0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.09/0.36 % Computer : n023.cluster.edu 0.09/0.36 % Model : x86_64 x86_64 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.36 % Memory : 8046.5625MB 0.09/0.36 % OS : Linux 6.8.0-71-generic 0.09/0.36 % CPULimit : 1440 0.09/0.36 % WCLimit : 180 0.09/0.36 % DateTime : Mon Jul 27 11:15:50 UTC 2026 0.09/0.37 % CPUTime : 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.14/0.41 Running higher-order theorem proving 0.21/0.47 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p 0.65/0.63 % Version: 3.5.1-ho 0.65/0.63 % Preprocessing class: HSLMSLSSLLLCHFA. 0.65/0.63 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.65/0.63 % Starting ehoh_best5 with 180s (1) cores 0.65/0.63 % Starting almost_fo_3_lam with 180s (1) cores 0.65/0.63 % Starting new_bool_5 with 180s (1) cores 0.65/0.63 % Starting pre_casc_3 with 180s (1) cores 0.65/0.63 % Starting ho_unfolding_8 with 180s (1) cores 0.65/0.63 % Starting new_ho_10_cnf2 with 180s (1) cores 0.65/0.63 % Starting new_bool_3 with 180s (1) cores 0.65/0.63 % Starting new_ho_5 with 180s (1) cores 0.65/0.63 % new_bool_5 with pid 820841 completed with status 0 0.65/0.63 % Result found by new_bool_5 0.65/0.63 % Preprocessing class: HSLMSLSSLLLCHFA. 0.65/0.63 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.65/0.63 % Starting ehoh_best5 with 180s (1) cores 0.65/0.63 % Starting almost_fo_3_lam with 180s (1) cores 0.65/0.63 % Starting new_bool_5 with 180s (1) cores 0.65/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)) 0.65/0.63 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.65/0.63 % Search class: HGHSM-FSLM32-MHFMMSBN 0.65/0.63 % Scheduled 11 strats onto 1 cores with 180 seconds (180 total) 0.65/0.63 % Starting SubtermCWHack with 17s (1) cores 0.65/0.63 % SubtermCWHack with pid 820847 completed with status 0 0.65/0.63 % Result found by SubtermCWHack 0.65/0.63 % Preprocessing class: HSLMSLSSLLLCHFA. 0.65/0.63 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.65/0.63 % Starting ehoh_best5 with 180s (1) cores 0.65/0.63 % Starting almost_fo_3_lam with 180s (1) cores 0.65/0.63 % Starting new_bool_5 with 180s (1) cores 0.65/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)) 0.65/0.63 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.65/0.63 % Search class: HGHSM-FSLM32-MHFMMSBN 0.65/0.63 % Scheduled 11 strats onto 1 cores with 180 seconds (180 total) 0.65/0.63 % Starting SubtermCWHack with 17s (1) cores 0.65/0.63 % Preprocessing time : 0.004 s 0.65/0.63 0.65/0.63 % Proof found! 0.65/0.63 % SZS status Theorem 0.65/0.63 % SZS output start CNFRefutation 0.65/0.63 thf(decl_23, type, in: $i > $i > $o). 0.65/0.63 thf(decl_24, type, exu: ($i > $o) > $o). 0.65/0.63 thf(decl_25, type, setextAx: $o). 0.65/0.63 thf(decl_26, type, emptyset: $i). 0.65/0.63 thf(decl_27, type, emptysetAx: $o). 0.65/0.63 thf(decl_28, type, setadjoin: $i > $i > $i). 0.65/0.63 thf(decl_29, type, setadjoinAx: $o). 0.65/0.63 thf(decl_30, type, powerset: $i > $i). 0.65/0.63 thf(decl_31, type, powersetAx: $o). 0.65/0.63 thf(decl_32, type, setunion: $i > $i). 0.65/0.63 thf(decl_33, type, setunionAx: $o). 0.65/0.63 thf(decl_34, type, omega: $i). 0.65/0.63 thf(decl_35, type, omega0Ax: $o). 0.65/0.63 thf(decl_36, type, omegaSAx: $o). 0.65/0.63 thf(decl_37, type, omegaIndAx: $o). 0.65/0.63 thf(decl_38, type, replAx: $o). 0.65/0.63 thf(decl_39, type, foundationAx: $o). 0.65/0.63 thf(decl_40, type, wellorderingAx: $o). 0.65/0.63 thf(decl_41, type, descr: ($i > $o) > $i). 0.65/0.63 thf(decl_42, type, descrp: $o). 0.65/0.63 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_44, type, dsetconstrI: $o). 0.65/0.63 thf(decl_45, type, dsetconstrEL: $o). 0.65/0.63 thf(decl_46, type, dsetconstrER: $o). 0.65/0.63 thf(decl_47, type, exuE1: $o). 0.65/0.63 thf(decl_48, type, prop2set: $o > $i). 0.65/0.63 thf(decl_49, type, prop2setE: $o). 0.65/0.63 thf(decl_50, type, emptysetE: $o). 0.65/0.63 thf(decl_51, type, emptysetimpfalse: $o). 0.65/0.63 thf(decl_52, type, notinemptyset: $o). 0.65/0.63 thf(decl_53, type, exuE3e: $o). 0.65/0.63 thf(decl_54, type, setext: $o). 0.65/0.63 thf(decl_55, type, emptyI: $o). 0.65/0.63 thf(decl_56, type, noeltsimpempty: $o). 0.65/0.63 thf(decl_57, type, setbeta: $o). 0.65/0.63 thf(decl_58, type, nonempty: $i > $o). 0.65/0.63 thf(decl_59, type, nonemptyE1: $o). 0.65/0.63 thf(decl_60, type, nonemptyI: $o). 0.65/0.63 thf(decl_61, type, nonemptyI1: $o). 0.65/0.63 thf(decl_62, type, setadjoinIL: $o). 0.65/0.63 thf(decl_63, type, emptyinunitempty: $o). 0.65/0.63 thf(decl_64, type, setadjoinIR: $o). 0.65/0.63 thf(decl_65, type, setadjoinE: $o). 0.65/0.63 thf(decl_66, type, setadjoinOr: $o). 0.65/0.63 thf(decl_67, type, setoftrueEq: $o). 0.65/0.63 thf(decl_68, type, powersetI: $o). 0.65/0.63 thf(decl_69, type, emptyinPowerset: $o). 0.65/0.63 thf(decl_70, type, emptyInPowerset: $o). 0.65/0.63 thf(decl_71, type, powersetE: $o). 0.65/0.63 thf(decl_72, type, setunionI: $o). 0.65/0.63 thf(decl_73, type, setunionE: $o). 0.65/0.63 thf(decl_74, type, subPowSU: $o). 0.65/0.63 thf(decl_75, type, exuE2: $o). 0.65/0.63 thf(decl_76, type, nonemptyImpWitness: $o). 0.65/0.63 thf(decl_77, type, uniqinunit: $o). 0.65/0.63 thf(decl_78, type, notinsingleton: $o). 0.65/0.63 thf(decl_79, type, eqinunit: $o). 0.65/0.63 thf(decl_80, type, singletonsswitch: $o). 0.65/0.63 thf(decl_81, type, upairsetE: $o). 0.65/0.63 thf(decl_82, type, upairsetIL: $o). 0.65/0.63 thf(decl_83, type, upairsetIR: $o). 0.65/0.63 thf(decl_84, type, emptyE1: $o). 0.65/0.63 thf(decl_85, type, vacuousDall: $o). 0.65/0.63 thf(decl_86, type, quantDeMorgan1: $o). 0.65/0.63 thf(decl_87, type, quantDeMorgan2: $o). 0.65/0.63 thf(decl_88, type, quantDeMorgan3: $o). 0.65/0.63 thf(decl_89, type, quantDeMorgan4: $o). 0.65/0.63 thf(decl_90, type, prop2setI: $o). 0.65/0.63 thf(decl_92, type, prop2set2propI: $o). 0.65/0.63 thf(decl_93, type, notdexE: $o). 0.65/0.63 thf(decl_94, type, notdallE: $o). 0.65/0.63 thf(decl_95, type, exuI1: $o). 0.65/0.63 thf(decl_96, type, exuI3: $o). 0.65/0.63 thf(decl_97, type, exuI2: $o). 0.65/0.63 thf(decl_98, type, inCongP: $o). 0.65/0.63 thf(decl_99, type, in__Cong: $o). 0.65/0.63 thf(decl_100, type, exuE3u: $o). 0.65/0.63 thf(decl_101, type, exu__Cong: $o). 0.65/0.63 thf(decl_102, type, emptyset__Cong: $o). 0.65/0.63 thf(decl_103, type, setadjoin__Cong: $o). 0.65/0.63 thf(decl_104, type, powerset__Cong: $o). 0.65/0.63 thf(decl_105, type, setunion__Cong: $o). 0.65/0.63 thf(decl_106, type, omega__Cong: $o). 0.65/0.63 thf(decl_107, type, exuEu: $o). 0.65/0.63 thf(decl_108, type, descr__Cong: $o). 0.65/0.63 thf(decl_109, type, dsetconstr__Cong: $o). 0.65/0.63 thf(decl_110, type, subset: $i > $i > $o). 0.65/0.63 thf(decl_113, type, subsetI1: $o). 0.65/0.63 thf(decl_114, type, eqimpsubset2: $o). 0.65/0.63 thf(decl_115, type, eqimpsubset1: $o). 0.65/0.63 thf(decl_116, type, subsetI2: $o). 0.65/0.63 thf(decl_117, type, emptysetsubset: $o). 0.65/0.63 thf(decl_118, type, subsetE: $o). 0.65/0.63 thf(decl_119, type, subsetE2: $o). 0.65/0.63 thf(decl_120, type, notsubsetI: $o). 0.65/0.63 thf(decl_121, type, notequalI1: $o). 0.65/0.63 thf(decl_122, type, notequalI2: $o). 0.65/0.63 thf(decl_123, type, subsetRefl: $o). 0.65/0.63 thf(decl_124, type, subsetTrans: $o). 0.65/0.63 thf(decl_125, type, setadjoinSub: $o). 0.65/0.63 thf(decl_126, type, setadjoinSub2: $o). 0.65/0.63 thf(decl_127, type, subset2powerset: $o). 0.65/0.63 thf(decl_128, type, setextsub: $o). 0.65/0.63 thf(decl_129, type, subsetemptysetimpeq: $o). 0.65/0.63 thf(decl_130, type, powersetI1: $o). 0.65/0.63 thf(decl_131, type, powersetE1: $o). 0.65/0.63 thf(decl_132, type, inPowerset: $o). 0.65/0.63 thf(decl_133, type, powersetsubset: $o). 0.65/0.63 thf(decl_134, type, sepInPowerset: $o). 0.65/0.63 thf(decl_135, type, sepSubset: $o). 0.65/0.63 thf(decl_136, type, binunion: $i > $i > $i). 0.65/0.63 thf(decl_137, type, binunionIL: $o). 0.65/0.63 thf(decl_138, type, upairset2IR: $o). 0.65/0.63 thf(decl_139, type, binunionIR: $o). 0.65/0.63 thf(decl_140, type, binunionEcases: $o). 0.65/0.63 thf(decl_141, type, binunionE: $o). 0.65/0.63 thf(decl_142, type, binunionLsub: $o). 0.65/0.63 thf(decl_143, type, binunionRsub: $o). 0.65/0.63 thf(decl_144, type, binintersect: $i > $i > $i). 0.65/0.63 thf(decl_145, type, binintersectI: $o). 0.65/0.63 thf(decl_146, type, binintersectSubset5: $o). 0.65/0.63 thf(decl_147, type, binintersectEL: $o). 0.65/0.63 thf(decl_148, type, binintersectLsub: $o). 0.65/0.63 thf(decl_149, type, binintersectSubset2: $o). 0.65/0.63 thf(decl_150, type, binintersectSubset3: $o). 0.65/0.63 thf(decl_151, type, binintersectER: $o). 0.65/0.63 thf(decl_152, type, disjointsetsI1: $o). 0.65/0.63 thf(decl_153, type, binintersectRsub: $o). 0.65/0.63 thf(decl_154, type, binintersectSubset4: $o). 0.65/0.63 thf(decl_155, type, binintersectSubset1: $o). 0.65/0.63 thf(decl_156, type, bs114d: $o). 0.65/0.63 thf(decl_158, type, setminus: $i > $i > $i). 0.65/0.63 thf(decl_159, type, setminusI: $o). 0.65/0.63 thf(decl_160, type, setminusEL: $o). 0.65/0.63 thf(decl_161, type, setminusER: $o). 0.65/0.63 thf(decl_162, type, setminusSubset2: $o). 0.65/0.63 thf(decl_163, type, setminusERneg: $o). 0.65/0.63 thf(decl_164, type, setminusELneg: $o). 0.65/0.63 thf(decl_165, type, setminusILneg: $o). 0.65/0.63 thf(decl_166, type, setminusIRneg: $o). 0.65/0.63 thf(decl_167, type, setminusLsub: $o). 0.65/0.63 thf(decl_168, type, setminusSubset1: $o). 0.65/0.63 thf(decl_169, type, symdiff: $i > $i > $i). 0.65/0.63 thf(decl_170, type, symdiffE: $o). 0.65/0.63 thf(decl_171, type, symdiffI1: $o). 0.65/0.63 thf(decl_172, type, symdiffI2: $o). 0.65/0.63 thf(decl_173, type, symdiffIneg1: $o). 0.65/0.63 thf(decl_174, type, symdiffIneg2: $o). 0.65/0.63 thf(decl_175, type, iskpair: $i > $o). 0.65/0.63 thf(decl_176, type, secondinupair: $o). 0.65/0.63 thf(decl_177, type, setukpairIL: $o). 0.65/0.63 thf(decl_178, type, setukpairIR: $o). 0.65/0.63 thf(decl_179, type, kpairiskpair: $o). 0.65/0.63 thf(decl_180, type, kpair: $i > $i > $i). 0.65/0.63 thf(decl_181, type, kpairp: $o). 0.65/0.63 thf(decl_182, type, cartprod: $i > $i > $i). 0.65/0.63 thf(decl_183, type, singletonsubset: $o). 0.65/0.63 thf(decl_184, type, singletoninpowerset: $o). 0.65/0.63 thf(decl_185, type, singletoninpowunion: $o). 0.65/0.63 thf(decl_186, type, upairset2E: $o). 0.65/0.63 thf(decl_187, type, upairsubunion: $o). 0.65/0.63 thf(decl_188, type, upairinpowunion: $o). 0.65/0.63 thf(decl_189, type, ubforcartprodlem1: $o). 0.65/0.63 thf(decl_190, type, ubforcartprodlem2: $o). 0.65/0.63 thf(decl_191, type, ubforcartprodlem3: $o). 0.65/0.63 thf(decl_192, type, cartprodpairin: $o). 0.65/0.63 thf(decl_193, type, cartprodmempair1: $o). 0.65/0.63 thf(decl_194, type, cartprodmempair: $o). 0.65/0.63 thf(decl_195, type, setunionE2: $o). 0.65/0.63 thf(decl_196, type, setunionsingleton1: $o). 0.65/0.63 thf(decl_197, type, setunionsingleton2: $o). 0.65/0.63 thf(decl_198, type, setunionsingleton: $o). 0.65/0.63 thf(decl_199, type, singleton: $i > $o). 0.65/0.63 thf(decl_200, type, singletonprop: $o). 0.65/0.63 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 0.65/0.63 thf(decl_202, type, ex1E1: $o). 0.65/0.63 thf(decl_203, type, ex1I: $o). 0.65/0.63 thf(decl_204, type, ex1I2: $o). 0.65/0.63 thf(decl_205, type, singletonsuniq: $o). 0.65/0.63 thf(decl_210, type, setukpairinjL1: $o). 0.65/0.63 thf(decl_211, type, kfstsingleton: $o). 0.65/0.63 thf(decl_212, type, theprop: $o). 0.65/0.63 thf(decl_213, type, kfst: $i > $i). 0.65/0.63 thf(decl_214, type, kfstpairEq: $o). 0.65/0.63 thf(decl_215, type, cartprodfstin: $o). 0.65/0.63 thf(decl_216, type, setukpairinjL2: $o). 0.65/0.63 thf(decl_217, type, setukpairinjL: $o). 0.65/0.63 thf(decl_218, type, setukpairinjR11: $o). 0.65/0.63 thf(decl_219, type, setukpairinjR12: $o). 0.65/0.63 thf(decl_220, type, setukpairinjR1: $o). 0.65/0.63 thf(decl_221, type, upairequniteq: $o). 0.65/0.63 thf(decl_222, type, setukpairinjR2: $o). 0.65/0.63 thf(decl_223, type, setukpairinjR: $o). 0.65/0.63 thf(decl_224, type, ksndsingleton: $o). 0.65/0.63 thf(decl_225, type, ksnd: $i > $i). 0.65/0.63 thf(decl_226, type, ksndpairEq: $o). 0.65/0.63 thf(decl_227, type, kpairsurjEq: $o). 0.65/0.63 thf(decl_228, type, cartprodsndin: $o). 0.65/0.63 thf(decl_229, type, cartprodpairmemEL: $o). 0.65/0.63 thf(decl_230, type, cartprodpairmemER: $o). 0.65/0.63 thf(decl_231, type, cartprodmempaircEq: $o). 0.65/0.63 thf(decl_232, type, cartprodfstpairEq: $o). 0.65/0.63 thf(decl_233, type, cartprodsndpairEq: $o). 0.65/0.63 thf(decl_234, type, cartprodpairsurjEq: $o). 0.65/0.63 thf(decl_235, type, breln: $i > $i > $i > $o). 0.65/0.63 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.65/0.63 thf(decl_237, type, dpsetconstrI: $o). 0.65/0.63 thf(decl_238, type, dpsetconstrSub: $o). 0.65/0.63 thf(decl_239, type, setOfPairsIsBReln: $o). 0.65/0.63 thf(decl_240, type, dpsetconstrERa: $o). 0.65/0.63 thf(decl_241, type, dpsetconstrEL1: $o). 0.65/0.63 thf(decl_242, type, dpsetconstrEL2: $o). 0.65/0.63 thf(decl_243, type, dpsetconstrER: $o). 0.65/0.63 thf(decl_244, type, func: $i > $i > $i > $o). 0.65/0.63 thf(decl_245, type, funcSet: $i > $i > $i). 0.65/0.63 thf(decl_246, type, funcImageSingleton: $o). 0.65/0.63 thf(decl_247, type, apProp: $o). 0.65/0.63 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 0.65/0.63 thf(decl_249, type, app: $o). 0.65/0.63 thf(decl_250, type, infuncsetfunc: $o). 0.65/0.63 thf(decl_251, type, ap2p: $o). 0.65/0.63 thf(decl_252, type, funcinfuncset: $o). 0.65/0.63 thf(decl_253, type, lamProp: $o). 0.65/0.63 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 0.65/0.63 thf(decl_255, type, lamp: $o). 0.65/0.63 thf(decl_256, type, lam2p: $o). 0.65/0.63 thf(decl_257, type, brelnall1: $o). 0.65/0.63 thf(decl_258, type, brelnall2: $o). 0.65/0.63 thf(decl_259, type, ex1E2: $o). 0.65/0.63 thf(decl_260, type, funcGraphProp1: $o). 0.65/0.63 thf(decl_261, type, funcGraphProp3: $o). 0.65/0.63 thf(decl_262, type, funcGraphProp2: $o). 0.65/0.63 thf(decl_263, type, funcextLem: $o). 0.65/0.63 thf(decl_264, type, funcGraphProp4: $o). 0.65/0.63 thf(decl_265, type, subbreln: $o). 0.65/0.63 thf(decl_266, type, eqbreln: $o). 0.65/0.63 thf(decl_267, type, funcext: $o). 0.65/0.63 thf(decl_268, type, funcext2: $o). 0.65/0.63 thf(decl_269, type, ap2apEq1: $o). 0.65/0.63 thf(decl_270, type, ap2apEq2: $o). 0.65/0.63 thf(decl_271, type, beta1: $o). 0.65/0.63 thf(decl_272, type, eta1: $o). 0.65/0.63 thf(decl_273, type, lam2lamEq: $o). 0.65/0.63 thf(decl_274, type, beta2: $o). 0.65/0.63 thf(decl_275, type, eta2: $o). 0.65/0.63 thf(decl_276, type, iffalseProp1: $o). 0.65/0.63 thf(decl_277, type, iffalseProp2: $o). 0.65/0.63 thf(decl_278, type, iftrueProp1: $o). 0.65/0.63 thf(decl_279, type, iftrueProp2: $o). 0.65/0.63 thf(decl_280, type, ifSingleton: $o). 0.65/0.63 thf(decl_281, type, if: $i > $o > $i > $i > $i). 0.65/0.63 thf(decl_282, type, ifp: $o). 0.65/0.63 thf(decl_283, type, theeq: $o). 0.65/0.63 thf(decl_284, type, iftrue: $o). 0.65/0.63 thf(decl_285, type, iffalse: $o). 0.65/0.63 thf(decl_286, type, iftrueorfalse: $o). 0.65/0.63 thf(decl_287, type, binintersectT_lem: $o). 0.65/0.63 thf(decl_288, type, binunionT_lem: $o). 0.65/0.63 thf(decl_289, type, powersetT_lem: $o). 0.65/0.63 thf(decl_290, type, setminusT_lem: $o). 0.65/0.63 thf(decl_291, type, complementT_lem: $o). 0.65/0.63 thf(decl_292, type, setextT: $o). 0.65/0.63 thf(decl_293, type, subsetTI: $o). 0.65/0.63 thf(decl_294, type, powersetTI1: $o). 0.65/0.63 thf(decl_295, type, powersetTE1: $o). 0.65/0.63 thf(decl_296, type, complementTI1: $o). 0.65/0.63 thf(decl_297, type, complementTE1: $o). 0.65/0.63 thf(decl_298, type, binintersectTELcontra: $o). 0.65/0.63 thf(decl_299, type, binintersectTERcontra: $o). 0.65/0.63 thf(decl_300, type, contrasubsetT: $o). 0.65/0.63 thf(decl_301, type, contrasubsetT1: $o). 0.65/0.63 thf(decl_302, type, contrasubsetT2: $o). 0.65/0.63 thf(decl_303, type, contrasubsetT3: $o). 0.65/0.63 thf(decl_304, type, doubleComplementI1: $o). 0.65/0.63 thf(decl_305, type, doubleComplementE1: $o). 0.65/0.63 thf(decl_306, type, doubleComplementSub1: $o). 0.65/0.63 thf(decl_307, type, doubleComplementSub2: $o). 0.65/0.63 thf(decl_308, type, doubleComplementEq: $o). 0.65/0.63 thf(decl_309, type, complementTnotintersectT: $o). 0.65/0.63 thf(decl_310, type, epred1_0: $o). 0.65/0.63 thf(decl_311, type, esk1_2: $i > $i > $i). 0.65/0.63 thf(decl_312, type, esk2_2: $i > $i > $i). 0.65/0.63 thf(decl_313, type, esk3_2: $i > $i > $i). 0.65/0.63 thf(decl_314, type, esk4_1: $i > $i). 0.65/0.63 thf(decl_315, type, esk5_2: ($i > $i > $o) > $i > $i). 0.65/0.63 thf(decl_316, type, esk6_2: ($i > $i > $o) > $i > $i). 0.65/0.63 thf(decl_317, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 0.65/0.63 thf(decl_318, type, esk8_1: $i > $i). 0.65/0.63 thf(decl_319, type, esk9_1: ($i > $o) > $i). 0.65/0.63 thf(decl_320, type, esk10_1: ($i > $o) > $i). 0.65/0.63 thf(decl_321, type, esk11_2: $i > $i > $i). 0.65/0.63 thf(decl_322, type, esk12_2: $i > $i > $i). 0.65/0.63 thf(decl_323, type, esk13_1: $i > $i). 0.65/0.63 thf(decl_324, type, esk14_1: $i > $i). 0.65/0.63 thf(decl_325, type, esk15_1: $i > $i). 0.65/0.63 thf(decl_326, type, esk16_2: $i > $i > $i). 0.65/0.63 thf(decl_327, type, esk17_3: $i > $i > $o > $i). 0.65/0.63 thf(decl_328, type, esk18_1: ($i > $o) > $i). 0.65/0.63 thf(decl_329, type, esk19_1: $i > $i). 0.65/0.63 thf(decl_330, type, esk20_2: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_331, type, esk21_2: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_332, type, esk22_2: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_333, type, esk23_2: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_334, type, esk24_2: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_335, type, esk25_2: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_336, type, esk26_2: ($i > $o) > $i > $i). 0.65/0.63 thf(decl_337, type, esk27_1: ($i > $o) > $i). 0.65/0.63 thf(decl_338, type, esk28_1: ($i > $o) > $i). 0.65/0.63 thf(decl_339, type, esk29_2: ($i > $o) > $i > $i). 0.65/0.63 thf(decl_340, type, esk30_2: ($i > $o) > ($i > $o) > $i). 0.65/0.63 thf(decl_341, type, esk31_2: ($i > $o) > ($i > $o) > $i). 0.65/0.63 thf(decl_342, type, esk32_2: ($i > $o) > ($i > $o) > $i). 0.65/0.63 thf(decl_343, type, esk33_2: ($i > $o) > ($i > $o) > $i). 0.65/0.63 thf(decl_344, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.65/0.63 thf(decl_345, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.65/0.63 thf(decl_346, type, esk36_2: $i > $i > $i). 0.65/0.63 thf(decl_347, type, esk37_2: $i > $i > $i). 0.65/0.63 thf(decl_348, type, esk38_2: $i > $i > $i). 0.65/0.63 thf(decl_349, type, esk39_3: $i > $i > $i > $i). 0.65/0.63 thf(decl_350, type, esk40_3: $i > $i > $i > $i). 0.65/0.63 thf(decl_351, type, esk41_2: $i > $i > $i). 0.65/0.63 thf(decl_352, type, esk42_2: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_353, type, esk43_2: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_354, type, esk44_2: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_355, type, esk45_3: $i > ($i > $o) > $i > $i). 0.65/0.63 thf(decl_356, type, esk46_2: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_357, type, esk47_2: $i > ($i > $o) > $i). 0.65/0.63 thf(decl_358, type, esk48_3: $i > $i > ($i > $i) > $i). 0.65/0.63 thf(decl_359, type, esk49_3: $i > $i > ($i > $i) > $i). 0.65/0.63 thf(decl_360, type, esk50_3: $i > $i > ($i > $i) > $i). 0.65/0.63 thf(decl_361, type, esk51_4: $i > $i > $i > ($i > $o) > $i). 0.65/0.63 thf(decl_362, type, esk52_4: $i > $i > $i > ($i > $o) > $i). 0.65/0.63 thf(decl_363, type, esk53_4: $i > $i > $i > ($i > $o) > $i). 0.65/0.63 thf(decl_364, type, esk54_4: $i > $i > $i > ($i > $o) > $i). 0.65/0.63 thf(decl_365, type, esk55_4: $i > $i > $i > $i > $i). 0.65/0.63 thf(decl_366, type, esk56_4: $i > $i > $i > $i > $i). 0.65/0.63 thf(decl_367, type, esk57_4: $i > $i > $i > $i > $i). 0.65/0.63 thf(decl_368, type, esk58_4: $i > $i > $i > $i > $i). 0.65/0.63 thf(decl_369, type, esk59_4: $i > $i > $i > $i > $i). 0.65/0.63 thf(decl_370, type, esk60_4: $i > $i > $i > $i > $i). 0.65/0.63 thf(decl_371, type, esk61_4: $i > $i > $i > $i > $i). 0.65/0.63 thf(decl_372, type, esk62_4: $i > $i > $i > $i > $i). 0.65/0.63 thf(decl_373, type, esk63_4: $i > $i > $i > $i > $i). 0.65/0.63 thf(decl_374, type, esk64_3: $i > $i > ($i > $i) > $i). 0.65/0.63 thf(decl_375, type, esk65_3: $i > $i > ($i > $i) > $i). 0.65/0.63 thf(decl_376, type, esk66_3: $i > $i > ($i > $i) > $i). 0.65/0.63 thf(decl_377, type, esk67_3: $i > $i > $i > $i). 0.65/0.63 thf(decl_378, type, esk68_3: $i > $i > $i > $i). 0.65/0.63 thf(decl_379, type, esk69_3: $i > $i > $i > $i). 0.65/0.63 thf(decl_380, type, esk70_3: $i > $i > $i > $i). 0.65/0.63 thf(decl_381, type, esk71_0: $i). 0.65/0.63 thf(decl_382, type, esk72_0: $i). 0.65/0.63 thf(decl_383, type, esk73_0: $i). 0.65/0.63 thf(decl_384, type, esk74_0: $i). 0.65/0.63 thf(complementImpComplementIntersect, conjecture, ((((setadjoinAx)=>(((setunionAx)=>((omega0Ax)=>(((omegaIndAx)=>(((foundationAx)=>((wellorderingAx)=>(((dsetconstrI)=>((dsetconstrEL)=>(((exuE1)=>(((((notinemptyset)=>(((((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((((setadjoinE)=>(((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((((((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((((((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((((notdallE)=>((((exuI2)=>((((exuE3u)=>((exu__Cong)=>((((powerset__Cong)=>(((omega__Cong)=>((((dsetconstr__Cong)=>((subsetI1)=>(((eqimpsubset1)=>(((((subsetE2)=>(((((((((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((((powersetsubset)=>(((sepSubset)=>(((((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((((((binintersectSubset3)=>((binintersectER)=>(((binintersectRsub)=>((binintersectSubset4)=>(((((((setminusSubset2)=>(((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>((symdiffE)=>(((((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>(((kpairiskpair)=>(((((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>(((ubforcartprodlem2)=>(((cartprodpairin)=>((cartprodmempair1)=>(((setunionE2)=>(((setunionsingleton2)=>((setunionsingleton)=>((((ex1I)=>((ex1I2)=>((((kfstsingleton)=>((theprop)=>((((setukpairinjL2)=>(((setukpairinjR11)=>(((setukpairinjR1)=>(((setukpairinjR2)=>((setukpairinjR)=>(((ksndpairEq)=>((((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>(((((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>(((dpsetconstrER)=>(((apProp)=>(((infuncsetfunc)=>((ap2p)=>(((lamProp)=>((lamp)=>((((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((((subbreln)=>((((((ap2apEq2)=>((((lam2lamEq)=>((beta2)=>((eta2)=>((((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>(((iffalse)=>(((binintersectT_lem)=>(((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>(((((powersetTE1)=>((complementTI1)=>(((binintersectTELcontra)=>((binintersectTERcontra)=>((((contrasubsetT2)=>((((((doubleComplementSub2)=>((doubleComplementEq)=>(![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))))))))))<=(complementTnotintersectT))))<=(doubleComplementSub1))<=(doubleComplementE1))<=(doubleComplementI1))<=(contrasubsetT3)))<=(contrasubsetT1))<=(contrasubsetT))))<=(complementTE1))))<=(powersetTI1))<=(subsetTI))<=(setextT)))))<=(binunionT_lem)))<=(iftrueorfalse)))<=(iftrue)))))))<=(iffalseProp2))<=(iffalseProp1)))))<=(eta1))<=(beta1)))<=(ap2apEq1))<=(funcext2))<=(funcext))<=(eqbreln)))<=(funcGraphProp4))<=(funcextLem)))))))<=(brelnall1))<=(lam2p))))<=(funcinfuncset))))<=(app)))<=(funcImageSingleton)))<=(dpsetconstrEL2)))))))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))))<=(cartprodsndin))<=(kpairsurjEq)))<=(ksndsingleton))))<=(upairequniteq)))<=(setukpairinjR12)))<=(setukpairinjL)))<=(cartprodfstin))<=(kfstpairEq))))<=(setukpairinjL1))<=(singletonsuniq))))<=(ex1E1))<=(singletonprop))))<=(setunionsingleton1)))<=(cartprodmempair))))<=(ubforcartprodlem3)))<=(ubforcartprodlem1))))))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp)))<=(setukpairIR)))))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1))))<=(setminusLsub)))))<=(setminusERneg)))<=(setminusER))<=(setminusEL))<=(setminusI))<=(bs114d))<=(binintersectSubset1))))<=(disjointsetsI1))))<=(binintersectSubset2))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5)))))))<=(binunionIR))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset)))<=(inPowerset))<=(powersetE1))))))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl))<=(notequalI2))<=(notequalI1))<=(notsubsetI)))<=(subsetE))<=(emptysetsubset))<=(subsetI2)))<=(eqimpsubset2))))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong))))<=(in__Cong))<=(inCongP)))<=(exuI3))<=(exuI1)))<=(notdexE))<=(prop2set2propI)))))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1)))))<=(singletonsswitch))<=(eqinunit))<=(notinsingleton))<=(uniqinunit)))))))<=(powersetE))<=(emptyInPowerset)))))<=(setadjoinOr)))<=(setadjoinIR))<=(emptyinunitempty))))))))<=(emptyI))<=(setext))<=(exuE3e)))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE)))<=(dsetconstrER))))<=(descrp))))<=(replAx)))<=(omegaSAx))))<=(powersetAx)))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', complementImpComplementIntersect)). 0.65/0.63 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', descr__Cong)). 0.65/0.63 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', exuEu)). 0.65/0.63 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', exuI3)). 0.65/0.63 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', exuI1)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', emptyE1)). 0.65/0.63 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', exuE3e)). 0.65/0.63 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', dsetconstrER)). 0.65/0.63 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', descrp)). 0.65/0.63 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', replAx)). 0.65/0.63 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', eta2)). 0.65/0.63 thf(beta2, axiom, ((beta2)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', beta2)). 0.65/0.63 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ex1I2)). 0.65/0.63 thf(ex1I, axiom, ((ex1I)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ex1I)). 0.65/0.63 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', kfstsingleton)). 0.65/0.63 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:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', dpsetconstrEL1)). 0.65/0.63 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', dpsetconstrERa)). 0.65/0.63 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setOfPairsIsBReln)). 0.65/0.63 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', dpsetconstrSub)). 0.65/0.63 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', dpsetconstrI)). 0.65/0.63 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', dpsetconstrER)). 0.65/0.63 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ex1E2)). 0.65/0.63 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', lamp)). 0.65/0.63 thf(lamProp, axiom, ((lamProp)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', lamProp)). 0.65/0.63 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', apProp)). 0.65/0.63 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', lam2lamEq)). 0.65/0.63 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', iftrueProp1)). 0.65/0.63 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ifSingleton)). 0.65/0.63 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', iftrueProp2)). 0.65/0.63 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', iffalseProp2)). 0.65/0.63 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', iffalseProp1)). 0.65/0.63 thf(beta1, axiom, ((beta1)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', beta1)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', eta1)). 0.65/0.63 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:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', dpsetconstrEL2)). 0.65/0.63 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', funcImageSingleton)). 0.65/0.63 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', lam2p)). 0.65/0.63 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ksndsingleton)). 0.65/0.63 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', singletonprop)). 0.65/0.63 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ex1E1)). 0.65/0.63 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', sepInPowerset)). 0.65/0.63 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', sepSubset)). 0.65/0.63 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', dsetconstr__Cong)). 0.65/0.63 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', exu__Cong)). 0.65/0.63 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', exuE3u)). 0.65/0.63 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', exuI2)). 0.65/0.63 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', exuE2)). 0.65/0.63 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setoftrueEq)). 0.65/0.63 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', nonemptyI)). 0.65/0.63 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setbeta)). 0.65/0.63 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', exuE1)). 0.65/0.63 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', dsetconstrEL)). 0.65/0.63 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', dsetconstrI)). 0.65/0.63 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', subsetRefl)). 0.65/0.63 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', subsetTrans)). 0.65/0.63 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', notequalI2)). 0.65/0.63 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', notequalI1)). 0.65/0.63 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectER)). 0.65/0.63 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', notsubsetI)). 0.65/0.63 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectSubset3)). 0.65/0.63 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', subsetE)). 0.65/0.63 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectI)). 0.65/0.63 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', emptysetsubset)). 0.65/0.63 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binunionRsub)). 0.65/0.63 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', subsetI2)). 0.65/0.63 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binunionLsub)). 0.65/0.63 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', eqimpsubset2)). 0.65/0.63 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binunionE)). 0.65/0.63 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectRsub)). 0.65/0.63 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setunion__Cong)). 0.65/0.63 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setadjoin__Cong)). 0.65/0.63 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', emptyset__Cong)). 0.65/0.63 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', in__Cong)). 0.65/0.63 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', inCongP)). 0.65/0.63 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', notdexE)). 0.65/0.63 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', quantDeMorgan2)). 0.65/0.63 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', quantDeMorgan1)). 0.65/0.63 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', vacuousDall)). 0.65/0.63 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', singletonsswitch)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', symdiffE)). 0.65/0.63 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', eqinunit)). 0.65/0.63 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setminusSubset1)). 0.65/0.63 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', notinsingleton)). 0.65/0.63 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setminusIRneg)). 0.65/0.63 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', uniqinunit)). 0.65/0.63 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setminusILneg)). 0.65/0.63 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', powersetE)). 0.65/0.63 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setminusELneg)). 0.65/0.63 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', emptyInPowerset)). 0.65/0.63 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setminusSubset2)). 0.65/0.63 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setadjoinOr)). 0.65/0.63 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectSubset4)). 0.65/0.63 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setadjoinIR)). 0.65/0.63 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', symdiffIneg2)). 0.65/0.63 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', emptyinunitempty)). 0.65/0.63 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', emptyI)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setext)). 0.65/0.63 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', emptysetimpfalse)). 0.65/0.63 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', emptysetE)). 0.65/0.63 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', prop2setE)). 0.65/0.63 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', omegaSAx)). 0.65/0.63 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', powersetAx)). 0.65/0.63 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', emptysetAx)). 0.65/0.63 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', upairinpowunion)). 0.65/0.63 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setextAx)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', upairsubunion)). 0.65/0.63 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', upairset2E)). 0.65/0.63 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', singletoninpowunion)). 0.65/0.63 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', kpairiskpair)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setukpairIL)). 0.65/0.63 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', secondinupair)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ubforcartprodlem2)). 0.65/0.63 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setunionsingleton)). 0.65/0.63 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setunionsingleton2)). 0.65/0.63 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setunionE2)). 0.65/0.63 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', cartprodmempair1)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', cartprodpairin)). 0.65/0.63 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ksndpairEq)). 0.65/0.63 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setukpairinjR)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setukpairinjR2)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setukpairinjR1)). 0.65/0.63 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setukpairinjR11)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setukpairinjL2)). 0.65/0.63 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', theprop)). 0.65/0.63 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', cartprodpairmemEL)). 0.65/0.63 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', cartprodmempaircEq)). 0.65/0.63 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', cartprodpairmemER)). 0.65/0.63 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', brelnall2)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ap2p)). 0.65/0.63 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', infuncsetfunc)). 0.65/0.63 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', funcGraphProp1)). 0.65/0.63 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ap2apEq2)). 0.65/0.63 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', subbreln)). 0.65/0.63 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', funcGraphProp2)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', funcGraphProp3)). 0.65/0.63 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', powersetT_lem)). 0.65/0.63 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectT_lem)). 0.65/0.63 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', iffalse)). 0.65/0.63 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', theeq)). 0.65/0.63 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ifp)). 0.65/0.63 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setminusT_lem)). 0.65/0.63 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', doubleComplementSub2)). 0.65/0.63 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', contrasubsetT2)). 0.65/0.63 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectTERcontra)). 0.65/0.63 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectTELcontra)). 0.65/0.63 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', complementTI1)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', powersetTE1)). 0.65/0.63 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', complementT_lem)). 0.65/0.63 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', doubleComplementEq)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', contrasubsetT)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', contrasubsetT1)). 0.65/0.63 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', contrasubsetT3)). 0.65/0.63 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', doubleComplementI1)). 0.65/0.63 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', doubleComplementE1)). 0.65/0.63 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', doubleComplementSub1)). 0.65/0.63 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', complementTnotintersectT)). 0.65/0.63 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', complementTE1)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', iftrue)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', iftrueorfalse)). 0.65/0.63 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binunionT_lem)). 0.65/0.63 thf(setextT, axiom, ((setextT)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setextT)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', subsetTI)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', powersetTI1)). 0.65/0.63 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', funcGraphProp4)). 0.65/0.63 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', eqbreln)). 0.65/0.63 thf(funcext, axiom, ((funcext)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', funcext)). 0.65/0.63 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', funcext2)). 0.65/0.63 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ap2apEq1)). 0.65/0.63 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', funcextLem)). 0.65/0.63 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', cartprodpairsurjEq)). 0.65/0.63 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', app)). 0.65/0.63 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', funcinfuncset)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', brelnall1)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', cartprodsndpairEq)). 0.65/0.63 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setukpairinjL)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setukpairinjR12)). 0.65/0.63 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', upairequniteq)). 0.65/0.63 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', kpairsurjEq)). 0.65/0.63 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', cartprodsndin)). 0.65/0.63 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', cartprodfstpairEq)). 0.65/0.63 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', cartprodfstin)). 0.65/0.63 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', cartprodmempair)). 0.65/0.63 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setunionsingleton1)). 0.65/0.63 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', singletonsuniq)). 0.65/0.63 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setukpairinjL1)). 0.65/0.63 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', kfstpairEq)). 0.65/0.63 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ubforcartprodlem3)). 0.65/0.63 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', symdiffI2)). 0.65/0.63 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', symdiffIneg1)). 0.65/0.63 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setukpairIR)). 0.65/0.63 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', kpairp)). 0.65/0.63 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', singletonsubset)). 0.65/0.63 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', singletoninpowerset)). 0.65/0.63 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', ubforcartprodlem1)). 0.65/0.63 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', symdiffI1)). 0.65/0.63 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectSubset1)). 0.65/0.63 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', bs114d)). 0.65/0.63 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setminusI)). 0.65/0.63 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setminusEL)). 0.65/0.63 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setminusER)). 0.65/0.63 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setminusERneg)). 0.65/0.63 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setminusLsub)). 0.65/0.63 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', disjointsetsI1)). 0.65/0.63 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binunionIL)). 0.65/0.63 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', upairset2IR)). 0.65/0.63 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binunionIR)). 0.65/0.63 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectSubset5)). 0.65/0.63 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectEL)). 0.65/0.63 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectLsub)). 0.65/0.63 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binintersectSubset2)). 0.65/0.63 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', inPowerset)). 0.65/0.63 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', powersetE1)). 0.65/0.63 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setadjoinSub2)). 0.65/0.63 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setadjoinSub)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', binunionEcases)). 0.65/0.63 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', powersetsubset)). 0.65/0.63 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', powersetI1)). 0.65/0.63 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', subsetemptysetimpeq)). 0.65/0.63 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setextsub)). 0.65/0.63 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', subset2powerset)). 0.65/0.63 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', subsetE2)). 0.65/0.63 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', eqimpsubset1)). 0.65/0.63 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', subsetI1)). 0.65/0.63 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', omega__Cong)). 0.65/0.63 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', powerset__Cong)). 0.65/0.63 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', notdallE)). 0.65/0.63 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', prop2setI)). 0.65/0.63 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', quantDeMorgan4)). 0.65/0.63 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', quantDeMorgan3)). 0.65/0.63 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', upairsetIR)). 0.65/0.63 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', upairsetIL)). 0.65/0.63 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', upairsetE)). 0.65/0.63 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', nonemptyImpWitness)). 0.65/0.63 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', subPowSU)). 0.65/0.63 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setunionE)). 0.65/0.63 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setunionI)). 0.65/0.63 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', emptyinPowerset)). 0.65/0.63 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', powersetI)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setadjoinE)). 0.65/0.63 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setadjoinIL)). 0.65/0.63 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', nonemptyI1)). 0.65/0.63 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', nonemptyE1)). 0.65/0.63 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', noeltsimpempty)). 0.65/0.63 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', notinemptyset)). 0.65/0.63 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', wellorderingAx)). 0.65/0.63 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/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', foundationAx)). 0.65/0.63 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', omegaIndAx)). 0.65/0.63 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', omega0Ax)). 0.65/0.63 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setunionAx)). 0.65/0.63 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.jHKKKjQSAD/E---3.1_820826.p', setadjoinAx)). 0.65/0.63 thf(c_0_249, negated_conjecture, ~(((((setadjoinAx)=>(((setunionAx)=>((omega0Ax)=>(((omegaIndAx)=>(((foundationAx)=>((wellorderingAx)=>(((dsetconstrI)=>((dsetconstrEL)=>(((exuE1)=>(((((notinemptyset)=>(((((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((((setadjoinE)=>(((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((((((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((((((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((((notdallE)=>((((exuI2)=>((((exuE3u)=>((exu__Cong)=>((((powerset__Cong)=>(((omega__Cong)=>((((dsetconstr__Cong)=>((subsetI1)=>(((eqimpsubset1)=>(((((subsetE2)=>(((((((((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((((powersetsubset)=>(((sepSubset)=>(((((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((((((binintersectSubset3)=>((binintersectER)=>(((binintersectRsub)=>((binintersectSubset4)=>(((((((setminusSubset2)=>(((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>((symdiffE)=>(((((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>(((kpairiskpair)=>(((((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>(((ubforcartprodlem2)=>(((cartprodpairin)=>((cartprodmempair1)=>(((setunionE2)=>(((setunionsingleton2)=>((setunionsingleton)=>((((ex1I)=>((ex1I2)=>((((kfstsingleton)=>((theprop)=>((((setukpairinjL2)=>(((setukpairinjR11)=>(((setukpairinjR1)=>(((setukpairinjR2)=>((setukpairinjR)=>(((ksndpairEq)=>((((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>(((((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>(((dpsetconstrER)=>(((apProp)=>(((infuncsetfunc)=>((ap2p)=>(((lamProp)=>((lamp)=>((((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((((subbreln)=>((((((ap2apEq2)=>((((lam2lamEq)=>((beta2)=>((eta2)=>((((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>(((iffalse)=>(((binintersectT_lem)=>(((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>(((((powersetTE1)=>((complementTI1)=>(((binintersectTELcontra)=>((binintersectTERcontra)=>((((contrasubsetT2)=>((((((doubleComplementSub2)=>((doubleComplementEq)=>(![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))))))))))<=(complementTnotintersectT))))<=(doubleComplementSub1))<=(doubleComplementE1))<=(doubleComplementI1))<=(contrasubsetT3)))<=(contrasubsetT1))<=(contrasubsetT))))<=(complementTE1))))<=(powersetTI1))<=(subsetTI))<=(setextT)))))<=(binunionT_lem)))<=(iftrueorfalse)))<=(iftrue)))))))<=(iffalseProp2))<=(iffalseProp1)))))<=(eta1))<=(beta1)))<=(ap2apEq1))<=(funcext2))<=(funcext))<=(eqbreln)))<=(funcGraphProp4))<=(funcextLem)))))))<=(brelnall1))<=(lam2p))))<=(funcinfuncset))))<=(app)))<=(funcImageSingleton)))<=(dpsetconstrEL2)))))))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))))<=(cartprodsndin))<=(kpairsurjEq)))<=(ksndsingleton))))<=(upairequniteq)))<=(setukpairinjR12)))<=(setukpairinjL)))<=(cartprodfstin))<=(kfstpairEq))))<=(setukpairinjL1))<=(singletonsuniq))))<=(ex1E1))<=(singletonprop))))<=(setunionsingleton1)))<=(cartprodmempair))))<=(ubforcartprodlem3)))<=(ubforcartprodlem1))))))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp)))<=(setukpairIR)))))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1))))<=(setminusLsub)))))<=(setminusERneg)))<=(setminusER))<=(setminusEL))<=(setminusI))<=(bs114d))<=(binintersectSubset1))))<=(disjointsetsI1))))<=(binintersectSubset2))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5)))))))<=(binunionIR))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset)))<=(inPowerset))<=(powersetE1))))))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl))<=(notequalI2))<=(notequalI1))<=(notsubsetI)))<=(subsetE))<=(emptysetsubset))<=(subsetI2)))<=(eqimpsubset2))))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong))))<=(in__Cong))<=(inCongP)))<=(exuI3))<=(exuI1)))<=(notdexE))<=(prop2set2propI)))))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1)))))<=(singletonsswitch))<=(eqinunit))<=(notinsingleton))<=(uniqinunit)))))))<=(powersetE))<=(emptyInPowerset)))))<=(setadjoinOr)))<=(setadjoinIR))<=(emptyinunitempty))))))))<=(emptyI))<=(setext))<=(exuE3e)))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE)))<=(dsetconstrER))))<=(descrp))))<=(replAx)))<=(omegaSAx))))<=(powersetAx)))<=(emptysetAx))<=(setextAx))), inference(assume_negation,[status(cth)],[complementImpComplementIntersect])). 0.65/0.63 thf(c_0_250, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.65/0.63 thf(c_0_251, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.65/0.63 thf(c_0_252, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.65/0.63 thf(c_0_253, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.65/0.63 thf(c_0_254, 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])). 0.65/0.63 thf(c_0_255, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.65/0.63 thf(c_0_256, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.65/0.63 thf(c_0_257, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.65/0.63 thf(c_0_258, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.65/0.63 thf(c_0_259, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 0.65/0.63 thf(c_0_260, plain, ((beta2)<=>![X4:$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])). 0.65/0.63 thf(c_0_261, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.65/0.63 thf(c_0_262, plain, ((ex1I)<=>![X4:$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])). 0.65/0.63 thf(c_0_263, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 0.65/0.63 thf(c_0_264, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 0.65/0.63 thf(c_0_265, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 0.65/0.63 thf(c_0_266, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 0.65/0.63 thf(c_0_267, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 0.65/0.63 thf(c_0_268, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 0.65/0.63 thf(c_0_269, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 0.65/0.63 thf(c_0_270, plain, ((ex1E2)<=>![X4:$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])). 0.65/0.63 thf(c_0_271, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 0.65/0.63 thf(c_0_272, plain, ((lamProp)<=>![X4:$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])). 0.65/0.63 thf(c_0_273, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 0.65/0.63 thf(c_0_274, plain, ((lam2lamEq)<=>![X4:$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])). 0.65/0.63 thf(c_0_275, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 0.65/0.63 thf(c_0_276, plain, ((ifSingleton)<=>![X4:$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])). 0.65/0.63 thf(c_0_277, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 0.65/0.63 thf(c_0_278, plain, ((iffalseProp2)<=>![X4:$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])). 0.65/0.63 thf(c_0_279, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 0.65/0.63 thf(c_0_280, plain, ((beta1)<=>![X4:$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])). 0.65/0.63 thf(c_0_281, 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])). 0.65/0.63 thf(c_0_282, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 0.65/0.63 thf(c_0_283, plain, ((funcImageSingleton)<=>![X4:$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])). 0.65/0.63 thf(c_0_284, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 0.65/0.63 thf(c_0_285, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 0.65/0.63 thf(c_0_286, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.65/0.63 thf(c_0_287, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.65/0.63 thf(c_0_288, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.65/0.63 thf(c_0_289, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.65/0.63 thf(c_0_290, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.65/0.63 thf(c_0_291, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.65/0.63 thf(c_0_292, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.65/0.63 thf(c_0_293, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.65/0.63 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])). 0.65/0.63 thf(c_0_295, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.65/0.63 thf(c_0_296, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.65/0.63 thf(c_0_297, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.65/0.63 thf(c_0_298, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.65/0.63 thf(c_0_299, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.65/0.63 thf(c_0_300, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.65/0.63 thf(c_0_301, plain, ((epred1_0)<=>![X835:$i]:(?[X836:$i]:((((![X837:$i]:(((in @ X837 @ X836)=>![X838:$i]:(((in @ X838 @ X837)=>(in @ X838 @ X835)))))&![X839:$i, X840:$i]:((((in @ X839 @ X835)&(in @ X840 @ X835))=>(![X841:$i]:(((in @ X841 @ X836)=>((in @ X839 @ X841)<=>(in @ X840 @ X841))))=>((X839)=(X840))))))&![X842:$i, X843:$i]:((((in @ X842 @ X836)&(in @ X843 @ X836))=>(![X844:$i]:(((in @ X844 @ X842)=>(in @ X844 @ X843)))|![X845:$i]:(((in @ X845 @ X843)=>(in @ X845 @ X842)))))))&![X846:$i]:(((![X847:$i]:(((in @ X847 @ X846)=>(in @ X847 @ X835)))&?[X848:$i]:((in @ X848 @ X846)))=>?[X849:$i, X850:$i]:(((((in @ X849 @ X836)&(in @ X850 @ X846))&~(?[X851:$i]:(((in @ X851 @ X849)&(in @ X851 @ X846)))))&![X852:$i]:(((in @ X852 @ X836)=>(![X853:$i]:(((in @ X853 @ X852)=>(in @ X853 @ X849)))|(in @ X850 @ X852)))))))))))), introduced(definition)). 0.65/0.63 thf(c_0_302, negated_conjecture, ~((![X1588:$i, X1589:$i]:((![X1590:$i]:(((in @ X1590 @ X1588)<=>(in @ X1590 @ X1589)))=>((X1588)=(X1589))))=>(![X1587:$i]:(~(in @ X1587 @ emptyset))=>(![X822:$i, X823:$i, X824:$i]:(((in @ X824 @ (setadjoin @ X822 @ X823))<=>(((X824)=(X822))|(in @ X824 @ X823))))=>(![X1584:$i, X1585:$i]:(((in @ X1585 @ (powerset @ X1584))<=>![X1586:$i]:(((in @ X1586 @ X1585)=>(in @ X1586 @ X1584)))))=>(![X825:$i, X826:$i]:(((in @ X826 @ (setunion @ X825))<=>?[X827:$i]:(((in @ X826 @ X827)&(in @ X827 @ X825)))))=>((in @ emptyset @ omega)=>(![X1583:$i]:(((in @ X1583 @ omega)=>(in @ (setadjoin @ X1583 @ X1583) @ omega)))=>(![X828:$i]:((((in @ emptyset @ X828)&![X829:$i]:((((in @ X829 @ omega)&(in @ X829 @ X828))=>(in @ (setadjoin @ X829 @ X829) @ X828))))=>![X830:$i]:(((in @ X830 @ omega)=>(in @ X830 @ X828)))))=>(![X1577:$i > $i > $o, X1578:$i]:((![X1579:$i]:(((in @ X1579 @ X1578)=>(exu @ (X1577 @ X1579))))=>?[X1580:$i]:(![X1581:$i]:(((in @ X1581 @ X1580)<=>?[X1582:$i]:(((in @ X1582 @ X1578)&(X1577 @ X1582 @ X1581))))))))=>(![X831:$i]:((?[X832:$i]:((in @ X832 @ X831))=>?[X833:$i]:(((in @ X833 @ X831)&~(?[X834:$i]:(((in @ X834 @ X833)&(in @ X834 @ X831))))))))=>((epred1_0)=>(![X1576:$i > $o]:(((exu @ X1576)=>(X1576 @ (descr @ (^[Z0:$i]:(X1576 @ Z0))))))=>(![X854:$i, X855:$i > $o, X856:$i]:(((in @ X856 @ X854)=>((X855 @ X856)=>(in @ X856 @ (dsetconstr @ X854 @ X855)))))=>(![X857:$i, X858:$i > $o, X859:$i]:(((in @ X859 @ (dsetconstr @ X857 @ X858))=>(in @ X859 @ X857)))=>(![X1573:$i, X1574:$i > $o, X1575:$i]:(((in @ X1575 @ (dsetconstr @ X1573 @ X1574))=>(X1574 @ X1575)))=>(![X860:$i > $o]:(((exu @ X860)=>?[X861:$i]:(((X860 @ X861)&![X862:$i]:(((X860 @ X862)=>((X861)=(X862))))))))=>(![X1571:$o, X1572:$i]:(((in @ X1572 @ (prop2set @ ((X1571))))=>(X1571)))=>(![X1569:$i]:(((in @ X1569 @ emptyset)=>![X1570:$o]:((X1570))))=>(![X1568:$i]:(((in @ X1568 @ emptyset)=>~($true)))=>(![X863:$i]:(~(in @ X863 @ emptyset))=>(![X1566:$i > $o]:(((exu @ X1566)=>?[X1567:$i]:((X1566 @ X1567))))=>(![X1562:$i, X1563:$i]:((![X1564:$i]:(((in @ X1564 @ X1562)=>(in @ 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X879)=>(X881))=>(X881))))))=>(![X1554:$i, X1555:$i, X1556:$i]:(((in @ X1556 @ (setadjoin @ X1554 @ X1555))=>(((X1556)=(X1554))|(in @ X1556 @ X1555))))=>(![X882:$i]:(((dsetconstr @ X882 @ (^[Z0:$i]:($true)))=(X882)))=>(![X883:$i, X884:$i]:((![X885:$i]:(((in @ X885 @ X884)=>(in @ X885 @ X883)))=>(in @ X884 @ (powerset @ X883))))=>(![X886:$i]:((in @ emptyset @ (powerset @ X886)))=>(![X1553:$i]:((in @ emptyset @ (powerset @ X1553)))=>(![X1550:$i, X1551:$i, X1552:$i]:(((in @ X1551 @ (powerset @ X1550))=>((in @ X1552 @ X1551)=>(in @ X1552 @ X1550))))=>(![X887:$i, X888:$i, X889:$i]:(((in @ X888 @ X889)=>((in @ X889 @ X887)=>(in @ X888 @ (setunion @ X887)))))=>(![X890:$i, X891:$i]:(((in @ X891 @ (setunion @ X890))=>![X892:$o]:((![X893:$i]:(((in @ X891 @ X893)=>((in @ X893 @ X890)=>(X892))))=>(X892)))))=>(![X894:$i, X895:$i]:(((in @ X895 @ X894)=>(in @ X895 @ (powerset @ (setunion @ X894)))))=>(![X896:$i > $o]:(((exu @ X896)=>?[X897:$i]:(![X898:$i]:(((X896 @ 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X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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subsetRefl]), subsetTrans]), notequalI2]), notequalI1]), binintersectER]), notsubsetI]), binintersectSubset3]), subsetE]), binintersectI]), emptysetsubset]), binunionRsub]), subsetI2]), binunionLsub]), eqimpsubset2]), binunionE]), c_0_250]), binintersectRsub]), c_0_251]), setunion__Cong]), setadjoin__Cong]), emptyset__Cong]), in__Cong]), inCongP]), c_0_252]), c_0_253]), notdexE]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_254]), singletonsswitch]), symdiffE]), eqinunit]), setminusSubset1]), notinsingleton]), setminusIRneg]), uniqinunit]), setminusILneg]), powersetE]), setminusELneg]), emptyInPowerset]), setminusSubset2]), setadjoinOr]), binintersectSubset4]), setadjoinIR]), symdiffIneg2]), emptyinunitempty]), emptyI]), setext]), c_0_255]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_256]), c_0_257]), c_0_258]), omegaSAx]), powersetAx]), emptysetAx]), upairinpowunion]), setextAx]), upairsubunion]), upairset2E]), singletoninpowunion]), kpairiskpair]), setukpairIL]), secondinupair]), ubforcartprodlem2]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), setunionsingleton]), setunionsingleton2]), setunionE2]), cartprodmempair1]), cartprodpairin]), c_0_263]), ksndpairEq]), setukpairinjR]), setukpairinjR2]), setukpairinjR1]), setukpairinjR11]), setukpairinjL2]), theprop]), cartprodpairmemEL]), c_0_264]), c_0_265]), c_0_266]), c_0_267]), c_0_268]), cartprodmempaircEq]), cartprodpairmemER]), c_0_269]), c_0_270]), brelnall2]), c_0_271]), c_0_272]), ap2p]), infuncsetfunc]), c_0_273]), funcGraphProp1]), c_0_274]), ap2apEq2]), subbreln]), funcGraphProp2]), funcGraphProp3]), c_0_275]), powersetT_lem]), binintersectT_lem]), iffalse]), theeq]), ifp]), c_0_276]), c_0_277]), setminusT_lem]), doubleComplementSub2]), contrasubsetT2]), binintersectTERcontra]), binintersectTELcontra]), complementTI1]), powersetTE1]), complementT_lem]), doubleComplementEq]), contrasubsetT]), contrasubsetT1]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), complementTnotintersectT]), complementTE1]), c_0_278]), iftrue]), iftrueorfalse]), binunionT_lem]), setextT]), subsetTI]), powersetTI1]), c_0_279]), funcGraphProp4]), eqbreln]), funcext]), funcext2]), ap2apEq1]), c_0_280]), c_0_281]), funcextLem]), cartprodpairsurjEq]), c_0_282]), c_0_283]), app]), funcinfuncset]), c_0_284]), brelnall1]), cartprodsndpairEq]), setukpairinjL]), setukpairinjR12]), upairequniteq]), c_0_285]), kpairsurjEq]), cartprodsndin]), cartprodfstpairEq]), cartprodfstin]), cartprodmempair]), setunionsingleton1]), c_0_286]), c_0_287]), singletonsuniq]), setukpairinjL1]), kfstpairEq]), ubforcartprodlem3]), symdiffI2]), symdiffIneg1]), setukpairIR]), kpairp]), singletonsubset]), singletoninpowerset]), ubforcartprodlem1]), symdiffI1]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusERneg]), setminusLsub]), disjointsetsI1]), binunionIL]), upairset2IR]), binunionIR]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), inPowerset]), powersetE1]), setadjoinSub2]), setadjoinSub]), c_0_288]), binunionEcases]), c_0_289]), powersetsubset]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), subsetE2]), eqimpsubset1]), subsetI1]), c_0_290]), omega__Cong]), powerset__Cong]), c_0_291]), c_0_292]), c_0_293]), notdallE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), upairsetIR]), upairsetIL]), upairsetE]), nonemptyImpWitness]), c_0_294]), subPowSU]), setunionE]), setunionI]), emptyinPowerset]), powersetI]), c_0_295]), setadjoinE]), setadjoinIL]), nonemptyI1]), c_0_296]), nonemptyE1]), c_0_297]), noeltsimpempty]), notinemptyset]), c_0_298]), c_0_299]), c_0_300]), wellorderingAx]), foundationAx]), omegaIndAx]), omega0Ax]), setunionAx]), setadjoinAx])])]), c_0_301])). 0.65/0.63 thf(c_0_303, negated_conjecture, ![X1591:$i, X1592:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1604:$i, X1605:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1613:$i, X1614:$i > $i > $o, X1615:$i, X1618:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1625:$i, X1626:$i > $o, X1627:$i, X1628:$i > $o, X1629:$i, X1630:$i, X1631:$i > $o, X1632:$i, X1633:$i, X1634:$i > $o, X1635:$i, X1636:$i > $o, X1638:$i, X1639:$o, X1640:$i, X1641:$i, X1642:$o, X1643:$i, X1644:$i, X1645:$i > $o, X1647:$i, X1648:$i, X1651:$i, X1653:$i, X1655:$i, X1656:$i > $o, X1657:$i, X1658:$i, X1660:$i, X1661:$i > $o, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$o, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$o, X1693:$i, X1694:$i, X1695:$i > $o, X1697:$i, X1698:$i, X1699:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i > $o, X1718:$i, X1719:$i > $o, X1720:$i, X1721:$i, X1722:$i > $o, X1723:$i, X1725:$i, X1726:$i > $o, X1728:$i, X1729:$i, X1730:$i > $o, X1732:$i, X1733:$i, X1734:$i > $o, X1735:$i, X1737:$o, X1738:$i, X1739:$i > $o, X1741:$i, X1742:$i, X1743:$i > $o, X1744:$i, X1746:$i > $o, X1747:$i, X1749:$i > $o, X1750:$i, X1753:$i > $o, X1754:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i > $o, X1765:$i, X1766:$i, X1767:$i > $o, X1768:$i > $o, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i > $o, X1780:$i, X1781:$i, X1782:$i > $o, X1783:$i > $o, X1786:$i, X1787:$i, X1788:$i > $o, X1789:$i > $o, X1792:$i, X1793:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i > $o, X1840:$i, X1841:$i > $o, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$o, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$o, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i > $o, X1996:$i, X1997:$i, X1998:$i > $o, X2000:$i, X2001:$i > $o, X2002:$i, X2004:$i, X2005:$i > $o, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i > $i > $o, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i > $i > $o, X2086:$i, X2087:$i, X2088:$i > $i > $o, X2089:$i, X2090:$i, X2091:$i > $i > $o, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i > $i > $o, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i > $i > $o, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i > $i > $o, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i > $i, X2135:$i, X2136:$i, X2137:$i > $i, X2139:$i, X2140:$i, X2141:$i > $i, X2143:$i, X2144:$i, X2145:$i, X2146:$i > $o, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i > $o, X2156:$i, X2157:$i, X2158:$i > $o, X2159:$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, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i > $i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i > $i, X2230:$i, X2231:$i, X2232:$i > $i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$o, X2240:$i, X2241:$i, X2242:$i, X2243:$o, X2244:$i, X2245:$i, X2246:$i, X2247:$o, X2248:$i, X2249:$i, X2250:$i, X2251:$o, X2252:$i, X2253:$i, X2254:$i, X2255:$o, X2256:$i, X2257:$i, X2258:$i, X2259:$o, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$o, X2266:$i, X2267:$i, X2268:$i, X2269:$o, X2270:$i, X2271:$i, X2272:$i, X2273:$o, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2294:$i, X2295:$i, X2296:$i, X2298:$i, X2299:$i, X2300:$i, X2302:$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:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, 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X2289 @ X2290 @ X2291) @ X2290)|((X2290)=(X2291))|(in @ (esk67_3 @ X2289 @ X2290 @ X2291) @ X2289)|~(in @ X2291 @ (powerset @ X2289))|~(in @ X2290 @ (powerset @ X2289)))))&((((in @ (esk68_3 @ X2289 @ X2290 @ X2291) @ X2289)|((X2290)=(X2291))|(in @ (esk67_3 @ X2289 @ X2290 @ X2291) @ X2290)|~(in @ X2291 @ (powerset @ X2289))|~(in @ X2290 @ (powerset @ X2289)))&(((in @ (esk68_3 @ X2289 @ X2290 @ X2291) @ X2291)|((X2290)=(X2291))|(in @ (esk67_3 @ X2289 @ X2290 @ X2291) @ X2290)|~(in @ X2291 @ (powerset @ X2289))|~(in @ X2290 @ (powerset @ X2289)))&(~(in @ (esk68_3 @ X2289 @ X2290 @ X2291) @ X2290)|((X2290)=(X2291))|(in @ (esk67_3 @ X2289 @ X2290 @ X2291) @ X2290)|~(in @ X2291 @ (powerset @ X2289))|~(in @ X2290 @ (powerset @ X2289)))))&(((in @ (esk68_3 @ X2289 @ X2290 @ X2291) @ X2289)|((X2290)=(X2291))|~(in @ (esk67_3 @ X2289 @ X2290 @ X2291) @ X2291)|~(in @ X2291 @ (powerset @ X2289))|~(in @ X2290 @ (powerset @ X2289)))&(((in @ (esk68_3 @ X2289 @ X2290 @ X2291) @ X2291)|((X2290)=(X2291))|~(in @ (esk67_3 @ X2289 @ X2290 @ X2291) @ X2291)|~(in @ X2291 @ (powerset @ X2289))|~(in @ X2290 @ (powerset @ X2289)))&(~(in @ (esk68_3 @ X2289 @ X2290 @ X2291) @ X2290)|((X2290)=(X2291))|~(in @ (esk67_3 @ X2289 @ X2290 @ X2291) @ X2291)|~(in @ X2291 @ (powerset @ X2289))|~(in @ X2290 @ (powerset @ X2289)))))))&((((in @ (esk69_3 @ X2294 @ X2295 @ X2296) @ X2294)|(subset @ X2295 @ X2296)|~(in @ X2296 @ (powerset @ X2294))|~(in @ X2295 @ (powerset @ X2294)))&(((in @ (esk69_3 @ X2294 @ X2295 @ X2296) @ X2295)|(subset @ X2295 @ X2296)|~(in @ X2296 @ (powerset @ X2294))|~(in @ X2295 @ (powerset @ X2294)))&(~(in @ (esk69_3 @ X2294 @ X2295 @ X2296) @ X2296)|(subset @ X2295 @ X2296)|~(in @ X2296 @ (powerset @ X2294))|~(in @ X2295 @ (powerset @ X2294)))))&((((in @ (esk70_3 @ X2298 @ X2299 @ X2300) @ X2298)|(in @ X2299 @ (powerset @ X2300))|~(in @ X2300 @ (powerset @ X2298))|~(in @ X2299 @ (powerset @ X2298)))&(((in @ (esk70_3 @ X2298 @ X2299 @ X2300) @ X2299)|(in @ X2299 @ (powerset @ X2300))|~(in @ X2300 @ (powerset @ X2298))|~(in @ X2299 @ (powerset @ X2298)))&(~(in @ (esk70_3 @ X2298 @ X2299 @ X2300) @ X2300)|(in @ X2299 @ (powerset @ X2300))|~(in @ X2300 @ (powerset @ X2298))|~(in @ X2299 @ (powerset @ X2298)))))&((~(in @ X2303 @ (powerset @ X2302))|(~(in @ X2304 @ (powerset @ X2302))|(~(in @ X2305 @ X2302)|(~(in @ X2303 @ (powerset @ X2304))|(~(in @ X2305 @ X2303)|(in @ X2305 @ X2304))))))&((~(in @ X2307 @ (powerset @ X2306))|(~(in @ X2308 @ X2306)|(~(in @ X2308 @ X2307)|~(in @ X2308 @ (setminus @ X2306 @ X2307)))))&((~(in @ X2310 @ (powerset @ X2309))|(~(in @ X2311 @ X2309)|((in @ X2311 @ (setminus @ X2309 @ X2310))|(in @ X2311 @ X2310))))&((~(in @ X2313 @ (powerset @ X2312))|(~(in @ X2314 @ (powerset @ X2312))|(~(in @ X2315 @ X2312)|((in @ X2315 @ X2313)|~(in @ X2315 @ (binintersect @ X2313 @ X2314))))))&((~(in @ X2317 @ (powerset @ X2316))|(~(in @ X2318 @ (powerset @ X2316))|(~(in @ X2319 @ X2316)|((in @ X2319 @ X2318)|~(in @ X2319 @ (binintersect @ X2317 @ X2318))))))&((~(in @ X2321 @ (powerset @ X2320))|(~(in @ X2322 @ (powerset @ X2320))|(~(in @ X2323 @ X2320)|(~(subset @ X2321 @ (setminus @ X2320 @ X2322))|(~(in @ X2323 @ X2322)|~(in @ X2323 @ X2321))))))&((~(in @ X2325 @ (powerset @ X2324))|(~(in @ X2326 @ (powerset @ X2324))|(~(in @ X2327 @ X2324)|(~(subset @ X2325 @ X2326)|((in @ X2327 @ X2326)|~(in @ X2327 @ X2325))))))&((~(in @ X2329 @ (powerset @ X2328))|(~(in @ X2330 @ (powerset @ X2328))|(~(subset @ X2329 @ X2330)|(subset @ (setminus @ X2328 @ X2330) @ (setminus @ X2328 @ X2329)))))&((~(in @ X2332 @ (powerset @ X2331))|(~(in @ X2333 @ (powerset @ X2331))|(~(subset @ (setminus @ X2331 @ X2333) @ (setminus @ X2331 @ X2332))|(subset @ X2332 @ X2333))))&((~(in @ X2335 @ (powerset @ X2334))|(~(in @ X2336 @ X2334)|(~(in @ X2336 @ X2335)|(in @ X2336 @ (setminus @ X2334 @ (setminus @ X2334 @ X2335))))))&((~(in @ X2338 @ (powerset @ X2337))|(~(in @ X2339 @ X2337)|(~(in @ X2339 @ (setminus @ X2337 @ (setminus @ X2337 @ X2338)))|(in @ X2339 @ X2338))))&((~(in @ X2341 @ (powerset @ X2340))|(subset @ X2341 @ (setminus @ X2340 @ (setminus @ X2340 @ X2341))))&((~(in @ X2343 @ (powerset @ X2342))|(subset @ (setminus @ X2342 @ (setminus @ X2342 @ X2343)) @ X2343))&((~(in @ X2345 @ (powerset @ X2344))|((X2345)=(setminus @ X2344 @ (setminus @ X2344 @ X2345))))&((~(in @ X2347 @ (powerset @ X2346))|(~(in @ X2348 @ (powerset @ X2346))|(~(in @ X2349 @ X2346)|(~(in @ X2349 @ (setminus @ X2346 @ X2347))|~(in @ X2349 @ (binintersect @ X2347 @ X2348))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ esk71_0)&((in @ esk74_0 @ (setminus @ esk71_0 @ esk72_0))&~(in @ esk74_0 @ (setminus @ esk71_0 @ (binintersect @ esk72_0 @ esk73_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_302])])])])])])])). 0.65/0.63 thf(c_0_304, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ (binintersect @ esk72_0 @ esk73_0)))), inference(split_conjunct,[status(thm)],[c_0_303])). 0.65/0.63 thf(c_0_305, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_303])). 0.65/0.63 thf(c_0_306, negated_conjecture, (in @ esk74_0 @ esk71_0), inference(split_conjunct,[status(thm)],[c_0_303])). 0.65/0.63 thf(c_0_307, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_303])). 0.65/0.63 thf(c_0_308, negated_conjecture, (in @ esk74_0 @ (setminus @ esk71_0 @ esk72_0)), inference(split_conjunct,[status(thm)],[c_0_303])). 0.65/0.63 thf(c_0_309, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_303])). 0.65/0.63 thf(c_0_310, negated_conjecture, (in @ esk74_0 @ (binintersect @ esk72_0 @ esk73_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_304, c_0_305]), c_0_306])])). 0.65/0.63 thf(c_0_311, negated_conjecture, ~((in @ esk74_0 @ esk72_0)), inference(spm,[status(thm)],[c_0_307, c_0_308])). 0.65/0.63 thf(c_0_312, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_309, c_0_310]), c_0_311]), ['proof']). 0.65/0.63 % SZS output end CNFRefutation 0.65/0.63 % Parsed axioms : 541 0.65/0.63 % Removed by relevancy pruning/SinE : 292 0.65/0.63 % Initial clauses : 411 0.65/0.63 % Removed in clause preprocessing : 34 0.65/0.63 % Initial clauses in saturation : 377 0.65/0.63 % Processed clauses : 705 0.65/0.63 % ...of these trivial : 48 0.65/0.63 % ...subsumed : 308 0.65/0.63 % ...remaining for further processing : 349 0.65/0.63 % Other redundant clauses eliminated : 29 0.65/0.63 % Clauses deleted for lack of memory : 0 0.65/0.63 % Backward-subsumed : 1 0.65/0.63 % Backward-rewritten : 12 0.65/0.63 % Generated clauses : 2706 0.65/0.63 % ...of the previous two non-redundant : 2335 0.65/0.63 % ...aggressively subsumed : 0 0.65/0.63 % Contextual simplify-reflections : 0 0.65/0.63 % Paramodulations : 2673 0.65/0.63 % Factorizations : 0 0.65/0.63 % NegExts : 0 0.65/0.63 % Equation resolutions : 32 0.65/0.63 % Disequality decompositions : 0 0.65/0.63 % Total rewrite steps : 412 0.65/0.63 % ...of those cached : 317 0.65/0.63 % Propositional unsat checks : 0 0.65/0.63 % Propositional check models : 0 0.65/0.63 % Propositional check unsatisfiable : 0 0.65/0.63 % Propositional clauses : 0 0.65/0.63 % Propositional clauses after purity: 0 0.65/0.63 % Propositional unsat core size : 0 0.65/0.63 % Propositional preprocessing time : 0.000 0.65/0.63 % Propositional encoding time : 0.000 0.65/0.63 % Propositional solver time : 0.000 0.65/0.63 % Success case prop preproc time : 0.000 0.65/0.63 % Success case prop encoding time : 0.000 0.65/0.63 % Success case prop solver time : 0.000 0.65/0.63 % Current number of processed clauses : 326 0.65/0.63 % Positive orientable unit clauses : 78 0.65/0.63 % Positive unorientable unit clauses: 0 0.65/0.63 % Negative unit clauses : 11 0.65/0.63 % Non-unit-clauses : 237 0.65/0.63 % Current number of unprocessed clauses: 1929 0.65/0.63 % ...number of literals in the above : 5258 0.65/0.63 % Current number of archived formulas : 0 0.65/0.63 % Current number of archived clauses : 13 0.65/0.63 % Clause-clause subsumption calls (NU) : 10658 0.65/0.63 % Rec. Clause-clause subsumption calls : 8942 0.65/0.63 % Non-unit clause-clause subsumptions : 272 0.65/0.63 % Unit Clause-clause subsumption calls : 820 0.65/0.63 % Rewrite failures with RHS unbound : 0 0.65/0.63 % BW rewrite match attempts : 24 0.65/0.63 % BW rewrite match successes : 9 0.65/0.63 % Condensation attempts : 0 0.65/0.63 % Condensation successes : 0 0.65/0.63 % Termbank termtop insertions : 88505 0.65/0.63 % Search garbage collected termcells : 24738 0.65/0.63 0.65/0.63 % ------------------------------------------------- 0.65/0.63 % User time : 0.101 s 0.65/0.63 % System time : 0.019 s 0.65/0.63 % Total time : 0.121 s 0.65/0.63 % Maximum resident set size: 10112 pages 0.65/0.63 0.65/0.63 % ------------------------------------------------- 0.65/0.63 % User time : 0.115 s 0.65/0.63 % System time : 0.029 s 0.65/0.63 % Total time : 0.144 s 0.65/0.63 % Maximum resident set size: 5120 pages 0.65/0.63 % E exiting 0.65/0.64 EOF