0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.12/0.38 % Computer : n003.cluster.edu 0.12/0.38 % Model : x86_64 x86_64 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.38 % Memory : 8046.5625MB 0.12/0.38 % OS : Linux 6.8.0-71-generic 0.12/0.38 % CPULimit : 1440 0.12/0.38 % WCLimit : 180 0.12/0.38 % DateTime : Mon Jul 27 09:51:23 UTC 2026 0.12/0.39 % CPUTime : 0.12/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.12/0.44 Running higher-order theorem proving 0.19/0.51 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.dIr5dk4u0r/E---3.1_3800979.p 3.78/1.18 % Version: 3.5.1-ho 3.78/1.18 % Preprocessing class: HSLMSLSSLLLCHFA. 3.78/1.18 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 3.78/1.18 % Starting ehoh_best5 with 180s (1) cores 3.78/1.18 % Starting almost_fo_3_lam with 180s (1) cores 3.78/1.18 % Starting new_bool_5 with 180s (1) cores 3.78/1.18 % Starting pre_casc_3 with 180s (1) cores 3.78/1.18 % Starting ho_unfolding_8 with 180s (1) cores 3.78/1.18 % Starting new_ho_10_cnf2 with 180s (1) cores 3.78/1.18 % Starting new_bool_3 with 180s (1) cores 3.78/1.18 % Starting new_ho_5 with 180s (1) cores 3.78/1.18 % ehoh_best5 with pid 3800992 completed with status 0 3.78/1.18 % Result found by ehoh_best5 3.78/1.18 % Preprocessing class: HSLMSLSSLLLCHFA. 3.78/1.18 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 3.78/1.18 % Starting ehoh_best5 with 180s (1) cores 3.78/1.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 3.78/1.18 % No SInE strategy applied 3.78/1.18 % Search class: HGHSM-FSLM32-MHFMMSBN 3.78/1.18 % Scheduled 11 strats onto 1 cores with 180 seconds (180 total) 3.78/1.18 % Starting SubtermCWHack with 17s (1) cores 3.78/1.18 % SubtermCWHack with pid 3801003 completed with status 0 3.78/1.18 % Result found by SubtermCWHack 3.78/1.18 % Preprocessing class: HSLMSLSSLLLCHFA. 3.78/1.18 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 3.78/1.18 % Starting ehoh_best5 with 180s (1) cores 3.78/1.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 3.78/1.18 % No SInE strategy applied 3.78/1.18 % Search class: HGHSM-FSLM32-MHFMMSBN 3.78/1.18 % Scheduled 11 strats onto 1 cores with 180 seconds (180 total) 3.78/1.18 % Starting SubtermCWHack with 17s (1) cores 3.78/1.18 % Preprocessing time : 0.009 s 3.78/1.18 3.78/1.18 % Proof found! 3.78/1.18 % SZS status Theorem 3.78/1.18 % SZS output start CNFRefutation 3.78/1.18 thf(decl_23, type, in: $i > $i > $o). 3.78/1.18 thf(decl_24, type, exu: ($i > $o) > $o). 3.78/1.18 thf(decl_25, type, setextAx: $o). 3.78/1.18 thf(decl_26, type, emptyset: $i). 3.78/1.18 thf(decl_27, type, emptysetAx: $o). 3.78/1.18 thf(decl_28, type, setadjoin: $i > $i > $i). 3.78/1.18 thf(decl_29, type, setadjoinAx: $o). 3.78/1.18 thf(decl_30, type, powerset: $i > $i). 3.78/1.18 thf(decl_31, type, powersetAx: $o). 3.78/1.18 thf(decl_32, type, setunion: $i > $i). 3.78/1.18 thf(decl_33, type, setunionAx: $o). 3.78/1.18 thf(decl_34, type, omega: $i). 3.78/1.18 thf(decl_35, type, omega0Ax: $o). 3.78/1.18 thf(decl_36, type, omegaSAx: $o). 3.78/1.18 thf(decl_37, type, omegaIndAx: $o). 3.78/1.18 thf(decl_38, type, replAx: $o). 3.78/1.18 thf(decl_39, type, foundationAx: $o). 3.78/1.18 thf(decl_40, type, wellorderingAx: $o). 3.78/1.18 thf(decl_41, type, descr: ($i > $o) > $i). 3.78/1.18 thf(decl_42, type, descrp: $o). 3.78/1.18 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_44, type, dsetconstrI: $o). 3.78/1.18 thf(decl_45, type, dsetconstrEL: $o). 3.78/1.18 thf(decl_46, type, dsetconstrER: $o). 3.78/1.18 thf(decl_47, type, exuE1: $o). 3.78/1.18 thf(decl_48, type, prop2set: $o > $i). 3.78/1.18 thf(decl_49, type, prop2setE: $o). 3.78/1.18 thf(decl_50, type, emptysetE: $o). 3.78/1.18 thf(decl_51, type, emptysetimpfalse: $o). 3.78/1.18 thf(decl_52, type, notinemptyset: $o). 3.78/1.18 thf(decl_53, type, exuE3e: $o). 3.78/1.18 thf(decl_54, type, setext: $o). 3.78/1.18 thf(decl_55, type, emptyI: $o). 3.78/1.18 thf(decl_56, type, noeltsimpempty: $o). 3.78/1.18 thf(decl_57, type, setbeta: $o). 3.78/1.18 thf(decl_58, type, nonempty: $i > $o). 3.78/1.18 thf(decl_59, type, nonemptyE1: $o). 3.78/1.18 thf(decl_60, type, nonemptyI: $o). 3.78/1.18 thf(decl_61, type, nonemptyI1: $o). 3.78/1.18 thf(decl_62, type, setadjoinIL: $o). 3.78/1.18 thf(decl_63, type, emptyinunitempty: $o). 3.78/1.18 thf(decl_64, type, setadjoinIR: $o). 3.78/1.18 thf(decl_65, type, setadjoinE: $o). 3.78/1.18 thf(decl_66, type, setadjoinOr: $o). 3.78/1.18 thf(decl_67, type, setoftrueEq: $o). 3.78/1.18 thf(decl_68, type, powersetI: $o). 3.78/1.18 thf(decl_69, type, emptyinPowerset: $o). 3.78/1.18 thf(decl_70, type, emptyInPowerset: $o). 3.78/1.18 thf(decl_71, type, powersetE: $o). 3.78/1.18 thf(decl_72, type, setunionI: $o). 3.78/1.18 thf(decl_73, type, setunionE: $o). 3.78/1.18 thf(decl_74, type, subPowSU: $o). 3.78/1.18 thf(decl_75, type, exuE2: $o). 3.78/1.18 thf(decl_76, type, nonemptyImpWitness: $o). 3.78/1.18 thf(decl_77, type, uniqinunit: $o). 3.78/1.18 thf(decl_78, type, notinsingleton: $o). 3.78/1.18 thf(decl_79, type, eqinunit: $o). 3.78/1.18 thf(decl_80, type, singletonsswitch: $o). 3.78/1.18 thf(decl_81, type, upairsetE: $o). 3.78/1.18 thf(decl_82, type, upairsetIL: $o). 3.78/1.18 thf(decl_83, type, upairsetIR: $o). 3.78/1.18 thf(decl_84, type, emptyE1: $o). 3.78/1.18 thf(decl_85, type, vacuousDall: $o). 3.78/1.18 thf(decl_86, type, quantDeMorgan1: $o). 3.78/1.18 thf(decl_87, type, quantDeMorgan2: $o). 3.78/1.18 thf(decl_88, type, quantDeMorgan3: $o). 3.78/1.18 thf(decl_89, type, quantDeMorgan4: $o). 3.78/1.18 thf(decl_90, type, prop2setI: $o). 3.78/1.18 thf(decl_91, type, set2prop: $i > $o). 3.78/1.18 thf(decl_92, type, prop2set2propI: $o). 3.78/1.18 thf(decl_93, type, notdexE: $o). 3.78/1.18 thf(decl_94, type, notdallE: $o). 3.78/1.18 thf(decl_95, type, exuI1: $o). 3.78/1.18 thf(decl_96, type, exuI3: $o). 3.78/1.18 thf(decl_97, type, exuI2: $o). 3.78/1.18 thf(decl_98, type, inCongP: $o). 3.78/1.18 thf(decl_99, type, in__Cong: $o). 3.78/1.18 thf(decl_100, type, exuE3u: $o). 3.78/1.18 thf(decl_101, type, exu__Cong: $o). 3.78/1.18 thf(decl_102, type, emptyset__Cong: $o). 3.78/1.18 thf(decl_103, type, setadjoin__Cong: $o). 3.78/1.18 thf(decl_104, type, powerset__Cong: $o). 3.78/1.18 thf(decl_105, type, setunion__Cong: $o). 3.78/1.18 thf(decl_106, type, omega__Cong: $o). 3.78/1.18 thf(decl_107, type, exuEu: $o). 3.78/1.18 thf(decl_108, type, descr__Cong: $o). 3.78/1.18 thf(decl_109, type, dsetconstr__Cong: $o). 3.78/1.18 thf(decl_110, type, subset: $i > $i > $o). 3.78/1.18 thf(decl_113, type, subsetI1: $o). 3.78/1.18 thf(decl_114, type, eqimpsubset2: $o). 3.78/1.18 thf(decl_115, type, eqimpsubset1: $o). 3.78/1.18 thf(decl_116, type, subsetI2: $o). 3.78/1.18 thf(decl_117, type, emptysetsubset: $o). 3.78/1.18 thf(decl_118, type, subsetE: $o). 3.78/1.18 thf(decl_119, type, subsetE2: $o). 3.78/1.18 thf(decl_120, type, notsubsetI: $o). 3.78/1.18 thf(decl_121, type, notequalI1: $o). 3.78/1.18 thf(decl_122, type, notequalI2: $o). 3.78/1.18 thf(decl_123, type, subsetRefl: $o). 3.78/1.18 thf(decl_124, type, subsetTrans: $o). 3.78/1.18 thf(decl_125, type, setadjoinSub: $o). 3.78/1.18 thf(decl_126, type, setadjoinSub2: $o). 3.78/1.18 thf(decl_127, type, subset2powerset: $o). 3.78/1.18 thf(decl_128, type, setextsub: $o). 3.78/1.18 thf(decl_129, type, subsetemptysetimpeq: $o). 3.78/1.18 thf(decl_130, type, powersetI1: $o). 3.78/1.18 thf(decl_131, type, powersetE1: $o). 3.78/1.18 thf(decl_132, type, inPowerset: $o). 3.78/1.18 thf(decl_133, type, powersetsubset: $o). 3.78/1.18 thf(decl_134, type, sepInPowerset: $o). 3.78/1.18 thf(decl_135, type, sepSubset: $o). 3.78/1.18 thf(decl_136, type, binunion: $i > $i > $i). 3.78/1.18 thf(decl_137, type, binunionIL: $o). 3.78/1.18 thf(decl_138, type, upairset2IR: $o). 3.78/1.18 thf(decl_139, type, binunionIR: $o). 3.78/1.18 thf(decl_140, type, binunionEcases: $o). 3.78/1.18 thf(decl_141, type, binunionE: $o). 3.78/1.18 thf(decl_142, type, binunionLsub: $o). 3.78/1.18 thf(decl_143, type, binunionRsub: $o). 3.78/1.18 thf(decl_144, type, binintersect: $i > $i > $i). 3.78/1.18 thf(decl_145, type, binintersectI: $o). 3.78/1.18 thf(decl_146, type, binintersectSubset5: $o). 3.78/1.18 thf(decl_147, type, binintersectEL: $o). 3.78/1.18 thf(decl_148, type, binintersectLsub: $o). 3.78/1.18 thf(decl_149, type, binintersectSubset2: $o). 3.78/1.18 thf(decl_150, type, binintersectSubset3: $o). 3.78/1.18 thf(decl_151, type, binintersectER: $o). 3.78/1.18 thf(decl_152, type, disjointsetsI1: $o). 3.78/1.18 thf(decl_153, type, binintersectRsub: $o). 3.78/1.18 thf(decl_154, type, binintersectSubset4: $o). 3.78/1.18 thf(decl_155, type, binintersectSubset1: $o). 3.78/1.18 thf(decl_156, type, bs114d: $o). 3.78/1.18 thf(decl_158, type, setminus: $i > $i > $i). 3.78/1.18 thf(decl_159, type, setminusI: $o). 3.78/1.18 thf(decl_160, type, setminusEL: $o). 3.78/1.18 thf(decl_161, type, setminusER: $o). 3.78/1.18 thf(decl_162, type, setminusSubset2: $o). 3.78/1.18 thf(decl_163, type, setminusERneg: $o). 3.78/1.18 thf(decl_164, type, setminusELneg: $o). 3.78/1.18 thf(decl_165, type, setminusILneg: $o). 3.78/1.18 thf(decl_166, type, setminusIRneg: $o). 3.78/1.18 thf(decl_167, type, setminusLsub: $o). 3.78/1.18 thf(decl_168, type, setminusSubset1: $o). 3.78/1.18 thf(decl_169, type, symdiff: $i > $i > $i). 3.78/1.18 thf(decl_170, type, symdiffE: $o). 3.78/1.18 thf(decl_171, type, symdiffI1: $o). 3.78/1.18 thf(decl_172, type, symdiffI2: $o). 3.78/1.18 thf(decl_173, type, symdiffIneg1: $o). 3.78/1.18 thf(decl_174, type, symdiffIneg2: $o). 3.78/1.18 thf(decl_175, type, iskpair: $i > $o). 3.78/1.18 thf(decl_176, type, secondinupair: $o). 3.78/1.18 thf(decl_177, type, setukpairIL: $o). 3.78/1.18 thf(decl_178, type, setukpairIR: $o). 3.78/1.18 thf(decl_179, type, kpairiskpair: $o). 3.78/1.18 thf(decl_180, type, kpair: $i > $i > $i). 3.78/1.18 thf(decl_181, type, kpairp: $o). 3.78/1.18 thf(decl_182, type, cartprod: $i > $i > $i). 3.78/1.18 thf(decl_183, type, singletonsubset: $o). 3.78/1.18 thf(decl_184, type, singletoninpowerset: $o). 3.78/1.18 thf(decl_185, type, singletoninpowunion: $o). 3.78/1.18 thf(decl_186, type, upairset2E: $o). 3.78/1.18 thf(decl_187, type, upairsubunion: $o). 3.78/1.18 thf(decl_188, type, upairinpowunion: $o). 3.78/1.18 thf(decl_189, type, ubforcartprodlem1: $o). 3.78/1.18 thf(decl_190, type, ubforcartprodlem2: $o). 3.78/1.18 thf(decl_191, type, ubforcartprodlem3: $o). 3.78/1.18 thf(decl_192, type, cartprodpairin: $o). 3.78/1.18 thf(decl_193, type, cartprodmempair1: $o). 3.78/1.18 thf(decl_194, type, cartprodmempair: $o). 3.78/1.18 thf(decl_195, type, setunionE2: $o). 3.78/1.18 thf(decl_196, type, setunionsingleton1: $o). 3.78/1.18 thf(decl_197, type, setunionsingleton2: $o). 3.78/1.18 thf(decl_198, type, setunionsingleton: $o). 3.78/1.18 thf(decl_199, type, singleton: $i > $o). 3.78/1.18 thf(decl_200, type, singletonprop: $o). 3.78/1.18 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 3.78/1.18 thf(decl_202, type, ex1E1: $o). 3.78/1.18 thf(decl_203, type, ex1I: $o). 3.78/1.18 thf(decl_204, type, ex1I2: $o). 3.78/1.18 thf(decl_205, type, singletonsuniq: $o). 3.78/1.18 thf(decl_210, type, setukpairinjL1: $o). 3.78/1.18 thf(decl_211, type, kfstsingleton: $o). 3.78/1.18 thf(decl_212, type, theprop: $o). 3.78/1.18 thf(decl_213, type, kfst: $i > $i). 3.78/1.18 thf(decl_214, type, kfstpairEq: $o). 3.78/1.18 thf(decl_215, type, cartprodfstin: $o). 3.78/1.18 thf(decl_216, type, setukpairinjL2: $o). 3.78/1.18 thf(decl_217, type, setukpairinjL: $o). 3.78/1.18 thf(decl_218, type, setukpairinjR11: $o). 3.78/1.18 thf(decl_219, type, setukpairinjR12: $o). 3.78/1.18 thf(decl_220, type, setukpairinjR1: $o). 3.78/1.18 thf(decl_221, type, upairequniteq: $o). 3.78/1.18 thf(decl_222, type, setukpairinjR2: $o). 3.78/1.18 thf(decl_223, type, setukpairinjR: $o). 3.78/1.18 thf(decl_224, type, ksndsingleton: $o). 3.78/1.18 thf(decl_225, type, ksnd: $i > $i). 3.78/1.18 thf(decl_226, type, ksndpairEq: $o). 3.78/1.18 thf(decl_227, type, kpairsurjEq: $o). 3.78/1.18 thf(decl_228, type, cartprodsndin: $o). 3.78/1.18 thf(decl_229, type, cartprodpairmemEL: $o). 3.78/1.18 thf(decl_230, type, cartprodpairmemER: $o). 3.78/1.18 thf(decl_231, type, cartprodmempaircEq: $o). 3.78/1.18 thf(decl_232, type, cartprodfstpairEq: $o). 3.78/1.18 thf(decl_233, type, cartprodsndpairEq: $o). 3.78/1.18 thf(decl_234, type, cartprodpairsurjEq: $o). 3.78/1.18 thf(decl_235, type, breln: $i > $i > $i > $o). 3.78/1.18 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 3.78/1.18 thf(decl_237, type, dpsetconstrI: $o). 3.78/1.18 thf(decl_238, type, dpsetconstrSub: $o). 3.78/1.18 thf(decl_239, type, setOfPairsIsBReln: $o). 3.78/1.18 thf(decl_240, type, dpsetconstrERa: $o). 3.78/1.18 thf(decl_241, type, dpsetconstrEL1: $o). 3.78/1.18 thf(decl_242, type, dpsetconstrEL2: $o). 3.78/1.18 thf(decl_243, type, dpsetconstrER: $o). 3.78/1.18 thf(decl_244, type, func: $i > $i > $i > $o). 3.78/1.18 thf(decl_245, type, funcSet: $i > $i > $i). 3.78/1.18 thf(decl_246, type, funcImageSingleton: $o). 3.78/1.18 thf(decl_247, type, apProp: $o). 3.78/1.18 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 3.78/1.18 thf(decl_249, type, app: $o). 3.78/1.18 thf(decl_250, type, infuncsetfunc: $o). 3.78/1.18 thf(decl_251, type, ap2p: $o). 3.78/1.18 thf(decl_252, type, funcinfuncset: $o). 3.78/1.18 thf(decl_253, type, lamProp: $o). 3.78/1.18 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 3.78/1.18 thf(decl_255, type, lamp: $o). 3.78/1.18 thf(decl_256, type, lam2p: $o). 3.78/1.18 thf(decl_257, type, brelnall1: $o). 3.78/1.18 thf(decl_258, type, brelnall2: $o). 3.78/1.18 thf(decl_259, type, ex1E2: $o). 3.78/1.18 thf(decl_260, type, funcGraphProp1: $o). 3.78/1.18 thf(decl_261, type, funcGraphProp3: $o). 3.78/1.18 thf(decl_262, type, funcGraphProp2: $o). 3.78/1.18 thf(decl_263, type, funcextLem: $o). 3.78/1.18 thf(decl_264, type, funcGraphProp4: $o). 3.78/1.18 thf(decl_265, type, subbreln: $o). 3.78/1.18 thf(decl_266, type, eqbreln: $o). 3.78/1.18 thf(decl_267, type, funcext: $o). 3.78/1.18 thf(decl_268, type, funcext2: $o). 3.78/1.18 thf(decl_269, type, ap2apEq1: $o). 3.78/1.18 thf(decl_270, type, ap2apEq2: $o). 3.78/1.18 thf(decl_271, type, beta1: $o). 3.78/1.18 thf(decl_272, type, eta1: $o). 3.78/1.18 thf(decl_273, type, lam2lamEq: $o). 3.78/1.18 thf(decl_274, type, beta2: $o). 3.78/1.18 thf(decl_275, type, eta2: $o). 3.78/1.18 thf(decl_276, type, iffalseProp1: $o). 3.78/1.18 thf(decl_277, type, iffalseProp2: $o). 3.78/1.18 thf(decl_278, type, iftrueProp1: $o). 3.78/1.18 thf(decl_279, type, iftrueProp2: $o). 3.78/1.18 thf(decl_280, type, ifSingleton: $o). 3.78/1.18 thf(decl_281, type, if: $i > $o > $i > $i > $i). 3.78/1.18 thf(decl_282, type, ifp: $o). 3.78/1.18 thf(decl_283, type, theeq: $o). 3.78/1.18 thf(decl_284, type, iftrue: $o). 3.78/1.18 thf(decl_285, type, iffalse: $o). 3.78/1.18 thf(decl_286, type, iftrueorfalse: $o). 3.78/1.18 thf(decl_287, type, binintersectT_lem: $o). 3.78/1.18 thf(decl_288, type, binunionT_lem: $o). 3.78/1.18 thf(decl_289, type, powersetT_lem: $o). 3.78/1.18 thf(decl_290, type, setminusT_lem: $o). 3.78/1.18 thf(decl_291, type, complementT_lem: $o). 3.78/1.18 thf(decl_292, type, setextT: $o). 3.78/1.18 thf(decl_293, type, subsetTI: $o). 3.78/1.18 thf(decl_294, type, powersetTI1: $o). 3.78/1.18 thf(decl_295, type, powersetTE1: $o). 3.78/1.18 thf(decl_296, type, complementTI1: $o). 3.78/1.18 thf(decl_297, type, complementTE1: $o). 3.78/1.18 thf(decl_298, type, binintersectTELcontra: $o). 3.78/1.18 thf(decl_299, type, binintersectTERcontra: $o). 3.78/1.18 thf(decl_300, type, contrasubsetT: $o). 3.78/1.18 thf(decl_301, type, contrasubsetT1: $o). 3.78/1.18 thf(decl_302, type, contrasubsetT2: $o). 3.78/1.18 thf(decl_303, type, contrasubsetT3: $o). 3.78/1.18 thf(decl_304, type, doubleComplementI1: $o). 3.78/1.18 thf(decl_305, type, doubleComplementE1: $o). 3.78/1.18 thf(decl_306, type, doubleComplementSub1: $o). 3.78/1.18 thf(decl_307, type, doubleComplementSub2: $o). 3.78/1.18 thf(decl_308, type, doubleComplementEq: $o). 3.78/1.18 thf(decl_309, type, complementTnotintersectT: $o). 3.78/1.18 thf(decl_310, type, complementImpComplementIntersect: $o). 3.78/1.18 thf(decl_311, type, complementSubsetComplementIntersect: $o). 3.78/1.18 thf(decl_312, type, complementInPowersetComplementIntersect: $o). 3.78/1.18 thf(decl_313, type, contraSubsetComplement: $o). 3.78/1.18 thf(decl_314, type, complementTcontraSubset: $o). 3.78/1.18 thf(decl_315, type, binunionTILcontra: $o). 3.78/1.18 thf(decl_316, type, binunionTIRcontra: $o). 3.78/1.18 thf(decl_317, type, inIntersectImpInUnion: $o). 3.78/1.18 thf(decl_318, type, inIntersectImpInUnion2: $o). 3.78/1.18 thf(decl_319, type, inIntersectImpInIntersectUnions: $o). 3.78/1.18 thf(decl_320, type, intersectInPowersetIntersectUnions: $o). 3.78/1.18 thf(decl_321, type, inComplementUnionImpNotIn1: $o). 3.78/1.18 thf(decl_322, type, inComplementUnionImpInComplement1: $o). 3.78/1.18 thf(decl_323, type, binunionTE: $o). 3.78/1.18 thf(decl_324, type, binunionTEcontra: $o). 3.78/1.18 thf(decl_325, type, demorgan2a1: $o). 3.78/1.18 thf(decl_326, type, complementUnionInPowersetComplement: $o). 3.78/1.18 thf(decl_327, type, demorgan2a2: $o). 3.78/1.18 thf(decl_328, type, demorgan1a: $o). 3.78/1.18 thf(decl_329, type, demorgan1b: $o). 3.78/1.18 thf(decl_330, type, demorgan1: $o). 3.78/1.18 thf(decl_331, type, demorgan2a: $o). 3.78/1.18 thf(decl_332, type, demorgan2b2: $o). 3.78/1.18 thf(decl_333, type, demorgan2b: $o). 3.78/1.18 thf(decl_334, type, demorgan2: $o). 3.78/1.18 thf(decl_335, type, woz13rule0: $o). 3.78/1.18 thf(decl_336, type, woz13rule1: $o). 3.78/1.18 thf(decl_337, type, woz13rule2: $o). 3.78/1.18 thf(decl_338, type, woz13rule3: $o). 3.78/1.18 thf(decl_339, type, woz13rule4: $o). 3.78/1.18 thf(decl_340, type, woz1_1: $o). 3.78/1.18 thf(decl_341, type, woz1_2: $o). 3.78/1.18 thf(decl_342, type, woz1_3: $o). 3.78/1.18 thf(decl_343, type, epred1_0: $o). 3.78/1.18 thf(decl_344, type, esk1_2: $i > $i > $i). 3.78/1.18 thf(decl_345, type, esk2_2: $i > $i > $i). 3.78/1.18 thf(decl_346, type, esk3_2: $i > $i > $i). 3.78/1.18 thf(decl_347, type, esk4_1: $i > $i). 3.78/1.18 thf(decl_348, type, esk5_2: ($i > $i > $o) > $i > $i). 3.78/1.18 thf(decl_349, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 3.78/1.18 thf(decl_350, type, esk7_2: ($i > $i > $o) > $i > $i). 3.78/1.18 thf(decl_351, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 3.78/1.18 thf(decl_352, type, esk9_1: $i > $i). 3.78/1.18 thf(decl_353, type, esk10_2: ($i > $o) > $i > $i). 3.78/1.18 thf(decl_354, type, esk11_2: ($i > $o) > $i > $i). 3.78/1.18 thf(decl_355, type, esk12_1: ($i > $o) > $i). 3.78/1.18 thf(decl_356, type, esk13_2: ($i > $o) > $i > $i). 3.78/1.18 thf(decl_357, type, esk14_1: ($i > $o) > $i). 3.78/1.18 thf(decl_358, type, esk15_2: $i > $i > $i). 3.78/1.18 thf(decl_359, type, esk16_2: $i > $i > $i). 3.78/1.18 thf(decl_360, type, esk17_1: $i > $i). 3.78/1.18 thf(decl_361, type, esk18_1: $i > $i). 3.78/1.18 thf(decl_362, type, esk19_1: $i > $i). 3.78/1.18 thf(decl_363, type, esk20_2: $i > $i > $i). 3.78/1.18 thf(decl_364, type, esk21_3: $i > $i > $o > $i). 3.78/1.18 thf(decl_365, type, esk22_2: ($i > $o) > $i > $i). 3.78/1.18 thf(decl_366, type, esk23_1: ($i > $o) > $i). 3.78/1.18 thf(decl_367, type, esk24_1: $i > $i). 3.78/1.18 thf(decl_368, type, esk25_2: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_369, type, esk26_2: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_370, type, esk27_2: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_371, type, esk28_2: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_372, type, esk29_2: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_373, type, esk30_2: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_374, type, esk31_2: ($i > $o) > $i > $i). 3.78/1.18 thf(decl_375, type, esk32_1: ($i > $o) > $i). 3.78/1.18 thf(decl_376, type, esk33_1: ($i > $o) > $i). 3.78/1.18 thf(decl_377, type, esk34_1: ($i > $o) > $i). 3.78/1.18 thf(decl_378, type, esk35_1: ($i > $o) > $i). 3.78/1.18 thf(decl_379, type, esk36_2: ($i > $o) > $i > $i). 3.78/1.18 thf(decl_380, type, esk37_1: ($i > $o) > $i). 3.78/1.18 thf(decl_381, type, esk38_2: ($i > $o) > $i > $i). 3.78/1.18 thf(decl_382, type, esk39_2: ($i > $o) > ($i > $o) > $i). 3.78/1.18 thf(decl_383, type, esk40_2: ($i > $o) > ($i > $o) > $i). 3.78/1.18 thf(decl_384, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 3.78/1.18 thf(decl_385, type, esk42_2: ($i > $o) > ($i > $o) > $i). 3.78/1.18 thf(decl_386, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 3.78/1.18 thf(decl_387, type, esk44_2: ($i > $o) > ($i > $o) > $i). 3.78/1.18 thf(decl_388, type, esk45_2: ($i > $o) > $i > $i). 3.78/1.18 thf(decl_389, type, esk46_2: ($i > $o) > ($i > $o) > $i). 3.78/1.18 thf(decl_390, type, esk47_2: ($i > $o) > ($i > $o) > $i). 3.78/1.18 thf(decl_391, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 3.78/1.18 thf(decl_392, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 3.78/1.18 thf(decl_393, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 3.78/1.18 thf(decl_394, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 3.78/1.18 thf(decl_395, type, esk52_2: $i > $i > $i). 3.78/1.18 thf(decl_396, type, esk53_2: $i > $i > $i). 3.78/1.18 thf(decl_397, type, esk54_2: $i > $i > $i). 3.78/1.18 thf(decl_398, type, esk55_3: $i > $i > $i > $i). 3.78/1.18 thf(decl_399, type, esk56_3: $i > $i > $i > $i). 3.78/1.18 thf(decl_400, type, esk57_2: $i > $i > $i). 3.78/1.18 thf(decl_401, type, esk58_2: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_402, type, esk59_2: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_403, type, esk60_2: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_404, type, esk61_3: $i > ($i > $o) > $i > $i). 3.78/1.18 thf(decl_405, type, esk62_2: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_406, type, esk63_2: $i > ($i > $o) > $i). 3.78/1.18 thf(decl_407, type, esk64_3: $i > $i > ($i > $i) > $i). 3.78/1.18 thf(decl_408, type, esk65_3: $i > $i > ($i > $i) > $i). 3.78/1.18 thf(decl_409, type, esk66_3: $i > $i > ($i > $i) > $i). 3.78/1.18 thf(decl_410, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 3.78/1.18 thf(decl_411, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 3.78/1.18 thf(decl_412, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 3.78/1.18 thf(decl_413, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 3.78/1.18 thf(decl_414, type, esk71_4: $i > $i > $i > $i > $i). 3.78/1.18 thf(decl_415, type, esk72_4: $i > $i > $i > $i > $i). 3.78/1.18 thf(decl_416, type, esk73_4: $i > $i > $i > $i > $i). 3.78/1.18 thf(decl_417, type, esk74_4: $i > $i > $i > $i > $i). 3.78/1.18 thf(decl_418, type, esk75_4: $i > $i > $i > $i > $i). 3.78/1.18 thf(decl_419, type, esk76_4: $i > $i > $i > $i > $i). 3.78/1.18 thf(decl_420, type, esk77_4: $i > $i > $i > $i > $i). 3.78/1.18 thf(decl_421, type, esk78_4: $i > $i > $i > $i > $i). 3.78/1.18 thf(decl_422, type, esk79_4: $i > $i > $i > $i > $i). 3.78/1.18 thf(decl_423, type, esk80_3: $i > $i > ($i > $i) > $i). 3.78/1.18 thf(decl_424, type, esk81_3: $i > $i > ($i > $i) > $i). 3.78/1.18 thf(decl_425, type, esk82_3: $i > $i > ($i > $i) > $i). 3.78/1.18 thf(decl_426, type, esk83_3: $i > $i > $i > $i). 3.78/1.18 thf(decl_427, type, esk84_3: $i > $i > $i > $i). 3.78/1.18 thf(decl_428, type, esk85_3: $i > $i > $i > $i). 3.78/1.18 thf(decl_429, type, esk86_3: $i > $i > $i > $i). 3.78/1.18 thf(decl_430, type, esk87_0: $i). 3.78/1.18 thf(decl_431, type, esk88_0: $i). 3.78/1.18 thf(decl_432, type, esk89_0: $i). 3.78/1.18 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', replAx)). 3.78/1.18 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', exu)). 3.78/1.18 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', descrp)). 3.78/1.18 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', exuE1)). 3.78/1.18 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', exuE3e)). 3.78/1.18 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', nonempty)). 3.78/1.18 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', nonemptyI)). 3.78/1.18 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', exuE2)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', exuI1)). 3.78/1.18 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', exuI3)). 3.78/1.18 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', exuI2)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', exuE3u)). 3.78/1.18 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', exu__Cong)). 3.78/1.18 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', exuEu)). 3.78/1.18 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', descr__Cong)). 3.78/1.18 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ex1E1)). 3.78/1.18 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ex1)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', ex1I)). 3.78/1.18 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ex1I2)). 3.78/1.18 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setOfPairsIsBReln)). 3.78/1.18 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', breln)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', ex1E2)). 3.78/1.18 thf(woz1_4, conjecture, ((((setadjoinAx)=>(((((omegaSAx)=>((omegaIndAx)=>(((foundationAx)=>(((descrp)=>(((dsetconstrEL)=>((((prop2setE)=>((((notinemptyset)=>((((emptyI)=>((noeltsimpempty)=>((((((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((((((emptyInPowerset)=>((powersetE)=>((((subPowSU)=>((((uniqinunit)=>((notinsingleton)=>(((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>((notdallE)=>(((((inCongP)=>((((exu__Cong)=>((((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>(((dsetconstr__Cong)=>((subsetI1)=>(((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>(((((notequalI1)=>((notequalI2)=>((subsetRefl)=>(((setadjoinSub)=>((setadjoinSub2)=>((((subsetemptysetimpeq)=>(((powersetE1)=>((inPowerset)=>((powersetsubset)=>(((sepSubset)=>(((((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>(((binintersectLsub)=>(((binintersectSubset3)=>(((disjointsetsI1)=>((((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>(((setminusSubset2)=>(((setminusELneg)=>(((setminusIRneg)=>((setminusLsub)=>(((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>((((((singletoninpowerset)=>(((upairset2E)=>(((upairinpowunion)=>((ubforcartprodlem1)=>((((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((((((((ex1I)=>((ex1I2)=>(((setukpairinjL1)=>(((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>(((setukpairinjR11)=>(((setukpairinjR1)=>(((((ksndsingleton)=>((((cartprodsndin)=>(((((((cartprodpairsurjEq)=>((dpsetconstrI)=>(((((dpsetconstrEL1)=>((dpsetconstrEL2)=>(((funcImageSingleton)=>((apProp)=>(((infuncsetfunc)=>(((funcinfuncset)=>((((((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(((eqbreln)=>((funcext)=>((((((eta1)=>((((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((((theeq)=>((iftrue)=>(((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>(((setminusT_lem)=>((complementT_lem)=>(((subsetTI)=>(((powersetTE1)=>((complementTI1)=>((complementTE1)=>(((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((((doubleComplementSub2)=>(((((complementSubsetComplementIntersect)=>(((contraSubsetComplement)=>((complementTcontraSubset)=>(((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>(((inComplementUnionImpInComplement1)=>(((binunionTEcontra)=>(((((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((((((woz13rule2)=>((((woz1_1)=>((![X4:$i, X21:$i]:((![X48:$i]:((((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))<=(in @ X48 @ (powerset @ X4))))<=(in @ X21 @ (powerset @ X4))))<=(woz1_3))<=(woz1_2)))<=(woz13rule4))<=(woz13rule3)))<=(woz13rule1))<=(woz13rule0))<=(demorgan2))<=(demorgan2b)))))))<=(demorgan2a2))<=(complementUnionInPowersetComplement))<=(demorgan2a1)))<=(binunionTE)))<=(inComplementUnionImpNotIn1)))))))<=(binunionTILcontra))))<=(complementInPowersetComplementIntersect)))<=(complementImpComplementIntersect))<=(complementTnotintersectT))<=(doubleComplementEq)))<=(doubleComplementSub1))<=(doubleComplementE1))))))))<=(binintersectTELcontra)))))<=(powersetTI1)))<=(setextT))))<=(powersetT_lem)))))<=(iffalse))))<=(ifp))<=(ifSingleton)))))))<=(beta2))<=(lam2lamEq)))<=(beta1))<=(ap2apEq2))<=(ap2apEq1))<=(funcext2))))<=(subbreln)))))))))<=(brelnall1))<=(lam2p))<=(lamp))<=(lamProp)))<=(ap2p)))<=(app))))<=(dpsetconstrER))))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub))))<=(cartprodsndpairEq))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL)))<=(kpairsurjEq))<=(ksndpairEq)))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12)))<=(setukpairinjL))))))<=(kfstsingleton)))<=(singletonsuniq))))<=(ex1E1))<=(singletonprop))<=(setunionsingleton))<=(setunionsingleton2))<=(setunionsingleton1))<=(setunionE2)))))<=(ubforcartprodlem3))<=(ubforcartprodlem2))))<=(upairsubunion)))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))))<=(symdiffIneg2))))))<=(setminusSubset1))))<=(setminusILneg)))<=(setminusERneg)))<=(setminusER))))))<=(binintersectSubset4))<=(binintersectRsub)))<=(binintersectER)))<=(binintersectSubset2)))<=(binintersectEL))))))))<=(binunionIR))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset)))))<=(powersetI1)))<=(setextsub))<=(subset2powerset))))<=(subsetTrans)))))<=(notsubsetI))<=(subsetE2))<=(subsetE)))))<=(eqimpsubset2))))<=(descr__Cong))))))<=(setadjoin__Cong))<=(emptyset__Cong)))<=(exuE3u))<=(in__Cong)))<=(exuI2))<=(exuI3))<=(exuI1))))<=(prop2set2propI))))<=(quantDeMorgan3))<=(quantDeMorgan2)))))))))<=(eqinunit))))<=(nonemptyImpWitness))<=(exuE2)))<=(setunionE))<=(setunionI))))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))))))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1))<=(setbeta))))<=(setext))<=(exuE3e)))<=(emptysetimpfalse))<=(emptysetE)))<=(exuE1))<=(dsetconstrER)))<=(dsetconstrI)))<=(wellorderingAx)))<=(replAx))))<=(omega0Ax))<=(setunionAx))<=(powersetAx)))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', woz1_4)). 3.78/1.18 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', dsetconstrI)). 3.78/1.18 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', dsetconstrEL)). 3.78/1.18 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', dsetconstrER)). 3.78/1.18 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setbeta)). 3.78/1.18 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', nonemptyE1)). 3.78/1.18 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', nonemptyI1)). 3.78/1.18 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setoftrueEq)). 3.78/1.18 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', nonemptyImpWitness)). 3.78/1.18 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.dIr5dk4u0r/E---3.1_3800979.p', emptyE1)). 3.78/1.18 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', dsetconstr__Cong)). 3.78/1.18 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', sepInPowerset)). 3.78/1.18 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', sepSubset)). 3.78/1.18 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', singletonprop)). 3.78/1.18 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', kfstsingleton)). 3.78/1.18 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ksndsingleton)). 3.78/1.18 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', dpsetconstrI)). 3.78/1.18 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', dpsetconstrSub)). 3.78/1.18 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', dpsetconstrERa)). 3.78/1.18 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', dpsetconstrEL1)). 3.78/1.18 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', dpsetconstrEL2)). 3.78/1.18 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', dpsetconstrER)). 3.78/1.18 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.dIr5dk4u0r/E---3.1_3800979.p', funcImageSingleton)). 3.78/1.18 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', apProp)). 3.78/1.18 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.dIr5dk4u0r/E---3.1_3800979.p', lamProp)). 3.78/1.18 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', lamp)). 3.78/1.18 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', lam2p)). 3.78/1.18 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', brelnall1)). 3.78/1.18 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', brelnall2)). 3.78/1.18 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', subbreln)). 3.78/1.18 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', eqbreln)). 3.78/1.18 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', beta1)). 3.78/1.18 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', eta1)). 3.78/1.18 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', lam2lamEq)). 3.78/1.18 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', beta2)). 3.78/1.18 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', eta2)). 3.78/1.18 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', iffalseProp1)). 3.78/1.18 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', iffalseProp2)). 3.78/1.18 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', iftrueProp1)). 3.78/1.18 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', iftrueProp2)). 3.78/1.18 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ifSingleton)). 3.78/1.18 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setextAx)). 3.78/1.18 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', emptysetAx)). 3.78/1.18 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setadjoinAx)). 3.78/1.18 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', powersetAx)). 3.78/1.18 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setunionAx)). 3.78/1.18 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', omega0Ax)). 3.78/1.18 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', omegaSAx)). 3.78/1.18 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.dIr5dk4u0r/E---3.1_3800979.p', omegaIndAx)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', foundationAx)). 3.78/1.18 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', wellorderingAx)). 3.78/1.18 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', prop2setE)). 3.78/1.18 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', emptysetE)). 3.78/1.18 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', emptysetimpfalse)). 3.78/1.18 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', notinemptyset)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', setext)). 3.78/1.18 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', emptyI)). 3.78/1.18 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', noeltsimpempty)). 3.78/1.18 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setadjoinIL)). 3.78/1.18 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', emptyinunitempty)). 3.78/1.18 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setadjoinIR)). 3.78/1.18 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setadjoinE)). 3.78/1.18 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setadjoinOr)). 3.78/1.18 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', powersetI)). 3.78/1.18 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', emptyinPowerset)). 3.78/1.18 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', emptyInPowerset)). 3.78/1.18 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', powersetE)). 3.78/1.18 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setunionI)). 3.78/1.18 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setunionE)). 3.78/1.18 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', subPowSU)). 3.78/1.18 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', uniqinunit)). 3.78/1.18 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', notinsingleton)). 3.78/1.18 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', eqinunit)). 3.78/1.18 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', singletonsswitch)). 3.78/1.18 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', upairsetE)). 3.78/1.18 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', upairsetIL)). 3.78/1.18 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', upairsetIR)). 3.78/1.18 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', vacuousDall)). 3.78/1.18 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', quantDeMorgan1)). 3.78/1.18 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', quantDeMorgan2)). 3.78/1.18 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', quantDeMorgan3)). 3.78/1.18 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', quantDeMorgan4)). 3.78/1.18 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', prop2setI)). 3.78/1.18 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', prop2set2propI)). 3.78/1.18 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', notdexE)). 3.78/1.18 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', notdallE)). 3.78/1.18 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', inCongP)). 3.78/1.18 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', in__Cong)). 3.78/1.18 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', emptyset__Cong)). 3.78/1.18 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setadjoin__Cong)). 3.78/1.18 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', powerset__Cong)). 3.78/1.18 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setunion__Cong)). 3.78/1.18 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', omega__Cong)). 3.78/1.18 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', subsetI1)). 3.78/1.18 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', eqimpsubset2)). 3.78/1.18 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', eqimpsubset1)). 3.78/1.18 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', subsetI2)). 3.78/1.18 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', emptysetsubset)). 3.78/1.18 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', subsetE)). 3.78/1.18 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', subsetE2)). 3.78/1.18 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', notsubsetI)). 3.78/1.18 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', notequalI1)). 3.78/1.18 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', notequalI2)). 3.78/1.18 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', subsetRefl)). 3.78/1.18 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', subsetTrans)). 3.78/1.18 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setadjoinSub)). 3.78/1.18 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setadjoinSub2)). 3.78/1.18 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', subset2powerset)). 3.78/1.18 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setextsub)). 3.78/1.18 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', subsetemptysetimpeq)). 3.78/1.18 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', powersetI1)). 3.78/1.18 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', powersetE1)). 3.78/1.18 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', inPowerset)). 3.78/1.18 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', powersetsubset)). 3.78/1.18 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binunionIL)). 3.78/1.18 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', upairset2IR)). 3.78/1.18 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binunionIR)). 3.78/1.18 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binunionEcases)). 3.78/1.18 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binunionE)). 3.78/1.18 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binunionLsub)). 3.78/1.18 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binunionRsub)). 3.78/1.18 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectI)). 3.78/1.18 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectSubset5)). 3.78/1.18 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectEL)). 3.78/1.18 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectLsub)). 3.78/1.18 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectSubset2)). 3.78/1.18 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectSubset3)). 3.78/1.18 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectER)). 3.78/1.18 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', disjointsetsI1)). 3.78/1.18 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectRsub)). 3.78/1.18 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectSubset4)). 3.78/1.18 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectSubset1)). 3.78/1.18 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', bs114d)). 3.78/1.18 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setminusI)). 3.78/1.18 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setminusEL)). 3.78/1.18 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setminusER)). 3.78/1.18 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setminusSubset2)). 3.78/1.18 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setminusERneg)). 3.78/1.18 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setminusELneg)). 3.78/1.18 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setminusILneg)). 3.78/1.18 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setminusIRneg)). 3.78/1.18 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setminusLsub)). 3.78/1.18 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setminusSubset1)). 3.78/1.18 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', symdiffE)). 3.78/1.18 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', symdiffI1)). 3.78/1.18 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', symdiffI2)). 3.78/1.18 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', symdiffIneg1)). 3.78/1.18 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', symdiffIneg2)). 3.78/1.18 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', secondinupair)). 3.78/1.18 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setukpairIL)). 3.78/1.18 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setukpairIR)). 3.78/1.18 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', kpairiskpair)). 3.78/1.18 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', kpairp)). 3.78/1.18 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', singletonsubset)). 3.78/1.18 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', singletoninpowerset)). 3.78/1.18 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', singletoninpowunion)). 3.78/1.18 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', upairset2E)). 3.78/1.18 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', upairsubunion)). 3.78/1.18 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', upairinpowunion)). 3.78/1.18 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ubforcartprodlem1)). 3.78/1.18 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ubforcartprodlem2)). 3.78/1.18 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ubforcartprodlem3)). 3.78/1.18 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', cartprodpairin)). 3.78/1.18 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.dIr5dk4u0r/E---3.1_3800979.p', cartprodmempair1)). 3.78/1.18 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', cartprodmempair)). 3.78/1.18 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setunionE2)). 3.78/1.18 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setunionsingleton1)). 3.78/1.18 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setunionsingleton2)). 3.78/1.18 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setunionsingleton)). 3.78/1.18 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', singletonsuniq)). 3.78/1.18 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.dIr5dk4u0r/E---3.1_3800979.p', setukpairinjL1)). 3.78/1.18 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', theprop)). 3.78/1.18 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', kfstpairEq)). 3.78/1.18 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', cartprodfstin)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', setukpairinjL2)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', setukpairinjL)). 3.78/1.18 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setukpairinjR11)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', setukpairinjR12)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', setukpairinjR1)). 3.78/1.18 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', upairequniteq)). 3.78/1.18 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setukpairinjR2)). 3.78/1.18 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setukpairinjR)). 3.78/1.18 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ksndpairEq)). 3.78/1.18 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', kpairsurjEq)). 3.78/1.18 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', cartprodsndin)). 3.78/1.18 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', cartprodpairmemEL)). 3.78/1.18 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', cartprodpairmemER)). 3.78/1.18 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', cartprodmempaircEq)). 3.78/1.18 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', cartprodfstpairEq)). 3.78/1.18 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', cartprodsndpairEq)). 3.78/1.18 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', cartprodpairsurjEq)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', app)). 3.78/1.18 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', infuncsetfunc)). 3.78/1.18 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ap2p)). 3.78/1.18 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', funcinfuncset)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', funcGraphProp1)). 3.78/1.18 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.dIr5dk4u0r/E---3.1_3800979.p', funcGraphProp3)). 3.78/1.18 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', funcGraphProp2)). 3.78/1.18 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', funcextLem)). 3.78/1.18 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', funcGraphProp4)). 3.78/1.18 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', funcext)). 3.78/1.18 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', funcext2)). 3.78/1.18 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ap2apEq1)). 3.78/1.18 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ap2apEq2)). 3.78/1.18 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', ifp)). 3.78/1.18 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', theeq)). 3.78/1.18 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', iftrue)). 3.78/1.18 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', iffalse)). 3.78/1.18 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', iftrueorfalse)). 3.78/1.18 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectT_lem)). 3.78/1.18 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binunionT_lem)). 3.78/1.18 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', powersetT_lem)). 3.78/1.18 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setminusT_lem)). 3.78/1.18 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', complementT_lem)). 3.78/1.18 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', setextT)). 3.78/1.18 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', subsetTI)). 3.78/1.18 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', powersetTI1)). 3.78/1.18 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', powersetTE1)). 3.78/1.18 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', complementTI1)). 3.78/1.18 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', complementTE1)). 3.78/1.18 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectTELcontra)). 3.78/1.18 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binintersectTERcontra)). 3.78/1.18 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', contrasubsetT)). 3.78/1.18 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', contrasubsetT1)). 3.78/1.18 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', contrasubsetT2)). 3.78/1.18 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', contrasubsetT3)). 3.78/1.18 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', doubleComplementI1)). 3.78/1.18 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', doubleComplementE1)). 3.78/1.18 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', doubleComplementSub1)). 3.78/1.18 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', doubleComplementSub2)). 3.78/1.18 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', doubleComplementEq)). 3.78/1.18 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', complementTnotintersectT)). 3.78/1.18 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', complementImpComplementIntersect)). 3.78/1.18 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', complementSubsetComplementIntersect)). 3.78/1.18 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', complementInPowersetComplementIntersect)). 3.78/1.18 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', contraSubsetComplement)). 3.78/1.18 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', complementTcontraSubset)). 3.78/1.18 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binunionTILcontra)). 3.78/1.18 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binunionTIRcontra)). 3.78/1.18 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', inIntersectImpInUnion)). 3.78/1.18 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', inIntersectImpInUnion2)). 3.78/1.18 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', inIntersectImpInIntersectUnions)). 3.78/1.18 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', intersectInPowersetIntersectUnions)). 3.78/1.18 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', inComplementUnionImpNotIn1)). 3.78/1.18 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', inComplementUnionImpInComplement1)). 3.78/1.18 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binunionTE)). 3.78/1.18 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', binunionTEcontra)). 3.78/1.18 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', demorgan2a1)). 3.78/1.18 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', complementUnionInPowersetComplement)). 3.78/1.18 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', demorgan2a2)). 3.78/1.18 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', demorgan1a)). 3.78/1.18 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', demorgan1b)). 3.78/1.18 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', demorgan1)). 3.78/1.18 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', demorgan2a)). 3.78/1.18 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', demorgan2b2)). 3.78/1.18 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', demorgan2b)). 3.78/1.18 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', demorgan2)). 3.78/1.18 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', woz13rule0)). 3.78/1.18 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', woz13rule1)). 3.78/1.18 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', woz13rule2)). 3.78/1.18 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', woz13rule3)). 3.78/1.18 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', woz13rule4)). 3.78/1.18 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', woz1_1)). 3.78/1.18 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', woz1_2)). 3.78/1.18 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.dIr5dk4u0r/E---3.1_3800979.p', woz1_3)). 3.78/1.18 thf(c_0_287, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 3.78/1.18 thf(c_0_288, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])). 3.78/1.18 thf(c_0_289, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 3.78/1.18 thf(c_0_290, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 3.78/1.18 thf(c_0_291, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 3.78/1.18 thf(c_0_292, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 3.78/1.18 thf(c_0_293, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 3.78/1.18 thf(c_0_294, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 3.78/1.18 thf(c_0_295, 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])). 3.78/1.18 thf(c_0_296, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 3.78/1.18 thf(c_0_297, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 3.78/1.18 thf(c_0_298, 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])). 3.78/1.18 thf(c_0_299, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 3.78/1.18 thf(c_0_300, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 3.78/1.18 thf(c_0_301, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 3.78/1.18 thf(c_0_302, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 3.78/1.18 thf(c_0_303, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])). 3.78/1.18 thf(c_0_304, 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])). 3.78/1.18 thf(c_0_305, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 3.78/1.18 thf(c_0_306, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 3.78/1.18 thf(c_0_307, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 3.78/1.18 thf(c_0_308, 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])). 3.78/1.18 thf(c_0_309, negated_conjecture, ~(((((setadjoinAx)=>(((((omegaSAx)=>((omegaIndAx)=>(((foundationAx)=>(((descrp)=>(((dsetconstrEL)=>((((prop2setE)=>((((notinemptyset)=>((((emptyI)=>((noeltsimpempty)=>((((((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((((((emptyInPowerset)=>((powersetE)=>((((subPowSU)=>((((uniqinunit)=>((notinsingleton)=>(((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>((notdallE)=>(((((inCongP)=>((((exu__Cong)=>((((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>(((dsetconstr__Cong)=>((subsetI1)=>(((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>(((((notequalI1)=>((notequalI2)=>((subsetRefl)=>(((setadjoinSub)=>((setadjoinSub2)=>((((subsetemptysetimpeq)=>(((powersetE1)=>((inPowerset)=>((powersetsubset)=>(((sepSubset)=>(((((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>(((binintersectLsub)=>(((binintersectSubset3)=>(((disjointsetsI1)=>((((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>(((setminusSubset2)=>(((setminusELneg)=>(((setminusIRneg)=>((setminusLsub)=>(((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>((((((singletoninpowerset)=>(((upairset2E)=>(((upairinpowunion)=>((ubforcartprodlem1)=>((((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((((((((ex1I)=>((ex1I2)=>(((setukpairinjL1)=>(((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>(((setukpairinjR11)=>(((setukpairinjR1)=>(((((ksndsingleton)=>((((cartprodsndin)=>(((((((cartprodpairsurjEq)=>((dpsetconstrI)=>(((((dpsetconstrEL1)=>((dpsetconstrEL2)=>(((funcImageSingleton)=>((apProp)=>(((infuncsetfunc)=>(((funcinfuncset)=>((((((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(((eqbreln)=>((funcext)=>((((((eta1)=>((((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((((theeq)=>((iftrue)=>(((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>(((setminusT_lem)=>((complementT_lem)=>(((subsetTI)=>(((powersetTE1)=>((complementTI1)=>((complementTE1)=>(((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((((doubleComplementSub2)=>(((((complementSubsetComplementIntersect)=>(((contraSubsetComplement)=>((complementTcontraSubset)=>(((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>(((inComplementUnionImpInComplement1)=>(((binunionTEcontra)=>(((((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((((((woz13rule2)=>((((woz1_1)=>((![X4:$i, X21:$i]:((![X48:$i]:((((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))<=(in @ X48 @ (powerset @ X4))))<=(in @ X21 @ (powerset @ X4))))<=(woz1_3))<=(woz1_2)))<=(woz13rule4))<=(woz13rule3)))<=(woz13rule1))<=(woz13rule0))<=(demorgan2))<=(demorgan2b)))))))<=(demorgan2a2))<=(complementUnionInPowersetComplement))<=(demorgan2a1)))<=(binunionTE)))<=(inComplementUnionImpNotIn1)))))))<=(binunionTILcontra))))<=(complementInPowersetComplementIntersect)))<=(complementImpComplementIntersect))<=(complementTnotintersectT))<=(doubleComplementEq)))<=(doubleComplementSub1))<=(doubleComplementE1))))))))<=(binintersectTELcontra)))))<=(powersetTI1)))<=(setextT))))<=(powersetT_lem)))))<=(iffalse))))<=(ifp))<=(ifSingleton)))))))<=(beta2))<=(lam2lamEq)))<=(beta1))<=(ap2apEq2))<=(ap2apEq1))<=(funcext2))))<=(subbreln)))))))))<=(brelnall1))<=(lam2p))<=(lamp))<=(lamProp)))<=(ap2p)))<=(app))))<=(dpsetconstrER))))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub))))<=(cartprodsndpairEq))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL)))<=(kpairsurjEq))<=(ksndpairEq)))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12)))<=(setukpairinjL))))))<=(kfstsingleton)))<=(singletonsuniq))))<=(ex1E1))<=(singletonprop))<=(setunionsingleton))<=(setunionsingleton2))<=(setunionsingleton1))<=(setunionE2)))))<=(ubforcartprodlem3))<=(ubforcartprodlem2))))<=(upairsubunion)))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))))<=(symdiffIneg2))))))<=(setminusSubset1))))<=(setminusILneg)))<=(setminusERneg)))<=(setminusER))))))<=(binintersectSubset4))<=(binintersectRsub)))<=(binintersectER)))<=(binintersectSubset2)))<=(binintersectEL))))))))<=(binunionIR))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset)))))<=(powersetI1)))<=(setextsub))<=(subset2powerset))))<=(subsetTrans)))))<=(notsubsetI))<=(subsetE2))<=(subsetE)))))<=(eqimpsubset2))))<=(descr__Cong))))))<=(setadjoin__Cong))<=(emptyset__Cong)))<=(exuE3u))<=(in__Cong)))<=(exuI2))<=(exuI3))<=(exuI1))))<=(prop2set2propI))))<=(quantDeMorgan3))<=(quantDeMorgan2)))))))))<=(eqinunit))))<=(nonemptyImpWitness))<=(exuE2)))<=(setunionE))<=(setunionI))))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))))))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1))<=(setbeta))))<=(setext))<=(exuE3e)))<=(emptysetimpfalse))<=(emptysetE)))<=(exuE1))<=(dsetconstrER)))<=(dsetconstrI)))<=(wellorderingAx)))<=(replAx))))<=(omega0Ax))<=(setunionAx))<=(powersetAx)))<=(emptysetAx))<=(setextAx))), inference(assume_negation,[status(cth)],[woz1_4])). 3.78/1.18 thf(c_0_310, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X956:$i]:(((((X6 @ X2 @ X956)))&(![X957:$i]:(((((X6 @ X2 @ X957)))=>(((X956)=(X957)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_287, c_0_288])). 3.78/1.18 thf(c_0_311, plain, ((descrp)=(![X1:$i > $o]:((((?[X958:$i]:(((((X1 @ X958)))&(![X959:$i]:(((((X1 @ X959)))=>(((X958)=(X959))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_289, c_0_288])). 3.78/1.18 thf(c_0_312, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 3.78/1.18 thf(c_0_313, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 3.78/1.18 thf(c_0_314, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 3.78/1.18 thf(c_0_315, plain, ((exuE1)=(![X1:$i > $o]:((((?[X960:$i]:(((((X1 @ X960)))&(![X961:$i]:(((((X1 @ X961)))=>(((X960)=(X961))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_290, c_0_288])). 3.78/1.18 thf(c_0_316, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X962:$i]:(((((X1 @ X962)))&(![X963:$i]:(((((X1 @ X963)))=>(((X962)=(X963))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_291, c_0_288])). 3.78/1.18 thf(c_0_317, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 3.78/1.18 thf(c_0_318, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_292])). 3.78/1.18 thf(c_0_319, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_293, c_0_292])). 3.78/1.18 thf(c_0_320, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_292])). 3.78/1.18 thf(c_0_321, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 3.78/1.18 thf(c_0_322, plain, ((exuE2)=(![X1:$i > $o]:((((?[X964:$i]:(((((X1 @ X964)))&(![X965:$i]:(((((X1 @ X965)))=>(((X964)=(X965))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_294, c_0_288])). 3.78/1.18 thf(c_0_323, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_292])). 3.78/1.18 thf(c_0_324, 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])). 3.78/1.18 thf(c_0_325, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X966:$i]:(((((X1 @ X966)))&(![X967:$i]:(((((X1 @ X967)))=>(((X966)=(X967)))))))))))))), inference(apply_def,[status(thm)],[c_0_295, c_0_288])). 3.78/1.18 thf(c_0_326, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X968:$i]:(((((X1 @ X968)))&(![X969:$i]:(((((X1 @ X969)))=>(((X968)=(X969)))))))))))))))), inference(apply_def,[status(thm)],[c_0_296, c_0_288])). 3.78/1.18 thf(c_0_327, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X970:$i]:(((((X1 @ X970)))&(![X971:$i]:(((((X1 @ X971)))=>(((X970)=(X971)))))))))))))), inference(apply_def,[status(thm)],[c_0_297, c_0_288])). 3.78/1.18 thf(c_0_328, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X972:$i]:(((((X1 @ X972)))&(![X973:$i]:(((((X1 @ X973)))=>(((X972)=(X973))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_298, c_0_288])). 3.78/1.18 thf(c_0_329, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X974:$i]:(((((X1 @ X974)))&(![X975:$i]:(((((X1 @ X975)))=>(((X974)=(X975))))))))))<=>((?[X976:$i]:(((((X17 @ X976)))&(![X977:$i]:(((((X17 @ X977)))=>(((X976)=(X977)))))))))))))))), inference(apply_def,[status(thm)],[c_0_299, c_0_288])). 3.78/1.18 thf(c_0_330, plain, ((exuEu)=(![X1:$i > $o]:((((?[X978:$i]:(((((X1 @ X978)))&(![X979:$i]:(((((X1 @ X979)))=>(((X978)=(X979))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_300, c_0_288])). 3.78/1.19 thf(c_0_331, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X980:$i]:(((((X1 @ X980)))&(![X981:$i]:(((((X1 @ X981)))=>(((X980)=(X981))))))))))=>((((?[X982:$i]:(((((X17 @ X982)))&(![X983:$i]:(((((X17 @ X983)))=>(((X982)=(X983))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_301, c_0_288])). 3.78/1.19 thf(c_0_332, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 3.78/1.19 thf(c_0_333, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 3.78/1.19 thf(c_0_334, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 3.78/1.19 thf(c_0_335, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 3.78/1.19 thf(c_0_336, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_302, c_0_303])). 3.78/1.19 thf(c_0_337, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_303])). 3.78/1.19 thf(c_0_338, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))))=>(((?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2)))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_305, c_0_303])). 3.78/1.19 thf(c_0_339, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 3.78/1.19 thf(c_0_340, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 3.78/1.19 thf(c_0_341, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 3.78/1.19 thf(c_0_342, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 3.78/1.19 thf(c_0_343, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_306, c_0_307])). 3.78/1.19 thf(c_0_344, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 3.78/1.19 thf(c_0_345, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 3.78/1.19 thf(c_0_346, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 3.78/1.19 thf(c_0_347, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 3.78/1.19 thf(c_0_348, plain, ((funcImageSingleton)<=>![X4:$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])). 3.78/1.19 thf(c_0_349, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 3.78/1.19 thf(c_0_350, plain, ((lamProp)<=>![X4:$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])). 3.78/1.19 thf(c_0_351, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 3.78/1.19 thf(c_0_352, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 3.78/1.19 thf(c_0_353, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_307])). 3.78/1.19 thf(c_0_354, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((X1 @ (kpair @ X2 @ X3)))))))))))=>(![X2:$i]:((((in @ X2 @ X33))=>((X1 @ X2)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_307])). 3.78/1.19 thf(c_0_355, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_308, c_0_303])). 3.78/1.19 thf(c_0_356, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_307])). 3.78/1.19 thf(c_0_357, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X35))=>((in @ (kpair @ X2 @ X3) @ X33))))))))))=>(((X33)=(X35)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_307])). 3.78/1.19 thf(c_0_358, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 3.78/1.19 thf(c_0_359, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 3.78/1.19 thf(c_0_360, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 3.78/1.19 thf(c_0_361, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 3.78/1.19 thf(c_0_362, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 3.78/1.19 thf(c_0_363, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 3.78/1.19 thf(c_0_364, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 3.78/1.19 thf(c_0_365, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 3.78/1.19 thf(c_0_366, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 3.78/1.19 thf(c_0_367, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 3.78/1.19 thf(c_0_368, plain, ((epred1_0)<=>![X1876:$i]:(?[X1877:$i]:((((![X1878:$i]:(((in @ X1878 @ X1877)=>![X1879:$i]:(((in @ X1879 @ X1878)=>(in @ X1879 @ X1876)))))&![X1880:$i, X1881:$i]:((((in @ X1880 @ X1876)&(in @ X1881 @ X1876))=>(![X1882:$i]:(((in @ X1882 @ X1877)=>((in @ X1880 @ X1882)<=>(in @ X1881 @ X1882))))=>((X1880)=(X1881))))))&![X1883:$i, X1884:$i]:((((in @ X1883 @ X1877)&(in @ X1884 @ X1877))=>(![X1885:$i]:(((in @ X1885 @ X1883)=>(in @ X1885 @ X1884)))|![X1886:$i]:(((in @ X1886 @ X1884)=>(in @ X1886 @ X1883)))))))&![X1887:$i]:(((![X1888:$i]:(((in @ X1888 @ X1887)=>(in @ X1888 @ X1876)))&?[X1889:$i]:((in @ X1889 @ X1887)))=>?[X1890:$i, X1891:$i]:(((((in @ X1890 @ X1877)&(in @ X1891 @ X1887))&~(?[X1892:$i]:(((in @ X1892 @ X1890)&(in @ X1892 @ X1887)))))&![X1893:$i]:(((in @ X1893 @ X1877)=>(![X1894:$i]:(((in @ X1894 @ X1893)=>(in @ X1894 @ X1890)))|(in @ X1891 @ X1893)))))))))))), introduced(definition)). 3.78/1.19 thf(c_0_369, negated_conjecture, ~((![X1910:$i, X1911:$i]:((![X1912:$i]:(((in @ X1912 @ X1910)<=>(in @ X1912 @ X1911)))=>((X1910)=(X1911))))=>(![X1909:$i]:(~(in @ X1909 @ emptyset))=>(![X984:$i, X985:$i, X986:$i]:(((in @ X986 @ (setadjoin @ X984 @ X985))<=>(((X986)=(X984))|(in @ X986 @ X985))))=>(![X1906:$i, X1907:$i]:(((in @ X1907 @ (powerset @ X1906))<=>![X1908:$i]:(((in @ X1908 @ X1907)=>(in @ X1908 @ X1906)))))=>(![X1903:$i, X1904:$i]:(((in @ X1904 @ (setunion @ X1903))<=>?[X1905:$i]:(((in @ X1904 @ X1905)&(in @ X1905 @ X1903)))))=>((in @ emptyset @ omega)=>(![X987:$i]:(((in @ X987 @ omega)=>(in @ (setadjoin @ X987 @ X987) @ omega)))=>(![X988:$i]:((((in @ emptyset @ X988)&![X989:$i]:((((in @ X989 @ omega)&(in @ X989 @ X988))=>(in @ (setadjoin @ X989 @ X989) @ X988))))=>![X990:$i]:(((in @ X990 @ omega)=>(in @ X990 @ X988)))))=>(![X1895:$i > $i > $o, X1896:$i]:((![X1897:$i]:(((in @ X1897 @ X1896)=>?[X1898:$i]:(((X1895 @ X1897 @ X1898)&![X1899:$i]:(((X1895 @ X1897 @ X1899)=>((X1898)=(X1899))))))))=>?[X1900:$i]:(![X1901:$i]:(((in @ X1901 @ X1900)<=>?[X1902:$i]:(((in @ X1902 @ X1896)&(X1895 @ X1902 @ X1901))))))))=>(![X991:$i]:((?[X992:$i]:((in @ X992 @ X991))=>?[X993:$i]:(((in @ X993 @ X991)&~(?[X994:$i]:(((in @ X994 @ X993)&(in @ X994 @ X991))))))))=>((epred1_0)=>(![X995:$i > $o]:((?[X996:$i]:(((X995 @ X996)&![X997:$i]:(((X995 @ X997)=>((X996)=(X997))))))=>(X995 @ (descr @ (^[Z0:$i]:(X995 @ Z0))))))=>(![X1873:$i, X1874:$i > $o, X1875:$i]:(((in @ X1875 @ X1873)=>((X1874 @ X1875)=>(in @ X1875 @ (dsetconstr @ X1873 @ X1874)))))=>(![X998:$i, X999:$i > $o, X1000:$i]:(((in @ X1000 @ (dsetconstr @ X998 @ X999))=>(in @ X1000 @ X998)))=>(![X1870:$i, X1871:$i > $o, X1872:$i]:(((in @ X1872 @ (dsetconstr @ X1870 @ X1871))=>(X1871 @ X1872)))=>(![X1865:$i > $o]:((?[X1866:$i]:(((X1865 @ X1866)&![X1867:$i]:(((X1865 @ X1867)=>((X1866)=(X1867))))))=>?[X1868:$i]:(((X1865 @ X1868)&![X1869:$i]:(((X1865 @ X1869)=>((X1868)=(X1869))))))))=>(![X1001:$o, X1002:$i]:(((in @ X1002 @ (prop2set @ ((X1001))))=>(X1001)))=>(![X1863:$i]:(((in @ X1863 @ emptyset)=>![X1864:$o]:((X1864))))=>(![X1862:$i]:(((in @ X1862 @ emptyset)=>~($true)))=>(![X1003:$i]:(~(in @ X1003 @ emptyset))=>(![X1858:$i > $o]:((?[X1859:$i]:(((X1858 @ X1859)&![X1860:$i]:(((X1858 @ X1860)=>((X1859)=(X1860))))))=>?[X1861:$i]:((X1858 @ X1861))))=>(![X1854:$i, X1855:$i]:((![X1856:$i]:(((in @ X1856 @ X1854)=>(in @ X1856 @ X1855)))=>(![X1857:$i]:(((in @ X1857 @ X1855)=>(in @ X1857 @ X1854)))=>((X1854)=(X1855)))))=>(![X1004:$i]:((![X1005:$i]:(~(in @ X1005 @ X1004))=>((X1004)=(emptyset))))=>(![X1006:$i]:((![X1007:$i]:(~(in @ X1007 @ X1006))=>((X1006)=(emptyset))))=>(![X1851:$i, X1852:$i > $o, X1853:$i]:(((in @ X1853 @ X1851)=>((in @ X1853 @ (dsetconstr @ X1851 @ X1852))<=>(X1852 @ X1853))))=>(![X1849:$i]:((((X1849)!=(emptyset))=>?[X1850:$i]:((in @ X1850 @ X1849))))=>(![X1846:$i, X1847:$i > $o, X1848:$i]:(((in @ X1848 @ X1846)=>((X1847 @ X1848)=>((dsetconstr @ X1846 @ X1847)!=(emptyset)))))=>(![X1844:$i]:((?[X1845:$i]:((in @ X1845 @ X1844))=>((X1844)!=(emptyset))))=>(![X1008:$i, X1009:$i]:((in @ X1008 @ (setadjoin @ X1008 @ X1009)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1010:$i, X1011:$i, X1012:$i]:(((in @ X1012 @ X1011)=>(in @ X1012 @ (setadjoin @ X1010 @ X1011))))=>(![X1013:$i, X1014:$i, X1015:$i]:(((in @ X1015 @ (setadjoin @ X1013 @ X1014))=>![X1016:$o]:(((((X1015)=(X1013))=>(X1016))=>(((in @ X1015 @ X1014)=>(X1016))=>(X1016))))))=>(![X1841:$i, X1842:$i, X1843:$i]:(((in @ X1843 @ (setadjoin @ X1841 @ X1842))=>(((X1843)=(X1841))|(in @ X1843 @ X1842))))=>(![X1840:$i]:(((dsetconstr @ X1840 @ (^[Z0:$i]:($true)))=(X1840)))=>(![X1837:$i, X1838:$i]:((![X1839:$i]:(((in @ X1839 @ X1838)=>(in @ X1839 @ X1837)))=>(in @ X1838 @ (powerset @ X1837))))=>(![X1836:$i]:((in @ emptyset @ (powerset @ X1836)))=>(![X1017:$i]:((in @ emptyset @ (powerset @ X1017)))=>(![X1018:$i, X1019:$i, X1020:$i]:(((in @ X1019 @ (powerset @ X1018))=>((in @ X1020 @ X1019)=>(in @ X1020 @ X1018))))=>(![X1833:$i, X1834:$i, X1835:$i]:(((in @ X1834 @ X1835)=>((in @ X1835 @ X1833)=>(in @ X1834 @ (setunion @ X1833)))))=>(![X1829:$i, X1830:$i]:(((in @ X1830 @ (setunion @ X1829))=>![X1831:$o]:((![X1832:$i]:(((in @ X1830 @ X1832)=>((in @ X1832 @ X1829)=>(X1831))))=>(X1831)))))=>(![X1021:$i, X1022:$i]:(((in @ X1022 @ X1021)=>(in @ X1022 @ (powerset @ (setunion @ X1021)))))=>(![X1824:$i > $o]:((?[X1825:$i]:(((X1824 @ X1825)&![X1826:$i]:(((X1824 @ X1826)=>((X1825)=(X1826))))))=>?[X1827:$i]:(![X1828:$i]:(((X1824 @ X1828)<=>((X1828)=(X1827)))))))=>(![X1822:$i]:((((X1822)!=(emptyset))=>?[X1823:$i]:(((in @ X1823 @ X1822)&$true))))=>(![X1023:$i, X1024:$i]:(((in @ X1023 @ (setadjoin @ X1024 @ emptyset))=>((X1023)=(X1024))))=>(![X1025:$i, X1026:$i]:((((X1025)!=(X1026))=>~(in @ X1026 @ (setadjoin @ X1025 @ emptyset))))=>(![X1820:$i, X1821:$i]:((((X1820)=(X1821))=>(in @ X1820 @ (setadjoin @ X1821 @ emptyset))))=>(![X1027:$i, X1028:$i]:(((in @ X1027 @ (setadjoin @ X1028 @ emptyset))=>(in @ X1028 @ (setadjoin @ X1027 @ emptyset))))=>(![X1029:$i, X1030:$i, X1031:$i]:(((in @ X1031 @ (setadjoin @ X1029 @ (setadjoin @ X1030 @ emptyset)))=>(((X1031)=(X1029))|((X1031)=(X1030)))))=>(![X1032:$i, X1033:$i]:((in @ X1032 @ (setadjoin @ X1032 @ (setadjoin @ X1033 @ emptyset))))=>(![X1034:$i, X1035:$i]:((in @ X1035 @ (setadjoin @ X1034 @ (setadjoin @ X1035 @ emptyset))))=>(![X1036:$i, X1037:$i > $o]:((?[X1038:$i]:(((in @ X1038 @ X1036)&(X1037 @ X1038)))=>(((dsetconstr @ X1036 @ X1037)=(emptyset))=>~($true))))=>(![X1039:$i > $o, X1040:$i]:(((in @ X1040 @ emptyset)=>(X1039 @ X1040)))=>(![X1041:$i, X1042:$i > $o]:((~(![X1043:$i]:(((in @ X1043 @ X1041)=>(X1042 @ 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_310]), foundationAx]), wellorderingAx]), c_0_311]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_316]), setext]), emptyI]), noeltsimpempty]), c_0_317]), c_0_318]), c_0_319]), c_0_320]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_321]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_322]), c_0_323]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_324]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_325]), c_0_326]), c_0_327]), inCongP]), in__Cong]), c_0_328]), c_0_329]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_330]), c_0_331]), c_0_332]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_333]), c_0_334]), 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_335]), c_0_336]), c_0_337]), c_0_338]), singletonsuniq]), setukpairinjL1]), c_0_339]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_340]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_341]), c_0_342]), c_0_343]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), c_0_348]), c_0_349]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_350]), c_0_351]), c_0_352]), c_0_353]), c_0_354]), c_0_355]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_356]), c_0_357]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_358]), c_0_359]), c_0_360]), c_0_361]), c_0_362]), c_0_363]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3])])]), c_0_368])). 3.78/1.19 thf(c_0_370, negated_conjecture, ![X1913:$i, X1914:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1926:$i, X1927:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1935:$i, X1936:$i > $i > $o, X1937:$i, X1939:$i, X1942:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1949:$i, X1950:$i > $o, X1951:$i, X1953:$i, X1954:$i > $o, X1955:$i, X1956:$i, X1957:$i > $o, X1958:$i, X1959:$i, X1960:$i > $o, X1961:$i, X1962:$i > $o, X1963:$i, X1966:$i, X1967:$o, X1968:$i, X1969:$i, X1970:$o, X1971:$i, X1972:$i, X1973:$i > $o, X1974:$i, X1977:$i, X1978:$i, X1981:$i, X1983:$i, X1985:$i, X1986:$i > $o, X1987:$i, X1988:$i, X1990:$i, X1991:$i > $o, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$o, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$o, X2023:$i, X2024:$i, X2025:$i > $o, X2026:$i, X2029:$i, X2030:$i, X2031:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i > $o, X2050:$i, X2051:$i > $o, X2052:$i, X2053:$i, X2054:$i > $o, X2055:$i, X2057:$i, X2058:$i > $o, X2060:$i, X2061:$i, X2062:$i > $o, X2064:$i, X2065:$i, X2066:$i > $o, X2067:$i, X2069:$o, X2070:$o, X2071:$i, X2072:$i > $o, X2074:$i, X2075:$i, X2076:$i > $o, X2077:$i, X2079:$i > $o, X2080:$i, X2083:$i, X2084:$i > $o, X2085:$i, X2089:$i, X2090:$i > $o, X2091:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i > $o, X2104:$i, X2106:$i, X2107:$i, X2108:$i > $o, X2109:$i > $o, X2112:$i, X2115:$i, X2116:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i > $o, X2129:$i, X2131:$i, X2132:$i, X2133:$i > $o, X2134:$i > $o, X2137:$i, X2139:$i, X2141:$i, X2142:$i, X2143:$i > $o, X2144:$i > $o, X2147:$i, X2148:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i > $o, 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X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i > $o, X2351:$i, X2352:$i, X2353:$i > $o, X2355:$i, X2356:$i > $o, X2357:$i, X2359:$i, X2360:$i > $o, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, 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(powerset @ X2735))|(~(in @ X2739 @ X2735)|(~(in @ X2739 @ (binintersect @ X2736 @ X2737))|(in @ X2739 @ (binunion @ X2737 @ X2738)))))))&((~(in @ X2741 @ (powerset @ X2740))|(~(in @ X2742 @ (powerset @ X2740))|(~(in @ X2743 @ (powerset @ X2740))|(~(in @ X2744 @ X2740)|(~(in @ X2744 @ (binintersect @ X2741 @ X2742))|(in @ X2744 @ (binintersect @ (binunion @ X2741 @ X2743) @ (binunion @ X2742 @ X2743))))))))&((~(in @ X2746 @ (powerset @ X2745))|(~(in @ X2747 @ (powerset @ X2745))|(~(in @ X2748 @ (powerset @ X2745))|(in @ (binintersect @ X2746 @ X2747) @ (powerset @ (binintersect @ (binunion @ X2746 @ X2748) @ (binunion @ X2747 @ X2748)))))))&((~(in @ X2750 @ (powerset @ X2749))|(~(in @ X2751 @ (powerset @ X2749))|(~(in @ X2752 @ X2749)|(~(in @ X2752 @ (setminus @ X2749 @ (binunion @ X2750 @ X2751)))|~(in @ X2752 @ X2750)))))&((~(in @ X2754 @ (powerset @ X2753))|(~(in @ X2755 @ (powerset @ X2753))|(~(in @ X2756 @ X2753)|(~(in @ X2756 @ (setminus @ X2753 @ (binunion @ X2754 @ X2755)))|(in @ X2756 @ (setminus @ X2753 @ X2754))))))&(((((in @ X2761 @ X2759)|(X2760)|(in @ X2761 @ X2758)|~(in @ X2761 @ (binunion @ X2758 @ X2759))|~(in @ X2761 @ X2757)|~(in @ X2759 @ (powerset @ X2757))|~(in @ X2758 @ (powerset @ X2757)))&(~(X2760)|(X2760)|(in @ X2761 @ X2758)|~(in @ X2761 @ (binunion @ X2758 @ X2759))|~(in @ X2761 @ X2757)|~(in @ X2759 @ (powerset @ X2757))|~(in @ X2758 @ (powerset @ X2757))))&(((in @ X2761 @ X2759)|(X2760)|~(X2760)|~(in @ X2761 @ (binunion @ X2758 @ X2759))|~(in @ X2761 @ X2757)|~(in @ X2759 @ (powerset @ X2757))|~(in @ X2758 @ (powerset @ X2757)))&(~(X2760)|(X2760)|~(X2760)|~(in @ X2761 @ (binunion @ X2758 @ X2759))|~(in @ X2761 @ X2757)|~(in @ X2759 @ (powerset @ X2757))|~(in @ X2758 @ (powerset @ X2757)))))&((~(in @ X2763 @ (powerset @ X2762))|(~(in @ X2764 @ (powerset @ X2762))|(~(in @ X2765 @ X2762)|((in @ X2765 @ X2763)|((in @ X2765 @ X2764)|~(in @ X2765 @ (binunion @ X2763 @ X2764)))))))&((~(in @ X2767 @ (powerset @ X2766))|(~(in @ X2768 @ (powerset @ X2766))|(~(in @ X2769 @ X2766)|(~(in @ X2769 @ (setminus @ X2766 @ (binunion @ X2767 @ X2768)))|(in @ X2769 @ (setminus @ X2766 @ X2767))))))&((~(in @ X2771 @ (powerset @ X2770))|(~(in @ X2772 @ (powerset @ X2770))|(in @ (setminus @ X2770 @ (binunion @ X2771 @ X2772)) @ (powerset @ (setminus @ X2770 @ X2771)))))&((~(in @ X2774 @ (powerset @ X2773))|(~(in @ X2775 @ (powerset @ X2773))|(~(in @ X2776 @ X2773)|(~(in @ X2776 @ (setminus @ X2773 @ (binunion @ X2774 @ X2775)))|(in @ X2776 @ (setminus @ X2773 @ X2775))))))&((~(in @ X2778 @ (powerset @ X2777))|(~(in @ X2779 @ (powerset @ X2777))|(~(in @ X2780 @ X2777)|(~(in @ X2780 @ (setminus @ X2777 @ (binintersect @ X2778 @ X2779)))|(in @ X2780 @ (binunion @ (setminus @ X2777 @ X2778) @ (setminus @ X2777 @ X2779)))))))&((~(in @ X2782 @ (powerset @ X2781))|(~(in @ X2783 @ (powerset @ X2781))|(~(in @ X2784 @ X2781)|(~(in @ X2784 @ (binunion @ (setminus @ X2781 @ X2782) @ (setminus @ X2781 @ X2783)))|(in @ X2784 @ (setminus @ X2781 @ (binintersect @ X2782 @ X2783)))))))&((~(in @ X2786 @ (powerset @ X2785))|(~(in @ X2787 @ (powerset @ X2785))|((setminus @ X2785 @ (binintersect @ X2786 @ X2787))=(binunion @ (setminus @ X2785 @ X2786) @ (setminus @ X2785 @ X2787)))))&((~(in @ X2789 @ (powerset @ X2788))|(~(in @ X2790 @ (powerset @ X2788))|(~(in @ X2791 @ X2788)|(~(in @ X2791 @ (setminus @ X2788 @ (binunion @ X2789 @ X2790)))|(in @ X2791 @ (binintersect @ (setminus @ X2788 @ X2789) @ (setminus @ X2788 @ X2790)))))))&((~(in @ X2793 @ (powerset @ X2792))|(~(in @ X2794 @ (powerset @ X2792))|(~(in @ X2795 @ X2792)|(~(in @ X2795 @ (setminus @ X2792 @ X2793))|(~(in @ X2795 @ (setminus @ X2792 @ X2794))|(in @ X2795 @ (setminus @ X2792 @ (binunion @ X2793 @ X2794))))))))&((~(in @ X2797 @ (powerset @ X2796))|(~(in @ X2798 @ (powerset @ X2796))|(~(in @ X2799 @ X2796)|(~(in @ X2799 @ (binintersect @ (setminus @ X2796 @ X2797) @ (setminus @ X2796 @ X2798)))|(in @ X2799 @ (setminus @ X2796 @ (binunion @ X2797 @ X2798)))))))&((~(in @ X2801 @ (powerset @ X2800))|(~(in @ X2802 @ (powerset @ X2800))|((setminus @ X2800 @ (binunion @ X2801 @ X2802))=(binintersect @ (setminus @ X2800 @ X2801) @ (setminus @ X2800 @ X2802)))))&((~(in @ X2804 @ (powerset @ X2803))|(~(in @ X2805 @ (powerset @ X2803))|(~(in @ X2806 @ (binintersect @ X2804 @ X2805))|(in @ X2806 @ X2803))))&((~(in @ X2808 @ (powerset @ X2807))|(~(in @ X2809 @ (powerset @ X2807))|(~(in @ X2810 @ (powerset @ X2807))|(~(subset @ X2808 @ X2810)|(subset @ (binintersect @ X2808 @ X2809) @ X2810)))))&((~(in @ X2812 @ (powerset @ X2811))|(~(in @ X2813 @ (powerset @ X2811))|(~(in @ X2814 @ (powerset @ X2811))|(~(subset @ X2813 @ X2814)|(subset @ (binintersect @ X2812 @ X2813) @ X2814)))))&((~(in @ X2816 @ (powerset @ X2815))|(~(in @ X2817 @ (powerset @ X2815))|(~(in @ X2818 @ (powerset @ X2815))|(~(subset @ X2816 @ X2817)|(~(subset @ X2816 @ X2818)|(subset @ X2816 @ (binintersect @ X2817 @ X2818)))))))&((~(in @ X2820 @ (powerset @ X2819))|(~(in @ X2821 @ (powerset @ X2819))|(~(in @ X2822 @ (powerset @ X2819))|(~(in @ X2823 @ (powerset @ X2819))|(~(subset @ X2820 @ X2822)|(~(subset @ X2821 @ X2823)|(subset @ (binintersect @ X2820 @ X2821) @ (binintersect @ X2822 @ X2823))))))))&((~(in @ X2825 @ (powerset @ X2824))|(~(in @ X2826 @ (powerset @ X2824))|(in @ (setminus @ X2824 @ X2825) @ (powerset @ (setminus @ X2824 @ (binintersect @ X2825 @ X2826))))))&((~(in @ X2828 @ (powerset @ X2827))|(~(in @ X2829 @ (powerset @ X2827))|(~(in @ X2830 @ (powerset @ X2827))|(~(in @ X2831 @ (powerset @ X2827))|((setminus @ X2827 @ (binintersect @ (binunion @ X2828 @ X2829) @ (binunion @ X2830 @ X2831)))=(binunion @ (binintersect @ (setminus @ X2827 @ X2828) @ (setminus @ X2827 @ X2829)) @ (binintersect @ (setminus @ X2827 @ X2830) @ (setminus @ X2827 @ X2831))))))))&((~(in @ X2833 @ (powerset @ X2832))|(~(in @ X2834 @ (powerset @ X2832))|(~(in @ X2835 @ (powerset @ X2832))|(in @ (binintersect @ X2833 @ X2834) @ (powerset @ (binintersect @ (binunion @ X2833 @ X2835) @ (binunion @ X2834 @ X2835)))))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((subset @ esk88_0 @ (setminus @ esk87_0 @ esk89_0))&~(subset @ esk89_0 @ (setminus @ 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_369])])])])])])])). 3.78/1.19 thf(c_0_371, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X4 @ (setminus @ X3 @ X2))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((subset @ X2 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_370])). 3.78/1.19 thf(c_0_372, negated_conjecture, (subset @ esk88_0 @ (setminus @ esk87_0 @ esk89_0)), inference(split_conjunct,[status(thm)],[c_0_370])). 3.78/1.19 thf(c_0_373, negated_conjecture, (in @ esk89_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_370])). 3.78/1.19 thf(c_0_374, negated_conjecture, (in @ esk88_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_370])). 3.78/1.19 thf(c_0_375, negated_conjecture, ~((subset @ esk89_0 @ (setminus @ esk87_0 @ esk88_0))), inference(split_conjunct,[status(thm)],[c_0_370])). 3.78/1.19 thf(c_0_376, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_371, c_0_372]), c_0_373]), c_0_374])]), c_0_375]), ['proof']). 3.78/1.19 % SZS output end CNFRefutation 3.78/1.19 % Parsed axioms : 607 3.78/1.19 % Removed by relevancy pruning/SinE : 0 3.78/1.19 % Initial clauses : 811 3.78/1.19 % Removed in clause preprocessing : 357 3.78/1.19 % Initial clauses in saturation : 454 3.78/1.19 % Processed clauses : 1848 3.78/1.19 % ...of these trivial : 88 3.78/1.19 % ...subsumed : 946 3.78/1.19 % ...remaining for further processing : 814 3.78/1.19 % Other redundant clauses eliminated : 36 3.78/1.19 % Clauses deleted for lack of memory : 0 3.78/1.19 % Backward-subsumed : 9 3.78/1.19 % Backward-rewritten : 8 3.78/1.19 % Generated clauses : 21879 3.78/1.19 % ...of the previous two non-redundant : 18514 3.78/1.19 % ...aggressively subsumed : 0 3.78/1.19 % Contextual simplify-reflections : 0 3.78/1.19 % Paramodulations : 21835 3.78/1.19 % Factorizations : 2 3.78/1.19 % NegExts : 0 3.78/1.19 % Equation resolutions : 39 3.78/1.19 % Disequality decompositions : 0 3.78/1.19 % Total rewrite steps : 5989 3.78/1.19 % ...of those cached : 5590 3.78/1.19 % Propositional unsat checks : 0 3.78/1.19 % Propositional check models : 0 3.78/1.19 % Propositional check unsatisfiable : 0 3.78/1.19 % Propositional clauses : 0 3.78/1.19 % Propositional clauses after purity: 0 3.78/1.19 % Propositional unsat core size : 0 3.78/1.19 % Propositional preprocessing time : 0.000 3.78/1.19 % Propositional encoding time : 0.000 3.78/1.19 % Propositional solver time : 0.000 3.78/1.19 % Success case prop preproc time : 0.000 3.78/1.19 % Success case prop encoding time : 0.000 3.78/1.19 % Success case prop solver time : 0.000 3.78/1.19 % Current number of processed clauses : 784 3.78/1.19 % Positive orientable unit clauses : 285 3.78/1.19 % Positive unorientable unit clauses: 0 3.78/1.19 % Negative unit clauses : 8 3.78/1.19 % Non-unit-clauses : 491 3.78/1.19 % Current number of unprocessed clauses: 17058 3.78/1.19 % ...number of literals in the above : 50808 3.78/1.19 % Current number of archived formulas : 0 3.78/1.19 % Current number of archived clauses : 18 3.78/1.19 % Clause-clause subsumption calls (NU) : 30650 3.78/1.19 % Rec. Clause-clause subsumption calls : 26136 3.78/1.19 % Non-unit clause-clause subsumptions : 806 3.78/1.19 % Unit Clause-clause subsumption calls : 665 3.78/1.19 % Rewrite failures with RHS unbound : 0 3.78/1.19 % BW rewrite match attempts : 687 3.78/1.19 % BW rewrite match successes : 5 3.78/1.19 % Condensation attempts : 0 3.78/1.19 % Condensation successes : 0 3.78/1.19 % Termbank termtop insertions : 383107 3.78/1.19 % Search garbage collected termcells : 30510 3.78/1.19 3.78/1.19 % ------------------------------------------------- 3.78/1.19 % User time : 0.487 s 3.78/1.19 % System time : 0.041 s 3.78/1.19 % Total time : 0.528 s 3.78/1.19 % Maximum resident set size: 10712 pages 3.78/1.19 3.78/1.19 % ------------------------------------------------- 3.78/1.19 % User time : 0.503 s 3.78/1.19 % System time : 0.053 s 3.78/1.19 % Total time : 0.556 s 3.78/1.19 % Maximum resident set size: 5888 pages 3.78/1.19 % E exiting 3.78/1.19 EOF