0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : run_E %s %d THM 0.12/0.32 % Computer : n010.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 1440 0.12/0.32 % WCLimit : 180 0.12/0.32 % DateTime : Thu Jul 4 05:33:38 EDT 2024 0.12/0.33 % CPUTime : 0.19/0.46 Running higher-order theorem proving 0.37/0.55 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p 185.90/180.07 # Version: 3.2.0-ho 185.90/180.07 # Preprocessing class: HSLMSLSSLLLCHFA. 185.90/180.07 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 185.90/180.07 # Starting ehoh_best5 with 180s (1) cores 185.90/180.07 # Starting almost_fo_3_lam with 180s (1) cores 185.90/180.07 # Starting new_bool_5 with 180s (1) cores 185.90/180.07 # Starting pre_casc_3 with 180s (1) cores 185.90/180.07 # Starting ho_unfolding_8 with 180s (1) cores 185.90/180.07 # Starting new_ho_10_cnf2 with 180s (1) cores 185.90/180.07 # Starting new_bool_3 with 180s (1) cores 185.90/180.07 # Starting new_ho_5 with 180s (1) cores 185.90/180.07 # almost_fo_3_lam with pid 8820 completed with status 0 185.90/180.07 # Result found by almost_fo_3_lam 185.90/180.07 # Preprocessing class: HSLMSLSSLLLCHFA. 185.90/180.07 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 185.90/180.07 # Starting ehoh_best5 with 180s (1) cores 185.90/180.07 # Starting almost_fo_3_lam with 180s (1) cores 185.90/180.07 # No SInE strategy applied 185.90/180.07 # Search class: HGHSM-SMLM32-DHFMMSBN 185.90/180.07 # partial match(1): HGHSM-SMLM32-MHFMMSBN 185.90/180.07 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 185.90/180.07 # Starting sh3 with 98s (1) cores 185.90/180.07 # sh3 with pid 8831 completed with status 0 185.90/180.07 # Result found by sh3 185.90/180.07 # Preprocessing class: HSLMSLSSLLLCHFA. 185.90/180.07 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 185.90/180.07 # Starting ehoh_best5 with 180s (1) cores 185.90/180.07 # Starting almost_fo_3_lam with 180s (1) cores 185.90/180.07 # No SInE strategy applied 185.90/180.07 # Search class: HGHSM-SMLM32-DHFMMSBN 185.90/180.07 # partial match(1): HGHSM-SMLM32-MHFMMSBN 185.90/180.07 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 185.90/180.07 # Starting sh3 with 98s (1) cores 185.90/180.07 # Preprocessing time : 0.020 s 185.90/180.07 # Presaturation interreduction done 185.90/180.07 185.90/180.07 # Proof found! 185.90/180.07 # SZS status Theorem 185.90/180.07 # SZS output start CNFRefutation 185.90/180.07 thf(decl_22, type, in: $i > $i > $o). 185.90/180.07 thf(decl_23, type, exu: ($i > $o) > $o). 185.90/180.07 thf(decl_24, type, setextAx: $o). 185.90/180.07 thf(decl_25, type, emptyset: $i). 185.90/180.07 thf(decl_26, type, emptysetAx: $o). 185.90/180.07 thf(decl_27, type, setadjoin: $i > $i > $i). 185.90/180.07 thf(decl_28, type, setadjoinAx: $o). 185.90/180.07 thf(decl_29, type, powerset: $i > $i). 185.90/180.07 thf(decl_30, type, powersetAx: $o). 185.90/180.07 thf(decl_31, type, setunion: $i > $i). 185.90/180.07 thf(decl_32, type, setunionAx: $o). 185.90/180.07 thf(decl_33, type, omega: $i). 185.90/180.07 thf(decl_34, type, omega0Ax: $o). 185.90/180.07 thf(decl_35, type, omegaSAx: $o). 185.90/180.07 thf(decl_36, type, omegaIndAx: $o). 185.90/180.07 thf(decl_37, type, replAx: $o). 185.90/180.07 thf(decl_38, type, foundationAx: $o). 185.90/180.07 thf(decl_39, type, wellorderingAx: $o). 185.90/180.07 thf(decl_40, type, descr: ($i > $o) > $i). 185.90/180.07 thf(decl_41, type, descrp: $o). 185.90/180.07 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_43, type, dsetconstrI: $o). 185.90/180.07 thf(decl_44, type, dsetconstrEL: $o). 185.90/180.07 thf(decl_45, type, dsetconstrER: $o). 185.90/180.07 thf(decl_46, type, exuE1: $o). 185.90/180.07 thf(decl_47, type, prop2set: $o > $i). 185.90/180.07 thf(decl_48, type, prop2setE: $o). 185.90/180.07 thf(decl_49, type, emptysetE: $o). 185.90/180.07 thf(decl_50, type, emptysetimpfalse: $o). 185.90/180.07 thf(decl_51, type, notinemptyset: $o). 185.90/180.07 thf(decl_52, type, exuE3e: $o). 185.90/180.07 thf(decl_53, type, setext: $o). 185.90/180.07 thf(decl_54, type, emptyI: $o). 185.90/180.07 thf(decl_55, type, noeltsimpempty: $o). 185.90/180.07 thf(decl_56, type, setbeta: $o). 185.90/180.07 thf(decl_57, type, nonempty: $i > $o). 185.90/180.07 thf(decl_58, type, nonemptyE1: $o). 185.90/180.07 thf(decl_59, type, nonemptyI: $o). 185.90/180.07 thf(decl_60, type, nonemptyI1: $o). 185.90/180.07 thf(decl_61, type, setadjoinIL: $o). 185.90/180.07 thf(decl_62, type, emptyinunitempty: $o). 185.90/180.07 thf(decl_63, type, setadjoinIR: $o). 185.90/180.07 thf(decl_64, type, setadjoinE: $o). 185.90/180.07 thf(decl_65, type, setadjoinOr: $o). 185.90/180.07 thf(decl_66, type, setoftrueEq: $o). 185.90/180.07 thf(decl_67, type, powersetI: $o). 185.90/180.07 thf(decl_68, type, emptyinPowerset: $o). 185.90/180.07 thf(decl_69, type, emptyInPowerset: $o). 185.90/180.07 thf(decl_70, type, powersetE: $o). 185.90/180.07 thf(decl_71, type, setunionI: $o). 185.90/180.07 thf(decl_72, type, setunionE: $o). 185.90/180.07 thf(decl_73, type, subPowSU: $o). 185.90/180.07 thf(decl_74, type, exuE2: $o). 185.90/180.07 thf(decl_75, type, nonemptyImpWitness: $o). 185.90/180.07 thf(decl_76, type, uniqinunit: $o). 185.90/180.07 thf(decl_77, type, notinsingleton: $o). 185.90/180.07 thf(decl_78, type, eqinunit: $o). 185.90/180.07 thf(decl_79, type, singletonsswitch: $o). 185.90/180.07 thf(decl_80, type, upairsetE: $o). 185.90/180.07 thf(decl_81, type, upairsetIL: $o). 185.90/180.07 thf(decl_82, type, upairsetIR: $o). 185.90/180.07 thf(decl_83, type, emptyE1: $o). 185.90/180.07 thf(decl_84, type, vacuousDall: $o). 185.90/180.07 thf(decl_85, type, quantDeMorgan1: $o). 185.90/180.07 thf(decl_86, type, quantDeMorgan2: $o). 185.90/180.07 thf(decl_87, type, quantDeMorgan3: $o). 185.90/180.07 thf(decl_88, type, quantDeMorgan4: $o). 185.90/180.07 thf(decl_89, type, prop2setI: $o). 185.90/180.07 thf(decl_90, type, set2prop: $i > $o). 185.90/180.07 thf(decl_91, type, prop2set2propI: $o). 185.90/180.07 thf(decl_92, type, notdexE: $o). 185.90/180.07 thf(decl_93, type, notdallE: $o). 185.90/180.07 thf(decl_94, type, exuI1: $o). 185.90/180.07 thf(decl_95, type, exuI3: $o). 185.90/180.07 thf(decl_96, type, exuI2: $o). 185.90/180.07 thf(decl_97, type, inCongP: $o). 185.90/180.07 thf(decl_98, type, in__Cong: $o). 185.90/180.07 thf(decl_99, type, exuE3u: $o). 185.90/180.07 thf(decl_100, type, exu__Cong: $o). 185.90/180.07 thf(decl_101, type, emptyset__Cong: $o). 185.90/180.07 thf(decl_102, type, setadjoin__Cong: $o). 185.90/180.07 thf(decl_103, type, powerset__Cong: $o). 185.90/180.07 thf(decl_104, type, setunion__Cong: $o). 185.90/180.07 thf(decl_105, type, omega__Cong: $o). 185.90/180.07 thf(decl_106, type, exuEu: $o). 185.90/180.07 thf(decl_107, type, descr__Cong: $o). 185.90/180.07 thf(decl_108, type, dsetconstr__Cong: $o). 185.90/180.07 thf(decl_109, type, subset: $i > $i > $o). 185.90/180.07 thf(decl_112, type, subsetI1: $o). 185.90/180.07 thf(decl_113, type, eqimpsubset2: $o). 185.90/180.07 thf(decl_114, type, eqimpsubset1: $o). 185.90/180.07 thf(decl_115, type, subsetI2: $o). 185.90/180.07 thf(decl_116, type, emptysetsubset: $o). 185.90/180.07 thf(decl_117, type, subsetE: $o). 185.90/180.07 thf(decl_118, type, subsetE2: $o). 185.90/180.07 thf(decl_119, type, notsubsetI: $o). 185.90/180.07 thf(decl_120, type, notequalI1: $o). 185.90/180.07 thf(decl_121, type, notequalI2: $o). 185.90/180.07 thf(decl_122, type, subsetRefl: $o). 185.90/180.07 thf(decl_123, type, subsetTrans: $o). 185.90/180.07 thf(decl_124, type, setadjoinSub: $o). 185.90/180.07 thf(decl_125, type, setadjoinSub2: $o). 185.90/180.07 thf(decl_126, type, subset2powerset: $o). 185.90/180.07 thf(decl_127, type, setextsub: $o). 185.90/180.07 thf(decl_128, type, subsetemptysetimpeq: $o). 185.90/180.07 thf(decl_129, type, powersetI1: $o). 185.90/180.07 thf(decl_130, type, powersetE1: $o). 185.90/180.07 thf(decl_131, type, inPowerset: $o). 185.90/180.07 thf(decl_132, type, powersetsubset: $o). 185.90/180.07 thf(decl_133, type, sepInPowerset: $o). 185.90/180.07 thf(decl_134, type, sepSubset: $o). 185.90/180.07 thf(decl_135, type, binunion: $i > $i > $i). 185.90/180.07 thf(decl_136, type, binunionIL: $o). 185.90/180.07 thf(decl_137, type, upairset2IR: $o). 185.90/180.07 thf(decl_138, type, binunionIR: $o). 185.90/180.07 thf(decl_139, type, binunionEcases: $o). 185.90/180.07 thf(decl_140, type, binunionE: $o). 185.90/180.07 thf(decl_141, type, binunionLsub: $o). 185.90/180.07 thf(decl_142, type, binunionRsub: $o). 185.90/180.07 thf(decl_143, type, binintersect: $i > $i > $i). 185.90/180.07 thf(decl_144, type, binintersectI: $o). 185.90/180.07 thf(decl_145, type, binintersectSubset5: $o). 185.90/180.07 thf(decl_146, type, binintersectEL: $o). 185.90/180.07 thf(decl_147, type, binintersectLsub: $o). 185.90/180.07 thf(decl_148, type, binintersectSubset2: $o). 185.90/180.07 thf(decl_149, type, binintersectSubset3: $o). 185.90/180.07 thf(decl_150, type, binintersectER: $o). 185.90/180.07 thf(decl_151, type, disjointsetsI1: $o). 185.90/180.07 thf(decl_152, type, binintersectRsub: $o). 185.90/180.07 thf(decl_153, type, binintersectSubset4: $o). 185.90/180.07 thf(decl_154, type, binintersectSubset1: $o). 185.90/180.07 thf(decl_155, type, bs114d: $o). 185.90/180.07 thf(decl_157, type, setminus: $i > $i > $i). 185.90/180.07 thf(decl_158, type, setminusI: $o). 185.90/180.07 thf(decl_159, type, setminusEL: $o). 185.90/180.07 thf(decl_160, type, setminusER: $o). 185.90/180.07 thf(decl_161, type, setminusSubset2: $o). 185.90/180.07 thf(decl_162, type, setminusERneg: $o). 185.90/180.07 thf(decl_163, type, setminusELneg: $o). 185.90/180.07 thf(decl_164, type, setminusILneg: $o). 185.90/180.07 thf(decl_165, type, setminusIRneg: $o). 185.90/180.07 thf(decl_166, type, setminusLsub: $o). 185.90/180.07 thf(decl_167, type, setminusSubset1: $o). 185.90/180.07 thf(decl_168, type, symdiff: $i > $i > $i). 185.90/180.07 thf(decl_169, type, symdiffE: $o). 185.90/180.07 thf(decl_170, type, symdiffI1: $o). 185.90/180.07 thf(decl_171, type, symdiffI2: $o). 185.90/180.07 thf(decl_172, type, symdiffIneg1: $o). 185.90/180.07 thf(decl_173, type, symdiffIneg2: $o). 185.90/180.07 thf(decl_174, type, iskpair: $i > $o). 185.90/180.07 thf(decl_175, type, secondinupair: $o). 185.90/180.07 thf(decl_176, type, setukpairIL: $o). 185.90/180.07 thf(decl_177, type, setukpairIR: $o). 185.90/180.07 thf(decl_178, type, kpairiskpair: $o). 185.90/180.07 thf(decl_179, type, kpair: $i > $i > $i). 185.90/180.07 thf(decl_180, type, kpairp: $o). 185.90/180.07 thf(decl_181, type, cartprod: $i > $i > $i). 185.90/180.07 thf(decl_182, type, singletonsubset: $o). 185.90/180.07 thf(decl_183, type, singletoninpowerset: $o). 185.90/180.07 thf(decl_184, type, singletoninpowunion: $o). 185.90/180.07 thf(decl_185, type, upairset2E: $o). 185.90/180.07 thf(decl_186, type, upairsubunion: $o). 185.90/180.07 thf(decl_187, type, upairinpowunion: $o). 185.90/180.07 thf(decl_188, type, ubforcartprodlem1: $o). 185.90/180.07 thf(decl_189, type, ubforcartprodlem2: $o). 185.90/180.07 thf(decl_190, type, ubforcartprodlem3: $o). 185.90/180.07 thf(decl_191, type, cartprodpairin: $o). 185.90/180.07 thf(decl_192, type, cartprodmempair1: $o). 185.90/180.07 thf(decl_193, type, cartprodmempair: $o). 185.90/180.07 thf(decl_194, type, setunionE2: $o). 185.90/180.07 thf(decl_195, type, setunionsingleton1: $o). 185.90/180.07 thf(decl_196, type, setunionsingleton2: $o). 185.90/180.07 thf(decl_197, type, setunionsingleton: $o). 185.90/180.07 thf(decl_198, type, singleton: $i > $o). 185.90/180.07 thf(decl_199, type, singletonprop: $o). 185.90/180.07 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 185.90/180.07 thf(decl_201, type, ex1E1: $o). 185.90/180.07 thf(decl_202, type, ex1I: $o). 185.90/180.07 thf(decl_203, type, ex1I2: $o). 185.90/180.07 thf(decl_204, type, singletonsuniq: $o). 185.90/180.07 thf(decl_209, type, setukpairinjL1: $o). 185.90/180.07 thf(decl_210, type, kfstsingleton: $o). 185.90/180.07 thf(decl_211, type, theprop: $o). 185.90/180.07 thf(decl_212, type, kfst: $i > $i). 185.90/180.07 thf(decl_213, type, kfstpairEq: $o). 185.90/180.07 thf(decl_214, type, cartprodfstin: $o). 185.90/180.07 thf(decl_215, type, setukpairinjL2: $o). 185.90/180.07 thf(decl_216, type, setukpairinjL: $o). 185.90/180.07 thf(decl_217, type, setukpairinjR11: $o). 185.90/180.07 thf(decl_218, type, setukpairinjR12: $o). 185.90/180.07 thf(decl_219, type, setukpairinjR1: $o). 185.90/180.07 thf(decl_220, type, upairequniteq: $o). 185.90/180.07 thf(decl_221, type, setukpairinjR2: $o). 185.90/180.07 thf(decl_222, type, setukpairinjR: $o). 185.90/180.07 thf(decl_223, type, ksndsingleton: $o). 185.90/180.07 thf(decl_224, type, ksnd: $i > $i). 185.90/180.07 thf(decl_225, type, ksndpairEq: $o). 185.90/180.07 thf(decl_226, type, kpairsurjEq: $o). 185.90/180.07 thf(decl_227, type, cartprodsndin: $o). 185.90/180.07 thf(decl_228, type, cartprodpairmemEL: $o). 185.90/180.07 thf(decl_229, type, cartprodpairmemER: $o). 185.90/180.07 thf(decl_230, type, cartprodmempaircEq: $o). 185.90/180.07 thf(decl_231, type, cartprodfstpairEq: $o). 185.90/180.07 thf(decl_232, type, cartprodsndpairEq: $o). 185.90/180.07 thf(decl_233, type, cartprodpairsurjEq: $o). 185.90/180.07 thf(decl_234, type, breln: $i > $i > $i > $o). 185.90/180.07 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 185.90/180.07 thf(decl_236, type, dpsetconstrI: $o). 185.90/180.07 thf(decl_237, type, dpsetconstrSub: $o). 185.90/180.07 thf(decl_238, type, setOfPairsIsBReln: $o). 185.90/180.07 thf(decl_239, type, dpsetconstrERa: $o). 185.90/180.07 thf(decl_240, type, dpsetconstrEL1: $o). 185.90/180.07 thf(decl_241, type, dpsetconstrEL2: $o). 185.90/180.07 thf(decl_242, type, dpsetconstrER: $o). 185.90/180.07 thf(decl_243, type, func: $i > $i > $i > $o). 185.90/180.07 thf(decl_244, type, funcSet: $i > $i > $i). 185.90/180.07 thf(decl_245, type, funcImageSingleton: $o). 185.90/180.07 thf(decl_246, type, apProp: $o). 185.90/180.07 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 185.90/180.07 thf(decl_248, type, app: $o). 185.90/180.07 thf(decl_249, type, infuncsetfunc: $o). 185.90/180.07 thf(decl_250, type, ap2p: $o). 185.90/180.07 thf(decl_251, type, funcinfuncset: $o). 185.90/180.07 thf(decl_252, type, lamProp: $o). 185.90/180.07 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 185.90/180.07 thf(decl_254, type, lamp: $o). 185.90/180.07 thf(decl_255, type, lam2p: $o). 185.90/180.07 thf(decl_256, type, brelnall1: $o). 185.90/180.07 thf(decl_257, type, brelnall2: $o). 185.90/180.07 thf(decl_258, type, ex1E2: $o). 185.90/180.07 thf(decl_259, type, funcGraphProp1: $o). 185.90/180.07 thf(decl_260, type, funcGraphProp3: $o). 185.90/180.07 thf(decl_261, type, funcGraphProp2: $o). 185.90/180.07 thf(decl_262, type, funcextLem: $o). 185.90/180.07 thf(decl_263, type, funcGraphProp4: $o). 185.90/180.07 thf(decl_264, type, subbreln: $o). 185.90/180.07 thf(decl_265, type, eqbreln: $o). 185.90/180.07 thf(decl_266, type, funcext: $o). 185.90/180.07 thf(decl_267, type, funcext2: $o). 185.90/180.07 thf(decl_268, type, ap2apEq1: $o). 185.90/180.07 thf(decl_269, type, ap2apEq2: $o). 185.90/180.07 thf(decl_270, type, beta1: $o). 185.90/180.07 thf(decl_271, type, eta1: $o). 185.90/180.07 thf(decl_272, type, lam2lamEq: $o). 185.90/180.07 thf(decl_273, type, beta2: $o). 185.90/180.07 thf(decl_274, type, eta2: $o). 185.90/180.07 thf(decl_275, type, iffalseProp1: $o). 185.90/180.07 thf(decl_276, type, iffalseProp2: $o). 185.90/180.07 thf(decl_277, type, iftrueProp1: $o). 185.90/180.07 thf(decl_278, type, iftrueProp2: $o). 185.90/180.07 thf(decl_279, type, ifSingleton: $o). 185.90/180.07 thf(decl_280, type, if: $i > $o > $i > $i > $i). 185.90/180.07 thf(decl_281, type, ifp: $o). 185.90/180.07 thf(decl_282, type, theeq: $o). 185.90/180.07 thf(decl_283, type, iftrue: $o). 185.90/180.07 thf(decl_284, type, iffalse: $o). 185.90/180.07 thf(decl_285, type, iftrueorfalse: $o). 185.90/180.07 thf(decl_286, type, binintersectT_lem: $o). 185.90/180.07 thf(decl_287, type, binunionT_lem: $o). 185.90/180.07 thf(decl_288, type, powersetT_lem: $o). 185.90/180.07 thf(decl_289, type, setminusT_lem: $o). 185.90/180.07 thf(decl_290, type, complementT_lem: $o). 185.90/180.07 thf(decl_291, type, setextT: $o). 185.90/180.07 thf(decl_292, type, subsetTI: $o). 185.90/180.07 thf(decl_293, type, powersetTI1: $o). 185.90/180.07 thf(decl_294, type, powersetTE1: $o). 185.90/180.07 thf(decl_295, type, complementTI1: $o). 185.90/180.07 thf(decl_296, type, complementTE1: $o). 185.90/180.07 thf(decl_297, type, binintersectTELcontra: $o). 185.90/180.07 thf(decl_298, type, binintersectTERcontra: $o). 185.90/180.07 thf(decl_299, type, contrasubsetT: $o). 185.90/180.07 thf(decl_300, type, contrasubsetT1: $o). 185.90/180.07 thf(decl_301, type, contrasubsetT2: $o). 185.90/180.07 thf(decl_302, type, contrasubsetT3: $o). 185.90/180.07 thf(decl_303, type, doubleComplementI1: $o). 185.90/180.07 thf(decl_304, type, doubleComplementE1: $o). 185.90/180.07 thf(decl_305, type, doubleComplementSub1: $o). 185.90/180.07 thf(decl_306, type, doubleComplementSub2: $o). 185.90/180.07 thf(decl_307, type, doubleComplementEq: $o). 185.90/180.07 thf(decl_308, type, complementTnotintersectT: $o). 185.90/180.07 thf(decl_309, type, complementImpComplementIntersect: $o). 185.90/180.07 thf(decl_310, type, complementSubsetComplementIntersect: $o). 185.90/180.07 thf(decl_311, type, complementInPowersetComplementIntersect: $o). 185.90/180.07 thf(decl_312, type, contraSubsetComplement: $o). 185.90/180.07 thf(decl_313, type, complementTcontraSubset: $o). 185.90/180.07 thf(decl_314, type, binunionTILcontra: $o). 185.90/180.07 thf(decl_315, type, binunionTIRcontra: $o). 185.90/180.07 thf(decl_316, type, inIntersectImpInUnion: $o). 185.90/180.07 thf(decl_317, type, inIntersectImpInUnion2: $o). 185.90/180.07 thf(decl_318, type, inIntersectImpInIntersectUnions: $o). 185.90/180.07 thf(decl_319, type, intersectInPowersetIntersectUnions: $o). 185.90/180.07 thf(decl_320, type, inComplementUnionImpNotIn1: $o). 185.90/180.07 thf(decl_321, type, inComplementUnionImpInComplement1: $o). 185.90/180.07 thf(decl_322, type, binunionTE: $o). 185.90/180.07 thf(decl_323, type, binunionTEcontra: $o). 185.90/180.07 thf(decl_324, type, demorgan2a1: $o). 185.90/180.07 thf(decl_325, type, complementUnionInPowersetComplement: $o). 185.90/180.07 thf(decl_326, type, demorgan2a2: $o). 185.90/180.07 thf(decl_327, type, demorgan1a: $o). 185.90/180.07 thf(decl_328, type, demorgan1b: $o). 185.90/180.07 thf(decl_329, type, demorgan1: $o). 185.90/180.07 thf(decl_330, type, demorgan2a: $o). 185.90/180.07 thf(decl_331, type, demorgan2b2: $o). 185.90/180.07 thf(decl_332, type, demorgan2b: $o). 185.90/180.07 thf(decl_333, type, demorgan2: $o). 185.90/180.07 thf(decl_334, type, woz13rule0: $o). 185.90/180.07 thf(decl_335, type, woz13rule1: $o). 185.90/180.07 thf(decl_336, type, woz13rule2: $o). 185.90/180.07 thf(decl_337, type, woz13rule3: $o). 185.90/180.07 thf(decl_338, type, woz13rule4: $o). 185.90/180.07 thf(decl_339, type, woz1_1: $o). 185.90/180.07 thf(decl_340, type, woz1_2: $o). 185.90/180.07 thf(decl_341, type, woz1_3: $o). 185.90/180.07 thf(decl_342, type, woz1_4: $o). 185.90/180.07 thf(decl_343, type, woz1_5: $o). 185.90/180.07 thf(decl_344, type, breln1: $i > $i > $o). 185.90/180.07 thf(decl_345, type, breln1all2: $o). 185.90/180.07 thf(decl_346, type, breln1Set: $i > $i). 185.90/180.07 thf(decl_347, type, breln1SetBreln1: $o). 185.90/180.07 thf(decl_353, type, reflwellordering: $i > $i > $o). 185.90/180.07 thf(decl_354, type, choice2fnsingleton: $o). 185.90/180.07 thf(decl_355, type, setOfPairsIsBReln1: $o). 185.90/180.07 thf(decl_356, type, breln1all1: $o). 185.90/180.07 thf(decl_357, type, subbreln1: $o). 185.90/180.07 thf(decl_358, type, eqbreln1: $o). 185.90/180.07 thf(decl_359, type, breln1invset: $i > $i > $i). 185.90/180.07 thf(decl_360, type, breln1invprop: $o). 185.90/180.07 thf(decl_361, type, breln1invI: $o). 185.90/180.07 thf(decl_362, type, breln1invE: $o). 185.90/180.07 thf(decl_363, type, breln1compset: $i > $i > $i > $i). 185.90/180.07 thf(decl_364, type, breln1compprop: $o). 185.90/180.07 thf(decl_365, type, breln1compI: $o). 185.90/180.07 thf(decl_366, type, breln1compE: $o). 185.90/180.07 thf(decl_367, type, breln1compEex: $o). 185.90/180.07 thf(decl_368, type, breln1unionprop: $o). 185.90/180.07 thf(decl_369, type, breln1unionIL: $o). 185.90/180.07 thf(decl_370, type, breln1unionIR: $o). 185.90/180.07 thf(decl_371, type, breln1unionI: $o). 185.90/180.07 thf(decl_372, type, breln1unionE: $o). 185.90/180.07 thf(decl_373, type, breln1unionEcases: $o). 185.90/180.07 thf(decl_374, type, breln1unionCommutes: $o). 185.90/180.07 thf(decl_375, type, woz2Ex: $o). 185.90/180.07 thf(decl_376, type, woz2W: $o). 185.90/180.07 thf(decl_377, type, woz2A: $o). 185.90/180.07 thf(decl_378, type, woz2B: $o). 185.90/180.07 thf(decl_379, type, image1Ex: $o). 185.90/180.07 thf(decl_380, type, image1Ex1: $o). 185.90/180.07 thf(decl_381, type, image1: $i > ($i > $i) > $i). 185.90/180.07 thf(decl_382, type, image1Equiv: $o). 185.90/180.07 thf(decl_383, type, image1E: $o). 185.90/180.07 thf(decl_384, type, image1I: $o). 185.90/180.07 thf(decl_385, type, injective: $i > $i > $i > $o). 185.90/180.07 thf(decl_386, type, injFuncSet: $i > $i > $i). 185.90/180.07 thf(decl_387, type, injFuncInInjFuncSet: $o). 185.90/180.07 thf(decl_388, type, injFuncSetFuncIn: $o). 185.90/180.07 thf(decl_389, type, injFuncSetFuncInj: $o). 185.90/180.07 thf(decl_390, type, surjective: $i > $i > $i > $o). 185.90/180.07 thf(decl_391, type, surjFuncSet: $i > $i > $i). 185.90/180.07 thf(decl_392, type, surjFuncSetFuncIn: $o). 185.90/180.07 thf(decl_393, type, surjFuncSetFuncSurj: $o). 185.90/180.07 thf(decl_394, type, leftInvIsSurj: $o). 185.90/180.07 thf(decl_395, type, surjCantorThm: $o). 185.90/180.07 thf(decl_396, type, foundation2: $o). 185.90/180.07 thf(decl_397, type, notinself: $o). 185.90/180.07 thf(decl_398, type, notinself2: $o). 185.90/180.07 thf(decl_399, type, omegaS: $i > $i). 185.90/180.07 thf(decl_400, type, omegaSp: $o). 185.90/180.07 thf(decl_401, type, omegaSclos: $o). 185.90/180.07 thf(decl_402, type, peano0notS: $o). 185.90/180.07 thf(decl_406, type, peanoSinj: $o). 185.90/180.07 thf(decl_408, type, transitiveset: $i > $o). 185.90/180.07 thf(decl_409, type, transitivesetOp1: $o). 185.90/180.07 thf(decl_410, type, binintTransitive: $o). 185.90/180.07 thf(decl_411, type, transitivesetOp2: $o). 185.90/180.07 thf(decl_412, type, setunionTransitive: $o). 185.90/180.07 thf(decl_413, type, stricttotalorderedByIn: $i > $o). 185.90/180.07 thf(decl_414, type, wellorderedByIn: $i > $o). 185.90/180.07 thf(decl_415, type, ordinal: $i > $o). 185.90/180.07 thf(decl_417, type, ordinalMinLem1: $o). 185.90/180.07 thf(decl_418, type, ordinalTransSet: $o). 185.90/180.07 thf(decl_419, type, ordinalTransSet1: $o). 185.90/180.07 thf(decl_420, type, setunionOrdinalLem1: $o). 185.90/180.07 thf(decl_422, type, epred1_0: $o). 185.90/180.07 thf(decl_423, type, epred2_1: $i > $o). 185.90/180.07 thf(decl_424, type, epred3_1: $i > $o). 185.90/180.07 thf(decl_425, type, epred4_1: $i > $o). 185.90/180.07 thf(decl_426, type, epred5_1: $i > $o). 185.90/180.07 thf(decl_427, type, epred6_1: $i > $o). 185.90/180.07 thf(decl_428, type, epred7_0: $o). 185.90/180.07 thf(decl_429, type, esk1_2: $i > $i > $i). 185.90/180.07 thf(decl_430, type, esk2_2: $i > $i > $i). 185.90/180.07 thf(decl_431, type, esk3_2: $i > $i > $i). 185.90/180.07 thf(decl_432, type, esk4_1: $i > $i). 185.90/180.07 thf(decl_433, type, esk5_2: ($i > $i > $o) > $i > $i). 185.90/180.07 thf(decl_434, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 185.90/180.07 thf(decl_435, type, esk7_2: ($i > $i > $o) > $i > $i). 185.90/180.07 thf(decl_436, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 185.90/180.07 thf(decl_437, type, esk9_1: $i > $i). 185.90/180.07 thf(decl_438, type, esk10_2: ($i > $o) > $i > $i). 185.90/180.07 thf(decl_439, type, esk11_2: ($i > $o) > $i > $i). 185.90/180.07 thf(decl_440, type, esk12_1: ($i > $o) > $i). 185.90/180.07 thf(decl_441, type, esk13_2: ($i > $o) > $i > $i). 185.90/180.07 thf(decl_442, type, esk14_1: ($i > $o) > $i). 185.90/180.07 thf(decl_443, type, esk15_2: $i > $i > $i). 185.90/180.07 thf(decl_444, type, esk16_2: $i > $i > $i). 185.90/180.07 thf(decl_445, type, esk17_1: $i > $i). 185.90/180.07 thf(decl_446, type, esk18_1: $i > $i). 185.90/180.07 thf(decl_447, type, esk19_1: $i > $i). 185.90/180.07 thf(decl_448, type, esk20_2: $i > $i > $i). 185.90/180.07 thf(decl_449, type, esk21_3: $i > $i > $o > $i). 185.90/180.07 thf(decl_450, type, esk22_2: ($i > $o) > $i > $i). 185.90/180.07 thf(decl_451, type, esk23_1: ($i > $o) > $i). 185.90/180.07 thf(decl_452, type, esk24_1: $i > $i). 185.90/180.07 thf(decl_453, type, esk25_2: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_454, type, esk26_2: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_455, type, esk27_2: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_456, type, esk28_2: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_457, type, esk29_2: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_458, type, esk30_2: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_459, type, esk31_2: ($i > $o) > $i > $i). 185.90/180.07 thf(decl_460, type, esk32_1: ($i > $o) > $i). 185.90/180.07 thf(decl_461, type, esk33_1: ($i > $o) > $i). 185.90/180.07 thf(decl_462, type, esk34_1: ($i > $o) > $i). 185.90/180.07 thf(decl_463, type, esk35_1: ($i > $o) > $i). 185.90/180.07 thf(decl_464, type, esk36_2: ($i > $o) > $i > $i). 185.90/180.07 thf(decl_465, type, esk37_1: ($i > $o) > $i). 185.90/180.07 thf(decl_466, type, esk38_2: ($i > $o) > $i > $i). 185.90/180.07 thf(decl_467, type, esk39_2: ($i > $o) > ($i > $o) > $i). 185.90/180.07 thf(decl_468, type, esk40_2: ($i > $o) > ($i > $o) > $i). 185.90/180.07 thf(decl_469, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 185.90/180.07 thf(decl_470, type, esk42_2: ($i > $o) > ($i > $o) > $i). 185.90/180.07 thf(decl_471, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 185.90/180.07 thf(decl_472, type, esk44_2: ($i > $o) > ($i > $o) > $i). 185.90/180.07 thf(decl_473, type, esk45_2: ($i > $o) > $i > $i). 185.90/180.07 thf(decl_474, type, esk46_2: ($i > $o) > ($i > $o) > $i). 185.90/180.07 thf(decl_475, type, esk47_2: ($i > $o) > ($i > $o) > $i). 185.90/180.07 thf(decl_476, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 185.90/180.07 thf(decl_477, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 185.90/180.07 thf(decl_478, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 185.90/180.07 thf(decl_479, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 185.90/180.07 thf(decl_480, type, esk52_2: $i > $i > $i). 185.90/180.07 thf(decl_481, type, esk53_2: $i > $i > $i). 185.90/180.07 thf(decl_482, type, esk54_2: $i > $i > $i). 185.90/180.07 thf(decl_483, type, esk55_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_484, type, esk56_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_485, type, esk57_2: $i > $i > $i). 185.90/180.07 thf(decl_486, type, esk58_2: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_487, type, esk59_2: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_488, type, esk60_2: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_489, type, esk61_3: $i > ($i > $o) > $i > $i). 185.90/180.07 thf(decl_490, type, esk62_2: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_491, type, esk63_2: $i > ($i > $o) > $i). 185.90/180.07 thf(decl_492, type, esk64_3: $i > $i > ($i > $i) > $i). 185.90/180.07 thf(decl_493, type, esk65_3: $i > $i > ($i > $i) > $i). 185.90/180.07 thf(decl_494, type, esk66_3: $i > $i > ($i > $i) > $i). 185.90/180.07 thf(decl_495, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 185.90/180.07 thf(decl_496, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 185.90/180.07 thf(decl_497, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 185.90/180.07 thf(decl_498, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 185.90/180.07 thf(decl_499, type, esk71_4: $i > $i > $i > $i > $i). 185.90/180.07 thf(decl_500, type, esk72_4: $i > $i > $i > $i > $i). 185.90/180.07 thf(decl_501, type, esk73_4: $i > $i > $i > $i > $i). 185.90/180.07 thf(decl_502, type, esk74_4: $i > $i > $i > $i > $i). 185.90/180.07 thf(decl_503, type, esk75_4: $i > $i > $i > $i > $i). 185.90/180.07 thf(decl_504, type, esk76_4: $i > $i > $i > $i > $i). 185.90/180.07 thf(decl_505, type, esk77_4: $i > $i > $i > $i > $i). 185.90/180.07 thf(decl_506, type, esk78_4: $i > $i > $i > $i > $i). 185.90/180.07 thf(decl_507, type, esk79_4: $i > $i > $i > $i > $i). 185.90/180.07 thf(decl_508, type, esk80_3: $i > $i > ($i > $i) > $i). 185.90/180.07 thf(decl_509, type, esk81_3: $i > $i > ($i > $i) > $i). 185.90/180.07 thf(decl_510, type, esk82_3: $i > $i > ($i > $i) > $i). 185.90/180.07 thf(decl_511, type, esk83_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_512, type, esk84_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_513, type, esk85_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_514, type, esk86_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_515, type, esk87_3: $i > $i > ($i > $o) > $i). 185.90/180.07 thf(decl_516, type, esk88_3: $i > $i > ($i > $o) > $i). 185.90/180.07 thf(decl_517, type, esk89_3: $i > $i > ($i > $i > $o) > $i). 185.90/180.07 thf(decl_518, type, esk90_3: $i > $i > ($i > $o) > $i). 185.90/180.07 thf(decl_519, type, esk91_3: $i > $i > ($i > $o) > $i). 185.90/180.07 thf(decl_520, type, esk92_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_521, type, esk93_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_522, type, esk94_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_523, type, esk95_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_524, type, esk96_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_525, type, esk97_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_526, type, esk98_5: $i > $i > $i > $i > $i > $i). 185.90/180.07 thf(decl_527, type, esk99_6: $i > $i > $i > $i > $i > $o > $i). 185.90/180.07 thf(decl_528, type, esk100_2: $i > ($i > $i) > $i). 185.90/180.07 thf(decl_529, type, esk101_3: $i > ($i > $i) > $i > $i). 185.90/180.07 thf(decl_530, type, esk102_2: $i > ($i > $i) > $i). 185.90/180.07 thf(decl_531, type, esk103_3: $i > ($i > $i) > $i > $i). 185.90/180.07 thf(decl_532, type, esk104_3: $i > ($i > $i) > $i > $i). 185.90/180.07 thf(decl_533, type, esk105_3: $i > ($i > $i) > $i > $i). 185.90/180.07 thf(decl_534, type, esk106_3: $i > ($i > $i) > $i > $i). 185.90/180.07 thf(decl_535, type, esk107_3: $i > ($i > $i) > $i > $i). 185.90/180.07 thf(decl_536, type, esk108_3: $i > $i > ($i > $i) > $i). 185.90/180.07 thf(decl_537, type, esk109_4: $i > $i > ($i > $i) > $i > $i). 185.90/180.07 thf(decl_538, type, esk110_1: $i > $i). 185.90/180.07 thf(decl_539, type, esk111_1: $i > $i). 185.90/180.07 thf(decl_540, type, esk112_1: $i > $i). 185.90/180.07 thf(decl_541, type, esk113_2: $i > $i > $i). 185.90/180.07 thf(decl_542, type, esk114_1: $i > $i). 185.90/180.07 thf(decl_543, type, esk115_1: $i > $i). 185.90/180.07 thf(decl_544, type, esk116_1: $i > $i). 185.90/180.07 thf(decl_545, type, esk117_1: $i > $i). 185.90/180.07 thf(decl_546, type, esk118_1: $i > $i). 185.90/180.07 thf(decl_547, type, esk119_1: $i > $i). 185.90/180.07 thf(decl_548, type, esk120_2: $i > $i > $i). 185.90/180.07 thf(decl_549, type, esk121_2: $i > $i > $i). 185.90/180.07 thf(decl_550, type, esk122_2: $i > $i > $i). 185.90/180.07 thf(decl_551, type, esk123_2: $i > $i > $i). 185.90/180.07 thf(decl_552, type, esk124_3: $i > $i > $i > $i). 185.90/180.07 thf(decl_553, type, esk125_1: $i > $i). 185.90/180.07 thf(decl_554, type, esk126_1: $i > $i). 185.90/180.07 thf(decl_555, type, esk127_1: $i > $i). 185.90/180.07 thf(decl_556, type, esk128_2: $i > $i > $i). 185.90/180.07 thf(decl_557, type, esk129_1: $i > $i). 185.90/180.07 thf(decl_558, type, esk130_1: $i > $i). 185.90/180.07 thf(decl_559, type, esk131_1: $i > $i). 185.90/180.07 thf(decl_560, type, esk132_2: $i > $i > $i). 185.90/180.07 thf(decl_561, type, esk133_1: $i > $i). 185.90/180.07 thf(decl_562, type, esk134_1: $i > $i). 185.90/180.07 thf(decl_563, type, esk135_1: $i > $i). 185.90/180.07 thf(decl_564, type, esk136_1: $i > $i). 185.90/180.07 thf(decl_565, type, esk137_2: $i > $i > $i). 185.90/180.07 thf(decl_566, type, esk138_0: $i). 185.90/180.07 thf(decl_567, type, esk139_0: $i). 185.90/180.07 thf(decl_568, type, esk140_0: $i). 185.90/180.07 thf(decl_569, type, esk141_1: $i > $i). 185.90/180.07 thf(decl_600, type, esk172_0: $i). 185.90/180.07 thf(decl_601, type, esk173_0: $i). 185.90/180.07 thf(decl_602, type, esk174_0: $i). 185.90/180.07 thf(decl_603, type, esk175_0: $i). 185.90/180.07 thf(decl_604, type, esk176_0: $i). 185.90/180.07 thf(wellorderedByIn, axiom, ((wellorderedByIn)=(^[X4:$i]:(((stricttotalorderedByIn @ X4)&![X21:$i]:(((in @ X21 @ (powerset @ X4))=>((nonempty @ X21)=>?[X2:$i]:(((in @ X2 @ X21)&![X48:$i]:(((in @ X48 @ X21)=>(((X2)=(X48))|(in @ X2 @ X48))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', wellorderedByIn)). 185.90/180.07 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', nonempty)). 185.90/180.07 thf(stricttotalorderedByIn, axiom, ((stricttotalorderedByIn)=(^[X4:$i]:(((![X2:$i]:(((in @ X2 @ X4)=>![X21:$i]:(((in @ X21 @ X4)=>![X48:$i]:(((in @ X48 @ X4)=>(((in @ X2 @ X21)&(in @ X21 @ X48))=>(in @ X2 @ X48))))))))&![X21:$i]:(((in @ X21 @ X4)=>![X48:$i]:(((in @ X48 @ X4)=>((((X21)=(X48))|(in @ X21 @ X48))|(in @ X48 @ X21)))))))&![X21:$i]:(((in @ X21 @ X4)=>~((in @ X21 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', stricttotalorderedByIn)). 185.90/180.07 thf(ordinal, axiom, ((ordinal)=(^[X2:$i]:(((transitiveset @ X2)&(wellorderedByIn @ X2))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ordinal)). 185.90/180.07 thf(transitiveset, axiom, ((transitiveset)=(^[X4:$i]:(![X21:$i]:(((in @ X21 @ X4)=>(subset @ X21 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', transitiveset)). 185.90/180.07 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', replAx)). 185.90/180.07 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', exu)). 185.90/180.07 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', descrp)). 185.90/180.07 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', exuE1)). 185.90/180.07 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', exuE3e)). 185.90/180.07 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', nonemptyI)). 185.90/180.07 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', exuE2)). 185.90/180.07 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', exuI1)). 185.90/180.07 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', exuI3)). 185.90/180.07 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', exuI2)). 185.90/180.07 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', exuE3u)). 185.90/180.07 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', exu__Cong)). 185.90/180.07 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', exuEu)). 185.90/180.07 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', descr__Cong)). 185.90/180.07 thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', image1Ex1)). 185.90/180.07 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', dsetconstrI)). 185.90/180.07 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', dsetconstrEL)). 185.90/180.07 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', dsetconstrER)). 185.90/180.07 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setbeta)). 185.90/180.07 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', nonemptyE1)). 185.90/180.07 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', nonemptyI1)). 185.90/180.07 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setoftrueEq)). 185.90/180.07 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', nonemptyImpWitness)). 185.90/180.07 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', emptyE1)). 185.90/180.07 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', dsetconstr__Cong)). 185.90/180.07 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', sepInPowerset)). 185.90/180.07 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', sepSubset)). 185.90/180.07 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', singletonprop)). 185.90/180.07 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ex1E1)). 185.90/180.07 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ex1I)). 185.90/180.07 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ex1I2)). 185.90/180.07 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', kfstsingleton)). 185.90/180.07 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ksndsingleton)). 185.90/180.07 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', dpsetconstrI)). 185.90/180.07 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', dpsetconstrSub)). 185.90/180.07 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setOfPairsIsBReln)). 185.90/180.07 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', dpsetconstrERa)). 185.90/180.07 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', dpsetconstrEL1)). 185.90/180.07 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', dpsetconstrEL2)). 185.90/180.07 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', dpsetconstrER)). 185.90/180.07 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', funcImageSingleton)). 185.90/180.07 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', apProp)). 185.90/180.07 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', lamProp)). 185.90/180.07 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', lamp)). 185.90/180.07 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', lam2p)). 185.90/180.07 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ex1E2)). 185.90/180.07 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', beta1)). 185.90/180.07 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', eta1)). 185.90/180.07 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', lam2lamEq)). 185.90/180.07 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', beta2)). 185.90/180.07 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', eta2)). 185.90/180.07 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', iffalseProp1)). 185.90/180.07 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', iffalseProp2)). 185.90/180.07 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', iftrueProp1)). 185.90/180.07 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', iftrueProp2)). 185.90/180.07 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ifSingleton)). 185.90/180.07 thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$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:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ X3 @ X14) @ X33))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', choice2fnsingleton)). 185.90/180.07 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setOfPairsIsBReln1)). 185.90/180.07 thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', image1Equiv)). 185.90/180.07 thf(image1E, axiom, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', image1E)). 185.90/180.07 thf(image1I, axiom, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X61 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', image1I)). 185.90/180.07 thf(foundation2, axiom, ((foundation2)<=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', foundation2)). 185.90/180.07 thf(transitivesetOp1, axiom, ((transitivesetOp1)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', transitivesetOp1)). 185.90/180.07 thf(binintTransitive, axiom, ((binintTransitive)<=>![X21:$i]:(((transitiveset @ X21)=>![X48:$i]:(((transitiveset @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintTransitive)). 185.90/180.07 thf(transitivesetOp2, axiom, ((transitivesetOp2)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i, X2:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', transitivesetOp2)). 185.90/180.07 thf(setunionTransitive, axiom, ((setunionTransitive)<=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(transitiveset @ X2)))=>(transitiveset @ (setunion @ X21))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setunionTransitive)). 185.90/180.07 thf(ordinalMinLem1, axiom, ((ordinalMinLem1)<=>![X21:$i]:(((ordinal @ X21)=>![X48:$i]:(((ordinal @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ordinalMinLem1)). 185.90/180.07 thf(ordinalTransSet, axiom, ((ordinalTransSet)<=>![X21:$i]:(((ordinal @ X21)=>![X2:$i, X4:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ordinalTransSet)). 185.90/180.07 thf(ordinalTransSet1, axiom, ((ordinalTransSet1)<=>![X21:$i]:(((ordinal @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ordinalTransSet1)). 185.90/180.07 thf(setunionOrdinalLem1, axiom, ((setunionOrdinalLem1)<=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(ordinal @ X2)))=>(transitiveset @ (setunion @ X21))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setunionOrdinalLem1)). 185.90/180.07 thf(emptysetOrdinal, conjecture, ((setextAx)=>((emptysetAx)=>((((((omegaSAx)=>((((foundationAx)=>((((dsetconstrI)=>((dsetconstrEL)=>(((((((((setext)=>(((noeltsimpempty)=>((((nonemptyI)=>((nonemptyI1)=>(((emptyinunitempty)=>((setadjoinIR)=>((((setoftrueEq)=>(((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>(((subPowSU)=>(((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((((vacuousDall)=>(((quantDeMorgan2)=>((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>(((exuI3)=>((exuI2)=>(((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>(((powerset__Cong)=>(((omega__Cong)=>(((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>(((((((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>(((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((((sepInPowerset)=>((((((binunionEcases)=>((((binunionRsub)=>((((binintersectEL)=>(((binintersectSubset2)=>((((disjointsetsI1)=>((binintersectRsub)=>(((binintersectSubset1)=>((((setminusEL)=>((setminusER)=>((setminusSubset2)=>((((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>(((symdiffI1)=>((((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((((singletoninpowunion)=>(((upairsubunion)=>(((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((cartprodpairin)=>((((setunionE2)=>((setunionsingleton1)=>((((singletonprop)=>((ex1E1)=>((ex1I)=>((((setukpairinjL1)=>(((((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>(((setukpairinjR12)=>((((((((((((cartprodmempaircEq)=>(((((dpsetconstrI)=>((((dpsetconstrERa)=>(((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>(((((((lamp)=>((((brelnall2)=>((ex1E2)=>(((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((((eqbreln)=>((funcext)=>(((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>(((beta2)=>((eta2)=>(((iffalseProp2)=>((((((((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>(((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>(((subsetTI)=>((powersetTI1)=>((((complementTE1)=>((binintersectTELcontra)=>((((contrasubsetT1)=>(((((doubleComplementE1)=>((doubleComplementSub1)=>(((doubleComplementEq)=>(((((complementInPowersetComplementIntersect)=>(((((binunionTIRcontra)=>((inIntersectImpInUnion)=>((((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>(((binunionTE)=>(((demorgan2a1)=>(((demorgan2a2)=>((((demorgan1)=>((((((woz13rule0)=>((((woz13rule3)=>((((woz1_2)=>((woz1_3)=>(((((((((subbreln1)=>((eqbreln1)=>((((breln1invE)=>(((breln1compI)=>((breln1compE)=>(((breln1unionprop)=>((breln1unionIL)=>(((breln1unionI)=>(((((woz2Ex)=>((woz2W)=>((woz2A)=>((woz2B)=>(((image1Ex1)=>(((image1E)=>(((injFuncInInjFuncSet)=>((injFuncSetFuncIn)=>((injFuncSetFuncInj)=>((((leftInvIsSurj)=>((surjCantorThm)=>((foundation2)=>((notinself)=>(((omegaSp)=>(((peano0notS)=>(((transitivesetOp1)=>((((setunionTransitive)=>(((((ordinal @ emptyset)<=(setunionOrdinalLem1))<=(ordinalTransSet1))<=(ordinalTransSet))<=(ordinalMinLem1)))<=(transitivesetOp2))<=(binintTransitive)))<=(peanoSinj)))<=(omegaSclos)))<=(notinself2))))))<=(surjFuncSetFuncSurj))<=(surjFuncSetFuncIn)))))<=(image1I)))<=(image1Equiv)))<=(image1Ex))))))<=(breln1unionCommutes))<=(breln1unionEcases))<=(breln1unionE)))<=(breln1unionIR))))<=(breln1compEex))))<=(breln1compprop)))<=(breln1invI))<=(breln1invprop))))<=(breln1all1))<=(setOfPairsIsBReln1))<=(choice2fnsingleton))<=(breln1SetBreln1))<=(breln1all2))<=(woz1_5))<=(woz1_4))))<=(woz1_1))<=(woz13rule4)))<=(woz13rule2))<=(woz13rule1)))<=(demorgan2))<=(demorgan2b))<=(demorgan2b2))<=(demorgan2a)))<=(demorgan1b))<=(demorgan1a)))<=(complementUnionInPowersetComplement)))<=(binunionTEcontra)))<=(inComplementUnionImpInComplement1))))<=(inIntersectImpInIntersectUnions))<=(inIntersectImpInUnion2))))<=(binunionTILcontra))<=(complementTcontraSubset))<=(contraSubsetComplement)))<=(complementSubsetComplementIntersect))<=(complementImpComplementIntersect))<=(complementTnotintersectT)))<=(doubleComplementSub2))))<=(doubleComplementI1))<=(contrasubsetT3))<=(contrasubsetT2)))<=(contrasubsetT))<=(binintersectTERcontra))))<=(complementTI1))<=(powersetTE1))))<=(setextT)))))<=(binunionT_lem)))))<=(iftrue))<=(theeq))<=(ifp))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1)))<=(iffalseProp1))))<=(lam2lamEq))))))<=(funcext2))))<=(subbreln))<=(funcGraphProp4)))))<=(funcGraphProp1))))<=(brelnall1))<=(lam2p)))<=(lamProp))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc))<=(app))))))<=(dpsetconstrEL1)))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1)))<=(setukpairinjR11)))))<=(kfstpairEq))<=(theprop))<=(kfstsingleton)))<=(singletonsuniq))<=(ex1I2)))))<=(setunionsingleton))<=(setunionsingleton2))))<=(cartprodmempair))<=(cartprodmempair1))))<=(ubforcartprodlem2)))<=(upairinpowunion)))<=(upairset2E)))<=(singletoninpowerset))<=(singletonsubset))))))))<=(symdiffIneg1))<=(symdiffI2)))<=(symdiffE)))<=(setminusLsub))))<=(setminusELneg))<=(setminusERneg)))))<=(setminusI))<=(bs114d)))<=(binintersectSubset4))))<=(binintersectER))<=(binintersectSubset3)))<=(binintersectLsub)))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub))<=(binunionE)))<=(binunionIR))<=(upairset2IR))<=(binunionIL))<=(sepSubset)))<=(powersetsubset))<=(inPowerset)))))))))<=(subsetTrans))))))<=(subsetE2))<=(subsetE))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1))))))<=(exuEu)))<=(setunion__Cong)))<=(setadjoin__Cong))))<=(exuE3u)))<=(inCongP))))<=(exuI1))))))<=(quantDeMorgan4))))<=(quantDeMorgan1)))<=(emptyE1))<=(upairsetIR)))))))))<=(exuE2)))<=(setunionE)))<=(powersetE))))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE))))<=(setadjoinIL))))<=(nonemptyE1))<=(setbeta)))<=(emptyI)))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE))<=(exuE1))<=(dsetconstrER))))<=(descrp))<=(wellorderingAx)))<=(replAx))<=(omegaIndAx)))<=(omega0Ax))<=(setunionAx))<=(powersetAx))<=(setadjoinAx)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', emptysetOrdinal)). 185.90/180.07 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setextAx)). 185.90/180.07 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', emptysetAx)). 185.90/180.07 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setadjoinAx)). 185.90/180.07 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', powersetAx)). 185.90/180.07 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setunionAx)). 185.90/180.07 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', omega0Ax)). 185.90/180.07 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', omegaSAx)). 185.90/180.07 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', omegaIndAx)). 185.90/180.07 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', foundationAx)). 185.90/180.07 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', wellorderingAx)). 185.90/180.07 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', prop2setE)). 185.90/180.07 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', emptysetE)). 185.90/180.07 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', emptysetimpfalse)). 185.90/180.07 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', notinemptyset)). 185.90/180.07 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setext)). 185.90/180.07 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', emptyI)). 185.90/180.07 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', noeltsimpempty)). 185.90/180.07 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setadjoinIL)). 185.90/180.07 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', emptyinunitempty)). 185.90/180.07 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setadjoinIR)). 185.90/180.07 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setadjoinE)). 185.90/180.07 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setadjoinOr)). 185.90/180.07 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', powersetI)). 185.90/180.07 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', emptyinPowerset)). 185.90/180.07 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', emptyInPowerset)). 185.90/180.07 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', powersetE)). 185.90/180.07 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setunionI)). 185.90/180.07 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setunionE)). 185.90/180.07 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subPowSU)). 185.90/180.07 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', uniqinunit)). 185.90/180.07 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', notinsingleton)). 185.90/180.07 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', eqinunit)). 185.90/180.07 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', singletonsswitch)). 185.90/180.07 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', upairsetE)). 185.90/180.07 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', upairsetIL)). 185.90/180.07 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', upairsetIR)). 185.90/180.07 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', vacuousDall)). 185.90/180.07 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', quantDeMorgan1)). 185.90/180.07 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', quantDeMorgan2)). 185.90/180.07 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', quantDeMorgan3)). 185.90/180.07 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', quantDeMorgan4)). 185.90/180.07 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', prop2setI)). 185.90/180.07 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', prop2set2propI)). 185.90/180.07 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', notdexE)). 185.90/180.07 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', notdallE)). 185.90/180.07 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', inCongP)). 185.90/180.07 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', in__Cong)). 185.90/180.07 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', emptyset__Cong)). 185.90/180.07 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setadjoin__Cong)). 185.90/180.07 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', powerset__Cong)). 185.90/180.07 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setunion__Cong)). 185.90/180.07 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', omega__Cong)). 185.90/180.07 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subsetI1)). 185.90/180.07 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', eqimpsubset2)). 185.90/180.07 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', eqimpsubset1)). 185.90/180.07 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subsetI2)). 185.90/180.07 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', emptysetsubset)). 185.90/180.07 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subsetE)). 185.90/180.07 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subsetE2)). 185.90/180.07 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', notsubsetI)). 185.90/180.07 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', notequalI1)). 185.90/180.07 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', notequalI2)). 185.90/180.07 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subsetRefl)). 185.90/180.07 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subsetTrans)). 185.90/180.07 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setadjoinSub)). 185.90/180.07 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setadjoinSub2)). 185.90/180.07 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subset2powerset)). 185.90/180.07 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setextsub)). 185.90/180.07 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subsetemptysetimpeq)). 185.90/180.07 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', powersetI1)). 185.90/180.07 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', powersetE1)). 185.90/180.07 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', inPowerset)). 185.90/180.07 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', powersetsubset)). 185.90/180.07 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binunionIL)). 185.90/180.07 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', upairset2IR)). 185.90/180.07 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binunionIR)). 185.90/180.07 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binunionEcases)). 185.90/180.07 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binunionE)). 185.90/180.07 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binunionLsub)). 185.90/180.07 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binunionRsub)). 185.90/180.07 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectI)). 185.90/180.07 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectSubset5)). 185.90/180.07 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectEL)). 185.90/180.07 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectLsub)). 185.90/180.07 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectSubset2)). 185.90/180.07 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectSubset3)). 185.90/180.07 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectER)). 185.90/180.07 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', disjointsetsI1)). 185.90/180.07 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectRsub)). 185.90/180.07 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectSubset4)). 185.90/180.07 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectSubset1)). 185.90/180.07 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', bs114d)). 185.90/180.07 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setminusI)). 185.90/180.07 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setminusEL)). 185.90/180.07 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setminusER)). 185.90/180.07 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setminusSubset2)). 185.90/180.07 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setminusERneg)). 185.90/180.07 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setminusELneg)). 185.90/180.07 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setminusILneg)). 185.90/180.07 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setminusIRneg)). 185.90/180.07 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setminusLsub)). 185.90/180.07 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setminusSubset1)). 185.90/180.07 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', symdiffE)). 185.90/180.07 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', symdiffI1)). 185.90/180.07 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', symdiffI2)). 185.90/180.07 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', symdiffIneg1)). 185.90/180.07 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', symdiffIneg2)). 185.90/180.07 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', secondinupair)). 185.90/180.07 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setukpairIL)). 185.90/180.07 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setukpairIR)). 185.90/180.07 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', kpairiskpair)). 185.90/180.07 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', kpairp)). 185.90/180.07 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', singletonsubset)). 185.90/180.07 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', singletoninpowerset)). 185.90/180.07 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', singletoninpowunion)). 185.90/180.07 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', upairset2E)). 185.90/180.07 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', upairsubunion)). 185.90/180.07 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', upairinpowunion)). 185.90/180.07 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ubforcartprodlem1)). 185.90/180.07 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ubforcartprodlem2)). 185.90/180.07 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ubforcartprodlem3)). 185.90/180.07 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', cartprodpairin)). 185.90/180.07 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', cartprodmempair1)). 185.90/180.07 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', cartprodmempair)). 185.90/180.07 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setunionE2)). 185.90/180.07 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setunionsingleton1)). 185.90/180.07 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setunionsingleton2)). 185.90/180.07 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setunionsingleton)). 185.90/180.07 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', singletonsuniq)). 185.90/180.07 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setukpairinjL1)). 185.90/180.07 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', theprop)). 185.90/180.07 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', kfstpairEq)). 185.90/180.07 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', cartprodfstin)). 185.90/180.07 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setukpairinjL2)). 185.90/180.07 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setukpairinjL)). 185.90/180.07 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setukpairinjR11)). 185.90/180.07 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setukpairinjR12)). 185.90/180.07 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setukpairinjR1)). 185.90/180.07 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', upairequniteq)). 185.90/180.07 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setukpairinjR2)). 185.90/180.07 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setukpairinjR)). 185.90/180.07 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ksndpairEq)). 185.90/180.07 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', kpairsurjEq)). 185.90/180.07 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', cartprodsndin)). 185.90/180.07 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', cartprodpairmemEL)). 185.90/180.07 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', cartprodpairmemER)). 185.90/180.07 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', cartprodmempaircEq)). 185.90/180.07 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', cartprodfstpairEq)). 185.90/180.07 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', cartprodsndpairEq)). 185.90/180.07 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', cartprodpairsurjEq)). 185.90/180.07 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', app)). 185.90/180.07 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', infuncsetfunc)). 185.90/180.07 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ap2p)). 185.90/180.07 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', funcinfuncset)). 185.90/180.07 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', brelnall1)). 185.90/180.07 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', brelnall2)). 185.90/180.07 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', funcGraphProp1)). 185.90/180.07 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', funcGraphProp3)). 185.90/180.07 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', funcGraphProp2)). 185.90/180.07 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', funcextLem)). 185.90/180.07 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', funcGraphProp4)). 185.90/180.07 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subbreln)). 185.90/180.07 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', eqbreln)). 185.90/180.07 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', funcext)). 185.90/180.07 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', funcext2)). 185.90/180.07 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ap2apEq1)). 185.90/180.07 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ap2apEq2)). 185.90/180.07 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', ifp)). 185.90/180.07 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', theeq)). 185.90/180.07 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', iftrue)). 185.90/180.07 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', iffalse)). 185.90/180.07 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', iftrueorfalse)). 185.90/180.07 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectT_lem)). 185.90/180.07 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binunionT_lem)). 185.90/180.07 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', powersetT_lem)). 185.90/180.07 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setminusT_lem)). 185.90/180.07 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', complementT_lem)). 185.90/180.07 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', setextT)). 185.90/180.07 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subsetTI)). 185.90/180.07 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', powersetTI1)). 185.90/180.07 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', powersetTE1)). 185.90/180.07 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', complementTI1)). 185.90/180.07 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', complementTE1)). 185.90/180.07 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectTELcontra)). 185.90/180.07 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binintersectTERcontra)). 185.90/180.07 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', contrasubsetT)). 185.90/180.07 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', contrasubsetT1)). 185.90/180.07 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', contrasubsetT2)). 185.90/180.07 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', contrasubsetT3)). 185.90/180.07 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', doubleComplementI1)). 185.90/180.07 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', doubleComplementE1)). 185.90/180.07 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', doubleComplementSub1)). 185.90/180.07 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', doubleComplementSub2)). 185.90/180.07 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', doubleComplementEq)). 185.90/180.07 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', complementTnotintersectT)). 185.90/180.07 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', complementImpComplementIntersect)). 185.90/180.07 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', complementSubsetComplementIntersect)). 185.90/180.07 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', complementInPowersetComplementIntersect)). 185.90/180.07 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', contraSubsetComplement)). 185.90/180.07 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', complementTcontraSubset)). 185.90/180.07 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binunionTILcontra)). 185.90/180.07 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binunionTIRcontra)). 185.90/180.07 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', inIntersectImpInUnion)). 185.90/180.07 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', inIntersectImpInUnion2)). 185.90/180.07 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', inIntersectImpInIntersectUnions)). 185.90/180.07 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', intersectInPowersetIntersectUnions)). 185.90/180.07 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', inComplementUnionImpNotIn1)). 185.90/180.07 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', inComplementUnionImpInComplement1)). 185.90/180.07 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binunionTE)). 185.90/180.07 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', binunionTEcontra)). 185.90/180.07 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', demorgan2a1)). 185.90/180.07 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', complementUnionInPowersetComplement)). 185.90/180.07 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', demorgan2a2)). 185.90/180.07 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', demorgan1a)). 185.90/180.07 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', demorgan1b)). 185.90/180.07 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', demorgan1)). 185.90/180.07 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', demorgan2a)). 185.90/180.07 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', demorgan2b2)). 185.90/180.07 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', demorgan2b)). 185.90/180.07 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', demorgan2)). 185.90/180.07 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz13rule0)). 185.90/180.07 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz13rule1)). 185.90/180.07 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz13rule2)). 185.90/180.07 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz13rule3)). 185.90/180.07 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz13rule4)). 185.90/180.07 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz1_1)). 185.90/180.07 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz1_2)). 185.90/180.07 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz1_3)). 185.90/180.07 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz1_4)). 185.90/180.07 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz1_5)). 185.90/180.07 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1all2)). 185.90/180.07 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1SetBreln1)). 185.90/180.07 thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1all1)). 185.90/180.07 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', subbreln1)). 185.90/180.07 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', eqbreln1)). 185.90/180.07 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1invprop)). 185.90/180.07 thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1invI)). 185.90/180.07 thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1invE)). 185.90/180.07 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1compprop)). 185.90/180.07 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1compI)). 185.90/180.07 thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1compE)). 185.90/180.07 thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1compEex)). 185.90/180.07 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1unionprop)). 185.90/180.07 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1unionIL)). 185.90/180.07 thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1unionIR)). 185.90/180.07 thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1unionI)). 185.90/180.07 thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1unionE)). 185.90/180.07 thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1unionEcases)). 185.90/180.07 thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', breln1unionCommutes)). 185.90/180.07 thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz2Ex)). 185.90/180.07 thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz2W)). 185.90/180.07 thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz2A)). 185.90/180.07 thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', woz2B)). 185.90/180.07 thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', image1Ex)). 185.90/180.07 thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', injFuncInInjFuncSet)). 185.90/180.07 thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', injFuncSetFuncIn)). 185.90/180.07 thf(injFuncSetFuncInj, axiom, ((injFuncSetFuncInj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', injFuncSetFuncInj)). 185.90/180.07 thf(surjFuncSetFuncIn, axiom, ((surjFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', surjFuncSetFuncIn)). 185.90/180.07 thf(surjFuncSetFuncSurj, axiom, ((surjFuncSetFuncSurj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X2 @ X3))=>(surjective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', surjFuncSetFuncSurj)). 185.90/180.07 thf(leftInvIsSurj, axiom, ((leftInvIsSurj)<=>![X4:$i, X5:$i, X62:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X62 @ X2) @ X5)))=>![X34:$i]:(((in @ X34 @ (funcSet @ X5 @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X5 @ X4 @ X34 @ (X62 @ X2))=(X2))))=>(surjective @ X5 @ X4 @ X34))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', leftInvIsSurj)). 185.90/180.07 thf(surjCantorThm, axiom, ((surjCantorThm)<=>![X4:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ (powerset @ X4)))=>~((surjective @ X4 @ (powerset @ X4) @ X29))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', surjCantorThm)). 185.90/180.07 thf(notinself, axiom, ((notinself)<=>![X4:$i]:(~((in @ X4 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', notinself)). 185.90/180.07 thf(notinself2, axiom, ((notinself2)<=>![X4:$i, X5:$i]:(((in @ X4 @ X5)=>~((in @ X5 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', notinself2)). 185.90/180.07 thf(omegaSp, axiom, ((omegaSp)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (omegaS @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', omegaSp)). 185.90/180.07 thf(omegaSclos, axiom, ((omegaSclos)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', omegaSclos)). 185.90/180.07 thf(peano0notS, axiom, ((peano0notS)<=>![X2:$i]:(((in @ X2 @ omega)=>((omegaS @ X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', peano0notS)). 185.90/180.07 thf(peanoSinj, axiom, ((peanoSinj)<=>![X2:$i]:(((in @ X2 @ omega)=>![X3:$i]:(((in @ X3 @ omega)=>(((omegaS @ X2)=(omegaS @ X3))=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.j54mgVPzXG/E---3.1_8741.p', peanoSinj)). 185.90/180.07 thf(c_0_343, plain, ((wellorderedByIn)=(^[Z0/* 8 */:$i]:(((((![X1189:$i]:(((in @ X1189 @ Z0)=>![X1190:$i]:(((in @ X1190 @ Z0)=>![X1191:$i]:(((in @ X1191 @ Z0)=>(((in @ X1189 @ X1190)&(in @ X1190 @ X1191))=>(in @ X1189 @ X1191))))))))&![X1192:$i]:(((in @ X1192 @ Z0)=>![X1193:$i]:(((in @ X1193 @ Z0)=>((((X1192)=(X1193))|(in @ X1192 @ X1193))|(in @ X1193 @ X1192)))))))&![X1194:$i]:(((in @ X1194 @ Z0)=>~((in @ X1194 @ X1194))))))&![X21:$i]:(((in @ X21 @ (powerset @ Z0))=>((((X21)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X21)&![X48:$i]:(((in @ X48 @ X21)=>(((X2)=(X48))|(in @ X2 @ X48))))))))))))), inference(fof_simplification,[status(thm)],[wellorderedByIn])). 185.90/180.07 thf(c_0_344, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 185.90/180.07 thf(c_0_345, plain, ((stricttotalorderedByIn)=(^[Z0/* 8 */:$i]:(((![X2:$i]:(((in @ X2 @ Z0)=>![X21:$i]:(((in @ X21 @ Z0)=>![X48:$i]:(((in @ X48 @ Z0)=>(((in @ X2 @ X21)&(in @ X21 @ X48))=>(in @ X2 @ X48))))))))&![X21:$i]:(((in @ X21 @ Z0)=>![X48:$i]:(((in @ X48 @ Z0)=>((((X21)=(X48))|(in @ X21 @ X48))|(in @ X48 @ X21)))))))&![X21:$i]:(((in @ X21 @ Z0)=>~((in @ X21 @ X21)))))))), inference(fof_simplification,[status(thm)],[stricttotalorderedByIn])). 185.90/180.07 thf(c_0_346, plain, ((ordinal)=(^[Z0/* 8 */:$i]:(((![X1195:$i]:(((in @ X1195 @ Z0)=>(subset @ X1195 @ Z0))))&(((((![X1196:$i]:(((in @ X1196 @ Z0)=>![X1197:$i]:(((in @ X1197 @ Z0)=>![X1198:$i]:(((in @ X1198 @ Z0)=>(((in @ X1196 @ X1197)&(in @ X1197 @ X1198))=>(in @ X1196 @ X1198))))))))&![X1199:$i]:(((in @ X1199 @ Z0)=>![X1200:$i]:(((in @ X1200 @ Z0)=>((((X1199)=(X1200))|(in @ X1199 @ X1200))|(in @ X1200 @ X1199)))))))&![X1201:$i]:(((in @ X1201 @ Z0)=>~((in @ X1201 @ X1201))))))&![X1202:$i]:(((in @ X1202 @ (powerset @ Z0))=>((((X1202)!=(emptyset)))=>?[X1203:$i]:(((in @ X1203 @ X1202)&![X1204:$i]:(((in @ X1204 @ X1202)=>(((X1203)=(X1204))|(in @ X1203 @ X1204))))))))))))))), inference(fof_simplification,[status(thm)],[ordinal])). 185.90/180.07 thf(c_0_347, plain, ((transitiveset)=(^[Z0/* 6 */:$i]:(![X21:$i]:(((in @ X21 @ Z0)=>(subset @ X21 @ Z0)))))), inference(fof_simplification,[status(thm)],[transitiveset])). 185.90/180.07 thf(c_0_348, plain, ((wellorderedByIn)=(^[Z0/* 8 */:$i]:(((((![X1189:$i]:(((in @ X1189 @ Z0)=>![X1190:$i]:(((in @ X1190 @ Z0)=>![X1191:$i]:(((in @ X1191 @ Z0)=>(((in @ X1189 @ X1190)&(in @ X1190 @ X1191))=>(in @ X1189 @ X1191))))))))&![X1192:$i]:(((in @ X1192 @ Z0)=>![X1193:$i]:(((in @ X1193 @ Z0)=>((((X1192)=(X1193))|(in @ X1192 @ X1193))|(in @ X1193 @ X1192)))))))&![X1194:$i]:(((in @ X1194 @ Z0)=>~((in @ X1194 @ X1194))))))&![X21:$i]:(((in @ X21 @ (powerset @ Z0))=>((((X21)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X21)&![X48:$i]:(((in @ X48 @ X21)=>(((X2)=(X48))|(in @ X2 @ X48))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_343, c_0_344]), c_0_345])). 185.90/180.07 thf(c_0_349, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 185.90/180.07 thf(c_0_350, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 185.90/180.07 thf(c_0_351, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 185.90/180.07 thf(c_0_352, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 185.90/180.07 thf(c_0_353, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 185.90/180.07 thf(c_0_354, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 185.90/180.07 thf(c_0_355, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 185.90/180.07 thf(c_0_356, 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])). 185.90/180.07 thf(c_0_357, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 185.90/180.07 thf(c_0_358, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 185.90/180.07 thf(c_0_359, 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])). 185.90/180.07 thf(c_0_360, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 185.90/180.07 thf(c_0_361, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 185.90/180.07 thf(c_0_362, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 185.90/180.07 thf(c_0_363, plain, ((image1Ex1)<=>![X4:$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])). 185.90/180.07 thf(c_0_364, plain, ((ordinal)=(^[Z0/* 8 */:$i]:(((![X1195:$i]:(((in @ X1195 @ Z0)=>(subset @ X1195 @ Z0))))&(((((![X1196:$i]:(((in @ X1196 @ Z0)=>![X1197:$i]:(((in @ X1197 @ Z0)=>![X1198:$i]:(((in @ X1198 @ Z0)=>(((in @ X1196 @ X1197)&(in @ X1197 @ X1198))=>(in @ X1196 @ X1198))))))))&![X1199:$i]:(((in @ X1199 @ Z0)=>![X1200:$i]:(((in @ X1200 @ Z0)=>((((X1199)=(X1200))|(in @ X1199 @ X1200))|(in @ X1200 @ X1199)))))))&![X1201:$i]:(((in @ X1201 @ Z0)=>~((in @ X1201 @ X1201))))))&![X1202:$i]:(((in @ X1202 @ (powerset @ Z0))=>((((X1202)!=(emptyset)))=>?[X1203:$i]:(((in @ X1203 @ X1202)&![X1204:$i]:(((in @ X1204 @ X1202)=>(((X1203)=(X1204))|(in @ X1203 @ X1204))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_346, c_0_347]), c_0_348])). 185.90/180.07 thf(c_0_365, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1152:$i]:((((X6 @ X2 @ X1152))&![X1153:$i]:((((X6 @ X2 @ X1153))=>((X1152)=(X1153)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_349, c_0_350])). 185.90/180.07 thf(c_0_366, plain, ((descrp)=(![X1:$i > $o]:(((?[X1154:$i]:((((X1 @ X1154))&![X1155:$i]:((((X1 @ X1155))=>((X1154)=(X1155)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_351, c_0_350])). 185.90/180.07 thf(c_0_367, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 185.90/180.07 thf(c_0_368, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 185.90/180.07 thf(c_0_369, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 185.90/180.07 thf(c_0_370, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1156:$i]:((((X1 @ X1156))&![X1157:$i]:((((X1 @ X1157))=>((X1156)=(X1157)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_352, c_0_350])). 185.90/180.07 thf(c_0_371, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1158:$i]:((((X1 @ X1158))&![X1159:$i]:((((X1 @ X1159))=>((X1158)=(X1159)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_353, c_0_350])). 185.90/180.07 thf(c_0_372, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 185.90/180.07 thf(c_0_373, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_344])). 185.90/180.07 thf(c_0_374, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_354, c_0_344])). 185.90/180.07 thf(c_0_375, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_344])). 185.90/180.07 thf(c_0_376, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 185.90/180.07 thf(c_0_377, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1160:$i]:((((X1 @ X1160))&![X1161:$i]:((((X1 @ X1161))=>((X1160)=(X1161)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_355, c_0_350])). 185.90/180.07 thf(c_0_378, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_344])). 185.90/180.07 thf(c_0_379, 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])). 185.90/180.07 thf(c_0_380, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1162:$i]:((((X1 @ X1162))&![X1163:$i]:((((X1 @ X1163))=>((X1162)=(X1163))))))))))), inference(apply_def,[status(thm)],[c_0_356, c_0_350])). 185.90/180.07 thf(c_0_381, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1164:$i]:((((X1 @ X1164))&![X1165:$i]:((((X1 @ X1165))=>((X1164)=(X1165)))))))))))), inference(apply_def,[status(thm)],[c_0_357, c_0_350])). 185.90/180.07 thf(c_0_382, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1166:$i]:((((X1 @ X1166))&![X1167:$i]:((((X1 @ X1167))=>((X1166)=(X1167))))))))))), inference(apply_def,[status(thm)],[c_0_358, c_0_350])). 185.90/180.07 thf(c_0_383, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1168:$i]:((((X1 @ X1168))&![X1169:$i]:((((X1 @ X1169))=>((X1168)=(X1169)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_359, c_0_350])). 185.90/180.07 thf(c_0_384, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1170:$i]:((((X1 @ X1170))&![X1171:$i]:((((X1 @ X1171))=>((X1170)=(X1171)))))))<=>(?[X1172:$i]:((((X17 @ X1172))&![X1173:$i]:((((X17 @ X1173))=>((X1172)=(X1173)))))))))))), inference(apply_def,[status(thm)],[c_0_360, c_0_350])). 185.90/180.07 thf(c_0_385, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1174:$i]:((((X1 @ X1174))&![X1175:$i]:((((X1 @ X1175))=>((X1174)=(X1175)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_361, c_0_350])). 185.90/180.07 thf(c_0_386, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1176:$i]:((((X1 @ X1176))&![X1177:$i]:((((X1 @ X1177))=>((X1176)=(X1177)))))))=>((?[X1178:$i]:((((X17 @ X1178))&![X1179:$i]:((((X17 @ X1179))=>((X1178)=(X1179)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_362, c_0_350])). 185.90/180.07 thf(c_0_387, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 185.90/180.07 thf(c_0_388, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 185.90/180.07 thf(c_0_389, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 185.90/180.07 thf(c_0_390, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 185.90/180.07 thf(c_0_391, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 185.90/180.07 thf(c_0_392, plain, ((ex1I)<=>![X4:$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])). 185.90/180.07 thf(c_0_393, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 185.90/180.07 thf(c_0_394, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 185.90/180.07 thf(c_0_395, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 185.90/180.07 thf(c_0_396, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 185.90/180.07 thf(c_0_397, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 185.90/180.07 thf(c_0_398, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 185.90/180.07 thf(c_0_399, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 185.90/180.07 thf(c_0_400, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 185.90/180.07 thf(c_0_401, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 185.90/180.07 thf(c_0_402, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 185.90/180.07 thf(c_0_403, plain, ((funcImageSingleton)<=>![X4:$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])). 185.90/180.07 thf(c_0_404, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 185.90/180.07 thf(c_0_405, plain, ((lamProp)<=>![X4:$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])). 185.90/180.07 thf(c_0_406, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 185.90/180.07 thf(c_0_407, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 185.90/180.07 thf(c_0_408, plain, ((ex1E2)<=>![X4:$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])). 185.90/180.07 thf(c_0_409, 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])). 185.90/180.07 thf(c_0_410, 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])). 185.90/180.07 thf(c_0_411, 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])). 185.90/180.07 thf(c_0_412, 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])). 185.90/180.07 thf(c_0_413, 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])). 185.90/180.07 thf(c_0_414, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 185.90/180.07 thf(c_0_415, plain, ((iffalseProp2)<=>![X4:$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])). 185.90/180.07 thf(c_0_416, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 185.90/180.07 thf(c_0_417, plain, ((iftrueProp2)<=>![X4:$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])). 185.90/180.07 thf(c_0_418, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 185.90/180.07 thf(c_0_419, plain, ((choice2fnsingleton)<=>![X4:$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:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ Z0 @ X14) @ X33))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])). 185.90/180.07 thf(c_0_420, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])). 185.90/180.07 thf(c_0_421, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1180:$i]:(((![X2:$i]:(((in @ X2 @ X1180)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))&![X1181:$i]:(((![X2:$i]:(((in @ X2 @ X1181)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))=>((X1180)=(X1181)))))))))), inference(apply_def,[status(thm)],[c_0_363, c_0_350])). 185.90/180.07 thf(c_0_422, plain, ((image1Equiv)<=>![X4:$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])). 185.90/180.07 thf(c_0_423, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])). 185.90/180.07 thf(c_0_424, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])). 185.90/180.07 thf(c_0_425, axiom, ((foundation2)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset)))))))), inference(apply_def,[status(thm)],[foundation2, c_0_344])). 185.90/180.07 thf(c_0_426, axiom, ((transitivesetOp1)=(![X21:$i]:(((![X1182:$i]:(((in @ X1182 @ X21)=>(subset @ X1182 @ X21))))=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21))))))), inference(apply_def,[status(thm)],[transitivesetOp1, c_0_347])). 185.90/180.07 thf(c_0_427, axiom, ((binintTransitive)=(![X21:$i]:(((![X1183:$i]:(((in @ X1183 @ X21)=>(subset @ X1183 @ X21))))=>![X48:$i]:(((![X1184:$i]:(((in @ X1184 @ X48)=>(subset @ X1184 @ X48))))=>(![X1185:$i]:(((in @ X1185 @ (binintersect @ X21 @ X48))=>(subset @ X1185 @ (binintersect @ X21 @ X48))))))))))), inference(apply_def,[status(thm)],[binintTransitive, c_0_347])). 185.90/180.07 thf(c_0_428, axiom, ((transitivesetOp2)=(![X21:$i]:(((![X1186:$i]:(((in @ X1186 @ X21)=>(subset @ X1186 @ X21))))=>![X4:$i, X2:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21)))))))), inference(apply_def,[status(thm)],[transitivesetOp2, c_0_347])). 185.90/180.07 thf(c_0_429, axiom, ((setunionTransitive)=(![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(![X1187:$i]:(((in @ X1187 @ X2)=>(subset @ X1187 @ X2))))))=>(![X1188:$i]:(((in @ X1188 @ (setunion @ X21))=>(subset @ X1188 @ (setunion @ X21))))))))), inference(apply_def,[status(thm)],[setunionTransitive, c_0_347])). 185.90/180.07 thf(c_0_430, axiom, ((ordinalMinLem1)=(![X21:$i]:(((((![X1205:$i]:(((in @ X1205 @ X21)=>(subset @ X1205 @ X21))))&(((((![X1206:$i]:(((in @ X1206 @ X21)=>![X1207:$i]:(((in @ X1207 @ X21)=>![X1208:$i]:(((in @ X1208 @ X21)=>(((in @ X1206 @ X1207)&(in @ X1207 @ X1208))=>(in @ X1206 @ X1208))))))))&![X1209:$i]:(((in @ X1209 @ X21)=>![X1210:$i]:(((in @ X1210 @ X21)=>((((X1209)=(X1210))|(in @ X1209 @ X1210))|(in @ X1210 @ X1209)))))))&![X1211:$i]:(((in @ X1211 @ X21)=>~((in @ X1211 @ X1211))))))&![X1212:$i]:(((in @ X1212 @ (powerset @ X21))=>((((X1212)!=(emptyset)))=>?[X1213:$i]:(((in @ X1213 @ X1212)&![X1214:$i]:(((in @ X1214 @ X1212)=>(((X1213)=(X1214))|(in @ X1213 @ X1214)))))))))))))=>![X48:$i]:(((((![X1215:$i]:(((in @ X1215 @ X48)=>(subset @ X1215 @ X48))))&(((((![X1216:$i]:(((in @ X1216 @ X48)=>![X1217:$i]:(((in @ X1217 @ X48)=>![X1218:$i]:(((in @ X1218 @ X48)=>(((in @ X1216 @ X1217)&(in @ X1217 @ X1218))=>(in @ X1216 @ X1218))))))))&![X1219:$i]:(((in @ X1219 @ X48)=>![X1220:$i]:(((in @ X1220 @ X48)=>((((X1219)=(X1220))|(in @ X1219 @ X1220))|(in @ X1220 @ X1219)))))))&![X1221:$i]:(((in @ X1221 @ X48)=>~((in @ X1221 @ X1221))))))&![X1222:$i]:(((in @ X1222 @ (powerset @ X48))=>((((X1222)!=(emptyset)))=>?[X1223:$i]:(((in @ X1223 @ X1222)&![X1224:$i]:(((in @ X1224 @ X1222)=>(((X1223)=(X1224))|(in @ X1223 @ X1224)))))))))))))=>(![X1225:$i]:(((in @ X1225 @ (binintersect @ X21 @ X48))=>(subset @ X1225 @ (binintersect @ X21 @ X48))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ordinalMinLem1, c_0_347]), c_0_364])). 185.90/180.07 thf(c_0_431, axiom, ((ordinalTransSet)=(![X21:$i]:(((((![X1226:$i]:(((in @ X1226 @ X21)=>(subset @ X1226 @ X21))))&(((((![X1227:$i]:(((in @ X1227 @ X21)=>![X1228:$i]:(((in @ X1228 @ X21)=>![X1229:$i]:(((in @ X1229 @ X21)=>(((in @ X1227 @ X1228)&(in @ X1228 @ X1229))=>(in @ X1227 @ X1229))))))))&![X1230:$i]:(((in @ X1230 @ X21)=>![X1231:$i]:(((in @ X1231 @ X21)=>((((X1230)=(X1231))|(in @ X1230 @ X1231))|(in @ X1231 @ X1230)))))))&![X1232:$i]:(((in @ X1232 @ X21)=>~((in @ X1232 @ X1232))))))&![X1233:$i]:(((in @ X1233 @ (powerset @ X21))=>((((X1233)!=(emptyset)))=>?[X1234:$i]:(((in @ X1234 @ X1233)&![X1235:$i]:(((in @ X1235 @ X1233)=>(((X1234)=(X1235))|(in @ X1234 @ X1235)))))))))))))=>![X2:$i, X4:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21)))))))), inference(apply_def,[status(thm)],[ordinalTransSet, c_0_364])). 185.90/180.07 thf(c_0_432, axiom, ((ordinalTransSet1)=(![X21:$i]:(((((![X1236:$i]:(((in @ X1236 @ X21)=>(subset @ X1236 @ X21))))&(((((![X1237:$i]:(((in @ X1237 @ X21)=>![X1238:$i]:(((in @ X1238 @ X21)=>![X1239:$i]:(((in @ X1239 @ X21)=>(((in @ X1237 @ X1238)&(in @ X1238 @ X1239))=>(in @ X1237 @ X1239))))))))&![X1240:$i]:(((in @ X1240 @ X21)=>![X1241:$i]:(((in @ X1241 @ X21)=>((((X1240)=(X1241))|(in @ X1240 @ X1241))|(in @ X1241 @ X1240)))))))&![X1242:$i]:(((in @ X1242 @ X21)=>~((in @ X1242 @ X1242))))))&![X1243:$i]:(((in @ X1243 @ (powerset @ X21))=>((((X1243)!=(emptyset)))=>?[X1244:$i]:(((in @ X1244 @ X1243)&![X1245:$i]:(((in @ X1245 @ X1243)=>(((X1244)=(X1245))|(in @ X1244 @ X1245)))))))))))))=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21))))))), inference(apply_def,[status(thm)],[ordinalTransSet1, c_0_364])). 185.90/180.07 thf(c_0_433, axiom, ((setunionOrdinalLem1)=(![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(((![X1246:$i]:(((in @ X1246 @ X2)=>(subset @ X1246 @ X2))))&(((((![X1247:$i]:(((in @ X1247 @ X2)=>![X1248:$i]:(((in @ X1248 @ X2)=>![X1249:$i]:(((in @ X1249 @ X2)=>(((in @ X1247 @ X1248)&(in @ X1248 @ X1249))=>(in @ X1247 @ X1249))))))))&![X1250:$i]:(((in @ X1250 @ X2)=>![X1251:$i]:(((in @ X1251 @ X2)=>((((X1250)=(X1251))|(in @ X1250 @ X1251))|(in @ X1251 @ X1250)))))))&![X1252:$i]:(((in @ X1252 @ X2)=>~((in @ X1252 @ X1252))))))&![X1253:$i]:(((in @ X1253 @ (powerset @ X2))=>((((X1253)!=(emptyset)))=>?[X1254:$i]:(((in @ X1254 @ X1253)&![X1255:$i]:(((in @ X1255 @ X1253)=>(((X1254)=(X1255))|(in @ X1254 @ X1255)))))))))))))))=>(![X1256:$i]:(((in @ X1256 @ (setunion @ X21))=>(subset @ X1256 @ (setunion @ X21))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[setunionOrdinalLem1, c_0_347]), c_0_364])). 185.90/180.07 thf(c_0_434, plain, ((epred1_0)<=>![X2411:$i]:(?[X2412:$i]:((((![X2413:$i]:(((in @ X2413 @ X2412)=>![X2414:$i]:(((in @ X2414 @ X2413)=>(in @ X2414 @ X2411)))))&![X2415:$i, X2416:$i]:((((in @ X2415 @ X2411)&(in @ X2416 @ X2411))=>(![X2417:$i]:(((in @ X2417 @ X2412)=>((in @ X2415 @ X2417)<=>(in @ X2416 @ X2417))))=>((X2415)=(X2416))))))&![X2418:$i, X2419:$i]:((((in @ X2418 @ X2412)&(in @ X2419 @ X2412))=>(![X2420:$i]:(((in @ X2420 @ X2418)=>(in @ X2420 @ X2419)))|![X2421:$i]:(((in @ X2421 @ X2419)=>(in @ X2421 @ X2418)))))))&![X2422:$i]:(((![X2423:$i]:(((in @ X2423 @ X2422)=>(in @ X2423 @ X2411)))&?[X2424:$i]:((in @ X2424 @ X2422)))=>?[X2425:$i, X2426:$i]:(((((in @ X2425 @ X2412)&(in @ X2426 @ X2422))&~(?[X2427:$i]:(((in @ X2427 @ X2425)&(in @ X2427 @ X2422)))))&![X2428:$i]:(((in @ X2428 @ X2412)=>(![X2429:$i]:(((in @ X2429 @ X2428)=>(in @ X2429 @ X2425)))|(in @ X2426 @ X2428)))))))))))), introduced(definition)). 185.90/180.07 thf(c_0_435, plain, ![X1843:$i]:(((epred2_1 @ X1843)<=>(![X1845:$i]:(((in @ X1845 @ X1843)=>![X1846:$i]:(((in @ X1846 @ X1843)=>![X1847:$i]:(((in @ X1847 @ X1843)=>(((in @ X1845 @ X1846)&(in @ X1846 @ X1847))=>(in @ X1845 @ X1847))))))))&![X1848:$i]:(((in @ X1848 @ X1843)=>![X1849:$i]:(((in @ X1849 @ X1843)=>(((X1848)=(X1849))|(in @ X1848 @ X1849)|(in @ X1849 @ X1848))))))))), introduced(definition)). 185.90/180.07 thf(c_0_436, plain, ![X1854:$i]:(((epred3_1 @ X1854)<=>(![X1856:$i]:(((in @ X1856 @ X1854)=>![X1857:$i]:(((in @ X1857 @ X1854)=>![X1858:$i]:(((in @ X1858 @ X1854)=>(((in @ X1856 @ X1857)&(in @ X1857 @ X1858))=>(in @ X1856 @ X1858))))))))&![X1859:$i]:(((in @ X1859 @ X1854)=>![X1860:$i]:(((in @ X1860 @ X1854)=>(((X1859)=(X1860))|(in @ X1859 @ X1860)|(in @ X1860 @ X1859))))))))), introduced(definition)). 185.90/180.07 thf(c_0_437, plain, ![X1830:$i]:(((epred4_1 @ X1830)<=>(![X1832:$i]:(((in @ X1832 @ X1830)=>![X1833:$i]:(((in @ X1833 @ X1830)=>![X1834:$i]:(((in @ X1834 @ X1830)=>(((in @ X1832 @ X1833)&(in @ X1833 @ X1834))=>(in @ X1832 @ X1834))))))))&![X1835:$i]:(((in @ X1835 @ X1830)=>![X1836:$i]:(((in @ X1836 @ X1830)=>(((X1835)=(X1836))|(in @ X1835 @ X1836)|(in @ X1836 @ X1835))))))))), introduced(definition)). 185.90/180.07 thf(c_0_438, plain, ![X1818:$i]:(((epred5_1 @ X1818)<=>(![X1820:$i]:(((in @ X1820 @ X1818)=>![X1821:$i]:(((in @ X1821 @ X1818)=>![X1822:$i]:(((in @ X1822 @ X1818)=>(((in @ X1820 @ X1821)&(in @ X1821 @ X1822))=>(in @ X1820 @ X1822))))))))&![X1823:$i]:(((in @ X1823 @ X1818)=>![X1824:$i]:(((in @ X1824 @ X1818)=>(((X1823)=(X1824))|(in @ X1823 @ X1824)|(in @ X1824 @ X1823))))))))), introduced(definition)). 185.90/180.07 thf(c_0_439, plain, ![X1806:$i]:(((epred6_1 @ X1806)<=>(![X1808:$i]:(((in @ X1808 @ X1806)=>![X1809:$i]:(((in @ X1809 @ X1806)=>![X1810:$i]:(((in @ X1810 @ X1806)=>(((in @ X1808 @ X1809)&(in @ X1809 @ X1810))=>(in @ X1808 @ X1810))))))))&![X1811:$i]:(((in @ X1811 @ X1806)=>![X1812:$i]:(((in @ X1812 @ X1806)=>(((X1811)=(X1812))|(in @ X1811 @ X1812)|(in @ X1812 @ X1811))))))))), introduced(definition)). 185.90/180.07 thf(c_0_440, plain, ((epred7_0)<=>(![X1796:$i]:(((in @ X1796 @ emptyset)=>![X1797:$i]:(((in @ X1797 @ emptyset)=>![X1798:$i]:(((in @ X1798 @ emptyset)=>(((in @ X1796 @ X1797)&(in @ X1797 @ X1798))=>(in @ X1796 @ X1798))))))))&![X1799:$i]:(((in @ X1799 @ emptyset)=>![X1800:$i]:(((in @ X1800 @ emptyset)=>(((X1799)=(X1800))|(in @ X1799 @ X1800)|(in @ X1800 @ X1799)))))))), introduced(definition)). 185.90/180.07 thf(c_0_441, negated_conjecture, ~((![X1257:$i, X1258:$i]:((![X1259:$i]:(((in @ X1259 @ X1257)<=>(in @ X1259 @ X1258)))=>((X1257)=(X1258))))=>(![X1260:$i]:(~(in @ X1260 @ emptyset))=>(![X2447:$i, X2448:$i, X2449:$i]:(((in @ X2449 @ (setadjoin @ X2447 @ X2448))<=>(((X2449)=(X2447))|(in @ X2449 @ X2448))))=>(![X2444:$i, X2445:$i]:(((in @ X2445 @ (powerset @ X2444))<=>![X2446:$i]:(((in @ X2446 @ X2445)=>(in @ X2446 @ X2444)))))=>(![X2441:$i, X2442:$i]:(((in @ X2442 @ (setunion @ X2441))<=>?[X2443:$i]:(((in @ X2442 @ X2443)&(in @ X2443 @ X2441)))))=>((in @ emptyset @ omega)=>(![X1261:$i]:(((in @ X1261 @ omega)=>(in @ (setadjoin @ X1261 @ X1261) @ omega)))=>(![X2438:$i]:((((in @ emptyset @ X2438)&![X2439:$i]:((((in @ X2439 @ omega)&(in @ X2439 @ X2438))=>(in @ (setadjoin @ X2439 @ X2439) @ X2438))))=>![X2440:$i]:(((in @ X2440 @ omega)=>(in @ X2440 @ X2438)))))=>(![X2430:$i > $i > $o, X2431:$i]:((![X2432:$i]:(((in @ X2432 @ X2431)=>?[X2433:$i]:(((X2430 @ X2432 @ X2433)&![X2434:$i]:(((X2430 @ X2432 @ X2434)=>((X2433)=(X2434))))))))=>?[X2435:$i]:(![X2436:$i]:(((in @ X2436 @ X2435)<=>?[X2437:$i]:(((in @ X2437 @ X2431)&(X2430 @ X2437 @ X2436))))))))=>(![X1262:$i]:((?[X1263:$i]:((in @ X1263 @ X1262))=>?[X1264:$i]:(((in @ X1264 @ X1262)&~(?[X1265:$i]:(((in @ X1265 @ X1264)&(in @ X1265 @ X1262))))))))=>((epred1_0)=>(![X2408:$i > $o]:((?[X2409:$i]:(((X2408 @ X2409)&![X2410:$i]:(((X2408 @ X2410)=>((X2409)=(X2410))))))=>(X2408 @ (descr @ (^[Z0/* 17 */:$i]:(X2408 @ Z0))))))=>(![X1266:$i, X1267:$i > $o, X1268:$i]:(((in @ X1268 @ X1266)=>((X1267 @ X1268)=>(in @ X1268 @ (dsetconstr @ X1266 @ X1267)))))=>(![X1269:$i, X1270:$i > $o, X1271:$i]:(((in @ X1271 @ (dsetconstr @ X1269 @ X1270))=>(in @ X1271 @ X1269)))=>(![X2405:$i, X2406:$i > $o, X2407:$i]:(((in @ X2407 @ (dsetconstr @ X2405 @ X2406))=>(X2406 @ X2407)))=>(![X2400:$i > $o]:((?[X2401:$i]:(((X2400 @ X2401)&![X2402:$i]:(((X2400 @ X2402)=>((X2401)=(X2402))))))=>?[X2403:$i]:(((X2400 @ X2403)&![X2404:$i]:(((X2400 @ X2404)=>((X2403)=(X2404))))))))=>(![X2398:$o, X2399:$i]:(((in @ X2399 @ (prop2set @ ((X2398))))=>(X2398)))=>(![X2396:$i]:(((in @ X2396 @ emptyset)=>![X2397:$o]:((X2397))))=>(![X2395:$i]:(((in @ X2395 @ emptyset)=>~($true)))=>(![X2394:$i]:(~(in @ X2394 @ emptyset))=>(![X2390:$i > $o]:((?[X2391:$i]:(((X2390 @ X2391)&![X2392:$i]:(((X2390 @ X2392)=>((X2391)=(X2392))))))=>?[X2393:$i]:((X2390 @ X2393))))=>(![X1272:$i, X1273:$i]:((![X1274:$i]:(((in @ X1274 @ X1272)=>(in @ X1274 @ X1273)))=>(![X1275:$i]:(((in @ X1275 @ X1273)=>(in @ X1275 @ X1272)))=>((X1272)=(X1273)))))=>(![X2388:$i]:((![X2389:$i]:(~(in @ X2389 @ X2388))=>((X2388)=(emptyset))))=>(![X1276:$i]:((![X1277:$i]:(~(in @ X1277 @ X1276))=>((X1276)=(emptyset))))=>(![X2385:$i, X2386:$i > $o, X2387:$i]:(((in @ X2387 @ X2385)=>((in @ X2387 @ (dsetconstr @ X2385 @ X2386))<=>(X2386 @ X2387))))=>(![X2383:$i]:((((X2383)!=(emptyset))=>?[X2384:$i]:((in @ X2384 @ X2383))))=>(![X1278:$i, X1279:$i > $o, X1280:$i]:(((in @ X1280 @ X1278)=>((X1279 @ X1280)=>((dsetconstr @ X1278 @ X1279)!=(emptyset)))))=>(![X1281:$i]:((?[X1282:$i]:((in @ X1282 @ X1281))=>((X1281)!=(emptyset))))=>(![X2381:$i, X2382:$i]:((in @ X2381 @ (setadjoin @ X2381 @ X2382)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1283:$i, X1284:$i, X1285:$i]:(((in @ X1285 @ X1284)=>(in @ X1285 @ (setadjoin @ X1283 @ X1284))))=>(![X2377:$i, X2378:$i, X2379:$i]:(((in @ X2379 @ (setadjoin @ X2377 @ X2378))=>![X2380:$o]:(((((X2379)=(X2377))=>(X2380))=>(((in @ X2379 @ X2378)=>(X2380))=>(X2380))))))=>(![X2374:$i, X2375:$i, X2376:$i]:(((in @ X2376 @ (setadjoin @ X2374 @ X2375))=>(((X2376)=(X2374))|(in @ X2376 @ X2375))))=>(![X1286:$i]:(((dsetconstr @ X1286 @ (^[Z0/* 1 */:$i]:($true)))=(X1286)))=>(![X2371:$i, X2372:$i]:((![X2373:$i]:(((in @ X2373 @ X2372)=>(in @ X2373 @ X2371)))=>(in @ X2372 @ (powerset @ X2371))))=>(![X1287:$i]:((in @ emptyset @ (powerset @ X1287)))=>(![X1288:$i]:((in @ emptyset @ (powerset @ X1288)))=>(![X2368:$i, X2369:$i, X2370:$i]:(((in @ X2369 @ (powerset @ X2368))=>((in @ X2370 @ X2369)=>(in @ X2370 @ X2368))))=>(![X1289:$i, X1290:$i, X1291:$i]:(((in @ X1290 @ X1291)=>((in @ X1291 @ X1289)=>(in @ X1290 @ (setunion @ X1289)))))=>(![X2364:$i, X2365:$i]:(((in @ X2365 @ (setunion @ X2364))=>![X2366:$o]:((![X2367:$i]:(((in @ X2365 @ X2367)=>((in @ X2367 @ X2364)=>(X2366))))=>(X2366)))))=>(![X1292:$i, X1293:$i]:(((in @ X1293 @ X1292)=>(in @ X1293 @ (powerset @ (setunion @ X1292)))))=>(![X2359:$i > $o]:((?[X2360:$i]:(((X2359 @ 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y_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[emptysetOrdinal]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_365]), foundationAx]), wellorderingAx]), c_0_366]), c_0_367]), c_0_368]), c_0_369]), c_0_370]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_371]), setext]), emptyI]), noeltsimpempty]), c_0_372]), c_0_373]), c_0_374]), c_0_375]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_376]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_377]), c_0_378]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_379]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_380]), c_0_381]), c_0_382]), inCongP]), in__Cong]), c_0_383]), c_0_384]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_385]), c_0_386]), c_0_387]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_388]), c_0_389]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_390]), c_0_391]), c_0_392]), c_0_393]), singletonsuniq]), setukpairinjL1]), c_0_394]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_395]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_396]), c_0_397]), c_0_398]), c_0_399]), c_0_400]), c_0_401]), c_0_402]), c_0_403]), c_0_404]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_405]), c_0_406]), c_0_407]), brelnall1]), brelnall2]), c_0_408]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), subbreln]), eqbreln]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_409]), c_0_410]), c_0_411]), c_0_412]), c_0_413]), c_0_414]), c_0_415]), c_0_416]), c_0_417]), c_0_418]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3]), woz1_4]), woz1_5]), breln1all2]), breln1SetBreln1]), c_0_419]), c_0_420]), breln1all1]), subbreln1]), eqbreln1]), breln1invprop]), breln1invI]), breln1invE]), breln1compprop]), breln1compI]), breln1compE]), breln1compEex]), breln1unionprop]), breln1unionIL]), breln1unionIR]), breln1unionI]), breln1unionE]), breln1unionEcases]), breln1unionCommutes]), woz2Ex]), woz2W]), woz2A]), woz2B]), image1Ex]), c_0_421]), c_0_422]), c_0_423]), c_0_424]), injFuncInInjFuncSet]), injFuncSetFuncIn]), injFuncSetFuncInj]), surjFuncSetFuncIn]), surjFuncSetFuncSurj]), leftInvIsSurj]), surjCantorThm]), c_0_425]), notinself]), notinself2]), omegaSp]), omegaSclos]), peano0notS]), peanoSinj]), c_0_426]), c_0_427]), c_0_428]), c_0_429]), c_0_364]), c_0_430]), c_0_431]), c_0_432]), c_0_433])])]), c_0_434]), c_0_435]), c_0_436]), c_0_437]), c_0_438]), c_0_439]), c_0_440])). 185.90/180.07 thf(c_0_442, plain, ((![X1796:$i]:(((in @ X1796 @ emptyset)=>![X1797:$i]:(((in @ X1797 @ emptyset)=>![X1798:$i]:(((in @ X1798 @ emptyset)=>(((in @ X1796 @ X1797)&(in @ X1797 @ X1798))=>(in @ X1796 @ X1798))))))))&![X1799:$i]:(((in @ X1799 @ emptyset)=>![X1800:$i]:(((in @ X1800 @ emptyset)=>(((X1799)=(X1800))|(in @ X1799 @ X1800)|(in @ X1800 @ X1799)))))))=>(epred7_0)), inference(split_equiv,[status(thm)],[c_0_440])). 185.90/180.07 thf(c_0_443, negated_conjecture, ![X2450:$i, X2451:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2463:$i, X2464:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2472:$i, X2473:$i > $i > $o, X2474:$i, X2476:$i, X2479:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2486:$i, X2487:$i > $o, X2488:$i, X2490:$i, X2491:$i > $o, X2492:$i, X2493:$i, X2494:$i > $o, X2495:$i, X2496:$i, X2497:$i > $o, X2498:$i, X2499:$i > $o, X2500:$i, X2503:$i, X2504:$o, X2505:$i, X2506:$i, X2507:$o, X2508:$i, X2509:$i, X2510:$i > $o, X2511:$i, X2514:$i, X2515:$i, X2518:$i, X2520:$i, X2522:$i, X2523:$i > $o, X2524:$i, X2525:$i, X2527:$i, X2528:$i > $o, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$o, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$o, X2560:$i, X2561:$i, X2562:$i > $o, X2563:$i, X2566:$i, X2567:$i, X2568:$i, X2570:$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 > $o, X2587:$i, X2588:$i > $o, X2589:$i, X2590:$i, X2591:$i > $o, X2592:$i, X2594:$i, X2595:$i > $o, X2597:$i, X2598:$i, X2599:$i > $o, X2601:$i, X2602:$i, X2603:$i > $o, X2604:$i, X2606:$o, X2607:$o, X2608:$i, X2609:$i > $o, X2611:$i, X2612:$i, X2613:$i > $o, X2614:$i, X2616:$i > $o, X2617:$i, X2620:$i, X2621:$i > $o, X2622:$i, X2626:$i, X2627:$i > $o, X2628:$i, X2631:$i, X2632:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i > $o, X2641:$i, X2643:$i, X2644:$i, X2645:$i > $o, X2646:$i > $o, X2649:$i, X2652:$i, X2653:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i > $o, X2666:$i, X2668:$i, X2669:$i, X2670:$i > $o, X2671:$i > $o, X2674:$i, X2676:$i, X2678:$i, X2679:$i, X2680:$i > $o, X2681:$i > $o, X2684:$i, X2685:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$i, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i > $o, X2732:$i, X2733:$i > $o, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$o, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$o, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2851:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2856:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i, X2871:$i, X2872:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$i, X2885:$i > $o, X2888:$i, X2889:$i, X2890:$i > $o, X2892:$i, X2893:$i > $o, X2894:$i, X2896:$i, X2897:$i > $o, X2900:$i, X2901:$i, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$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 > $i > $o, X2973:$i, X2974:$i, X2975:$i, X2976:$i, X2977:$i > $i > $o, X2978:$i, X2979:$i, X2980:$i > $i > $o, X2981:$i, X2982:$i, X2983:$i > $i > $o, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i > $i > $o, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i > $i > $o, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i > $i > $o, X2999:$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 > $i, X3027:$i, X3028:$i, X3029:$i > $i, X3031:$i, X3032:$i, X3033:$i > $i, X3035:$i, X3036:$i, X3037:$i, X3038:$i > $o, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i > $o, X3048:$i, X3049:$i, X3050:$i > $o, X3051:$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, X3071:$i, X3072:$i, X3073:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i, X3079:$i, X3080:$i, X3081:$i, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i > $i, X3114:$i, X3115:$i, X3116:$i, X3117:$i, X3118:$i, X3119:$i, X3120:$i > $i, X3122:$i, X3123:$i, X3124:$i > $i, X3126:$i, X3127:$i, X3128:$i, X3129:$i, X3130:$i, X3131:$o, X3132:$i, X3133:$i, X3134:$i, X3135:$o, X3136:$i, X3137:$i, X3138:$i, X3139:$o, X3140:$i, X3141:$i, X3142:$i, X3143:$o, X3144:$i, X3145:$i, X3146:$i, X3147:$o, X3148:$i, X3149:$i, X3150:$i, X3151:$o, X3152:$i, X3153:$i, X3154:$i, X3155:$i, X3156:$i, X3157:$o, X3158:$i, X3159:$i, X3160:$i, X3161:$o, X3162:$i, X3163:$i, X3164:$i, X3165:$o, X3166:$i, X3167:$i, X3168:$i, X3169:$i, X3170:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i, X3176:$i, X3177:$i, X3178:$i, X3179:$i, X3180:$i, X3181:$i, X3182:$i, X3183:$i, X3186:$i, X3187:$i, X3188:$i, X3190:$i, X3191:$i, X3192:$i, X3194:$i, X3195:$i, X3196:$i, X3197:$i, X3198:$i, X3199:$i, X3200:$i, X3201:$i, X3202:$i, X3203:$i, X3204:$i, X3205:$i, X3206:$i, X3207:$i, X3208:$i, X3209:$i, X3210:$i, X3211:$i, X3212:$i, X3213:$i, X3214:$i, X3215:$i, X3216:$i, X3217:$i, X3218:$i, X3219:$i, X3220:$i, X3221:$i, X3222:$i, X3223:$i, X3224:$i, X3225:$i, X3226:$i, X3227:$i, X3228:$i, X3229:$i, X3230:$i, X3231:$i, X3232:$i, X3233:$i, X3234:$i, X3235:$i, X3236:$i, X3237:$i, X3238:$i, X3239:$i, X3240:$i, X3241:$i, X3242:$i, X3243:$i, X3244:$i, X3245:$i, X3246:$i, X3247:$i, X3248:$i, X3249:$i, X3250:$i, X3251:$i, X3252:$i, X3253:$i, X3254:$i, X3255:$i, X3256:$i, X3257:$i, X3258:$i, X3259:$i, X3260:$i, X3261:$i, X3262:$i, X3263:$i, X3264:$i, X3265:$i, X3266:$i, X3267:$i, X3268:$i, X3269:$i, X3270:$i, X3271:$i, X3272:$i, X3273:$i, X3274:$i, X3275:$i, X3276:$i, X3277:$i, X3278:$i, X3279:$i, X3280:$i, X3281:$i, X3282:$i, X3283:$i, X3284:$i, X3285:$i, X3286:$i, X3287:$i, X3288:$i, X3289:$i, X3290:$i, X3291:$i, X3292:$i, X3293:$i, X3294:$i, X3295:$i, X3296:$i, X3297:$o, X3298:$i, X3299:$i, X3300:$i, X3301:$i, X3302:$i, X3303:$i, X3304:$i, X3305:$i, X3306:$i, X3307:$i, X3308:$i, X3309:$i, X3310:$i, X3311:$i, X3312:$i, X3313:$i, X3314:$i, X3315:$i, X3316:$i, X3317:$i, X3318:$i, X3319:$i, X3320:$i, X3321:$i, X3322:$i, X3323:$i, X3324:$i, X3325:$i, X3326:$i, X3327:$i, X3328:$i, X3329:$i, X3330:$i, X3331:$i, X3332:$i, X3333:$i, X3334:$i, X3335:$i, X3336:$i, X3337:$i, X3338:$i, X3339:$i, X3340:$i, X3341:$i, X3342:$i, X3343:$i, X3344:$i, X3345:$i, X3346:$i, X3347:$i, X3348:$i, X3349:$i, X3350:$i, X3351:$i, X3352:$i, X3353:$i, X3354:$i, X3355:$i, X3356:$i, X3357:$i, X3358:$i, X3359:$i, X3360:$i, X3361:$i, X3362:$i, X3363:$i, X3364:$i, X3365:$i, X3366:$i, X3367:$i, X3368:$i, X3369:$i, X3370:$i, X3371:$i, X3372:$i, X3373:$i, X3374:$i, X3375:$i, X3376:$i, X3377:$i, X3378:$i, X3379:$i, X3380:$i, X3381:$i > $o, X3384:$i, X3385:$i, X3386:$i, X3387:$i, X3388:$i, X3389:$i > $i > $o, X3391:$i, X3392:$i, X3393:$i, X3394:$i, X3395:$i > $i > $o, X3396:$i, X3397:$i, X3398:$i > $o, X3401:$i, X3402:$i, X3403:$i, X3404:$i, X3407:$i, X3408:$i, X3409:$i, X3414:$i, X3415:$i, X3416:$i, X3417:$i, X3418:$i, X3419:$i, X3420:$i, X3421:$i, X3422:$i, X3423:$i, X3424:$i, X3425:$i, X3426:$i, X3427:$i, X3428:$i, 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X3595) @ (esk130_1 @ X3595))|~(epred5_1 @ X3595))|(in @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))&((((X3599)!=(esk132_2 @ X3595 @ X3599))|~(in @ X3599 @ (esk131_1 @ X3595))|((in @ (esk130_1 @ X3595) @ (esk130_1 @ X3595))|~(epred5_1 @ X3595))|(in @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))&(~(in @ X3599 @ (esk132_2 @ X3595 @ X3599))|~(in @ X3599 @ (esk131_1 @ X3595))|((in @ (esk130_1 @ X3595) @ (esk130_1 @ X3595))|~(epred5_1 @ X3595))|(in @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595))))))))&((((in @ (esk131_1 @ X3595) @ (powerset @ X3595))|((in @ (esk130_1 @ X3595) @ X3595)|~(epred5_1 @ X3595))|~(subset @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))&((((esk131_1 @ X3595)!=(emptyset))|((in @ (esk130_1 @ X3595) @ X3595)|~(epred5_1 @ X3595))|~(subset @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))&(((in @ (esk132_2 @ X3595 @ X3599) @ (esk131_1 @ X3595))|~(in @ X3599 @ (esk131_1 @ X3595))|((in @ (esk130_1 @ X3595) @ X3595)|~(epred5_1 @ X3595))|~(subset @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))&((((X3599)!=(esk132_2 @ X3595 @ X3599))|~(in @ X3599 @ (esk131_1 @ X3595))|((in @ (esk130_1 @ X3595) @ X3595)|~(epred5_1 @ X3595))|~(subset @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))&(~(in @ X3599 @ (esk132_2 @ X3595 @ X3599))|~(in @ X3599 @ (esk131_1 @ X3595))|((in @ (esk130_1 @ X3595) @ X3595)|~(epred5_1 @ X3595))|~(subset @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))))))&(((in @ (esk131_1 @ X3595) @ (powerset @ X3595))|((in @ (esk130_1 @ X3595) @ (esk130_1 @ X3595))|~(epred5_1 @ X3595))|~(subset @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))&((((esk131_1 @ X3595)!=(emptyset))|((in @ (esk130_1 @ X3595) @ (esk130_1 @ X3595))|~(epred5_1 @ X3595))|~(subset @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))&(((in @ (esk132_2 @ X3595 @ X3599) @ (esk131_1 @ X3595))|~(in @ X3599 @ (esk131_1 @ X3595))|((in @ (esk130_1 @ X3595) @ (esk130_1 @ X3595))|~(epred5_1 @ X3595))|~(subset @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))&((((X3599)!=(esk132_2 @ X3595 @ X3599))|~(in @ X3599 @ (esk131_1 @ X3595))|((in @ (esk130_1 @ X3595) @ (esk130_1 @ X3595))|~(epred5_1 @ X3595))|~(subset @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))&(~(in @ X3599 @ (esk132_2 @ X3595 @ X3599))|~(in @ X3599 @ (esk131_1 @ X3595))|((in @ (esk130_1 @ X3595) @ (esk130_1 @ X3595))|~(epred5_1 @ X3595))|~(subset @ (esk129_1 @ X3595) @ X3595)|(~(in @ X3601 @ X3595)|(subset @ X3601 @ X3595)))))))))&((((in @ (esk133_1 @ X3602) @ X3602)|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&(((((in @ (esk136_1 @ X3602) @ (powerset @ (esk133_1 @ X3602)))|((in @ (esk135_1 @ X3602) @ (esk133_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|(in @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&((((esk136_1 @ X3602)!=(emptyset))|((in @ (esk135_1 @ X3602) @ (esk133_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|(in @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&(((in @ (esk137_2 @ X3602 @ X3607) @ (esk136_1 @ X3602))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk133_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|(in @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&((((X3607)!=(esk137_2 @ X3602 @ X3607))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk133_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|(in @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&(~(in @ X3607 @ (esk137_2 @ X3602 @ X3607))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk133_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|(in @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))))))&(((in @ (esk136_1 @ X3602) @ (powerset @ (esk133_1 @ X3602)))|((in @ (esk135_1 @ X3602) @ (esk135_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|(in @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&((((esk136_1 @ X3602)!=(emptyset))|((in @ (esk135_1 @ X3602) @ (esk135_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|(in @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&(((in @ (esk137_2 @ X3602 @ X3607) @ (esk136_1 @ X3602))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk135_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|(in @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&((((X3607)!=(esk137_2 @ X3602 @ X3607))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk135_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|(in @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&(~(in @ X3607 @ (esk137_2 @ X3602 @ X3607))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk135_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|(in @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602)))))))))&((((in @ (esk136_1 @ X3602) @ (powerset @ (esk133_1 @ X3602)))|((in @ (esk135_1 @ X3602) @ (esk133_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|~(subset @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&((((esk136_1 @ X3602)!=(emptyset))|((in @ (esk135_1 @ X3602) @ (esk133_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|~(subset @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&(((in @ (esk137_2 @ X3602 @ X3607) @ (esk136_1 @ X3602))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk133_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|~(subset @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&((((X3607)!=(esk137_2 @ X3602 @ X3607))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk133_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|~(subset @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&(~(in @ X3607 @ (esk137_2 @ X3602 @ X3607))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk133_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|~(subset @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))))))&(((in @ (esk136_1 @ X3602) @ (powerset @ (esk133_1 @ X3602)))|((in @ (esk135_1 @ X3602) @ (esk135_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|~(subset @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&((((esk136_1 @ X3602)!=(emptyset))|((in @ (esk135_1 @ X3602) @ (esk135_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|~(subset @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&(((in @ (esk137_2 @ X3602 @ X3607) @ (esk136_1 @ X3602))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk135_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|~(subset @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&((((X3607)!=(esk137_2 @ X3602 @ X3607))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk135_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|~(subset @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602))))&(~(in @ X3607 @ (esk137_2 @ X3602 @ X3607))|~(in @ X3607 @ (esk136_1 @ X3602))|((in @ (esk135_1 @ X3602) @ (esk135_1 @ X3602))|~(epred6_1 @ (esk133_1 @ X3602)))|~(subset @ (esk134_1 @ X3602) @ (esk133_1 @ X3602))|(~(in @ X3609 @ (setunion @ X3602))|(subset @ X3609 @ (setunion @ X3602)))))))))))&(((((in @ esk140_0 @ (powerset @ emptyset))|((in @ esk139_0 @ emptyset)|~(epred7_0))|(in @ esk138_0 @ emptyset))&((((esk140_0)!=(emptyset))|((in @ esk139_0 @ emptyset)|~(epred7_0))|(in @ esk138_0 @ emptyset))&(((in @ (esk141_1 @ X3613) @ esk140_0)|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ emptyset)|~(epred7_0))|(in @ esk138_0 @ emptyset))&((((X3613)!=(esk141_1 @ X3613))|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ emptyset)|~(epred7_0))|(in @ esk138_0 @ emptyset))&(~(in @ X3613 @ (esk141_1 @ X3613))|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ emptyset)|~(epred7_0))|(in @ esk138_0 @ emptyset))))))&(((in @ esk140_0 @ (powerset @ emptyset))|((in @ esk139_0 @ esk139_0)|~(epred7_0))|(in @ esk138_0 @ emptyset))&((((esk140_0)!=(emptyset))|((in @ esk139_0 @ esk139_0)|~(epred7_0))|(in @ esk138_0 @ emptyset))&(((in @ (esk141_1 @ X3613) @ esk140_0)|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ esk139_0)|~(epred7_0))|(in @ esk138_0 @ emptyset))&((((X3613)!=(esk141_1 @ X3613))|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ esk139_0)|~(epred7_0))|(in @ esk138_0 @ emptyset))&(~(in @ X3613 @ (esk141_1 @ X3613))|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ esk139_0)|~(epred7_0))|(in @ esk138_0 @ emptyset)))))))&((((in @ esk140_0 @ (powerset @ emptyset))|((in @ esk139_0 @ emptyset)|~(epred7_0))|~(subset @ esk138_0 @ emptyset))&((((esk140_0)!=(emptyset))|((in @ esk139_0 @ emptyset)|~(epred7_0))|~(subset @ esk138_0 @ emptyset))&(((in @ (esk141_1 @ X3613) @ esk140_0)|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ emptyset)|~(epred7_0))|~(subset @ esk138_0 @ emptyset))&((((X3613)!=(esk141_1 @ X3613))|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ emptyset)|~(epred7_0))|~(subset @ esk138_0 @ emptyset))&(~(in @ X3613 @ (esk141_1 @ X3613))|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ emptyset)|~(epred7_0))|~(subset @ esk138_0 @ emptyset))))))&(((in @ esk140_0 @ (powerset @ emptyset))|((in @ esk139_0 @ esk139_0)|~(epred7_0))|~(subset @ esk138_0 @ emptyset))&((((esk140_0)!=(emptyset))|((in @ esk139_0 @ esk139_0)|~(epred7_0))|~(subset @ esk138_0 @ emptyset))&(((in @ (esk141_1 @ X3613) @ esk140_0)|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ esk139_0)|~(epred7_0))|~(subset @ esk138_0 @ emptyset))&((((X3613)!=(esk141_1 @ X3613))|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ esk139_0)|~(epred7_0))|~(subset @ esk138_0 @ emptyset))&(~(in @ X3613 @ (esk141_1 @ X3613))|~(in @ X3613 @ esk140_0)|((in @ esk139_0 @ esk139_0)|~(epred7_0))|~(subset @ esk138_0 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[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_441])])])])])])])). 185.90/180.07 thf(c_0_444, plain, ((((in @ esk175_0 @ emptyset)|(in @ esk172_0 @ emptyset)|(epred7_0))&(((in @ esk176_0 @ emptyset)|(in @ esk172_0 @ emptyset)|(epred7_0))&(((((esk175_0)!=(esk176_0))|(in @ esk172_0 @ emptyset)|(epred7_0))&(~(in @ esk175_0 @ esk176_0)|(in @ esk172_0 @ emptyset)|(epred7_0)))&(~(in @ esk176_0 @ esk175_0)|(in @ esk172_0 @ emptyset)|(epred7_0)))))&((((in @ esk175_0 @ emptyset)|(in @ esk173_0 @ emptyset)|(epred7_0))&(((in @ esk176_0 @ emptyset)|(in @ esk173_0 @ emptyset)|(epred7_0))&(((((esk175_0)!=(esk176_0))|(in @ esk173_0 @ emptyset)|(epred7_0))&(~(in @ esk175_0 @ esk176_0)|(in @ esk173_0 @ emptyset)|(epred7_0)))&(~(in @ esk176_0 @ esk175_0)|(in @ esk173_0 @ emptyset)|(epred7_0)))))&((((in @ esk175_0 @ emptyset)|(in @ esk174_0 @ emptyset)|(epred7_0))&(((in @ esk176_0 @ emptyset)|(in @ esk174_0 @ emptyset)|(epred7_0))&(((((esk175_0)!=(esk176_0))|(in @ esk174_0 @ emptyset)|(epred7_0))&(~(in @ esk175_0 @ esk176_0)|(in @ esk174_0 @ emptyset)|(epred7_0)))&(~(in @ esk176_0 @ esk175_0)|(in @ esk174_0 @ emptyset)|(epred7_0)))))&(((((in @ esk175_0 @ emptyset)|(in @ esk172_0 @ esk173_0)|(epred7_0))&(((in @ esk176_0 @ emptyset)|(in @ esk172_0 @ esk173_0)|(epred7_0))&(((((esk175_0)!=(esk176_0))|(in @ esk172_0 @ esk173_0)|(epred7_0))&(~(in @ esk175_0 @ esk176_0)|(in @ esk172_0 @ esk173_0)|(epred7_0)))&(~(in @ esk176_0 @ esk175_0)|(in @ esk172_0 @ esk173_0)|(epred7_0)))))&(((in @ esk175_0 @ emptyset)|(in @ esk173_0 @ esk174_0)|(epred7_0))&(((in @ esk176_0 @ emptyset)|(in @ esk173_0 @ esk174_0)|(epred7_0))&(((((esk175_0)!=(esk176_0))|(in @ esk173_0 @ esk174_0)|(epred7_0))&(~(in @ esk175_0 @ esk176_0)|(in @ esk173_0 @ esk174_0)|(epred7_0)))&(~(in @ esk176_0 @ esk175_0)|(in @ esk173_0 @ esk174_0)|(epred7_0))))))&(((in @ esk175_0 @ emptyset)|~(in @ esk172_0 @ esk174_0)|(epred7_0))&(((in @ esk176_0 @ emptyset)|~(in @ esk172_0 @ esk174_0)|(epred7_0))&(((((esk175_0)!=(esk176_0))|~(in @ esk172_0 @ esk174_0)|(epred7_0))&(~(in @ esk175_0 @ esk176_0)|~(in @ esk172_0 @ esk174_0)|(epred7_0)))&(~(in @ esk176_0 @ esk175_0)|~(in @ esk172_0 @ esk174_0)|(epred7_0))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_442])])])])])). 185.90/180.07 thf(c_0_445, negated_conjecture, ((in @ esk140_0 @ (powerset @ emptyset))|(in @ esk139_0 @ esk139_0)|(in @ esk138_0 @ emptyset)|~((epred7_0))), inference(split_conjunct,[status(thm)],[c_0_443])). 185.90/180.07 thf(c_0_446, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_443])). 185.90/180.07 thf(c_0_447, negated_conjecture, ![X2:$i]:(~((in @ X2 @ X2))), inference(split_conjunct,[status(thm)],[c_0_443])). 185.90/180.07 thf(c_0_448, plain, ((in @ esk175_0 @ emptyset)|(in @ esk172_0 @ emptyset)|(epred7_0)), inference(split_conjunct,[status(thm)],[c_0_444])). 185.90/180.07 thf(c_0_449, negated_conjecture, ((in @ esk140_0 @ (powerset @ emptyset))|~((epred7_0))), inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_445, c_0_446]), c_0_447])). 185.90/180.07 thf(c_0_450, plain, (epred7_0), inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_448, c_0_446]), c_0_446])). 185.90/180.07 thf(c_0_451, negated_conjecture, ((in @ esk139_0 @ emptyset)|(in @ esk138_0 @ emptyset)|((esk140_0)!=(emptyset))|~((epred7_0))), inference(split_conjunct,[status(thm)],[c_0_443])). 185.90/180.07 thf(c_0_452, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_443])). 185.90/180.07 thf(c_0_453, negated_conjecture, (in @ esk140_0 @ (powerset @ emptyset)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_449, c_0_450])])). 185.90/180.07 thf(c_0_454, negated_conjecture, (((esk140_0)!=(emptyset))|~((epred7_0))), inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_451, c_0_446]), c_0_446])). 185.90/180.07 thf(c_0_455, negated_conjecture, ![X2:$i]:((((X2)=(emptyset))|~((subset @ X2 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_443])). 185.90/180.07 thf(c_0_456, negated_conjecture, (subset @ esk140_0 @ emptyset), inference(spm,[status(thm)],[c_0_452, c_0_453])). 185.90/180.07 thf(c_0_457, negated_conjecture, ((esk140_0)!=(emptyset)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_454, c_0_450])])). 185.90/180.07 thf(c_0_458, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_455, c_0_456]), c_0_457]), ['proof']). 185.90/180.07 # SZS output end CNFRefutation 185.90/180.07 # Parsed axioms : 743 185.90/180.07 # Removed by relevancy pruning/SinE : 0 185.90/180.07 # Initial clauses : 1632 185.90/180.07 # Removed in clause preprocessing : 436 185.90/180.07 # Initial clauses in saturation : 1196 185.90/180.07 # Processed clauses : 1245 185.90/180.07 # ...of these trivial : 33 185.90/180.07 # ...subsumed : 67 185.90/180.07 # ...remaining for further processing : 1145 185.90/180.07 # Other redundant clauses eliminated : 19 185.90/180.07 # Clauses deleted for lack of memory : 0 185.90/180.07 # Backward-subsumed : 337 185.90/180.07 # Backward-rewritten : 4 185.90/180.07 # Generated clauses : 29 185.90/180.07 # ...of the previous two non-redundant : 21 185.90/180.07 # ...aggressively subsumed : 0 185.90/180.07 # Contextual simplify-reflections : 15 185.90/180.07 # Paramodulations : 9 185.90/180.07 # Factorizations : 0 185.90/180.07 # NegExts : 0 185.90/180.07 # Equation resolutions : 19 185.90/180.07 # Disequality decompositions : 0 185.90/180.07 # Total rewrite steps : 73 185.90/180.07 # ...of those cached : 58 185.90/180.07 # Propositional unsat checks : 0 185.90/180.07 # Propositional check models : 0 185.90/180.07 # Propositional check unsatisfiable : 0 185.90/180.07 # Propositional clauses : 0 185.90/180.07 # Propositional clauses after purity: 0 185.90/180.07 # Propositional unsat core size : 0 185.90/180.07 # Propositional preprocessing time : 0.000 185.90/180.07 # Propositional encoding time : 0.000 185.90/180.07 # Propositional solver time : 0.000 185.90/180.07 # Success case prop preproc time : 0.000 185.90/180.07 # Success case prop encoding time : 0.000 185.90/180.07 # Success case prop solver time : 0.000 185.90/180.07 # Current number of processed clauses : 31 185.90/180.07 # Positive orientable unit clauses : 14 185.90/180.07 # Positive unorientable unit clauses: 0 185.90/180.07 # Negative unit clauses : 6 185.90/180.07 # Non-unit-clauses : 11 185.90/180.07 # Current number of unprocessed clauses: 726 185.90/180.07 # ...number of literals in the above : 3111 185.90/180.07 # Current number of archived formulas : 0 185.90/180.07 # Current number of archived clauses : 1095 185.90/180.07 # Clause-clause subsumption calls (NU) : 1213154 185.90/180.07 # Rec. Clause-clause subsumption calls : 57433 185.90/180.07 # Non-unit clause-clause subsumptions : 411 185.90/180.07 # Unit Clause-clause subsumption calls : 133 185.90/180.07 # Rewrite failures with RHS unbound : 0 185.90/180.07 # BW rewrite match attempts : 16 185.90/180.07 # BW rewrite match successes : 2 185.90/180.07 # Condensation attempts : 0 185.90/180.07 # Condensation successes : 0 185.90/180.07 # Termbank termtop insertions : 568752 185.90/180.07 # Search garbage collected termcells : 42482 185.90/180.07 185.90/180.07 # ------------------------------------------------- 185.90/180.07 # User time : 0.834 s 185.90/180.07 # System time : 0.029 s 185.90/180.07 # Total time : 0.863 s 185.90/180.07 # Maximum resident set size: 12420 pages 185.90/180.07 185.90/180.07 # ------------------------------------------------- 185.90/180.07 # User time : 0.849 s 185.90/180.07 # System time : 0.035 s 185.90/180.07 # Total time : 0.884 s 185.90/180.07 # Maximum resident set size: 3140 pages 185.90/180.07 % E---3.1 exiting 185.90/180.08 % E exiting 185.90/180.11 EOF