.45/0.86 thf(decl_431, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 0.45/0.86 thf(decl_432, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 0.45/0.86 thf(decl_433, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.45/0.86 thf(decl_434, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.45/0.86 thf(decl_435, type, esk52_2: $i > $i > $i). 0.45/0.86 thf(decl_436, type, esk53_2: $i > $i > $i). 0.45/0.86 thf(decl_437, type, esk54_2: $i > $i > $i). 0.45/0.86 thf(decl_438, type, esk55_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_439, type, esk56_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_440, type, esk57_2: $i > $i > $i). 0.45/0.86 thf(decl_441, type, esk58_2: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_442, type, esk59_2: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_443, type, esk60_2: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_444, type, esk61_3: $i > ($i > $o) > $i > $i). 0.45/0.86 thf(decl_445, type, esk62_2: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_446, type, esk63_2: $i > ($i > $o) > $i). 0.45/0.86 thf(decl_447, type, esk64_3: $i > $i > ($i > $i) > $i). 0.45/0.86 thf(decl_448, type, esk65_3: $i > $i > ($i > $i) > $i). 0.45/0.86 thf(decl_449, type, esk66_3: $i > $i > ($i > $i) > $i). 0.45/0.86 thf(decl_450, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 0.45/0.86 thf(decl_451, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 0.45/0.86 thf(decl_452, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 0.45/0.86 thf(decl_453, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 0.45/0.86 thf(decl_454, type, esk71_4: $i > $i > $i > $i > $i). 0.45/0.86 thf(decl_455, type, esk72_4: $i > $i > $i > $i > $i). 0.45/0.86 thf(decl_456, type, esk73_4: $i > $i > $i > $i > $i). 0.45/0.86 thf(decl_457, type, esk74_4: $i > $i > $i > $i > $i). 0.45/0.86 thf(decl_458, type, esk75_4: $i > $i > $i > $i > $i). 0.45/0.86 thf(decl_459, type, esk76_4: $i > $i > $i > $i > $i). 0.45/0.86 thf(decl_460, type, esk77_4: $i > $i > $i > $i > $i). 0.45/0.86 thf(decl_461, type, esk78_4: $i > $i > $i > $i > $i). 0.45/0.86 thf(decl_462, type, esk79_4: $i > $i > $i > $i > $i). 0.45/0.86 thf(decl_463, type, esk80_3: $i > $i > ($i > $i) > $i). 0.45/0.86 thf(decl_464, type, esk81_3: $i > $i > ($i > $i) > $i). 0.45/0.86 thf(decl_465, type, esk82_3: $i > $i > ($i > $i) > $i). 0.45/0.86 thf(decl_466, type, esk83_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_467, type, esk84_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_468, type, esk85_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_469, type, esk86_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_470, type, esk87_3: $i > $i > ($i > $o) > $i). 0.45/0.86 thf(decl_471, type, esk88_3: $i > $i > ($i > $o) > $i). 0.45/0.86 thf(decl_472, type, esk89_3: $i > $i > ($i > $i > $o) > $i). 0.45/0.86 thf(decl_473, type, esk90_3: $i > $i > ($i > $o) > $i). 0.45/0.86 thf(decl_474, type, esk91_3: $i > $i > ($i > $o) > $i). 0.45/0.86 thf(decl_475, type, esk92_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_476, type, esk93_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_477, type, esk94_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_478, type, esk95_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_479, type, esk96_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_480, type, esk97_3: $i > $i > $i > $i). 0.45/0.86 thf(decl_481, type, esk98_5: $i > $i > $i > $i > $i > $i). 0.45/0.86 thf(decl_482, type, esk99_6: $i > $i > $i > $i > $i > $o > $i). 0.45/0.86 thf(decl_483, type, esk100_2: $i > ($i > $i) > $i). 0.45/0.86 thf(decl_484, type, esk101_3: $i > ($i > $i) > $i > $i). 0.45/0.86 thf(decl_485, type, esk102_2: $i > ($i > $i) > $i). 0.45/0.86 thf(decl_486, type, esk103_3: $i > ($i > $i) > $i > $i). 0.45/0.86 thf(decl_487, type, esk104_3: $i > ($i > $i) > $i > $i). 0.45/0.86 thf(decl_488, type, esk105_3: $i > ($i > $i) > $i > $i). 0.45/0.86 thf(decl_489, type, esk106_3: $i > ($i > $i) > $i > $i). 0.45/0.86 thf(decl_490, type, esk107_0: $i). 0.45/0.86 thf(decl_491, type, esk108_0: $i > $i). 0.45/0.86 thf(decl_492, type, esk109_0: $i). 0.45/0.86 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', replAx)). 0.45/0.86 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', exu)). 0.45/0.86 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', descrp)). 0.45/0.86 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', exuE1)). 0.45/0.86 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', exuE3e)). 0.45/0.86 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', nonempty)). 0.45/0.86 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', nonemptyI)). 0.45/0.86 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', exuE2)). 0.45/0.86 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', exuI1)). 0.45/0.86 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', exuI3)). 0.45/0.86 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', exuI2)). 0.45/0.86 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', exuE3u)). 0.45/0.86 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', exu__Cong)). 0.45/0.86 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', exuEu)). 0.45/0.86 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', descr__Cong)). 0.45/0.86 thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', image1Ex1)). 0.45/0.86 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', dsetconstrI)). 0.45/0.86 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', dsetconstrEL)). 0.45/0.86 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', dsetconstrER)). 0.45/0.86 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setbeta)). 0.45/0.86 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', nonemptyE1)). 0.45/0.86 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', nonemptyI1)). 0.45/0.86 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setoftrueEq)). 0.45/0.86 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', nonemptyImpWitness)). 0.45/0.86 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', emptyE1)). 0.45/0.86 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', dsetconstr__Cong)). 0.45/0.86 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', sepInPowerset)). 0.45/0.86 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', sepSubset)). 0.45/0.86 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', singletonprop)). 0.45/0.86 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ex1E1)). 0.45/0.86 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ex1I)). 0.45/0.86 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ex1I2)). 0.45/0.86 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', kfstsingleton)). 0.45/0.86 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ksndsingleton)). 0.45/0.86 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', dpsetconstrI)). 0.45/0.86 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', dpsetconstrSub)). 0.45/0.86 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setOfPairsIsBReln)). 0.45/0.86 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', dpsetconstrERa)). 0.45/0.86 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', dpsetconstrEL1)). 0.45/0.86 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', dpsetconstrEL2)). 0.45/0.86 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', dpsetconstrER)). 0.45/0.86 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', funcImageSingleton)). 0.45/0.86 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', apProp)). 0.45/0.86 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', lamProp)). 0.45/0.86 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', lamp)). 0.45/0.86 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', lam2p)). 0.45/0.86 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ex1E2)). 0.45/0.86 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', beta1)). 0.45/0.86 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', eta1)). 0.45/0.86 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', lam2lamEq)). 0.45/0.86 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', beta2)). 0.45/0.86 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', eta2)). 0.45/0.86 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', iffalseProp1)). 0.45/0.86 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', iffalseProp2)). 0.45/0.86 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', iftrueProp1)). 0.45/0.86 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', iftrueProp2)). 0.45/0.86 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ifSingleton)). 0.45/0.86 thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:(((X52 @ X2 @ X3)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ X3 @ X14) @ X33))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', choice2fnsingleton)). 0.45/0.86 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setOfPairsIsBReln1)). 0.45/0.86 thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', image1Equiv)). 0.45/0.86 thf(image1E, conjecture, (((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>(((((((foundationAx)=>((wellorderingAx)=>((descrp)=>(((((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((((((((nonemptyI)=>(((((((setadjoinOr)=>((((emptyinPowerset)=>((emptyInPowerset)=>(((((((nonemptyImpWitness)=>(((notinsingleton)=>((((upairsetE)=>(((((vacuousDall)=>((quantDeMorgan1)=>(((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>(((((emptyset__Cong)=>((setadjoin__Cong)=>((((omega__Cong)=>(((((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>(((emptysetsubset)=>((((notsubsetI)=>((notequalI1)=>((((subsetTrans)=>(((((setextsub)=>((subsetemptysetimpeq)=>(((powersetE1)=>(((powersetsubset)=>(((((upairset2IR)=>((binunionIR)=>(((binunionE)=>(((((binintersectSubset5)=>(((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>(((disjointsetsI1)=>((((binintersectSubset1)=>((bs114d)=>((((((setminusERneg)=>((setminusELneg)=>((((setminusLsub)=>(((symdiffE)=>(((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>(((setukpairIR)=>((kpairiskpair)=>(((singletonsubset)=>((((upairset2E)=>(((upairinpowunion)=>((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((((cartprodmempair)=>(((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>(((((setukpairinjL1)=>(((theprop)=>((((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>(((setukpairinjR1)=>((upairequniteq)=>((((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>(((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>(((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>(((((dpsetconstrEL2)=>(((((app)=>((infuncsetfunc)=>(((((lamp)=>(((((ex1E2)=>(((((funcextLem)=>((funcGraphProp4)=>((((funcext)=>(((ap2apEq1)=>((((eta1)=>((((eta2)=>((iffalseProp1)=>(((((ifSingleton)=>(((((((((powersetT_lem)=>((setminusT_lem)=>(((setextT)=>(((powersetTI1)=>(((((((contrasubsetT)=>((contrasubsetT1)=>(((contrasubsetT3)=>((doubleComplementI1)=>(((doubleComplementSub1)=>((((complementTnotintersectT)=>(((complementSubsetComplementIntersect)=>(((contraSubsetComplement)=>(((binunionTILcontra)=>((binunionTIRcontra)=>(((((intersectInPowersetIntersectUnions)=>((((((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((((demorgan1)=>((demorgan2a)=>(((demorgan2b)=>((demorgan2)=>(((woz13rule1)=>(((((((woz1_3)=>((((breln1all2)=>(((((breln1all1)=>((subbreln1)=>((eqbreln1)=>((((((((breln1compEex)=>((breln1unionprop)=>(((breln1unionIR)=>((breln1unionI)=>((breln1unionE)=>(((breln1unionCommutes)=>((woz2Ex)=>(((woz2A)=>((woz2B)=>((image1Ex)=>(((image1Equiv)=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3)))))))<=(image1Ex1)))))<=(woz2W))))<=(breln1unionEcases)))))<=(breln1unionIL))))<=(breln1compE))<=(breln1compI))<=(breln1compprop))<=(breln1invE))<=(breln1invI))<=(breln1invprop)))))<=(setOfPairsIsBReln1))<=(choice2fnsingleton))<=(breln1SetBreln1)))<=(woz1_5))<=(woz1_4)))<=(woz1_2))<=(woz1_1))<=(woz13rule4))<=(woz13rule3))<=(woz13rule2)))<=(woz13rule0))))<=(demorgan2b2))))<=(demorgan1b))<=(demorgan1a)))))<=(binunionTEcontra))<=(binunionTE))<=(inComplementUnionImpInComplement1))<=(inComplementUnionImpNotIn1)))<=(inIntersectImpInIntersectUnions))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion))))<=(complementTcontraSubset)))<=(complementInPowersetComplementIntersect)))<=(complementImpComplementIntersect)))<=(doubleComplementEq))<=(doubleComplementSub2)))<=(doubleComplementE1))))<=(contrasubsetT2))))<=(binintersectTERcontra))<=(binintersectTELcontra))<=(complementTE1))<=(complementTI1))<=(powersetTE1)))<=(subsetTI)))<=(complementT_lem))))<=(binunionT_lem))<=(binintersectT_lem))<=(iftrueorfalse))<=(iffalse))<=(iftrue))<=(theeq))<=(ifp)))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2))))<=(beta2))<=(lam2lamEq)))<=(beta1))<=(ap2apEq2)))<=(funcext2)))<=(eqbreln))<=(subbreln))))<=(funcGraphProp2))<=(funcGraphProp3))<=(funcGraphProp1)))<=(brelnall2))<=(brelnall1))<=(lam2p)))<=(lamProp))<=(funcinfuncset))<=(ap2p))))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER)))<=(dpsetconstrEL1))<=(dpsetconstrERa))<=(setOfPairsIsBReln)))))<=(cartprodsndpairEq))))))<=(cartprodsndin)))))<=(setukpairinjR))<=(setukpairinjR2))))<=(setukpairinjR12)))))<=(cartprodfstin))<=(kfstpairEq)))<=(kfstsingleton)))<=(singletonsuniq))<=(ex1I2))<=(ex1I)))))))<=(setunionE2)))<=(cartprodmempair1))<=(cartprodpairin)))<=(ubforcartprodlem2))))<=(upairsubunion)))<=(singletoninpowunion))<=(singletoninpowerset)))<=(kpairp))))<=(setukpairIL)))<=(symdiffIneg2))))<=(symdiffI1)))<=(setminusSubset1)))<=(setminusIRneg))<=(setminusILneg))))<=(setminusSubset2))<=(setminusER))<=(setminusEL))<=(setminusI))))<=(binintersectSubset4))<=(binintersectRsub)))<=(binintersectER)))))<=(binintersectEL)))<=(binintersectI))<=(binunionRsub))<=(binunionLsub)))<=(binunionEcases))))<=(binunionIL))<=(sepSubset))<=(sepInPowerset)))<=(inPowerset)))<=(powersetI1))))<=(subset2powerset))<=(setadjoinSub2))<=(setadjoinSub)))<=(subsetRefl))<=(notequalI2))))<=(subsetE2))<=(subsetE)))<=(subsetI2)))))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong))<=(powerset__Cong))))<=(exu__Cong))<=(exuE3u))<=(in__Cong)))))))<=(notdexE))<=(prop2set2propI)))))<=(quantDeMorgan2))))<=(emptyE1))<=(upairsetIR))<=(upairsetIL)))<=(singletonsswitch))<=(eqinunit)))<=(uniqinunit)))<=(exuE2))<=(subPowSU))<=(setunionE))<=(setunionI))<=(powersetE))))<=(powersetI))<=(setoftrueEq)))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1)))<=(nonemptyE1))<=(setbeta))<=(noeltsimpempty))<=(emptyI))<=(setext))<=(exuE3e)))))))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI)))))<=(replAx))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))<=(setunionAx)))))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', image1E)). 0.45/0.86 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setextAx)). 0.45/0.86 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', emptysetAx)). 0.45/0.86 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setadjoinAx)). 0.45/0.86 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', powersetAx)). 0.45/0.86 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setunionAx)). 0.45/0.86 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', omega0Ax)). 0.45/0.86 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', omegaSAx)). 0.45/0.86 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', omegaIndAx)). 0.45/0.86 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', foundationAx)). 0.45/0.86 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', wellorderingAx)). 0.45/0.86 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', prop2setE)). 0.45/0.86 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', emptysetE)). 0.45/0.86 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', emptysetimpfalse)). 0.45/0.86 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', notinemptyset)). 0.45/0.86 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setext)). 0.45/0.86 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', emptyI)). 0.45/0.86 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', noeltsimpempty)). 0.45/0.86 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setadjoinIL)). 0.45/0.86 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', emptyinunitempty)). 0.45/0.86 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setadjoinIR)). 0.45/0.86 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setadjoinE)). 0.45/0.86 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setadjoinOr)). 0.45/0.86 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', powersetI)). 0.45/0.86 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', emptyinPowerset)). 0.45/0.86 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', emptyInPowerset)). 0.45/0.86 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', powersetE)). 0.45/0.86 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setunionI)). 0.45/0.86 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setunionE)). 0.45/0.86 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subPowSU)). 0.45/0.86 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', uniqinunit)). 0.45/0.86 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', notinsingleton)). 0.45/0.86 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', eqinunit)). 0.45/0.86 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', singletonsswitch)). 0.45/0.86 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', upairsetE)). 0.45/0.86 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', upairsetIL)). 0.45/0.86 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', upairsetIR)). 0.45/0.86 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', vacuousDall)). 0.45/0.86 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', quantDeMorgan1)). 0.45/0.86 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', quantDeMorgan2)). 0.45/0.86 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', quantDeMorgan3)). 0.45/0.86 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', quantDeMorgan4)). 0.45/0.86 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', prop2setI)). 0.45/0.86 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', prop2set2propI)). 0.45/0.86 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', notdexE)). 0.45/0.86 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', notdallE)). 0.45/0.86 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', inCongP)). 0.45/0.86 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', in__Cong)). 0.45/0.86 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', emptyset__Cong)). 0.45/0.86 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setadjoin__Cong)). 0.45/0.86 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', powerset__Cong)). 0.45/0.86 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setunion__Cong)). 0.45/0.86 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', omega__Cong)). 0.45/0.86 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subsetI1)). 0.45/0.86 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', eqimpsubset2)). 0.45/0.86 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', eqimpsubset1)). 0.45/0.86 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subsetI2)). 0.45/0.86 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', emptysetsubset)). 0.45/0.86 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subsetE)). 0.45/0.86 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subsetE2)). 0.45/0.86 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', notsubsetI)). 0.45/0.86 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', notequalI1)). 0.45/0.86 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', notequalI2)). 0.45/0.86 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subsetRefl)). 0.45/0.86 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subsetTrans)). 0.45/0.86 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setadjoinSub)). 0.45/0.86 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setadjoinSub2)). 0.45/0.86 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subset2powerset)). 0.45/0.86 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setextsub)). 0.45/0.86 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subsetemptysetimpeq)). 0.45/0.86 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', powersetI1)). 0.45/0.86 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', powersetE1)). 0.45/0.86 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', inPowerset)). 0.45/0.86 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', powersetsubset)). 0.45/0.86 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binunionIL)). 0.45/0.86 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', upairset2IR)). 0.45/0.86 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binunionIR)). 0.45/0.86 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binunionEcases)). 0.45/0.86 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binunionE)). 0.45/0.86 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binunionLsub)). 0.45/0.86 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binunionRsub)). 0.45/0.86 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectI)). 0.45/0.86 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectSubset5)). 0.45/0.86 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectEL)). 0.45/0.86 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectLsub)). 0.45/0.86 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectSubset2)). 0.45/0.86 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectSubset3)). 0.45/0.86 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectER)). 0.45/0.86 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', disjointsetsI1)). 0.45/0.86 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectRsub)). 0.45/0.86 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectSubset4)). 0.45/0.86 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectSubset1)). 0.45/0.86 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', bs114d)). 0.45/0.86 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setminusI)). 0.45/0.86 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setminusEL)). 0.45/0.86 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setminusER)). 0.45/0.86 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setminusSubset2)). 0.45/0.86 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setminusERneg)). 0.45/0.86 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setminusELneg)). 0.45/0.86 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setminusILneg)). 0.45/0.86 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setminusIRneg)). 0.45/0.86 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setminusLsub)). 0.45/0.86 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setminusSubset1)). 0.45/0.86 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', symdiffE)). 0.45/0.86 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', symdiffI1)). 0.45/0.86 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', symdiffI2)). 0.45/0.86 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', symdiffIneg1)). 0.45/0.86 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', symdiffIneg2)). 0.45/0.86 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', secondinupair)). 0.45/0.86 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setukpairIL)). 0.45/0.86 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setukpairIR)). 0.45/0.86 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', kpairiskpair)). 0.45/0.86 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', kpairp)). 0.45/0.86 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', singletonsubset)). 0.45/0.86 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', singletoninpowerset)). 0.45/0.86 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', singletoninpowunion)). 0.45/0.86 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', upairset2E)). 0.45/0.86 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', upairsubunion)). 0.45/0.86 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', upairinpowunion)). 0.45/0.86 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ubforcartprodlem1)). 0.45/0.86 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ubforcartprodlem2)). 0.45/0.86 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ubforcartprodlem3)). 0.45/0.86 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', cartprodpairin)). 0.45/0.86 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', cartprodmempair1)). 0.45/0.86 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', cartprodmempair)). 0.45/0.86 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setunionE2)). 0.45/0.86 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setunionsingleton1)). 0.45/0.86 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setunionsingleton2)). 0.45/0.86 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setunionsingleton)). 0.45/0.86 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', singletonsuniq)). 0.45/0.86 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setukpairinjL1)). 0.45/0.86 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', theprop)). 0.45/0.86 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', kfstpairEq)). 0.45/0.86 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', cartprodfstin)). 0.45/0.86 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setukpairinjL2)). 0.45/0.86 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setukpairinjL)). 0.45/0.86 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setukpairinjR11)). 0.45/0.86 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setukpairinjR12)). 0.45/0.86 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setukpairinjR1)). 0.45/0.86 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', upairequniteq)). 0.45/0.86 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setukpairinjR2)). 0.45/0.86 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setukpairinjR)). 0.45/0.86 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ksndpairEq)). 0.45/0.86 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', kpairsurjEq)). 0.45/0.86 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', cartprodsndin)). 0.45/0.86 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', cartprodpairmemEL)). 0.45/0.86 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', cartprodpairmemER)). 0.45/0.86 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', cartprodmempaircEq)). 0.45/0.86 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', cartprodfstpairEq)). 0.45/0.86 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', cartprodsndpairEq)). 0.45/0.86 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', cartprodpairsurjEq)). 0.45/0.86 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', app)). 0.45/0.86 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', infuncsetfunc)). 0.45/0.86 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ap2p)). 0.45/0.86 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', funcinfuncset)). 0.45/0.86 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', brelnall1)). 0.45/0.86 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', brelnall2)). 0.45/0.86 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', funcGraphProp1)). 0.45/0.86 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', funcGraphProp3)). 0.45/0.86 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', funcGraphProp2)). 0.45/0.86 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', funcextLem)). 0.45/0.86 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', funcGraphProp4)). 0.45/0.86 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subbreln)). 0.45/0.86 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', eqbreln)). 0.45/0.86 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', funcext)). 0.45/0.86 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', funcext2)). 0.45/0.86 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ap2apEq1)). 0.45/0.86 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ap2apEq2)). 0.45/0.86 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', ifp)). 0.45/0.86 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', theeq)). 0.45/0.86 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', iftrue)). 0.45/0.86 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', iffalse)). 0.45/0.86 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', iftrueorfalse)). 0.45/0.86 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectT_lem)). 0.45/0.86 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binunionT_lem)). 0.45/0.86 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', powersetT_lem)). 0.45/0.86 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setminusT_lem)). 0.45/0.86 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', complementT_lem)). 0.45/0.86 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', setextT)). 0.45/0.86 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subsetTI)). 0.45/0.86 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', powersetTI1)). 0.45/0.86 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', powersetTE1)). 0.45/0.86 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', complementTI1)). 0.45/0.86 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', complementTE1)). 0.45/0.86 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectTELcontra)). 0.45/0.86 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binintersectTERcontra)). 0.45/0.86 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', contrasubsetT)). 0.45/0.86 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', contrasubsetT1)). 0.45/0.86 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', contrasubsetT2)). 0.45/0.86 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', contrasubsetT3)). 0.45/0.86 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', doubleComplementI1)). 0.45/0.86 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', doubleComplementE1)). 0.45/0.86 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', doubleComplementSub1)). 0.45/0.86 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', doubleComplementSub2)). 0.45/0.86 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', doubleComplementEq)). 0.45/0.86 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', complementTnotintersectT)). 0.45/0.86 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', complementImpComplementIntersect)). 0.45/0.86 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', complementSubsetComplementIntersect)). 0.45/0.86 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', complementInPowersetComplementIntersect)). 0.45/0.86 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', contraSubsetComplement)). 0.45/0.86 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', complementTcontraSubset)). 0.45/0.86 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binunionTILcontra)). 0.45/0.86 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binunionTIRcontra)). 0.45/0.86 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', inIntersectImpInUnion)). 0.45/0.86 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', inIntersectImpInUnion2)). 0.45/0.86 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', inIntersectImpInIntersectUnions)). 0.45/0.86 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', intersectInPowersetIntersectUnions)). 0.45/0.86 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', inComplementUnionImpNotIn1)). 0.45/0.86 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', inComplementUnionImpInComplement1)). 0.45/0.86 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binunionTE)). 0.45/0.86 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', binunionTEcontra)). 0.45/0.86 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', demorgan2a1)). 0.45/0.86 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', complementUnionInPowersetComplement)). 0.45/0.86 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', demorgan2a2)). 0.45/0.86 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', demorgan1a)). 0.45/0.86 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', demorgan1b)). 0.45/0.86 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', demorgan1)). 0.45/0.86 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', demorgan2a)). 0.45/0.86 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', demorgan2b2)). 0.45/0.86 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', demorgan2b)). 0.45/0.86 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', demorgan2)). 0.45/0.86 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz13rule0)). 0.45/0.86 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz13rule1)). 0.45/0.86 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz13rule2)). 0.45/0.86 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz13rule3)). 0.45/0.86 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz13rule4)). 0.45/0.86 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz1_1)). 0.45/0.86 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz1_2)). 0.45/0.86 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz1_3)). 0.45/0.86 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz1_4)). 0.45/0.86 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz1_5)). 0.45/0.86 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1all2)). 0.45/0.86 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1SetBreln1)). 0.45/0.86 thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1all1)). 0.45/0.86 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', subbreln1)). 0.45/0.86 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', eqbreln1)). 0.45/0.86 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1invprop)). 0.45/0.86 thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1invI)). 0.45/0.86 thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1invE)). 0.45/0.86 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1compprop)). 0.45/0.86 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1compI)). 0.45/0.86 thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1compE)). 0.45/0.86 thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1compEex)). 0.45/0.86 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1unionprop)). 0.45/0.86 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1unionIL)). 0.45/0.86 thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1unionIR)). 0.45/0.86 thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1unionI)). 0.45/0.86 thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1unionE)). 0.45/0.86 thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1unionEcases)). 0.45/0.86 thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', breln1unionCommutes)). 0.45/0.86 thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz2Ex)). 0.45/0.86 thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz2W)). 0.45/0.86 thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz2A)). 0.45/0.86 thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', woz2B)). 0.45/0.86 thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.n4DRl4qO7Z/Vampire---4.8_14217', image1Ex)). 0.45/0.86 thf(c_0_315, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.45/0.86 thf(c_0_316, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.45/0.86 thf(c_0_317, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.45/0.86 thf(c_0_318, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.45/0.86 thf(c_0_319, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.45/0.86 thf(c_0_320, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.45/0.86 thf(c_0_321, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.45/0.86 thf(c_0_322, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.45/0.86 thf(c_0_323, 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])). 0.45/0.86 thf(c_0_324, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.45/0.86 thf(c_0_325, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.45/0.86 thf(c_0_326, 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])). 0.45/0.86 thf(c_0_327, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.45/0.86 thf(c_0_328, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.45/0.86 thf(c_0_329, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.45/0.86 thf(c_0_330, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0/* 6 */:$i]:(![X2:$i]:(((in @ X2 @ Z0)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])). 0.45/0.86 thf(c_0_331, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1095:$i]:((((X6 @ X2 @ X1095))&![X1096:$i]:((((X6 @ X2 @ X1096))=>((X1095)=(X1096)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_315, c_0_316])). 0.45/0.86 thf(c_0_332, plain, ((descrp)=(![X1:$i > $o]:(((?[X1097:$i]:((((X1 @ X1097))&![X1098:$i]:((((X1 @ X1098))=>((X1097)=(X1098)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_317, c_0_316])). 0.45/0.86 thf(c_0_333, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.45/0.86 thf(c_0_334, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.45/0.86 thf(c_0_335, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.45/0.86 thf(c_0_336, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1099:$i]:((((X1 @ X1099))&![X1100:$i]:((((X1 @ X1100))=>((X1099)=(X1100)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_318, c_0_316])). 0.45/0.86 thf(c_0_337, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1101:$i]:((((X1 @ X1101))&![X1102:$i]:((((X1 @ X1102))=>((X1101)=(X1102)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_319, c_0_316])). 0.45/0.86 thf(c_0_338, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.45/0.86 thf(c_0_339, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_320])). 0.45/0.86 thf(c_0_340, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_321, c_0_320])). 0.45/0.86 thf(c_0_341, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_320])). 0.45/0.86 thf(c_0_342, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.45/0.86 thf(c_0_343, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1103:$i]:((((X1 @ X1103))&![X1104:$i]:((((X1 @ X1104))=>((X1103)=(X1104)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_322, c_0_316])). 0.45/0.86 thf(c_0_344, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_320])). 0.45/0.86 thf(c_0_345, 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])). 0.45/0.86 thf(c_0_346, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1105:$i]:((((X1 @ X1105))&![X1106:$i]:((((X1 @ X1106))=>((X1105)=(X1106))))))))))), inference(apply_def,[status(thm)],[c_0_323, c_0_316])). 0.45/0.86 thf(c_0_347, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1107:$i]:((((X1 @ X1107))&![X1108:$i]:((((X1 @ X1108))=>((X1107)=(X1108)))))))))))), inference(apply_def,[status(thm)],[c_0_324, c_0_316])). 0.45/0.86 thf(c_0_348, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1109:$i]:((((X1 @ X1109))&![X1110:$i]:((((X1 @ X1110))=>((X1109)=(X1110))))))))))), inference(apply_def,[status(thm)],[c_0_325, c_0_316])). 0.45/0.86 thf(c_0_349, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1111:$i]:((((X1 @ X1111))&![X1112:$i]:((((X1 @ X1112))=>((X1111)=(X1112)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_326, c_0_316])). 0.45/0.86 thf(c_0_350, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1113:$i]:((((X1 @ X1113))&![X1114:$i]:((((X1 @ X1114))=>((X1113)=(X1114)))))))<=>(?[X1115:$i]:((((X17 @ X1115))&![X1116:$i]:((((X17 @ X1116))=>((X1115)=(X1116)))))))))))), inference(apply_def,[status(thm)],[c_0_327, c_0_316])). 0.45/0.86 thf(c_0_351, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1117:$i]:((((X1 @ X1117))&![X1118:$i]:((((X1 @ X1118))=>((X1117)=(X1118)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_328, c_0_316])). 0.45/0.86 thf(c_0_352, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1119:$i]:((((X1 @ X1119))&![X1120:$i]:((((X1 @ X1120))=>((X1119)=(X1120)))))))=>((?[X1121:$i]:((((X17 @ X1121))&![X1122:$i]:((((X17 @ X1122))=>((X1121)=(X1122)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_329, c_0_316])). 0.45/0.86 thf(c_0_353, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.45/0.86 thf(c_0_354, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.45/0.86 thf(c_0_355, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.45/0.86 thf(c_0_356, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.45/0.86 thf(c_0_357, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.45/0.86 thf(c_0_358, plain, ((ex1I)<=>![X4:$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])). 0.45/0.86 thf(c_0_359, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.45/0.86 thf(c_0_360, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 0.45/0.86 thf(c_0_361, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 0.45/0.86 thf(c_0_362, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 0.45/0.86 thf(c_0_363, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 0.45/0.86 thf(c_0_364, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 0.45/0.86 thf(c_0_365, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 0.45/0.86 thf(c_0_366, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 0.45/0.86 thf(c_0_367, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 0.45/0.86 thf(c_0_368, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 0.45/0.86 thf(c_0_369, plain, ((funcImageSingleton)<=>![X4:$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])). 0.45/0.86 thf(c_0_370, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 0.45/0.86 thf(c_0_371, plain, ((lamProp)<=>![X4:$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])). 0.45/0.86 thf(c_0_372, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 0.45/0.86 thf(c_0_373, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 0.45/0.86 thf(c_0_374, plain, ((ex1E2)<=>![X4:$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])). 0.45/0.86 thf(c_0_375, 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])). 0.45/0.86 thf(c_0_376, 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])). 0.45/0.86 thf(c_0_377, 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])). 0.45/0.86 thf(c_0_378, 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])). 0.45/0.86 thf(c_0_379, 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])). 0.45/0.86 thf(c_0_380, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 0.45/0.86 thf(c_0_381, plain, ((iffalseProp2)<=>![X4:$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])). 0.45/0.86 thf(c_0_382, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 0.45/0.86 thf(c_0_383, plain, ((iftrueProp2)<=>![X4:$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])). 0.45/0.86 thf(c_0_384, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 0.45/0.86 thf(c_0_385, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 8 */:$i]:(((X52 @ X2 @ Z0)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ Z0 @ X14) @ X33))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])). 0.45/0.86 thf(c_0_386, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])). 0.45/0.86 thf(c_0_387, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1123:$i]:(((![X2:$i]:(((in @ X2 @ X1123)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))&![X1124:$i]:(((![X2:$i]:(((in @ X2 @ X1124)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))=>((X1123)=(X1124)))))))))), inference(apply_def,[status(thm)],[c_0_330, c_0_316])). 0.45/0.86 thf(c_0_388, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])). 0.45/0.86 thf(c_0_389, plain, ((epred1_0)<=>![X1136:$i]:(?[X1137:$i]:((((![X1138:$i]:(((in @ X1138 @ X1137)=>![X1139:$i]:(((in @ X1139 @ X1138)=>(in @ X1139 @ X1136)))))&![X1140:$i, X1141:$i]:((((in @ X1140 @ X1136)&(in @ X1141 @ X1136))=>(![X1142:$i]:(((in @ X1142 @ X1137)=>((in @ X1140 @ X1142)<=>(in @ X1141 @ X1142))))=>((X1140)=(X1141))))))&![X1143:$i, X1144:$i]:((((in @ X1143 @ X1137)&(in @ X1144 @ X1137))=>(![X1145:$i]:(((in @ X1145 @ X1143)=>(in @ X1145 @ X1144)))|![X1146:$i]:(((in @ X1146 @ X1144)=>(in @ X1146 @ X1143)))))))&![X1147:$i]:(((![X1148:$i]:(((in @ X1148 @ X1147)=>(in @ X1148 @ X1136)))&?[X1149:$i]:((in @ X1149 @ X1147)))=>?[X1150:$i, X1151:$i]:(((((in @ X1150 @ X1137)&(in @ X1151 @ X1147))&~(?[X1152:$i]:(((in @ X1152 @ X1150)&(in @ X1152 @ X1147)))))&![X1153:$i]:(((in @ X1153 @ X1137)=>(![X1154:$i]:(((in @ X1154 @ X1153)=>(in @ X1154 @ X1150)))|(in @ X1151 @ X1153)))))))))))), introduced(definition)). 0.45/0.86 thf(c_0_390, negated_conjecture, ~((![X2187:$i, X2188:$i]:((![X2189:$i]:(((in @ X2189 @ X2187)<=>(in @ X2189 @ X2188)))=>((X2187)=(X2188))))=>(![X1125:$i]:(~(in @ X1125 @ emptyset))=>(![X1126:$i, X1127:$i, X1128:$i]:(((in @ X1128 @ (setadjoin @ X1126 @ X1127))<=>(((X1128)=(X1126))|(in @ X1128 @ X1127))))=>(![X1129:$i, X1130:$i]:(((in @ X1130 @ (powerset @ X1129))<=>![X1131:$i]:(((in @ X1131 @ X1130)=>(in @ X1131 @ X1129)))))=>(![X2184:$i, X2185:$i]:(((in @ X2185 @ (setunion @ X2184))<=>?[X2186:$i]:(((in @ X2185 @ X2186)&(in @ X2186 @ X2184)))))=>((in @ emptyset @ omega)=>(![X2183:$i]:(((in @ X2183 @ omega)=>(in @ (setadjoin @ X2183 @ X2183) @ omega)))=>(![X2180:$i]:((((in @ emptyset @ X2180)&![X2181:$i]:((((in @ X2181 @ omega)&(in @ X2181 @ X2180))=>(in @ (setadjoin @ X2181 @ X2181) @ X2180))))=>![X2182:$i]:(((in @ X2182 @ omega)=>(in @ X2182 @ X2180)))))=>(![X2172:$i > $i > $o, X2173:$i]:((![X2174:$i]:(((in @ X2174 @ X2173)=>?[X2175:$i]:(((X2172 @ X2174 @ X2175)&![X2176:$i]:(((X2172 @ X2174 @ X2176)=>((X2175)=(X2176))))))))=>?[X2177:$i]:(![X2178:$i]:(((in @ X2178 @ X2177)<=>?[X2179:$i]:(((in @ X2179 @ X2173)&(X2172 @ X2179 @ X2178))))))))=>(![X1132:$i]:((?[X1133:$i]:((in @ X1133 @ X1132))=>?[X1134:$i]:(((in @ X1134 @ X1132)&~(?[X1135:$i]:(((in @ X1135 @ X1134)&(in @ X1135 @ X1132))))))))=>((epred1_0)=>(![X1155:$i > $o]:((?[X1156:$i]:(((X1155 @ X1156)&![X1157:$i]:(((X1155 @ X1157)=>((X1156)=(X1157))))))=>(X1155 @ (descr @ (^[Z0/* 3 */:$i]:((X1155 @ Z0)))))))=>(![X2169:$i, X2170:$i > $o, X2171:$i]:(((in @ X2171 @ X2169)=>((X2170 @ X2171)=>(in @ X2171 @ (dsetconstr @ X2169 @ (^[Z0/* 3 */:$i]:((X2170 @ Z0))))))))=>(![X2166:$i, X2167:$i > $o, X2168:$i]:(((in @ X2168 @ (dsetconstr @ X2166 @ (^[Z0/* 3 */:$i]:((X2167 @ Z0)))))=>(in @ X2168 @ X2166)))=>(![X2163:$i, X2164:$i > $o, X2165:$i]:(((in @ X2165 @ (dsetconstr @ X2163 @ (^[Z0/* 3 */:$i]:((X2164 @ Z0)))))=>(X2164 @ X2165)))=>(![X1158:$i > $o]:((?[X1159:$i]:(((X1158 @ X1159)&![X1160:$i]:(((X1158 @ X1160)=>((X1159)=(X1160))))))=>?[X1161:$i]:(((X1158 @ X1161)&![X1162:$i]:(((X1158 @ X1162)=>((X1161)=(X1162))))))))=>(![X1163:$o, X1164:$i]:(((in @ X1164 @ (prop2set @ ((X1163))))=>(X1163)))=>(![X1165:$i]:(((in @ X1165 @ emptyset)=>![X1166:$o]:((X1166))))=>(![X1167:$i]:(~(in @ X1167 @ emptyset))=>(![X1168:$i]:(~(in @ X1168 @ emptyset))=>(![X2159:$i > $o]:((?[X2160:$i]:(((X2159 @ X2160)&![X2161:$i]:(((X2159 @ X2161)=>((X2160)=(X2161))))))=>?[X2162:$i]:((X2159 @ X2162))))=>(![X2155:$i, X2156:$i]:((![X2157:$i]:(((in @ X2157 @ X2155)=>(in @ X2157 @ X2156)))=>(![X2158:$i]:(((in @ X2158 @ X2156)=>(in @ X2158 @ X2155)))=>((X2155)=(X2156)))))=>(![X2153:$i]:((![X2154:$i]:(~(in @ X2154 @ X2153))=>((X2153)=(emptyset))))=>(![X2151:$i]:((![X2152:$i]:(~(in @ X2152 @ X2151))=>((X2151)=(emptyset))))=>(![X2148:$i, X2149:$i > $o, X2150:$i]:(((in @ X2150 @ X2148)=>((in @ X2150 @ (dsetconstr @ X2148 @ (^[Z0/* 3 */:$i]:((X2149 @ Z0)))))<=>(X2149 @ X2150))))=>(![X2146:$i]:((((X2146)!=(emptyset))=>?[X2147:$i]:((in @ X2147 @ X2146))))=>(![X1169:$i, X1170:$i > $o, X1171:$i]:(((in @ X1171 @ X1169)=>((X1170 @ X1171)=>((dsetconstr @ X1169 @ (^[Z0/* 3 */:$i]:((X1170 @ Z0))))!=(emptyset)))))=>(![X2144:$i]:((?[X2145:$i]:((in @ X2145 @ X2144))=>((X2144)!=(emptyset))))=>(![X2142:$i, X2143:$i]:((in @ X2142 @ (setadjoin @ X2142 @ X2143)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X2139:$i, X2140:$i, X2141:$i]:(((in @ X2141 @ X2140)=>(in @ X2141 @ (setadjoin @ X2139 @ X2140))))=>(![X2135:$i, X2136:$i, X2137:$i]:(((in @ X2137 @ (setadjoin @ X2135 @ X2136))=>![X2138:$o]:(((((X2137)=(X2135))=>(X2138))=>(((in @ X2137 @ X2136)=>(X2138))=>(X2138))))))=>(![X1172:$i, X1173:$i, X1174:$i]:(((in @ X1174 @ (setadjoin @ X1172 @ X1173))=>(((X1174)=(X1172))|(in @ X1174 @ X1173))))=>(![X2134:$i]:(((dsetconstr @ X2134 @ (^[Z0/* 3 */:$i]:(($true))))=(X2134)))=>(![X2131:$i, X2132:$i]:((![X2133:$i]:(((in @ X2133 @ X2132)=>(in @ X2133 @ X2131)))=>(in @ X2132 @ (powerset @ X2131))))=>(![X1175:$i]:((in @ emptyset @ (powerset @ X1175)))=>(![X1176:$i]:((in @ emptyset @ (powerset @ X1176)))=>(![X2128:$i, X2129:$i, X2130:$i]:(((in @ X2129 @ (powerset @ X2128))=>((in @ X2130 @ X2129)=>(in @ X2130 @ X2128))))=>(![X2125:$i, X2126:$i, X2127:$i]:(((in @ X2126 @ X2127)=>((in @ X2127 @ X2125)=>(in @ X2126 @ (setunion @ X2125)))))=>(![X2121:$i, X2122:$i]:(((in @ X2122 @ (setunion @ X2121))=>![X2123:$o]:((![X2124:$i]:(((in @ X2122 @ X2124)=>((in @ X2124 @ X2121)=>(X2123))))=>(X2123)))))=>(![X2119:$i, X2120:$i]:(((in @ X2120 @ X2119)=>(in @ X2120 @ (powerset @ (setunion @ X2119)))))=>(![X2114:$i > $o]:((?[X2115:$i]:(((X2114 @ X2115)&![X2116:$i]:(((X2114 @ X2116)=>((X2115)=(X2116))))))=>?[X2117:$i]:(![X2118:$i]:(((X2114 @ X2118)<=>((X2118)=(X2117)))))))=>(![X1177:$i]:((((X1177)!=(emptyset))=>?[X1178:$i]:((in @ X1178 @ X1177))))=>(![X2112:$i, X2113:$i]:(((in @ X2112 @ (setadjoin @ X2113 @ emptyset))=>((X2112)=(X2113))))=>(![X1179:$i, X1180:$i]:((((X1179)!=(X1180))=>~(in @ X1180 @ (setadjoin @ X1179 @ emptyset))))=>(![X2110:$i, X2111:$i]:((((X2110)=(X2111))=>(in @ X2110 @ (setadjoin @ X2111 @ emptyset))))=>(![X2108:$i, X2109:$i]:(((in @ X2108 @ (setadjoin @ X2109 @ emptyset))=>(in @ X2109 @ (setadjoin @ X2108 @ emptyset))))=>(![X1181:$i, X1182:$i, X1183:$i]:(((in @ X1183 @ (setadjoin @ X1181 @ (setadjoin @ X1182 @ emptyset)))=>(((X1183)=(X1181))|((X1183)=(X1182)))))=>(![X2106:$i, X2107:$i]:((in @ X2106 @ (setadjoin @ X2106 @ (setadjoin @ X2107 @ emptyset))))=>(![X2104:$i, X2105:$i]:((in @ X2105 @ (setadjoin @ X2104 @ (setadjoin @ X2105 @ emptyset))))=>(![X2101:$i, X2102:$i > $o]:((?[X2103:$i]:(((in @ X2103 @ X2101)&(X2102 @ X2103)))=>((dsetconstr @ X2101 @ (^[Z0/* 3 */:$i]:((X2102 @ Z0))))!=(emptyset))))=>(![X1184:$i > $o, X1185:$i]:(((in @ X1185 @ emptyset)=>(X1184 @ X1185)))=>(![X1186:$i, X1187:$i > $o]:((~(![X1188:$i]:(((in @ X1188 @ X1186)=>(X1187 @ X1188))))=>?[X1189:$i]:(((in @ X1189 @ X1186)&~(X1187 @ X1189)))))=>(![X2097:$i, X2098:$i > $o]:((![X2099:$i]:(((in @ X2099 @ X2097)=>~(X2098 @ X2099)))=>~(?[X2100:$i]:(((in @ X2100 @ X2097)&(X2098 @ X2100))))))=>(![X1190:$i, X1191:$i > $o]:((~(?[X1192:$i]:(((in @ X1192 @ X1190)&(X1191 @ X1192))))=>![X1193:$i]:(((in @ X1193 @ X1190)=>~(X1191 @ X1193)))))=>(![X1194:$i, X1195:$i > $o]:((?[X1196:$i]:(((in @ X1196 @ X1194)&~(X1195 @ X1196)))=>~(![X1197:$i]:(((in @ X1197 @ X1194)=>(X1195 @ X1197))))))=>(![X1198:$o]:(((X1198)=>(in @ emptyset @ (prop2set @ ((X1198))))))=>(![X2096:$o]:(((X2096)=>(set2prop @ (prop2set @ ((X2096))))))=>(![X2092:$i, X2093:$i > $o]:((~(?[X2094:$i]:(((in @ X2094 @ X2092)&(X2093 @ X2094))))=>![X2095:$i]:(((in @ X2095 @ X2092)=>~(X2093 @ X2095)))))=>(![X1199:$i, X1200:$i > $o]:((~(![X1201:$i]:(((in @ X1201 @ X1199)=>(X1200 @ X1201))))=>?[X1202:$i]:(((in @ X1202 @ X1199)&~(X1200 @ X1202)))))=>(![X1203:$i > $o]:((?[X1204:$i]:(((X1203 @ X1204)&![X1205:$i]:(((X1203 @ X1205)=>((X1204)=(X1205))))))=>?[X1206:$i]:(((X1203 @ X1206)&![X1207:$i]:(((X1203 @ X1207)=>((X1206)=(X1207))))))))=>(![X1208:$i > $o]:((?[X1209:$i]:((X1208 @ X1209))=>(![X1210:$i, X1211:$i]:(((X1208 @ X1210)=>((X1208 @ X1211)=>((X1210)=(X1211)))))=>?[X1212:$i]:(((X1208 @ X1212)&![X1213:$i]:(((X1208 @ X1213)=>((X1212)=(X1213)))))))))=>(![X1214:$i > $o]:((?[X1215:$i]:(![X1216:$i]:(((X1214 @ X1216)<=>((X1216)=(X1215)))))=>?[X1217:$i]:(((X1214 @ X1217)&![X1218:$i]:(((X1214 @ X1218)=>((X1217)=(X1218))))))))=>(![X1219:$i, X1220:$i]:((((X1219)=(X1220))=>![X1221:$i, X1222:$i]:((((X1221)=(X1222))=>((in @ X1221 @ X1219)=>(in @ X1222 @ X1220))))))=>(![X2088:$i, X2089:$i]:((((X2088)=(X2089))=>![X2090:$i, X2091:$i]:((((X2090)=(X2091))=>((in @ X2090 @ X2088)<=>(in @ X2091 @ X2089))))))=>(![X2083:$i > $o]:((?[X2084:$i]:(((X2083 @ X2084)&![X2085:$i]:(((X2083 @ X2085)=>((X2084)=(X2085))))))=>![X2086:$i, X2087:$i]:(((X2083 @ X2086)=>((X2083 @ X2087)=>((X2086)=(X2087)))))))=>(![X2075:$i > $o, X2076:$i > $o]:((![X2077:$i, X2078:$i]:((((X2077)=(X2078))=>((X2075 @ X2077)<=>(X2076 @ X2078))))=>(?[X2079:$i]:(((X2075 @ X2079)&![X2080:$i]:(((X2075 @ X2080)=>((X2079)=(X2080))))))<=>?[X2081:$i]:(((X2076 @ X2081)&![X2082:$i]:(((X2076 @ X2082)=>((X2081)=(X2082)))))))))=>(((emptyset)=(emptyset))=>(![X1223:$i, X1224:$i]:((((X1223)=(X1224))=>![X1225:$i, X1226:$i]:((((X1225)=(X1226))=>((setadjoin @ X1223 @ X1225)=(setadjoin @ X1224 @ X1226))))))=>(![X2073:$i, X2074:$i]:((((X2073)=(X2074))=>((powerset @ X2073)=(powerset @ X2074))))=>(![X2071:$i, X2072:$i]:((((X2071)=(X2072))=>((setunion @ X2071)=(setunion @ X2072))))=>(((omega)=(omega))=>(![X2066:$i > $o]:((?[X2067:$i]:(((X2066 @ X2067)&![X2068:$i]:(((X2066 @ X2068)=>((X2067)=(X2068))))))=>![X2069:$i, X2070:$i]:(((X2066 @ X2069)=>((X2066 @ X2070)=>((X2069)=(X2070)))))))=>(![X2058:$i > $o, X2059:$i > $o]:((![X2060:$i, X2061:$i]:((((X2060)=(X2061))=>((X2058 @ X2060)<=>(X2059 @ X2061))))=>(?[X2062:$i]:(((X2058 @ X2062)&![X2063:$i]:(((X2058 @ X2063)=>((X2062)=(X2063))))))=>(?[X2064:$i]:(((X2059 @ X2064)&![X2065:$i]:(((X2059 @ X2065)=>((X2064)=(X2065))))))=>((descr @ (^[Z0/* 3 */:$i]:((X2058 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X2059 @ Z0)))))))))=>(![X2052:$i, X2053:$i]:((((X2052)=(X2053))=>![X2054:$i > $o, X2055:$i > $o]:((![X2056:$i]:(((in @ X2056 @ X2052)=>![X2057:$i]:(((in @ X2057 @ X2053)=>(((X2056)=(X2057))=>((X2054 @ X2056)<=>(X2055 @ X2057)))))))=>((dsetconstr @ X2052 @ (^[Z0/* 3 */:$i]:((X2054 @ Z0))))=(dsetconstr @ X2053 @ (^[Z0/* 3 */:$i]:((X2055 @ Z0)))))))))=>(![X1227:$i, X1228:$i]:((![X1229:$i]:(((in @ X1229 @ X1227)=>(in @ X1229 @ X1228)))=>(subset @ X1227 @ X1228)))=>(![X1230:$i, X1231:$i]:((((X1230)=(X1231))=>(subset @ X1231 @ X1230)))=>(![X1232:$i, X1233:$i]:((((X1232)=(X1233))=>(subset @ X1232 @ X1233)))=>(![X2049:$i, X2050:$i]:((![X2051:$i]:(((in @ X2051 @ X2049)=>(in @ X2051 @ X2050)))=>(subset @ X2049 @ X2050)))=>(![X1234:$i]:((subset @ emptyset @ X1234))=>(![X2046:$i, X2047:$i, X2048:$i]:(((subset @ X2046 @ X2047)=>((in @ X2048 @ X2046)=>(in @ X2048 @ X2047))))=>(![X2043:$i, X2044:$i, X2045:$i]:(((subset @ X2043 @ X2044)=>(~(in @ X2045 @ X2044)=>~(in @ X2045 @ X2043))))=>(![X1235:$i, X1236:$i, X1237:$i]:(((in @ X1237 @ X1235)=>(~(in @ X1237 @ X1236)=>~(subset @ X1235 @ X1236))))=>(![X1238:$i, X1239:$i]:((~(subset @ X1238 @ X1239)=>((X1238)!=(X1239))))=>(![X2040:$i, X2041:$i, X2042:$i]:(((in @ X2042 @ X2040)=>(~(in @ X2042 @ X2041)=>((X2040)!=(X2041)))))=>(![X2039:$i]:((subset @ X2039 @ X2039))=>(![X1240:$i, X1241:$i, X1242:$i]:(((subset @ X1240 @ X1241)=>((subset @ X1241 @ X1242)=>(subset @ X1240 @ X1242))))=>(![X2037:$i, 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X1673:$i]:(((in @ X1673 @ (powerset @ X1672))=>![X1674:$i]:(((in @ X1674 @ (powerset @ X1672))=>![X1675:$i]:(((in @ X1675 @ (powerset @ X1672))=>((subset @ X1673 @ X1674)=>((subset @ X1673 @ X1675)=>(subset @ X1673 @ (binintersect @ X1674 @ X1675))))))))))=>(![X1667:$i, X1668:$i]:(((in @ X1668 @ (powerset @ X1667))=>![X1669:$i]:(((in @ X1669 @ (powerset @ X1667))=>![X1670:$i]:(((in @ X1670 @ (powerset @ X1667))=>![X1671:$i]:(((in @ X1671 @ (powerset @ X1667))=>((subset @ X1668 @ X1670)=>((subset @ X1669 @ X1671)=>(subset @ (binintersect @ X1668 @ X1669) @ (binintersect @ X1670 @ X1671))))))))))))=>(![X1664:$i, X1665:$i]:(((in @ X1665 @ (powerset @ X1664))=>![X1666:$i]:(((in @ X1666 @ (powerset @ X1664))=>(in @ (setminus @ X1664 @ X1665) @ (powerset @ (setminus @ X1664 @ (binintersect @ X1665 @ X1666))))))))=>(![X1659:$i, X1660:$i]:(((in @ X1660 @ (powerset @ X1659))=>![X1661:$i]:(((in @ X1661 @ (powerset @ X1659))=>![X1662:$i]:(((in @ X1662 @ (powerset @ X1659))=>![X1663:$i]:(((in @ 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X1654)))))))=>(![X1523:$i, X1524:$i]:(((breln1 @ X1523 @ X1524)=>![X1525:$i > $o]:((![X1526:$i]:(((in @ X1526 @ X1523)=>![X1527:$i]:(((in @ X1527 @ X1523)=>((in @ (kpair @ X1526 @ X1527) @ X1524)=>(X1525 @ (kpair @ X1526 @ X1527)))))))=>![X1528:$i]:(((in @ X1528 @ X1524)=>(X1525 @ X1528)))))))=>(![X1651:$i, X1652:$i]:(((in @ X1652 @ (breln1Set @ X1651))=>(breln1 @ X1651 @ X1652)))=>(![X1643:$i, X1644:$i, X1645:$i > $i > $o]:((![X1646:$i]:(((in @ X1646 @ X1643)=>?[X1647:$i]:(((in @ X1647 @ X1644)&(X1645 @ X1646 @ X1647)))))=>![X1648:$i]:(((in @ X1648 @ (breln1Set @ X1644))=>((reflwellordering @ X1644 @ X1648)=>![X1649:$i]:(((in @ X1649 @ X1643)=>(singleton @ (dsetconstr @ X1644 @ (^[Z0/* 8 */:$i]:(((X1645 @ X1649 @ Z0)&![X1650:$i]:(((in @ X1650 @ X1644)=>((X1645 @ X1649 @ X1650)=>(in @ (kpair @ Z0 @ X1650) @ X1648))))))))))))))))=>(![X1641:$i, X1642:$i > $i > $o]:((breln1 @ X1641 @ (dpsetconstr @ X1641 @ X1641 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1642 @ Z0 @ Z1))))))=>(![X1529:$i, X1530:$i]:(((breln1 @ X1529 @ X1530)=>![X1531:$i > $o]:((![X1532:$i]:(((in @ X1532 @ X1529)=>![X1533:$i]:(((in @ X1533 @ X1529)=>((in @ (kpair @ X1532 @ X1533) @ X1530)=>(X1531 @ (kpair @ X1532 @ X1533)))))))=>![X1534:$i]:(((in @ X1534 @ X1530)=>(X1531 @ X1534)))))))=>(![X1535:$i, X1536:$i]:(((breln1 @ X1535 @ X1536)=>![X1537:$i]:(((breln1 @ X1535 @ X1537)=>(![X1538:$i]:(((in @ X1538 @ X1535)=>![X1539:$i]:(((in @ X1539 @ X1535)=>((in @ (kpair @ X1538 @ X1539) @ X1536)=>(in @ (kpair @ X1538 @ X1539) @ X1537))))))=>(subset @ X1536 @ X1537))))))=>(![X1540:$i, X1541:$i]:(((breln1 @ X1540 @ X1541)=>![X1542:$i]:(((breln1 @ X1540 @ X1542)=>(![X1543:$i]:(((in @ X1543 @ X1540)=>![X1544:$i]:(((in @ X1544 @ X1540)=>((in @ (kpair @ X1543 @ X1544) @ X1541)=>(in @ (kpair @ X1543 @ X1544) @ X1542))))))=>(![X1545:$i]:(((in @ X1545 @ X1540)=>![X1546:$i]:(((in @ X1546 @ X1540)=>((in @ (kpair @ X1545 @ X1546) @ X1542)=>(in @ (kpair @ X1545 @ X1546) @ X1541))))))=>((X1541)=(X1542))))))))=>(![X1639:$i, 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_331]), foundationAx]), wellorderingAx]), c_0_332]), c_0_333]), c_0_334]), c_0_335]), c_0_336]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_337]), setext]), emptyI]), noeltsimpempty]), c_0_338]), c_0_339]), c_0_340]), c_0_341]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_342]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_343]), c_0_344]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_345]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_346]), c_0_347]), c_0_348]), inCongP]), in__Cong]), c_0_349]), c_0_350]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), 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brelnall2]), c_0_374]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), subbreln]), eqbreln]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_375]), c_0_376]), c_0_377]), c_0_378]), c_0_379]), c_0_380]), c_0_381]), c_0_382]), c_0_383]), c_0_384]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), 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X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i > $o, X2327:$i, X2328:$i > $o, X2329:$i, X2330:$i, X2331:$i > $o, X2332:$i, X2334:$i, X2335:$i > $o, X2337:$i, X2338:$i, X2339:$i > $o, X2341:$i, X2342:$i, X2343:$i > $o, X2344:$i, X2346:$o, X2347:$o, X2348:$i, X2349:$i > $o, X2351:$i, X2352:$i, X2353:$i > $o, X2354:$i, X2356:$i > $o, X2357:$i, X2360:$i, X2361:$i > $o, X2362:$i, X2366:$i, X2367:$i > $o, X2368:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i > $o, X2381:$i, X2383:$i, X2384:$i, X2385:$i > $o, X2386:$i > $o, X2389:$i, X2392:$i, X2393:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i > $o, X2406:$i, X2408:$i, X2409:$i, X2410:$i > $o, X2411:$i > $o, X2414:$i, X2416:$i, X2418:$i, X2419:$i, X2420:$i > $o, X2421:$i > $o, X2424:$i, X2425:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i > $o, X2472:$i, X2473:$i > $o, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$o, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$o, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2621:$i, X2622:$i, X2623:$i, X2624:$i, X2625:$i > $o, X2628:$i, X2629:$i, X2630:$i > $o, X2632:$i, X2633:$i > $o, X2634:$i, X2636:$i, X2637:$i > $o, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2711:$i, X2712:$i > $i > $o, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i > $i > $o, X2718:$i, X2719:$i, X2720:$i > $i > $o, X2721:$i, X2722:$i, X2723:$i > $i > $o, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i > $i > $o, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i > $i > $o, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i > $i > $o, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i > $i, X2767:$i, X2768:$i, X2769:$i > $i, X2771:$i, X2772:$i, X2773:$i > $i, X2775:$i, X2776:$i, X2777:$i, X2778:$i > $o, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i > $o, X2788:$i, X2789:$i, X2790:$i > $o, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2851:$i, X2852:$i > $i, X2854:$i, X2855:$i, X2856:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i > $i, X2862:$i, X2863:$i, X2864:$i > $i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i, X2871:$o, X2872:$i, X2873:$i, X2874:$i, X2875:$o, X2876:$i, X2877:$i, X2878:$i, X2879:$o, X2880:$i, X2881:$i, X2882:$i, X2883:$o, X2884:$i, X2885:$i, X2886:$i, X2887:$o, X2888:$i, X2889:$i, X2890:$i, X2891:$o, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$o, X2898:$i, X2899:$i, X2900:$i, X2901:$o, X2902:$i, X2903:$i, X2904:$i, X2905:$o, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2926:$i, X2927:$i, X2928:$i, X2930:$i, X2931:$i, X2932:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$i, X2951:$i, X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i, X2976:$i, X2977:$i, X2978:$i, X2979:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3002:$i, X3003:$i, X3004:$i, X3005:$i, X3006:$i, X3007:$i, X3008:$i, X3009:$i, X3010:$i, X3011:$i, X3012:$i, X3013:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i, X3023:$i, X3024:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i, X3037:$o, X3038:$i, X3039:$i, X3040:$i, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3047:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3059:$i, X3060:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i, X3068:$i, X3069:$i, X3070:$i, X3071:$i, X3072:$i, X3073:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i, X3079:$i, X3080:$i, X3081:$i, X3082:$i, X3083:$i, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i, X3090:$i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$i, X3115:$i, X3116:$i, X3117:$i, X3118:$i, X3119:$i, X3120:$i, X3121:$i > $o, X3124:$i, X3125:$i, X3126:$i, X3127:$i, X3128:$i, X3129:$i > $i > $o, X3131:$i, X3132:$i, X3133:$i, X3134:$i, X3135:$i > $i > $o, X3136:$i, X3137:$i, X3138:$i > $o, X3141:$i, X3142:$i, X3143:$i, X3144:$i, X3147:$i, X3148:$i, X3149:$i, X3154:$i, X3155:$i, X3156:$i, X3157:$i, X3158:$i, X3159:$i, X3160:$i, X3161:$i, X3162:$i, X3163:$i, X3164:$i, X3165:$i, X3166:$i, X3167:$i, X3168:$i, X3169:$i, X3170:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i, X3176:$i, X3177:$i, X3179:$i, X3180:$i, X3181:$i, X3182:$i, X3183:$i, X3184:$o, X3186:$i, X3187:$i, X3188:$i, X3189:$i, X3190:$i, X3191:$i, X3192:$i, X3193:$i, X3194:$i, X3195:$i, X3196:$i, X3197:$i, X3198:$i, X3199:$i, X3200:$i, X3201:$i, X3202:$i, X3203:$i, X3204:$i, X3205:$i, X3206:$i, X3207:$i, X3208:$i, X3209:$i, X3210:$i, X3211:$i, X3212:$i, X3213:$i, X3214:$o, X3215:$i, X3216:$i, X3217:$i, X3218:$i, X3219:$i, X3220:$i, X3221:$i, X3222:$i, X3223:$i, X3224:$i, X3225:$i, X3226:$i, X3227:$i, X3228:$i, X3229:$i, X3230:$i, X3231:$i, X3232:$i > $i, X3234:$i, X3236:$i, X3237:$i, X3238:$i, X3239:$i > $i, X3241:$i, X3243:$i, X3244:$i, X3245:$i, X3247:$i, X3249:$i, X3250:$i > $i, X3251:$i, X3253:$i, X3254:$i > $i, X3255:$i, X3256:$i, X3260:$i]:((((~(in @ (esk1_2 @ X2190 @ X2191) @ 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X3128)=>((X3129 @ X3133 @ X1650)=>(in @ (kpair @ Z0 @ X1650) @ X3132)))))))))))))&(~(in @ X3131 @ X3128)|~(X3129 @ (esk89_3 @ X3127 @ X3128 @ X3129) @ X3131)|(~(in @ X3132 @ (breln1Set @ X3128))|(~(reflwellordering @ X3128 @ X3132)|(~(in @ X3133 @ X3127)|(singleton @ (dsetconstr @ X3128 @ (^[Z0/* 8 */:$i]:(((X3129 @ X3133 @ Z0)&![X1650:$i]:(((in @ X1650 @ X3128)=>((X3129 @ X3133 @ X1650)=>(in @ (kpair @ Z0 @ X1650) @ X3132))))))))))))))&((breln1 @ X3134 @ (dpsetconstr @ X3134 @ X3134 @ (^[Z0/* 19 */:$i, Z1:$i]:((X3135 @ Z0 @ Z1)))))&((((in @ (esk90_3 @ X3136 @ X3137 @ X3138) @ X3136)|(~(in @ X3141 @ X3137)|(X3138 @ X3141))|~(breln1 @ X3136 @ X3137))&(((in @ (esk91_3 @ X3136 @ X3137 @ X3138) @ X3136)|(~(in @ X3141 @ X3137)|(X3138 @ X3141))|~(breln1 @ X3136 @ X3137))&(((in @ (kpair @ (esk90_3 @ X3136 @ X3137 @ X3138) @ (esk91_3 @ X3136 @ X3137 @ X3138)) @ X3137)|(~(in @ X3141 @ X3137)|(X3138 @ X3141))|~(breln1 @ X3136 @ X3137))&(~(X3138 @ (kpair @ (esk90_3 @ X3136 @ X3137 @ X3138) @ (esk91_3 @ X3136 @ X3137 @ X3138)))|(~(in @ X3141 @ X3137)|(X3138 @ X3141))|~(breln1 @ X3136 @ X3137)))))&((((in @ (esk92_3 @ X3142 @ X3143 @ X3144) @ X3142)|(subset @ X3143 @ X3144)|~(breln1 @ X3142 @ X3144)|~(breln1 @ X3142 @ X3143))&(((in @ (esk93_3 @ X3142 @ X3143 @ X3144) @ X3142)|(subset @ X3143 @ X3144)|~(breln1 @ X3142 @ X3144)|~(breln1 @ X3142 @ X3143))&(((in @ (kpair @ (esk92_3 @ X3142 @ X3143 @ X3144) @ (esk93_3 @ X3142 @ X3143 @ X3144)) @ X3143)|(subset @ X3143 @ X3144)|~(breln1 @ X3142 @ X3144)|~(breln1 @ X3142 @ X3143))&(~(in @ (kpair @ (esk92_3 @ X3142 @ X3143 @ X3144) @ (esk93_3 @ X3142 @ X3143 @ X3144)) @ X3144)|(subset @ X3143 @ X3144)|~(breln1 @ X3142 @ X3144)|~(breln1 @ X3142 @ X3143)))))&(((((in @ (esk96_3 @ X3147 @ X3148 @ X3149) @ X3147)|((X3148)=(X3149))|(in @ (esk94_3 @ X3147 @ X3148 @ X3149) @ X3147)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(((in @ (esk97_3 @ X3147 @ X3148 @ X3149) @ X3147)|((X3148)=(X3149))|(in @ (esk94_3 @ X3147 @ X3148 @ X3149) @ X3147)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(((in @ (kpair @ (esk96_3 @ X3147 @ X3148 @ X3149) @ (esk97_3 @ X3147 @ X3148 @ X3149)) @ X3149)|((X3148)=(X3149))|(in @ (esk94_3 @ X3147 @ X3148 @ X3149) @ X3147)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(~(in @ (kpair @ (esk96_3 @ X3147 @ X3148 @ X3149) @ (esk97_3 @ X3147 @ X3148 @ X3149)) @ X3148)|((X3148)=(X3149))|(in @ (esk94_3 @ X3147 @ X3148 @ X3149) @ X3147)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148)))))&((((in @ (esk96_3 @ X3147 @ X3148 @ X3149) @ X3147)|((X3148)=(X3149))|(in @ (esk95_3 @ X3147 @ X3148 @ X3149) @ X3147)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(((in @ (esk97_3 @ X3147 @ X3148 @ X3149) @ X3147)|((X3148)=(X3149))|(in @ (esk95_3 @ X3147 @ X3148 @ X3149) @ X3147)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(((in @ (kpair @ (esk96_3 @ X3147 @ X3148 @ X3149) @ (esk97_3 @ X3147 @ X3148 @ X3149)) @ X3149)|((X3148)=(X3149))|(in @ (esk95_3 @ X3147 @ X3148 @ X3149) @ X3147)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(~(in @ (kpair @ (esk96_3 @ X3147 @ X3148 @ X3149) @ (esk97_3 @ X3147 @ X3148 @ X3149)) @ X3148)|((X3148)=(X3149))|(in @ (esk95_3 @ X3147 @ X3148 @ X3149) @ X3147)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148)))))&((((in @ (esk96_3 @ X3147 @ X3148 @ X3149) @ X3147)|((X3148)=(X3149))|(in @ (kpair @ (esk94_3 @ X3147 @ X3148 @ X3149) @ (esk95_3 @ X3147 @ X3148 @ X3149)) @ X3148)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(((in @ (esk97_3 @ X3147 @ X3148 @ X3149) @ X3147)|((X3148)=(X3149))|(in @ (kpair @ (esk94_3 @ X3147 @ X3148 @ X3149) @ (esk95_3 @ X3147 @ X3148 @ X3149)) @ X3148)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(((in @ (kpair @ (esk96_3 @ X3147 @ X3148 @ X3149) @ (esk97_3 @ X3147 @ X3148 @ X3149)) @ X3149)|((X3148)=(X3149))|(in @ (kpair @ (esk94_3 @ X3147 @ X3148 @ X3149) @ (esk95_3 @ X3147 @ X3148 @ X3149)) @ X3148)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(~(in @ (kpair @ (esk96_3 @ X3147 @ X3148 @ X3149) @ (esk97_3 @ X3147 @ X3148 @ X3149)) @ X3148)|((X3148)=(X3149))|(in @ (kpair @ (esk94_3 @ X3147 @ X3148 @ X3149) @ (esk95_3 @ X3147 @ X3148 @ X3149)) @ X3148)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148)))))&(((in @ (esk96_3 @ X3147 @ X3148 @ X3149) @ X3147)|((X3148)=(X3149))|~(in @ (kpair @ (esk94_3 @ X3147 @ X3148 @ X3149) @ (esk95_3 @ X3147 @ X3148 @ X3149)) @ X3149)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(((in @ (esk97_3 @ X3147 @ X3148 @ X3149) @ X3147)|((X3148)=(X3149))|~(in @ (kpair @ (esk94_3 @ X3147 @ X3148 @ X3149) @ (esk95_3 @ X3147 @ X3148 @ X3149)) @ X3149)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(((in @ (kpair @ (esk96_3 @ X3147 @ X3148 @ X3149) @ (esk97_3 @ X3147 @ X3148 @ X3149)) @ X3149)|((X3148)=(X3149))|~(in @ (kpair @ (esk94_3 @ X3147 @ X3148 @ X3149) @ (esk95_3 @ X3147 @ X3148 @ X3149)) @ X3149)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))&(~(in @ (kpair @ (esk96_3 @ X3147 @ X3148 @ X3149) @ (esk97_3 @ X3147 @ X3148 @ X3149)) @ X3148)|((X3148)=(X3149))|~(in @ (kpair @ (esk94_3 @ X3147 @ X3148 @ X3149) @ (esk95_3 @ X3147 @ X3148 @ X3149)) @ X3149)|~(breln1 @ X3147 @ X3149)|~(breln1 @ X3147 @ X3148))))))))&((~(breln1 @ X3154 @ X3155)|(breln1 @ X3154 @ (breln1invset @ X3154 @ X3155)))&((~(breln1 @ X3156 @ X3157)|(~(in @ X3158 @ X3156)|(~(in @ X3159 @ X3156)|(~(in @ (kpair @ X3158 @ X3159) @ X3157)|(in @ (kpair @ X3159 @ X3158) @ (breln1invset @ X3156 @ X3157))))))&((~(breln1 @ X3160 @ X3161)|(~(in @ X3162 @ X3160)|(~(in @ X3163 @ X3160)|(~(in @ (kpair @ X3163 @ X3162) @ (breln1invset @ X3160 @ X3161))|(in @ (kpair @ X3162 @ X3163) @ X3161)))))&((~(breln1 @ X3164 @ X3165)|(~(breln1 @ X3164 @ X3166)|(breln1 @ X3164 @ (breln1compset @ X3164 @ X3165 @ X3166))))&((~(breln1 @ X3167 @ X3168)|(~(breln1 @ X3167 @ X3169)|(~(in @ X3170 @ X3167)|(~(in @ X3171 @ X3167)|(~(in @ X3172 @ X3167)|(~(in @ (kpair @ X3170 @ X3172) @ X3168)|(~(in @ (kpair @ X3172 @ X3171) @ X3169)|(in @ (kpair @ X3170 @ X3171) @ (breln1compset @ X3167 @ X3168 @ X3169)))))))))&(((((in @ (esk98_5 @ X3173 @ X3174 @ X3175 @ X3176 @ X3177) @ X3173)|~(in @ (kpair @ X3176 @ X3177) @ (breln1compset @ X3173 @ X3174 @ X3175))|~(in @ X3177 @ X3173)|~(in @ X3176 @ X3173)|~(breln1 @ X3173 @ X3175)|~(breln1 @ X3173 @ X3174))&((in @ (kpair @ X3176 @ (esk98_5 @ X3173 @ X3174 @ X3175 @ X3176 @ X3177)) @ X3174)|~(in @ (kpair @ X3176 @ X3177) @ (breln1compset @ X3173 @ X3174 @ X3175))|~(in @ X3177 @ X3173)|~(in @ X3176 @ X3173)|~(breln1 @ X3173 @ X3175)|~(breln1 @ X3173 @ X3174)))&((in @ (kpair @ (esk98_5 @ X3173 @ X3174 @ X3175 @ X3176 @ X3177) @ X3177) @ X3175)|~(in @ (kpair @ X3176 @ X3177) @ (breln1compset @ X3173 @ X3174 @ X3175))|~(in @ X3177 @ X3173)|~(in @ X3176 @ X3173)|~(breln1 @ X3173 @ X3175)|~(breln1 @ X3173 @ X3174)))&((((in @ (esk99_6 @ X3179 @ X3180 @ X3181 @ X3182 @ X3183 @ X3184) @ X3179)|(X3184)|~(in @ (kpair @ X3182 @ X3183) @ (breln1compset @ X3179 @ X3180 @ X3181))|~(in @ X3183 @ X3179)|~(in @ X3182 @ X3179)|~(breln1 @ X3179 @ X3181)|~(breln1 @ X3179 @ X3180))&(((in @ (kpair @ X3182 @ (esk99_6 @ X3179 @ X3180 @ X3181 @ X3182 @ X3183 @ X3184)) @ X3180)|(X3184)|~(in @ (kpair @ X3182 @ X3183) @ (breln1compset @ X3179 @ X3180 @ X3181))|~(in @ X3183 @ X3179)|~(in @ X3182 @ X3179)|~(breln1 @ X3179 @ X3181)|~(breln1 @ X3179 @ X3180))&(((in @ (kpair @ (esk99_6 @ X3179 @ X3180 @ X3181 @ X3182 @ X3183 @ X3184) @ X3183) @ X3181)|(X3184)|~(in @ (kpair @ X3182 @ X3183) @ (breln1compset @ X3179 @ X3180 @ X3181))|~(in @ X3183 @ X3179)|~(in @ X3182 @ X3179)|~(breln1 @ X3179 @ X3181)|~(breln1 @ X3179 @ X3180))&(~(X3184)|(X3184)|~(in @ (kpair @ X3182 @ X3183) @ (breln1compset @ X3179 @ X3180 @ X3181))|~(in @ X3183 @ X3179)|~(in @ X3182 @ X3179)|~(breln1 @ X3179 @ X3181)|~(breln1 @ X3179 @ X3180)))))&((~(breln1 @ X3186 @ X3187)|(~(breln1 @ X3186 @ X3188)|(breln1 @ X3186 @ (binunion @ X3187 @ X3188))))&((~(breln1 @ X3189 @ X3190)|(~(breln1 @ X3189 @ X3191)|(~(in @ X3192 @ X3189)|(~(in @ X3193 @ X3189)|(~(in @ (kpair @ X3192 @ X3193) @ X3190)|(in @ (kpair @ X3192 @ X3193) @ (binunion @ X3190 @ X3191)))))))&((~(breln1 @ X3194 @ X3195)|(~(breln1 @ X3194 @ X3196)|(~(in @ X3197 @ X3194)|(~(in @ X3198 @ X3194)|(~(in @ (kpair @ X3197 @ X3198) @ X3196)|(in @ (kpair @ X3197 @ X3198) @ (binunion @ X3195 @ X3196)))))))&(((~(in @ (kpair @ X3202 @ X3203) @ X3200)|(in @ (kpair @ X3202 @ X3203) @ (binunion @ X3200 @ X3201))|~(in @ X3203 @ X3199)|~(in @ X3202 @ X3199)|~(breln1 @ X3199 @ X3201)|~(breln1 @ X3199 @ X3200))&(~(in @ (kpair @ X3202 @ X3203) @ X3201)|(in @ (kpair @ X3202 @ X3203) @ (binunion @ X3200 @ X3201))|~(in @ X3203 @ X3199)|~(in @ X3202 @ X3199)|~(breln1 @ X3199 @ X3201)|~(breln1 @ X3199 @ X3200)))&((~(breln1 @ X3204 @ X3205)|(~(breln1 @ X3204 @ X3206)|(~(in @ X3207 @ X3204)|(~(in @ X3208 @ X3204)|(~(in @ (kpair @ X3207 @ X3208) @ (binunion @ X3205 @ X3206))|((in @ (kpair @ X3207 @ X3208) @ X3205)|(in @ (kpair @ X3207 @ X3208) @ X3206)))))))&(((((in @ (kpair @ X3212 @ X3213) @ X3211)|(X3214)|(in @ (kpair @ X3212 @ X3213) @ X3210)|~(in @ (kpair @ X3212 @ X3213) @ (binunion @ X3210 @ X3211))|~(in @ X3213 @ X3209)|~(in @ X3212 @ X3209)|~(breln1 @ X3209 @ X3211)|~(breln1 @ X3209 @ X3210))&(~(X3214)|(X3214)|(in @ (kpair @ X3212 @ X3213) @ X3210)|~(in @ (kpair @ X3212 @ X3213) @ (binunion @ X3210 @ X3211))|~(in @ X3213 @ X3209)|~(in @ X3212 @ X3209)|~(breln1 @ X3209 @ X3211)|~(breln1 @ X3209 @ X3210)))&(((in @ (kpair @ X3212 @ X3213) @ X3211)|(X3214)|~(X3214)|~(in @ (kpair @ X3212 @ X3213) @ (binunion @ X3210 @ X3211))|~(in @ X3213 @ X3209)|~(in @ X3212 @ X3209)|~(breln1 @ X3209 @ X3211)|~(breln1 @ X3209 @ X3210))&(~(X3214)|(X3214)|~(X3214)|~(in @ (kpair @ X3212 @ X3213) @ (binunion @ X3210 @ X3211))|~(in @ X3213 @ X3209)|~(in @ X3212 @ X3209)|~(breln1 @ X3209 @ X3211)|~(breln1 @ X3209 @ X3210))))&((~(breln1 @ X3215 @ X3216)|(~(breln1 @ X3215 @ X3217)|((binunion @ X3216 @ X3217)=(binunion @ X3217 @ X3216))))&((~(breln1 @ X3218 @ X3219)|((X3219)=(breln1invset @ X3218 @ (breln1invset @ X3218 @ X3219))))&((~(breln1 @ X3220 @ X3221)|(~(breln1 @ X3220 @ X3222)|((breln1invset @ X3220 @ (breln1compset @ X3220 @ X3221 @ X3222))=(breln1compset @ X3220 @ (breln1invset @ X3220 @ X3222) @ (breln1invset @ X3220 @ X3221)))))&((~(breln1 @ X3223 @ X3224)|(~(breln1 @ X3223 @ X3225)|(~(breln1 @ X3223 @ X3226)|((breln1compset @ X3223 @ (binunion @ X3224 @ X3225) @ X3226)=(binunion @ (breln1compset @ X3223 @ X3224 @ X3226) @ (breln1compset @ X3223 @ X3225 @ X3226))))))&((~(breln1 @ X3227 @ X3228)|(~(breln1 @ X3227 @ X3229)|(~(breln1 @ X3227 @ X3230)|((breln1compset @ X3227 @ (binunion @ X3228 @ X3229) @ X3230)=(binunion @ (breln1invset @ X3227 @ (breln1compset @ X3227 @ (breln1invset @ X3227 @ X3230) @ (breln1invset @ X3227 @ X3229))) @ (breln1invset @ X3227 @ (breln1compset @ X3227 @ (breln1invset @ X3227 @ X3230) @ (breln1invset @ X3227 @ X3228))))))))&(((((in @ (esk101_3 @ X3231 @ X3232 @ X3234) @ X3231)|~(in @ X3234 @ (esk100_2 @ X3231 @ X3232)))&(((X3234)=(X3232 @ (esk101_3 @ X3231 @ X3232 @ X3234)))|~(in @ X3234 @ (esk100_2 @ X3231 @ X3232))))&(~(in @ X3237 @ X3231)|((X3236)!=(X3232 @ X3237))|(in @ X3236 @ (esk100_2 @ X3231 @ X3232))))&((((((in @ (esk103_3 @ X3238 @ X3239 @ X3241) @ X3238)|~(in @ X3241 @ (esk102_2 @ X3238 @ X3239)))&(((X3241)=(X3239 @ (esk103_3 @ X3238 @ X3239 @ X3241)))|~(in @ X3241 @ (esk102_2 @ X3238 @ X3239))))&(~(in @ X3244 @ X3238)|((X3243)!=(X3239 @ X3244))|(in @ X3243 @ (esk102_2 @ X3238 @ X3239))))&((~(in @ (esk104_3 @ X3238 @ X3239 @ X3245) @ X3245)|(~(in @ X3247 @ X3238)|((esk104_3 @ X3238 @ X3239 @ X3245)!=(X3239 @ X3247)))|((esk102_2 @ X3238 @ X3239)=(X3245)))&(((in @ (esk105_3 @ X3238 @ X3239 @ X3245) @ X3238)|(in @ (esk104_3 @ X3238 @ X3239 @ X3245) @ X3245)|((esk102_2 @ X3238 @ X3239)=(X3245)))&(((esk104_3 @ X3238 @ X3239 @ X3245)=(X3239 @ (esk105_3 @ X3238 @ X3239 @ X3245)))|(in @ (esk104_3 @ X3238 @ X3239 @ X3245) @ X3245)|((esk102_2 @ X3238 @ X3239)=(X3245))))))&(((((in @ (esk106_3 @ X3249 @ X3250 @ X3251) @ X3249)|~(in @ X3251 @ (image1 @ X3249 @ X3250)))&(((X3251)=(X3250 @ (esk106_3 @ X3249 @ X3250 @ X3251)))|~(in @ X3251 @ (image1 @ X3249 @ X3250))))&(~(in @ X3256 @ X3253)|((X3255)!=(X3254 @ X3256))|(in @ X3255 @ (image1 @ X3253 @ X3254))))&((in @ esk109_0 @ (image1 @ esk107_0 @ esk108_0))&(~(in @ X3260 @ esk107_0)|((esk109_0)!=(esk108_0 @ X3260))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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_390])])])])])])). 0.45/0.86 thf(c_0_392, negated_conjecture, ![X2:$i, X3:$i, X30:$i > $i]:((((X2)=(X30 @ (esk106_3 @ X3 @ X30 @ X2)))|~((in @ X2 @ (image1 @ X3 @ X30))))), inference(split_conjunct,[status(thm)],[c_0_391])). 0.45/0.86 thf(c_0_393, negated_conjecture, (in @ esk109_0 @ (image1 @ esk107_0 @ esk108_0)), inference(split_conjunct,[status(thm)],[c_0_391])). 0.45/0.86 thf(c_0_394, negated_conjecture, ![X2:$i, X3:$i, X30:$i > $i]:(((in @ (esk106_3 @ X2 @ X30 @ X3) @ X2)|~((in @ X3 @ (image1 @ X2 @ X30))))), inference(split_conjunct,[status(thm)],[c_0_391])). 0.45/0.86 thf(c_0_395, negated_conjecture, ![X2:$i]:((~((in @ X2 @ esk107_0))|((esk109_0)!=(esk108_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_391])). 0.45/0.86 thf(c_0_396, negated_conjecture, ((esk108_0 @ (esk106_3 @ esk107_0 @ esk108_0 @ esk109_0))=(esk109_0)), inference(spm,[status(thm)],[c_0_392, c_0_393])). 0.45/0.86 thf(c_0_397, negated_conjecture, (in @ (esk106_3 @ esk107_0 @ esk108_0 @ esk109_0) @ esk107_0), inference(spm,[status(thm)],[c_0_394, c_0_393])). 0.45/0.86 thf(c_0_398, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_395, c_0_396]), c_0_397])]), ['proof']). 0.45/0.86 # SZS output end CNFRefutation 0.45/0.86 # Parsed axioms : 676 0.45/0.86 # Removed by relevancy pruning/SinE : 0 0.45/0.86 # Initial clauses : 922 0.45/0.86 # Removed in clause preprocessing : 399 0.45/0.86 # Initial clauses in saturation : 523 0.45/0.86 # Processed clauses : 904 0.45/0.86 # ...of these trivial : 16 0.45/0.86 # ...subsumed : 99 0.45/0.86 # ...remaining for further processing : 789 0.45/0.86 # Other redundant clauses eliminated : 30 0.45/0.86 # Clauses deleted for lack of memory : 0 0.45/0.86 # Backward-subsumed : 0 0.45/0.86 # Backward-rewritten : 2 0.45/0.86 # Generated clauses : 3057 0.45/0.86 # ...of the previous two non-redundant : 2904 0.45/0.86 # ...aggressively subsumed : 0 0.45/0.86 # Contextual simplify-reflections : 15 0.45/0.86 # Paramodulations : 3017 0.45/0.86 # Factorizations : 0 0.45/0.86 # NegExts : 0 0.45/0.86 # Equation resolutions : 33 0.45/0.86 # Total rewrite steps : 192 0.45/0.86 # Propositional unsat checks : 0 0.45/0.86 # Propositional check models : 0 0.45/0.86 # Propositional check unsatisfiable : 0 0.45/0.86 # Propositional clauses : 0 0.45/0.86 # Propositional clauses after purity: 0 0.45/0.86 # Propositional unsat core size : 0 0.45/0.86 # Propositional preprocessing time : 0.000 0.45/0.86 # Propositional encoding time : 0.000 0.45/0.86 # Propositional solver time : 0.000 0.45/0.86 # Success case prop preproc time : 0.000 0.45/0.86 # Success case prop encoding time : 0.000 0.45/0.86 # Success case prop solver time : 0.000 0.45/0.86 # Current number of processed clauses : 307 0.45/0.86 # Positive orientable unit clauses : 80 0.45/0.86 # Positive unorientable unit clauses: 0 0.45/0.86 # Negative unit clauses : 25 0.45/0.86 # Non-unit-clauses : 202 0.45/0.86 # Current number of unprocessed clauses: 2982 0.45/0.86 # ...number of literals in the above : 7052 0.45/0.86 # Current number of archived formulas : 0 0.45/0.86 # Current number of archived clauses : 463 0.45/0.86 # Clause-clause subsumption calls (NU) : 71635 0.45/0.86 # Rec. Clause-clause subsumption calls : 22772 0.45/0.86 # Non-unit clause-clause subsumptions : 78 0.45/0.86 # Unit Clause-clause subsumption calls : 303 0.45/0.86 # Rewrite failures with RHS unbound : 0 0.45/0.86 # BW rewrite match attempts : 41 0.45/0.86 # BW rewrite match successes : 2 0.45/0.86 # Condensation attempts : 904 0.45/0.86 # Condensation successes : 5 0.45/0.86 # Termbank termtop insertions : 150561 0.45/0.86 0.45/0.86 # ------------------------------------------------- 0.45/0.86 # User time : 0.197 s 0.45/0.86 # System time : 0.017 s 0.45/0.86 # Total time : 0.214 s 0.45/0.86 # Maximum resident set size: 9944 pages 1.95/180.07 1.95/180.07 # ------------------------------------------------- 1.95/180.07 # User time : 0.600 s 1.95/180.07 # System time : 0.045 s 1.95/180.07 # Total time : 0.645 s 1.95/180.07 # Maximum resident set size: 2888 pages 1.95/180.07 % E---3.1 exiting 1.95/180.07 EOF