0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.11 % Command : run_E %s %d THM 0.11/0.32 % Computer : n024.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 1440 0.11/0.32 % WCLimit : 180 0.11/0.32 % DateTime : Thu Jul 4 07:38:08 EDT 2024 0.11/0.32 % CPUTime : 0.18/0.47 Running higher-order theorem proving 0.36/0.54 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.Y1hbpNh5zn/E---3.1_11410.p 0.37/0.89 # Version: 3.2.0-ho 0.37/0.89 # Preprocessing class: HSLMSLSSLLLCHFA. 0.37/0.89 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.37/0.89 # Starting ehoh_best5 with 180s (1) cores 0.37/0.89 # Starting almost_fo_3_lam with 180s (1) cores 0.37/0.89 # Starting new_bool_5 with 180s (1) cores 0.37/0.89 # Starting pre_casc_3 with 180s (1) cores 0.37/0.89 # Starting ho_unfolding_8 with 180s (1) cores 0.37/0.89 # Starting new_ho_10_cnf2 with 180s (1) cores 0.37/0.89 # Starting new_bool_3 with 180s (1) cores 0.37/0.89 # Starting new_ho_5 with 180s (1) cores 0.37/0.89 # new_bool_3 with pid 11570 completed with status 0 0.37/0.89 # Result found by new_bool_3 0.37/0.89 # Preprocessing class: HSLMSLSSLLLCHFA. 0.37/0.89 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.37/0.89 # Starting ehoh_best5 with 180s (1) cores 0.37/0.89 # Starting almost_fo_3_lam with 180s (1) cores 0.37/0.89 # Starting new_bool_5 with 180s (1) cores 0.37/0.89 # Starting pre_casc_3 with 180s (1) cores 0.37/0.89 # Starting ho_unfolding_8 with 180s (1) cores 0.37/0.89 # Starting new_ho_10_cnf2 with 180s (1) cores 0.37/0.89 # Starting new_bool_3 with 180s (1) cores 0.37/0.89 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.37/0.89 # Search class: HGHSM-FSLM32-MHFMMSBN 0.37/0.89 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 0.37/0.89 # Starting ho_unfolding_8 with 37s (1) cores 0.37/0.89 # ho_unfolding_8 with pid 11626 completed with status 0 0.37/0.89 # Result found by ho_unfolding_8 0.37/0.89 # Preprocessing class: HSLMSLSSLLLCHFA. 0.37/0.89 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.37/0.89 # Starting ehoh_best5 with 180s (1) cores 0.37/0.89 # Starting almost_fo_3_lam with 180s (1) cores 0.37/0.89 # Starting new_bool_5 with 180s (1) cores 0.37/0.89 # Starting pre_casc_3 with 180s (1) cores 0.37/0.89 # Starting ho_unfolding_8 with 180s (1) cores 0.37/0.89 # Starting new_ho_10_cnf2 with 180s (1) cores 0.37/0.89 # Starting new_bool_3 with 180s (1) cores 0.37/0.89 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.37/0.89 # Search class: HGHSM-FSLM32-MHFMMSBN 0.37/0.89 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 0.37/0.89 # Starting ho_unfolding_8 with 37s (1) cores 0.37/0.89 # Preprocessing time : 0.070 s 0.37/0.89 # Presaturation interreduction done 0.37/0.89 0.37/0.89 # Proof found! 0.37/0.89 # SZS status Theorem 0.37/0.89 # SZS output start CNFRefutation 0.37/0.89 thf(decl_22, type, in: $i > $i > $o). 0.37/0.89 thf(decl_23, type, exu: ($i > $o) > $o). 0.37/0.89 thf(decl_24, type, setextAx: $o). 0.37/0.89 thf(decl_25, type, emptyset: $i). 0.37/0.89 thf(decl_26, type, emptysetAx: $o). 0.37/0.89 thf(decl_27, type, setadjoin: $i > $i > $i). 0.37/0.89 thf(decl_28, type, setadjoinAx: $o). 0.37/0.89 thf(decl_29, type, powerset: $i > $i). 0.37/0.89 thf(decl_30, type, powersetAx: $o). 0.37/0.89 thf(decl_31, type, setunion: $i > $i). 0.37/0.89 thf(decl_32, type, setunionAx: $o). 0.37/0.89 thf(decl_33, type, omega: $i). 0.37/0.89 thf(decl_34, type, omega0Ax: $o). 0.37/0.89 thf(decl_35, type, omegaSAx: $o). 0.37/0.89 thf(decl_36, type, omegaIndAx: $o). 0.37/0.89 thf(decl_37, type, replAx: $o). 0.37/0.89 thf(decl_38, type, foundationAx: $o). 0.37/0.89 thf(decl_39, type, wellorderingAx: $o). 0.37/0.89 thf(decl_40, type, descr: ($i > $o) > $i). 0.37/0.89 thf(decl_41, type, descrp: $o). 0.37/0.89 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_43, type, dsetconstrI: $o). 0.37/0.89 thf(decl_44, type, dsetconstrEL: $o). 0.37/0.89 thf(decl_45, type, dsetconstrER: $o). 0.37/0.89 thf(decl_46, type, exuE1: $o). 0.37/0.89 thf(decl_47, type, prop2set: $o > $i). 0.37/0.89 thf(decl_48, type, prop2setE: $o). 0.37/0.89 thf(decl_49, type, emptysetE: $o). 0.37/0.89 thf(decl_50, type, emptysetimpfalse: $o). 0.37/0.89 thf(decl_51, type, notinemptyset: $o). 0.37/0.89 thf(decl_52, type, exuE3e: $o). 0.37/0.89 thf(decl_53, type, setext: $o). 0.37/0.89 thf(decl_54, type, emptyI: $o). 0.37/0.89 thf(decl_55, type, noeltsimpempty: $o). 0.37/0.89 thf(decl_56, type, setbeta: $o). 0.37/0.89 thf(decl_57, type, nonempty: $i > $o). 0.37/0.89 thf(decl_58, type, nonemptyE1: $o). 0.37/0.89 thf(decl_59, type, nonemptyI: $o). 0.37/0.89 thf(decl_60, type, nonemptyI1: $o). 0.37/0.89 thf(decl_61, type, setadjoinIL: $o). 0.37/0.89 thf(decl_62, type, emptyinunitempty: $o). 0.37/0.89 thf(decl_63, type, setadjoinIR: $o). 0.37/0.89 thf(decl_64, type, setadjoinE: $o). 0.37/0.89 thf(decl_65, type, setadjoinOr: $o). 0.37/0.89 thf(decl_66, type, setoftrueEq: $o). 0.37/0.89 thf(decl_67, type, powersetI: $o). 0.37/0.89 thf(decl_68, type, emptyinPowerset: $o). 0.37/0.89 thf(decl_69, type, emptyInPowerset: $o). 0.37/0.89 thf(decl_70, type, powersetE: $o). 0.37/0.89 thf(decl_71, type, setunionI: $o). 0.37/0.89 thf(decl_72, type, setunionE: $o). 0.37/0.89 thf(decl_73, type, subPowSU: $o). 0.37/0.89 thf(decl_74, type, exuE2: $o). 0.37/0.89 thf(decl_75, type, nonemptyImpWitness: $o). 0.37/0.89 thf(decl_76, type, uniqinunit: $o). 0.37/0.89 thf(decl_77, type, notinsingleton: $o). 0.37/0.89 thf(decl_78, type, eqinunit: $o). 0.37/0.89 thf(decl_79, type, singletonsswitch: $o). 0.37/0.89 thf(decl_80, type, upairsetE: $o). 0.37/0.89 thf(decl_81, type, upairsetIL: $o). 0.37/0.89 thf(decl_82, type, upairsetIR: $o). 0.37/0.89 thf(decl_83, type, emptyE1: $o). 0.37/0.89 thf(decl_84, type, vacuousDall: $o). 0.37/0.89 thf(decl_85, type, quantDeMorgan1: $o). 0.37/0.89 thf(decl_86, type, quantDeMorgan2: $o). 0.37/0.89 thf(decl_87, type, quantDeMorgan3: $o). 0.37/0.89 thf(decl_88, type, quantDeMorgan4: $o). 0.37/0.89 thf(decl_89, type, prop2setI: $o). 0.37/0.89 thf(decl_91, type, prop2set2propI: $o). 0.37/0.89 thf(decl_92, type, notdexE: $o). 0.37/0.89 thf(decl_93, type, notdallE: $o). 0.37/0.89 thf(decl_94, type, exuI1: $o). 0.37/0.89 thf(decl_95, type, exuI3: $o). 0.37/0.89 thf(decl_96, type, exuI2: $o). 0.37/0.89 thf(decl_97, type, inCongP: $o). 0.37/0.89 thf(decl_98, type, in__Cong: $o). 0.37/0.89 thf(decl_99, type, exuE3u: $o). 0.37/0.89 thf(decl_100, type, exu__Cong: $o). 0.37/0.89 thf(decl_101, type, emptyset__Cong: $o). 0.37/0.89 thf(decl_102, type, setadjoin__Cong: $o). 0.37/0.89 thf(decl_103, type, powerset__Cong: $o). 0.37/0.89 thf(decl_104, type, setunion__Cong: $o). 0.37/0.89 thf(decl_105, type, omega__Cong: $o). 0.37/0.89 thf(decl_106, type, exuEu: $o). 0.37/0.89 thf(decl_107, type, descr__Cong: $o). 0.37/0.89 thf(decl_108, type, dsetconstr__Cong: $o). 0.37/0.89 thf(decl_109, type, subset: $i > $i > $o). 0.37/0.89 thf(decl_112, type, subsetI1: $o). 0.37/0.89 thf(decl_113, type, eqimpsubset2: $o). 0.37/0.89 thf(decl_114, type, eqimpsubset1: $o). 0.37/0.89 thf(decl_115, type, subsetI2: $o). 0.37/0.89 thf(decl_116, type, emptysetsubset: $o). 0.37/0.89 thf(decl_117, type, subsetE: $o). 0.37/0.89 thf(decl_118, type, subsetE2: $o). 0.37/0.89 thf(decl_119, type, notsubsetI: $o). 0.37/0.89 thf(decl_120, type, notequalI1: $o). 0.37/0.89 thf(decl_121, type, notequalI2: $o). 0.37/0.89 thf(decl_122, type, subsetRefl: $o). 0.37/0.89 thf(decl_123, type, subsetTrans: $o). 0.37/0.89 thf(decl_124, type, setadjoinSub: $o). 0.37/0.89 thf(decl_125, type, setadjoinSub2: $o). 0.37/0.89 thf(decl_126, type, subset2powerset: $o). 0.37/0.89 thf(decl_127, type, setextsub: $o). 0.37/0.89 thf(decl_128, type, subsetemptysetimpeq: $o). 0.37/0.89 thf(decl_129, type, powersetI1: $o). 0.37/0.89 thf(decl_130, type, powersetE1: $o). 0.37/0.89 thf(decl_131, type, inPowerset: $o). 0.37/0.89 thf(decl_132, type, powersetsubset: $o). 0.37/0.89 thf(decl_133, type, sepInPowerset: $o). 0.37/0.89 thf(decl_134, type, sepSubset: $o). 0.37/0.89 thf(decl_135, type, binunion: $i > $i > $i). 0.37/0.89 thf(decl_136, type, binunionIL: $o). 0.37/0.89 thf(decl_137, type, upairset2IR: $o). 0.37/0.89 thf(decl_138, type, binunionIR: $o). 0.37/0.89 thf(decl_139, type, binunionEcases: $o). 0.37/0.89 thf(decl_140, type, binunionE: $o). 0.37/0.89 thf(decl_141, type, binunionLsub: $o). 0.37/0.89 thf(decl_142, type, binunionRsub: $o). 0.37/0.89 thf(decl_143, type, binintersect: $i > $i > $i). 0.37/0.89 thf(decl_144, type, binintersectI: $o). 0.37/0.89 thf(decl_145, type, binintersectSubset5: $o). 0.37/0.89 thf(decl_146, type, binintersectEL: $o). 0.37/0.89 thf(decl_147, type, binintersectLsub: $o). 0.37/0.89 thf(decl_148, type, binintersectSubset2: $o). 0.37/0.89 thf(decl_149, type, binintersectSubset3: $o). 0.37/0.89 thf(decl_150, type, binintersectER: $o). 0.37/0.89 thf(decl_151, type, disjointsetsI1: $o). 0.37/0.89 thf(decl_152, type, binintersectRsub: $o). 0.37/0.89 thf(decl_153, type, binintersectSubset4: $o). 0.37/0.89 thf(decl_154, type, binintersectSubset1: $o). 0.37/0.89 thf(decl_155, type, bs114d: $o). 0.37/0.89 thf(decl_157, type, setminus: $i > $i > $i). 0.37/0.89 thf(decl_158, type, setminusI: $o). 0.37/0.89 thf(decl_159, type, setminusEL: $o). 0.37/0.89 thf(decl_160, type, setminusER: $o). 0.37/0.89 thf(decl_161, type, setminusSubset2: $o). 0.37/0.89 thf(decl_162, type, setminusERneg: $o). 0.37/0.89 thf(decl_163, type, setminusELneg: $o). 0.37/0.89 thf(decl_164, type, setminusILneg: $o). 0.37/0.89 thf(decl_165, type, setminusIRneg: $o). 0.37/0.89 thf(decl_166, type, setminusLsub: $o). 0.37/0.89 thf(decl_167, type, setminusSubset1: $o). 0.37/0.89 thf(decl_168, type, symdiff: $i > $i > $i). 0.37/0.89 thf(decl_169, type, symdiffE: $o). 0.37/0.89 thf(decl_170, type, symdiffI1: $o). 0.37/0.89 thf(decl_171, type, symdiffI2: $o). 0.37/0.89 thf(decl_172, type, symdiffIneg1: $o). 0.37/0.89 thf(decl_173, type, symdiffIneg2: $o). 0.37/0.89 thf(decl_174, type, iskpair: $i > $o). 0.37/0.89 thf(decl_175, type, secondinupair: $o). 0.37/0.89 thf(decl_176, type, setukpairIL: $o). 0.37/0.89 thf(decl_177, type, setukpairIR: $o). 0.37/0.89 thf(decl_178, type, kpairiskpair: $o). 0.37/0.89 thf(decl_179, type, kpair: $i > $i > $i). 0.37/0.89 thf(decl_180, type, kpairp: $o). 0.37/0.89 thf(decl_181, type, cartprod: $i > $i > $i). 0.37/0.89 thf(decl_182, type, singletonsubset: $o). 0.37/0.89 thf(decl_183, type, singletoninpowerset: $o). 0.37/0.89 thf(decl_184, type, singletoninpowunion: $o). 0.37/0.89 thf(decl_185, type, upairset2E: $o). 0.37/0.89 thf(decl_186, type, upairsubunion: $o). 0.37/0.89 thf(decl_187, type, upairinpowunion: $o). 0.37/0.89 thf(decl_188, type, ubforcartprodlem1: $o). 0.37/0.89 thf(decl_189, type, ubforcartprodlem2: $o). 0.37/0.89 thf(decl_190, type, ubforcartprodlem3: $o). 0.37/0.89 thf(decl_191, type, cartprodpairin: $o). 0.37/0.89 thf(decl_192, type, cartprodmempair1: $o). 0.37/0.89 thf(decl_193, type, cartprodmempair: $o). 0.37/0.89 thf(decl_194, type, setunionE2: $o). 0.37/0.89 thf(decl_195, type, setunionsingleton1: $o). 0.37/0.89 thf(decl_196, type, setunionsingleton2: $o). 0.37/0.89 thf(decl_197, type, setunionsingleton: $o). 0.37/0.89 thf(decl_198, type, singleton: $i > $o). 0.37/0.89 thf(decl_199, type, singletonprop: $o). 0.37/0.89 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 0.37/0.89 thf(decl_201, type, ex1E1: $o). 0.37/0.89 thf(decl_202, type, ex1I: $o). 0.37/0.89 thf(decl_203, type, ex1I2: $o). 0.37/0.89 thf(decl_204, type, singletonsuniq: $o). 0.37/0.89 thf(decl_209, type, setukpairinjL1: $o). 0.37/0.89 thf(decl_210, type, kfstsingleton: $o). 0.37/0.89 thf(decl_211, type, theprop: $o). 0.37/0.89 thf(decl_212, type, kfst: $i > $i). 0.37/0.89 thf(decl_213, type, kfstpairEq: $o). 0.37/0.89 thf(decl_214, type, cartprodfstin: $o). 0.37/0.89 thf(decl_215, type, setukpairinjL2: $o). 0.37/0.89 thf(decl_216, type, setukpairinjL: $o). 0.37/0.89 thf(decl_217, type, setukpairinjR11: $o). 0.37/0.89 thf(decl_218, type, setukpairinjR12: $o). 0.37/0.89 thf(decl_219, type, setukpairinjR1: $o). 0.37/0.89 thf(decl_220, type, upairequniteq: $o). 0.37/0.89 thf(decl_221, type, setukpairinjR2: $o). 0.37/0.89 thf(decl_222, type, setukpairinjR: $o). 0.37/0.89 thf(decl_223, type, ksndsingleton: $o). 0.37/0.89 thf(decl_224, type, ksnd: $i > $i). 0.37/0.89 thf(decl_225, type, ksndpairEq: $o). 0.37/0.89 thf(decl_226, type, kpairsurjEq: $o). 0.37/0.89 thf(decl_227, type, cartprodsndin: $o). 0.37/0.89 thf(decl_228, type, cartprodpairmemEL: $o). 0.37/0.89 thf(decl_229, type, cartprodpairmemER: $o). 0.37/0.89 thf(decl_230, type, cartprodmempaircEq: $o). 0.37/0.89 thf(decl_231, type, cartprodfstpairEq: $o). 0.37/0.89 thf(decl_232, type, cartprodsndpairEq: $o). 0.37/0.89 thf(decl_233, type, cartprodpairsurjEq: $o). 0.37/0.89 thf(decl_234, type, breln: $i > $i > $i > $o). 0.37/0.89 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.37/0.89 thf(decl_236, type, dpsetconstrI: $o). 0.37/0.89 thf(decl_237, type, dpsetconstrSub: $o). 0.37/0.89 thf(decl_238, type, setOfPairsIsBReln: $o). 0.37/0.89 thf(decl_239, type, dpsetconstrERa: $o). 0.37/0.89 thf(decl_240, type, dpsetconstrEL1: $o). 0.37/0.89 thf(decl_241, type, dpsetconstrEL2: $o). 0.37/0.89 thf(decl_242, type, dpsetconstrER: $o). 0.37/0.89 thf(decl_243, type, func: $i > $i > $i > $o). 0.37/0.89 thf(decl_244, type, funcSet: $i > $i > $i). 0.37/0.89 thf(decl_245, type, funcImageSingleton: $o). 0.37/0.89 thf(decl_246, type, apProp: $o). 0.37/0.89 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 0.37/0.89 thf(decl_248, type, app: $o). 0.37/0.89 thf(decl_249, type, infuncsetfunc: $o). 0.37/0.89 thf(decl_250, type, ap2p: $o). 0.37/0.89 thf(decl_251, type, funcinfuncset: $o). 0.37/0.89 thf(decl_252, type, lamProp: $o). 0.37/0.89 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 0.37/0.89 thf(decl_254, type, lamp: $o). 0.37/0.89 thf(decl_255, type, lam2p: $o). 0.37/0.89 thf(decl_256, type, brelnall1: $o). 0.37/0.89 thf(decl_257, type, brelnall2: $o). 0.37/0.89 thf(decl_258, type, ex1E2: $o). 0.37/0.89 thf(decl_259, type, funcGraphProp1: $o). 0.37/0.89 thf(decl_260, type, funcGraphProp3: $o). 0.37/0.89 thf(decl_261, type, funcGraphProp2: $o). 0.37/0.89 thf(decl_262, type, funcextLem: $o). 0.37/0.89 thf(decl_263, type, funcGraphProp4: $o). 0.37/0.89 thf(decl_264, type, subbreln: $o). 0.37/0.89 thf(decl_265, type, eqbreln: $o). 0.37/0.89 thf(decl_266, type, funcext: $o). 0.37/0.89 thf(decl_267, type, funcext2: $o). 0.37/0.89 thf(decl_268, type, ap2apEq1: $o). 0.37/0.89 thf(decl_269, type, ap2apEq2: $o). 0.37/0.89 thf(decl_270, type, beta1: $o). 0.37/0.89 thf(decl_271, type, eta1: $o). 0.37/0.89 thf(decl_272, type, lam2lamEq: $o). 0.37/0.89 thf(decl_273, type, beta2: $o). 0.37/0.89 thf(decl_274, type, eta2: $o). 0.37/0.89 thf(decl_275, type, iffalseProp1: $o). 0.37/0.89 thf(decl_276, type, iffalseProp2: $o). 0.37/0.89 thf(decl_277, type, iftrueProp1: $o). 0.37/0.89 thf(decl_278, type, iftrueProp2: $o). 0.37/0.89 thf(decl_279, type, ifSingleton: $o). 0.37/0.89 thf(decl_280, type, if: $i > $o > $i > $i > $i). 0.37/0.89 thf(decl_281, type, ifp: $o). 0.37/0.89 thf(decl_282, type, theeq: $o). 0.37/0.89 thf(decl_283, type, iftrue: $o). 0.37/0.89 thf(decl_284, type, iffalse: $o). 0.37/0.89 thf(decl_285, type, iftrueorfalse: $o). 0.37/0.89 thf(decl_286, type, binintersectT_lem: $o). 0.37/0.89 thf(decl_287, type, binunionT_lem: $o). 0.37/0.89 thf(decl_288, type, powersetT_lem: $o). 0.37/0.89 thf(decl_289, type, setminusT_lem: $o). 0.37/0.89 thf(decl_290, type, complementT_lem: $o). 0.37/0.89 thf(decl_291, type, setextT: $o). 0.37/0.89 thf(decl_292, type, subsetTI: $o). 0.37/0.89 thf(decl_293, type, powersetTI1: $o). 0.37/0.89 thf(decl_294, type, powersetTE1: $o). 0.37/0.89 thf(decl_295, type, complementTI1: $o). 0.37/0.89 thf(decl_296, type, complementTE1: $o). 0.37/0.89 thf(decl_297, type, binintersectTELcontra: $o). 0.37/0.89 thf(decl_298, type, binintersectTERcontra: $o). 0.37/0.89 thf(decl_299, type, contrasubsetT: $o). 0.37/0.89 thf(decl_300, type, contrasubsetT1: $o). 0.37/0.89 thf(decl_301, type, contrasubsetT2: $o). 0.37/0.89 thf(decl_302, type, contrasubsetT3: $o). 0.37/0.89 thf(decl_303, type, doubleComplementI1: $o). 0.37/0.89 thf(decl_304, type, doubleComplementE1: $o). 0.37/0.89 thf(decl_305, type, doubleComplementSub1: $o). 0.37/0.89 thf(decl_306, type, doubleComplementSub2: $o). 0.37/0.89 thf(decl_307, type, doubleComplementEq: $o). 0.37/0.89 thf(decl_308, type, complementTnotintersectT: $o). 0.37/0.89 thf(decl_309, type, complementImpComplementIntersect: $o). 0.37/0.89 thf(decl_310, type, complementSubsetComplementIntersect: $o). 0.37/0.89 thf(decl_311, type, complementInPowersetComplementIntersect: $o). 0.37/0.89 thf(decl_312, type, contraSubsetComplement: $o). 0.37/0.89 thf(decl_313, type, complementTcontraSubset: $o). 0.37/0.89 thf(decl_314, type, binunionTILcontra: $o). 0.37/0.89 thf(decl_315, type, binunionTIRcontra: $o). 0.37/0.89 thf(decl_316, type, inIntersectImpInUnion: $o). 0.37/0.89 thf(decl_317, type, inIntersectImpInUnion2: $o). 0.37/0.89 thf(decl_318, type, inIntersectImpInIntersectUnions: $o). 0.37/0.89 thf(decl_319, type, intersectInPowersetIntersectUnions: $o). 0.37/0.89 thf(decl_320, type, inComplementUnionImpNotIn1: $o). 0.37/0.89 thf(decl_321, type, inComplementUnionImpInComplement1: $o). 0.37/0.89 thf(decl_322, type, binunionTE: $o). 0.37/0.89 thf(decl_323, type, binunionTEcontra: $o). 0.37/0.89 thf(decl_324, type, demorgan2a1: $o). 0.37/0.89 thf(decl_325, type, complementUnionInPowersetComplement: $o). 0.37/0.89 thf(decl_326, type, demorgan2a2: $o). 0.37/0.89 thf(decl_327, type, demorgan1a: $o). 0.37/0.89 thf(decl_328, type, demorgan1b: $o). 0.37/0.89 thf(decl_329, type, demorgan1: $o). 0.37/0.89 thf(decl_330, type, demorgan2a: $o). 0.37/0.89 thf(decl_331, type, demorgan2b2: $o). 0.37/0.89 thf(decl_332, type, demorgan2b: $o). 0.37/0.89 thf(decl_333, type, demorgan2: $o). 0.37/0.89 thf(decl_334, type, woz13rule0: $o). 0.37/0.89 thf(decl_335, type, woz13rule1: $o). 0.37/0.89 thf(decl_336, type, woz13rule2: $o). 0.37/0.89 thf(decl_337, type, woz13rule3: $o). 0.37/0.89 thf(decl_338, type, woz13rule4: $o). 0.37/0.89 thf(decl_339, type, woz1_1: $o). 0.37/0.89 thf(decl_340, type, woz1_2: $o). 0.37/0.89 thf(decl_341, type, woz1_3: $o). 0.37/0.89 thf(decl_342, type, woz1_4: $o). 0.37/0.89 thf(decl_343, type, woz1_5: $o). 0.37/0.89 thf(decl_344, type, breln1: $i > $i > $o). 0.37/0.89 thf(decl_345, type, breln1all2: $o). 0.37/0.89 thf(decl_346, type, breln1Set: $i > $i). 0.37/0.89 thf(decl_347, type, breln1SetBreln1: $o). 0.37/0.89 thf(decl_354, type, choice2fnsingleton: $o). 0.37/0.89 thf(decl_355, type, setOfPairsIsBReln1: $o). 0.37/0.89 thf(decl_356, type, breln1all1: $o). 0.37/0.89 thf(decl_357, type, subbreln1: $o). 0.37/0.89 thf(decl_358, type, eqbreln1: $o). 0.37/0.89 thf(decl_359, type, breln1invset: $i > $i > $i). 0.37/0.89 thf(decl_360, type, breln1invprop: $o). 0.37/0.89 thf(decl_361, type, breln1invI: $o). 0.37/0.89 thf(decl_362, type, epred1_0: $o). 0.37/0.89 thf(decl_363, type, esk1_2: $i > $i > $i). 0.37/0.89 thf(decl_364, type, esk2_2: $i > $i > $i). 0.37/0.89 thf(decl_365, type, esk3_2: $i > $i > $i). 0.37/0.89 thf(decl_366, type, esk4_1: $i > $i). 0.37/0.89 thf(decl_367, type, esk5_2: ($i > $i > $o) > $i > $i). 0.37/0.89 thf(decl_368, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.37/0.89 thf(decl_369, type, esk7_2: ($i > $i > $o) > $i > $i). 0.37/0.89 thf(decl_370, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.37/0.89 thf(decl_371, type, esk9_1: $i > $i). 0.37/0.89 thf(decl_372, type, esk10_2: ($i > $o) > $i > $i). 0.37/0.89 thf(decl_373, type, esk11_2: ($i > $o) > $i > $i). 0.37/0.89 thf(decl_374, type, esk12_1: ($i > $o) > $i). 0.37/0.89 thf(decl_375, type, esk13_2: ($i > $o) > $i > $i). 0.37/0.89 thf(decl_376, type, esk14_1: ($i > $o) > $i). 0.37/0.89 thf(decl_377, type, esk15_2: $i > $i > $i). 0.37/0.89 thf(decl_378, type, esk16_2: $i > $i > $i). 0.37/0.89 thf(decl_379, type, esk17_1: $i > $i). 0.37/0.89 thf(decl_380, type, esk18_1: $i > $i). 0.37/0.89 thf(decl_381, type, esk19_1: $i > $i). 0.37/0.89 thf(decl_382, type, esk20_2: $i > $i > $i). 0.37/0.89 thf(decl_383, type, esk21_3: $i > $i > $o > $i). 0.37/0.89 thf(decl_384, type, esk22_2: ($i > $o) > $i > $i). 0.37/0.89 thf(decl_385, type, esk23_1: ($i > $o) > $i). 0.37/0.89 thf(decl_386, type, esk24_1: $i > $i). 0.37/0.89 thf(decl_387, type, esk25_2: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_388, type, esk26_2: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_389, type, esk27_2: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_390, type, esk28_2: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_391, type, esk29_2: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_392, type, esk30_2: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_393, type, esk31_2: ($i > $o) > $i > $i). 0.37/0.89 thf(decl_394, type, esk32_1: ($i > $o) > $i). 0.37/0.89 thf(decl_395, type, esk33_1: ($i > $o) > $i). 0.37/0.89 thf(decl_396, type, esk34_1: ($i > $o) > $i). 0.37/0.89 thf(decl_397, type, esk35_1: ($i > $o) > $i). 0.37/0.89 thf(decl_398, type, esk36_2: ($i > $o) > $i > $i). 0.37/0.89 thf(decl_399, type, esk37_1: ($i > $o) > $i). 0.37/0.89 thf(decl_400, type, esk38_2: ($i > $o) > $i > $i). 0.37/0.89 thf(decl_401, type, esk39_2: ($i > $o) > ($i > $o) > $i). 0.37/0.89 thf(decl_402, type, esk40_2: ($i > $o) > ($i > $o) > $i). 0.37/0.89 thf(decl_403, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 0.37/0.89 thf(decl_404, type, esk42_2: ($i > $o) > ($i > $o) > $i). 0.37/0.89 thf(decl_405, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 0.37/0.89 thf(decl_406, type, esk44_2: ($i > $o) > ($i > $o) > $i). 0.37/0.89 thf(decl_407, type, esk45_2: ($i > $o) > $i > $i). 0.37/0.89 thf(decl_408, type, esk46_2: ($i > $o) > ($i > $o) > $i). 0.37/0.89 thf(decl_409, type, esk47_2: ($i > $o) > ($i > $o) > $i). 0.37/0.89 thf(decl_410, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 0.37/0.89 thf(decl_411, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 0.37/0.89 thf(decl_412, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.37/0.89 thf(decl_413, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.37/0.89 thf(decl_414, type, esk52_2: $i > $i > $i). 0.37/0.89 thf(decl_415, type, esk53_2: $i > $i > $i). 0.37/0.89 thf(decl_416, type, esk54_2: $i > $i > $i). 0.37/0.89 thf(decl_417, type, esk55_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_418, type, esk56_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_419, type, esk57_2: $i > $i > $i). 0.37/0.89 thf(decl_420, type, esk58_2: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_421, type, esk59_2: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_422, type, esk60_2: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_423, type, esk61_3: $i > ($i > $o) > $i > $i). 0.37/0.89 thf(decl_424, type, esk62_2: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_425, type, esk63_2: $i > ($i > $o) > $i). 0.37/0.89 thf(decl_426, type, esk64_3: $i > $i > ($i > $i) > $i). 0.37/0.89 thf(decl_427, type, esk65_3: $i > $i > ($i > $i) > $i). 0.37/0.89 thf(decl_428, type, esk66_3: $i > $i > ($i > $i) > $i). 0.37/0.89 thf(decl_429, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 0.37/0.89 thf(decl_430, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 0.37/0.89 thf(decl_431, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 0.37/0.89 thf(decl_432, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 0.37/0.89 thf(decl_433, type, esk71_4: $i > $i > $i > $i > $i). 0.37/0.89 thf(decl_434, type, esk72_4: $i > $i > $i > $i > $i). 0.37/0.89 thf(decl_435, type, esk73_4: $i > $i > $i > $i > $i). 0.37/0.89 thf(decl_436, type, esk74_4: $i > $i > $i > $i > $i). 0.37/0.89 thf(decl_437, type, esk75_4: $i > $i > $i > $i > $i). 0.37/0.89 thf(decl_438, type, esk76_4: $i > $i > $i > $i > $i). 0.37/0.89 thf(decl_439, type, esk77_4: $i > $i > $i > $i > $i). 0.37/0.89 thf(decl_440, type, esk78_4: $i > $i > $i > $i > $i). 0.37/0.89 thf(decl_441, type, esk79_4: $i > $i > $i > $i > $i). 0.37/0.89 thf(decl_442, type, esk80_3: $i > $i > ($i > $i) > $i). 0.37/0.89 thf(decl_443, type, esk81_3: $i > $i > ($i > $i) > $i). 0.37/0.89 thf(decl_444, type, esk82_3: $i > $i > ($i > $i) > $i). 0.37/0.89 thf(decl_445, type, esk83_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_446, type, esk84_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_447, type, esk85_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_448, type, esk86_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_449, type, esk87_3: $i > $i > ($i > $o) > $i). 0.37/0.89 thf(decl_450, type, esk88_3: $i > $i > ($i > $o) > $i). 0.37/0.89 thf(decl_451, type, esk89_3: $i > $i > ($i > $o) > $i). 0.37/0.89 thf(decl_452, type, esk90_3: $i > $i > ($i > $o) > $i). 0.37/0.89 thf(decl_453, type, esk91_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_454, type, esk92_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_455, type, esk93_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_456, type, esk94_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_457, type, esk95_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_458, type, esk96_3: $i > $i > $i > $i). 0.37/0.89 thf(decl_459, type, esk97_0: $i). 0.37/0.89 thf(decl_460, type, esk98_0: $i). 0.37/0.89 thf(decl_461, type, esk99_0: $i). 0.37/0.89 thf(decl_462, type, esk100_0: $i). 0.37/0.89 thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', breln1)). 0.37/0.89 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', breln)). 0.37/0.89 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', descr__Cong)). 0.37/0.89 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', exu)). 0.37/0.89 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', exuEu)). 0.37/0.89 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', exu__Cong)). 0.37/0.89 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', exuI3)). 0.37/0.89 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', exuI1)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', exuE2)). 0.37/0.89 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', nonempty)). 0.37/0.89 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', exuE3e)). 0.37/0.89 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', replAx)). 0.37/0.89 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setOfPairsIsBReln)). 0.37/0.89 thf(breln1invset, axiom, ((breln1invset)=(^[X4:$i, X33:$i]:(dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((in @ (kpair @ X3 @ X2) @ X33)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', breln1invset)). 0.37/0.89 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setOfPairsIsBReln1)). 0.37/0.89 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', exuE3u)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', exuI2)). 0.37/0.89 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', nonemptyI)). 0.37/0.89 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', exuE1)). 0.37/0.89 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', descrp)). 0.37/0.89 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', ex1E1)). 0.37/0.89 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', ex1I)). 0.37/0.89 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', ex1I2)). 0.37/0.89 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', dsetconstr__Cong)). 0.37/0.89 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', kfstsingleton)). 0.37/0.89 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setoftrueEq)). 0.37/0.89 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', nonemptyI1)). 0.37/0.89 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', nonemptyE1)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', ksndsingleton)). 0.37/0.89 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', dsetconstrEL)). 0.37/0.89 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', dsetconstrI)). 0.37/0.89 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', dpsetconstrEL1)). 0.37/0.89 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', dpsetconstrER)). 0.37/0.89 thf(apProp, axiom, ((apProp)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', apProp)). 0.37/0.89 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', lamp)). 0.37/0.89 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', ex1E2)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', subbreln)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', eqbreln)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', beta1)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', eta1)). 0.37/0.89 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', iftrueProp1)). 0.37/0.89 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', ifSingleton)). 0.37/0.89 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', singletonprop)). 0.37/0.89 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', breln1SetBreln1)). 0.37/0.89 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', subbreln1)). 0.37/0.89 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', eqbreln1)). 0.37/0.89 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', breln1invprop)). 0.37/0.89 thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', breln1invI)). 0.37/0.89 thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', breln1all1)). 0.37/0.89 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', breln1all2)). 0.37/0.89 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', iftrueProp2)). 0.37/0.89 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', iffalseProp2)). 0.37/0.89 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', iffalseProp1)). 0.37/0.89 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', eta2)). 0.37/0.89 thf(beta2, axiom, ((beta2)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', beta2)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', lam2lamEq)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', brelnall2)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', brelnall1)). 0.37/0.89 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', lam2p)). 0.37/0.89 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', lamProp)). 0.37/0.89 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', funcImageSingleton)). 0.37/0.89 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', dpsetconstrEL2)). 0.37/0.89 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', dpsetconstrERa)). 0.37/0.89 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', dpsetconstrSub)). 0.37/0.89 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', dpsetconstrI)). 0.37/0.89 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', sepSubset)). 0.37/0.89 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', sepInPowerset)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', emptyE1)). 0.37/0.89 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', nonemptyImpWitness)). 0.37/0.89 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setbeta)). 0.37/0.89 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', dsetconstrER)). 0.37/0.89 thf(breln1invE, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>(((foundationAx)=>(((descrp)=>((((dsetconstrER)=>((exuE1)=>((((emptysetimpfalse)=>((((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>(((nonemptyI)=>(((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>(((((powersetI)=>((emptyinPowerset)=>(((powersetE)=>((((((nonemptyImpWitness)=>(((notinsingleton)=>(((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>(((quantDeMorgan1)=>((((quantDeMorgan4)=>(((prop2set2propI)=>((((((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>(((emptyset__Cong)=>(((powerset__Cong)=>(((omega__Cong)=>((((((eqimpsubset2)=>(((subsetI2)=>(((subsetE)=>(((((notequalI2)=>(((((setadjoinSub2)=>((subset2powerset)=>((((powersetI1)=>((powersetE1)=>(((powersetsubset)=>((((((binunionIR)=>((binunionEcases)=>(((binunionLsub)=>((binunionRsub)=>((((((binintersectSubset2)=>((binintersectSubset3)=>((((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((((setminusEL)=>((((((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>(((symdiffE)=>((symdiffI1)=>(((symdiffIneg1)=>((symdiffIneg2)=>((((setukpairIR)=>(((kpairp)=>((((singletoninpowunion)=>(((upairsubunion)=>(((((ubforcartprodlem3)=>((cartprodpairin)=>(((cartprodmempair)=>(((setunionsingleton1)=>(((setunionsingleton)=>(((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>(((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((((ksndsingleton)=>(((kpairsurjEq)=>((((cartprodpairmemER)=>((cartprodmempaircEq)=>(((cartprodsndpairEq)=>(((((setOfPairsIsBReln)=>(((dpsetconstrEL1)=>(((dpsetconstrER)=>(((apProp)=>((app)=>((((funcinfuncset)=>(((lamp)=>(((((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>(((ap2apEq1)=>(((beta1)=>((eta1)=>(((((((iftrueProp1)=>(((ifSingleton)=>(((theeq)=>((((iftrueorfalse)=>(((((((setextT)=>((subsetTI)=>((powersetTI1)=>(((complementTI1)=>((((binintersectTERcontra)=>(((contrasubsetT1)=>((contrasubsetT2)=>((((doubleComplementE1)=>((((((complementImpComplementIntersect)=>((((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>(((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>(((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>(((binunionTEcontra)=>(((complementUnionInPowersetComplement)=>(((demorgan1a)=>(((demorgan1)=>((((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>(((woz1_2)=>((((((breln1SetBreln1)=>(((((subbreln1)=>((eqbreln1)=>((breln1invprop)=>(![X4:$i, X33:$i]:((![X2:$i]:((![X3:$i]:((((in @ (kpair @ X2 @ X3) @ X33)<=(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))<=(in @ X3 @ X4)))<=(in @ X2 @ X4)))<=(breln1 @ X4 @ X33)))<=(breln1invI)))))<=(breln1all1))<=(setOfPairsIsBReln1))<=(choice2fnsingleton)))<=(breln1all2))<=(woz1_5))<=(woz1_4))<=(woz1_3)))<=(woz1_1)))))))))<=(demorgan2b2))<=(demorgan2a)))<=(demorgan1b)))<=(demorgan2a2)))<=(demorgan2a1)))<=(binunionTE))))<=(intersectInPowersetIntersectUnions)))))<=(binunionTIRcontra)))))<=(complementInPowersetComplementIntersect))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT))<=(doubleComplementEq))<=(doubleComplementSub2))<=(doubleComplementSub1)))<=(doubleComplementI1))<=(contrasubsetT3))))<=(contrasubsetT)))<=(binintersectTELcontra))<=(complementTE1)))<=(powersetTE1)))))<=(complementT_lem))<=(setminusT_lem))<=(powersetT_lem))<=(binunionT_lem))<=(binintersectT_lem)))<=(iffalse))<=(iftrue)))<=(ifp)))<=(iftrueProp2)))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))<=(beta2))<=(lam2lamEq))))<=(ap2apEq2)))<=(funcext2))))))<=(funcextLem))<=(funcGraphProp2)))))<=(brelnall2))<=(brelnall1))<=(lam2p)))<=(lamProp)))<=(ap2p))<=(infuncsetfunc))))<=(funcImageSingleton)))<=(dpsetconstrEL2)))<=(dpsetconstrERa)))<=(dpsetconstrSub))<=(dpsetconstrI))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))))<=(cartprodpairmemEL))<=(cartprodsndin)))<=(ksndpairEq)))<=(setukpairinjR))<=(setukpairinjR2)))))<=(setukpairinjR11))<=(setukpairinjL)))))<=(theprop))))))))<=(singletonprop)))<=(setunionsingleton2)))<=(setunionE2)))<=(cartprodmempair1))))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion)))<=(upairset2E)))<=(singletoninpowerset))<=(singletonsubset)))<=(kpairiskpair)))<=(setukpairIL))<=(secondinupair))))<=(symdiffI2))))<=(setminusSubset1)))))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2))<=(setminusER)))<=(setminusI))<=(bs114d)))))<=(disjointsetsI1))<=(binintersectER))))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))))<=(binunionE))))<=(upairset2IR))<=(binunionIL))<=(sepSubset))<=(sepInPowerset)))<=(inPowerset))))<=(subsetemptysetimpeq))<=(setextsub))))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1))<=(notsubsetI))<=(subsetE2)))<=(emptysetsubset)))<=(eqimpsubset1)))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong)))<=(setadjoin__Cong)))<=(exu__Cong))))))<=(exuI3))<=(exuI1))<=(notdallE))<=(notdexE)))<=(prop2setI)))<=(quantDeMorgan3))<=(quantDeMorgan2)))<=(vacuousDall)))))))<=(eqinunit)))<=(uniqinunit)))<=(exuE2))<=(subPowSU))<=(setunionE))<=(setunionI)))<=(emptyInPowerset))))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE)))))<=(nonemptyI1)))<=(nonemptyE1))))))<=(exuE3e))<=(notinemptyset)))<=(emptysetE))<=(prop2setE))))<=(dsetconstrEL))<=(dsetconstrI)))<=(wellorderingAx)))<=(replAx)))))<=(setunionAx))<=(powersetAx))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', breln1invE)). 0.37/0.89 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', notdexE)). 0.37/0.89 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', powersetAx)). 0.37/0.89 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', subsetemptysetimpeq)). 0.37/0.89 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setextsub)). 0.37/0.89 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setunionsingleton)). 0.37/0.89 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setadjoinSub)). 0.37/0.89 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', subsetTrans)). 0.37/0.89 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', subsetRefl)). 0.37/0.89 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', notequalI1)). 0.37/0.89 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', notsubsetI)). 0.37/0.89 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', subsetE2)). 0.37/0.89 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', emptysetsubset)). 0.37/0.89 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', eqimpsubset1)). 0.37/0.89 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', subsetI1)). 0.37/0.89 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', singletonsuniq)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', ubforcartprodlem3)). 0.37/0.89 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setunion__Cong)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', setadjoin__Cong)). 0.37/0.89 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setukpairinjL1)). 0.37/0.89 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', notdallE)). 0.37/0.89 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', app)). 0.37/0.89 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', prop2setI)). 0.37/0.89 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', kfstpairEq)). 0.37/0.89 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', quantDeMorgan3)). 0.37/0.89 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', quantDeMorgan2)). 0.37/0.89 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', cartprodfstin)). 0.37/0.89 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', vacuousDall)). 0.37/0.89 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', eqinunit)). 0.37/0.89 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', uniqinunit)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', setukpairinjL2)). 0.37/0.89 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', subPowSU)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', setukpairinjR12)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', setunionE)). 0.37/0.89 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setunionI)). 0.37/0.89 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', emptyInPowerset)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', setukpairinjR1)). 0.37/0.89 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setadjoinOr)). 0.37/0.89 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', upairequniteq)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', setadjoinE)). 0.37/0.89 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', notinemptyset)). 0.37/0.89 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', kpairsurjEq)). 0.37/0.89 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', emptysetE)). 0.37/0.89 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', prop2setE)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', cartprodpairin)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', cartprodpairmemER)). 0.37/0.89 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', wellorderingAx)). 0.37/0.89 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', cartprodmempaircEq)). 0.37/0.89 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setunionAx)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', cartprodsndpairEq)). 0.37/0.89 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', inComplementUnionImpNotIn1)). 0.37/0.89 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', inComplementUnionImpInComplement1)). 0.37/0.89 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', funcinfuncset)). 0.37/0.89 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', funcGraphProp1)). 0.37/0.89 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', funcGraphProp3)). 0.37/0.89 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', funcGraphProp4)). 0.37/0.89 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', cartprodmempair)). 0.37/0.89 thf(funcext, axiom, ((funcext)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', funcext)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', ap2apEq1)). 0.37/0.89 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', theeq)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', iftrueorfalse)). 0.37/0.89 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setextT)). 0.37/0.89 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', subsetTI)). 0.37/0.89 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', powersetTI1)). 0.37/0.89 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', complementTI1)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', binintersectTERcontra)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', contrasubsetT1)). 0.37/0.89 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', contrasubsetT2)). 0.37/0.89 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', doubleComplementE1)). 0.37/0.89 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', complementImpComplementIntersect)). 0.37/0.89 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', contraSubsetComplement)). 0.37/0.89 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', complementTcontraSubset)). 0.37/0.89 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binunionTILcontra)). 0.37/0.89 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', inIntersectImpInUnion)). 0.37/0.89 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', inIntersectImpInUnion2)). 0.37/0.89 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', inIntersectImpInIntersectUnions)). 0.37/0.89 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', ksndpairEq)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', setukpairinjR)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', setukpairinjR2)). 0.37/0.89 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setukpairinjR11)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', setukpairinjL)). 0.37/0.89 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', theprop)). 0.37/0.89 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binunionTEcontra)). 0.37/0.89 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', complementUnionInPowersetComplement)). 0.37/0.89 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', demorgan1a)). 0.37/0.89 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', demorgan1)). 0.37/0.89 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', demorgan2b)). 0.37/0.89 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', demorgan2)). 0.37/0.89 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', woz13rule0)). 0.37/0.89 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', woz13rule1)). 0.37/0.89 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', woz13rule2)). 0.37/0.89 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', woz13rule3)). 0.37/0.89 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', woz13rule4)). 0.37/0.89 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', woz1_2)). 0.37/0.89 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setunionsingleton1)). 0.37/0.89 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', woz1_5)). 0.37/0.89 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', woz1_4)). 0.37/0.89 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', woz1_3)). 0.37/0.89 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', woz1_1)). 0.37/0.89 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', demorgan2b2)). 0.37/0.89 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', demorgan2a)). 0.37/0.89 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', demorgan1b)). 0.37/0.89 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', demorgan2a2)). 0.37/0.89 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', demorgan2a1)). 0.37/0.89 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binunionTE)). 0.37/0.89 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', intersectInPowersetIntersectUnions)). 0.37/0.89 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binunionTIRcontra)). 0.37/0.89 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', complementInPowersetComplementIntersect)). 0.37/0.89 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', complementSubsetComplementIntersect)). 0.37/0.89 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', complementTnotintersectT)). 0.37/0.89 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', doubleComplementEq)). 0.37/0.89 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', doubleComplementSub2)). 0.37/0.89 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', doubleComplementSub1)). 0.37/0.89 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', doubleComplementI1)). 0.37/0.89 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', contrasubsetT3)). 0.37/0.89 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', contrasubsetT)). 0.37/0.89 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectTELcontra)). 0.37/0.89 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', complementTE1)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', powersetTE1)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', complementT_lem)). 0.37/0.89 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setminusT_lem)). 0.37/0.89 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', powersetT_lem)). 0.37/0.89 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', binunionT_lem)). 0.37/0.89 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectT_lem)). 0.37/0.89 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', iffalse)). 0.37/0.89 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', iftrue)). 0.37/0.89 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', ifp)). 0.37/0.89 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', ap2apEq2)). 0.37/0.89 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', funcext2)). 0.37/0.89 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', funcextLem)). 0.37/0.89 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', funcGraphProp2)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', ap2p)). 0.37/0.89 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', infuncsetfunc)). 0.37/0.89 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', cartprodpairsurjEq)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', cartprodfstpairEq)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', cartprodpairmemEL)). 0.37/0.89 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', cartprodsndin)). 0.37/0.89 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setunionsingleton2)). 0.37/0.89 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setunionE2)). 0.37/0.89 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.Y1hbpNh5zn/E---3.1_11410.p', cartprodmempair1)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', ubforcartprodlem2)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', ubforcartprodlem1)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', upairinpowunion)). 0.37/0.89 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', upairset2E)). 0.37/0.89 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', singletoninpowerset)). 0.37/0.89 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', singletonsubset)). 0.37/0.89 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', kpairiskpair)). 0.37/0.89 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setukpairIL)). 0.37/0.89 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', secondinupair)). 0.37/0.89 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', symdiffI2)). 0.37/0.89 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setminusSubset1)). 0.37/0.89 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setminusELneg)). 0.37/0.89 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setminusERneg)). 0.37/0.89 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setminusSubset2)). 0.37/0.89 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setminusER)). 0.37/0.89 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setminusI)). 0.37/0.89 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', bs114d)). 0.37/0.89 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', disjointsetsI1)). 0.37/0.89 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectER)). 0.37/0.89 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectLsub)). 0.37/0.89 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectEL)). 0.37/0.89 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectSubset5)). 0.37/0.89 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectI)). 0.37/0.89 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binunionE)). 0.37/0.89 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', upairset2IR)). 0.37/0.89 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binunionIL)). 0.37/0.89 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', inPowerset)). 0.37/0.89 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', upairsubunion)). 0.37/0.89 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', singletoninpowunion)). 0.37/0.89 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', kpairp)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', setukpairIR)). 0.37/0.89 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', symdiffIneg2)). 0.37/0.89 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', symdiffIneg1)). 0.37/0.89 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', symdiffI1)). 0.37/0.89 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', symdiffE)). 0.37/0.89 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setminusLsub)). 0.37/0.89 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setminusIRneg)). 0.37/0.89 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setminusILneg)). 0.37/0.89 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setminusEL)). 0.37/0.89 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectSubset1)). 0.37/0.89 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectSubset4)). 0.37/0.89 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectRsub)). 0.37/0.89 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectSubset3)). 0.37/0.89 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binintersectSubset2)). 0.37/0.89 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binunionRsub)). 0.37/0.89 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binunionLsub)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', binunionEcases)). 0.37/0.89 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', binunionIR)). 0.37/0.89 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', powersetsubset)). 0.37/0.89 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', powersetE1)). 0.37/0.89 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', powersetI1)). 0.37/0.89 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', subset2powerset)). 0.37/0.89 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setadjoinSub2)). 0.37/0.89 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', notequalI2)). 0.37/0.89 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', subsetE)). 0.37/0.89 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', subsetI2)). 0.37/0.89 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', eqimpsubset2)). 0.37/0.89 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', omega__Cong)). 0.37/0.89 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', powerset__Cong)). 0.37/0.89 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', emptyset__Cong)). 0.37/0.89 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', in__Cong)). 0.37/0.89 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', inCongP)). 0.37/0.89 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', quantDeMorgan4)). 0.37/0.89 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', quantDeMorgan1)). 0.37/0.89 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', upairsetIR)). 0.37/0.89 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', upairsetIL)). 0.37/0.89 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', upairsetE)). 0.37/0.89 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', singletonsswitch)). 0.37/0.89 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', notinsingleton)). 0.37/0.89 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', powersetE)). 0.37/0.89 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', emptyinPowerset)). 0.37/0.89 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', powersetI)). 0.37/0.89 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setadjoinIR)). 0.37/0.89 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', emptyinunitempty)). 0.37/0.89 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setadjoinIL)). 0.37/0.89 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', noeltsimpempty)). 0.37/0.89 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', emptyI)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', setext)). 0.37/0.89 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', emptysetimpfalse)). 0.37/0.89 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.Y1hbpNh5zn/E---3.1_11410.p', foundationAx)). 0.37/0.89 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', omegaIndAx)). 0.37/0.89 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', omegaSAx)). 0.37/0.89 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', omega0Ax)). 0.37/0.89 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setadjoinAx)). 0.37/0.89 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', emptysetAx)). 0.37/0.89 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Y1hbpNh5zn/E---3.1_11410.p', setextAx)). 0.37/0.89 thf(c_0_297, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])). 0.37/0.89 thf(c_0_298, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 0.37/0.89 thf(c_0_299, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.37/0.89 thf(c_0_300, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.37/0.89 thf(c_0_301, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.37/0.89 thf(c_0_302, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.37/0.89 thf(c_0_303, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.37/0.89 thf(c_0_304, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.37/0.89 thf(c_0_305, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.37/0.89 thf(c_0_306, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.37/0.89 thf(c_0_307, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.37/0.89 thf(c_0_308, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.37/0.89 thf(c_0_309, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 0.37/0.89 thf(c_0_310, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_297, c_0_298])). 0.37/0.89 thf(c_0_311, plain, ((breln1invset)=(^[Z0/* 19 */:$i, Z1:$i]:(dpsetconstr @ Z0 @ Z0 @ (^[Z2/* 19 */:$i, Z3:$i]:((in @ (kpair @ Z3 @ Z2) @ Z1)))))), inference(fof_simplification,[status(thm)],[breln1invset])). 0.37/0.89 thf(c_0_312, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])). 0.37/0.89 thf(c_0_313, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.37/0.89 thf(c_0_314, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.37/0.89 thf(c_0_315, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.37/0.89 thf(c_0_316, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.37/0.89 thf(c_0_317, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.37/0.89 thf(c_0_318, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.37/0.89 thf(c_0_319, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 0.37/0.89 thf(c_0_320, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.37/0.89 thf(c_0_321, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.37/0.89 thf(c_0_322, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1022:$i]:((((X1 @ X1022))&![X1023:$i]:((((X1 @ X1023))=>((X1022)=(X1023)))))))=>((?[X1024:$i]:((((X17 @ X1024))&![X1025:$i]:((((X17 @ X1025))=>((X1024)=(X1025)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_299, c_0_300])). 0.37/0.89 thf(c_0_323, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1020:$i]:((((X1 @ X1020))&![X1021:$i]:((((X1 @ X1021))=>((X1020)=(X1021)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_301, c_0_300])). 0.37/0.89 thf(c_0_324, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1016:$i]:((((X1 @ X1016))&![X1017:$i]:((((X1 @ X1017))=>((X1016)=(X1017)))))))<=>(?[X1018:$i]:((((X17 @ X1018))&![X1019:$i]:((((X17 @ X1019))=>((X1018)=(X1019)))))))))))), inference(apply_def,[status(thm)],[c_0_302, c_0_300])). 0.37/0.89 thf(c_0_325, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1010:$i]:((((X1 @ X1010))&![X1011:$i]:((((X1 @ X1011))=>((X1010)=(X1011)))))))))))), inference(apply_def,[status(thm)],[c_0_303, c_0_300])). 0.37/0.89 thf(c_0_326, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 0.37/0.89 thf(c_0_327, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1008:$i]:((((X1 @ X1008))&![X1009:$i]:((((X1 @ X1009))=>((X1008)=(X1009))))))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_300])). 0.37/0.89 thf(c_0_328, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1006:$i]:((((X1 @ X1006))&![X1007:$i]:((((X1 @ X1007))=>((X1006)=(X1007)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_305, c_0_300])). 0.37/0.89 thf(c_0_329, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.37/0.89 thf(c_0_330, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_306])). 0.37/0.89 thf(c_0_331, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_306])). 0.37/0.89 thf(c_0_332, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 0.37/0.89 thf(c_0_333, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1004:$i]:((((X1 @ X1004))&![X1005:$i]:((((X1 @ X1005))=>((X1004)=(X1005)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_307, c_0_300])). 0.37/0.89 thf(c_0_334, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.37/0.89 thf(c_0_335, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.37/0.89 thf(c_0_336, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X998:$i]:((((X6 @ X2 @ X998))&![X999:$i]:((((X6 @ X2 @ X999))=>((X998)=(X999)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_308, c_0_300])). 0.37/0.89 thf(c_0_337, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_309, c_0_298])). 0.37/0.89 thf(c_0_338, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 0.37/0.89 thf(c_0_339, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 0.37/0.89 thf(c_0_340, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 0.37/0.89 thf(c_0_341, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 0.37/0.89 thf(c_0_342, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 0.37/0.89 thf(c_0_343, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_298])). 0.37/0.89 thf(c_0_344, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_298])). 0.37/0.89 thf(c_0_345, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 0.37/0.89 thf(c_0_346, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 0.37/0.89 thf(c_0_347, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 0.37/0.89 thf(c_0_348, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 0.37/0.89 thf(c_0_349, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.37/0.89 thf(c_0_350, axiom, ((breln1SetBreln1)=(![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>((subset @ X33 @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[breln1SetBreln1, c_0_310])). 0.37/0.89 thf(c_0_351, axiom, ((subbreln1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln1, c_0_310])). 0.37/0.89 thf(c_0_352, axiom, ((eqbreln1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln1, c_0_310])). 0.37/0.89 thf(c_0_353, axiom, ((breln1invprop)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X33)))) @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[breln1invprop, c_0_311]), c_0_310])). 0.37/0.89 thf(c_0_354, axiom, ((breln1invI)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X33)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[breln1invI, c_0_311]), c_0_310])). 0.37/0.89 thf(c_0_355, axiom, ((breln1all1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[breln1all1, c_0_310])). 0.37/0.89 thf(c_0_356, plain, ((setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X4)))))), inference(apply_def,[status(thm)],[c_0_312, c_0_310])). 0.37/0.89 thf(c_0_357, axiom, ((breln1all2)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[breln1all2, c_0_310])). 0.37/0.89 thf(c_0_358, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 0.37/0.89 thf(c_0_359, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 0.37/0.89 thf(c_0_360, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 0.37/0.89 thf(c_0_361, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 0.37/0.89 thf(c_0_362, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 0.37/0.89 thf(c_0_363, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 0.37/0.89 thf(c_0_364, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_298])). 0.37/0.89 thf(c_0_365, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_298])). 0.37/0.89 thf(c_0_366, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 0.37/0.89 thf(c_0_367, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 0.37/0.89 thf(c_0_368, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 0.37/0.89 thf(c_0_369, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 0.37/0.89 thf(c_0_370, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 0.37/0.89 thf(c_0_371, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 0.37/0.89 thf(c_0_372, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 0.37/0.89 thf(c_0_373, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.37/0.89 thf(c_0_374, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.37/0.89 thf(c_0_375, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1014:$i]:((((X1 @ X1014))&![X1015:$i]:((((X1 @ X1015))=>((X1014)=(X1015)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_313, c_0_300])). 0.37/0.89 thf(c_0_376, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1012:$i]:((((X1 @ X1012))&![X1013:$i]:((((X1 @ X1013))=>((X1012)=(X1013))))))))))), inference(apply_def,[status(thm)],[c_0_314, c_0_300])). 0.37/0.89 thf(c_0_377, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 0.37/0.89 thf(c_0_378, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_306])). 0.37/0.89 thf(c_0_379, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_315, c_0_306])). 0.37/0.89 thf(c_0_380, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.37/0.89 thf(c_0_381, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1002:$i]:((((X1 @ X1002))&![X1003:$i]:((((X1 @ X1003))=>((X1002)=(X1003)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_316, c_0_300])). 0.37/0.89 thf(c_0_382, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.37/0.89 thf(c_0_383, plain, ((descrp)=(![X1:$i > $o]:(((?[X1000:$i]:((((X1 @ X1000))&![X1001:$i]:((((X1 @ X1001))=>((X1000)=(X1001)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_317, c_0_300])). 0.37/0.89 thf(c_0_384, plain, ((epred1_0)<=>![X1961:$i]:(?[X1962:$i]:((((![X1963:$i]:(((in @ X1963 @ X1962)=>![X1964:$i]:(((in @ X1964 @ X1963)=>(in @ X1964 @ X1961)))))&![X1965:$i, X1966:$i]:((((in @ X1965 @ X1961)&(in @ X1966 @ X1961))=>(![X1967:$i]:(((in @ X1967 @ X1962)=>((in @ X1965 @ X1967)<=>(in @ X1966 @ X1967))))=>((X1965)=(X1966))))))&![X1968:$i, X1969:$i]:((((in @ X1968 @ X1962)&(in @ X1969 @ X1962))=>(![X1970:$i]:(((in @ X1970 @ X1968)=>(in @ X1970 @ X1969)))|![X1971:$i]:(((in @ X1971 @ X1969)=>(in @ X1971 @ X1968)))))))&![X1972:$i]:(((![X1973:$i]:(((in @ X1973 @ X1972)=>(in @ X1973 @ X1961)))&?[X1974:$i]:((in @ X1974 @ X1972)))=>?[X1975:$i, X1976:$i]:(((((in @ X1975 @ X1962)&(in @ X1976 @ X1972))&~(?[X1977:$i]:(((in @ X1977 @ X1975)&(in @ X1977 @ X1972)))))&![X1978:$i]:(((in @ X1978 @ X1962)=>(![X1979:$i]:(((in @ X1979 @ X1978)=>(in @ X1979 @ X1975)))|(in @ X1976 @ X1978)))))))))))), introduced(definition)). 0.37/0.89 thf(c_0_385, negated_conjecture, ~((![X1026:$i, X1027:$i]:((![X1028:$i]:(((in @ X1028 @ X1026)<=>(in @ X1028 @ X1027)))=>((X1026)=(X1027))))=>(![X1029:$i]:(~(in @ X1029 @ emptyset))=>(![X1030:$i, X1031:$i, X1032:$i]:(((in @ X1032 @ (setadjoin @ X1030 @ X1031))<=>(((X1032)=(X1030))|(in @ X1032 @ X1031))))=>(![X1991:$i, X1992:$i]:(((in @ X1992 @ (powerset @ X1991))<=>![X1993:$i]:(((in @ X1993 @ X1992)=>(in @ X1993 @ X1991)))))=>(![X1988:$i, X1989:$i]:(((in @ X1989 @ (setunion @ X1988))<=>?[X1990:$i]:(((in @ X1989 @ X1990)&(in @ X1990 @ X1988)))))=>((in @ emptyset @ omega)=>(![X1033:$i]:(((in @ X1033 @ omega)=>(in @ (setadjoin @ X1033 @ X1033) @ omega)))=>(![X1034:$i]:((((in @ emptyset @ X1034)&![X1035:$i]:((((in @ X1035 @ omega)&(in @ X1035 @ X1034))=>(in @ (setadjoin @ X1035 @ X1035) @ X1034))))=>![X1036:$i]:(((in @ X1036 @ omega)=>(in @ X1036 @ X1034)))))=>(![X1980:$i > $i > $o, X1981:$i]:((![X1982:$i]:(((in @ X1982 @ X1981)=>?[X1983:$i]:(((X1980 @ X1982 @ X1983)&![X1984:$i]:(((X1980 @ X1982 @ X1984)=>((X1983)=(X1984))))))))=>?[X1985:$i]:(![X1986:$i]:(((in @ X1986 @ X1985)<=>?[X1987:$i]:(((in @ X1987 @ X1981)&(X1980 @ X1987 @ X1986))))))))=>(![X1037:$i]:((?[X1038:$i]:((in @ X1038 @ X1037))=>?[X1039:$i]:(((in @ X1039 @ X1037)&~(?[X1040:$i]:(((in @ X1040 @ X1039)&(in @ X1040 @ X1037))))))))=>((epred1_0)=>(![X1041:$i > $o]:((?[X1042:$i]:(((X1041 @ X1042)&![X1043:$i]:(((X1041 @ X1043)=>((X1042)=(X1043))))))=>(X1041 @ (descr @ (^[Z0/* 17 */:$i]:(X1041 @ Z0))))))=>(![X1958:$i, X1959:$i > $o, X1960:$i]:(((in @ X1960 @ X1958)=>((X1959 @ X1960)=>(in @ X1960 @ (dsetconstr @ X1958 @ X1959)))))=>(![X1955:$i, X1956:$i > $o, X1957:$i]:(((in @ X1957 @ (dsetconstr @ X1955 @ X1956))=>(in @ X1957 @ X1955)))=>(![X1044:$i, X1045:$i > $o, X1046:$i]:(((in @ X1046 @ (dsetconstr @ X1044 @ X1045))=>(X1045 @ X1046)))=>(![X1047:$i > $o]:((?[X1048:$i]:(((X1047 @ X1048)&![X1049:$i]:(((X1047 @ X1049)=>((X1048)=(X1049))))))=>?[X1050:$i]:(((X1047 @ X1050)&![X1051:$i]:(((X1047 @ X1051)=>((X1050)=(X1051))))))))=>(![X1953:$o, X1954:$i]:(((in @ X1954 @ (prop2set @ ((X1953))))=>(X1953)))=>(![X1951:$i]:(((in @ X1951 @ emptyset)=>![X1952:$o]:((X1952))))=>(![X1052:$i]:(((in @ X1052 @ emptyset)=>~($true)))=>(![X1950:$i]:(~(in @ X1950 @ emptyset))=>(![X1946:$i > $o]:((?[X1947:$i]:(((X1946 @ X1947)&![X1948:$i]:(((X1946 @ X1948)=>((X1947)=(X1948))))))=>?[X1949:$i]:((X1946 @ X1949))))=>(![X1053:$i, X1054:$i]:((![X1055:$i]:(((in @ X1055 @ X1053)=>(in @ X1055 @ X1054)))=>(![X1056:$i]:(((in @ X1056 @ X1054)=>(in @ X1056 @ X1053)))=>((X1053)=(X1054)))))=>(![X1057:$i]:((![X1058:$i]:(~(in @ X1058 @ X1057))=>((X1057)=(emptyset))))=>(![X1059:$i]:((![X1060:$i]:(~(in @ X1060 @ X1059))=>((X1059)=(emptyset))))=>(![X1061:$i, X1062:$i > $o, X1063:$i]:(((in @ X1063 @ X1061)=>((in @ X1063 @ (dsetconstr @ X1061 @ X1062))<=>(X1062 @ X1063))))=>(![X1944:$i]:((((X1944)!=(emptyset))=>?[X1945:$i]:((in @ X1945 @ X1944))))=>(![X1064:$i, X1065:$i > $o, X1066:$i]:(((in @ X1066 @ X1064)=>((X1065 @ X1066)=>((dsetconstr @ X1064 @ X1065)!=(emptyset)))))=>(![X1942:$i]:((?[X1943:$i]:((in @ X1943 @ X1942))=>((X1942)!=(emptyset))))=>(![X1067:$i, X1068:$i]:((in @ X1067 @ (setadjoin @ X1067 @ X1068)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1069:$i, X1070:$i, X1071:$i]:(((in @ X1071 @ X1070)=>(in @ X1071 @ (setadjoin @ X1069 @ X1070))))=>(![X1938:$i, X1939:$i, X1940:$i]:(((in @ X1940 @ (setadjoin @ X1938 @ X1939))=>![X1941:$o]:(((((X1940)=(X1938))=>(X1941))=>(((in @ X1940 @ X1939)=>(X1941))=>(X1941))))))=>(![X1935:$i, X1936:$i, X1937:$i]:(((in @ X1937 @ (setadjoin @ X1935 @ X1936))=>(((X1937)=(X1935))|(in @ X1937 @ X1936))))=>(![X1934:$i]:(((dsetconstr @ X1934 @ (^[Z0/* 1 */:$i]:($true)))=(X1934)))=>(![X1072:$i, X1073:$i]:((![X1074:$i]:(((in @ X1074 @ X1073)=>(in @ X1074 @ X1072)))=>(in @ X1073 @ (powerset @ X1072))))=>(![X1075:$i]:((in @ emptyset @ (powerset @ X1075)))=>(![X1933:$i]:((in @ emptyset @ (powerset @ X1933)))=>(![X1076:$i, X1077:$i, X1078:$i]:(((in @ X1077 @ (powerset @ X1076))=>((in @ X1078 @ X1077)=>(in @ X1078 @ X1076))))=>(![X1930:$i, X1931:$i, X1932:$i]:(((in @ X1931 @ X1932)=>((in @ X1932 @ X1930)=>(in @ X1931 @ (setunion @ 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y_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[breln1invE]), notdexE]), powersetAx]), subsetemptysetimpeq]), setextsub]), setunionsingleton]), setadjoinSub]), subsetTrans]), subsetRefl]), c_0_318]), notequalI1]), notsubsetI]), c_0_319]), subsetE2]), emptysetsubset]), eqimpsubset1]), c_0_320]), subsetI1]), c_0_321]), singletonsuniq]), c_0_322]), c_0_323]), ubforcartprodlem3]), setunion__Cong]), setadjoin__Cong]), setukpairinjL1]), c_0_324]), c_0_325]), c_0_326]), c_0_327]), notdallE]), app]), prop2setI]), kfstpairEq]), quantDeMorgan3]), quantDeMorgan2]), cartprodfstin]), vacuousDall]), eqinunit]), uniqinunit]), setukpairinjL2]), c_0_328]), subPowSU]), setukpairinjR12]), setunionE]), setunionI]), emptyInPowerset]), setukpairinjR1]), c_0_329]), setadjoinOr]), upairequniteq]), setadjoinE]), c_0_330]), c_0_331]), c_0_332]), c_0_333]), notinemptyset]), kpairsurjEq]), emptysetE]), prop2setE]), c_0_334]), cartprodpairin]), c_0_335]), cartprodpairmemER]), wellorderingAx]), c_0_336]), cartprodmempaircEq]), setunionAx]), cartprodsndpairEq]), c_0_337]), c_0_338]), c_0_339]), c_0_340]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), funcinfuncset]), c_0_341]), c_0_342]), funcGraphProp1]), funcGraphProp3]), funcGraphProp4]), c_0_343]), c_0_344]), cartprodmempair]), funcext]), ap2apEq1]), c_0_345]), c_0_346]), c_0_347]), c_0_348]), theeq]), iftrueorfalse]), setextT]), subsetTI]), powersetTI1]), complementTI1]), binintersectTERcontra]), contrasubsetT1]), contrasubsetT2]), doubleComplementE1]), complementImpComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), ksndpairEq]), setukpairinjR]), setukpairinjR2]), setukpairinjR11]), setukpairinjL]), theprop]), c_0_349]), binunionTEcontra]), complementUnionInPowersetComplement]), demorgan1a]), demorgan1]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_2]), c_0_350]), c_0_351]), c_0_352]), c_0_353]), c_0_311]), c_0_310]), setunionsingleton1]), c_0_354]), c_0_355]), c_0_356]), c_0_357]), woz1_5]), woz1_4]), woz1_3]), woz1_1]), demorgan2b2]), demorgan2a]), demorgan1b]), demorgan2a2]), demorgan2a1]), binunionTE]), intersectInPowersetIntersectUnions]), binunionTIRcontra]), complementInPowersetComplementIntersect]), complementSubsetComplementIntersect]), complementTnotintersectT]), doubleComplementEq]), doubleComplementSub2]), doubleComplementSub1]), doubleComplementI1]), contrasubsetT3]), contrasubsetT]), binintersectTELcontra]), complementTE1]), powersetTE1]), complementT_lem]), setminusT_lem]), powersetT_lem]), binunionT_lem]), binintersectT_lem]), iffalse]), iftrue]), ifp]), c_0_358]), c_0_359]), c_0_360]), c_0_361]), c_0_362]), c_0_363]), ap2apEq2]), funcext2]), funcextLem]), funcGraphProp2]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), ap2p]), infuncsetfunc]), c_0_368]), c_0_369]), c_0_370]), c_0_371]), c_0_372]), cartprodpairsurjEq]), cartprodfstpairEq]), cartprodpairmemEL]), cartprodsndin]), setunionsingleton2]), setunionE2]), cartprodmempair1]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairset2E]), singletoninpowerset]), singletonsubset]), kpairiskpair]), setukpairIL]), secondinupair]), symdiffI2]), setminusSubset1]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), setminusI]), bs114d]), disjointsetsI1]), binintersectER]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionE]), upairset2IR]), binunionIL]), c_0_373]), c_0_374]), inPowerset]), upairsubunion]), singletoninpowunion]), kpairp]), setukpairIR]), symdiffIneg2]), symdiffIneg1]), symdiffI1]), symdiffE]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusEL]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), binintersectSubset3]), binintersectSubset2]), binunionRsub]), binunionLsub]), binunionEcases]), binunionIR]), powersetsubset]), powersetE1]), powersetI1]), subset2powerset]), setadjoinSub2]), notequalI2]), subsetE]), subsetI2]), eqimpsubset2]), omega__Cong]), powerset__Cong]), emptyset__Cong]), c_0_375]), in__Cong]), inCongP]), c_0_376]), quantDeMorgan4]), quantDeMorgan1]), c_0_377]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), notinsingleton]), c_0_378]), powersetE]), emptyinPowerset]), powersetI]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_379]), c_0_380]), noeltsimpempty]), emptyI]), setext]), emptysetimpfalse]), c_0_381]), c_0_382]), c_0_383]), foundationAx]), omegaIndAx]), omegaSAx]), omega0Ax]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_384])). 0.37/0.89 thf(c_0_386, negated_conjecture, ![X1994:$i, X1995:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2007:$i, X2008:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2016:$i, X2017:$i > $i > $o, X2018:$i, X2020:$i, X2023:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2030:$i, X2031:$i > $o, X2032:$i, X2034:$i, X2035:$i > $o, X2036:$i, X2037:$i, X2038:$i > $o, X2039:$i, X2040:$i, X2041:$i > $o, X2042:$i, X2043:$i > $o, X2044:$i, X2047:$i, X2048:$o, X2049:$i, X2050:$i, X2051:$o, X2052:$i, X2053:$i, X2054:$i > $o, X2055:$i, X2058:$i, X2059:$i, X2062:$i, X2064:$i, X2066:$i, X2067:$i > $o, X2068:$i, X2069:$i, X2071:$i, X2072:$i > $o, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$o, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$o, X2104:$i, X2105:$i, X2106:$i > $o, X2107:$i, X2110:$i, X2111:$i, X2112:$i, X2114:$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 > $o, X2131:$i, X2132:$i > $o, X2133:$i, X2134:$i, X2135:$i > $o, X2136:$i, X2138:$i, X2139:$i > $o, X2141:$i, X2142:$i, X2143:$i > $o, X2145:$i, X2146:$i, X2147:$i > $o, X2148:$i, X2150:$o, X2151:$i, X2152:$i > $o, X2154:$i, X2155:$i, X2156:$i > $o, X2157:$i, X2159:$i > $o, X2160:$i, X2163:$i, X2164:$i > $o, X2165:$i, X2169:$i, X2170:$i > $o, X2171:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i > $o, X2184:$i, X2186:$i, X2187:$i, X2188:$i > $o, X2189:$i > $o, X2192:$i, X2195:$i, X2196:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i > $o, X2209:$i, X2211:$i, X2212:$i, X2213:$i > $o, X2214:$i > $o, X2217:$i, X2219:$i, X2221:$i, X2222:$i, X2223:$i > $o, X2224:$i > $o, X2227:$i, X2228:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i > $o, X2275:$i, X2276:$i > $o, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$o, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, 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, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$o, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, 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X2945)|~(subset @ X2945 @ (cartprod @ X2943 @ X2943))|~(subset @ X2944 @ (cartprod @ X2943 @ X2943)))))))))&((~(subset @ X2951 @ (cartprod @ X2950 @ X2950))|(subset @ (dpsetconstr @ X2950 @ X2950 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X2951)))) @ (cartprod @ X2950 @ X2950)))&((~(subset @ X2953 @ (cartprod @ X2952 @ X2952))|(~(in @ X2954 @ X2952)|(~(in @ X2955 @ X2952)|(~(in @ (kpair @ X2954 @ X2955) @ X2953)|(in @ (kpair @ X2955 @ X2954) @ (dpsetconstr @ X2952 @ X2952 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X2953)))))))))&((subset @ esk98_0 @ (cartprod @ esk97_0 @ esk97_0))&((in @ esk99_0 @ esk97_0)&((in @ esk100_0 @ esk97_0)&((in @ (kpair @ esk100_0 @ esk99_0) @ (dpsetconstr @ esk97_0 @ esk97_0 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ esk98_0)))))&~(in @ (kpair @ esk99_0 @ esk100_0) @ esk98_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_385])])])])])])])). 0.37/0.89 thf(c_0_387, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i, X6:$i > $i > $o]:(((X6 @ X2 @ X3)|~((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ X6))))), inference(split_conjunct,[status(thm)],[c_0_386])). 0.37/0.89 thf(c_0_388, negated_conjecture, (in @ (kpair @ esk100_0 @ esk99_0) @ (dpsetconstr @ esk97_0 @ esk97_0 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ esk98_0))))), inference(split_conjunct,[status(thm)],[c_0_386])). 0.37/0.89 thf(c_0_389, negated_conjecture, ~((in @ (kpair @ esk99_0 @ esk100_0) @ esk98_0)), inference(split_conjunct,[status(thm)],[c_0_386])). 0.37/0.89 thf(c_0_390, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_387, c_0_388]), c_0_389]), ['proof']). 0.37/0.89 # SZS output end CNFRefutation 0.37/0.89 # Parsed axioms : 639 0.37/0.89 # Removed by relevancy pruning/SinE : 342 0.37/0.89 # Initial clauses : 506 0.37/0.89 # Removed in clause preprocessing : 32 0.37/0.89 # Initial clauses in saturation : 474 0.37/0.89 # Processed clauses : 628 0.37/0.89 # ...of these trivial : 11 0.37/0.89 # ...subsumed : 43 0.37/0.89 # ...remaining for further processing : 574 0.37/0.89 # Other redundant clauses eliminated : 24 0.37/0.89 # Clauses deleted for lack of memory : 0 0.37/0.89 # Backward-subsumed : 2 0.37/0.89 # Backward-rewritten : 1 0.37/0.89 # Generated clauses : 999 0.37/0.89 # ...of the previous two non-redundant : 919 0.37/0.89 # ...aggressively subsumed : 0 0.37/0.89 # Contextual simplify-reflections : 14 0.37/0.89 # Paramodulations : 967 0.37/0.89 # Factorizations : 0 0.37/0.89 # NegExts : 0 0.37/0.89 # Equation resolutions : 29 0.37/0.89 # Disequality decompositions : 0 0.37/0.89 # Total rewrite steps : 96 0.37/0.89 # ...of those cached : 66 0.37/0.89 # Propositional unsat checks : 0 0.37/0.89 # Propositional check models : 0 0.37/0.89 # Propositional check unsatisfiable : 0 0.37/0.89 # Propositional clauses : 0 0.37/0.89 # Propositional clauses after purity: 0 0.37/0.89 # Propositional unsat core size : 0 0.37/0.89 # Propositional preprocessing time : 0.000 0.37/0.89 # Propositional encoding time : 0.000 0.37/0.89 # Propositional solver time : 0.000 0.37/0.89 # Success case prop preproc time : 0.000 0.37/0.89 # Success case prop encoding time : 0.000 0.37/0.89 # Success case prop solver time : 0.000 0.37/0.89 # Current number of processed clauses : 144 0.37/0.89 # Positive orientable unit clauses : 34 0.37/0.89 # Positive unorientable unit clauses: 0 0.37/0.89 # Negative unit clauses : 3 0.37/0.89 # Non-unit-clauses : 107 0.37/0.89 # Current number of unprocessed clauses: 1176 0.37/0.89 # ...number of literals in the above : 3533 0.37/0.89 # Current number of archived formulas : 0 0.37/0.89 # Current number of archived clauses : 415 0.37/0.89 # Clause-clause subsumption calls (NU) : 44641 0.37/0.89 # Rec. Clause-clause subsumption calls : 14088 0.37/0.89 # Non-unit clause-clause subsumptions : 54 0.37/0.89 # Unit Clause-clause subsumption calls : 67 0.37/0.89 # Rewrite failures with RHS unbound : 0 0.37/0.89 # BW rewrite match attempts : 23 0.37/0.89 # BW rewrite match successes : 1 0.37/0.89 # Condensation attempts : 0 0.37/0.89 # Condensation successes : 0 0.37/0.89 # Termbank termtop insertions : 112613 0.37/0.89 # Search garbage collected termcells : 31992 0.37/0.89 0.37/0.89 # ------------------------------------------------- 0.37/0.89 # User time : 0.269 s 0.37/0.89 # System time : 0.023 s 0.37/0.89 # Total time : 0.291 s 0.37/0.89 # Maximum resident set size: 9828 pages 0.37/0.89 0.37/0.89 # ------------------------------------------------- 0.37/0.89 # User time : 0.286 s 0.37/0.89 # System time : 0.027 s 0.37/0.89 # Total time : 0.313 s 0.37/0.89 # Maximum resident set size: 2748 pages 0.37/0.89 % E---3.1 exiting 0.37/0.89 % E exiting 0.37/0.89 EOF