0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : run_E %s %d THM 0.11/0.32 % Computer : n008.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 1440 0.11/0.32 % WCLimit : 180 0.11/0.32 % DateTime : Thu Jul 4 07:47:23 EDT 2024 0.11/0.32 % CPUTime : 0.18/0.47 Running higher-order theorem proving 0.18/0.53 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.WkjC4FAFUI/E---3.1_6980.p 0.36/0.95 # Version: 3.2.0-ho 0.36/0.95 # Preprocessing class: HSLMSLSSLLLCHFA. 0.36/0.95 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.36/0.95 # Starting ehoh_best5 with 180s (1) cores 0.36/0.95 # Starting almost_fo_3_lam with 180s (1) cores 0.36/0.95 # Starting new_bool_5 with 180s (1) cores 0.36/0.95 # Starting pre_casc_3 with 180s (1) cores 0.36/0.95 # Starting ho_unfolding_8 with 180s (1) cores 0.36/0.95 # Starting new_ho_10_cnf2 with 180s (1) cores 0.36/0.95 # Starting new_bool_3 with 180s (1) cores 0.36/0.95 # Starting new_ho_5 with 180s (1) cores 0.36/0.95 # new_bool_5 with pid 7117 completed with status 0 0.36/0.95 # Result found by new_bool_5 0.36/0.95 # Preprocessing class: HSLMSLSSLLLCHFA. 0.36/0.95 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.36/0.95 # Starting ehoh_best5 with 180s (1) cores 0.36/0.95 # Starting almost_fo_3_lam with 180s (1) cores 0.36/0.95 # Starting new_bool_5 with 180s (1) cores 0.36/0.95 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.36/0.95 # Search class: HGHSM-FSLM32-MHFMMSBN 0.36/0.95 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 0.36/0.95 # Starting ho_unfolding_8 with 33s (1) cores 0.36/0.95 # ho_unfolding_8 with pid 7153 completed with status 0 0.36/0.95 # Result found by ho_unfolding_8 0.36/0.95 # Preprocessing class: HSLMSLSSLLLCHFA. 0.36/0.95 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.36/0.95 # Starting ehoh_best5 with 180s (1) cores 0.36/0.95 # Starting almost_fo_3_lam with 180s (1) cores 0.36/0.95 # Starting new_bool_5 with 180s (1) cores 0.36/0.95 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.36/0.95 # Search class: HGHSM-FSLM32-MHFMMSBN 0.36/0.95 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 0.36/0.95 # Starting ho_unfolding_8 with 33s (1) cores 0.36/0.95 # Preprocessing time : 0.048 s 0.36/0.95 # Presaturation interreduction done 0.36/0.95 0.36/0.95 # Proof found! 0.36/0.95 # SZS status Theorem 0.36/0.95 # SZS output start CNFRefutation 0.36/0.95 thf(decl_22, type, in: $i > $i > $o). 0.36/0.95 thf(decl_23, type, exu: ($i > $o) > $o). 0.36/0.95 thf(decl_24, type, setextAx: $o). 0.36/0.95 thf(decl_25, type, emptyset: $i). 0.36/0.95 thf(decl_26, type, emptysetAx: $o). 0.36/0.95 thf(decl_27, type, setadjoin: $i > $i > $i). 0.36/0.95 thf(decl_28, type, setadjoinAx: $o). 0.36/0.95 thf(decl_29, type, powerset: $i > $i). 0.36/0.95 thf(decl_30, type, powersetAx: $o). 0.36/0.95 thf(decl_31, type, setunion: $i > $i). 0.36/0.95 thf(decl_32, type, setunionAx: $o). 0.36/0.95 thf(decl_33, type, omega: $i). 0.36/0.95 thf(decl_34, type, omega0Ax: $o). 0.36/0.95 thf(decl_35, type, omegaSAx: $o). 0.36/0.95 thf(decl_36, type, omegaIndAx: $o). 0.36/0.95 thf(decl_37, type, replAx: $o). 0.36/0.95 thf(decl_38, type, foundationAx: $o). 0.36/0.95 thf(decl_39, type, wellorderingAx: $o). 0.36/0.95 thf(decl_40, type, descr: ($i > $o) > $i). 0.36/0.95 thf(decl_41, type, descrp: $o). 0.36/0.95 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_43, type, dsetconstrI: $o). 0.36/0.95 thf(decl_44, type, dsetconstrEL: $o). 0.36/0.95 thf(decl_45, type, dsetconstrER: $o). 0.36/0.95 thf(decl_46, type, exuE1: $o). 0.36/0.95 thf(decl_47, type, prop2set: $o > $i). 0.36/0.95 thf(decl_48, type, prop2setE: $o). 0.36/0.95 thf(decl_49, type, emptysetE: $o). 0.36/0.95 thf(decl_50, type, emptysetimpfalse: $o). 0.36/0.95 thf(decl_51, type, notinemptyset: $o). 0.36/0.95 thf(decl_52, type, exuE3e: $o). 0.36/0.95 thf(decl_53, type, setext: $o). 0.36/0.95 thf(decl_54, type, emptyI: $o). 0.36/0.95 thf(decl_55, type, noeltsimpempty: $o). 0.36/0.95 thf(decl_56, type, setbeta: $o). 0.36/0.95 thf(decl_57, type, nonempty: $i > $o). 0.36/0.95 thf(decl_58, type, nonemptyE1: $o). 0.36/0.95 thf(decl_59, type, nonemptyI: $o). 0.36/0.95 thf(decl_60, type, nonemptyI1: $o). 0.36/0.95 thf(decl_61, type, setadjoinIL: $o). 0.36/0.95 thf(decl_62, type, emptyinunitempty: $o). 0.36/0.95 thf(decl_63, type, setadjoinIR: $o). 0.36/0.95 thf(decl_64, type, setadjoinE: $o). 0.36/0.95 thf(decl_65, type, setadjoinOr: $o). 0.36/0.95 thf(decl_66, type, setoftrueEq: $o). 0.36/0.95 thf(decl_67, type, powersetI: $o). 0.36/0.95 thf(decl_68, type, emptyinPowerset: $o). 0.36/0.95 thf(decl_69, type, emptyInPowerset: $o). 0.36/0.95 thf(decl_70, type, powersetE: $o). 0.36/0.95 thf(decl_71, type, setunionI: $o). 0.36/0.95 thf(decl_72, type, setunionE: $o). 0.36/0.95 thf(decl_73, type, subPowSU: $o). 0.36/0.95 thf(decl_74, type, exuE2: $o). 0.36/0.95 thf(decl_75, type, nonemptyImpWitness: $o). 0.36/0.95 thf(decl_76, type, uniqinunit: $o). 0.36/0.95 thf(decl_77, type, notinsingleton: $o). 0.36/0.95 thf(decl_78, type, eqinunit: $o). 0.36/0.95 thf(decl_79, type, singletonsswitch: $o). 0.36/0.95 thf(decl_80, type, upairsetE: $o). 0.36/0.95 thf(decl_81, type, upairsetIL: $o). 0.36/0.95 thf(decl_82, type, upairsetIR: $o). 0.36/0.95 thf(decl_83, type, emptyE1: $o). 0.36/0.95 thf(decl_84, type, vacuousDall: $o). 0.36/0.95 thf(decl_85, type, quantDeMorgan1: $o). 0.36/0.95 thf(decl_86, type, quantDeMorgan2: $o). 0.36/0.95 thf(decl_87, type, quantDeMorgan3: $o). 0.36/0.95 thf(decl_88, type, quantDeMorgan4: $o). 0.36/0.95 thf(decl_89, type, prop2setI: $o). 0.36/0.95 thf(decl_91, type, prop2set2propI: $o). 0.36/0.95 thf(decl_92, type, notdexE: $o). 0.36/0.95 thf(decl_93, type, notdallE: $o). 0.36/0.95 thf(decl_94, type, exuI1: $o). 0.36/0.95 thf(decl_95, type, exuI3: $o). 0.36/0.95 thf(decl_96, type, exuI2: $o). 0.36/0.95 thf(decl_97, type, inCongP: $o). 0.36/0.95 thf(decl_98, type, in__Cong: $o). 0.36/0.95 thf(decl_99, type, exuE3u: $o). 0.36/0.95 thf(decl_100, type, exu__Cong: $o). 0.36/0.95 thf(decl_101, type, emptyset__Cong: $o). 0.36/0.95 thf(decl_102, type, setadjoin__Cong: $o). 0.36/0.95 thf(decl_103, type, powerset__Cong: $o). 0.36/0.95 thf(decl_104, type, setunion__Cong: $o). 0.36/0.95 thf(decl_105, type, omega__Cong: $o). 0.36/0.95 thf(decl_106, type, exuEu: $o). 0.36/0.95 thf(decl_107, type, descr__Cong: $o). 0.36/0.95 thf(decl_108, type, dsetconstr__Cong: $o). 0.36/0.95 thf(decl_109, type, subset: $i > $i > $o). 0.36/0.95 thf(decl_112, type, subsetI1: $o). 0.36/0.95 thf(decl_113, type, eqimpsubset2: $o). 0.36/0.95 thf(decl_114, type, eqimpsubset1: $o). 0.36/0.95 thf(decl_115, type, subsetI2: $o). 0.36/0.95 thf(decl_116, type, emptysetsubset: $o). 0.36/0.95 thf(decl_117, type, subsetE: $o). 0.36/0.95 thf(decl_118, type, subsetE2: $o). 0.36/0.95 thf(decl_119, type, notsubsetI: $o). 0.36/0.95 thf(decl_120, type, notequalI1: $o). 0.36/0.95 thf(decl_121, type, notequalI2: $o). 0.36/0.95 thf(decl_122, type, subsetRefl: $o). 0.36/0.95 thf(decl_123, type, subsetTrans: $o). 0.36/0.95 thf(decl_124, type, setadjoinSub: $o). 0.36/0.95 thf(decl_125, type, setadjoinSub2: $o). 0.36/0.95 thf(decl_126, type, subset2powerset: $o). 0.36/0.95 thf(decl_127, type, setextsub: $o). 0.36/0.95 thf(decl_128, type, subsetemptysetimpeq: $o). 0.36/0.95 thf(decl_129, type, powersetI1: $o). 0.36/0.95 thf(decl_130, type, powersetE1: $o). 0.36/0.95 thf(decl_131, type, inPowerset: $o). 0.36/0.95 thf(decl_132, type, powersetsubset: $o). 0.36/0.95 thf(decl_133, type, sepInPowerset: $o). 0.36/0.95 thf(decl_134, type, sepSubset: $o). 0.36/0.95 thf(decl_135, type, binunion: $i > $i > $i). 0.36/0.95 thf(decl_136, type, binunionIL: $o). 0.36/0.95 thf(decl_137, type, upairset2IR: $o). 0.36/0.95 thf(decl_138, type, binunionIR: $o). 0.36/0.95 thf(decl_139, type, binunionEcases: $o). 0.36/0.95 thf(decl_140, type, binunionE: $o). 0.36/0.95 thf(decl_141, type, binunionLsub: $o). 0.36/0.95 thf(decl_142, type, binunionRsub: $o). 0.36/0.95 thf(decl_143, type, binintersect: $i > $i > $i). 0.36/0.95 thf(decl_144, type, binintersectI: $o). 0.36/0.95 thf(decl_145, type, binintersectSubset5: $o). 0.36/0.95 thf(decl_146, type, binintersectEL: $o). 0.36/0.95 thf(decl_147, type, binintersectLsub: $o). 0.36/0.95 thf(decl_148, type, binintersectSubset2: $o). 0.36/0.95 thf(decl_149, type, binintersectSubset3: $o). 0.36/0.95 thf(decl_150, type, binintersectER: $o). 0.36/0.95 thf(decl_151, type, disjointsetsI1: $o). 0.36/0.95 thf(decl_152, type, binintersectRsub: $o). 0.36/0.95 thf(decl_153, type, binintersectSubset4: $o). 0.36/0.95 thf(decl_154, type, binintersectSubset1: $o). 0.36/0.95 thf(decl_155, type, bs114d: $o). 0.36/0.95 thf(decl_157, type, setminus: $i > $i > $i). 0.36/0.95 thf(decl_158, type, setminusI: $o). 0.36/0.95 thf(decl_159, type, setminusEL: $o). 0.36/0.95 thf(decl_160, type, setminusER: $o). 0.36/0.95 thf(decl_161, type, setminusSubset2: $o). 0.36/0.95 thf(decl_162, type, setminusERneg: $o). 0.36/0.95 thf(decl_163, type, setminusELneg: $o). 0.36/0.95 thf(decl_164, type, setminusILneg: $o). 0.36/0.95 thf(decl_165, type, setminusIRneg: $o). 0.36/0.95 thf(decl_166, type, setminusLsub: $o). 0.36/0.95 thf(decl_167, type, setminusSubset1: $o). 0.36/0.95 thf(decl_168, type, symdiff: $i > $i > $i). 0.36/0.95 thf(decl_169, type, symdiffE: $o). 0.36/0.95 thf(decl_170, type, symdiffI1: $o). 0.36/0.95 thf(decl_171, type, symdiffI2: $o). 0.36/0.95 thf(decl_172, type, symdiffIneg1: $o). 0.36/0.95 thf(decl_173, type, symdiffIneg2: $o). 0.36/0.95 thf(decl_174, type, iskpair: $i > $o). 0.36/0.95 thf(decl_175, type, secondinupair: $o). 0.36/0.95 thf(decl_176, type, setukpairIL: $o). 0.36/0.95 thf(decl_177, type, setukpairIR: $o). 0.36/0.95 thf(decl_178, type, kpairiskpair: $o). 0.36/0.95 thf(decl_179, type, kpair: $i > $i > $i). 0.36/0.95 thf(decl_180, type, kpairp: $o). 0.36/0.95 thf(decl_181, type, cartprod: $i > $i > $i). 0.36/0.95 thf(decl_182, type, singletonsubset: $o). 0.36/0.95 thf(decl_183, type, singletoninpowerset: $o). 0.36/0.95 thf(decl_184, type, singletoninpowunion: $o). 0.36/0.95 thf(decl_185, type, upairset2E: $o). 0.36/0.95 thf(decl_186, type, upairsubunion: $o). 0.36/0.95 thf(decl_187, type, upairinpowunion: $o). 0.36/0.95 thf(decl_188, type, ubforcartprodlem1: $o). 0.36/0.95 thf(decl_189, type, ubforcartprodlem2: $o). 0.36/0.95 thf(decl_190, type, ubforcartprodlem3: $o). 0.36/0.95 thf(decl_191, type, cartprodpairin: $o). 0.36/0.95 thf(decl_192, type, cartprodmempair1: $o). 0.36/0.95 thf(decl_193, type, cartprodmempair: $o). 0.36/0.95 thf(decl_194, type, setunionE2: $o). 0.36/0.95 thf(decl_195, type, setunionsingleton1: $o). 0.36/0.95 thf(decl_196, type, setunionsingleton2: $o). 0.36/0.95 thf(decl_197, type, setunionsingleton: $o). 0.36/0.95 thf(decl_198, type, singleton: $i > $o). 0.36/0.95 thf(decl_199, type, singletonprop: $o). 0.36/0.95 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 0.36/0.95 thf(decl_201, type, ex1E1: $o). 0.36/0.95 thf(decl_202, type, ex1I: $o). 0.36/0.95 thf(decl_203, type, ex1I2: $o). 0.36/0.95 thf(decl_204, type, singletonsuniq: $o). 0.36/0.95 thf(decl_209, type, setukpairinjL1: $o). 0.36/0.95 thf(decl_210, type, kfstsingleton: $o). 0.36/0.95 thf(decl_211, type, theprop: $o). 0.36/0.95 thf(decl_212, type, kfst: $i > $i). 0.36/0.95 thf(decl_213, type, kfstpairEq: $o). 0.36/0.95 thf(decl_214, type, cartprodfstin: $o). 0.36/0.95 thf(decl_215, type, setukpairinjL2: $o). 0.36/0.95 thf(decl_216, type, setukpairinjL: $o). 0.36/0.95 thf(decl_217, type, setukpairinjR11: $o). 0.36/0.95 thf(decl_218, type, setukpairinjR12: $o). 0.36/0.95 thf(decl_219, type, setukpairinjR1: $o). 0.36/0.95 thf(decl_220, type, upairequniteq: $o). 0.36/0.95 thf(decl_221, type, setukpairinjR2: $o). 0.36/0.95 thf(decl_222, type, setukpairinjR: $o). 0.36/0.95 thf(decl_223, type, ksndsingleton: $o). 0.36/0.95 thf(decl_224, type, ksnd: $i > $i). 0.36/0.95 thf(decl_225, type, ksndpairEq: $o). 0.36/0.95 thf(decl_226, type, kpairsurjEq: $o). 0.36/0.95 thf(decl_227, type, cartprodsndin: $o). 0.36/0.95 thf(decl_228, type, cartprodpairmemEL: $o). 0.36/0.95 thf(decl_229, type, cartprodpairmemER: $o). 0.36/0.95 thf(decl_230, type, cartprodmempaircEq: $o). 0.36/0.95 thf(decl_231, type, cartprodfstpairEq: $o). 0.36/0.95 thf(decl_232, type, cartprodsndpairEq: $o). 0.36/0.95 thf(decl_233, type, cartprodpairsurjEq: $o). 0.36/0.95 thf(decl_234, type, breln: $i > $i > $i > $o). 0.36/0.95 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.36/0.95 thf(decl_236, type, dpsetconstrI: $o). 0.36/0.95 thf(decl_237, type, dpsetconstrSub: $o). 0.36/0.95 thf(decl_238, type, setOfPairsIsBReln: $o). 0.36/0.95 thf(decl_239, type, dpsetconstrERa: $o). 0.36/0.95 thf(decl_240, type, dpsetconstrEL1: $o). 0.36/0.95 thf(decl_241, type, dpsetconstrEL2: $o). 0.36/0.95 thf(decl_242, type, dpsetconstrER: $o). 0.36/0.95 thf(decl_243, type, func: $i > $i > $i > $o). 0.36/0.95 thf(decl_244, type, funcSet: $i > $i > $i). 0.36/0.95 thf(decl_245, type, funcImageSingleton: $o). 0.36/0.95 thf(decl_246, type, apProp: $o). 0.36/0.95 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 0.36/0.95 thf(decl_248, type, app: $o). 0.36/0.95 thf(decl_249, type, infuncsetfunc: $o). 0.36/0.95 thf(decl_250, type, ap2p: $o). 0.36/0.95 thf(decl_251, type, funcinfuncset: $o). 0.36/0.95 thf(decl_252, type, lamProp: $o). 0.36/0.95 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 0.36/0.95 thf(decl_254, type, lamp: $o). 0.36/0.95 thf(decl_255, type, lam2p: $o). 0.36/0.95 thf(decl_256, type, brelnall1: $o). 0.36/0.95 thf(decl_257, type, brelnall2: $o). 0.36/0.95 thf(decl_258, type, ex1E2: $o). 0.36/0.95 thf(decl_259, type, funcGraphProp1: $o). 0.36/0.95 thf(decl_260, type, funcGraphProp3: $o). 0.36/0.95 thf(decl_261, type, funcGraphProp2: $o). 0.36/0.95 thf(decl_262, type, funcextLem: $o). 0.36/0.95 thf(decl_263, type, funcGraphProp4: $o). 0.36/0.95 thf(decl_264, type, subbreln: $o). 0.36/0.95 thf(decl_265, type, eqbreln: $o). 0.36/0.95 thf(decl_266, type, funcext: $o). 0.36/0.95 thf(decl_267, type, funcext2: $o). 0.36/0.95 thf(decl_268, type, ap2apEq1: $o). 0.36/0.95 thf(decl_269, type, ap2apEq2: $o). 0.36/0.95 thf(decl_270, type, beta1: $o). 0.36/0.95 thf(decl_271, type, eta1: $o). 0.36/0.95 thf(decl_272, type, lam2lamEq: $o). 0.36/0.95 thf(decl_273, type, beta2: $o). 0.36/0.95 thf(decl_274, type, eta2: $o). 0.36/0.95 thf(decl_275, type, iffalseProp1: $o). 0.36/0.95 thf(decl_276, type, iffalseProp2: $o). 0.36/0.95 thf(decl_277, type, iftrueProp1: $o). 0.36/0.95 thf(decl_278, type, iftrueProp2: $o). 0.36/0.95 thf(decl_279, type, ifSingleton: $o). 0.36/0.95 thf(decl_280, type, if: $i > $o > $i > $i > $i). 0.36/0.95 thf(decl_281, type, ifp: $o). 0.36/0.95 thf(decl_282, type, theeq: $o). 0.36/0.95 thf(decl_283, type, iftrue: $o). 0.36/0.95 thf(decl_284, type, iffalse: $o). 0.36/0.95 thf(decl_285, type, iftrueorfalse: $o). 0.36/0.95 thf(decl_286, type, binintersectT_lem: $o). 0.36/0.95 thf(decl_287, type, binunionT_lem: $o). 0.36/0.95 thf(decl_288, type, powersetT_lem: $o). 0.36/0.95 thf(decl_289, type, setminusT_lem: $o). 0.36/0.95 thf(decl_290, type, complementT_lem: $o). 0.36/0.95 thf(decl_291, type, setextT: $o). 0.36/0.95 thf(decl_292, type, subsetTI: $o). 0.36/0.95 thf(decl_293, type, powersetTI1: $o). 0.36/0.95 thf(decl_294, type, powersetTE1: $o). 0.36/0.95 thf(decl_295, type, complementTI1: $o). 0.36/0.95 thf(decl_296, type, complementTE1: $o). 0.36/0.95 thf(decl_297, type, binintersectTELcontra: $o). 0.36/0.95 thf(decl_298, type, binintersectTERcontra: $o). 0.36/0.95 thf(decl_299, type, contrasubsetT: $o). 0.36/0.95 thf(decl_300, type, contrasubsetT1: $o). 0.36/0.95 thf(decl_301, type, contrasubsetT2: $o). 0.36/0.95 thf(decl_302, type, contrasubsetT3: $o). 0.36/0.95 thf(decl_303, type, doubleComplementI1: $o). 0.36/0.95 thf(decl_304, type, doubleComplementE1: $o). 0.36/0.95 thf(decl_305, type, doubleComplementSub1: $o). 0.36/0.95 thf(decl_306, type, doubleComplementSub2: $o). 0.36/0.95 thf(decl_307, type, doubleComplementEq: $o). 0.36/0.95 thf(decl_308, type, complementTnotintersectT: $o). 0.36/0.95 thf(decl_309, type, complementImpComplementIntersect: $o). 0.36/0.95 thf(decl_310, type, complementSubsetComplementIntersect: $o). 0.36/0.95 thf(decl_311, type, complementInPowersetComplementIntersect: $o). 0.36/0.95 thf(decl_312, type, contraSubsetComplement: $o). 0.36/0.95 thf(decl_313, type, complementTcontraSubset: $o). 0.36/0.95 thf(decl_314, type, binunionTILcontra: $o). 0.36/0.95 thf(decl_315, type, binunionTIRcontra: $o). 0.36/0.95 thf(decl_316, type, inIntersectImpInUnion: $o). 0.36/0.95 thf(decl_317, type, inIntersectImpInUnion2: $o). 0.36/0.95 thf(decl_318, type, epred1_0: $o). 0.36/0.95 thf(decl_319, type, esk1_2: $i > $i > $i). 0.36/0.95 thf(decl_320, type, esk2_2: $i > $i > $i). 0.36/0.95 thf(decl_321, type, esk3_2: $i > $i > $i). 0.36/0.95 thf(decl_322, type, esk4_1: $i > $i). 0.36/0.95 thf(decl_323, type, esk5_2: ($i > $i > $o) > $i > $i). 0.36/0.95 thf(decl_324, type, esk6_2: ($i > $i > $o) > $i > $i). 0.36/0.95 thf(decl_325, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 0.36/0.95 thf(decl_326, type, esk8_1: $i > $i). 0.36/0.95 thf(decl_327, type, esk9_1: ($i > $o) > $i). 0.36/0.95 thf(decl_328, type, esk10_1: ($i > $o) > $i). 0.36/0.95 thf(decl_329, type, esk11_2: $i > $i > $i). 0.36/0.95 thf(decl_330, type, esk12_2: $i > $i > $i). 0.36/0.95 thf(decl_331, type, esk13_1: $i > $i). 0.36/0.95 thf(decl_332, type, esk14_1: $i > $i). 0.36/0.95 thf(decl_333, type, esk15_1: $i > $i). 0.36/0.95 thf(decl_334, type, esk16_2: $i > $i > $i). 0.36/0.95 thf(decl_335, type, esk17_3: $i > $i > $o > $i). 0.36/0.95 thf(decl_336, type, esk18_1: ($i > $o) > $i). 0.36/0.95 thf(decl_337, type, esk19_1: $i > $i). 0.36/0.95 thf(decl_338, type, esk20_2: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_339, type, esk21_2: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_340, type, esk22_2: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_341, type, esk23_2: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_342, type, esk24_2: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_343, type, esk25_2: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_344, type, esk26_2: ($i > $o) > $i > $i). 0.36/0.95 thf(decl_345, type, esk27_1: ($i > $o) > $i). 0.36/0.95 thf(decl_346, type, esk28_1: ($i > $o) > $i). 0.36/0.95 thf(decl_347, type, esk29_2: ($i > $o) > $i > $i). 0.36/0.95 thf(decl_348, type, esk30_2: ($i > $o) > ($i > $o) > $i). 0.36/0.95 thf(decl_349, type, esk31_2: ($i > $o) > ($i > $o) > $i). 0.36/0.95 thf(decl_350, type, esk32_2: ($i > $o) > ($i > $o) > $i). 0.36/0.95 thf(decl_351, type, esk33_2: ($i > $o) > ($i > $o) > $i). 0.36/0.95 thf(decl_352, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.36/0.95 thf(decl_353, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.36/0.95 thf(decl_354, type, esk36_2: $i > $i > $i). 0.36/0.95 thf(decl_355, type, esk37_2: $i > $i > $i). 0.36/0.95 thf(decl_356, type, esk38_2: $i > $i > $i). 0.36/0.95 thf(decl_357, type, esk39_3: $i > $i > $i > $i). 0.36/0.95 thf(decl_358, type, esk40_3: $i > $i > $i > $i). 0.36/0.95 thf(decl_359, type, esk41_2: $i > $i > $i). 0.36/0.95 thf(decl_360, type, esk42_2: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_361, type, esk43_2: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_362, type, esk44_2: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_363, type, esk45_3: $i > ($i > $o) > $i > $i). 0.36/0.95 thf(decl_364, type, esk46_2: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_365, type, esk47_2: $i > ($i > $o) > $i). 0.36/0.95 thf(decl_366, type, esk48_3: $i > $i > ($i > $i) > $i). 0.36/0.95 thf(decl_367, type, esk49_3: $i > $i > ($i > $i) > $i). 0.36/0.95 thf(decl_368, type, esk50_3: $i > $i > ($i > $i) > $i). 0.36/0.95 thf(decl_369, type, esk51_4: $i > $i > $i > ($i > $o) > $i). 0.36/0.95 thf(decl_370, type, esk52_4: $i > $i > $i > ($i > $o) > $i). 0.36/0.95 thf(decl_371, type, esk53_4: $i > $i > $i > ($i > $o) > $i). 0.36/0.95 thf(decl_372, type, esk54_4: $i > $i > $i > ($i > $o) > $i). 0.36/0.95 thf(decl_373, type, esk55_4: $i > $i > $i > $i > $i). 0.36/0.95 thf(decl_374, type, esk56_4: $i > $i > $i > $i > $i). 0.36/0.95 thf(decl_375, type, esk57_4: $i > $i > $i > $i > $i). 0.36/0.95 thf(decl_376, type, esk58_4: $i > $i > $i > $i > $i). 0.36/0.95 thf(decl_377, type, esk59_4: $i > $i > $i > $i > $i). 0.36/0.95 thf(decl_378, type, esk60_4: $i > $i > $i > $i > $i). 0.36/0.95 thf(decl_379, type, esk61_4: $i > $i > $i > $i > $i). 0.36/0.95 thf(decl_380, type, esk62_4: $i > $i > $i > $i > $i). 0.36/0.95 thf(decl_381, type, esk63_4: $i > $i > $i > $i > $i). 0.36/0.95 thf(decl_382, type, esk64_3: $i > $i > ($i > $i) > $i). 0.36/0.95 thf(decl_383, type, esk65_3: $i > $i > ($i > $i) > $i). 0.36/0.95 thf(decl_384, type, esk66_3: $i > $i > ($i > $i) > $i). 0.36/0.95 thf(decl_385, type, esk67_3: $i > $i > $i > $i). 0.36/0.95 thf(decl_386, type, esk68_3: $i > $i > $i > $i). 0.36/0.95 thf(decl_387, type, esk69_3: $i > $i > $i > $i). 0.36/0.95 thf(decl_388, type, esk70_3: $i > $i > $i > $i). 0.36/0.95 thf(decl_389, type, esk71_0: $i). 0.36/0.95 thf(decl_390, type, esk72_0: $i). 0.36/0.95 thf(decl_391, type, esk73_0: $i). 0.36/0.95 thf(decl_392, type, esk74_0: $i). 0.36/0.95 thf(decl_393, type, esk75_0: $i). 0.36/0.95 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', dsetconstr__Cong)). 0.36/0.95 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', descr__Cong)). 0.36/0.95 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', exuEu)). 0.36/0.95 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', exu__Cong)). 0.36/0.95 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', exuE3u)). 0.36/0.95 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', exuE2)). 0.36/0.95 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setoftrueEq)). 0.36/0.95 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', nonemptyI)). 0.36/0.95 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ex1E1)). 0.36/0.95 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', exuE1)). 0.36/0.95 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', descrp)). 0.36/0.95 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ex1I)). 0.36/0.95 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', replAx)). 0.36/0.95 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ex1I2)). 0.36/0.95 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', dpsetconstrI)). 0.36/0.95 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setOfPairsIsBReln)). 0.36/0.95 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', dpsetconstrERa)). 0.36/0.95 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', lamProp)). 0.36/0.95 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', lamp)). 0.36/0.95 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', lam2p)). 0.36/0.95 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', eta1)). 0.36/0.95 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', lam2lamEq)). 0.36/0.95 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', beta2)). 0.36/0.95 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', iffalseProp1)). 0.36/0.95 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', iffalseProp2)). 0.36/0.95 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', iftrueProp2)). 0.36/0.95 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ifSingleton)). 0.36/0.95 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', iftrueProp1)). 0.36/0.95 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', eta2)). 0.36/0.95 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', beta1)). 0.36/0.95 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ex1E2)). 0.36/0.95 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', apProp)). 0.36/0.95 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', funcImageSingleton)). 0.36/0.95 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', dpsetconstrER)). 0.36/0.95 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', dpsetconstrEL2)). 0.36/0.95 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', dpsetconstrEL1)). 0.36/0.95 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', dpsetconstrSub)). 0.36/0.95 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ksndsingleton)). 0.36/0.95 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', kfstsingleton)). 0.36/0.95 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', singletonprop)). 0.36/0.95 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', sepSubset)). 0.36/0.95 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', sepInPowerset)). 0.36/0.95 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', exuI2)). 0.36/0.95 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', exuI3)). 0.36/0.95 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', exuI1)). 0.36/0.95 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', emptyE1)). 0.36/0.95 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setbeta)). 0.36/0.95 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', exuE3e)). 0.36/0.95 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', dsetconstrER)). 0.36/0.95 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', dsetconstrEL)). 0.36/0.95 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', dsetconstrI)). 0.36/0.95 thf(inIntersectImpInIntersectUnions, conjecture, ((setextAx)=>((((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>(((((((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>(((prop2setE)=>((emptysetE)=>(((notinemptyset)=>((exuE3e)=>(((emptyI)=>(((setbeta)=>(((((setadjoinIL)=>((emptyinunitempty)=>(((setadjoinE)=>((((powersetI)=>((((powersetE)=>(((setunionE)=>((((((notinsingleton)=>((((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>(((((quantDeMorgan3)=>(((prop2setI)=>((((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((((((powerset__Cong)=>(((omega__Cong)=>((((((((subsetI2)=>((((((notequalI1)=>((notequalI2)=>((((setadjoinSub)=>((setadjoinSub2)=>(((setextsub)=>((subsetemptysetimpeq)=>(((powersetE1)=>((((sepInPowerset)=>(((binunionIL)=>((upairset2IR)=>((((((binunionRsub)=>((binintersectI)=>((((((binintersectSubset3)=>(((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>(((setminusER)=>((setminusSubset2)=>((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>(((symdiffE)=>(((symdiffI2)=>(((symdiffIneg2)=>(((setukpairIL)=>((setukpairIR)=>((((((singletoninpowunion)=>(((upairsubunion)=>(((ubforcartprodlem1)=>(((ubforcartprodlem3)=>(((cartprodmempair1)=>((cartprodmempair)=>((((setunionsingleton2)=>((setunionsingleton)=>(((ex1E1)=>((ex1I)=>((ex1I2)=>(((setukpairinjL1)=>((((((setukpairinjL2)=>((((setukpairinjR12)=>(((upairequniteq)=>((setukpairinjR2)=>(((((kpairsurjEq)=>((((cartprodpairmemER)=>(((cartprodfstpairEq)=>((cartprodsndpairEq)=>(((dpsetconstrI)=>(((setOfPairsIsBReln)=>((dpsetconstrERa)=>(((((((app)=>((((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>(((brelnall2)=>((((funcGraphProp3)=>((funcGraphProp2)=>(((funcGraphProp4)=>((((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>(((eta1)=>((lam2lamEq)=>((beta2)=>(((iffalseProp1)=>((iffalseProp2)=>(((iftrueProp2)=>((ifSingleton)=>(((((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>(((powersetT_lem)=>((((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>(((((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>(((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>(((complementSubsetComplementIntersect)=>(((((binunionTILcontra)=>(((inIntersectImpInUnion)=>(![X4:$i, X21:$i]:((![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:((![X2:$i]:((((in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49)))<=(in @ X2 @ (binintersect @ X21 @ X48)))<=(in @ X2 @ X4)))<=(in @ X49 @ (powerset @ X4))))))<=(in @ X21 @ (powerset @ X4))))<=(inIntersectImpInUnion2)))<=(binunionTIRcontra)))<=(complementTcontraSubset))<=(contraSubsetComplement))<=(complementInPowersetComplementIntersect)))<=(complementImpComplementIntersect))))))))<=(contrasubsetT3))))))<=(binintersectTELcontra))<=(complementTE1))<=(complementTI1))))))<=(complementT_lem))<=(setminusT_lem)))<=(binunionT_lem)))))<=(iftrue))<=(theeq))<=(ifp))))<=(iftrueProp1))))<=(eta2)))))<=(beta1))))))<=(eqbreln))<=(subbreln)))<=(funcextLem))))<=(funcGraphProp1))<=(ex1E2)))<=(brelnall1))))))<=(ap2p))<=(infuncsetfunc)))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER))<=(dpsetconstrEL2))<=(dpsetconstrEL1))))<=(dpsetconstrSub)))<=(cartprodpairsurjEq))))<=(cartprodmempaircEq)))<=(cartprodpairmemEL))<=(cartprodsndin)))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))))<=(setukpairinjR1)))<=(setukpairinjR11))<=(setukpairinjL)))<=(cartprodfstin))<=(kfstpairEq))<=(theprop))<=(kfstsingleton)))<=(singletonsuniq)))))<=(singletonprop))))<=(setunionsingleton1))<=(setunionE2))))<=(cartprodpairin)))<=(ubforcartprodlem2)))<=(upairinpowunion)))<=(upairset2E)))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))))<=(secondinupair)))<=(symdiffIneg1)))<=(symdiffI1)))<=(setminusSubset1)))))<=(setminusELneg)))))<=(setminusEL))))))))<=(binintersectER)))<=(binintersectSubset2))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))))<=(binunionLsub))<=(binunionE))<=(binunionEcases))<=(binunionIR))))<=(sepSubset)))<=(powersetsubset))<=(inPowerset)))<=(powersetI1))))<=(subset2powerset))))<=(subsetTrans))<=(subsetRefl))))<=(notsubsetI))<=(subsetE2))<=(subsetE))<=(emptysetsubset)))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))))))))<=(notdexE))<=(prop2set2propI)))<=(quantDeMorgan4)))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall))))))<=(singletonsswitch))<=(eqinunit)))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))<=(setunionI)))<=(emptyInPowerset))<=(emptyinPowerset)))<=(setoftrueEq))<=(setadjoinOr)))<=(setadjoinIR))))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1)))<=(noeltsimpempty)))<=(setext))))<=(emptysetimpfalse))))<=(exuE1)))))<=(descrp))<=(wellorderingAx))<=(foundationAx))<=(replAx))<=(omegaIndAx))))))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', inIntersectImpInIntersectUnions)). 0.36/0.95 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', uniqinunit)). 0.36/0.95 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', emptysetAx)). 0.36/0.95 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', subsetE2)). 0.36/0.95 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', subsetE)). 0.36/0.95 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', symdiffE)). 0.36/0.95 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', emptysetsubset)). 0.36/0.95 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', eqimpsubset1)). 0.36/0.95 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', eqimpsubset2)). 0.36/0.95 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', symdiffI2)). 0.36/0.95 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', subsetI1)). 0.36/0.95 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', symdiffIneg2)). 0.36/0.95 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setunion__Cong)). 0.36/0.95 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setukpairIL)). 0.36/0.95 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setadjoin__Cong)). 0.36/0.95 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', emptyset__Cong)). 0.36/0.95 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setukpairIR)). 0.36/0.95 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', notdexE)). 0.36/0.95 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setminusILneg)). 0.36/0.95 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', quantDeMorgan4)). 0.36/0.95 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', singletoninpowunion)). 0.36/0.95 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', quantDeMorgan2)). 0.36/0.95 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', quantDeMorgan1)). 0.36/0.95 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', upairsubunion)). 0.36/0.95 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', vacuousDall)). 0.36/0.95 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', singletonsswitch)). 0.36/0.95 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', eqinunit)). 0.36/0.95 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', cartprodfstpairEq)). 0.36/0.95 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ubforcartprodlem1)). 0.36/0.95 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', nonemptyImpWitness)). 0.36/0.95 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ubforcartprodlem3)). 0.36/0.95 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', subPowSU)). 0.36/0.95 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setunionI)). 0.36/0.95 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', emptyInPowerset)). 0.36/0.95 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', cartprodmempair1)). 0.36/0.95 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', emptyinPowerset)). 0.36/0.95 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', cartprodmempair)). 0.36/0.95 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setadjoinOr)). 0.36/0.95 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setadjoinIR)). 0.36/0.95 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', nonemptyI1)). 0.36/0.95 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setunionsingleton2)). 0.36/0.95 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', nonemptyE1)). 0.36/0.95 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setunionsingleton)). 0.36/0.95 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', noeltsimpempty)). 0.36/0.95 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setext)). 0.36/0.95 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', emptysetimpfalse)). 0.36/0.95 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', wellorderingAx)). 0.36/0.95 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', foundationAx)). 0.36/0.95 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', omegaIndAx)). 0.36/0.95 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setadjoinAx)). 0.36/0.95 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setminusIRneg)). 0.36/0.95 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setukpairinjL1)). 0.36/0.95 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setukpairinjL2)). 0.36/0.95 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setukpairinjR12)). 0.36/0.95 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', upairequniteq)). 0.36/0.95 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setukpairinjR2)). 0.36/0.95 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', kpairsurjEq)). 0.36/0.95 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', cartprodpairmemER)). 0.36/0.95 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', powersetTE1)). 0.36/0.95 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectTERcontra)). 0.36/0.95 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', cartprodsndpairEq)). 0.36/0.95 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', app)). 0.36/0.95 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', funcinfuncset)). 0.36/0.95 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setminusLsub)). 0.36/0.95 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', brelnall2)). 0.36/0.95 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', funcGraphProp3)). 0.36/0.95 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', funcGraphProp2)). 0.36/0.95 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', funcGraphProp4)). 0.36/0.95 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', funcext)). 0.36/0.95 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', funcext2)). 0.36/0.95 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ap2apEq1)). 0.36/0.95 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ap2apEq2)). 0.36/0.95 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', iffalse)). 0.36/0.95 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', iftrueorfalse)). 0.36/0.95 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectT_lem)). 0.36/0.95 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', powersetT_lem)). 0.36/0.95 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setextT)). 0.36/0.95 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', subsetTI)). 0.36/0.95 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', powersetTI1)). 0.36/0.95 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', contrasubsetT)). 0.36/0.95 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', contrasubsetT1)). 0.36/0.95 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', contrasubsetT2)). 0.36/0.95 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', doubleComplementI1)). 0.36/0.95 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', doubleComplementE1)). 0.36/0.95 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', doubleComplementSub1)). 0.36/0.95 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', doubleComplementSub2)). 0.36/0.95 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', doubleComplementEq)). 0.36/0.95 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', complementTnotintersectT)). 0.36/0.95 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', complementSubsetComplementIntersect)). 0.36/0.95 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binunionTILcontra)). 0.36/0.95 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', inIntersectImpInUnion)). 0.36/0.95 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', inIntersectImpInUnion2)). 0.36/0.95 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binunionTIRcontra)). 0.36/0.95 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', complementTcontraSubset)). 0.36/0.95 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', contraSubsetComplement)). 0.36/0.95 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', complementInPowersetComplementIntersect)). 0.36/0.95 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', complementImpComplementIntersect)). 0.36/0.95 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', contrasubsetT3)). 0.36/0.95 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectTELcontra)). 0.36/0.95 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', complementTE1)). 0.36/0.95 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', complementTI1)). 0.36/0.95 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', complementT_lem)). 0.36/0.95 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setminusT_lem)). 0.36/0.95 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binunionT_lem)). 0.36/0.95 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', iftrue)). 0.36/0.95 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', theeq)). 0.36/0.95 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ifp)). 0.36/0.95 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', eqbreln)). 0.36/0.95 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', subbreln)). 0.36/0.95 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', funcextLem)). 0.36/0.95 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', funcGraphProp1)). 0.36/0.95 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', brelnall1)). 0.36/0.95 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ap2p)). 0.36/0.95 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', infuncsetfunc)). 0.36/0.95 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', cartprodpairsurjEq)). 0.36/0.95 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', cartprodmempaircEq)). 0.36/0.95 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', cartprodpairmemEL)). 0.36/0.95 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', cartprodsndin)). 0.36/0.95 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ksndpairEq)). 0.36/0.95 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setukpairinjR)). 0.36/0.95 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setukpairinjR1)). 0.36/0.95 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setukpairinjR11)). 0.36/0.95 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setukpairinjL)). 0.36/0.95 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', cartprodfstin)). 0.36/0.95 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', kfstpairEq)). 0.36/0.95 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', theprop)). 0.36/0.95 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', singletonsuniq)). 0.36/0.95 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setunionsingleton1)). 0.36/0.95 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setunionE2)). 0.36/0.95 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', cartprodpairin)). 0.36/0.95 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', ubforcartprodlem2)). 0.36/0.95 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', upairinpowunion)). 0.36/0.95 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', upairset2E)). 0.36/0.95 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', singletoninpowerset)). 0.36/0.95 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', singletonsubset)). 0.36/0.95 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', kpairp)). 0.36/0.95 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', kpairiskpair)). 0.36/0.95 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', secondinupair)). 0.36/0.95 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', symdiffIneg1)). 0.36/0.95 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', symdiffI1)). 0.36/0.95 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setminusSubset1)). 0.36/0.95 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setminusELneg)). 0.36/0.95 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setminusEL)). 0.36/0.95 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectER)). 0.36/0.95 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectSubset2)). 0.36/0.95 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectLsub)). 0.36/0.95 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectEL)). 0.36/0.95 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectSubset5)). 0.36/0.95 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binunionLsub)). 0.36/0.95 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binunionE)). 0.36/0.95 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binunionEcases)). 0.36/0.95 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binunionIR)). 0.36/0.95 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', powersetsubset)). 0.36/0.95 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', inPowerset)). 0.36/0.95 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', powersetI1)). 0.36/0.95 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', subset2powerset)). 0.36/0.95 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', subsetTrans)). 0.36/0.95 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', subsetRefl)). 0.36/0.95 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', notsubsetI)). 0.36/0.95 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setminusERneg)). 0.36/0.95 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setminusSubset2)). 0.36/0.95 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setminusER)). 0.36/0.95 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setminusI)). 0.36/0.95 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', bs114d)). 0.36/0.95 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectSubset1)). 0.36/0.95 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectSubset4)). 0.36/0.95 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectRsub)). 0.36/0.95 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', disjointsetsI1)). 0.36/0.95 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectSubset3)). 0.36/0.95 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binintersectI)). 0.36/0.95 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binunionRsub)). 0.36/0.95 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', upairset2IR)). 0.36/0.95 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', binunionIL)). 0.36/0.95 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', powersetE1)). 0.36/0.95 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', subsetemptysetimpeq)). 0.36/0.95 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setextsub)). 0.36/0.95 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setadjoinSub2)). 0.36/0.95 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setadjoinSub)). 0.36/0.95 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', notequalI2)). 0.36/0.95 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', notequalI1)). 0.36/0.95 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', subsetI2)). 0.36/0.95 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', omega__Cong)). 0.36/0.95 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', powerset__Cong)). 0.36/0.95 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', in__Cong)). 0.36/0.95 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', inCongP)). 0.36/0.95 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', notdallE)). 0.36/0.95 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', prop2setI)). 0.36/0.95 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', quantDeMorgan3)). 0.36/0.95 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', upairsetIR)). 0.36/0.95 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', upairsetIL)). 0.36/0.95 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', upairsetE)). 0.36/0.95 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', notinsingleton)). 0.36/0.95 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setunionE)). 0.36/0.95 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', powersetE)). 0.36/0.95 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', powersetI)). 0.36/0.95 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setadjoinE)). 0.36/0.95 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', emptyinunitempty)). 0.36/0.95 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setadjoinIL)). 0.36/0.95 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', emptyI)). 0.36/0.95 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', notinemptyset)). 0.36/0.95 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', emptysetE)). 0.36/0.95 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', prop2setE)). 0.36/0.95 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', omegaSAx)). 0.36/0.95 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', omega0Ax)). 0.36/0.95 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setunionAx)). 0.36/0.95 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', powersetAx)). 0.36/0.95 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.WkjC4FAFUI/E---3.1_6980.p', setextAx)). 0.36/0.95 thf(c_0_258, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.36/0.95 thf(c_0_259, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.36/0.95 thf(c_0_260, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.36/0.95 thf(c_0_261, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.36/0.95 thf(c_0_262, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.36/0.95 thf(c_0_263, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.36/0.95 thf(c_0_264, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.36/0.95 thf(c_0_265, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.36/0.95 thf(c_0_266, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.36/0.95 thf(c_0_267, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.36/0.95 thf(c_0_268, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.36/0.95 thf(c_0_269, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 0.36/0.95 thf(c_0_270, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.36/0.95 thf(c_0_271, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.36/0.95 thf(c_0_272, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 0.36/0.95 thf(c_0_273, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 0.36/0.95 thf(c_0_274, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 0.36/0.95 thf(c_0_275, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 0.36/0.95 thf(c_0_276, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 0.36/0.95 thf(c_0_277, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 0.36/0.95 thf(c_0_278, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 0.36/0.95 thf(c_0_279, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 0.36/0.95 thf(c_0_280, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 0.36/0.95 thf(c_0_281, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 0.36/0.95 thf(c_0_282, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 0.36/0.95 thf(c_0_283, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 0.36/0.95 thf(c_0_284, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 0.36/0.95 thf(c_0_285, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 0.36/0.95 thf(c_0_286, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 0.36/0.95 thf(c_0_287, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 0.36/0.95 thf(c_0_288, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 0.36/0.95 thf(c_0_289, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 0.36/0.95 thf(c_0_290, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 0.36/0.95 thf(c_0_291, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 0.36/0.95 thf(c_0_292, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 0.36/0.95 thf(c_0_293, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 0.36/0.95 thf(c_0_294, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 0.36/0.95 thf(c_0_295, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 0.36/0.95 thf(c_0_296, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 0.36/0.95 thf(c_0_297, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.36/0.95 thf(c_0_298, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.36/0.95 thf(c_0_299, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.36/0.95 thf(c_0_300, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.36/0.95 thf(c_0_301, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.36/0.95 thf(c_0_302, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.36/0.95 thf(c_0_303, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 0.36/0.95 thf(c_0_304, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.36/0.95 thf(c_0_305, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.36/0.95 thf(c_0_306, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.36/0.95 thf(c_0_307, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.36/0.95 thf(c_0_308, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.36/0.95 thf(c_0_309, plain, ((epred1_0)<=>![X1627:$i]:(?[X1628:$i]:((((![X1629:$i]:(((in @ X1629 @ X1628)=>![X1630:$i]:(((in @ X1630 @ X1629)=>(in @ X1630 @ X1627)))))&![X1631:$i, X1632:$i]:((((in @ X1631 @ X1627)&(in @ X1632 @ X1627))=>(![X1633:$i]:(((in @ X1633 @ X1628)=>((in @ X1631 @ X1633)<=>(in @ X1632 @ X1633))))=>((X1631)=(X1632))))))&![X1634:$i, X1635:$i]:((((in @ X1634 @ X1628)&(in @ X1635 @ X1628))=>(![X1636:$i]:(((in @ X1636 @ X1634)=>(in @ X1636 @ X1635)))|![X1637:$i]:(((in @ X1637 @ X1635)=>(in @ X1637 @ X1634)))))))&![X1638:$i]:(((![X1639:$i]:(((in @ X1639 @ X1638)=>(in @ X1639 @ X1627)))&?[X1640:$i]:((in @ X1640 @ X1638)))=>?[X1641:$i, X1642:$i]:(((((in @ X1641 @ X1628)&(in @ X1642 @ X1638))&~(?[X1643:$i]:(((in @ X1643 @ X1641)&(in @ X1643 @ X1638)))))&![X1644:$i]:(((in @ X1644 @ X1628)=>(![X1645:$i]:(((in @ X1645 @ X1644)=>(in @ X1645 @ X1641)))|(in @ X1642 @ X1644)))))))))))), introduced(definition)). 0.36/0.95 thf(c_0_310, negated_conjecture, ~((![X859:$i, X860:$i]:((![X861:$i]:(((in @ X861 @ X859)<=>(in @ X861 @ X860)))=>((X859)=(X860))))=>(![X1662:$i]:(~(in @ X1662 @ emptyset))=>(![X1659:$i, X1660:$i, X1661:$i]:(((in @ X1661 @ (setadjoin @ X1659 @ X1660))<=>(((X1661)=(X1659))|(in @ X1661 @ X1660))))=>(![X862:$i, X863:$i]:(((in @ X863 @ (powerset @ X862))<=>![X864:$i]:(((in @ X864 @ X863)=>(in @ X864 @ X862)))))=>(![X865:$i, X866:$i]:(((in @ X866 @ (setunion @ X865))<=>?[X867:$i]:(((in @ X866 @ X867)&(in @ X867 @ X865)))))=>((in @ emptyset @ omega)=>(![X868:$i]:(((in @ X868 @ omega)=>(in @ (setadjoin @ X868 @ X868) @ omega)))=>(![X1656:$i]:((((in @ emptyset @ X1656)&![X1657:$i]:((((in @ X1657 @ omega)&(in @ X1657 @ X1656))=>(in @ (setadjoin @ X1657 @ X1657) @ X1656))))=>![X1658:$i]:(((in @ X1658 @ omega)=>(in @ X1658 @ X1656)))))=>(![X1650:$i > $i > $o, X1651:$i]:((![X1652:$i]:(((in @ X1652 @ X1651)=>(exu @ (X1650 @ X1652))))=>?[X1653:$i]:(![X1654:$i]:(((in @ X1654 @ X1653)<=>?[X1655:$i]:(((in @ X1655 @ X1651)&(X1650 @ X1655 @ X1654))))))))=>(![X1646:$i]:((?[X1647:$i]:((in @ X1647 @ X1646))=>?[X1648:$i]:(((in @ X1648 @ X1646)&~(?[X1649:$i]:(((in @ X1649 @ X1648)&(in @ X1649 @ X1646))))))))=>((epred1_0)=>(![X1626:$i > $o]:(((exu @ X1626)=>(X1626 @ (descr @ (^[Z0/* 17 */:$i]:(X1626 @ Z0))))))=>(![X869:$i, X870:$i > $o, X871:$i]:(((in @ X871 @ X869)=>((X870 @ X871)=>(in @ X871 @ (dsetconstr @ X869 @ X870)))))=>(![X872:$i, X873:$i > $o, X874:$i]:(((in @ X874 @ (dsetconstr @ X872 @ X873))=>(in @ X874 @ X872)))=>(![X875:$i, X876:$i > $o, X877:$i]:(((in @ X877 @ (dsetconstr @ X875 @ X876))=>(X876 @ X877)))=>(![X1623:$i > $o]:(((exu @ X1623)=>?[X1624:$i]:(((X1623 @ X1624)&![X1625:$i]:(((X1623 @ X1625)=>((X1624)=(X1625))))))))=>(![X878:$o, X879:$i]:(((in @ X879 @ (prop2set @ ((X878))))=>(X878)))=>(![X880:$i]:(((in @ X880 @ emptyset)=>![X881:$o]:((X881))))=>(![X1622:$i]:(((in @ X1622 @ emptyset)=>~($true)))=>(![X882:$i]:(~(in @ X882 @ emptyset))=>(![X883:$i > $o]:(((exu @ X883)=>?[X884:$i]:((X883 @ X884))))=>(![X1618:$i, X1619:$i]:((![X1620:$i]:(((in @ X1620 @ X1618)=>(in @ X1620 @ X1619)))=>(![X1621:$i]:(((in @ X1621 @ X1619)=>(in @ X1621 @ X1618)))=>((X1618)=(X1619)))))=>(![X885:$i]:((![X886:$i]:(~(in @ X886 @ X885))=>((X885)=(emptyset))))=>(![X1616:$i]:((![X1617:$i]:(~(in @ X1617 @ X1616))=>((X1616)=(emptyset))))=>(![X887:$i, X888:$i > $o, X889:$i]:(((in @ X889 @ X887)=>((in @ X889 @ (dsetconstr @ X887 @ X888))<=>(X888 @ X889))))=>(![X1614:$i]:(((nonempty @ X1614)=>?[X1615:$i]:((in @ X1615 @ X1614))))=>(![X1611:$i, X1612:$i > $o, X1613:$i]:(((in @ X1613 @ X1611)=>((X1612 @ X1613)=>(nonempty @ (dsetconstr @ X1611 @ X1612)))))=>(![X1609:$i]:((?[X1610:$i]:((in @ X1610 @ X1609))=>(nonempty @ X1609)))=>(![X890:$i, X891:$i]:((in @ X890 @ (setadjoin @ X890 @ X891)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1606:$i, X1607:$i, X1608:$i]:(((in @ X1608 @ X1607)=>(in @ X1608 @ (setadjoin @ X1606 @ X1607))))=>(![X892:$i, X893:$i, X894:$i]:(((in @ X894 @ (setadjoin @ X892 @ X893))=>![X895:$o]:(((((X894)=(X892))=>(X895))=>(((in @ X894 @ X893)=>(X895))=>(X895))))))=>(![X1603:$i, X1604:$i, X1605:$i]:(((in @ X1605 @ (setadjoin @ X1603 @ X1604))=>(((X1605)=(X1603))|(in @ X1605 @ 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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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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uniqinunit]), emptysetAx]), subsetE2]), subsetE]), symdiffE]), emptysetsubset]), eqimpsubset1]), eqimpsubset2]), symdiffI2]), subsetI1]), c_0_258]), symdiffIneg2]), c_0_259]), c_0_260]), setunion__Cong]), setukpairIL]), setadjoin__Cong]), emptyset__Cong]), setukpairIR]), c_0_261]), c_0_262]), notdexE]), setminusILneg]), quantDeMorgan4]), singletoninpowunion]), quantDeMorgan2]), quantDeMorgan1]), upairsubunion]), vacuousDall]), singletonsswitch]), eqinunit]), cartprodfstpairEq]), ubforcartprodlem1]), nonemptyImpWitness]), c_0_263]), ubforcartprodlem3]), subPowSU]), setunionI]), emptyInPowerset]), cartprodmempair1]), emptyinPowerset]), c_0_264]), cartprodmempair]), setadjoinOr]), setadjoinIR]), nonemptyI1]), setunionsingleton2]), c_0_265]), nonemptyE1]), setunionsingleton]), noeltsimpempty]), setext]), emptysetimpfalse]), c_0_266]), c_0_267]), c_0_268]), c_0_269]), wellorderingAx]), foundationAx]), c_0_270]), c_0_271]), omegaIndAx]), setadjoinAx]), setminusIRneg]), setukpairinjL1]), setukpairinjL2]), setukpairinjR12]), upairequniteq]), setukpairinjR2]), kpairsurjEq]), cartprodpairmemER]), powersetTE1]), binintersectTERcontra]), cartprodsndpairEq]), c_0_272]), c_0_273]), c_0_274]), app]), funcinfuncset]), c_0_275]), c_0_276]), setminusLsub]), c_0_277]), brelnall2]), funcGraphProp3]), funcGraphProp2]), funcGraphProp4]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_278]), c_0_279]), c_0_280]), c_0_281]), c_0_282]), c_0_283]), c_0_284]), iffalse]), iftrueorfalse]), binintersectT_lem]), powersetT_lem]), setextT]), subsetTI]), powersetTI1]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementSubsetComplementIntersect]), binunionTILcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), binunionTIRcontra]), complementTcontraSubset]), contraSubsetComplement]), complementInPowersetComplementIntersect]), complementImpComplementIntersect]), contrasubsetT3]), binintersectTELcontra]), complementTE1]), complementTI1]), complementT_lem]), setminusT_lem]), binunionT_lem]), iftrue]), theeq]), ifp]), c_0_285]), c_0_286]), c_0_287]), eqbreln]), subbreln]), funcextLem]), funcGraphProp1]), c_0_288]), brelnall1]), ap2p]), infuncsetfunc]), c_0_289]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), cartprodpairsurjEq]), cartprodmempaircEq]), cartprodpairmemEL]), cartprodsndin]), ksndpairEq]), c_0_295]), setukpairinjR]), setukpairinjR1]), setukpairinjR11]), setukpairinjL]), cartprodfstin]), kfstpairEq]), theprop]), c_0_296]), singletonsuniq]), c_0_297]), setunionsingleton1]), setunionE2]), cartprodpairin]), ubforcartprodlem2]), upairinpowunion]), upairset2E]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), secondinupair]), symdiffIneg1]), symdiffI1]), setminusSubset1]), setminusELneg]), setminusEL]), binintersectER]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), c_0_298]), powersetsubset]), inPowerset]), powersetI1]), subset2powerset]), subsetTrans]), subsetRefl]), notsubsetI]), setminusERneg]), setminusSubset2]), setminusER]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectSubset3]), binintersectI]), binunionRsub]), upairset2IR]), binunionIL]), c_0_299]), powersetE1]), subsetemptysetimpeq]), setextsub]), setadjoinSub2]), setadjoinSub]), notequalI2]), notequalI1]), subsetI2]), omega__Cong]), powerset__Cong]), in__Cong]), inCongP]), c_0_300]), c_0_301]), c_0_302]), notdallE]), prop2setI]), quantDeMorgan3]), c_0_303]), upairsetIR]), upairsetIL]), upairsetE]), notinsingleton]), setunionE]), powersetE]), powersetI]), setadjoinE]), emptyinunitempty]), setadjoinIL]), c_0_304]), emptyI]), c_0_305]), notinemptyset]), emptysetE]), prop2setE]), c_0_306]), c_0_307]), c_0_308]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setextAx])])]), c_0_309])). 0.36/0.95 thf(c_0_311, negated_conjecture, ![X1663:$i, X1664:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1676:$i, X1677:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1685:$i, X1686:$i > $i > $o, X1687:$i, X1690:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1697:$i, X1698:$i > $o, X1699:$i, X1700:$i > $o, X1701:$i, X1702:$i, X1703:$i > $o, X1704:$i, X1705:$i, X1706:$i > $o, X1707:$i, X1708:$i > $o, X1710:$i, X1711:$o, X1712:$i, X1713:$i, X1714:$o, X1715:$i, X1716:$i, X1717:$i > $o, X1719:$i, X1720:$i, X1723:$i, X1725:$i, X1727:$i, X1728:$i > $o, X1729:$i, X1730:$i, X1732:$i, X1733:$i > $o, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$o, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$o, X1765:$i, X1766:$i, X1767:$i > $o, X1769:$i, X1770:$i, X1771:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i > $o, X1790:$i, X1791:$i > $o, X1792:$i, X1793:$i, X1794:$i > $o, X1795:$i, X1797:$i, X1798:$i > $o, X1800:$i, X1801:$i, X1802:$i > $o, X1804:$i, X1805:$i, X1806:$i > $o, X1807:$i, X1809:$o, X1810:$i, X1811:$i > $o, X1813:$i, X1814:$i, X1815:$i > $o, X1816:$i, X1818:$i > $o, X1819:$i, X1821:$i > $o, X1822:$i, X1825:$i > $o, X1826:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i > $o, X1837:$i, X1838:$i, X1839:$i > $o, X1840:$i > $o, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i > $o, X1852:$i, X1853:$i, X1854:$i > $o, X1855:$i > $o, X1858:$i, X1859:$i, X1860:$i > $o, X1861:$i > $o, X1864:$i, X1865:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i > $o, X1912:$i, X1913:$i > $o, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$o, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$o, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i > $o, X2068:$i, X2069:$i, X2070:$i > $o, X2072:$i, X2073:$i > $o, X2074:$i, X2076:$i, X2077:$i > $o, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i > $i > $o, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i > $i > $o, X2158:$i, X2159:$i, X2160:$i > $i > $o, X2161:$i, X2162:$i, X2163:$i > $i > $o, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i > $i > $o, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i > $i > $o, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i > $i > $o, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i > $i, X2207:$i, X2208:$i, X2209:$i > $i, X2211:$i, X2212:$i, X2213:$i > $i, X2215:$i, X2216:$i, X2217:$i, X2218:$i > $o, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i > $o, X2228:$i, X2229:$i, X2230:$i > $o, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i > $i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i > $i, X2302:$i, X2303:$i, X2304:$i > $i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$o, X2312:$i, X2313:$i, X2314:$i, X2315:$o, X2316:$i, X2317:$i, X2318:$i, X2319:$o, X2320:$i, X2321:$i, X2322:$i, X2323:$o, X2324:$i, X2325:$i, X2326:$i, X2327:$o, X2328:$i, X2329:$i, X2330:$i, X2331:$o, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$o, X2338:$i, X2339:$i, X2340:$i, X2341:$o, X2342:$i, X2343:$i, X2344:$i, X2345:$o, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2366:$i, X2367:$i, X2368:$i, X2370:$i, X2371:$i, X2372:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i]:((((~(in @ (esk1_2 @ X1663 @ X1664) @ X1663)|~(in @ (esk1_2 @ X1663 @ X1664) @ X1664)|((X1663)=(X1664)))&((in @ (esk1_2 @ X1663 @ X1664) @ X1663)|(in @ (esk1_2 @ X1663 @ X1664) @ X1664)|((X1663)=(X1664))))&(~(in @ X1666 @ emptyset)&(((~(in @ X1669 @ (setadjoin @ X1667 @ X1668))|(((X1669)=(X1667))|(in @ X1669 @ 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X2354))|(in @ (powerset @ X2355) @ (powerset @ (powerset @ X2354))))&((~(in @ X2357 @ (powerset @ X2356))|(~(in @ X2358 @ (powerset @ X2356))|(in @ (setminus @ X2357 @ X2358) @ (powerset @ X2356))))&((~(in @ X2360 @ (powerset @ X2359))|(in @ (setminus @ X2359 @ X2360) @ (powerset @ X2359)))&(((((in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2361)|((X2362)=(X2363))|(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2361)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))&(((in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2363)|((X2362)=(X2363))|(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2361)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))&(~(in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2362)|((X2362)=(X2363))|(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2361)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))))&((((in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2361)|((X2362)=(X2363))|(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2362)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))&(((in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2363)|((X2362)=(X2363))|(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2362)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))&(~(in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2362)|((X2362)=(X2363))|(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2362)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))))&(((in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2361)|((X2362)=(X2363))|~(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2363)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))&(((in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2363)|((X2362)=(X2363))|~(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2363)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))&(~(in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2362)|((X2362)=(X2363))|~(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2363)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))))))&((((in @ (esk69_3 @ X2366 @ X2367 @ X2368) @ X2366)|(subset @ X2367 @ X2368)|~(in @ X2368 @ (powerset @ X2366))|~(in @ X2367 @ (powerset @ X2366)))&(((in @ (esk69_3 @ X2366 @ X2367 @ X2368) @ X2367)|(subset @ X2367 @ X2368)|~(in @ X2368 @ (powerset @ X2366))|~(in @ X2367 @ (powerset @ X2366)))&(~(in @ (esk69_3 @ X2366 @ X2367 @ X2368) @ X2368)|(subset @ X2367 @ X2368)|~(in @ X2368 @ (powerset @ X2366))|~(in @ X2367 @ (powerset @ X2366)))))&((((in @ (esk70_3 @ X2370 @ X2371 @ X2372) @ X2370)|(in @ X2371 @ (powerset @ X2372))|~(in @ X2372 @ (powerset @ X2370))|~(in @ X2371 @ (powerset @ X2370)))&(((in @ (esk70_3 @ X2370 @ X2371 @ X2372) @ X2371)|(in @ X2371 @ (powerset @ X2372))|~(in @ X2372 @ (powerset @ X2370))|~(in @ X2371 @ (powerset @ X2370)))&(~(in @ (esk70_3 @ X2370 @ X2371 @ X2372) @ X2372)|(in @ X2371 @ (powerset @ X2372))|~(in @ X2372 @ (powerset @ X2370))|~(in @ X2371 @ (powerset @ X2370)))))&((~(in @ X2375 @ (powerset @ X2374))|(~(in @ X2376 @ (powerset @ X2374))|(~(in @ X2377 @ X2374)|(~(in @ X2375 @ (powerset @ X2376))|(~(in @ X2377 @ X2375)|(in @ X2377 @ X2376))))))&((~(in @ X2379 @ (powerset @ X2378))|(~(in @ X2380 @ X2378)|(~(in @ X2380 @ X2379)|~(in @ X2380 @ (setminus @ X2378 @ X2379)))))&((~(in @ X2382 @ (powerset @ X2381))|(~(in @ X2383 @ X2381)|((in @ X2383 @ (setminus @ X2381 @ X2382))|(in @ X2383 @ X2382))))&((~(in @ X2385 @ (powerset @ X2384))|(~(in @ X2386 @ (powerset @ X2384))|(~(in @ X2387 @ X2384)|((in @ X2387 @ X2385)|~(in @ X2387 @ (binintersect @ X2385 @ X2386))))))&((~(in @ X2389 @ (powerset @ X2388))|(~(in @ X2390 @ (powerset @ X2388))|(~(in @ X2391 @ X2388)|((in @ X2391 @ X2390)|~(in @ X2391 @ (binintersect @ X2389 @ X2390))))))&((~(in @ X2393 @ (powerset @ X2392))|(~(in @ X2394 @ (powerset @ X2392))|(~(in @ X2395 @ X2392)|(~(subset @ X2393 @ (setminus @ X2392 @ X2394))|(~(in @ X2395 @ X2394)|~(in @ X2395 @ X2393))))))&((~(in @ X2397 @ (powerset @ X2396))|(~(in @ X2398 @ (powerset @ X2396))|(~(in @ X2399 @ X2396)|(~(subset @ X2397 @ X2398)|((in @ X2399 @ X2398)|~(in @ X2399 @ X2397))))))&((~(in @ X2401 @ (powerset @ X2400))|(~(in @ X2402 @ (powerset @ X2400))|(~(subset @ X2401 @ X2402)|(subset @ (setminus @ X2400 @ X2402) @ (setminus @ X2400 @ X2401)))))&((~(in @ X2404 @ (powerset @ X2403))|(~(in @ X2405 @ (powerset @ X2403))|(~(subset @ (setminus @ X2403 @ X2405) @ (setminus @ X2403 @ X2404))|(subset @ X2404 @ X2405))))&((~(in @ X2407 @ (powerset @ X2406))|(~(in @ X2408 @ X2406)|(~(in @ X2408 @ X2407)|(in @ X2408 @ (setminus @ X2406 @ (setminus @ X2406 @ X2407))))))&((~(in @ X2410 @ (powerset @ X2409))|(~(in @ X2411 @ X2409)|(~(in @ X2411 @ (setminus @ X2409 @ (setminus @ X2409 @ X2410)))|(in @ X2411 @ X2410))))&((~(in @ X2413 @ (powerset @ X2412))|(subset @ X2413 @ (setminus @ X2412 @ (setminus @ X2412 @ X2413))))&((~(in @ X2415 @ (powerset @ X2414))|(subset @ (setminus @ X2414 @ (setminus @ X2414 @ X2415)) @ X2415))&((~(in @ X2417 @ (powerset @ X2416))|((X2417)=(setminus @ X2416 @ (setminus @ X2416 @ X2417))))&((~(in @ X2419 @ (powerset @ X2418))|(~(in @ X2420 @ (powerset @ X2418))|(~(in @ X2421 @ X2418)|(~(in @ X2421 @ (setminus @ X2418 @ X2419))|~(in @ X2421 @ (binintersect @ X2419 @ X2420))))))&((~(in @ X2423 @ (powerset @ X2422))|(~(in @ X2424 @ (powerset @ X2422))|(~(in @ X2425 @ X2422)|(~(in @ X2425 @ (setminus @ X2422 @ X2423))|(in @ X2425 @ (setminus @ X2422 @ (binintersect @ X2423 @ X2424)))))))&((~(in @ X2427 @ (powerset @ X2426))|(~(in @ X2428 @ (powerset @ X2426))|(subset @ (setminus @ X2426 @ X2427) @ (setminus @ X2426 @ (binintersect @ X2427 @ X2428)))))&((~(in @ X2430 @ (powerset @ X2429))|(~(in @ X2431 @ (powerset @ X2429))|(in @ (setminus @ X2429 @ X2430) @ (powerset @ (setminus @ X2429 @ (binintersect @ X2430 @ X2431))))))&((~(in @ X2433 @ (powerset @ X2432))|(~(in @ X2434 @ (powerset @ X2432))|(~(subset @ X2433 @ (setminus @ X2432 @ X2434))|(~(in @ X2435 @ X2432)|(~(in @ X2435 @ X2434)|(in @ X2435 @ (setminus @ X2432 @ X2433)))))))&((~(in @ X2437 @ (powerset @ X2436))|(~(in @ X2438 @ (powerset @ X2436))|(~(subset @ X2437 @ (setminus @ X2436 @ X2438))|(subset @ X2438 @ (setminus @ X2436 @ X2437)))))&((~(in @ X2440 @ (powerset @ X2439))|(~(in @ X2441 @ (powerset @ X2439))|(~(in @ X2442 @ X2439)|((in @ X2442 @ (binunion @ X2440 @ X2441))|~(in @ X2442 @ X2440)))))&((~(in @ X2444 @ (powerset @ X2443))|(~(in @ X2445 @ (powerset @ X2443))|(~(in @ X2446 @ X2443)|((in @ X2446 @ (binunion @ X2444 @ X2445))|~(in @ X2446 @ X2445)))))&((~(in @ X2448 @ (powerset @ X2447))|(~(in @ X2449 @ (powerset @ X2447))|(~(in @ X2450 @ (powerset @ X2447))|(~(in @ X2451 @ X2447)|(~(in @ X2451 @ (binintersect @ X2448 @ X2449))|(in @ X2451 @ (binunion @ X2448 @ X2450)))))))&((~(in @ X2453 @ (powerset @ X2452))|(~(in @ X2454 @ (powerset @ X2452))|(~(in @ X2455 @ (powerset @ X2452))|(~(in @ X2456 @ X2452)|(~(in @ X2456 @ (binintersect @ X2453 @ X2454))|(in @ X2456 @ (binunion @ X2454 @ X2455)))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ (powerset @ esk71_0))&((in @ esk75_0 @ esk71_0)&((in @ esk75_0 @ (binintersect @ esk72_0 @ esk73_0))&~(in @ esk75_0 @ (binintersect @ (binunion @ esk72_0 @ esk74_0) @ (binunion @ esk73_0 @ esk74_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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_310])])])])])])])). 0.36/0.95 thf(c_0_312, negated_conjecture, ~((in @ esk75_0 @ (binintersect @ (binunion @ esk72_0 @ esk74_0) @ (binunion @ esk73_0 @ esk74_0)))), inference(split_conjunct,[status(thm)],[c_0_311])). 0.36/0.95 thf(c_0_313, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ (binintersect @ X3 @ X4))|~((in @ X2 @ X3))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_311])). 0.36/0.95 thf(c_0_314, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X4)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_311])). 0.36/0.95 thf(c_0_315, negated_conjecture, (in @ esk75_0 @ (binintersect @ esk72_0 @ esk73_0)), inference(split_conjunct,[status(thm)],[c_0_311])). 0.36/0.95 thf(c_0_316, negated_conjecture, (~((in @ esk75_0 @ (binunion @ esk73_0 @ esk74_0)))|~((in @ esk75_0 @ (binunion @ esk72_0 @ esk74_0)))), inference(spm,[status(thm)],[c_0_312, c_0_313])). 0.36/0.95 thf(c_0_317, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_311])). 0.36/0.95 thf(c_0_318, negated_conjecture, (in @ esk75_0 @ esk73_0), inference(spm,[status(thm)],[c_0_314, c_0_315])). 0.36/0.95 thf(c_0_319, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_311])). 0.36/0.95 thf(c_0_320, negated_conjecture, ~((in @ esk75_0 @ (binunion @ esk72_0 @ esk74_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316, c_0_317]), c_0_318])])). 0.36/0.95 thf(c_0_321, negated_conjecture, (in @ esk75_0 @ esk72_0), inference(spm,[status(thm)],[c_0_319, c_0_315])). 0.36/0.95 thf(c_0_322, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320, c_0_317]), c_0_321])]), ['proof']). 0.36/0.95 # SZS output end CNFRefutation 0.36/0.95 # Parsed axioms : 559 0.36/0.95 # Removed by relevancy pruning/SinE : 301 0.36/0.95 # Initial clauses : 421 0.36/0.95 # Removed in clause preprocessing : 34 0.36/0.95 # Initial clauses in saturation : 387 0.36/0.95 # Processed clauses : 764 0.36/0.95 # ...of these trivial : 12 0.36/0.95 # ...subsumed : 41 0.36/0.95 # ...remaining for further processing : 711 0.36/0.95 # Other redundant clauses eliminated : 54 0.36/0.95 # Clauses deleted for lack of memory : 0 0.36/0.95 # Backward-subsumed : 1 0.36/0.95 # Backward-rewritten : 3 0.36/0.95 # Generated clauses : 7837 0.36/0.95 # ...of the previous two non-redundant : 7599 0.36/0.95 # ...aggressively subsumed : 0 0.36/0.95 # Contextual simplify-reflections : 6 0.36/0.95 # Paramodulations : 7748 0.36/0.95 # Factorizations : 2 0.36/0.95 # NegExts : 0 0.36/0.95 # Equation resolutions : 61 0.36/0.95 # Disequality decompositions : 0 0.36/0.95 # Total rewrite steps : 204 0.36/0.95 # ...of those cached : 136 0.36/0.95 # Propositional unsat checks : 0 0.36/0.95 # Propositional check models : 0 0.36/0.95 # Propositional check unsatisfiable : 0 0.36/0.95 # Propositional clauses : 0 0.36/0.95 # Propositional clauses after purity: 0 0.36/0.95 # Propositional unsat core size : 0 0.36/0.95 # Propositional preprocessing time : 0.000 0.36/0.95 # Propositional encoding time : 0.000 0.36/0.95 # Propositional solver time : 0.000 0.36/0.95 # Success case prop preproc time : 0.000 0.36/0.95 # Success case prop encoding time : 0.000 0.36/0.95 # Success case prop solver time : 0.000 0.36/0.95 # Current number of processed clauses : 353 0.36/0.95 # Positive orientable unit clauses : 50 0.36/0.95 # Positive unorientable unit clauses: 0 0.36/0.95 # Negative unit clauses : 5 0.36/0.95 # Non-unit-clauses : 298 0.36/0.95 # Current number of unprocessed clauses: 7556 0.36/0.95 # ...number of literals in the above : 31642 0.36/0.95 # Current number of archived formulas : 0 0.36/0.95 # Current number of archived clauses : 342 0.36/0.95 # Clause-clause subsumption calls (NU) : 60371 0.36/0.95 # Rec. Clause-clause subsumption calls : 25185 0.36/0.95 # Non-unit clause-clause subsumptions : 39 0.36/0.95 # Unit Clause-clause subsumption calls : 1832 0.36/0.95 # Rewrite failures with RHS unbound : 0 0.36/0.95 # BW rewrite match attempts : 34 0.36/0.95 # BW rewrite match successes : 2 0.36/0.95 # Condensation attempts : 0 0.36/0.95 # Condensation successes : 0 0.36/0.95 # Termbank termtop insertions : 206533 0.36/0.95 # Search garbage collected termcells : 25911 0.36/0.95 0.36/0.95 # ------------------------------------------------- 0.36/0.95 # User time : 0.339 s 0.36/0.95 # System time : 0.030 s 0.36/0.95 # Total time : 0.369 s 0.36/0.95 # Maximum resident set size: 8472 pages 0.36/0.95 0.36/0.95 # ------------------------------------------------- 0.36/0.95 # User time : 0.357 s 0.36/0.95 # System time : 0.031 s 0.36/0.95 # Total time : 0.388 s 0.36/0.95 # Maximum resident set size: 2480 pages 0.36/0.95 % E---3.1 exiting 0.36/0.95 % E exiting 0.36/0.95 EOF