0.11/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.14 % Command : run_E %s %d THM 0.11/0.35 % Computer : n016.cluster.edu 0.11/0.35 % Model : x86_64 x86_64 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.35 % Memory : 8042.1875MB 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.35 % CPULimit : 1440 0.11/0.35 % WCLimit : 180 0.11/0.35 % DateTime : Thu Jul 4 09:07:23 EDT 2024 0.11/0.35 % CPUTime : 0.19/0.50 Running higher-order theorem proving 0.19/0.55 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p 9.37/180.02 Alarm clock 9.37/180.03 # Version: 3.2.0-ho 9.37/180.03 # Preprocessing class: HSLMSLSSLLLCHFA. 9.37/180.03 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 9.37/180.03 # Starting ehoh_best5 with 180s (1) cores 9.37/180.03 # Starting almost_fo_3_lam with 180s (1) cores 9.37/180.03 # Starting new_bool_5 with 180s (1) cores 9.37/180.03 # Starting pre_casc_3 with 180s (1) cores 9.37/180.03 # Starting ho_unfolding_8 with 180s (1) cores 9.37/180.03 # Starting new_ho_10_cnf2 with 180s (1) cores 9.37/180.03 # Starting new_bool_3 with 180s (1) cores 9.37/180.03 # Starting new_ho_5 with 180s (1) cores 9.37/180.03 # new_bool_3 with pid 6340 completed with status 0 9.37/180.03 # Result found by new_bool_3 9.37/180.03 # Preprocessing class: HSLMSLSSLLLCHFA. 9.37/180.03 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 9.37/180.03 # Starting ehoh_best5 with 180s (1) cores 9.37/180.03 # Starting almost_fo_3_lam with 180s (1) cores 9.37/180.03 # Starting new_bool_5 with 180s (1) cores 9.37/180.03 # Starting pre_casc_3 with 180s (1) cores 9.37/180.03 # Starting ho_unfolding_8 with 180s (1) cores 9.37/180.03 # Starting new_ho_10_cnf2 with 180s (1) cores 9.37/180.03 # Starting new_bool_3 with 180s (1) cores 9.37/180.03 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 9.37/180.03 # Search class: HGHSM-FSLM32-MHFMMSBN 9.37/180.03 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 9.37/180.03 # Starting ho_unfolding_8 with 37s (1) cores 9.37/180.03 # ho_unfolding_8 with pid 6354 completed with status 0 9.37/180.03 # Result found by ho_unfolding_8 9.37/180.03 # Preprocessing class: HSLMSLSSLLLCHFA. 9.37/180.03 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 9.37/180.03 # Starting ehoh_best5 with 180s (1) cores 9.37/180.03 # Starting almost_fo_3_lam with 180s (1) cores 9.37/180.03 # Starting new_bool_5 with 180s (1) cores 9.37/180.03 # Starting pre_casc_3 with 180s (1) cores 9.37/180.03 # Starting ho_unfolding_8 with 180s (1) cores 9.37/180.03 # Starting new_ho_10_cnf2 with 180s (1) cores 9.37/180.03 # Starting new_bool_3 with 180s (1) cores 9.37/180.03 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 9.37/180.03 # Search class: HGHSM-FSLM32-MHFMMSBN 9.37/180.03 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 9.37/180.03 # Starting ho_unfolding_8 with 37s (1) cores 9.37/180.03 # Preprocessing time : 0.060 s 9.37/180.03 # Presaturation interreduction done 9.37/180.03 9.37/180.03 # Proof found! 9.37/180.03 # SZS status Theorem 9.37/180.03 # SZS output start CNFRefutation 9.37/180.03 thf(decl_22, type, in: $i > $i > $o). 9.37/180.03 thf(decl_23, type, exu: ($i > $o) > $o). 9.37/180.03 thf(decl_24, type, setextAx: $o). 9.37/180.03 thf(decl_25, type, emptyset: $i). 9.37/180.03 thf(decl_26, type, emptysetAx: $o). 9.37/180.03 thf(decl_27, type, setadjoin: $i > $i > $i). 9.37/180.03 thf(decl_28, type, setadjoinAx: $o). 9.37/180.03 thf(decl_29, type, powerset: $i > $i). 9.37/180.03 thf(decl_30, type, powersetAx: $o). 9.37/180.03 thf(decl_31, type, setunion: $i > $i). 9.37/180.03 thf(decl_32, type, setunionAx: $o). 9.37/180.03 thf(decl_33, type, omega: $i). 9.37/180.03 thf(decl_34, type, omega0Ax: $o). 9.37/180.03 thf(decl_35, type, omegaSAx: $o). 9.37/180.03 thf(decl_36, type, omegaIndAx: $o). 9.37/180.03 thf(decl_37, type, replAx: $o). 9.37/180.03 thf(decl_38, type, foundationAx: $o). 9.37/180.03 thf(decl_39, type, wellorderingAx: $o). 9.37/180.03 thf(decl_40, type, descr: ($i > $o) > $i). 9.37/180.03 thf(decl_41, type, descrp: $o). 9.37/180.03 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_43, type, dsetconstrI: $o). 9.37/180.03 thf(decl_44, type, dsetconstrEL: $o). 9.37/180.03 thf(decl_45, type, dsetconstrER: $o). 9.37/180.03 thf(decl_46, type, exuE1: $o). 9.37/180.03 thf(decl_47, type, prop2set: $o > $i). 9.37/180.03 thf(decl_48, type, prop2setE: $o). 9.37/180.03 thf(decl_49, type, emptysetE: $o). 9.37/180.03 thf(decl_50, type, emptysetimpfalse: $o). 9.37/180.03 thf(decl_51, type, notinemptyset: $o). 9.37/180.03 thf(decl_52, type, exuE3e: $o). 9.37/180.03 thf(decl_53, type, setext: $o). 9.37/180.03 thf(decl_54, type, emptyI: $o). 9.37/180.03 thf(decl_55, type, noeltsimpempty: $o). 9.37/180.03 thf(decl_56, type, setbeta: $o). 9.37/180.03 thf(decl_57, type, nonempty: $i > $o). 9.37/180.03 thf(decl_58, type, nonemptyE1: $o). 9.37/180.03 thf(decl_59, type, nonemptyI: $o). 9.37/180.03 thf(decl_60, type, nonemptyI1: $o). 9.37/180.03 thf(decl_61, type, setadjoinIL: $o). 9.37/180.03 thf(decl_62, type, emptyinunitempty: $o). 9.37/180.03 thf(decl_63, type, setadjoinIR: $o). 9.37/180.03 thf(decl_64, type, setadjoinE: $o). 9.37/180.03 thf(decl_65, type, setadjoinOr: $o). 9.37/180.03 thf(decl_66, type, setoftrueEq: $o). 9.37/180.03 thf(decl_67, type, powersetI: $o). 9.37/180.03 thf(decl_68, type, emptyinPowerset: $o). 9.37/180.03 thf(decl_69, type, emptyInPowerset: $o). 9.37/180.03 thf(decl_70, type, powersetE: $o). 9.37/180.03 thf(decl_71, type, setunionI: $o). 9.37/180.03 thf(decl_72, type, setunionE: $o). 9.37/180.03 thf(decl_73, type, subPowSU: $o). 9.37/180.03 thf(decl_74, type, exuE2: $o). 9.37/180.03 thf(decl_75, type, nonemptyImpWitness: $o). 9.37/180.03 thf(decl_76, type, uniqinunit: $o). 9.37/180.03 thf(decl_77, type, notinsingleton: $o). 9.37/180.03 thf(decl_78, type, eqinunit: $o). 9.37/180.03 thf(decl_79, type, singletonsswitch: $o). 9.37/180.03 thf(decl_80, type, upairsetE: $o). 9.37/180.03 thf(decl_81, type, upairsetIL: $o). 9.37/180.03 thf(decl_82, type, upairsetIR: $o). 9.37/180.03 thf(decl_83, type, emptyE1: $o). 9.37/180.03 thf(decl_84, type, vacuousDall: $o). 9.37/180.03 thf(decl_85, type, quantDeMorgan1: $o). 9.37/180.03 thf(decl_86, type, quantDeMorgan2: $o). 9.37/180.03 thf(decl_87, type, quantDeMorgan3: $o). 9.37/180.03 thf(decl_88, type, quantDeMorgan4: $o). 9.37/180.03 thf(decl_89, type, prop2setI: $o). 9.37/180.03 thf(decl_91, type, prop2set2propI: $o). 9.37/180.03 thf(decl_92, type, notdexE: $o). 9.37/180.03 thf(decl_93, type, notdallE: $o). 9.37/180.03 thf(decl_94, type, exuI1: $o). 9.37/180.03 thf(decl_95, type, exuI3: $o). 9.37/180.03 thf(decl_96, type, exuI2: $o). 9.37/180.03 thf(decl_97, type, inCongP: $o). 9.37/180.03 thf(decl_98, type, in__Cong: $o). 9.37/180.03 thf(decl_99, type, exuE3u: $o). 9.37/180.03 thf(decl_100, type, exu__Cong: $o). 9.37/180.03 thf(decl_101, type, emptyset__Cong: $o). 9.37/180.03 thf(decl_102, type, setadjoin__Cong: $o). 9.37/180.03 thf(decl_103, type, powerset__Cong: $o). 9.37/180.03 thf(decl_104, type, setunion__Cong: $o). 9.37/180.03 thf(decl_105, type, omega__Cong: $o). 9.37/180.03 thf(decl_106, type, exuEu: $o). 9.37/180.03 thf(decl_107, type, descr__Cong: $o). 9.37/180.03 thf(decl_108, type, dsetconstr__Cong: $o). 9.37/180.03 thf(decl_109, type, subset: $i > $i > $o). 9.37/180.03 thf(decl_112, type, subsetI1: $o). 9.37/180.03 thf(decl_113, type, eqimpsubset2: $o). 9.37/180.03 thf(decl_114, type, eqimpsubset1: $o). 9.37/180.03 thf(decl_115, type, subsetI2: $o). 9.37/180.03 thf(decl_116, type, emptysetsubset: $o). 9.37/180.03 thf(decl_117, type, subsetE: $o). 9.37/180.03 thf(decl_118, type, subsetE2: $o). 9.37/180.03 thf(decl_119, type, notsubsetI: $o). 9.37/180.03 thf(decl_120, type, notequalI1: $o). 9.37/180.03 thf(decl_121, type, notequalI2: $o). 9.37/180.03 thf(decl_122, type, subsetRefl: $o). 9.37/180.03 thf(decl_123, type, subsetTrans: $o). 9.37/180.03 thf(decl_124, type, setadjoinSub: $o). 9.37/180.03 thf(decl_125, type, setadjoinSub2: $o). 9.37/180.03 thf(decl_126, type, subset2powerset: $o). 9.37/180.03 thf(decl_127, type, setextsub: $o). 9.37/180.03 thf(decl_128, type, subsetemptysetimpeq: $o). 9.37/180.03 thf(decl_129, type, powersetI1: $o). 9.37/180.03 thf(decl_130, type, powersetE1: $o). 9.37/180.03 thf(decl_131, type, inPowerset: $o). 9.37/180.03 thf(decl_132, type, powersetsubset: $o). 9.37/180.03 thf(decl_133, type, sepInPowerset: $o). 9.37/180.03 thf(decl_134, type, sepSubset: $o). 9.37/180.03 thf(decl_135, type, binunion: $i > $i > $i). 9.37/180.03 thf(decl_136, type, binunionIL: $o). 9.37/180.03 thf(decl_137, type, upairset2IR: $o). 9.37/180.03 thf(decl_138, type, binunionIR: $o). 9.37/180.03 thf(decl_139, type, binunionEcases: $o). 9.37/180.03 thf(decl_140, type, binunionE: $o). 9.37/180.03 thf(decl_141, type, binunionLsub: $o). 9.37/180.03 thf(decl_142, type, binunionRsub: $o). 9.37/180.03 thf(decl_143, type, binintersect: $i > $i > $i). 9.37/180.03 thf(decl_144, type, binintersectI: $o). 9.37/180.03 thf(decl_145, type, binintersectSubset5: $o). 9.37/180.03 thf(decl_146, type, binintersectEL: $o). 9.37/180.03 thf(decl_147, type, binintersectLsub: $o). 9.37/180.03 thf(decl_148, type, binintersectSubset2: $o). 9.37/180.03 thf(decl_149, type, binintersectSubset3: $o). 9.37/180.03 thf(decl_150, type, binintersectER: $o). 9.37/180.03 thf(decl_151, type, disjointsetsI1: $o). 9.37/180.03 thf(decl_152, type, binintersectRsub: $o). 9.37/180.03 thf(decl_153, type, binintersectSubset4: $o). 9.37/180.03 thf(decl_154, type, binintersectSubset1: $o). 9.37/180.03 thf(decl_155, type, bs114d: $o). 9.37/180.03 thf(decl_157, type, setminus: $i > $i > $i). 9.37/180.03 thf(decl_158, type, setminusI: $o). 9.37/180.03 thf(decl_159, type, setminusEL: $o). 9.37/180.03 thf(decl_160, type, setminusER: $o). 9.37/180.03 thf(decl_161, type, setminusSubset2: $o). 9.37/180.03 thf(decl_162, type, setminusERneg: $o). 9.37/180.03 thf(decl_163, type, setminusELneg: $o). 9.37/180.03 thf(decl_164, type, setminusILneg: $o). 9.37/180.03 thf(decl_165, type, setminusIRneg: $o). 9.37/180.03 thf(decl_166, type, setminusLsub: $o). 9.37/180.03 thf(decl_167, type, setminusSubset1: $o). 9.37/180.03 thf(decl_168, type, symdiff: $i > $i > $i). 9.37/180.03 thf(decl_169, type, symdiffE: $o). 9.37/180.03 thf(decl_170, type, symdiffI1: $o). 9.37/180.03 thf(decl_171, type, symdiffI2: $o). 9.37/180.03 thf(decl_172, type, symdiffIneg1: $o). 9.37/180.03 thf(decl_173, type, symdiffIneg2: $o). 9.37/180.03 thf(decl_174, type, iskpair: $i > $o). 9.37/180.03 thf(decl_175, type, secondinupair: $o). 9.37/180.03 thf(decl_176, type, setukpairIL: $o). 9.37/180.03 thf(decl_177, type, setukpairIR: $o). 9.37/180.03 thf(decl_178, type, kpairiskpair: $o). 9.37/180.03 thf(decl_179, type, kpair: $i > $i > $i). 9.37/180.03 thf(decl_180, type, kpairp: $o). 9.37/180.03 thf(decl_181, type, cartprod: $i > $i > $i). 9.37/180.03 thf(decl_182, type, singletonsubset: $o). 9.37/180.03 thf(decl_183, type, singletoninpowerset: $o). 9.37/180.03 thf(decl_184, type, singletoninpowunion: $o). 9.37/180.03 thf(decl_185, type, upairset2E: $o). 9.37/180.03 thf(decl_186, type, upairsubunion: $o). 9.37/180.03 thf(decl_187, type, upairinpowunion: $o). 9.37/180.03 thf(decl_188, type, ubforcartprodlem1: $o). 9.37/180.03 thf(decl_189, type, ubforcartprodlem2: $o). 9.37/180.03 thf(decl_190, type, ubforcartprodlem3: $o). 9.37/180.03 thf(decl_191, type, cartprodpairin: $o). 9.37/180.03 thf(decl_192, type, cartprodmempair1: $o). 9.37/180.03 thf(decl_193, type, cartprodmempair: $o). 9.37/180.03 thf(decl_194, type, setunionE2: $o). 9.37/180.03 thf(decl_195, type, setunionsingleton1: $o). 9.37/180.03 thf(decl_196, type, setunionsingleton2: $o). 9.37/180.03 thf(decl_197, type, setunionsingleton: $o). 9.37/180.03 thf(decl_198, type, singleton: $i > $o). 9.37/180.03 thf(decl_199, type, singletonprop: $o). 9.37/180.03 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 9.37/180.03 thf(decl_201, type, ex1E1: $o). 9.37/180.03 thf(decl_202, type, ex1I: $o). 9.37/180.03 thf(decl_203, type, ex1I2: $o). 9.37/180.03 thf(decl_204, type, singletonsuniq: $o). 9.37/180.03 thf(decl_209, type, setukpairinjL1: $o). 9.37/180.03 thf(decl_210, type, kfstsingleton: $o). 9.37/180.03 thf(decl_211, type, theprop: $o). 9.37/180.03 thf(decl_212, type, kfst: $i > $i). 9.37/180.03 thf(decl_213, type, kfstpairEq: $o). 9.37/180.03 thf(decl_214, type, cartprodfstin: $o). 9.37/180.03 thf(decl_215, type, setukpairinjL2: $o). 9.37/180.03 thf(decl_216, type, setukpairinjL: $o). 9.37/180.03 thf(decl_217, type, setukpairinjR11: $o). 9.37/180.03 thf(decl_218, type, setukpairinjR12: $o). 9.37/180.03 thf(decl_219, type, setukpairinjR1: $o). 9.37/180.03 thf(decl_220, type, upairequniteq: $o). 9.37/180.03 thf(decl_221, type, setukpairinjR2: $o). 9.37/180.03 thf(decl_222, type, setukpairinjR: $o). 9.37/180.03 thf(decl_223, type, ksndsingleton: $o). 9.37/180.03 thf(decl_224, type, ksnd: $i > $i). 9.37/180.03 thf(decl_225, type, ksndpairEq: $o). 9.37/180.03 thf(decl_226, type, kpairsurjEq: $o). 9.37/180.03 thf(decl_227, type, cartprodsndin: $o). 9.37/180.03 thf(decl_228, type, cartprodpairmemEL: $o). 9.37/180.03 thf(decl_229, type, cartprodpairmemER: $o). 9.37/180.03 thf(decl_230, type, cartprodmempaircEq: $o). 9.37/180.03 thf(decl_231, type, cartprodfstpairEq: $o). 9.37/180.03 thf(decl_232, type, cartprodsndpairEq: $o). 9.37/180.03 thf(decl_233, type, cartprodpairsurjEq: $o). 9.37/180.03 thf(decl_234, type, breln: $i > $i > $i > $o). 9.37/180.03 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 9.37/180.03 thf(decl_236, type, dpsetconstrI: $o). 9.37/180.03 thf(decl_237, type, dpsetconstrSub: $o). 9.37/180.03 thf(decl_238, type, setOfPairsIsBReln: $o). 9.37/180.03 thf(decl_239, type, dpsetconstrERa: $o). 9.37/180.03 thf(decl_240, type, dpsetconstrEL1: $o). 9.37/180.03 thf(decl_241, type, dpsetconstrEL2: $o). 9.37/180.03 thf(decl_242, type, dpsetconstrER: $o). 9.37/180.03 thf(decl_243, type, func: $i > $i > $i > $o). 9.37/180.03 thf(decl_244, type, funcSet: $i > $i > $i). 9.37/180.03 thf(decl_245, type, funcImageSingleton: $o). 9.37/180.03 thf(decl_246, type, apProp: $o). 9.37/180.03 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 9.37/180.03 thf(decl_248, type, app: $o). 9.37/180.03 thf(decl_249, type, infuncsetfunc: $o). 9.37/180.03 thf(decl_250, type, ap2p: $o). 9.37/180.03 thf(decl_251, type, funcinfuncset: $o). 9.37/180.03 thf(decl_252, type, lamProp: $o). 9.37/180.03 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 9.37/180.03 thf(decl_254, type, lamp: $o). 9.37/180.03 thf(decl_255, type, lam2p: $o). 9.37/180.03 thf(decl_256, type, brelnall1: $o). 9.37/180.03 thf(decl_257, type, brelnall2: $o). 9.37/180.03 thf(decl_258, type, ex1E2: $o). 9.37/180.03 thf(decl_259, type, funcGraphProp1: $o). 9.37/180.03 thf(decl_260, type, funcGraphProp3: $o). 9.37/180.03 thf(decl_261, type, funcGraphProp2: $o). 9.37/180.03 thf(decl_262, type, funcextLem: $o). 9.37/180.03 thf(decl_263, type, funcGraphProp4: $o). 9.37/180.03 thf(decl_264, type, subbreln: $o). 9.37/180.03 thf(decl_265, type, eqbreln: $o). 9.37/180.03 thf(decl_266, type, funcext: $o). 9.37/180.03 thf(decl_267, type, funcext2: $o). 9.37/180.03 thf(decl_268, type, ap2apEq1: $o). 9.37/180.03 thf(decl_269, type, ap2apEq2: $o). 9.37/180.03 thf(decl_270, type, beta1: $o). 9.37/180.03 thf(decl_271, type, eta1: $o). 9.37/180.03 thf(decl_272, type, lam2lamEq: $o). 9.37/180.03 thf(decl_273, type, beta2: $o). 9.37/180.03 thf(decl_274, type, eta2: $o). 9.37/180.03 thf(decl_275, type, iffalseProp1: $o). 9.37/180.03 thf(decl_276, type, iffalseProp2: $o). 9.37/180.03 thf(decl_277, type, iftrueProp1: $o). 9.37/180.03 thf(decl_278, type, iftrueProp2: $o). 9.37/180.03 thf(decl_279, type, ifSingleton: $o). 9.37/180.03 thf(decl_280, type, if: $i > $o > $i > $i > $i). 9.37/180.03 thf(decl_281, type, ifp: $o). 9.37/180.03 thf(decl_282, type, theeq: $o). 9.37/180.03 thf(decl_283, type, iftrue: $o). 9.37/180.03 thf(decl_284, type, iffalse: $o). 9.37/180.03 thf(decl_285, type, iftrueorfalse: $o). 9.37/180.03 thf(decl_286, type, binintersectT_lem: $o). 9.37/180.03 thf(decl_287, type, binunionT_lem: $o). 9.37/180.03 thf(decl_288, type, powersetT_lem: $o). 9.37/180.03 thf(decl_289, type, setminusT_lem: $o). 9.37/180.03 thf(decl_290, type, complementT_lem: $o). 9.37/180.03 thf(decl_291, type, setextT: $o). 9.37/180.03 thf(decl_292, type, epred1_0: $o). 9.37/180.03 thf(decl_293, type, esk1_2: $i > $i > $i). 9.37/180.03 thf(decl_294, type, esk2_2: $i > $i > $i). 9.37/180.03 thf(decl_295, type, esk3_2: $i > $i > $i). 9.37/180.03 thf(decl_296, type, esk4_1: $i > $i). 9.37/180.03 thf(decl_297, type, esk5_2: ($i > $i > $o) > $i > $i). 9.37/180.03 thf(decl_298, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 9.37/180.03 thf(decl_299, type, esk7_2: ($i > $i > $o) > $i > $i). 9.37/180.03 thf(decl_300, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 9.37/180.03 thf(decl_301, type, esk9_1: $i > $i). 9.37/180.03 thf(decl_302, type, esk10_2: ($i > $o) > $i > $i). 9.37/180.03 thf(decl_303, type, esk11_2: ($i > $o) > $i > $i). 9.37/180.03 thf(decl_304, type, esk12_1: ($i > $o) > $i). 9.37/180.03 thf(decl_305, type, esk13_2: ($i > $o) > $i > $i). 9.37/180.03 thf(decl_306, type, esk14_1: ($i > $o) > $i). 9.37/180.03 thf(decl_307, type, esk15_2: $i > $i > $i). 9.37/180.03 thf(decl_308, type, esk16_2: $i > $i > $i). 9.37/180.03 thf(decl_309, type, esk17_1: $i > $i). 9.37/180.03 thf(decl_310, type, esk18_1: $i > $i). 9.37/180.03 thf(decl_311, type, esk19_1: $i > $i). 9.37/180.03 thf(decl_312, type, esk20_2: $i > $i > $i). 9.37/180.03 thf(decl_313, type, esk21_3: $i > $i > $o > $i). 9.37/180.03 thf(decl_314, type, esk22_2: ($i > $o) > $i > $i). 9.37/180.03 thf(decl_315, type, esk23_1: ($i > $o) > $i). 9.37/180.03 thf(decl_316, type, esk24_1: $i > $i). 9.37/180.03 thf(decl_317, type, esk25_2: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_318, type, esk26_2: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_319, type, esk27_2: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_320, type, esk28_2: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_321, type, esk29_2: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_322, type, esk30_2: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_323, type, esk31_2: ($i > $o) > $i > $i). 9.37/180.03 thf(decl_324, type, esk32_1: ($i > $o) > $i). 9.37/180.03 thf(decl_325, type, esk33_1: ($i > $o) > $i). 9.37/180.03 thf(decl_326, type, esk34_1: ($i > $o) > $i). 9.37/180.03 thf(decl_327, type, esk35_1: ($i > $o) > $i). 9.37/180.03 thf(decl_328, type, esk36_2: ($i > $o) > $i > $i). 9.37/180.03 thf(decl_329, type, esk37_1: ($i > $o) > $i). 9.37/180.03 thf(decl_330, type, esk38_2: ($i > $o) > $i > $i). 9.37/180.03 thf(decl_331, type, esk39_2: ($i > $o) > ($i > $o) > $i). 9.37/180.03 thf(decl_332, type, esk40_2: ($i > $o) > ($i > $o) > $i). 9.37/180.03 thf(decl_333, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 9.37/180.03 thf(decl_334, type, esk42_2: ($i > $o) > ($i > $o) > $i). 9.37/180.03 thf(decl_335, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 9.37/180.03 thf(decl_336, type, esk44_2: ($i > $o) > ($i > $o) > $i). 9.37/180.03 thf(decl_337, type, esk45_2: ($i > $o) > $i > $i). 9.37/180.03 thf(decl_338, type, esk46_2: ($i > $o) > ($i > $o) > $i). 9.37/180.03 thf(decl_339, type, esk47_2: ($i > $o) > ($i > $o) > $i). 9.37/180.03 thf(decl_340, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 9.37/180.03 thf(decl_341, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 9.37/180.03 thf(decl_342, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 9.37/180.03 thf(decl_343, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 9.37/180.03 thf(decl_344, type, esk52_2: $i > $i > $i). 9.37/180.03 thf(decl_345, type, esk53_2: $i > $i > $i). 9.37/180.03 thf(decl_346, type, esk54_2: $i > $i > $i). 9.37/180.03 thf(decl_347, type, esk55_3: $i > $i > $i > $i). 9.37/180.03 thf(decl_348, type, esk56_3: $i > $i > $i > $i). 9.37/180.03 thf(decl_349, type, esk57_2: $i > $i > $i). 9.37/180.03 thf(decl_350, type, esk58_2: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_351, type, esk59_2: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_352, type, esk60_2: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_353, type, esk61_3: $i > ($i > $o) > $i > $i). 9.37/180.03 thf(decl_354, type, esk62_2: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_355, type, esk63_2: $i > ($i > $o) > $i). 9.37/180.03 thf(decl_356, type, esk64_3: $i > $i > ($i > $i) > $i). 9.37/180.03 thf(decl_357, type, esk65_3: $i > $i > ($i > $i) > $i). 9.37/180.03 thf(decl_358, type, esk66_3: $i > $i > ($i > $i) > $i). 9.37/180.03 thf(decl_359, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 9.37/180.03 thf(decl_360, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 9.37/180.03 thf(decl_361, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 9.37/180.03 thf(decl_362, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 9.37/180.03 thf(decl_363, type, esk71_4: $i > $i > $i > $i > $i). 9.37/180.03 thf(decl_364, type, esk72_4: $i > $i > $i > $i > $i). 9.37/180.03 thf(decl_365, type, esk73_4: $i > $i > $i > $i > $i). 9.37/180.03 thf(decl_366, type, esk74_4: $i > $i > $i > $i > $i). 9.37/180.03 thf(decl_367, type, esk75_4: $i > $i > $i > $i > $i). 9.37/180.03 thf(decl_368, type, esk76_4: $i > $i > $i > $i > $i). 9.37/180.03 thf(decl_369, type, esk77_4: $i > $i > $i > $i > $i). 9.37/180.03 thf(decl_370, type, esk78_4: $i > $i > $i > $i > $i). 9.37/180.03 thf(decl_371, type, esk79_4: $i > $i > $i > $i > $i). 9.37/180.03 thf(decl_372, type, esk80_3: $i > $i > ($i > $i) > $i). 9.37/180.03 thf(decl_373, type, esk81_3: $i > $i > ($i > $i) > $i). 9.37/180.03 thf(decl_374, type, esk82_3: $i > $i > ($i > $i) > $i). 9.37/180.03 thf(decl_375, type, esk83_3: $i > $i > $i > $i). 9.37/180.03 thf(decl_376, type, esk84_3: $i > $i > $i > $i). 9.37/180.03 thf(decl_377, type, esk85_0: $i). 9.37/180.03 thf(decl_378, type, esk86_0: $i). 9.37/180.03 thf(decl_379, type, esk87_0: $i). 9.37/180.03 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', exuEu)). 9.37/180.03 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', exu)). 9.37/180.03 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', exu__Cong)). 9.37/180.03 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', exuI2)). 9.37/180.03 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', exuI3)). 9.37/180.03 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', exuI1)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', exuE2)). 9.37/180.03 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', nonempty)). 9.37/180.03 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', exuE3e)). 9.37/180.03 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', exuE1)). 9.37/180.03 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', descrp)). 9.37/180.03 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', ex1E1)). 9.37/180.03 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', ex1)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', ex1I)). 9.37/180.03 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', ex1I2)). 9.37/180.03 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setOfPairsIsBReln)). 9.37/180.03 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', breln)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', ex1E2)). 9.37/180.03 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', descr__Cong)). 9.37/180.03 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', exuE3u)). 9.37/180.03 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', nonemptyI)). 9.37/180.03 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', replAx)). 9.37/180.03 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', emptyE1)). 9.37/180.03 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setoftrueEq)). 9.37/180.03 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', nonemptyI1)). 9.37/180.03 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', dsetconstrER)). 9.37/180.03 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', dsetconstrEL)). 9.37/180.03 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', singletonprop)). 9.37/180.03 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', kfstsingleton)). 9.37/180.03 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', ksndsingleton)). 9.37/180.03 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', dpsetconstrSub)). 9.37/180.03 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', dpsetconstrERa)). 9.37/180.03 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', funcImageSingleton)). 9.37/180.03 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', apProp)). 9.37/180.03 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', lamProp)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', brelnall1)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', brelnall2)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', beta1)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', eta1)). 9.37/180.03 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', iftrueProp1)). 9.37/180.03 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', iftrueProp2)). 9.37/180.03 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', ifSingleton)). 9.37/180.03 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', iffalseProp2)). 9.37/180.03 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', iffalseProp1)). 9.37/180.03 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', eta2)). 9.37/180.03 thf(beta2, axiom, ((beta2)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', beta2)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', lam2lamEq)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', eqbreln)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', subbreln)). 9.37/180.03 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', lam2p)). 9.37/180.03 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', lamp)). 9.37/180.03 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', dpsetconstrER)). 9.37/180.03 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', dpsetconstrEL2)). 9.37/180.03 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', dpsetconstrEL1)). 9.37/180.03 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', dpsetconstrI)). 9.37/180.03 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', sepSubset)). 9.37/180.03 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', sepInPowerset)). 9.37/180.03 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', dsetconstr__Cong)). 9.37/180.03 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', nonemptyImpWitness)). 9.37/180.03 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', nonemptyE1)). 9.37/180.03 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setbeta)). 9.37/180.03 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', dsetconstrI)). 9.37/180.03 thf(subsetTI, conjecture, ((setextAx)=>(((setadjoinAx)=>(((setunionAx)=>(((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>(((dsetconstrI)=>((((((((notinemptyset)=>(((setext)=>((emptyI)=>(((setbeta)=>((nonemptyE1)=>((nonemptyI)=>(((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>(((((emptyinPowerset)=>(((powersetE)=>((((subPowSU)=>(((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>(((upairsetIL)=>((((vacuousDall)=>(((quantDeMorgan2)=>(((((prop2set2propI)=>(((notdallE)=>(((((inCongP)=>((in__Cong)=>((exuE3u)=>(((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>(((((descr__Cong)=>((dsetconstr__Cong)=>(((eqimpsubset2)=>((eqimpsubset1)=>((((subsetE)=>((((notequalI1)=>(((((((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>(((((powersetsubset)=>((sepInPowerset)=>(((((binunionIR)=>((((binunionLsub)=>((binunionRsub)=>((binintersectI)=>(((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>(((disjointsetsI1)=>((binintersectRsub)=>((((bs114d)=>((((setminusER)=>(((((((setminusLsub)=>((((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((((((((singletoninpowerset)=>(((upairset2E)=>(((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((((((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((((kfstsingleton)=>(((((((setukpairinjR11)=>(((setukpairinjR1)=>((upairequniteq)=>(((setukpairinjR)=>((ksndsingleton)=>(((kpairsurjEq)=>((cartprodsndin)=>(((cartprodpairmemER)=>(((cartprodfstpairEq)=>(((((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>(((((funcImageSingleton)=>((apProp)=>((((((lamProp)=>((((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(((((funcext2)=>(((ap2apEq2)=>((beta1)=>((eta1)=>(((((((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>(((iftrue)=>(((iftrueorfalse)=>((((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:((((subset @ X21 @ X48)<=![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)<=(in @ X2 @ X21)))))<=(in @ X48 @ (powerset @ X4))))))))))<=(binunionT_lem))<=(binintersectT_lem)))<=(iffalse)))<=(theeq))))))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))<=(beta2))<=(lam2lamEq)))))<=(ap2apEq1)))<=(funcext))<=(eqbreln))<=(subbreln))))))))))<=(lam2p))<=(lamp)))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc))<=(app))))<=(dpsetconstrER))<=(dpsetconstrEL2))<=(dpsetconstrEL1)))))<=(dpsetconstrI))<=(cartprodpairsurjEq))<=(cartprodsndpairEq)))<=(cartprodmempaircEq)))<=(cartprodpairmemEL))))<=(ksndpairEq))))<=(setukpairinjR2))))<=(setukpairinjR12)))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin))<=(kfstpairEq))<=(theprop)))<=(setukpairinjL1))<=(singletonsuniq))))))))<=(setunionsingleton1))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1)))))))<=(upairsubunion)))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))<=(secondinupair))))))<=(symdiffE))<=(setminusSubset1)))<=(setminusIRneg))<=(setminusILneg))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2)))<=(setminusEL))<=(setminusI)))<=(binintersectSubset1))<=(binintersectSubset4))))<=(binintersectER))))))<=(binintersectSubset5)))))<=(binunionE))<=(binunionEcases)))<=(upairset2IR))<=(binunionIL))<=(sepSubset))))<=(inPowerset))<=(powersetE1))<=(powersetI1)))))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl))<=(notequalI2)))<=(notsubsetI))<=(subsetE2)))<=(emptysetsubset))<=(subsetI2))))<=(subsetI1))))<=(exuEu))<=(omega__Cong))<=(setunion__Cong)))))<=(exu__Cong)))))<=(exuI2))<=(exuI3))<=(exuI1)))<=(notdexE)))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3)))<=(quantDeMorgan1)))<=(emptyE1))<=(upairsetIR)))<=(upairsetE)))))))<=(exuE2)))<=(setunionE))<=(setunionI)))<=(emptyInPowerset)))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))))))<=(nonemptyI1)))))<=(noeltsimpempty))))<=(exuE3e)))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp)))))))<=(omega0Ax)))<=(powersetAx)))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', subsetTI)). 9.37/180.03 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', emptyInPowerset)). 9.37/180.03 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', emptysetAx)). 9.37/180.03 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', subsetI2)). 9.37/180.03 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binintersectSubset3)). 9.37/180.03 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', subsetI1)). 9.37/180.03 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setminusER)). 9.37/180.03 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', omega__Cong)). 9.37/180.03 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setunion__Cong)). 9.37/180.03 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setminusLsub)). 9.37/180.03 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', symdiffI1)). 9.37/180.03 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', notdexE)). 9.37/180.03 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', symdiffI2)). 9.37/180.03 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', prop2setI)). 9.37/180.03 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', quantDeMorgan4)). 9.37/180.03 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', quantDeMorgan3)). 9.37/180.03 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', symdiffIneg1)). 9.37/180.03 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', quantDeMorgan1)). 9.37/180.03 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', disjointsetsI1)). 9.37/180.03 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', upairsetIR)). 9.37/180.03 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', symdiffIneg2)). 9.37/180.03 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', upairsetE)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', setunionE)). 9.37/180.03 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', singletoninpowerset)). 9.37/180.03 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setunionI)). 9.37/180.03 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', upairequniteq)). 9.37/180.03 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', powersetI)). 9.37/180.03 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', upairset2E)). 9.37/180.03 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setadjoinOr)). 9.37/180.03 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', upairinpowunion)). 9.37/180.03 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', noeltsimpempty)). 9.37/180.03 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', ubforcartprodlem1)). 9.37/180.03 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', emptysetimpfalse)). 9.37/180.03 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', emptysetE)). 9.37/180.03 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', prop2setE)). 9.37/180.03 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', ubforcartprodlem2)). 9.37/180.03 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', ubforcartprodlem3)). 9.37/180.03 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', omega0Ax)). 9.37/180.03 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', cartprodpairin)). 9.37/180.03 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', powersetAx)). 9.37/180.03 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setunionsingleton2)). 9.37/180.03 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setunionsingleton)). 9.37/180.03 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binintersectRsub)). 9.37/180.03 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setukpairinjR11)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', setukpairinjR1)). 9.37/180.03 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setminusT_lem)). 9.37/180.03 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', complementT_lem)). 9.37/180.03 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setukpairinjR)). 9.37/180.03 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', kpairsurjEq)). 9.37/180.03 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', cartprodsndin)). 9.37/180.03 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', cartprodpairmemER)). 9.37/180.03 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', cartprodfstpairEq)). 9.37/180.03 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', bs114d)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', funcGraphProp1)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', funcGraphProp3)). 9.37/180.03 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', funcGraphProp2)). 9.37/180.03 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', funcextLem)). 9.37/180.03 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', funcGraphProp4)). 9.37/180.03 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', funcext2)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', ap2apEq2)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', ifp)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', iftrue)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', iftrueorfalse)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', powersetT_lem)). 9.37/180.03 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setextT)). 9.37/180.03 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', binunionT_lem)). 9.37/180.03 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binintersectT_lem)). 9.37/180.03 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', iffalse)). 9.37/180.03 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', theeq)). 9.37/180.03 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', ap2apEq1)). 9.37/180.03 thf(funcext, axiom, ((funcext)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', funcext)). 9.37/180.03 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', funcinfuncset)). 9.37/180.03 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', ap2p)). 9.37/180.03 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', infuncsetfunc)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', app)). 9.37/180.03 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', cartprodpairsurjEq)). 9.37/180.03 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', cartprodsndpairEq)). 9.37/180.03 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', cartprodmempaircEq)). 9.37/180.03 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', cartprodpairmemEL)). 9.37/180.03 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', ksndpairEq)). 9.37/180.03 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setukpairinjR2)). 9.37/180.03 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setukpairinjR12)). 9.37/180.03 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setukpairinjL)). 9.37/180.03 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setukpairinjL2)). 9.37/180.03 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', cartprodfstin)). 9.37/180.03 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', kfstpairEq)). 9.37/180.03 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', theprop)). 9.37/180.03 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.L8xTg8DLw2/E---3.1_6163.p', setukpairinjL1)). 9.37/180.03 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', singletonsuniq)). 9.37/180.03 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setunionsingleton1)). 9.37/180.03 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setunionE2)). 9.37/180.03 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', cartprodmempair)). 9.37/180.03 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', cartprodmempair1)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', upairsubunion)). 9.37/180.03 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', singletoninpowunion)). 9.37/180.03 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', singletonsubset)). 9.37/180.03 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', kpairp)). 9.37/180.03 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', kpairiskpair)). 9.37/180.03 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setukpairIR)). 9.37/180.03 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setukpairIL)). 9.37/180.03 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', secondinupair)). 9.37/180.03 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', symdiffE)). 9.37/180.03 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setminusSubset1)). 9.37/180.03 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setminusIRneg)). 9.37/180.03 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setminusILneg)). 9.37/180.03 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setminusELneg)). 9.37/180.03 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setminusERneg)). 9.37/180.03 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setminusSubset2)). 9.37/180.03 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setminusEL)). 9.37/180.03 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setminusI)). 9.37/180.03 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binintersectSubset1)). 9.37/180.03 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binintersectSubset4)). 9.37/180.03 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binintersectER)). 9.37/180.03 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binintersectSubset5)). 9.37/180.03 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binunionE)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', binunionEcases)). 9.37/180.03 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', upairset2IR)). 9.37/180.03 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binunionIL)). 9.37/180.03 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', inPowerset)). 9.37/180.03 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', powersetE1)). 9.37/180.03 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', powersetI1)). 9.37/180.03 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setadjoinSub2)). 9.37/180.03 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setadjoinSub)). 9.37/180.03 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', subsetTrans)). 9.37/180.03 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', subsetRefl)). 9.37/180.03 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', notequalI2)). 9.37/180.03 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', notsubsetI)). 9.37/180.03 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', subsetE2)). 9.37/180.03 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', emptysetsubset)). 9.37/180.03 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binintersectSubset2)). 9.37/180.03 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binintersectLsub)). 9.37/180.03 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binintersectEL)). 9.37/180.03 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binintersectI)). 9.37/180.03 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binunionRsub)). 9.37/180.03 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binunionLsub)). 9.37/180.03 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', binunionIR)). 9.37/180.03 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', powersetsubset)). 9.37/180.03 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', subsetemptysetimpeq)). 9.37/180.03 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setextsub)). 9.37/180.03 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', subset2powerset)). 9.37/180.03 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', notequalI1)). 9.37/180.03 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', subsetE)). 9.37/180.03 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', eqimpsubset1)). 9.37/180.03 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', eqimpsubset2)). 9.37/180.03 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', powerset__Cong)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', setadjoin__Cong)). 9.37/180.03 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', emptyset__Cong)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', in__Cong)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', inCongP)). 9.37/180.03 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', notdallE)). 9.37/180.03 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', quantDeMorgan2)). 9.37/180.03 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', vacuousDall)). 9.37/180.03 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', upairsetIL)). 9.37/180.03 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', singletonsswitch)). 9.37/180.03 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', eqinunit)). 9.37/180.03 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', notinsingleton)). 9.37/180.03 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', uniqinunit)). 9.37/180.03 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', subPowSU)). 9.37/180.03 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', powersetE)). 9.37/180.03 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', emptyinPowerset)). 9.37/180.03 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.L8xTg8DLw2/E---3.1_6163.p', setadjoinE)). 9.37/180.03 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setadjoinIR)). 9.37/180.03 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', emptyinunitempty)). 9.37/180.03 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setadjoinIL)). 9.37/180.03 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', emptyI)). 9.37/180.03 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setext)). 9.37/180.03 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', notinemptyset)). 9.37/180.03 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', wellorderingAx)). 9.37/180.03 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', foundationAx)). 9.37/180.03 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.L8xTg8DLw2/E---3.1_6163.p', omegaIndAx)). 9.37/180.03 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', omegaSAx)). 9.37/180.03 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setunionAx)). 9.37/180.03 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setadjoinAx)). 9.37/180.03 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.L8xTg8DLw2/E---3.1_6163.p', setextAx)). 9.37/180.03 thf(c_0_236, 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])). 9.37/180.03 thf(c_0_237, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 9.37/180.03 thf(c_0_238, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 9.37/180.03 thf(c_0_239, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 9.37/180.03 thf(c_0_240, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 9.37/180.03 thf(c_0_241, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 9.37/180.03 thf(c_0_242, 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])). 9.37/180.03 thf(c_0_243, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 9.37/180.03 thf(c_0_244, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 9.37/180.03 thf(c_0_245, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 9.37/180.03 thf(c_0_246, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 9.37/180.03 thf(c_0_247, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 9.37/180.03 thf(c_0_248, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])). 9.37/180.03 thf(c_0_249, 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])). 9.37/180.03 thf(c_0_250, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 9.37/180.03 thf(c_0_251, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 9.37/180.03 thf(c_0_252, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 9.37/180.03 thf(c_0_253, 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])). 9.37/180.03 thf(c_0_254, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 9.37/180.03 thf(c_0_255, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 9.37/180.03 thf(c_0_256, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 9.37/180.03 thf(c_0_257, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 9.37/180.03 thf(c_0_258, plain, ((exuEu)=(![X1:$i > $o]:(((?[X788:$i]:((((X1 @ X788))&![X789:$i]:((((X1 @ X789))=>((X788)=(X789)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_237])). 9.37/180.03 thf(c_0_259, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X784:$i]:((((X1 @ X784))&![X785:$i]:((((X1 @ X785))=>((X784)=(X785)))))))<=>(?[X786:$i]:((((X17 @ X786))&![X787:$i]:((((X17 @ X787))=>((X786)=(X787)))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_237])). 9.37/180.03 thf(c_0_260, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X780:$i]:((((X1 @ X780))&![X781:$i]:((((X1 @ X781))=>((X780)=(X781))))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_237])). 9.37/180.03 thf(c_0_261, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X778:$i]:((((X1 @ X778))&![X779:$i]:((((X1 @ X779))=>((X778)=(X779)))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_237])). 9.37/180.03 thf(c_0_262, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X776:$i]:((((X1 @ X776))&![X777:$i]:((((X1 @ X777))=>((X776)=(X777))))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_237])). 9.37/180.03 thf(c_0_263, plain, ((emptyE1)<=>![X4:$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])). 9.37/180.03 thf(c_0_264, plain, ((exuE2)=(![X1:$i > $o]:(((?[X774:$i]:((((X1 @ X774))&![X775:$i]:((((X1 @ X775))=>((X774)=(X775)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_237])). 9.37/180.03 thf(c_0_265, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 9.37/180.03 thf(c_0_266, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_243])). 9.37/180.03 thf(c_0_267, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X772:$i]:((((X1 @ X772))&![X773:$i]:((((X1 @ X773))=>((X772)=(X773)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_244, c_0_237])). 9.37/180.03 thf(c_0_268, plain, ((exuE1)=(![X1:$i > $o]:(((?[X770:$i]:((((X1 @ X770))&![X771:$i]:((((X1 @ X771))=>((X770)=(X771)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_237])). 9.37/180.03 thf(c_0_269, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 9.37/180.03 thf(c_0_270, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 9.37/180.03 thf(c_0_271, plain, ((descrp)=(![X1:$i > $o]:(((?[X768:$i]:((((X1 @ X768))&![X769:$i]:((((X1 @ X769))=>((X768)=(X769)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_237])). 9.37/180.03 thf(c_0_272, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 9.37/180.03 thf(c_0_273, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_247, c_0_248])). 9.37/180.03 thf(c_0_274, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))))))))), inference(apply_def,[status(thm)],[c_0_249, c_0_248])). 9.37/180.03 thf(c_0_275, 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)))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))))))), inference(apply_def,[status(thm)],[c_0_250, c_0_248])). 9.37/180.03 thf(c_0_276, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 9.37/180.03 thf(c_0_277, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 9.37/180.03 thf(c_0_278, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 9.37/180.03 thf(c_0_279, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_251, c_0_252])). 9.37/180.03 thf(c_0_280, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 9.37/180.03 thf(c_0_281, plain, ((funcImageSingleton)<=>![X4:$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])). 9.37/180.03 thf(c_0_282, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 9.37/180.03 thf(c_0_283, plain, ((lamProp)<=>![X4:$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])). 9.37/180.03 thf(c_0_284, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$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))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_252])). 9.37/180.03 thf(c_0_285, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$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))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_252])). 9.37/180.03 thf(c_0_286, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_253, c_0_248])). 9.37/180.03 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])). 9.37/180.03 thf(c_0_288, 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])). 9.37/180.03 thf(c_0_289, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 9.37/180.03 thf(c_0_290, plain, ((iftrueProp2)<=>![X4:$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])). 9.37/180.03 thf(c_0_291, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 9.37/180.03 thf(c_0_292, plain, ((iffalseProp2)<=>![X4:$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])). 9.37/180.03 thf(c_0_293, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 9.37/180.03 thf(c_0_294, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 9.37/180.03 thf(c_0_295, plain, ((beta2)<=>![X4:$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])). 9.37/180.03 thf(c_0_296, 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])). 9.37/180.03 thf(c_0_297, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![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)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_252])). 9.37/180.03 thf(c_0_298, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_252])). 9.37/180.03 thf(c_0_299, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 9.37/180.03 thf(c_0_300, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 9.37/180.03 thf(c_0_301, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 9.37/180.03 thf(c_0_302, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 9.37/180.03 thf(c_0_303, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 9.37/180.03 thf(c_0_304, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 9.37/180.03 thf(c_0_305, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 9.37/180.03 thf(c_0_306, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 9.37/180.03 thf(c_0_307, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 9.37/180.03 thf(c_0_308, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X790:$i]:((((X1 @ X790))&![X791:$i]:((((X1 @ X791))=>((X790)=(X791)))))))=>((?[X792:$i]:((((X17 @ X792))&![X793:$i]:((((X17 @ X793))=>((X792)=(X793)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_254, c_0_237])). 9.37/180.03 thf(c_0_309, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X782:$i]:((((X1 @ X782))&![X783:$i]:((((X1 @ X783))=>((X782)=(X783)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_255, c_0_237])). 9.37/180.03 thf(c_0_310, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_243])). 9.37/180.03 thf(c_0_311, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_256, c_0_243])). 9.37/180.03 thf(c_0_312, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_243])). 9.37/180.03 thf(c_0_313, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 9.37/180.03 thf(c_0_314, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 9.37/180.03 thf(c_0_315, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X766:$i]:((((X6 @ X2 @ X766))&![X767:$i]:((((X6 @ X2 @ X767))=>((X766)=(X767)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_257, c_0_237])). 9.37/180.03 thf(c_0_316, plain, ((epred1_0)<=>![X819:$i]:(?[X820:$i]:((((![X821:$i]:(((in @ X821 @ X820)=>![X822:$i]:(((in @ X822 @ X821)=>(in @ X822 @ X819)))))&![X823:$i, X824:$i]:((((in @ X823 @ X819)&(in @ X824 @ X819))=>(![X825:$i]:(((in @ X825 @ X820)=>((in @ X823 @ X825)<=>(in @ X824 @ X825))))=>((X823)=(X824))))))&![X826:$i, X827:$i]:((((in @ X826 @ X820)&(in @ X827 @ X820))=>(![X828:$i]:(((in @ X828 @ X826)=>(in @ X828 @ X827)))|![X829:$i]:(((in @ X829 @ X827)=>(in @ X829 @ X826)))))))&![X830:$i]:(((![X831:$i]:(((in @ X831 @ X830)=>(in @ X831 @ X819)))&?[X832:$i]:((in @ X832 @ X830)))=>?[X833:$i, X834:$i]:(((((in @ X833 @ X820)&(in @ X834 @ X830))&~(?[X835:$i]:(((in @ X835 @ X833)&(in @ X835 @ X830)))))&![X836:$i]:(((in @ X836 @ X820)=>(![X837:$i]:(((in @ X837 @ X836)=>(in @ X837 @ X833)))|(in @ X834 @ X836)))))))))))), introduced(definition)). 9.37/180.03 thf(c_0_317, negated_conjecture, ~((![X794:$i, X795:$i]:((![X796:$i]:(((in @ X796 @ X794)<=>(in @ X796 @ X795)))=>((X794)=(X795))))=>(![X1534:$i]:(~(in @ X1534 @ emptyset))=>(![X797:$i, X798:$i, X799:$i]:(((in @ X799 @ (setadjoin @ X797 @ X798))<=>(((X799)=(X797))|(in @ X799 @ X798))))=>(![X1531:$i, X1532:$i]:(((in @ X1532 @ (powerset @ X1531))<=>![X1533:$i]:(((in @ X1533 @ X1532)=>(in @ X1533 @ X1531)))))=>(![X800:$i, X801:$i]:(((in @ X801 @ (setunion @ X800))<=>?[X802:$i]:(((in @ X801 @ X802)&(in @ X802 @ X800)))))=>((in @ emptyset @ omega)=>(![X803:$i]:(((in @ X803 @ omega)=>(in @ (setadjoin @ X803 @ X803) @ omega)))=>(![X804:$i]:((((in @ emptyset @ X804)&![X805:$i]:((((in @ X805 @ omega)&(in @ X805 @ X804))=>(in @ (setadjoin @ X805 @ X805) @ X804))))=>![X806:$i]:(((in @ X806 @ omega)=>(in @ X806 @ X804)))))=>(![X807:$i > $i > $o, X808:$i]:((![X809:$i]:(((in @ X809 @ X808)=>?[X810:$i]:(((X807 @ X809 @ X810)&![X811:$i]:(((X807 @ X809 @ X811)=>((X810)=(X811))))))))=>?[X812:$i]:(![X813:$i]:(((in @ X813 @ X812)<=>?[X814:$i]:(((in @ X814 @ X808)&(X807 @ X814 @ X813))))))))=>(![X815:$i]:((?[X816:$i]:((in @ X816 @ X815))=>?[X817:$i]:(((in @ X817 @ X815)&~(?[X818:$i]:(((in @ X818 @ X817)&(in @ X818 @ X815))))))))=>((epred1_0)=>(![X1528:$i > $o]:((?[X1529:$i]:(((X1528 @ X1529)&![X1530:$i]:(((X1528 @ X1530)=>((X1529)=(X1530))))))=>(X1528 @ (descr @ (^[Z0/* 17 */:$i]:(X1528 @ Z0))))))=>(![X838:$i, X839:$i > $o, X840:$i]:(((in @ X840 @ X838)=>((X839 @ X840)=>(in @ X840 @ (dsetconstr @ X838 @ X839)))))=>(![X1525:$i, X1526:$i > $o, X1527:$i]:(((in @ X1527 @ (dsetconstr @ X1525 @ X1526))=>(in @ X1527 @ X1525)))=>(![X1522:$i, X1523:$i > $o, X1524:$i]:(((in @ X1524 @ (dsetconstr @ X1522 @ X1523))=>(X1523 @ X1524)))=>(![X1517:$i > $o]:((?[X1518:$i]:(((X1517 @ X1518)&![X1519:$i]:(((X1517 @ X1519)=>((X1518)=(X1519))))))=>?[X1520:$i]:(((X1517 @ X1520)&![X1521:$i]:(((X1517 @ X1521)=>((X1520)=(X1521))))))))=>(![X1515:$o, X1516:$i]:(((in @ X1516 @ (prop2set @ ((X1515))))=>(X1515)))=>(![X1513:$i]:(((in @ X1513 @ emptyset)=>![X1514:$o]:((X1514))))=>(![X1512:$i]:(((in @ X1512 @ emptyset)=>~($true)))=>(![X841:$i]:(~(in @ X841 @ emptyset))=>(![X1508:$i > $o]:((?[X1509:$i]:(((X1508 @ X1509)&![X1510:$i]:(((X1508 @ X1510)=>((X1509)=(X1510))))))=>?[X1511:$i]:((X1508 @ X1511))))=>(![X842:$i, X843:$i]:((![X844:$i]:(((in @ X844 @ X842)=>(in @ X844 @ X843)))=>(![X845:$i]:(((in @ X845 @ X843)=>(in @ X845 @ X842)))=>((X842)=(X843)))))=>(![X846:$i]:((![X847:$i]:(~(in @ X847 @ X846))=>((X846)=(emptyset))))=>(![X1506:$i]:((![X1507:$i]:(~(in @ X1507 @ X1506))=>((X1506)=(emptyset))))=>(![X848:$i, X849:$i > $o, X850:$i]:(((in @ X850 @ X848)=>((in @ X850 @ (dsetconstr @ X848 @ X849))<=>(X849 @ X850))))=>(![X851:$i]:((((X851)!=(emptyset))=>?[X852:$i]:((in @ X852 @ X851))))=>(![X853:$i, X854:$i > $o, X855:$i]:(((in @ X855 @ X853)=>((X854 @ X855)=>((dsetconstr @ X853 @ X854)!=(emptyset)))))=>(![X1504:$i]:((?[X1505:$i]:((in @ X1505 @ X1504))=>((X1504)!=(emptyset))))=>(![X856:$i, X857:$i]:((in @ X856 @ (setadjoin @ X856 @ X857)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X858:$i, X859:$i, X860:$i]:(((in @ X860 @ X859)=>(in @ X860 @ (setadjoin @ X858 @ X859))))=>(![X861:$i, X862:$i, X863:$i]:(((in @ X863 @ (setadjoin @ X861 @ X862))=>![X864:$o]:(((((X863)=(X861))=>(X864))=>(((in @ X863 @ X862)=>(X864))=>(X864))))))=>(![X1501:$i, X1502:$i, X1503:$i]:(((in @ X1503 @ (setadjoin @ X1501 @ X1502))=>(((X1503)=(X1501))|(in @ X1503 @ X1502))))=>(![X1500:$i]:(((dsetconstr @ X1500 @ (^[Z0/* 1 */:$i]:($true)))=(X1500)))=>(![X1497:$i, X1498:$i]:((![X1499:$i]:(((in @ X1499 @ X1498)=>(in @ X1499 @ X1497)))=>(in @ X1498 @ (powerset @ X1497))))=>(![X865:$i]:((in @ emptyset @ (powerset @ X865)))=>(![X1496:$i]:((in @ emptyset @ (powerset @ X1496)))=>(![X866:$i, X867:$i, X868:$i]:(((in @ X867 @ (powerset @ X866))=>((in @ X868 @ X867)=>(in @ X868 @ X866))))=>(![X1493:$i, X1494:$i, X1495:$i]:(((in @ X1494 @ X1495)=>((in @ X1495 @ X1493)=>(in @ X1494 @ (setunion @ X1493)))))=>(![X1489:$i, X1490:$i]:(((in @ X1490 @ (setunion @ X1489))=>![X1491:$o]:((![X1492:$i]:(((in @ X1490 @ X1492)=>((in @ X1492 @ X1489)=>(X1491))))=>(X1491)))))=>(![X869:$i, X870:$i]:(((in @ X870 @ X869)=>(in @ X870 @ (powerset @ (setunion @ X869)))))=>(![X1484:$i > $o]:((?[X1485:$i]:(((X1484 @ X1485)&![X1486:$i]:(((X1484 @ X1486)=>((X1485)=(X1486))))))=>?[X1487:$i]:(![X1488:$i]:(((X1484 @ X1488)<=>((X1488)=(X1487)))))))=>(![X871:$i]:((((X871)!=(emptyset))=>?[X872:$i]:(((in @ X872 @ X871)&$true))))=>(![X873:$i, X874:$i]:(((in @ X873 @ (setadjoin @ X874 @ emptyset))=>((X873)=(X874))))=>(![X875:$i, X876:$i]:((((X875)!=(X876))=>~(in @ X876 @ (setadjoin @ X875 @ emptyset))))=>(![X877:$i, X878:$i]:((((X877)=(X878))=>(in @ X877 @ (setadjoin @ X878 @ emptyset))))=>(![X879:$i, X880:$i]:(((in @ X879 @ (setadjoin @ X880 @ emptyset))=>(in @ X880 @ (setadjoin @ X879 @ emptyset))))=>(![X1481:$i, X1482:$i, X1483:$i]:(((in @ X1483 @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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emptyInPowerset]), emptysetAx]), subsetI2]), binintersectSubset3]), subsetI1]), c_0_258]), setminusER]), omega__Cong]), setunion__Cong]), setminusLsub]), c_0_259]), c_0_260]), c_0_261]), symdiffI1]), c_0_262]), notdexE]), symdiffI2]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), symdiffIneg1]), quantDeMorgan1]), disjointsetsI1]), c_0_263]), upairsetIR]), symdiffIneg2]), upairsetE]), c_0_264]), setunionE]), singletoninpowerset]), setunionI]), upairequniteq]), powersetI]), upairset2E]), c_0_265]), setadjoinOr]), c_0_266]), upairinpowunion]), noeltsimpempty]), c_0_267]), ubforcartprodlem1]), emptysetimpfalse]), emptysetE]), prop2setE]), ubforcartprodlem2]), c_0_268]), c_0_269]), ubforcartprodlem3]), c_0_270]), c_0_271]), omega0Ax]), cartprodpairin]), powersetAx]), setunionsingleton2]), setunionsingleton]), binintersectRsub]), c_0_272]), c_0_273]), c_0_274]), c_0_275]), c_0_276]), setukpairinjR11]), setukpairinjR1]), setminusT_lem]), complementT_lem]), setukpairinjR]), c_0_277]), kpairsurjEq]), cartprodsndin]), cartprodpairmemER]), cartprodfstpairEq]), c_0_278]), c_0_279]), c_0_280]), bs114d]), c_0_281]), c_0_282]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), funcext2]), ap2apEq2]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), ifp]), iftrue]), iftrueorfalse]), powersetT_lem]), setextT]), binunionT_lem]), binintersectT_lem]), iffalse]), theeq]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), ap2apEq1]), funcext]), c_0_297]), c_0_298]), c_0_299]), c_0_300]), funcinfuncset]), ap2p]), infuncsetfunc]), app]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodmempaircEq]), cartprodpairmemEL]), ksndpairEq]), setukpairinjR2]), setukpairinjR12]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), theprop]), setukpairinjL1]), singletonsuniq]), setunionsingleton1]), setunionE2]), cartprodmempair]), cartprodmempair1]), upairsubunion]), singletoninpowunion]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), symdiffE]), setminusSubset1]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusEL]), setminusI]), binintersectSubset1]), binintersectSubset4]), binintersectER]), binintersectSubset5]), binunionE]), binunionEcases]), upairset2IR]), binunionIL]), c_0_305]), inPowerset]), powersetE1]), powersetI1]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notsubsetI]), subsetE2]), emptysetsubset]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectI]), binunionRsub]), binunionLsub]), binunionIR]), c_0_306]), powersetsubset]), subsetemptysetimpeq]), setextsub]), subset2powerset]), notequalI1]), subsetE]), eqimpsubset1]), eqimpsubset2]), c_0_307]), c_0_308]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_309]), in__Cong]), inCongP]), notdallE]), quantDeMorgan2]), vacuousDall]), upairsetIL]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_310]), subPowSU]), powersetE]), emptyinPowerset]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_311]), c_0_312]), c_0_313]), emptyI]), setext]), notinemptyset]), c_0_314]), wellorderingAx]), foundationAx]), c_0_315]), omegaIndAx]), omegaSAx]), setunionAx]), setadjoinAx]), setextAx])])]), c_0_316])). 9.37/180.03 thf(c_0_318, negated_conjecture, ![X1535:$i, X1536:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1548:$i, X1549:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1557:$i, X1558:$i > $i > $o, X1559:$i, X1561:$i, X1564:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1571:$i, X1572:$i > $o, X1573:$i, X1575:$i, X1576:$i > $o, X1577:$i, X1578:$i, X1579:$i > $o, X1580:$i, X1581:$i, X1582:$i > $o, X1583:$i, X1584:$i > $o, X1585:$i, X1588:$i, X1589:$o, X1590:$i, X1591:$i, X1592:$o, X1593:$i, X1594:$i, X1595:$i > $o, X1596:$i, X1599:$i, X1600:$i, X1603:$i, X1605:$i, X1607:$i, X1608:$i > $o, X1609:$i, X1610:$i, X1612:$i, X1613:$i > $o, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$o, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$o, X1645:$i, X1646:$i, X1647:$i > $o, X1648:$i, X1651:$i, X1652:$i, X1653:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i > $o, X1672:$i, X1673:$i > $o, X1674:$i, X1675:$i, X1676:$i > $o, X1677:$i, X1679:$i, X1680:$i > $o, X1682:$i, X1683:$i, X1684:$i > $o, X1686:$i, X1687:$i, X1688:$i > $o, X1689:$i, X1691:$o, X1692:$i, X1693:$i > $o, X1695:$i, X1696:$i, X1697:$i > $o, X1698:$i, X1700:$i > $o, X1701:$i, X1704:$i, X1705:$i > $o, X1706:$i, X1710:$i, X1711:$i > $o, X1712:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i > $o, X1725:$i, X1727:$i, X1728:$i, X1729:$i > $o, X1730:$i > $o, X1733:$i, X1736:$i, X1737:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i > $o, X1750:$i, X1752:$i, X1753:$i, X1754:$i > $o, X1755:$i > $o, X1758:$i, X1760:$i, X1762:$i, X1763:$i, X1764:$i > $o, X1765:$i > $o, X1768:$i, X1769:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i > $o, X1816:$i, X1817:$i > $o, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$o, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$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:$i, X1897:$o, 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, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, 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:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i > $o, X1972:$i, X1973:$i, X1974:$i > $o, X1976:$i, X1977:$i > $o, X1978:$i, X1980:$i, X1981:$i > $o, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$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, X2053:$i, X2054:$i, X2055:$i, X2056:$i > $i > $o, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i > $i > $o, X2062:$i, X2063:$i, X2064:$i > $i > $o, X2065:$i, X2066:$i, X2067:$i > $i > $o, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i > $i > $o, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i > $i > $o, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i > $i > $o, X2083:$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 > $i, X2111:$i, X2112:$i, X2113:$i > $i, X2115:$i, X2116:$i, X2117:$i > $i, X2119:$i, X2120:$i, X2121:$i, X2122:$i > $o, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i > $o, X2132:$i, X2133:$i, X2134:$i > $o, X2135:$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:$i, X2153:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i > $i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i > $i, X2206:$i, X2207:$i, X2208:$i > $i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$o, X2216:$i, X2217:$i, X2218:$i, X2219:$o, X2220:$i, X2221:$i, X2222:$i, X2223:$o, X2224:$i, X2225:$i, X2226:$i, X2227:$o, X2228:$i, X2229:$i, X2230:$i, X2231:$o, X2232:$i, X2233:$i, X2234:$i, X2235:$o, 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(esk74_4 @ X2168 @ X2169 @ X2170 @ X2171) @ (esk75_4 @ X2168 @ X2169 @ X2170 @ X2171)) @ X2170)|~(subset @ X2171 @ (cartprod @ X2168 @ X2169))|~(subset @ X2170 @ (cartprod @ X2168 @ X2169))))))&(((in @ (esk76_4 @ X2168 @ X2169 @ X2170 @ X2171) @ X2168)|((X2170)=(X2171))|~(in @ (kpair @ (esk74_4 @ X2168 @ X2169 @ X2170 @ X2171) @ (esk75_4 @ X2168 @ X2169 @ X2170 @ X2171)) @ X2171)|~(subset @ X2171 @ (cartprod @ X2168 @ X2169))|~(subset @ X2170 @ (cartprod @ X2168 @ X2169)))&(((in @ (esk77_4 @ X2168 @ X2169 @ X2170 @ X2171) @ X2169)|((X2170)=(X2171))|~(in @ (kpair @ (esk74_4 @ X2168 @ X2169 @ X2170 @ X2171) @ (esk75_4 @ X2168 @ X2169 @ X2170 @ X2171)) @ X2171)|~(subset @ X2171 @ (cartprod @ X2168 @ X2169))|~(subset @ X2170 @ (cartprod @ X2168 @ X2169)))&(((in @ (kpair @ (esk76_4 @ X2168 @ X2169 @ X2170 @ X2171) @ (esk77_4 @ X2168 @ X2169 @ X2170 @ X2171)) @ X2171)|((X2170)=(X2171))|~(in @ (kpair @ (esk74_4 @ X2168 @ X2169 @ X2170 @ X2171) @ (esk75_4 @ X2168 @ X2169 @ X2170 @ X2171)) @ X2171)|~(subset @ X2171 @ (cartprod @ X2168 @ X2169))|~(subset @ X2170 @ (cartprod @ X2168 @ X2169)))&(~(in @ (kpair @ (esk76_4 @ X2168 @ X2169 @ X2170 @ X2171) @ (esk77_4 @ X2168 @ X2169 @ X2170 @ X2171)) @ X2170)|((X2170)=(X2171))|~(in @ (kpair @ (esk74_4 @ X2168 @ X2169 @ X2170 @ X2171) @ (esk75_4 @ X2168 @ X2169 @ X2170 @ X2171)) @ X2171)|~(subset @ X2171 @ (cartprod @ X2168 @ X2169))|~(subset @ X2170 @ (cartprod @ X2168 @ X2169)))))))))&((((in @ (esk78_4 @ X2176 @ X2177 @ X2178 @ X2179) @ X2176)|((X2178)=(X2179))|~(func @ X2176 @ X2177 @ X2179)|~(func @ X2176 @ X2177 @ X2178))&(((ap @ X2176 @ X2177 @ X2178 @ (esk78_4 @ X2176 @ X2177 @ X2178 @ X2179))!=(ap @ X2176 @ X2177 @ X2179 @ (esk78_4 @ X2176 @ X2177 @ X2178 @ X2179)))|((X2178)=(X2179))|~(func @ X2176 @ X2177 @ X2179)|~(func @ X2176 @ X2177 @ X2178)))&((((in @ (esk79_4 @ X2181 @ X2182 @ X2183 @ X2184) @ X2181)|((X2183)=(X2184))|~(in @ X2184 @ (funcSet @ X2181 @ X2182))|~(in @ X2183 @ (funcSet @ X2181 @ X2182)))&(((ap @ X2181 @ X2182 @ X2183 @ (esk79_4 @ X2181 @ X2182 @ X2183 @ X2184))!=(ap @ X2181 @ X2182 @ X2184 @ (esk79_4 @ X2181 @ X2182 @ X2183 @ X2184)))|((X2183)=(X2184))|~(in @ X2184 @ (funcSet @ X2181 @ X2182))|~(in @ X2183 @ (funcSet @ X2181 @ X2182))))&((~(in @ X2188 @ (funcSet @ X2186 @ X2187))|(~(in @ X2189 @ X2186)|((ap @ X2186 @ X2187 @ X2188 @ X2189)=(ap @ X2186 @ X2187 @ X2188 @ X2189))))&((~(func @ X2190 @ X2191 @ X2192)|(~(in @ X2193 @ X2190)|((ap @ X2190 @ X2191 @ X2192 @ X2193)=(ap @ X2190 @ X2191 @ X2192 @ X2193))))&((((in @ (esk80_3 @ X2194 @ X2195 @ X2196) @ X2194)|(~(in @ X2198 @ X2194)|((ap @ X2194 @ X2195 @ (lam @ X2194 @ X2195 @ X2196) @ X2198)=(X2196 @ X2198))))&(~(in @ (X2196 @ (esk80_3 @ X2194 @ X2195 @ X2196)) @ X2195)|(~(in @ X2198 @ X2194)|((ap @ X2194 @ X2195 @ (lam @ X2194 @ X2195 @ X2196) @ X2198)=(X2196 @ X2198)))))&((~(func @ X2199 @ X2200 @ X2201)|((lam @ X2199 @ X2200 @ (ap @ X2199 @ X2200 @ X2201))=(X2201)))&((((in @ (esk81_3 @ X2202 @ X2203 @ X2204) @ X2202)|((lam @ X2202 @ X2203 @ X2204)=(lam @ X2202 @ X2203 @ X2204)))&(~(in @ (X2204 @ (esk81_3 @ X2202 @ X2203 @ X2204)) @ X2203)|((lam @ X2202 @ X2203 @ X2204)=(lam @ X2202 @ X2203 @ X2204))))&((((in @ (esk82_3 @ X2206 @ X2207 @ X2208) @ X2206)|(~(in @ X2210 @ X2206)|((ap @ X2206 @ X2207 @ (lam @ X2206 @ X2207 @ X2208) @ X2210)=(X2208 @ X2210))))&(~(in @ (X2208 @ (esk82_3 @ X2206 @ X2207 @ X2208)) @ X2207)|(~(in @ X2210 @ X2206)|((ap @ X2206 @ X2207 @ (lam @ X2206 @ X2207 @ X2208) @ X2210)=(X2208 @ X2210)))))&((~(in @ X2213 @ (funcSet @ X2211 @ X2212))|((lam @ X2211 @ X2212 @ (ap @ X2211 @ X2212 @ X2213))=(X2213)))&((~(in @ X2216 @ X2214)|(~(in @ X2217 @ X2214)|((X2215)|(in @ X2217 @ (dsetconstr @ X2214 @ (^[Z0/* 9 */:$i]:((((X2215)&((Z0)=(X2216)))|(~((X2215))&((Z0)=(X2217)))))))))))&((~(in @ X2220 @ X2218)|(~(in @ X2221 @ X2218)|((X2219)|((dsetconstr @ X2218 @ (^[Z0/* 9 */:$i]:((((X2219)&((Z0)=(X2220)))|(~((X2219))&((Z0)=(X2221)))))))=(setadjoin @ X2221 @ emptyset)))))&((~(in @ X2224 @ X2222)|(~(in @ X2225 @ X2222)|(~(X2223)|(in @ X2224 @ (dsetconstr @ X2222 @ (^[Z0/* 9 */:$i]:((((X2223)&((Z0)=(X2224)))|(~((X2223))&((Z0)=(X2225)))))))))))&((~(in @ X2228 @ X2226)|(~(in @ X2229 @ X2226)|(~(X2227)|((dsetconstr @ X2226 @ (^[Z0/* 9 */:$i]:((((X2227)&((Z0)=(X2228)))|(~((X2227))&((Z0)=(X2229)))))))=(setadjoin @ X2228 @ emptyset)))))&((~(in @ X2232 @ X2230)|(~(in @ X2233 @ X2230)|(singleton @ (dsetconstr @ X2230 @ (^[Z0/* 9 */:$i]:((((X2231)&((Z0)=(X2232)))|(~((X2231))&((Z0)=(X2233))))))))))&((~(in @ X2236 @ X2234)|(~(in @ X2237 @ X2234)|(in @ (if @ X2234 @ ((X2235)) @ X2236 @ X2237) @ X2234)))&((~(singleton @ X2238)|(~(in @ X2239 @ X2238)|((setunion @ X2238)=(X2239))))&((~(in @ X2242 @ X2240)|(~(in @ X2243 @ X2240)|(~(X2241)|((if @ X2240 @ ((X2241)) @ X2242 @ X2243)=(X2242)))))&((~(in @ X2246 @ X2244)|(~(in @ X2247 @ X2244)|((X2245)|((if @ X2244 @ ((X2245)) @ X2246 @ X2247)=(X2247)))))&((~(in @ X2250 @ X2248)|(~(in @ X2251 @ X2248)|(in @ (if @ X2248 @ ((X2249)) @ X2250 @ X2251) @ (setadjoin @ X2250 @ (setadjoin @ X2251 @ emptyset)))))&((~(in @ X2253 @ (powerset @ X2252))|(~(in @ X2254 @ (powerset @ X2252))|(in @ (binintersect @ X2253 @ X2254) @ (powerset @ X2252))))&((~(in @ X2256 @ (powerset @ X2255))|(~(in @ X2257 @ (powerset @ X2255))|(in @ (binunion @ X2256 @ X2257) @ (powerset @ X2255))))&((~(in @ X2259 @ (powerset @ X2258))|(in @ (powerset @ X2259) @ (powerset @ (powerset @ X2258))))&((~(in @ X2261 @ (powerset @ X2260))|(~(in @ X2262 @ (powerset @ X2260))|(in @ (setminus @ X2261 @ X2262) @ (powerset @ X2260))))&((~(in @ X2264 @ (powerset @ X2263))|(in @ (setminus @ X2263 @ X2264) @ (powerset @ X2263)))&(((((in @ (esk84_3 @ X2265 @ X2266 @ X2267) @ X2265)|((X2266)=(X2267))|(in @ (esk83_3 @ X2265 @ X2266 @ X2267) @ X2265)|~(in @ X2267 @ (powerset @ X2265))|~(in @ X2266 @ (powerset @ X2265)))&(((in @ (esk84_3 @ X2265 @ X2266 @ X2267) @ X2267)|((X2266)=(X2267))|(in @ (esk83_3 @ X2265 @ X2266 @ X2267) @ X2265)|~(in @ X2267 @ (powerset @ X2265))|~(in @ X2266 @ (powerset @ X2265)))&(~(in @ (esk84_3 @ X2265 @ X2266 @ X2267) @ X2266)|((X2266)=(X2267))|(in @ (esk83_3 @ X2265 @ X2266 @ X2267) @ X2265)|~(in @ X2267 @ (powerset @ X2265))|~(in @ X2266 @ (powerset @ X2265)))))&((((in @ (esk84_3 @ X2265 @ X2266 @ X2267) @ X2265)|((X2266)=(X2267))|(in @ (esk83_3 @ X2265 @ X2266 @ X2267) @ X2266)|~(in @ X2267 @ (powerset @ X2265))|~(in @ X2266 @ (powerset @ X2265)))&(((in @ (esk84_3 @ X2265 @ X2266 @ X2267) @ X2267)|((X2266)=(X2267))|(in @ (esk83_3 @ X2265 @ X2266 @ X2267) @ X2266)|~(in @ X2267 @ (powerset @ X2265))|~(in @ X2266 @ (powerset @ X2265)))&(~(in @ (esk84_3 @ X2265 @ X2266 @ X2267) @ X2266)|((X2266)=(X2267))|(in @ (esk83_3 @ X2265 @ X2266 @ X2267) @ X2266)|~(in @ X2267 @ (powerset @ X2265))|~(in @ X2266 @ (powerset @ X2265)))))&(((in @ (esk84_3 @ X2265 @ X2266 @ X2267) @ X2265)|((X2266)=(X2267))|~(in @ (esk83_3 @ X2265 @ X2266 @ X2267) @ X2267)|~(in @ X2267 @ (powerset @ X2265))|~(in @ X2266 @ (powerset @ X2265)))&(((in @ (esk84_3 @ X2265 @ X2266 @ X2267) @ X2267)|((X2266)=(X2267))|~(in @ (esk83_3 @ X2265 @ X2266 @ X2267) @ X2267)|~(in @ X2267 @ (powerset @ X2265))|~(in @ X2266 @ (powerset @ X2265)))&(~(in @ (esk84_3 @ X2265 @ X2266 @ X2267) @ X2266)|((X2266)=(X2267))|~(in @ (esk83_3 @ X2265 @ X2266 @ X2267) @ X2267)|~(in @ X2267 @ (powerset @ X2265))|~(in @ X2266 @ (powerset @ X2265)))))))&((in @ esk86_0 @ (powerset @ esk85_0))&((in @ esk87_0 @ (powerset @ esk85_0))&((~(in @ X2273 @ esk85_0)|(~(in @ X2273 @ esk86_0)|(in @ X2273 @ esk87_0)))&~(subset @ esk86_0 @ esk87_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_317])])])])])])])). 9.37/180.03 thf(c_0_319, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_318])). 9.37/180.03 thf(c_0_320, negated_conjecture, (in @ esk86_0 @ (powerset @ esk85_0)), inference(split_conjunct,[status(thm)],[c_0_318])). 9.37/180.03 thf(c_0_321, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk52_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_318])). 9.37/180.03 thf(c_0_322, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk87_0)|~((in @ X2 @ esk85_0))|~((in @ X2 @ esk86_0)))), inference(split_conjunct,[status(thm)],[c_0_318])). 9.37/180.03 thf(c_0_323, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk85_0)|~((in @ X2 @ esk86_0)))), inference(spm,[status(thm)],[c_0_319, c_0_320])). 9.37/180.03 thf(c_0_324, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk87_0)|~((in @ (esk52_2 @ X2 @ esk87_0) @ esk86_0)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_321, c_0_322]), c_0_323])). 9.37/180.03 thf(c_0_325, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk52_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_318])). 9.37/180.03 thf(c_0_326, negated_conjecture, ~((subset @ esk86_0 @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_318])). 9.37/180.03 thf(c_0_327, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_324, c_0_325]), c_0_326]), ['proof']). 9.37/180.03 # SZS output end CNFRefutation 9.37/180.03 # Parsed axioms : 507 9.37/180.03 # Removed by relevancy pruning/SinE : 271 9.37/180.03 # Initial clauses : 413 9.37/180.03 # Removed in clause preprocessing : 29 9.37/180.03 # Initial clauses in saturation : 384 9.37/180.03 # Processed clauses : 2603 9.37/180.03 # ...of these trivial : 22 9.37/180.03 # ...subsumed : 1105 9.37/180.03 # ...remaining for further processing : 1476 9.37/180.03 # Other redundant clauses eliminated : 66 9.37/180.03 # Clauses deleted for lack of memory : 0 9.37/180.03 # Backward-subsumed : 87 9.37/180.03 # Backward-rewritten : 16 9.37/180.03 # Generated clauses : 47556 9.37/180.03 # ...of the previous two non-redundant : 45877 9.37/180.03 # ...aggressively subsumed : 0 9.37/180.03 # Contextual simplify-reflections : 5 9.37/180.03 # Paramodulations : 47442 9.37/180.03 # Factorizations : 22 9.37/180.03 # NegExts : 2 9.37/180.03 # Equation resolutions : 74 9.37/180.03 # Disequality decompositions : 0 9.37/180.03 # Total rewrite steps : 5242 9.37/180.03 # ...of those cached : 5047 9.37/180.03 # Propositional unsat checks : 0 9.37/180.03 # Propositional check models : 0 9.37/180.03 # Propositional check unsatisfiable : 0 9.37/180.03 # Propositional clauses : 0 9.37/180.03 # Propositional clauses after purity: 0 9.37/180.03 # Propositional unsat core size : 0 9.37/180.03 # Propositional preprocessing time : 0.000 9.37/180.03 # Propositional encoding time : 0.000 9.37/180.03 # Propositional solver time : 0.000 9.37/180.03 # Success case prop preproc time : 0.000 9.37/180.03 # Success case prop encoding time : 0.000 9.37/180.03 # Success case prop solver time : 0.000 9.37/180.03 # Current number of processed clauses : 1019 9.37/180.03 # Positive orientable unit clauses : 52 9.37/180.03 # Positive unorientable unit clauses: 0 9.37/180.03 # Negative unit clauses : 57 9.37/180.03 # Non-unit-clauses : 910 9.37/180.03 # Current number of unprocessed clauses: 43903 9.37/180.03 # ...number of literals in the above : 171078 9.37/180.03 # Current number of archived formulas : 0 9.37/180.03 # Current number of archived clauses : 442 9.37/180.03 # Clause-clause subsumption calls (NU) : 109061 9.37/180.03 # Rec. Clause-clause subsumption calls : 50333 9.37/180.03 # Non-unit clause-clause subsumptions : 795 9.37/180.03 # Unit Clause-clause subsumption calls : 941 9.37/180.03 # Rewrite failures with RHS unbound : 0 9.37/180.03 # BW rewrite match attempts : 39 9.37/180.03 # BW rewrite match successes : 11 9.37/180.03 # Condensation attempts : 0 9.37/180.03 # Condensation successes : 0 9.37/180.03 # Termbank termtop insertions : 964306 9.37/180.03 # Search garbage collected termcells : 23871 9.37/180.03 9.37/180.03 # ------------------------------------------------- 9.37/180.03 # User time : 1.005 s 9.37/180.03 # System time : 0.050 s 9.37/180.03 # Total time : 1.055 s 9.37/180.03 # Maximum resident set size: 7980 pages 9.37/180.03 % E---3.1 exiting 9.37/180.03 % E exiting 9.37/180.03 EOF