0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.11/0.37 % Computer : n026.cluster.edu 0.11/0.37 % Model : x86_64 x86_64 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.37 % Memory : 8046.5625MB 0.11/0.37 % OS : Linux 6.8.0-71-generic 0.11/0.37 % CPULimit : 1440 0.11/0.37 % WCLimit : 180 0.11/0.37 % DateTime : Mon Jul 27 10:08:35 UTC 2026 0.11/0.37 % CPUTime : 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.11/0.42 Running higher-order theorem proving 0.19/0.46 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.brVt9xQby3/E---3.1_2566977.p 136.19/20.06 % Version: 3.5.1-ho 136.19/20.06 % Preprocessing class: HSLMSLSSLLLCHFA. 136.19/20.06 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 136.19/20.06 % Starting ehoh_best5 with 180s (1) cores 136.19/20.06 % Starting almost_fo_3_lam with 180s (1) cores 136.19/20.06 % Starting new_bool_5 with 180s (1) cores 136.19/20.06 % Starting pre_casc_3 with 180s (1) cores 136.19/20.06 % Starting ho_unfolding_8 with 180s (1) cores 136.19/20.06 % Starting new_ho_10_cnf2 with 180s (1) cores 136.19/20.06 % Starting new_bool_3 with 180s (1) cores 136.19/20.06 % Starting new_ho_5 with 180s (1) cores 136.19/20.06 % ho_unfolding_8 with pid 2566994 completed with status 0 136.19/20.06 % Result found by ho_unfolding_8 136.19/20.06 % Preprocessing class: HSLMSLSSLLLCHFA. 136.19/20.06 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 136.19/20.06 % Starting ehoh_best5 with 180s (1) cores 136.19/20.06 % Starting almost_fo_3_lam with 180s (1) cores 136.19/20.06 % Starting new_bool_5 with 180s (1) cores 136.19/20.06 % Starting pre_casc_3 with 180s (1) cores 136.19/20.06 % Starting ho_unfolding_8 with 180s (1) cores 136.19/20.06 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 136.19/20.06 % No SInE strategy applied 136.19/20.06 % Search class: HGHSM-FSLM32-MHFMMSBN 136.19/20.06 % Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 136.19/20.06 % Starting SubtermCWHack with 19s (1) cores 136.19/20.06 % SubtermCWHack with pid 2566998 completed with status 8 136.19/20.06 % Starting ho_unfolding_8 with 37s (1) cores 136.19/20.06 % ho_unfolding_8 with pid 2567237 completed with status 0 136.19/20.06 % Result found by ho_unfolding_8 136.19/20.06 % Preprocessing class: HSLMSLSSLLLCHFA. 136.19/20.06 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 136.19/20.06 % Starting ehoh_best5 with 180s (1) cores 136.19/20.06 % Starting almost_fo_3_lam with 180s (1) cores 136.19/20.06 % Starting new_bool_5 with 180s (1) cores 136.19/20.06 % Starting pre_casc_3 with 180s (1) cores 136.19/20.06 % Starting ho_unfolding_8 with 180s (1) cores 136.19/20.06 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 136.19/20.06 % No SInE strategy applied 136.19/20.06 % Search class: HGHSM-FSLM32-MHFMMSBN 136.19/20.06 % Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 136.19/20.06 % Starting SubtermCWHack with 19s (1) cores 136.19/20.06 % SubtermCWHack with pid 2566998 completed with status 8 136.19/20.06 % Starting ho_unfolding_8 with 37s (1) cores 136.19/20.06 % Preprocessing time : 0.047 s 136.19/20.06 % Presaturation interreduction done 136.19/20.06 136.19/20.06 % Proof found! 136.19/20.06 % SZS status Theorem 136.19/20.06 % SZS output start CNFRefutation 136.19/20.06 thf(decl_23, type, in: $i > $i > $o). 136.19/20.06 thf(decl_24, type, exu: ($i > $o) > $o). 136.19/20.06 thf(decl_25, type, setextAx: $o). 136.19/20.06 thf(decl_26, type, emptyset: $i). 136.19/20.06 thf(decl_27, type, emptysetAx: $o). 136.19/20.06 thf(decl_28, type, setadjoin: $i > $i > $i). 136.19/20.06 thf(decl_29, type, setadjoinAx: $o). 136.19/20.06 thf(decl_30, type, powerset: $i > $i). 136.19/20.06 thf(decl_31, type, powersetAx: $o). 136.19/20.06 thf(decl_32, type, setunion: $i > $i). 136.19/20.06 thf(decl_33, type, setunionAx: $o). 136.19/20.06 thf(decl_34, type, omega: $i). 136.19/20.06 thf(decl_35, type, omega0Ax: $o). 136.19/20.06 thf(decl_36, type, omegaSAx: $o). 136.19/20.06 thf(decl_37, type, omegaIndAx: $o). 136.19/20.06 thf(decl_38, type, replAx: $o). 136.19/20.06 thf(decl_39, type, foundationAx: $o). 136.19/20.06 thf(decl_40, type, wellorderingAx: $o). 136.19/20.06 thf(decl_41, type, descr: ($i > $o) > $i). 136.19/20.06 thf(decl_42, type, descrp: $o). 136.19/20.06 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_44, type, dsetconstrI: $o). 136.19/20.06 thf(decl_45, type, dsetconstrEL: $o). 136.19/20.06 thf(decl_46, type, dsetconstrER: $o). 136.19/20.06 thf(decl_47, type, exuE1: $o). 136.19/20.06 thf(decl_48, type, prop2set: $o > $i). 136.19/20.06 thf(decl_49, type, prop2setE: $o). 136.19/20.06 thf(decl_50, type, emptysetE: $o). 136.19/20.06 thf(decl_51, type, emptysetimpfalse: $o). 136.19/20.06 thf(decl_52, type, notinemptyset: $o). 136.19/20.06 thf(decl_53, type, exuE3e: $o). 136.19/20.06 thf(decl_54, type, setext: $o). 136.19/20.06 thf(decl_55, type, emptyI: $o). 136.19/20.06 thf(decl_56, type, noeltsimpempty: $o). 136.19/20.06 thf(decl_57, type, setbeta: $o). 136.19/20.06 thf(decl_58, type, nonempty: $i > $o). 136.19/20.06 thf(decl_59, type, nonemptyE1: $o). 136.19/20.06 thf(decl_60, type, nonemptyI: $o). 136.19/20.06 thf(decl_61, type, nonemptyI1: $o). 136.19/20.06 thf(decl_62, type, setadjoinIL: $o). 136.19/20.06 thf(decl_63, type, emptyinunitempty: $o). 136.19/20.06 thf(decl_64, type, setadjoinIR: $o). 136.19/20.06 thf(decl_65, type, setadjoinE: $o). 136.19/20.06 thf(decl_66, type, setadjoinOr: $o). 136.19/20.06 thf(decl_67, type, setoftrueEq: $o). 136.19/20.06 thf(decl_68, type, powersetI: $o). 136.19/20.06 thf(decl_69, type, emptyinPowerset: $o). 136.19/20.06 thf(decl_70, type, emptyInPowerset: $o). 136.19/20.06 thf(decl_71, type, powersetE: $o). 136.19/20.06 thf(decl_72, type, setunionI: $o). 136.19/20.06 thf(decl_73, type, setunionE: $o). 136.19/20.06 thf(decl_74, type, subPowSU: $o). 136.19/20.06 thf(decl_75, type, exuE2: $o). 136.19/20.06 thf(decl_76, type, nonemptyImpWitness: $o). 136.19/20.06 thf(decl_77, type, uniqinunit: $o). 136.19/20.06 thf(decl_78, type, notinsingleton: $o). 136.19/20.06 thf(decl_79, type, eqinunit: $o). 136.19/20.06 thf(decl_80, type, singletonsswitch: $o). 136.19/20.06 thf(decl_81, type, upairsetE: $o). 136.19/20.06 thf(decl_82, type, upairsetIL: $o). 136.19/20.06 thf(decl_83, type, upairsetIR: $o). 136.19/20.06 thf(decl_84, type, emptyE1: $o). 136.19/20.06 thf(decl_85, type, vacuousDall: $o). 136.19/20.06 thf(decl_86, type, quantDeMorgan1: $o). 136.19/20.06 thf(decl_87, type, quantDeMorgan2: $o). 136.19/20.06 thf(decl_88, type, quantDeMorgan3: $o). 136.19/20.06 thf(decl_89, type, quantDeMorgan4: $o). 136.19/20.06 thf(decl_90, type, prop2setI: $o). 136.19/20.06 thf(decl_91, type, set2prop: $i > $o). 136.19/20.06 thf(decl_92, type, prop2set2propI: $o). 136.19/20.06 thf(decl_93, type, notdexE: $o). 136.19/20.06 thf(decl_94, type, notdallE: $o). 136.19/20.06 thf(decl_95, type, exuI1: $o). 136.19/20.06 thf(decl_96, type, exuI3: $o). 136.19/20.06 thf(decl_97, type, exuI2: $o). 136.19/20.06 thf(decl_98, type, inCongP: $o). 136.19/20.06 thf(decl_99, type, in__Cong: $o). 136.19/20.06 thf(decl_100, type, exuE3u: $o). 136.19/20.06 thf(decl_101, type, exu__Cong: $o). 136.19/20.06 thf(decl_102, type, emptyset__Cong: $o). 136.19/20.06 thf(decl_103, type, setadjoin__Cong: $o). 136.19/20.06 thf(decl_104, type, powerset__Cong: $o). 136.19/20.06 thf(decl_105, type, setunion__Cong: $o). 136.19/20.06 thf(decl_106, type, omega__Cong: $o). 136.19/20.06 thf(decl_107, type, exuEu: $o). 136.19/20.06 thf(decl_108, type, descr__Cong: $o). 136.19/20.06 thf(decl_109, type, dsetconstr__Cong: $o). 136.19/20.06 thf(decl_110, type, subset: $i > $i > $o). 136.19/20.06 thf(decl_113, type, subsetI1: $o). 136.19/20.06 thf(decl_114, type, eqimpsubset2: $o). 136.19/20.06 thf(decl_115, type, eqimpsubset1: $o). 136.19/20.06 thf(decl_116, type, subsetI2: $o). 136.19/20.06 thf(decl_117, type, emptysetsubset: $o). 136.19/20.06 thf(decl_118, type, subsetE: $o). 136.19/20.06 thf(decl_119, type, subsetE2: $o). 136.19/20.06 thf(decl_120, type, notsubsetI: $o). 136.19/20.06 thf(decl_121, type, notequalI1: $o). 136.19/20.06 thf(decl_122, type, notequalI2: $o). 136.19/20.06 thf(decl_123, type, subsetRefl: $o). 136.19/20.06 thf(decl_124, type, subsetTrans: $o). 136.19/20.06 thf(decl_125, type, setadjoinSub: $o). 136.19/20.06 thf(decl_126, type, setadjoinSub2: $o). 136.19/20.06 thf(decl_127, type, subset2powerset: $o). 136.19/20.06 thf(decl_128, type, setextsub: $o). 136.19/20.06 thf(decl_129, type, subsetemptysetimpeq: $o). 136.19/20.06 thf(decl_130, type, powersetI1: $o). 136.19/20.06 thf(decl_131, type, powersetE1: $o). 136.19/20.06 thf(decl_132, type, inPowerset: $o). 136.19/20.06 thf(decl_133, type, powersetsubset: $o). 136.19/20.06 thf(decl_134, type, sepInPowerset: $o). 136.19/20.06 thf(decl_135, type, sepSubset: $o). 136.19/20.06 thf(decl_136, type, binunion: $i > $i > $i). 136.19/20.06 thf(decl_137, type, binunionIL: $o). 136.19/20.06 thf(decl_138, type, upairset2IR: $o). 136.19/20.06 thf(decl_139, type, binunionIR: $o). 136.19/20.06 thf(decl_140, type, binunionEcases: $o). 136.19/20.06 thf(decl_141, type, binunionE: $o). 136.19/20.06 thf(decl_142, type, binunionLsub: $o). 136.19/20.06 thf(decl_143, type, binunionRsub: $o). 136.19/20.06 thf(decl_144, type, binintersect: $i > $i > $i). 136.19/20.06 thf(decl_145, type, binintersectI: $o). 136.19/20.06 thf(decl_146, type, binintersectSubset5: $o). 136.19/20.06 thf(decl_147, type, binintersectEL: $o). 136.19/20.06 thf(decl_148, type, binintersectLsub: $o). 136.19/20.06 thf(decl_149, type, binintersectSubset2: $o). 136.19/20.06 thf(decl_150, type, binintersectSubset3: $o). 136.19/20.06 thf(decl_151, type, binintersectER: $o). 136.19/20.06 thf(decl_152, type, disjointsetsI1: $o). 136.19/20.06 thf(decl_153, type, binintersectRsub: $o). 136.19/20.06 thf(decl_154, type, binintersectSubset4: $o). 136.19/20.06 thf(decl_155, type, binintersectSubset1: $o). 136.19/20.06 thf(decl_156, type, bs114d: $o). 136.19/20.06 thf(decl_158, type, setminus: $i > $i > $i). 136.19/20.06 thf(decl_159, type, setminusI: $o). 136.19/20.06 thf(decl_160, type, setminusEL: $o). 136.19/20.06 thf(decl_161, type, setminusER: $o). 136.19/20.06 thf(decl_162, type, setminusSubset2: $o). 136.19/20.06 thf(decl_163, type, setminusERneg: $o). 136.19/20.06 thf(decl_164, type, setminusELneg: $o). 136.19/20.06 thf(decl_165, type, setminusILneg: $o). 136.19/20.06 thf(decl_166, type, setminusIRneg: $o). 136.19/20.06 thf(decl_167, type, setminusLsub: $o). 136.19/20.06 thf(decl_168, type, setminusSubset1: $o). 136.19/20.06 thf(decl_169, type, symdiff: $i > $i > $i). 136.19/20.06 thf(decl_170, type, symdiffE: $o). 136.19/20.06 thf(decl_171, type, symdiffI1: $o). 136.19/20.06 thf(decl_172, type, symdiffI2: $o). 136.19/20.06 thf(decl_173, type, symdiffIneg1: $o). 136.19/20.06 thf(decl_174, type, symdiffIneg2: $o). 136.19/20.06 thf(decl_175, type, iskpair: $i > $o). 136.19/20.06 thf(decl_176, type, secondinupair: $o). 136.19/20.06 thf(decl_177, type, setukpairIL: $o). 136.19/20.06 thf(decl_178, type, setukpairIR: $o). 136.19/20.06 thf(decl_179, type, kpairiskpair: $o). 136.19/20.06 thf(decl_180, type, kpair: $i > $i > $i). 136.19/20.06 thf(decl_181, type, kpairp: $o). 136.19/20.06 thf(decl_182, type, cartprod: $i > $i > $i). 136.19/20.06 thf(decl_183, type, singletonsubset: $o). 136.19/20.06 thf(decl_184, type, singletoninpowerset: $o). 136.19/20.06 thf(decl_185, type, singletoninpowunion: $o). 136.19/20.06 thf(decl_186, type, upairset2E: $o). 136.19/20.06 thf(decl_187, type, upairsubunion: $o). 136.19/20.06 thf(decl_188, type, upairinpowunion: $o). 136.19/20.06 thf(decl_189, type, ubforcartprodlem1: $o). 136.19/20.06 thf(decl_190, type, ubforcartprodlem2: $o). 136.19/20.06 thf(decl_191, type, ubforcartprodlem3: $o). 136.19/20.06 thf(decl_192, type, cartprodpairin: $o). 136.19/20.06 thf(decl_193, type, cartprodmempair1: $o). 136.19/20.06 thf(decl_194, type, cartprodmempair: $o). 136.19/20.06 thf(decl_195, type, setunionE2: $o). 136.19/20.06 thf(decl_196, type, setunionsingleton1: $o). 136.19/20.06 thf(decl_197, type, setunionsingleton2: $o). 136.19/20.06 thf(decl_198, type, setunionsingleton: $o). 136.19/20.06 thf(decl_199, type, singleton: $i > $o). 136.19/20.06 thf(decl_200, type, singletonprop: $o). 136.19/20.06 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 136.19/20.06 thf(decl_202, type, ex1E1: $o). 136.19/20.06 thf(decl_203, type, ex1I: $o). 136.19/20.06 thf(decl_204, type, ex1I2: $o). 136.19/20.06 thf(decl_205, type, singletonsuniq: $o). 136.19/20.06 thf(decl_210, type, setukpairinjL1: $o). 136.19/20.06 thf(decl_211, type, kfstsingleton: $o). 136.19/20.06 thf(decl_212, type, theprop: $o). 136.19/20.06 thf(decl_213, type, kfst: $i > $i). 136.19/20.06 thf(decl_214, type, kfstpairEq: $o). 136.19/20.06 thf(decl_215, type, cartprodfstin: $o). 136.19/20.06 thf(decl_216, type, setukpairinjL2: $o). 136.19/20.06 thf(decl_217, type, setukpairinjL: $o). 136.19/20.06 thf(decl_218, type, setukpairinjR11: $o). 136.19/20.06 thf(decl_219, type, setukpairinjR12: $o). 136.19/20.06 thf(decl_220, type, setukpairinjR1: $o). 136.19/20.06 thf(decl_221, type, upairequniteq: $o). 136.19/20.06 thf(decl_222, type, setukpairinjR2: $o). 136.19/20.06 thf(decl_223, type, setukpairinjR: $o). 136.19/20.06 thf(decl_224, type, ksndsingleton: $o). 136.19/20.06 thf(decl_225, type, ksnd: $i > $i). 136.19/20.06 thf(decl_226, type, ksndpairEq: $o). 136.19/20.06 thf(decl_227, type, kpairsurjEq: $o). 136.19/20.06 thf(decl_228, type, cartprodsndin: $o). 136.19/20.06 thf(decl_229, type, cartprodpairmemEL: $o). 136.19/20.06 thf(decl_230, type, cartprodpairmemER: $o). 136.19/20.06 thf(decl_231, type, cartprodmempaircEq: $o). 136.19/20.06 thf(decl_232, type, cartprodfstpairEq: $o). 136.19/20.06 thf(decl_233, type, cartprodsndpairEq: $o). 136.19/20.06 thf(decl_234, type, cartprodpairsurjEq: $o). 136.19/20.06 thf(decl_235, type, breln: $i > $i > $i > $o). 136.19/20.06 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 136.19/20.06 thf(decl_237, type, dpsetconstrI: $o). 136.19/20.06 thf(decl_238, type, dpsetconstrSub: $o). 136.19/20.06 thf(decl_239, type, setOfPairsIsBReln: $o). 136.19/20.06 thf(decl_240, type, dpsetconstrERa: $o). 136.19/20.06 thf(decl_241, type, dpsetconstrEL1: $o). 136.19/20.06 thf(decl_242, type, dpsetconstrEL2: $o). 136.19/20.06 thf(decl_243, type, dpsetconstrER: $o). 136.19/20.06 thf(decl_244, type, func: $i > $i > $i > $o). 136.19/20.06 thf(decl_245, type, funcSet: $i > $i > $i). 136.19/20.06 thf(decl_246, type, funcImageSingleton: $o). 136.19/20.06 thf(decl_247, type, apProp: $o). 136.19/20.06 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 136.19/20.06 thf(decl_249, type, app: $o). 136.19/20.06 thf(decl_250, type, infuncsetfunc: $o). 136.19/20.06 thf(decl_251, type, ap2p: $o). 136.19/20.06 thf(decl_252, type, funcinfuncset: $o). 136.19/20.06 thf(decl_253, type, lamProp: $o). 136.19/20.06 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 136.19/20.06 thf(decl_255, type, lamp: $o). 136.19/20.06 thf(decl_256, type, lam2p: $o). 136.19/20.06 thf(decl_257, type, brelnall1: $o). 136.19/20.06 thf(decl_258, type, brelnall2: $o). 136.19/20.06 thf(decl_259, type, ex1E2: $o). 136.19/20.06 thf(decl_260, type, funcGraphProp1: $o). 136.19/20.06 thf(decl_261, type, funcGraphProp3: $o). 136.19/20.06 thf(decl_262, type, funcGraphProp2: $o). 136.19/20.06 thf(decl_263, type, funcextLem: $o). 136.19/20.06 thf(decl_264, type, funcGraphProp4: $o). 136.19/20.06 thf(decl_265, type, subbreln: $o). 136.19/20.06 thf(decl_266, type, eqbreln: $o). 136.19/20.06 thf(decl_267, type, funcext: $o). 136.19/20.06 thf(decl_268, type, epred1_0: $o). 136.19/20.06 thf(decl_269, type, esk1_2: $i > $i > $i). 136.19/20.06 thf(decl_270, type, esk2_2: $i > $i > $i). 136.19/20.06 thf(decl_271, type, esk3_2: $i > $i > $i). 136.19/20.06 thf(decl_272, type, esk4_1: $i > $i). 136.19/20.06 thf(decl_273, type, esk5_2: ($i > $i > $o) > $i > $i). 136.19/20.06 thf(decl_274, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 136.19/20.06 thf(decl_275, type, esk7_2: ($i > $i > $o) > $i > $i). 136.19/20.06 thf(decl_276, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 136.19/20.06 thf(decl_277, type, esk9_1: $i > $i). 136.19/20.06 thf(decl_278, type, esk10_2: ($i > $o) > $i > $i). 136.19/20.06 thf(decl_279, type, esk11_2: ($i > $o) > $i > $i). 136.19/20.06 thf(decl_280, type, esk12_1: ($i > $o) > $i). 136.19/20.06 thf(decl_281, type, esk13_2: ($i > $o) > $i > $i). 136.19/20.06 thf(decl_282, type, esk14_1: ($i > $o) > $i). 136.19/20.06 thf(decl_283, type, esk15_2: $i > $i > $i). 136.19/20.06 thf(decl_284, type, esk16_2: $i > $i > $i). 136.19/20.06 thf(decl_285, type, esk17_1: $i > $i). 136.19/20.06 thf(decl_286, type, esk18_1: $i > $i). 136.19/20.06 thf(decl_287, type, esk19_1: $i > $i). 136.19/20.06 thf(decl_288, type, esk20_2: $i > $i > $i). 136.19/20.06 thf(decl_289, type, esk21_3: $i > $i > $o > $i). 136.19/20.06 thf(decl_290, type, esk22_2: ($i > $o) > $i > $i). 136.19/20.06 thf(decl_291, type, esk23_1: ($i > $o) > $i). 136.19/20.06 thf(decl_292, type, esk24_1: $i > $i). 136.19/20.06 thf(decl_293, type, esk25_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_294, type, esk26_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_295, type, esk27_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_296, type, esk28_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_297, type, esk29_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_298, type, esk30_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_299, type, esk31_2: ($i > $o) > $i > $i). 136.19/20.06 thf(decl_300, type, esk32_1: ($i > $o) > $i). 136.19/20.06 thf(decl_301, type, esk33_1: ($i > $o) > $i). 136.19/20.06 thf(decl_302, type, esk34_1: ($i > $o) > $i). 136.19/20.06 thf(decl_303, type, esk35_1: ($i > $o) > $i). 136.19/20.06 thf(decl_304, type, esk36_2: ($i > $o) > $i > $i). 136.19/20.06 thf(decl_305, type, esk37_1: ($i > $o) > $i). 136.19/20.06 thf(decl_306, type, esk38_2: ($i > $o) > $i > $i). 136.19/20.06 thf(decl_307, type, esk39_2: ($i > $o) > ($i > $o) > $i). 136.19/20.06 thf(decl_308, type, esk40_2: ($i > $o) > ($i > $o) > $i). 136.19/20.06 thf(decl_309, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 136.19/20.06 thf(decl_310, type, esk42_2: ($i > $o) > ($i > $o) > $i). 136.19/20.06 thf(decl_311, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 136.19/20.06 thf(decl_312, type, esk44_2: ($i > $o) > ($i > $o) > $i). 136.19/20.06 thf(decl_313, type, esk45_2: ($i > $o) > $i > $i). 136.19/20.06 thf(decl_314, type, esk46_2: ($i > $o) > ($i > $o) > $i). 136.19/20.06 thf(decl_315, type, esk47_2: ($i > $o) > ($i > $o) > $i). 136.19/20.06 thf(decl_316, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 136.19/20.06 thf(decl_317, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 136.19/20.06 thf(decl_318, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 136.19/20.06 thf(decl_319, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 136.19/20.06 thf(decl_320, type, esk52_2: $i > $i > $i). 136.19/20.06 thf(decl_321, type, esk53_2: $i > $i > $i). 136.19/20.06 thf(decl_322, type, esk54_2: $i > $i > $i). 136.19/20.06 thf(decl_323, type, esk55_3: $i > $i > $i > $i). 136.19/20.06 thf(decl_324, type, esk56_3: $i > $i > $i > $i). 136.19/20.06 thf(decl_325, type, esk57_2: $i > $i > $i). 136.19/20.06 thf(decl_326, type, esk58_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_327, type, esk59_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_328, type, esk60_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_329, type, esk61_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_330, type, esk62_3: $i > ($i > $o) > $i > $i). 136.19/20.06 thf(decl_331, type, esk63_3: $i > ($i > $o) > $i > $i). 136.19/20.06 thf(decl_332, type, esk64_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_333, type, esk65_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_334, type, esk66_2: $i > ($i > $o) > $i). 136.19/20.06 thf(decl_335, type, esk67_1: $i > $i). 136.19/20.06 thf(decl_336, type, esk68_1: $i > $i). 136.19/20.06 thf(decl_337, type, esk69_4: $i > $i > $i > $i > $i). 136.19/20.06 thf(decl_338, type, esk70_3: $i > $i > ($i > $i) > $i). 136.19/20.06 thf(decl_339, type, esk71_3: $i > $i > ($i > $i) > $i). 136.19/20.06 thf(decl_340, type, esk72_3: $i > $i > ($i > $i) > $i). 136.19/20.06 thf(decl_341, type, esk73_4: $i > $i > $i > ($i > $o) > $i). 136.19/20.06 thf(decl_342, type, esk74_4: $i > $i > $i > ($i > $o) > $i). 136.19/20.06 thf(decl_343, type, esk75_4: $i > $i > $i > ($i > $o) > $i). 136.19/20.06 thf(decl_344, type, esk76_4: $i > $i > $i > ($i > $o) > $i). 136.19/20.06 thf(decl_345, type, esk77_4: $i > $i > $i > $i > $i). 136.19/20.06 thf(decl_346, type, esk78_4: $i > $i > $i > $i > $i). 136.19/20.06 thf(decl_347, type, esk79_4: $i > $i > $i > $i > $i). 136.19/20.06 thf(decl_348, type, esk80_4: $i > $i > $i > $i > $i). 136.19/20.06 thf(decl_349, type, esk81_4: $i > $i > $i > $i > $i). 136.19/20.06 thf(decl_350, type, esk82_4: $i > $i > $i > $i > $i). 136.19/20.06 thf(decl_351, type, esk83_4: $i > $i > $i > $i > $i). 136.19/20.06 thf(decl_352, type, esk84_4: $i > $i > $i > $i > $i). 136.19/20.06 thf(decl_353, type, esk85_0: $i). 136.19/20.06 thf(decl_354, type, esk86_0: $i). 136.19/20.06 thf(decl_355, type, esk87_0: $i). 136.19/20.06 thf(decl_356, type, esk88_0: $i). 136.19/20.06 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', ex1)). 136.19/20.06 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', singleton)). 136.19/20.06 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', replAx)). 136.19/20.06 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', exu)). 136.19/20.06 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', descrp)). 136.19/20.06 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', exuE1)). 136.19/20.06 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', exuE3e)). 136.19/20.06 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', nonempty)). 136.19/20.06 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', nonemptyI)). 136.19/20.06 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', exuE2)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', exuI1)). 136.19/20.06 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', exuI3)). 136.19/20.06 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', exuI2)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', exuE3u)). 136.19/20.06 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', exu__Cong)). 136.19/20.06 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', exuEu)). 136.19/20.06 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', descr__Cong)). 136.19/20.06 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', singletonprop)). 136.19/20.06 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', ex1E1)). 136.19/20.06 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.brVt9xQby3/E---3.1_2566977.p', ex1I)). 136.19/20.06 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', ex1I2)). 136.19/20.06 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', kfstsingleton)). 136.19/20.06 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', ksndsingleton)). 136.19/20.06 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setOfPairsIsBReln)). 136.19/20.06 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', breln)). 136.19/20.06 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', funcImageSingleton)). 136.19/20.06 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.brVt9xQby3/E---3.1_2566977.p', ex1E2)). 136.19/20.06 thf(funcext2, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>(((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>(((exuE1)=>((prop2setE)=>(((emptysetimpfalse)=>(((((emptyI)=>((noeltsimpempty)=>(((nonemptyE1)=>((nonemptyI)=>((((emptyinunitempty)=>((setadjoinIR)=>((((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>(((powersetE)=>(((setunionE)=>(((((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>(((upairsetIL)=>((upairsetIR)=>((((quantDeMorgan1)=>(((quantDeMorgan3)=>((((((notdallE)=>(((exuI3)=>(((inCongP)=>(((exuE3u)=>(((((((omega__Cong)=>((((dsetconstr__Cong)=>(((eqimpsubset2)=>(((subsetI2)=>(((subsetE)=>(((notsubsetI)=>(((notequalI2)=>(((subsetTrans)=>(((setadjoinSub2)=>(((((((((sepInPowerset)=>((sepSubset)=>((binunionIL)=>(((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>(((((((binintersectSubset2)=>((binintersectSubset3)=>(((((binintersectSubset4)=>(((((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>(((setminusIRneg)=>(((((symdiffI1)=>((symdiffI2)=>(((((((kpairiskpair)=>(((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((((upairinpowunion)=>(((ubforcartprodlem2)=>((((cartprodmempair1)=>(((setunionE2)=>(((setunionsingleton2)=>((((ex1E1)=>((((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>(((kfstpairEq)=>((cartprodfstin)=>(((((((((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>(((cartprodsndin)=>((cartprodpairmemEL)=>((((((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>(((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((((lamp)=>((lam2p)=>((brelnall1)=>(((((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>(((funcext)=>![X4:$i, X5:$i, X29:$i]:((![X35:$i]:(((((X29)=(X35))<=![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X35 @ X2)))))<=(in @ X35 @ (funcSet @ X4 @ X5))))<=(in @ X29 @ (funcSet @ X4 @ X5)))))<=(eqbreln)))))))<=(funcGraphProp1))<=(ex1E2))<=(brelnall2)))))<=(lamProp))<=(funcinfuncset))))))<=(funcImageSingleton))))))))))<=(cartprodsndpairEq))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))))<=(kpairsurjEq)))))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1))<=(setukpairinjR12))<=(setukpairinjR11))<=(setukpairinjL))<=(setukpairinjL2))))<=(theprop)))))<=(ex1I2))<=(ex1I)))<=(singletonprop))<=(setunionsingleton)))<=(setunionsingleton1)))<=(cartprodmempair)))<=(cartprodpairin))<=(ubforcartprodlem3)))<=(ubforcartprodlem1)))<=(upairsubunion))<=(upairset2E)))))<=(kpairp)))<=(setukpairIR))<=(setukpairIL))<=(secondinupair))<=(symdiffIneg2))<=(symdiffIneg1))))<=(symdiffE))<=(setminusSubset1))<=(setminusLsub)))<=(setminusILneg)))))<=(setminusER)))<=(setminusI))<=(bs114d))<=(binintersectSubset1)))<=(binintersectRsub))<=(disjointsetsI1))<=(binintersectER))))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))))))<=(upairset2IR)))))<=(powersetsubset))<=(inPowerset))<=(powersetE1))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset)))<=(setadjoinSub)))<=(subsetRefl)))<=(notequalI1)))<=(subsetE2)))<=(emptysetsubset)))<=(eqimpsubset1)))<=(subsetI1)))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong)))<=(exuI2)))<=(exuI1)))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4)))<=(quantDeMorgan2)))<=(vacuousDall))<=(emptyE1))))<=(upairsetE))))))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))<=(setunionI)))<=(emptyInPowerset)))))<=(setadjoinOr))<=(setadjoinE))))<=(setadjoinIL))<=(nonemptyI1))))<=(setbeta))))<=(setext))<=(exuE3e))<=(notinemptyset)))<=(emptysetE))))<=(dsetconstrER)))))<=(wellorderingAx))<=(foundationAx))))))<=(setunionAx)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', funcext2)). 136.19/20.06 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', dsetconstrI)). 136.19/20.06 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', dsetconstrEL)). 136.19/20.06 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', dsetconstrER)). 136.19/20.06 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setbeta)). 136.19/20.06 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', nonemptyE1)). 136.19/20.06 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', nonemptyI1)). 136.19/20.06 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setoftrueEq)). 136.19/20.06 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', nonemptyImpWitness)). 136.19/20.06 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.brVt9xQby3/E---3.1_2566977.p', emptyE1)). 136.19/20.06 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', dsetconstr__Cong)). 136.19/20.06 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', sepInPowerset)). 136.19/20.06 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', sepSubset)). 136.19/20.06 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', theprop)). 136.19/20.06 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', dpsetconstrI)). 136.19/20.06 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', dpsetconstrSub)). 136.19/20.06 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', dpsetconstrERa)). 136.19/20.06 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', dpsetconstrEL1)). 136.19/20.06 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', dpsetconstrEL2)). 136.19/20.06 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', dpsetconstrER)). 136.19/20.06 thf(apProp, axiom, ((apProp)<=>![X4:$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.brVt9xQby3/E---3.1_2566977.p', apProp)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', lamProp)). 136.19/20.06 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', lamp)). 136.19/20.06 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X33 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', lam2p)). 136.19/20.06 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X34)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', brelnall1)). 136.19/20.06 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X34)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', brelnall2)). 136.19/20.06 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X36:$i]:(((breln @ X4 @ X5 @ X36)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X36))))))=>(subset @ X34 @ X36))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', subbreln)). 136.19/20.06 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X36:$i]:(((breln @ X4 @ X5 @ X36)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X36))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X36)=>(in @ (kpair @ X2 @ X3) @ X34))))))=>((X34)=(X36))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', eqbreln)). 136.19/20.06 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setextAx)). 136.19/20.06 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', emptysetAx)). 136.19/20.06 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setadjoinAx)). 136.19/20.06 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', powersetAx)). 136.19/20.06 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setunionAx)). 136.19/20.06 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', omega0Ax)). 136.19/20.06 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', omegaSAx)). 136.19/20.06 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', omegaIndAx)). 136.19/20.06 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', foundationAx)). 136.19/20.06 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.brVt9xQby3/E---3.1_2566977.p', wellorderingAx)). 136.19/20.06 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', prop2setE)). 136.19/20.06 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', emptysetE)). 136.19/20.06 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', emptysetimpfalse)). 136.19/20.06 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', notinemptyset)). 136.19/20.06 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setext)). 136.19/20.06 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', emptyI)). 136.19/20.06 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', noeltsimpempty)). 136.19/20.06 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setadjoinIL)). 136.19/20.06 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', emptyinunitempty)). 136.19/20.06 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setadjoinIR)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', setadjoinE)). 136.19/20.06 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setadjoinOr)). 136.19/20.06 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', powersetI)). 136.19/20.06 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', emptyinPowerset)). 136.19/20.06 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', emptyInPowerset)). 136.19/20.06 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', powersetE)). 136.19/20.06 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setunionI)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', setunionE)). 136.19/20.06 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', subPowSU)). 136.19/20.06 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', uniqinunit)). 136.19/20.06 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', notinsingleton)). 136.19/20.06 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', eqinunit)). 136.19/20.06 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', singletonsswitch)). 136.19/20.06 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', upairsetE)). 136.19/20.06 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', upairsetIL)). 136.19/20.06 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', upairsetIR)). 136.19/20.06 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', vacuousDall)). 136.19/20.06 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', quantDeMorgan1)). 136.19/20.06 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', quantDeMorgan2)). 136.19/20.06 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', quantDeMorgan3)). 136.19/20.06 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', quantDeMorgan4)). 136.19/20.06 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', prop2setI)). 136.19/20.06 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', prop2set2propI)). 136.19/20.06 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', notdexE)). 136.19/20.06 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', notdallE)). 136.19/20.06 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', inCongP)). 136.19/20.06 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', in__Cong)). 136.19/20.06 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', emptyset__Cong)). 136.19/20.06 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setadjoin__Cong)). 136.19/20.06 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', powerset__Cong)). 136.19/20.06 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setunion__Cong)). 136.19/20.06 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', omega__Cong)). 136.19/20.06 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', subsetI1)). 136.19/20.06 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', eqimpsubset2)). 136.19/20.06 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', eqimpsubset1)). 136.19/20.06 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', subsetI2)). 136.19/20.06 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', emptysetsubset)). 136.19/20.06 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', subsetE)). 136.19/20.06 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', subsetE2)). 136.19/20.06 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', notsubsetI)). 136.19/20.06 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', notequalI1)). 136.19/20.06 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', notequalI2)). 136.19/20.06 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', subsetRefl)). 136.19/20.06 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', subsetTrans)). 136.19/20.06 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setadjoinSub)). 136.19/20.06 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setadjoinSub2)). 136.19/20.06 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', subset2powerset)). 136.19/20.06 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setextsub)). 136.19/20.06 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', subsetemptysetimpeq)). 136.19/20.06 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', powersetI1)). 136.19/20.06 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', powersetE1)). 136.19/20.06 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', inPowerset)). 136.19/20.06 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', powersetsubset)). 136.19/20.06 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binunionIL)). 136.19/20.06 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', upairset2IR)). 136.19/20.06 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binunionIR)). 136.19/20.06 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binunionEcases)). 136.19/20.06 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binunionE)). 136.19/20.06 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binunionLsub)). 136.19/20.06 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binunionRsub)). 136.19/20.06 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binintersectI)). 136.19/20.06 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binintersectSubset5)). 136.19/20.06 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binintersectEL)). 136.19/20.06 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binintersectLsub)). 136.19/20.06 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binintersectSubset2)). 136.19/20.06 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binintersectSubset3)). 136.19/20.06 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binintersectER)). 136.19/20.06 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', disjointsetsI1)). 136.19/20.06 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binintersectRsub)). 136.19/20.06 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binintersectSubset4)). 136.19/20.06 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', binintersectSubset1)). 136.19/20.06 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', bs114d)). 136.19/20.06 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setminusI)). 136.19/20.06 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setminusEL)). 136.19/20.06 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setminusER)). 136.19/20.06 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setminusSubset2)). 136.19/20.06 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setminusERneg)). 136.19/20.06 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setminusELneg)). 136.19/20.06 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setminusILneg)). 136.19/20.06 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setminusIRneg)). 136.19/20.06 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setminusLsub)). 136.19/20.06 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setminusSubset1)). 136.19/20.06 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', symdiffE)). 136.19/20.06 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', symdiffI1)). 136.19/20.06 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', symdiffI2)). 136.19/20.06 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', symdiffIneg1)). 136.19/20.06 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', symdiffIneg2)). 136.19/20.06 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', secondinupair)). 136.19/20.06 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setukpairIL)). 136.19/20.06 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setukpairIR)). 136.19/20.06 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', kpairiskpair)). 136.19/20.06 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', kpairp)). 136.19/20.06 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', singletonsubset)). 136.19/20.06 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', singletoninpowerset)). 136.19/20.06 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', singletoninpowunion)). 136.19/20.06 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', upairset2E)). 136.19/20.06 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', upairsubunion)). 136.19/20.06 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', upairinpowunion)). 136.19/20.06 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', ubforcartprodlem1)). 136.19/20.06 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', ubforcartprodlem2)). 136.19/20.06 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', ubforcartprodlem3)). 136.19/20.06 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', cartprodpairin)). 136.19/20.06 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.brVt9xQby3/E---3.1_2566977.p', cartprodmempair1)). 136.19/20.06 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', cartprodmempair)). 136.19/20.06 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setunionE2)). 136.19/20.06 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setunionsingleton1)). 136.19/20.06 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setunionsingleton2)). 136.19/20.06 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setunionsingleton)). 136.19/20.06 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', singletonsuniq)). 136.19/20.06 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.brVt9xQby3/E---3.1_2566977.p', setukpairinjL1)). 136.19/20.06 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', kfstpairEq)). 136.19/20.06 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', cartprodfstin)). 136.19/20.06 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setukpairinjL2)). 136.19/20.06 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setukpairinjL)). 136.19/20.06 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setukpairinjR11)). 136.19/20.06 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setukpairinjR12)). 136.19/20.06 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', setukpairinjR1)). 136.19/20.06 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', upairequniteq)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', setukpairinjR2)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', setukpairinjR)). 136.19/20.06 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', ksndpairEq)). 136.19/20.06 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', kpairsurjEq)). 136.19/20.06 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', cartprodsndin)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', cartprodpairmemEL)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', cartprodpairmemER)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', cartprodmempaircEq)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', cartprodfstpairEq)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', cartprodsndpairEq)). 136.19/20.06 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', cartprodpairsurjEq)). 136.19/20.06 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', app)). 136.19/20.06 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', infuncsetfunc)). 136.19/20.06 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.brVt9xQby3/E---3.1_2566977.p', ap2p)). 136.19/20.06 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', funcinfuncset)). 136.19/20.06 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', funcGraphProp1)). 136.19/20.06 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', funcGraphProp3)). 136.19/20.06 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.brVt9xQby3/E---3.1_2566977.p', funcGraphProp2)). 136.19/20.06 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X35:$i]:(((func @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', funcextLem)). 136.19/20.06 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.brVt9xQby3/E---3.1_2566977.p', funcGraphProp4)). 136.19/20.06 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X35:$i]:(((func @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>((X29)=(X35)))))))), file('/export/starexec/sandbox/tmp/tmp.brVt9xQby3/E---3.1_2566977.p', funcext)). 136.19/20.06 thf(c_0_214, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X696:$i]:((((in @ X696 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X696 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])). 136.19/20.06 thf(c_0_215, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])). 136.19/20.06 thf(c_0_216, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 136.19/20.06 thf(c_0_217, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])). 136.19/20.06 thf(c_0_218, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 136.19/20.06 thf(c_0_219, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 136.19/20.06 thf(c_0_220, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 136.19/20.06 thf(c_0_221, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 136.19/20.06 thf(c_0_222, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 136.19/20.06 thf(c_0_223, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 136.19/20.06 thf(c_0_224, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 136.19/20.06 thf(c_0_225, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 136.19/20.06 thf(c_0_226, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 136.19/20.06 thf(c_0_227, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 136.19/20.06 thf(c_0_228, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 136.19/20.06 thf(c_0_229, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 136.19/20.06 thf(c_0_230, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 136.19/20.06 thf(c_0_231, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 136.19/20.06 thf(c_0_232, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 136.19/20.06 thf(c_0_233, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X696:$i]:((((in @ X696 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X696 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_214, c_0_215])). 136.19/20.06 thf(c_0_234, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 136.19/20.06 thf(c_0_235, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 136.19/20.06 thf(c_0_236, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 136.19/20.06 thf(c_0_237, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 136.19/20.06 thf(c_0_238, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 136.19/20.06 thf(c_0_239, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 136.19/20.06 thf(c_0_240, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 136.19/20.06 thf(c_0_241, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$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])). 136.19/20.06 thf(c_0_242, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>(((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>(((exuE1)=>((prop2setE)=>(((emptysetimpfalse)=>(((((emptyI)=>((noeltsimpempty)=>(((nonemptyE1)=>((nonemptyI)=>((((emptyinunitempty)=>((setadjoinIR)=>((((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>(((powersetE)=>(((setunionE)=>(((((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>(((upairsetIL)=>((upairsetIR)=>((((quantDeMorgan1)=>(((quantDeMorgan3)=>((((((notdallE)=>(((exuI3)=>(((inCongP)=>(((exuE3u)=>(((((((omega__Cong)=>((((dsetconstr__Cong)=>(((eqimpsubset2)=>(((subsetI2)=>(((subsetE)=>(((notsubsetI)=>(((notequalI2)=>(((subsetTrans)=>(((setadjoinSub2)=>(((((((((sepInPowerset)=>((sepSubset)=>((binunionIL)=>(((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>(((((((binintersectSubset2)=>((binintersectSubset3)=>(((((binintersectSubset4)=>(((((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>(((setminusIRneg)=>(((((symdiffI1)=>((symdiffI2)=>(((((((kpairiskpair)=>(((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((((upairinpowunion)=>(((ubforcartprodlem2)=>((((cartprodmempair1)=>(((setunionE2)=>(((setunionsingleton2)=>((((ex1E1)=>((((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>(((kfstpairEq)=>((cartprodfstin)=>(((((((((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>(((cartprodsndin)=>((cartprodpairmemEL)=>((((((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>(((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((((lamp)=>((lam2p)=>((brelnall1)=>(((((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>(((funcext)=>![X4:$i, X5:$i, X29:$i]:((![X35:$i]:(((((X29)=(X35))<=![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X35 @ X2)))))<=(in @ X35 @ (funcSet @ X4 @ X5))))<=(in @ X29 @ (funcSet @ X4 @ X5)))))<=(eqbreln)))))))<=(funcGraphProp1))<=(ex1E2))<=(brelnall2)))))<=(lamProp))<=(funcinfuncset))))))<=(funcImageSingleton))))))))))<=(cartprodsndpairEq))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))))<=(kpairsurjEq)))))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1))<=(setukpairinjR12))<=(setukpairinjR11))<=(setukpairinjL))<=(setukpairinjL2))))<=(theprop)))))<=(ex1I2))<=(ex1I)))<=(singletonprop))<=(setunionsingleton)))<=(setunionsingleton1)))<=(cartprodmempair)))<=(cartprodpairin))<=(ubforcartprodlem3)))<=(ubforcartprodlem1)))<=(upairsubunion))<=(upairset2E)))))<=(kpairp)))<=(setukpairIR))<=(setukpairIL))<=(secondinupair))<=(symdiffIneg2))<=(symdiffIneg1))))<=(symdiffE))<=(setminusSubset1))<=(setminusLsub)))<=(setminusILneg)))))<=(setminusER)))<=(setminusI))<=(bs114d))<=(binintersectSubset1)))<=(binintersectRsub))<=(disjointsetsI1))<=(binintersectER))))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))))))<=(upairset2IR)))))<=(powersetsubset))<=(inPowerset))<=(powersetE1))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset)))<=(setadjoinSub)))<=(subsetRefl)))<=(notequalI1)))<=(subsetE2)))<=(emptysetsubset)))<=(eqimpsubset1)))<=(subsetI1)))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong)))<=(exuI2)))<=(exuI1)))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4)))<=(quantDeMorgan2)))<=(vacuousDall))<=(emptyE1))))<=(upairsetE))))))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))<=(setunionI)))<=(emptyInPowerset)))))<=(setadjoinOr))<=(setadjoinE))))<=(setadjoinIL))<=(nonemptyI1))))<=(setbeta))))<=(setext))<=(exuE3e))<=(notinemptyset)))<=(emptysetE))))<=(dsetconstrER)))))<=(wellorderingAx))<=(foundationAx))))))<=(setunionAx))))))), inference(assume_negation,[status(cth)],[funcext2])). 136.19/20.06 thf(c_0_243, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X667:$i]:(((((X6 @ X2 @ X667)))&(![X668:$i]:(((((X6 @ X2 @ X668)))=>(((X667)=(X668)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_216, c_0_217])). 136.19/20.06 thf(c_0_244, plain, ((descrp)=(![X1:$i > $o]:((((?[X669:$i]:(((((X1 @ X669)))&(![X670:$i]:(((((X1 @ X670)))=>(((X669)=(X670))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_218, c_0_217])). 136.19/20.06 thf(c_0_245, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 136.19/20.06 thf(c_0_246, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 136.19/20.06 thf(c_0_247, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 136.19/20.06 thf(c_0_248, plain, ((exuE1)=(![X1:$i > $o]:((((?[X671:$i]:(((((X1 @ X671)))&(![X672:$i]:(((((X1 @ X672)))=>(((X671)=(X672))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_219, c_0_217])). 136.19/20.06 thf(c_0_249, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X673:$i]:(((((X1 @ X673)))&(![X674:$i]:(((((X1 @ X674)))=>(((X673)=(X674))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_220, c_0_217])). 136.19/20.06 thf(c_0_250, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 136.19/20.06 thf(c_0_251, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_221])). 136.19/20.06 thf(c_0_252, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_222, c_0_221])). 136.19/20.06 thf(c_0_253, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_221])). 136.19/20.06 thf(c_0_254, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 136.19/20.06 thf(c_0_255, plain, ((exuE2)=(![X1:$i > $o]:((((?[X675:$i]:(((((X1 @ X675)))&(![X676:$i]:(((((X1 @ X676)))=>(((X675)=(X676))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_223, c_0_217])). 136.19/20.06 thf(c_0_256, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_221])). 136.19/20.06 thf(c_0_257, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 136.19/20.06 thf(c_0_258, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X677:$i]:(((((X1 @ X677)))&(![X678:$i]:(((((X1 @ X678)))=>(((X677)=(X678)))))))))))))), inference(apply_def,[status(thm)],[c_0_224, c_0_217])). 136.19/20.06 thf(c_0_259, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X679:$i]:(((((X1 @ X679)))&(![X680:$i]:(((((X1 @ X680)))=>(((X679)=(X680)))))))))))))))), inference(apply_def,[status(thm)],[c_0_225, c_0_217])). 136.19/20.06 thf(c_0_260, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X681:$i]:(((((X1 @ X681)))&(![X682:$i]:(((((X1 @ X682)))=>(((X681)=(X682)))))))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_217])). 136.19/20.06 thf(c_0_261, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X683:$i]:(((((X1 @ X683)))&(![X684:$i]:(((((X1 @ X684)))=>(((X683)=(X684))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_227, c_0_217])). 136.19/20.06 thf(c_0_262, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X685:$i]:(((((X1 @ X685)))&(![X686:$i]:(((((X1 @ X686)))=>(((X685)=(X686))))))))))<=>((?[X687:$i]:(((((X17 @ X687)))&(![X688:$i]:(((((X17 @ X688)))=>(((X687)=(X688)))))))))))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_217])). 136.19/20.06 thf(c_0_263, plain, ((exuEu)=(![X1:$i > $o]:((((?[X689:$i]:(((((X1 @ X689)))&(![X690:$i]:(((((X1 @ X690)))=>(((X689)=(X690))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_229, c_0_217])). 136.19/20.06 thf(c_0_264, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X691:$i]:(((((X1 @ X691)))&(![X692:$i]:(((((X1 @ X692)))=>(((X691)=(X692))))))))))=>((((?[X693:$i]:(((((X17 @ X693)))&(![X694:$i]:(((((X17 @ X694)))=>(((X693)=(X694))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_217])). 136.19/20.06 thf(c_0_265, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 136.19/20.06 thf(c_0_266, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 136.19/20.06 thf(c_0_267, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 136.19/20.06 thf(c_0_268, 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)))))=>((?[X695:$i]:((((in @ X695 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X695 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_231, c_0_215])). 136.19/20.06 thf(c_0_269, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X697:$i]:((((in @ X697 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X697 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_233])). 136.19/20.06 thf(c_0_270, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X698:$i]:((((in @ X698 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X698 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_233])). 136.19/20.06 thf(c_0_271, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))))=>(((?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2)))))=>((?[X699:$i]:((((in @ X699 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X699 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_235, c_0_233])). 136.19/20.06 thf(c_0_272, plain, ((kfstsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X700:$i]:((((in @ X700 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X700 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_215])). 136.19/20.06 thf(c_0_273, axiom, ((theprop)=(![X21:$i]:((((?[X701:$i]:((((in @ X701 @ X21))&(((X21)=(setadjoin @ X701 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_215])). 136.19/20.06 thf(c_0_274, plain, ((ksndsingleton)=(![X18:$i]:((((iskpair @ X18))=>((?[X702:$i]:((((in @ X702 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X702 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_215])). 136.19/20.06 thf(c_0_275, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 136.19/20.06 thf(c_0_276, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 136.19/20.06 thf(c_0_277, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_238, c_0_239])). 136.19/20.06 thf(c_0_278, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 136.19/20.06 thf(c_0_279, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 136.19/20.06 thf(c_0_280, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 136.19/20.06 thf(c_0_281, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 136.19/20.06 thf(c_0_282, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:((((func @ X4 @ X5 @ X29))=>(![X2:$i]:((((in @ X2 @ X4))=>((?[X703:$i]:((((in @ X703 @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))))&(((dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X703 @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_215])). 136.19/20.06 thf(c_0_283, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 136.19/20.06 thf(c_0_284, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 136.19/20.06 thf(c_0_285, plain, ((lamp)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 136.19/20.06 thf(c_0_286, plain, ((lam2p)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X33 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 136.19/20.06 thf(c_0_287, axiom, ((brelnall1)=(![X4:$i, X5:$i, X34:$i]:(((((subset @ X34 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X34))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X34))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_239])). 136.19/20.06 thf(c_0_288, axiom, ((brelnall2)=(![X4:$i, X5:$i, X34:$i]:(((((subset @ X34 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X34))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X34))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_239])). 136.19/20.06 thf(c_0_289, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((?[X704:$i]:((((in @ X704 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X704 @ emptyset)))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_233])). 136.19/20.06 thf(c_0_290, axiom, ((subbreln)=(![X4:$i, X5:$i, X34:$i]:(((((subset @ X34 @ (cartprod @ X4 @ X5))))=>(![X36:$i]:(((((subset @ X36 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X34))=>((in @ (kpair @ X2 @ X3) @ X36))))))))))=>((subset @ X34 @ X36))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_239])). 136.19/20.06 thf(c_0_291, axiom, ((eqbreln)=(![X4:$i, X5:$i, X34:$i]:(((((subset @ X34 @ (cartprod @ X4 @ X5))))=>(![X36:$i]:(((((subset @ X36 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X34))=>((in @ (kpair @ X2 @ X3) @ X36))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X36))=>((in @ (kpair @ X2 @ X3) @ X34))))))))))=>(((X34)=(X36)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_239])). 136.19/20.06 thf(c_0_292, plain, ((epred1_0)<=>![X1341:$i]:(?[X1342:$i]:((((![X1343:$i]:(((in @ X1343 @ X1342)=>![X1344:$i]:(((in @ X1344 @ X1343)=>(in @ X1344 @ X1341)))))&![X1345:$i, X1346:$i]:((((in @ X1345 @ X1341)&(in @ X1346 @ X1341))=>(![X1347:$i]:(((in @ X1347 @ X1342)=>((in @ X1345 @ X1347)<=>(in @ X1346 @ X1347))))=>((X1345)=(X1346))))))&![X1348:$i, X1349:$i]:((((in @ X1348 @ X1342)&(in @ X1349 @ X1342))=>(![X1350:$i]:(((in @ X1350 @ X1348)=>(in @ X1350 @ X1349)))|![X1351:$i]:(((in @ X1351 @ X1349)=>(in @ X1351 @ X1348)))))))&![X1352:$i]:(((![X1353:$i]:(((in @ X1353 @ X1352)=>(in @ X1353 @ X1341)))&?[X1354:$i]:((in @ X1354 @ X1352)))=>?[X1355:$i, X1356:$i]:(((((in @ X1355 @ X1342)&(in @ X1356 @ X1352))&~(?[X1357:$i]:(((in @ X1357 @ X1355)&(in @ X1357 @ X1352)))))&![X1358:$i]:(((in @ X1358 @ X1342)=>(![X1359:$i]:(((in @ X1359 @ X1358)=>(in @ X1359 @ X1355)))|(in @ X1356 @ X1358)))))))))))), introduced(definition)). 136.19/20.06 thf(c_0_293, negated_conjecture, ~((![X705:$i, X706:$i]:((![X707:$i]:(((in @ X707 @ X705)<=>(in @ X707 @ X706)))=>((X705)=(X706))))=>(![X708:$i]:(~(in @ X708 @ emptyset))=>(![X709:$i, X710:$i, X711:$i]:(((in @ X711 @ (setadjoin @ X709 @ X710))<=>(((X711)=(X709))|(in @ X711 @ X710))))=>(![X712:$i, X713:$i]:(((in @ X713 @ (powerset @ X712))<=>![X714:$i]:(((in @ X714 @ X713)=>(in @ X714 @ X712)))))=>(![X1364:$i, X1365:$i]:(((in @ X1365 @ (setunion @ X1364))<=>?[X1366:$i]:(((in @ X1365 @ X1366)&(in @ X1366 @ X1364)))))=>((in @ emptyset @ omega)=>(![X715:$i]:(((in @ X715 @ omega)=>(in @ (setadjoin @ X715 @ X715) @ omega)))=>(![X716:$i]:((((in @ emptyset @ X716)&![X717:$i]:((((in @ X717 @ omega)&(in @ X717 @ X716))=>(in @ (setadjoin @ X717 @ X717) @ X716))))=>![X718:$i]:(((in @ X718 @ omega)=>(in @ X718 @ X716)))))=>(![X719:$i > $i > $o, X720:$i]:((![X721:$i]:(((in @ X721 @ X720)=>?[X722:$i]:(((X719 @ X721 @ X722)&![X723:$i]:(((X719 @ X721 @ X723)=>((X722)=(X723))))))))=>?[X724:$i]:(![X725:$i]:(((in @ X725 @ X724)<=>?[X726:$i]:(((in @ X726 @ X720)&(X719 @ X726 @ X725))))))))=>(![X1360:$i]:((?[X1361:$i]:((in @ X1361 @ X1360))=>?[X1362:$i]:(((in @ X1362 @ X1360)&~(?[X1363:$i]:(((in @ X1363 @ X1362)&(in @ X1363 @ X1360))))))))=>((epred1_0)=>(![X727:$i > $o]:((?[X728:$i]:(((X727 @ X728)&![X729:$i]:(((X727 @ X729)=>((X728)=(X729))))))=>(X727 @ (descr @ (^[Z0:$i]:(X727 @ Z0))))))=>(![X730:$i, X731:$i > $o, X732:$i]:(((in @ X732 @ X730)=>((X731 @ X732)=>(in @ X732 @ (dsetconstr @ X730 @ X731)))))=>(![X733:$i, X734:$i > $o, X735:$i]:(((in @ X735 @ (dsetconstr @ X733 @ X734))=>(in @ X735 @ X733)))=>(![X1338:$i, X1339:$i > $o, X1340:$i]:(((in @ X1340 @ (dsetconstr @ X1338 @ X1339))=>(X1339 @ X1340)))=>(![X736:$i > $o]:((?[X737:$i]:(((X736 @ X737)&![X738:$i]:(((X736 @ X738)=>((X737)=(X738))))))=>?[X739:$i]:(((X736 @ X739)&![X740:$i]:(((X736 @ X740)=>((X739)=(X740))))))))=>(![X741:$o, X742:$i]:(((in @ X742 @ (prop2set @ ((X741))))=>(X741)))=>(![X1336:$i]:(((in @ X1336 @ emptyset)=>![X1337:$o]:((X1337))))=>(![X743:$i]:(((in @ X743 @ emptyset)=>~($true)))=>(![X1335:$i]:(~(in @ X1335 @ emptyset))=>(![X1331:$i > $o]:((?[X1332:$i]:(((X1331 @ X1332)&![X1333:$i]:(((X1331 @ X1333)=>((X1332)=(X1333))))))=>?[X1334:$i]:((X1331 @ X1334))))=>(![X1327:$i, X1328:$i]:((![X1329:$i]:(((in @ X1329 @ X1327)=>(in @ X1329 @ X1328)))=>(![X1330:$i]:(((in @ X1330 @ X1328)=>(in @ X1330 @ X1327)))=>((X1327)=(X1328)))))=>(![X744:$i]:((![X745:$i]:(~(in @ X745 @ X744))=>((X744)=(emptyset))))=>(![X746:$i]:((![X747:$i]:(~(in @ X747 @ X746))=>((X746)=(emptyset))))=>(![X1324:$i, X1325:$i > $o, X1326:$i]:(((in @ X1326 @ X1324)=>((in @ X1326 @ (dsetconstr @ X1324 @ X1325))<=>(X1325 @ X1326))))=>(![X748:$i]:((((X748)!=(emptyset))=>?[X749:$i]:((in @ X749 @ X748))))=>(![X750:$i, X751:$i > $o, X752:$i]:(((in @ X752 @ X750)=>((X751 @ X752)=>((dsetconstr @ X750 @ X751)!=(emptyset)))))=>(![X1322:$i]:((?[X1323:$i]:((in @ X1323 @ X1322))=>((X1322)!=(emptyset))))=>(![X1320:$i, X1321:$i]:((in @ X1320 @ (setadjoin @ X1320 @ X1321)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X753:$i, X754:$i, X755:$i]:(((in @ X755 @ X754)=>(in @ X755 @ (setadjoin @ X753 @ X754))))=>(![X1316:$i, X1317:$i, X1318:$i]:(((in @ X1318 @ (setadjoin @ X1316 @ X1317))=>![X1319:$o]:(((((X1318)=(X1316))=>(X1319))=>(((in @ X1318 @ X1317)=>(X1319))=>(X1319))))))=>(![X1313:$i, X1314:$i, X1315:$i]:(((in @ X1315 @ (setadjoin @ X1313 @ X1314))=>(((X1315)=(X1313))|(in @ X1315 @ X1314))))=>(![X756:$i]:(((dsetconstr @ X756 @ (^[Z0:$i]:($true)))=(X756)))=>(![X757:$i, X758:$i]:((![X759:$i]:(((in @ X759 @ X758)=>(in @ X759 @ X757)))=>(in @ X758 @ (powerset @ X757))))=>(![X760:$i]:((in @ emptyset @ (powerset @ X760)))=>(![X1312:$i]:((in @ emptyset @ (powerset @ X1312)))=>(![X761:$i, X762:$i, X763:$i]:(((in @ X762 @ (powerset @ X761))=>((in @ X763 @ X762)=>(in @ X763 @ X761))))=>(![X1309:$i, X1310:$i, X1311:$i]:(((in @ X1310 @ X1311)=>((in @ X1311 @ X1309)=>(in @ X1310 @ (setunion @ X1309)))))=>(![X764:$i, X765:$i]:(((in @ X765 @ (setunion @ X764))=>![X766:$o]:((![X767:$i]:(((in @ X765 @ X767)=>((in @ X767 @ X764)=>(X766))))=>(X766)))))=>(![X1307:$i, X1308:$i]:(((in @ X1308 @ X1307)=>(in @ X1308 @ (powerset @ (setunion @ X1307)))))=>(![X1302:$i > $o]:((?[X1303:$i]:(((X1302 @ X1303)&![X1304:$i]:(((X1302 @ X1304)=>((X1303)=(X1304))))))=>?[X1305:$i]:(![X1306:$i]:(((X1302 @ X1306)<=>((X1306)=(X1305)))))))=>(![X1300:$i]:((((X1300)!=(emptyset))=>?[X1301:$i]:(((in @ X1301 @ X1300)&$true))))=>(![X768:$i, X769:$i]:(((in @ X768 @ (setadjoin @ X769 @ emptyset))=>((X768)=(X769))))=>(![X770:$i, X771:$i]:((((X770)!=(X771))=>~(in @ X771 @ (setadjoin @ X770 @ emptyset))))=>(![X772:$i, X773:$i]:((((X772)=(X773))=>(in @ X772 @ (setadjoin @ X773 @ emptyset))))=>(![X774:$i, X775:$i]:(((in @ X774 @ (setadjoin @ X775 @ emptyset))=>(in @ X775 @ (setadjoin @ X774 @ emptyset))))=>(![X1297:$i, X1298:$i, X1299:$i]:(((in @ X1299 @ (setadjoin @ X1297 @ (setadjoin @ X1298 @ emptyset)))=>(((X1299)=(X1297))|((X1299)=(X1298)))))=>(![X776:$i, X777:$i]:((in @ X776 @ (setadjoin @ X776 @ (setadjoin @ X777 @ emptyset))))=>(![X778:$i, X779:$i]:((in @ X779 @ (setadjoin @ X778 @ (setadjoin @ X779 @ emptyset))))=>(![X1294:$i, X1295:$i > $o]:((?[X1296:$i]:(((in @ X1296 @ X1294)&(X1295 @ X1296)))=>(((dsetconstr @ X1294 @ X1295)=(emptyset))=>~($true))))=>(![X1292:$i > $o, X1293:$i]:(((in @ X1293 @ emptyset)=>(X1292 @ X1293)))=>(![X780:$i, X781:$i > $o]:((~(![X782:$i]:(((in @ X782 @ X780)=>(X781 @ X782))))=>?[X783:$i]:(((in @ X783 @ X780)&~((X781 @ X783))))))=>(![X1288:$i, X1289:$i > $o]:((![X1290:$i]:(((in @ X1290 @ X1288)=>~((X1289 @ X1290))))=>~(?[X1291:$i]:(((in @ X1291 @ X1288)&(X1289 @ X1291))))))=>(![X784:$i, X785:$i > $o]:((~(?[X786:$i]:(((in @ X786 @ X784)&(X785 @ X786))))=>![X787:$i]:(((in @ X787 @ X784)=>~((X785 @ X787))))))=>(![X1284:$i, X1285:$i > $o]:((?[X1286:$i]:(((in @ X1286 @ X1284)&~((X1285 @ X1286))))=>~(![X1287:$i]:(((in @ X1287 @ X1284)=>(X1285 @ X1287))))))=>(![X1283:$o]:(((X1283)=>(in @ emptyset @ (prop2set @ ((X1283))))))=>(![X1282:$o]:(((X1282)=>(set2prop @ (prop2set @ ((X1282))))))=>(![X1278:$i, X1279:$i > $o]:((~(?[X1280:$i]:(((in @ X1280 @ X1278)&(X1279 @ X1280))))=>![X1281:$i]:(((in @ X1281 @ X1278)=>~((X1279 @ X1281))))))=>(![X788:$i, X789:$i > $o]:((~(![X790:$i]:(((in @ X790 @ X788)=>(X789 @ X790))))=>?[X791:$i]:(((in @ X791 @ X788)&~((X789 @ X791))))))=>(![X1273:$i > $o]:((?[X1274:$i]:(((X1273 @ X1274)&![X1275:$i]:(((X1273 @ X1275)=>((X1274)=(X1275))))))=>?[X1276:$i]:(((X1273 @ X1276)&![X1277:$i]:(((X1273 @ X1277)=>((X1276)=(X1277))))))))=>(![X792:$i > $o]:((?[X793:$i]:((X792 @ X793))=>(![X794:$i, X795:$i]:(((X792 @ X794)=>((X792 @ X795)=>((X794)=(X795)))))=>?[X796:$i]:(((X792 @ X796)&![X797:$i]:(((X792 @ X797)=>((X796)=(X797)))))))))=>(![X1268:$i > $o]:((?[X1269:$i]:(![X1270:$i]:(((X1268 @ X1270)<=>((X1270)=(X1269)))))=>?[X1271:$i]:(((X1268 @ X1271)&![X1272:$i]:(((X1268 @ X1272)=>((X1271)=(X1272))))))))=>(![X798:$i, X799:$i]:((((X798)=(X799))=>![X800:$i, X801:$i]:((((X800)=(X801))=>((in @ X800 @ X798)=>(in @ X801 @ X799))))))=>(![X1264:$i, X1265:$i]:((((X1264)=(X1265))=>![X1266:$i, X1267:$i]:((((X1266)=(X1267))=>((in @ X1266 @ X1264)<=>(in @ X1267 @ X1265))))))=>(![X802:$i > $o]:((?[X803:$i]:(((X802 @ X803)&![X804:$i]:(((X802 @ X804)=>((X803)=(X804))))))=>![X805:$i, X806:$i]:(((X802 @ X805)=>((X802 @ X806)=>((X805)=(X806)))))))=>(![X1256:$i > $o, X1257:$i > $o]:((![X1258:$i, X1259:$i]:((((X1258)=(X1259))=>((X1256 @ X1258)<=>(X1257 @ X1259))))=>(?[X1260:$i]:(((X1256 @ X1260)&![X1261:$i]:(((X1256 @ X1261)=>((X1260)=(X1261))))))<=>?[X1262:$i]:(((X1257 @ X1262)&![X1263:$i]:(((X1257 @ X1263)=>((X1262)=(X1263)))))))))=>(((emptyset)=(emptyset))=>(![X1252:$i, X1253:$i]:((((X1252)=(X1253))=>![X1254:$i, X1255:$i]:((((X1254)=(X1255))=>((setadjoin @ X1252 @ X1254)=(setadjoin @ X1253 @ X1255))))))=>(![X1250:$i, X1251:$i]:((((X1250)=(X1251))=>((powerset @ X1250)=(powerset @ X1251))))=>(![X1248:$i, X1249:$i]:((((X1248)=(X1249))=>((setunion @ X1248)=(setunion @ X1249))))=>(((omega)=(omega))=>(![X1243:$i > $o]:((?[X1244:$i]:(((X1243 @ X1244)&![X1245:$i]:(((X1243 @ X1245)=>((X1244)=(X1245))))))=>![X1246:$i, X1247:$i]:(((X1243 @ X1246)=>((X1243 @ X1247)=>((X1246)=(X1247)))))))=>(![X1235:$i > $o, X1236:$i > $o]:((![X1237:$i, X1238:$i]:((((X1237)=(X1238))=>((X1235 @ X1237)<=>(X1236 @ X1238))))=>(?[X1239:$i]:(((X1235 @ X1239)&![X1240:$i]:(((X1235 @ X1240)=>((X1239)=(X1240))))))=>(?[X1241:$i]:(((X1236 @ X1241)&![X1242:$i]:(((X1236 @ X1242)=>((X1241)=(X1242))))))=>((descr @ X1235)=(descr @ X1236))))))=>(![X807:$i, X808:$i]:((((X807)=(X808))=>![X809:$i > $o, X810:$i > $o]:((![X811:$i]:(((in @ X811 @ X807)=>![X812:$i]:(((in @ X812 @ X808)=>(((X811)=(X812))=>((X809 @ X811)<=>(X810 @ X812)))))))=>((dsetconstr @ X807 @ X809)=(dsetconstr @ X808 @ X810))))))=>(![X1232:$i, X1233:$i]:((![X1234:$i]:(((in @ X1234 @ X1232)=>(in @ X1234 @ X1233)))=>(subset @ X1232 @ X1233)))=>(![X813:$i, X814:$i]:((((X813)=(X814))=>(subset @ X814 @ X813)))=>(![X1230:$i, X1231:$i]:((((X1230)=(X1231))=>(subset @ X1230 @ X1231)))=>(![X815:$i, X816:$i]:((![X817:$i]:(((in @ X817 @ X815)=>(in @ X817 @ X816)))=>(subset @ X815 @ X816)))=>(![X1229:$i]:((subset @ emptyset 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$i]:((![X991:$i]:(((in @ X991 @ X988)=>(in @ (X990 @ X991) @ X989)))=>(in @ (lam @ X988 @ X989 @ X990) @ (funcSet @ X988 @ X989))))=>(![X992:$i, X993:$i, X994:$i]:(((subset @ X994 @ (cartprod @ X992 @ X993))=>![X995:$i > $o]:((![X996:$i]:(((in @ X996 @ X992)=>![X997:$i]:(((in @ X997 @ X993)=>((in @ (kpair @ X996 @ X997) @ X994)=>(X995 @ (kpair @ X996 @ X997)))))))=>![X998:$i]:(((in @ X998 @ X994)=>(X995 @ X998)))))))=>(![X1048:$i, X1049:$i, X1050:$i]:(((subset @ X1050 @ (cartprod @ X1048 @ X1049))=>![X1051:$i > $o]:((![X1052:$i]:(((in @ X1052 @ X1048)=>![X1053:$i]:(((in @ X1053 @ X1049)=>((in @ (kpair @ X1052 @ X1053) @ X1050)=>(X1051 @ (kpair @ X1052 @ X1053)))))))=>![X1054:$i]:(((in @ X1054 @ X1050)=>(X1051 @ X1054)))))))=>(![X1043:$i, X1044:$i > $o]:((?[X1045:$i]:(((in @ X1045 @ (dsetconstr @ X1043 @ X1044))&((dsetconstr @ X1043 @ X1044)=(setadjoin @ X1045 @ emptyset))))=>![X1046:$i]:(((in @ X1046 @ X1043)=>![X1047:$i]:(((in @ X1047 @ X1043)=>((X1044 @ X1046)=>((X1044 @ X1047)=>((X1046)=(X1047))))))))))=>(![X1039:$i, X1040:$i, X1041:$i]:(((func @ X1039 @ X1040 @ X1041)=>![X1042:$i]:(((in @ X1042 @ X1039)=>(in @ (kpair @ X1042 @ (ap @ X1039 @ X1040 @ X1041 @ X1042)) @ X1041)))))=>(![X999:$i, X1000:$i, X1001:$i]:(((in @ X1001 @ (funcSet @ X999 @ X1000))=>![X1002:$i]:(((in @ X1002 @ X999)=>(in @ (kpair @ X1002 @ (ap @ X999 @ X1000 @ X1001 @ X1002)) @ X1001)))))=>(![X1003:$i, X1004:$i, X1005:$i]:(((func @ X1003 @ X1004 @ X1005)=>![X1006:$i]:(((in @ X1006 @ X1003)=>![X1007:$i]:(((in @ X1007 @ X1004)=>((in @ (kpair @ X1006 @ X1007) @ X1005)=>((ap @ X1003 @ X1004 @ X1005 @ X1006)=(X1007)))))))))=>(![X1008:$i, X1009:$i, X1010:$i]:(((func @ X1008 @ X1009 @ X1010)=>![X1011:$i]:(((func @ X1008 @ X1009 @ X1011)=>(![X1012:$i]:(((in @ X1012 @ X1008)=>((ap @ X1008 @ X1009 @ X1010 @ X1012)=(ap @ X1008 @ X1009 @ X1011 @ X1012))))=>![X1013:$i]:(((in @ X1013 @ X1008)=>![X1014:$i]:(((in @ X1014 @ X1009)=>((in @ (kpair @ X1013 @ X1014) @ X1011)=>(in @ (kpair @ X1013 @ X1014) @ X1010)))))))))))=>(![X1015:$i, X1016:$i, X1017:$i]:(((in @ X1017 @ (funcSet @ X1015 @ X1016))=>![X1018:$i]:(((in @ X1018 @ X1015)=>![X1019:$i]:(((in @ X1019 @ X1016)=>((in @ (kpair @ X1018 @ X1019) @ X1017)=>((ap @ X1015 @ X1016 @ X1017 @ X1018)=(X1019)))))))))=>(![X1020:$i, X1021:$i, X1022:$i]:(((subset @ X1022 @ (cartprod @ X1020 @ X1021))=>![X1023:$i]:(((subset @ X1023 @ (cartprod @ X1020 @ X1021))=>(![X1024:$i]:(((in @ X1024 @ X1020)=>![X1025:$i]:(((in @ X1025 @ X1021)=>((in @ (kpair @ X1024 @ X1025) @ X1022)=>(in @ (kpair @ X1024 @ X1025) @ X1023))))))=>(subset @ X1022 @ X1023))))))=>(![X1031:$i, X1032:$i, X1033:$i]:(((subset @ X1033 @ (cartprod @ X1031 @ X1032))=>![X1034:$i]:(((subset @ X1034 @ (cartprod @ X1031 @ X1032))=>(![X1035:$i]:(((in @ X1035 @ X1031)=>![X1036:$i]:(((in @ X1036 @ X1032)=>((in @ (kpair @ X1035 @ X1036) @ X1033)=>(in @ (kpair @ X1035 @ X1036) @ X1034))))))=>(![X1037:$i]:(((in @ X1037 @ X1031)=>![X1038:$i]:(((in @ X1038 @ X1032)=>((in @ (kpair @ X1037 @ X1038) @ X1034)=>(in @ (kpair @ X1037 @ X1038) @ X1033))))))=>((X1033)=(X1034))))))))=>(![X1026:$i, X1027:$i, X1028:$i]:(((func @ X1026 @ X1027 @ X1028)=>![X1029:$i]:(((func @ X1026 @ X1027 @ X1029)=>(![X1030:$i]:(((in @ X1030 @ X1026)=>((ap @ X1026 @ X1027 @ X1028 @ X1030)=(ap @ X1026 @ X1027 @ X1029 @ X1030))))=>((X1028)=(X1029)))))))=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X35:$i]:(((in @ X35 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>((X29)=(X35)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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,[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)],[c_0_242, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_243]), foundationAx]), wellorderingAx]), c_0_244]), c_0_245]), c_0_246]), c_0_247]), c_0_248]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_249]), setext]), emptyI]), noeltsimpempty]), c_0_250]), c_0_251]), c_0_252]), c_0_253]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_254]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_255]), c_0_256]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_257]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_258]), c_0_259]), c_0_260]), inCongP]), in__Cong]), c_0_261]), c_0_262]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_263]), c_0_264]), c_0_265]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_266]), c_0_267]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_268]), c_0_269]), c_0_270]), c_0_271]), singletonsuniq]), setukpairinjL1]), c_0_272]), c_0_273]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_274]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_275]), c_0_276]), c_0_277]), c_0_278]), c_0_279]), c_0_280]), c_0_281]), c_0_282]), c_0_283]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_290]), c_0_291]), funcext])])]), c_0_292])). 136.19/20.06 thf(c_0_294, negated_conjecture, ![X1373:$i, X1374:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1386:$i, X1387:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1395:$i, X1396:$i > $i > $o, X1397:$i, X1399:$i, X1402:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1409:$i, X1410:$i > $o, X1411:$i, X1413:$i, X1414:$i > $o, X1415:$i, X1416:$i, X1417:$i > $o, X1418:$i, X1419:$i, X1420:$i > $o, X1421:$i, X1422:$i > $o, X1423:$i, X1426:$i, X1427:$o, X1428:$i, X1429:$i, X1430:$o, X1431:$i, X1432:$i, X1433:$i > $o, X1434:$i, X1437:$i, X1438:$i, X1441:$i, X1443:$i, X1445:$i, X1446:$i > $o, X1447:$i, X1448:$i, X1450:$i, X1451:$i > $o, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$o, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$o, X1483:$i, X1484:$i, X1485:$i > $o, X1486:$i, X1489:$i, X1490:$i, X1491:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i > $o, X1510:$i, X1511:$i > $o, X1512:$i, X1513:$i, X1514:$i > $o, X1515:$i, X1517:$i, X1518:$i > $o, X1520:$i, X1521:$i, X1522:$i > $o, X1524:$i, X1525:$i, X1526:$i > $o, X1527:$i, X1529:$o, X1530:$o, X1531:$i, X1532:$i > $o, X1534:$i, X1535:$i, X1536:$i > $o, X1537:$i, X1539:$i > $o, X1540:$i, X1543:$i, X1544:$i > $o, X1545:$i, X1549:$i, X1550:$i > $o, X1551:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i > $o, X1564:$i, X1566:$i, X1567:$i, X1568:$i > $o, X1569:$i > $o, X1572:$i, X1575:$i, X1576:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i > $o, X1589:$i, X1591:$i, X1592:$i, X1593:$i > $o, X1594:$i > $o, X1597:$i, X1599:$i, X1601:$i, X1602:$i, X1603:$i > $o, X1604:$i > $o, X1607:$i, X1608:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i > $o, X1655:$i, X1656:$i > $o, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$o, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$o, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i > $o, X1811:$i, X1813:$i, X1814:$i > $o, X1815:$i, X1817:$i, X1818:$i > $o, X1819:$i, X1822:$i, X1823:$i > $o, X1826:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$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, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1871:$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:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i > $i > $o, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i > $i > $o, X1908:$i, X1909:$i, X1910:$i > $i > $o, X1911:$i, X1912:$i, X1913:$i > $i > $o, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i > $i > $o, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i > $i > $o, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i > $i > $o, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1936:$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 > $i, X1958:$i, X1959:$i, X1960:$i > $i, X1962:$i, X1963:$i, X1964:$i > $i, X1966:$i, X1967:$i, X1968:$i, X1969:$i > $o, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i > $o, X1979:$i, X1980:$i, X1981:$i > $o, X1982:$i, X1983:$i, X1984:$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, 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@ X1960)))&(~(in @ (X1960 @ (esk71_3 @ X1958 @ X1959 @ X1960)) @ X1959)|(func @ X1958 @ X1959 @ (lam @ X1958 @ X1959 @ X1960))))&((((in @ (esk72_3 @ X1962 @ X1963 @ X1964) @ X1962)|(in @ (lam @ X1962 @ X1963 @ X1964) @ (funcSet @ X1962 @ X1963)))&(~(in @ (X1964 @ (esk72_3 @ X1962 @ X1963 @ X1964)) @ X1963)|(in @ (lam @ X1962 @ X1963 @ X1964) @ (funcSet @ X1962 @ X1963))))&((((in @ (esk73_4 @ X1966 @ X1967 @ X1968 @ X1969) @ X1966)|(~(in @ X1972 @ X1968)|(X1969 @ X1972))|~(subset @ X1968 @ (cartprod @ X1966 @ X1967)))&(((in @ (esk74_4 @ X1966 @ X1967 @ X1968 @ X1969) @ X1967)|(~(in @ X1972 @ X1968)|(X1969 @ X1972))|~(subset @ X1968 @ (cartprod @ X1966 @ X1967)))&(((in @ (kpair @ (esk73_4 @ X1966 @ X1967 @ X1968 @ X1969) @ (esk74_4 @ X1966 @ X1967 @ X1968 @ X1969)) @ X1968)|(~(in @ X1972 @ X1968)|(X1969 @ X1972))|~(subset @ X1968 @ (cartprod @ X1966 @ X1967)))&(~(X1969 @ (kpair @ (esk73_4 @ X1966 @ X1967 @ X1968 @ X1969) @ (esk74_4 @ X1966 @ X1967 @ X1968 @ X1969)))|(~(in @ X1972 @ X1968)|(X1969 @ X1972))|~(subset @ X1968 @ (cartprod @ X1966 @ X1967))))))&((((in @ (esk75_4 @ X1973 @ X1974 @ X1975 @ X1976) @ X1973)|(~(in @ X1979 @ X1975)|(X1976 @ X1979))|~(subset @ X1975 @ (cartprod @ X1973 @ X1974)))&(((in @ (esk76_4 @ X1973 @ X1974 @ X1975 @ X1976) @ X1974)|(~(in @ X1979 @ X1975)|(X1976 @ X1979))|~(subset @ X1975 @ (cartprod @ X1973 @ X1974)))&(((in @ (kpair @ (esk75_4 @ X1973 @ X1974 @ X1975 @ X1976) @ (esk76_4 @ X1973 @ X1974 @ X1975 @ X1976)) @ X1975)|(~(in @ X1979 @ X1975)|(X1976 @ X1979))|~(subset @ X1975 @ (cartprod @ X1973 @ X1974)))&(~(X1976 @ (kpair @ (esk75_4 @ X1973 @ X1974 @ X1975 @ X1976) @ (esk76_4 @ X1973 @ X1974 @ X1975 @ X1976)))|(~(in @ X1979 @ X1975)|(X1976 @ X1979))|~(subset @ X1975 @ (cartprod @ X1973 @ X1974))))))&((~(in @ X1982 @ (dsetconstr @ X1980 @ X1981))|((dsetconstr @ X1980 @ X1981)!=(setadjoin @ X1982 @ emptyset))|(~(in @ X1983 @ X1980)|(~(in @ X1984 @ X1980)|(~(X1981 @ X1983)|(~(X1981 @ X1984)|((X1983)=(X1984)))))))&((~(func @ X1985 @ X1986 @ X1987)|(~(in @ X1988 @ X1985)|(in @ (kpair @ X1988 @ (ap @ X1985 @ X1986 @ X1987 @ X1988)) @ X1987)))&((~(in @ X1991 @ (funcSet @ X1989 @ X1990))|(~(in @ X1992 @ X1989)|(in @ (kpair @ X1992 @ (ap @ X1989 @ X1990 @ X1991 @ X1992)) @ X1991)))&((~(func @ X1993 @ X1994 @ X1995)|(~(in @ X1996 @ X1993)|(~(in @ X1997 @ X1994)|(~(in @ (kpair @ X1996 @ X1997) @ X1995)|((ap @ X1993 @ X1994 @ X1995 @ X1996)=(X1997))))))&((((in @ (esk77_4 @ X1998 @ X1999 @ X2000 @ X2001) @ X1998)|(~(in @ X2003 @ X1998)|(~(in @ X2004 @ X1999)|(~(in @ (kpair @ X2003 @ X2004) @ X2001)|(in @ (kpair @ X2003 @ X2004) @ X2000))))|~(func @ X1998 @ X1999 @ X2001)|~(func @ X1998 @ X1999 @ X2000))&(((ap @ X1998 @ X1999 @ X2000 @ (esk77_4 @ X1998 @ X1999 @ X2000 @ X2001))!=(ap @ X1998 @ X1999 @ X2001 @ (esk77_4 @ X1998 @ X1999 @ X2000 @ X2001)))|(~(in @ X2003 @ X1998)|(~(in @ X2004 @ X1999)|(~(in @ (kpair @ X2003 @ X2004) @ X2001)|(in @ (kpair @ X2003 @ X2004) @ X2000))))|~(func @ X1998 @ X1999 @ X2001)|~(func @ X1998 @ X1999 @ X2000)))&((~(in @ X2007 @ (funcSet @ X2005 @ X2006))|(~(in @ X2008 @ X2005)|(~(in @ X2009 @ X2006)|(~(in @ (kpair @ X2008 @ X2009) @ X2007)|((ap @ X2005 @ X2006 @ X2007 @ X2008)=(X2009))))))&((((in @ (esk78_4 @ X2010 @ X2011 @ X2012 @ X2013) @ X2010)|(subset @ X2012 @ X2013)|~(subset @ X2013 @ (cartprod @ X2010 @ X2011))|~(subset @ X2012 @ (cartprod @ X2010 @ X2011)))&(((in @ (esk79_4 @ X2010 @ X2011 @ X2012 @ X2013) @ X2011)|(subset @ X2012 @ X2013)|~(subset @ X2013 @ (cartprod @ X2010 @ X2011))|~(subset @ X2012 @ (cartprod @ X2010 @ X2011)))&(((in @ (kpair @ (esk78_4 @ X2010 @ X2011 @ X2012 @ X2013) @ (esk79_4 @ X2010 @ X2011 @ X2012 @ X2013)) @ X2012)|(subset @ X2012 @ X2013)|~(subset @ X2013 @ (cartprod @ X2010 @ X2011))|~(subset @ X2012 @ (cartprod @ X2010 @ X2011)))&(~(in @ (kpair @ (esk78_4 @ X2010 @ X2011 @ X2012 @ X2013) @ (esk79_4 @ X2010 @ X2011 @ X2012 @ X2013)) @ X2013)|(subset @ X2012 @ X2013)|~(subset @ X2013 @ (cartprod @ X2010 @ X2011))|~(subset @ X2012 @ (cartprod @ X2010 @ X2011))))))&(((((in @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2016)|((X2018)=(X2019))|(in @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2016)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(((in @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2017)|((X2018)=(X2019))|(in @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2016)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(((in @ (kpair @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2019)|((X2018)=(X2019))|(in @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2016)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(~(in @ (kpair @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2018)|((X2018)=(X2019))|(in @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2016)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017))))))&((((in @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2016)|((X2018)=(X2019))|(in @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2017)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(((in @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2017)|((X2018)=(X2019))|(in @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2017)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(((in @ (kpair @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2019)|((X2018)=(X2019))|(in @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2017)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(~(in @ (kpair @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2018)|((X2018)=(X2019))|(in @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2017)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017))))))&((((in @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2016)|((X2018)=(X2019))|(in @ (kpair @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2018)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(((in @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2017)|((X2018)=(X2019))|(in @ (kpair @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2018)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(((in @ (kpair @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2019)|((X2018)=(X2019))|(in @ (kpair @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2018)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(~(in @ (kpair @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2018)|((X2018)=(X2019))|(in @ (kpair @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2018)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017))))))&(((in @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2016)|((X2018)=(X2019))|~(in @ (kpair @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2019)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(((in @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019) @ X2017)|((X2018)=(X2019))|~(in @ (kpair @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2019)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(((in @ (kpair @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2019)|((X2018)=(X2019))|~(in @ (kpair @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2019)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))&(~(in @ (kpair @ (esk82_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk83_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2018)|((X2018)=(X2019))|~(in @ (kpair @ (esk80_4 @ X2016 @ X2017 @ X2018 @ X2019) @ (esk81_4 @ X2016 @ X2017 @ X2018 @ X2019)) @ X2019)|~(subset @ X2019 @ (cartprod @ X2016 @ X2017))|~(subset @ X2018 @ (cartprod @ X2016 @ X2017)))))))))&((((in @ (esk84_4 @ X2024 @ X2025 @ X2026 @ X2027) @ X2024)|((X2026)=(X2027))|~(func @ X2024 @ X2025 @ X2027)|~(func @ X2024 @ X2025 @ X2026))&(((ap @ X2024 @ X2025 @ X2026 @ (esk84_4 @ X2024 @ X2025 @ X2026 @ X2027))!=(ap @ X2024 @ X2025 @ X2027 @ (esk84_4 @ X2024 @ X2025 @ X2026 @ X2027)))|((X2026)=(X2027))|~(func @ X2024 @ X2025 @ X2027)|~(func @ X2024 @ X2025 @ X2026)))&((in @ esk87_0 @ (funcSet @ esk85_0 @ esk86_0))&((in @ esk88_0 @ (funcSet @ esk85_0 @ esk86_0))&((~(in @ X2033 @ esk85_0)|((ap @ esk85_0 @ esk86_0 @ esk87_0 @ X2033)=(ap @ esk85_0 @ esk86_0 @ esk88_0 @ X2033)))&((esk87_0)!=(esk88_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_293])])])])])])])). 136.19/20.06 thf(c_0_295, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((func @ X3 @ X4 @ X2)|~((in @ X2 @ (funcSet @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_294])). 136.19/20.06 thf(c_0_296, negated_conjecture, (in @ esk88_0 @ (funcSet @ esk85_0 @ esk86_0)), inference(split_conjunct,[status(thm)],[c_0_294])). 136.19/20.06 thf(c_0_297, negated_conjecture, ![X2:$i, X3:$i, X5:$i, X4:$i]:((((X4)=(X5))|((ap @ X2 @ X3 @ X4 @ (esk84_4 @ X2 @ X3 @ X4 @ X5))!=(ap @ X2 @ X3 @ X5 @ (esk84_4 @ X2 @ X3 @ X4 @ X5)))|~((func @ X2 @ X3 @ X5))|~((func @ X2 @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_294])). 136.19/20.06 thf(c_0_298, negated_conjecture, ![X2:$i]:((((ap @ esk85_0 @ esk86_0 @ esk87_0 @ X2)=(ap @ esk85_0 @ esk86_0 @ esk88_0 @ X2))|~((in @ X2 @ esk85_0)))), inference(split_conjunct,[status(thm)],[c_0_294])). 136.19/20.06 thf(c_0_299, negated_conjecture, (func @ esk85_0 @ esk86_0 @ esk88_0), inference(spm,[status(thm)],[c_0_295, c_0_296])). 136.19/20.06 thf(c_0_300, negated_conjecture, (in @ esk87_0 @ (funcSet @ esk85_0 @ esk86_0)), inference(split_conjunct,[status(thm)],[c_0_294])). 136.19/20.06 thf(c_0_301, negated_conjecture, ![X2:$i]:((((X2)=(esk88_0))|((ap @ esk85_0 @ esk86_0 @ X2 @ (esk84_4 @ esk85_0 @ esk86_0 @ X2 @ esk88_0))!=(ap @ esk85_0 @ esk86_0 @ esk87_0 @ (esk84_4 @ esk85_0 @ esk86_0 @ X2 @ esk88_0)))|~((in @ (esk84_4 @ esk85_0 @ esk86_0 @ X2 @ esk88_0) @ esk85_0))|~((func @ esk85_0 @ esk86_0 @ X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297, c_0_298]), c_0_299])])). 136.19/20.06 thf(c_0_302, negated_conjecture, (func @ esk85_0 @ esk86_0 @ esk87_0), inference(spm,[status(thm)],[c_0_295, c_0_300])). 136.19/20.06 thf(c_0_303, negated_conjecture, ((esk87_0)!=(esk88_0)), inference(split_conjunct,[status(thm)],[c_0_294])). 136.19/20.06 thf(c_0_304, negated_conjecture, ~((in @ (esk84_4 @ esk85_0 @ esk86_0 @ esk87_0 @ esk88_0) @ esk85_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_301]), c_0_302])]), c_0_303])). 136.19/20.06 thf(c_0_305, negated_conjecture, ![X2:$i, X3:$i, X5:$i, X4:$i]:(((in @ (esk84_4 @ X2 @ X3 @ X4 @ X5) @ X2)|((X4)=(X5))|~((func @ X2 @ X3 @ X5))|~((func @ X2 @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_294])). 136.19/20.06 thf(c_0_306, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_304, c_0_305]), c_0_299]), c_0_302])]), c_0_303]), ['proof']). 136.19/20.06 % SZS output end CNFRefutation 136.19/20.06 % Parsed axioms : 460 136.19/20.06 % Removed by relevancy pruning/SinE : 0 136.19/20.06 % Initial clauses : 639 136.19/20.06 % Removed in clause preprocessing : 271 136.19/20.06 % Initial clauses in saturation : 368 136.19/20.06 % Processed clauses : 894 136.19/20.06 % ...of these trivial : 12 136.19/20.06 % ...subsumed : 103 136.19/20.06 % ...remaining for further processing : 779 136.19/20.06 % Other redundant clauses eliminated : 54 136.19/20.06 % Clauses deleted for lack of memory : 0 136.19/20.06 % Backward-subsumed : 0 136.19/20.06 % Backward-rewritten : 3 136.19/20.06 % Generated clauses : 12938 136.19/20.06 % ...of the previous two non-redundant : 12732 136.19/20.06 % ...aggressively subsumed : 0 136.19/20.06 % Contextual simplify-reflections : 0 136.19/20.06 % Paramodulations : 12849 136.19/20.06 % Factorizations : 2 136.19/20.06 % NegExts : 0 136.19/20.06 % Equation resolutions : 61 136.19/20.06 % Disequality decompositions : 0 136.19/20.06 % Total rewrite steps : 238 136.19/20.06 % ...of those cached : 156 136.19/20.06 % Propositional unsat checks : 0 136.19/20.06 % Propositional check models : 0 136.19/20.06 % Propositional check unsatisfiable : 0 136.19/20.06 % Propositional clauses : 0 136.19/20.06 % Propositional clauses after purity: 0 136.19/20.06 % Propositional unsat core size : 0 136.19/20.06 % Propositional preprocessing time : 0.000 136.19/20.06 % Propositional encoding time : 0.000 136.19/20.06 % Propositional solver time : 0.000 136.19/20.06 % Success case prop preproc time : 0.000 136.19/20.06 % Success case prop encoding time : 0.000 136.19/20.06 % Success case prop solver time : 0.000 136.19/20.06 % Current number of processed clauses : 436 136.19/20.06 % Positive orientable unit clauses : 39 136.19/20.06 % Positive unorientable unit clauses: 0 136.19/20.06 % Negative unit clauses : 17 136.19/20.06 % Non-unit-clauses : 380 136.19/20.06 % Current number of unprocessed clauses: 12510 136.19/20.06 % ...number of literals in the above : 53448 136.19/20.06 % Current number of archived formulas : 0 136.19/20.06 % Current number of archived clauses : 328 136.19/20.06 % Clause-clause subsumption calls (NU) : 46060 136.19/20.06 % Rec. Clause-clause subsumption calls : 15606 136.19/20.06 % Non-unit clause-clause subsumptions : 82 136.19/20.06 % Unit Clause-clause subsumption calls : 896 136.19/20.06 % Rewrite failures with RHS unbound : 0 136.19/20.06 % BW rewrite match attempts : 28 136.19/20.06 % BW rewrite match successes : 3 136.19/20.06 % Condensation attempts : 0 136.19/20.06 % Condensation successes : 0 136.19/20.06 % Termbank termtop insertions : 326751 136.19/20.06 % Search garbage collected termcells : 21644 136.19/20.06 136.19/20.06 % ------------------------------------------------- 136.19/20.06 % User time : 18.738 s 136.19/20.06 % System time : 0.713 s 136.19/20.06 % Total time : 19.451 s 136.19/20.07 % Maximum resident set size: 8720 pages 136.19/20.07 136.19/20.07 % ------------------------------------------------- 136.19/20.07 % User time : 18.751 s 136.19/20.07 % System time : 0.721 s 136.19/20.07 % Total time : 19.472 s 136.19/20.07 % Maximum resident set size: 5376 pages 136.19/20.07 % E exiting 136.19/20.07 EOF