0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.12 % Command : run_E %s %d THM 0.11/0.33 % Computer : n008.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 1440 0.11/0.33 % WCLimit : 180 0.11/0.33 % DateTime : Thu Jul 4 09:08:09 EDT 2024 0.11/0.33 % CPUTime : 0.20/0.47 Running higher-order theorem proving 0.20/0.54 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.QAQCxMG3Yr/E---3.1_5856.p 269.18/34.90 # Version: 3.2.0-ho 269.18/34.90 # Preprocessing class: HSLMSLSSLLLCHFA. 269.18/34.90 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 269.18/34.90 # Starting ehoh_best5 with 180s (1) cores 269.18/34.90 # Starting almost_fo_3_lam with 180s (1) cores 269.18/34.90 # Starting new_bool_5 with 180s (1) cores 269.18/34.90 # Starting pre_casc_3 with 180s (1) cores 269.18/34.90 # Starting ho_unfolding_8 with 180s (1) cores 269.18/34.90 # Starting new_ho_10_cnf2 with 180s (1) cores 269.18/34.90 # Starting new_bool_3 with 180s (1) cores 269.18/34.90 # Starting new_ho_5 with 180s (1) cores 269.18/34.90 # new_bool_5 with pid 5938 completed with status 0 269.18/34.90 # Result found by new_bool_5 269.18/34.90 # Preprocessing class: HSLMSLSSLLLCHFA. 269.18/34.90 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 269.18/34.90 # Starting ehoh_best5 with 180s (1) cores 269.18/34.90 # Starting almost_fo_3_lam with 180s (1) cores 269.18/34.90 # Starting new_bool_5 with 180s (1) cores 269.18/34.90 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 269.18/34.90 # Search class: HGHSM-FSLM32-MHFMMSBN 269.18/34.90 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 269.18/34.90 # Starting ho_unfolding_8 with 33s (1) cores 269.18/34.90 # ho_unfolding_8 with pid 5944 completed with status 7 269.18/34.90 # Starting new_bool_5 with 19s (1) cores 269.18/34.90 # new_bool_5 with pid 6570 completed with status 0 269.18/34.90 # Result found by new_bool_5 269.18/34.90 # Preprocessing class: HSLMSLSSLLLCHFA. 269.18/34.90 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 269.18/34.90 # Starting ehoh_best5 with 180s (1) cores 269.18/34.90 # Starting almost_fo_3_lam with 180s (1) cores 269.18/34.90 # Starting new_bool_5 with 180s (1) cores 269.18/34.90 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 269.18/34.90 # Search class: HGHSM-FSLM32-MHFMMSBN 269.18/34.90 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 269.18/34.90 # Starting ho_unfolding_8 with 33s (1) cores 269.18/34.90 # ho_unfolding_8 with pid 5944 completed with status 7 269.18/34.90 # Starting new_bool_5 with 19s (1) cores 269.18/34.90 # Preprocessing time : 0.007 s 269.18/34.90 # Presaturation interreduction done 269.18/34.90 269.18/34.90 # Proof found! 269.18/34.90 # SZS status Theorem 269.18/34.90 # SZS output start CNFRefutation 269.18/34.90 thf(decl_22, type, in: $i > $i > $o). 269.18/34.90 thf(decl_23, type, exu: ($i > $o) > $o). 269.18/34.90 thf(decl_24, type, setextAx: $o). 269.18/34.90 thf(decl_25, type, emptyset: $i). 269.18/34.90 thf(decl_26, type, emptysetAx: $o). 269.18/34.90 thf(decl_27, type, setadjoin: $i > $i > $i). 269.18/34.90 thf(decl_28, type, setadjoinAx: $o). 269.18/34.90 thf(decl_29, type, powerset: $i > $i). 269.18/34.90 thf(decl_30, type, powersetAx: $o). 269.18/34.90 thf(decl_31, type, setunion: $i > $i). 269.18/34.90 thf(decl_32, type, setunionAx: $o). 269.18/34.90 thf(decl_33, type, omega: $i). 269.18/34.90 thf(decl_34, type, omega0Ax: $o). 269.18/34.90 thf(decl_35, type, omegaSAx: $o). 269.18/34.90 thf(decl_36, type, omegaIndAx: $o). 269.18/34.90 thf(decl_37, type, replAx: $o). 269.18/34.90 thf(decl_38, type, foundationAx: $o). 269.18/34.90 thf(decl_39, type, wellorderingAx: $o). 269.18/34.90 thf(decl_40, type, descr: ($i > $o) > $i). 269.18/34.90 thf(decl_41, type, descrp: $o). 269.18/34.90 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_43, type, dsetconstrI: $o). 269.18/34.90 thf(decl_44, type, dsetconstrEL: $o). 269.18/34.90 thf(decl_45, type, dsetconstrER: $o). 269.18/34.90 thf(decl_46, type, exuE1: $o). 269.18/34.90 thf(decl_47, type, prop2set: $o > $i). 269.18/34.90 thf(decl_48, type, prop2setE: $o). 269.18/34.90 thf(decl_49, type, emptysetE: $o). 269.18/34.90 thf(decl_50, type, emptysetimpfalse: $o). 269.18/34.90 thf(decl_51, type, notinemptyset: $o). 269.18/34.90 thf(decl_52, type, exuE3e: $o). 269.18/34.90 thf(decl_53, type, setext: $o). 269.18/34.90 thf(decl_54, type, emptyI: $o). 269.18/34.90 thf(decl_55, type, noeltsimpempty: $o). 269.18/34.90 thf(decl_56, type, setbeta: $o). 269.18/34.90 thf(decl_57, type, nonempty: $i > $o). 269.18/34.90 thf(decl_58, type, nonemptyE1: $o). 269.18/34.90 thf(decl_59, type, nonemptyI: $o). 269.18/34.90 thf(decl_60, type, nonemptyI1: $o). 269.18/34.90 thf(decl_61, type, setadjoinIL: $o). 269.18/34.90 thf(decl_62, type, emptyinunitempty: $o). 269.18/34.90 thf(decl_63, type, setadjoinIR: $o). 269.18/34.90 thf(decl_64, type, setadjoinE: $o). 269.18/34.90 thf(decl_65, type, setadjoinOr: $o). 269.18/34.90 thf(decl_66, type, setoftrueEq: $o). 269.18/34.90 thf(decl_67, type, powersetI: $o). 269.18/34.90 thf(decl_68, type, emptyinPowerset: $o). 269.18/34.90 thf(decl_69, type, emptyInPowerset: $o). 269.18/34.90 thf(decl_70, type, powersetE: $o). 269.18/34.90 thf(decl_71, type, setunionI: $o). 269.18/34.90 thf(decl_72, type, setunionE: $o). 269.18/34.90 thf(decl_73, type, subPowSU: $o). 269.18/34.90 thf(decl_74, type, exuE2: $o). 269.18/34.90 thf(decl_75, type, nonemptyImpWitness: $o). 269.18/34.90 thf(decl_76, type, uniqinunit: $o). 269.18/34.90 thf(decl_77, type, notinsingleton: $o). 269.18/34.90 thf(decl_78, type, eqinunit: $o). 269.18/34.90 thf(decl_79, type, singletonsswitch: $o). 269.18/34.90 thf(decl_80, type, upairsetE: $o). 269.18/34.90 thf(decl_81, type, upairsetIL: $o). 269.18/34.90 thf(decl_82, type, upairsetIR: $o). 269.18/34.90 thf(decl_83, type, emptyE1: $o). 269.18/34.90 thf(decl_84, type, vacuousDall: $o). 269.18/34.90 thf(decl_85, type, quantDeMorgan1: $o). 269.18/34.90 thf(decl_86, type, quantDeMorgan2: $o). 269.18/34.90 thf(decl_87, type, quantDeMorgan3: $o). 269.18/34.90 thf(decl_88, type, quantDeMorgan4: $o). 269.18/34.90 thf(decl_89, type, prop2setI: $o). 269.18/34.90 thf(decl_91, type, prop2set2propI: $o). 269.18/34.90 thf(decl_92, type, notdexE: $o). 269.18/34.90 thf(decl_93, type, notdallE: $o). 269.18/34.90 thf(decl_94, type, exuI1: $o). 269.18/34.90 thf(decl_95, type, exuI3: $o). 269.18/34.90 thf(decl_96, type, exuI2: $o). 269.18/34.90 thf(decl_97, type, inCongP: $o). 269.18/34.90 thf(decl_98, type, in__Cong: $o). 269.18/34.90 thf(decl_99, type, exuE3u: $o). 269.18/34.90 thf(decl_100, type, exu__Cong: $o). 269.18/34.90 thf(decl_101, type, emptyset__Cong: $o). 269.18/34.90 thf(decl_102, type, setadjoin__Cong: $o). 269.18/34.90 thf(decl_103, type, powerset__Cong: $o). 269.18/34.90 thf(decl_104, type, setunion__Cong: $o). 269.18/34.90 thf(decl_105, type, omega__Cong: $o). 269.18/34.90 thf(decl_106, type, exuEu: $o). 269.18/34.90 thf(decl_107, type, descr__Cong: $o). 269.18/34.90 thf(decl_108, type, dsetconstr__Cong: $o). 269.18/34.90 thf(decl_109, type, subset: $i > $i > $o). 269.18/34.90 thf(decl_112, type, subsetI1: $o). 269.18/34.90 thf(decl_113, type, eqimpsubset2: $o). 269.18/34.90 thf(decl_114, type, eqimpsubset1: $o). 269.18/34.90 thf(decl_115, type, subsetI2: $o). 269.18/34.90 thf(decl_116, type, emptysetsubset: $o). 269.18/34.90 thf(decl_117, type, subsetE: $o). 269.18/34.90 thf(decl_118, type, subsetE2: $o). 269.18/34.90 thf(decl_119, type, notsubsetI: $o). 269.18/34.90 thf(decl_120, type, notequalI1: $o). 269.18/34.90 thf(decl_121, type, notequalI2: $o). 269.18/34.90 thf(decl_122, type, subsetRefl: $o). 269.18/34.90 thf(decl_123, type, subsetTrans: $o). 269.18/34.90 thf(decl_124, type, setadjoinSub: $o). 269.18/34.90 thf(decl_125, type, setadjoinSub2: $o). 269.18/34.90 thf(decl_126, type, subset2powerset: $o). 269.18/34.90 thf(decl_127, type, setextsub: $o). 269.18/34.90 thf(decl_128, type, subsetemptysetimpeq: $o). 269.18/34.90 thf(decl_129, type, powersetI1: $o). 269.18/34.90 thf(decl_130, type, powersetE1: $o). 269.18/34.90 thf(decl_131, type, inPowerset: $o). 269.18/34.90 thf(decl_132, type, powersetsubset: $o). 269.18/34.90 thf(decl_133, type, sepInPowerset: $o). 269.18/34.90 thf(decl_134, type, sepSubset: $o). 269.18/34.90 thf(decl_135, type, binunion: $i > $i > $i). 269.18/34.90 thf(decl_136, type, binunionIL: $o). 269.18/34.90 thf(decl_137, type, upairset2IR: $o). 269.18/34.90 thf(decl_138, type, binunionIR: $o). 269.18/34.90 thf(decl_139, type, binunionEcases: $o). 269.18/34.90 thf(decl_140, type, binunionE: $o). 269.18/34.90 thf(decl_141, type, binunionLsub: $o). 269.18/34.90 thf(decl_142, type, binunionRsub: $o). 269.18/34.90 thf(decl_143, type, binintersect: $i > $i > $i). 269.18/34.90 thf(decl_144, type, binintersectI: $o). 269.18/34.90 thf(decl_145, type, binintersectSubset5: $o). 269.18/34.90 thf(decl_146, type, binintersectEL: $o). 269.18/34.90 thf(decl_147, type, binintersectLsub: $o). 269.18/34.90 thf(decl_148, type, binintersectSubset2: $o). 269.18/34.90 thf(decl_149, type, binintersectSubset3: $o). 269.18/34.90 thf(decl_150, type, binintersectER: $o). 269.18/34.90 thf(decl_151, type, disjointsetsI1: $o). 269.18/34.90 thf(decl_152, type, binintersectRsub: $o). 269.18/34.90 thf(decl_153, type, binintersectSubset4: $o). 269.18/34.90 thf(decl_154, type, binintersectSubset1: $o). 269.18/34.90 thf(decl_155, type, bs114d: $o). 269.18/34.90 thf(decl_157, type, setminus: $i > $i > $i). 269.18/34.90 thf(decl_158, type, setminusI: $o). 269.18/34.90 thf(decl_159, type, setminusEL: $o). 269.18/34.90 thf(decl_160, type, setminusER: $o). 269.18/34.90 thf(decl_161, type, setminusSubset2: $o). 269.18/34.90 thf(decl_162, type, setminusERneg: $o). 269.18/34.90 thf(decl_163, type, setminusELneg: $o). 269.18/34.90 thf(decl_164, type, setminusILneg: $o). 269.18/34.90 thf(decl_165, type, setminusIRneg: $o). 269.18/34.90 thf(decl_166, type, setminusLsub: $o). 269.18/34.90 thf(decl_167, type, setminusSubset1: $o). 269.18/34.90 thf(decl_168, type, symdiff: $i > $i > $i). 269.18/34.90 thf(decl_169, type, symdiffE: $o). 269.18/34.90 thf(decl_170, type, symdiffI1: $o). 269.18/34.90 thf(decl_171, type, symdiffI2: $o). 269.18/34.90 thf(decl_172, type, symdiffIneg1: $o). 269.18/34.90 thf(decl_173, type, symdiffIneg2: $o). 269.18/34.90 thf(decl_174, type, iskpair: $i > $o). 269.18/34.90 thf(decl_175, type, secondinupair: $o). 269.18/34.90 thf(decl_176, type, setukpairIL: $o). 269.18/34.90 thf(decl_177, type, setukpairIR: $o). 269.18/34.90 thf(decl_178, type, kpairiskpair: $o). 269.18/34.90 thf(decl_179, type, kpair: $i > $i > $i). 269.18/34.90 thf(decl_180, type, kpairp: $o). 269.18/34.90 thf(decl_181, type, cartprod: $i > $i > $i). 269.18/34.90 thf(decl_182, type, singletonsubset: $o). 269.18/34.90 thf(decl_183, type, singletoninpowerset: $o). 269.18/34.90 thf(decl_184, type, singletoninpowunion: $o). 269.18/34.90 thf(decl_185, type, upairset2E: $o). 269.18/34.90 thf(decl_186, type, upairsubunion: $o). 269.18/34.90 thf(decl_187, type, upairinpowunion: $o). 269.18/34.90 thf(decl_188, type, ubforcartprodlem1: $o). 269.18/34.90 thf(decl_189, type, ubforcartprodlem2: $o). 269.18/34.90 thf(decl_190, type, ubforcartprodlem3: $o). 269.18/34.90 thf(decl_191, type, cartprodpairin: $o). 269.18/34.90 thf(decl_192, type, cartprodmempair1: $o). 269.18/34.90 thf(decl_193, type, cartprodmempair: $o). 269.18/34.90 thf(decl_194, type, setunionE2: $o). 269.18/34.90 thf(decl_195, type, setunionsingleton1: $o). 269.18/34.90 thf(decl_196, type, setunionsingleton2: $o). 269.18/34.90 thf(decl_197, type, setunionsingleton: $o). 269.18/34.90 thf(decl_198, type, singleton: $i > $o). 269.18/34.90 thf(decl_199, type, singletonprop: $o). 269.18/34.90 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 269.18/34.90 thf(decl_201, type, ex1E1: $o). 269.18/34.90 thf(decl_202, type, ex1I: $o). 269.18/34.90 thf(decl_203, type, ex1I2: $o). 269.18/34.90 thf(decl_204, type, singletonsuniq: $o). 269.18/34.90 thf(decl_209, type, setukpairinjL1: $o). 269.18/34.90 thf(decl_210, type, kfstsingleton: $o). 269.18/34.90 thf(decl_211, type, theprop: $o). 269.18/34.90 thf(decl_212, type, kfst: $i > $i). 269.18/34.90 thf(decl_213, type, kfstpairEq: $o). 269.18/34.90 thf(decl_214, type, cartprodfstin: $o). 269.18/34.90 thf(decl_215, type, setukpairinjL2: $o). 269.18/34.90 thf(decl_216, type, setukpairinjL: $o). 269.18/34.90 thf(decl_217, type, setukpairinjR11: $o). 269.18/34.90 thf(decl_218, type, setukpairinjR12: $o). 269.18/34.90 thf(decl_219, type, setukpairinjR1: $o). 269.18/34.90 thf(decl_220, type, upairequniteq: $o). 269.18/34.90 thf(decl_221, type, setukpairinjR2: $o). 269.18/34.90 thf(decl_222, type, setukpairinjR: $o). 269.18/34.90 thf(decl_223, type, ksndsingleton: $o). 269.18/34.90 thf(decl_224, type, ksnd: $i > $i). 269.18/34.90 thf(decl_225, type, ksndpairEq: $o). 269.18/34.90 thf(decl_226, type, kpairsurjEq: $o). 269.18/34.90 thf(decl_227, type, cartprodsndin: $o). 269.18/34.90 thf(decl_228, type, cartprodpairmemEL: $o). 269.18/34.90 thf(decl_229, type, cartprodpairmemER: $o). 269.18/34.90 thf(decl_230, type, cartprodmempaircEq: $o). 269.18/34.90 thf(decl_231, type, cartprodfstpairEq: $o). 269.18/34.90 thf(decl_232, type, cartprodsndpairEq: $o). 269.18/34.90 thf(decl_233, type, cartprodpairsurjEq: $o). 269.18/34.90 thf(decl_234, type, breln: $i > $i > $i > $o). 269.18/34.90 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 269.18/34.90 thf(decl_236, type, dpsetconstrI: $o). 269.18/34.90 thf(decl_237, type, dpsetconstrSub: $o). 269.18/34.90 thf(decl_238, type, setOfPairsIsBReln: $o). 269.18/34.90 thf(decl_239, type, dpsetconstrERa: $o). 269.18/34.90 thf(decl_240, type, dpsetconstrEL1: $o). 269.18/34.90 thf(decl_241, type, dpsetconstrEL2: $o). 269.18/34.90 thf(decl_242, type, dpsetconstrER: $o). 269.18/34.90 thf(decl_243, type, func: $i > $i > $i > $o). 269.18/34.90 thf(decl_244, type, funcSet: $i > $i > $i). 269.18/34.90 thf(decl_245, type, funcImageSingleton: $o). 269.18/34.90 thf(decl_246, type, apProp: $o). 269.18/34.90 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 269.18/34.90 thf(decl_248, type, app: $o). 269.18/34.90 thf(decl_249, type, infuncsetfunc: $o). 269.18/34.90 thf(decl_250, type, ap2p: $o). 269.18/34.90 thf(decl_251, type, funcinfuncset: $o). 269.18/34.90 thf(decl_252, type, lamProp: $o). 269.18/34.90 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 269.18/34.90 thf(decl_254, type, lamp: $o). 269.18/34.90 thf(decl_255, type, lam2p: $o). 269.18/34.90 thf(decl_256, type, brelnall1: $o). 269.18/34.90 thf(decl_257, type, brelnall2: $o). 269.18/34.90 thf(decl_258, type, ex1E2: $o). 269.18/34.90 thf(decl_259, type, funcGraphProp1: $o). 269.18/34.90 thf(decl_260, type, funcGraphProp3: $o). 269.18/34.90 thf(decl_261, type, funcGraphProp2: $o). 269.18/34.90 thf(decl_262, type, funcextLem: $o). 269.18/34.90 thf(decl_263, type, funcGraphProp4: $o). 269.18/34.90 thf(decl_264, type, subbreln: $o). 269.18/34.90 thf(decl_265, type, eqbreln: $o). 269.18/34.90 thf(decl_266, type, funcext: $o). 269.18/34.90 thf(decl_267, type, funcext2: $o). 269.18/34.90 thf(decl_268, type, ap2apEq1: $o). 269.18/34.90 thf(decl_269, type, ap2apEq2: $o). 269.18/34.90 thf(decl_270, type, beta1: $o). 269.18/34.90 thf(decl_271, type, eta1: $o). 269.18/34.90 thf(decl_272, type, lam2lamEq: $o). 269.18/34.90 thf(decl_273, type, beta2: $o). 269.18/34.90 thf(decl_274, type, eta2: $o). 269.18/34.90 thf(decl_275, type, iffalseProp1: $o). 269.18/34.90 thf(decl_276, type, iffalseProp2: $o). 269.18/34.90 thf(decl_277, type, iftrueProp1: $o). 269.18/34.90 thf(decl_278, type, iftrueProp2: $o). 269.18/34.90 thf(decl_279, type, ifSingleton: $o). 269.18/34.90 thf(decl_280, type, if: $i > $o > $i > $i > $i). 269.18/34.90 thf(decl_281, type, ifp: $o). 269.18/34.90 thf(decl_282, type, theeq: $o). 269.18/34.90 thf(decl_283, type, iftrue: $o). 269.18/34.90 thf(decl_284, type, iffalse: $o). 269.18/34.90 thf(decl_285, type, iftrueorfalse: $o). 269.18/34.90 thf(decl_286, type, binintersectT_lem: $o). 269.18/34.90 thf(decl_287, type, binunionT_lem: $o). 269.18/34.90 thf(decl_288, type, powersetT_lem: $o). 269.18/34.90 thf(decl_289, type, setminusT_lem: $o). 269.18/34.90 thf(decl_290, type, complementT_lem: $o). 269.18/34.90 thf(decl_291, type, setextT: $o). 269.18/34.90 thf(decl_292, type, subsetTI: $o). 269.18/34.90 thf(decl_293, type, powersetTI1: $o). 269.18/34.90 thf(decl_294, type, powersetTE1: $o). 269.18/34.90 thf(decl_295, type, complementTI1: $o). 269.18/34.90 thf(decl_296, type, complementTE1: $o). 269.18/34.90 thf(decl_297, type, binintersectTELcontra: $o). 269.18/34.90 thf(decl_298, type, binintersectTERcontra: $o). 269.18/34.90 thf(decl_299, type, contrasubsetT: $o). 269.18/34.90 thf(decl_300, type, contrasubsetT1: $o). 269.18/34.90 thf(decl_301, type, contrasubsetT2: $o). 269.18/34.90 thf(decl_302, type, contrasubsetT3: $o). 269.18/34.90 thf(decl_303, type, doubleComplementI1: $o). 269.18/34.90 thf(decl_304, type, doubleComplementE1: $o). 269.18/34.90 thf(decl_305, type, doubleComplementSub1: $o). 269.18/34.90 thf(decl_306, type, doubleComplementSub2: $o). 269.18/34.90 thf(decl_307, type, doubleComplementEq: $o). 269.18/34.90 thf(decl_308, type, complementTnotintersectT: $o). 269.18/34.90 thf(decl_309, type, complementImpComplementIntersect: $o). 269.18/34.90 thf(decl_310, type, complementSubsetComplementIntersect: $o). 269.18/34.90 thf(decl_311, type, complementInPowersetComplementIntersect: $o). 269.18/34.90 thf(decl_312, type, contraSubsetComplement: $o). 269.18/34.90 thf(decl_313, type, complementTcontraSubset: $o). 269.18/34.90 thf(decl_314, type, binunionTILcontra: $o). 269.18/34.90 thf(decl_315, type, binunionTIRcontra: $o). 269.18/34.90 thf(decl_316, type, inIntersectImpInUnion: $o). 269.18/34.90 thf(decl_317, type, inIntersectImpInUnion2: $o). 269.18/34.90 thf(decl_318, type, inIntersectImpInIntersectUnions: $o). 269.18/34.90 thf(decl_319, type, intersectInPowersetIntersectUnions: $o). 269.18/34.90 thf(decl_320, type, inComplementUnionImpNotIn1: $o). 269.18/34.90 thf(decl_321, type, inComplementUnionImpInComplement1: $o). 269.18/34.90 thf(decl_322, type, binunionTE: $o). 269.18/34.90 thf(decl_323, type, binunionTEcontra: $o). 269.18/34.90 thf(decl_324, type, demorgan2a1: $o). 269.18/34.90 thf(decl_325, type, epred1_0: $o). 269.18/34.90 thf(decl_326, type, esk1_2: $i > $i > $i). 269.18/34.90 thf(decl_327, type, esk2_2: $i > $i > $i). 269.18/34.90 thf(decl_328, type, esk3_2: $i > $i > $i). 269.18/34.90 thf(decl_329, type, esk4_1: $i > $i). 269.18/34.90 thf(decl_330, type, esk5_2: ($i > $i > $o) > $i > $i). 269.18/34.90 thf(decl_331, type, esk6_2: ($i > $i > $o) > $i > $i). 269.18/34.90 thf(decl_332, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 269.18/34.90 thf(decl_333, type, esk8_1: $i > $i). 269.18/34.90 thf(decl_334, type, esk9_1: ($i > $o) > $i). 269.18/34.90 thf(decl_335, type, esk10_1: ($i > $o) > $i). 269.18/34.90 thf(decl_336, type, esk11_2: $i > $i > $i). 269.18/34.90 thf(decl_337, type, esk12_2: $i > $i > $i). 269.18/34.90 thf(decl_338, type, esk13_1: $i > $i). 269.18/34.90 thf(decl_339, type, esk14_1: $i > $i). 269.18/34.90 thf(decl_340, type, esk15_1: $i > $i). 269.18/34.90 thf(decl_341, type, esk16_2: $i > $i > $i). 269.18/34.90 thf(decl_342, type, esk17_3: $i > $i > $o > $i). 269.18/34.90 thf(decl_343, type, esk18_1: ($i > $o) > $i). 269.18/34.90 thf(decl_344, type, esk19_1: $i > $i). 269.18/34.90 thf(decl_345, type, esk20_2: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_346, type, esk21_2: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_347, type, esk22_2: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_348, type, esk23_2: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_349, type, esk24_2: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_350, type, esk25_2: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_351, type, esk26_2: ($i > $o) > $i > $i). 269.18/34.90 thf(decl_352, type, esk27_1: ($i > $o) > $i). 269.18/34.90 thf(decl_353, type, esk28_1: ($i > $o) > $i). 269.18/34.90 thf(decl_354, type, esk29_2: ($i > $o) > $i > $i). 269.18/34.90 thf(decl_355, type, esk30_2: ($i > $o) > ($i > $o) > $i). 269.18/34.90 thf(decl_356, type, esk31_2: ($i > $o) > ($i > $o) > $i). 269.18/34.90 thf(decl_357, type, esk32_2: ($i > $o) > ($i > $o) > $i). 269.18/34.90 thf(decl_358, type, esk33_2: ($i > $o) > ($i > $o) > $i). 269.18/34.90 thf(decl_359, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 269.18/34.90 thf(decl_360, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 269.18/34.90 thf(decl_361, type, esk36_2: $i > $i > $i). 269.18/34.90 thf(decl_362, type, esk37_2: $i > $i > $i). 269.18/34.90 thf(decl_363, type, esk38_2: $i > $i > $i). 269.18/34.90 thf(decl_364, type, esk39_3: $i > $i > $i > $i). 269.18/34.90 thf(decl_365, type, esk40_3: $i > $i > $i > $i). 269.18/34.90 thf(decl_366, type, esk41_2: $i > $i > $i). 269.18/34.90 thf(decl_367, type, esk42_2: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_368, type, esk43_2: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_369, type, esk44_2: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_370, type, esk45_3: $i > ($i > $o) > $i > $i). 269.18/34.90 thf(decl_371, type, esk46_2: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_372, type, esk47_2: $i > ($i > $o) > $i). 269.18/34.90 thf(decl_373, type, esk48_3: $i > $i > ($i > $i) > $i). 269.18/34.90 thf(decl_374, type, esk49_3: $i > $i > ($i > $i) > $i). 269.18/34.90 thf(decl_375, type, esk50_3: $i > $i > ($i > $i) > $i). 269.18/34.90 thf(decl_376, type, esk51_4: $i > $i > $i > ($i > $o) > $i). 269.18/34.90 thf(decl_377, type, esk52_4: $i > $i > $i > ($i > $o) > $i). 269.18/34.90 thf(decl_378, type, esk53_4: $i > $i > $i > ($i > $o) > $i). 269.18/34.90 thf(decl_379, type, esk54_4: $i > $i > $i > ($i > $o) > $i). 269.18/34.90 thf(decl_380, type, esk55_4: $i > $i > $i > $i > $i). 269.18/34.90 thf(decl_381, type, esk56_4: $i > $i > $i > $i > $i). 269.18/34.90 thf(decl_382, type, esk57_4: $i > $i > $i > $i > $i). 269.18/34.90 thf(decl_383, type, esk58_4: $i > $i > $i > $i > $i). 269.18/34.90 thf(decl_384, type, esk59_4: $i > $i > $i > $i > $i). 269.18/34.90 thf(decl_385, type, esk60_4: $i > $i > $i > $i > $i). 269.18/34.90 thf(decl_386, type, esk61_4: $i > $i > $i > $i > $i). 269.18/34.90 thf(decl_387, type, esk62_4: $i > $i > $i > $i > $i). 269.18/34.90 thf(decl_388, type, esk63_4: $i > $i > $i > $i > $i). 269.18/34.90 thf(decl_389, type, esk64_3: $i > $i > ($i > $i) > $i). 269.18/34.90 thf(decl_390, type, esk65_3: $i > $i > ($i > $i) > $i). 269.18/34.90 thf(decl_391, type, esk66_3: $i > $i > ($i > $i) > $i). 269.18/34.90 thf(decl_392, type, esk67_3: $i > $i > $i > $i). 269.18/34.90 thf(decl_393, type, esk68_3: $i > $i > $i > $i). 269.18/34.90 thf(decl_394, type, esk69_3: $i > $i > $i > $i). 269.18/34.90 thf(decl_395, type, esk70_3: $i > $i > $i > $i). 269.18/34.90 thf(decl_396, type, esk71_0: $i). 269.18/34.90 thf(decl_397, type, esk72_0: $i). 269.18/34.90 thf(decl_398, type, esk73_0: $i). 269.18/34.90 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', exuE2)). 269.18/34.90 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', sepInPowerset)). 269.18/34.90 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', dsetconstr__Cong)). 269.18/34.90 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', exuI3)). 269.18/34.90 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', exuI1)). 269.18/34.90 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setoftrueEq)). 269.18/34.90 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', nonemptyI)). 269.18/34.90 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setbeta)). 269.18/34.90 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', exuE3e)). 269.18/34.90 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', dsetconstrI)). 269.18/34.90 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', descrp)). 269.18/34.90 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', replAx)). 269.18/34.90 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', kfstsingleton)). 269.18/34.90 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', ksndsingleton)). 269.18/34.90 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', dpsetconstrI)). 269.18/34.90 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setOfPairsIsBReln)). 269.18/34.90 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', dpsetconstrERa)). 269.18/34.90 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', dpsetconstrEL1)). 269.18/34.90 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', dpsetconstrER)). 269.18/34.90 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', funcImageSingleton)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', eta1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', lam2lamEq)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', eta2)). 269.18/34.90 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', iffalseProp1)). 269.18/34.90 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', iffalseProp2)). 269.18/34.90 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', iftrueProp1)). 269.18/34.90 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', ifSingleton)). 269.18/34.90 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', iftrueProp2)). 269.18/34.90 thf(beta2, axiom, ((beta2)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', beta2)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', beta1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', ex1E2)). 269.18/34.90 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', lam2p)). 269.18/34.90 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', lamp)). 269.18/34.90 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', lamProp)). 269.18/34.90 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', apProp)). 269.18/34.90 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', dpsetconstrEL2)). 269.18/34.90 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', dpsetconstrSub)). 269.18/34.90 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', ex1I2)). 269.18/34.90 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', ex1I)). 269.18/34.90 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', ex1E1)). 269.18/34.90 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', singletonprop)). 269.18/34.90 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', sepSubset)). 269.18/34.90 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', descr__Cong)). 269.18/34.90 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', exuEu)). 269.18/34.90 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', exu__Cong)). 269.18/34.90 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', exuE3u)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', exuI2)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', emptyE1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', exuE1)). 269.18/34.90 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', dsetconstrER)). 269.18/34.90 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', dsetconstrEL)). 269.18/34.90 thf(complementUnionInPowersetComplement, conjecture, ((setextAx)=>((emptysetAx)=>(((powersetAx)=>((((omegaSAx)=>((((foundationAx)=>(((((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>(((emptysetimpfalse)=>(((((((((((setadjoinIL)=>((emptyinunitempty)=>(((setadjoinE)=>((((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>(((setunionE)=>((((((notinsingleton)=>(((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>(((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>(((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>((notdallE)=>((((exuI2)=>((((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>(((powerset__Cong)=>(((omega__Cong)=>((exuEu)=>((descr__Cong)=>(((subsetI1)=>((((subsetI2)=>((emptysetsubset)=>((((notsubsetI)=>(((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>(((powersetI1)=>((powersetE1)=>(((powersetsubset)=>(((sepSubset)=>((((binunionIR)=>((((binunionLsub)=>(((binintersectI)=>((((binintersectLsub)=>((((((binintersectRsub)=>(((binintersectSubset1)=>((bs114d)=>((setminusI)=>(((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>(((((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>((((kpairiskpair)=>((kpairp)=>((singletonsubset)=>(((singletoninpowunion)=>((((upairinpowunion)=>(((((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>(((setunionsingleton1)=>((setunionsingleton2)=>(((((((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>(((cartprodfstin)=>((setukpairinjL2)=>(((setukpairinjR11)=>((setukpairinjR12)=>((((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>(((((((cartprodfstpairEq)=>((cartprodsndpairEq)=>(((dpsetconstrI)=>(((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>(((dpsetconstrER)=>((funcImageSingleton)=>(((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>(((((brelnall1)=>((((funcGraphProp1)=>((funcGraphProp3)=>(((funcextLem)=>((funcGraphProp4)=>(((((funcext2)=>(((((eta1)=>((lam2lamEq)=>(((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((((ifp)=>(((iftrue)=>((iffalse)=>(((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>(((complementT_lem)=>(((subsetTI)=>((((((binintersectTELcontra)=>((binintersectTERcontra)=>((((contrasubsetT2)=>(((doubleComplementI1)=>((doubleComplementE1)=>((((((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>(((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>(((inIntersectImpInIntersectUnions)=>((((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>![X4:$i, X21:$i]:((![X48:$i]:(((in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))<=(in @ X48 @ (powerset @ X4))))<=(in @ X21 @ (powerset @ X4))))))))<=(inComplementUnionImpNotIn1))<=(intersectInPowersetIntersectUnions)))<=(inIntersectImpInUnion2))))))<=(contraSubsetComplement)))))<=(complementTnotintersectT))<=(doubleComplementEq))<=(doubleComplementSub2))<=(doubleComplementSub1))))<=(contrasubsetT3)))<=(contrasubsetT1))<=(contrasubsetT))))<=(complementTE1))<=(complementTI1))<=(powersetTE1))<=(powersetTI1)))<=(setextT)))<=(setminusT_lem)))))<=(iftrueorfalse))))<=(theeq)))<=(ifSingleton))<=(iftrueProp2))))))<=(beta2))))<=(beta1))<=(ap2apEq2))<=(ap2apEq1)))<=(funcext))<=(eqbreln))<=(subbreln))))<=(funcGraphProp2))))<=(ex1E2))<=(brelnall2)))<=(lam2p))<=(lamp))<=(lamProp))))))<=(apProp))))<=(dpsetconstrEL2)))))<=(dpsetconstrSub)))<=(cartprodpairsurjEq))))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin))<=(kpairsurjEq))))))<=(upairequniteq))<=(setukpairinjR1))))<=(setukpairinjL))))<=(kfstpairEq))))))<=(ex1I2))<=(ex1I))<=(ex1E1))<=(singletonprop))<=(setunionsingleton))))<=(setunionE2)))))<=(ubforcartprodlem3))<=(ubforcartprodlem2))<=(ubforcartprodlem1)))<=(upairsubunion))<=(upairset2E)))<=(singletoninpowerset)))))<=(setukpairIR))<=(setukpairIL)))<=(symdiffIneg2))))))<=(setminusSubset1))<=(setminusLsub))<=(setminusIRneg)))))))<=(setminusEL)))))<=(binintersectSubset4)))<=(disjointsetsI1))<=(binintersectER))<=(binintersectSubset3))<=(binintersectSubset2)))<=(binintersectEL))<=(binintersectSubset5)))<=(binunionRsub)))<=(binunionE))<=(binunionEcases)))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset)))<=(inPowerset))))<=(subsetemptysetimpeq)))))))))<=(notequalI1)))<=(subsetE2))<=(subsetE))))<=(eqimpsubset1))<=(eqimpsubset2)))<=(dsetconstr__Cong)))))<=(setunion__Cong)))<=(setadjoin__Cong)))))<=(in__Cong))<=(inCongP)))<=(exuI3))<=(exuI1))))<=(prop2set2propI))))<=(quantDeMorgan3))))))<=(upairsetIR)))))<=(eqinunit)))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))<=(setunionI))))))<=(setoftrueEq))<=(setadjoinOr)))<=(setadjoinIR))))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1))<=(setbeta))<=(noeltsimpempty))<=(emptyI))<=(setext))<=(exuE3e))<=(notinemptyset)))<=(emptysetE))))))<=(dsetconstrI))<=(descrp))<=(wellorderingAx)))<=(replAx))<=(omegaIndAx)))<=(omega0Ax))<=(setunionAx)))<=(setadjoinAx)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', complementUnionInPowersetComplement)). 269.18/34.90 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setminusER)). 269.18/34.90 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setadjoinAx)). 269.18/34.90 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binunionIL)). 269.18/34.90 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setminusI)). 269.18/34.90 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', inPowerset)). 269.18/34.90 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setminusELneg)). 269.18/34.90 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', subsetemptysetimpeq)). 269.18/34.90 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', notequalI1)). 269.18/34.90 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', subsetE2)). 269.18/34.90 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setminusILneg)). 269.18/34.90 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', subsetE)). 269.18/34.90 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', eqimpsubset1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', symdiffE)). 269.18/34.90 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', eqimpsubset2)). 269.18/34.90 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setunion__Cong)). 269.18/34.90 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', symdiffI1)). 269.18/34.90 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setadjoin__Cong)). 269.18/34.90 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', in__Cong)). 269.18/34.90 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', symdiffI2)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', inCongP)). 269.18/34.90 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', quantDeMorgan3)). 269.18/34.90 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', symdiffIneg1)). 269.18/34.90 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', upairsetIR)). 269.18/34.90 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', eqinunit)). 269.18/34.90 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', secondinupair)). 269.18/34.90 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', uniqinunit)). 269.18/34.90 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', nonemptyImpWitness)). 269.18/34.90 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', subPowSU)). 269.18/34.90 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', kpairiskpair)). 269.18/34.90 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setunionI)). 269.18/34.90 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', kpairp)). 269.18/34.90 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setadjoinOr)). 269.18/34.90 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setadjoinIR)). 269.18/34.90 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', nonemptyI1)). 269.18/34.90 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', singletonsubset)). 269.18/34.90 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', nonemptyE1)). 269.18/34.90 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', singletoninpowunion)). 269.18/34.90 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', noeltsimpempty)). 269.18/34.90 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', emptyI)). 269.18/34.90 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', upairinpowunion)). 269.18/34.90 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setext)). 269.18/34.90 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', cartprodpairin)). 269.18/34.90 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', notinemptyset)). 269.18/34.90 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', emptysetE)). 269.18/34.90 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', cartprodmempair1)). 269.18/34.90 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', wellorderingAx)). 269.18/34.90 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', cartprodmempair)). 269.18/34.90 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', omegaIndAx)). 269.18/34.90 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', omega0Ax)). 269.18/34.90 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setunionsingleton1)). 269.18/34.90 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setunionAx)). 269.18/34.90 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setminusSubset2)). 269.18/34.90 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setunionsingleton2)). 269.18/34.90 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', singletonsuniq)). 269.18/34.90 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.QAQCxMG3Yr/E---3.1_5856.p', setukpairinjL1)). 269.18/34.90 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', theprop)). 269.18/34.90 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', cartprodfstin)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', setukpairinjL2)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', iftrue)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', iffalse)). 269.18/34.90 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setukpairinjR11)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', setukpairinjR12)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', setukpairinjR2)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', setukpairinjR)). 269.18/34.90 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', ksndpairEq)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', cartprodfstpairEq)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', cartprodsndpairEq)). 269.18/34.90 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setminusERneg)). 269.18/34.90 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', app)). 269.18/34.90 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', infuncsetfunc)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', ap2p)). 269.18/34.90 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', funcinfuncset)). 269.18/34.90 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', brelnall1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', funcGraphProp1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', funcGraphProp3)). 269.18/34.90 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', funcextLem)). 269.18/34.90 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', funcGraphProp4)). 269.18/34.90 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', funcext2)). 269.18/34.90 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', ifp)). 269.18/34.90 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binunionEcases)). 269.18/34.90 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', upairset2IR)). 269.18/34.90 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', binintersectT_lem)). 269.18/34.90 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binunionT_lem)). 269.18/34.90 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', powersetT_lem)). 269.18/34.90 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', complementT_lem)). 269.18/34.90 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', subsetTI)). 269.18/34.90 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectTELcontra)). 269.18/34.90 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectTERcontra)). 269.18/34.90 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', contrasubsetT2)). 269.18/34.90 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', doubleComplementI1)). 269.18/34.90 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', doubleComplementE1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', complementImpComplementIntersect)). 269.18/34.90 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', complementSubsetComplementIntersect)). 269.18/34.90 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', complementInPowersetComplementIntersect)). 269.18/34.90 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', complementTcontraSubset)). 269.18/34.90 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binunionTILcontra)). 269.18/34.90 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binunionTIRcontra)). 269.18/34.90 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', inIntersectImpInUnion)). 269.18/34.90 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', inIntersectImpInIntersectUnions)). 269.18/34.90 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', inComplementUnionImpInComplement1)). 269.18/34.90 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', binunionTE)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', binunionTEcontra)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', demorgan2a1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', inComplementUnionImpNotIn1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', intersectInPowersetIntersectUnions)). 269.18/34.90 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', inIntersectImpInUnion2)). 269.18/34.90 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', contraSubsetComplement)). 269.18/34.90 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', complementTnotintersectT)). 269.18/34.90 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', doubleComplementEq)). 269.18/34.90 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', doubleComplementSub2)). 269.18/34.90 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', doubleComplementSub1)). 269.18/34.90 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', contrasubsetT3)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', contrasubsetT1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', contrasubsetT)). 269.18/34.90 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', complementTE1)). 269.18/34.90 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', complementTI1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', powersetTE1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', powersetTI1)). 269.18/34.90 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setextT)). 269.18/34.90 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', setminusT_lem)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', iftrueorfalse)). 269.18/34.90 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', theeq)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', ap2apEq2)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', ap2apEq1)). 269.18/34.90 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', funcext)). 269.18/34.90 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', eqbreln)). 269.18/34.90 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', subbreln)). 269.18/34.90 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.QAQCxMG3Yr/E---3.1_5856.p', funcGraphProp2)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', brelnall2)). 269.18/34.90 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', cartprodpairsurjEq)). 269.18/34.90 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', cartprodmempaircEq)). 269.18/34.90 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', cartprodpairmemER)). 269.18/34.90 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', cartprodpairmemEL)). 269.18/34.90 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', cartprodsndin)). 269.18/34.90 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', kpairsurjEq)). 269.18/34.90 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', upairequniteq)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', setukpairinjR1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', setukpairinjL)). 269.18/34.90 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', kfstpairEq)). 269.18/34.90 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setunionsingleton)). 269.18/34.90 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setunionE2)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', ubforcartprodlem3)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', ubforcartprodlem2)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', ubforcartprodlem1)). 269.18/34.90 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.QAQCxMG3Yr/E---3.1_5856.p', upairsubunion)). 269.18/34.90 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', upairset2E)). 269.18/34.90 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', singletoninpowerset)). 269.18/34.90 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setukpairIR)). 269.18/34.90 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setukpairIL)). 269.18/34.90 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', symdiffIneg2)). 269.18/34.90 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setminusSubset1)). 269.18/34.90 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setminusLsub)). 269.18/34.90 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setminusIRneg)). 269.18/34.90 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setminusEL)). 269.18/34.90 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectSubset4)). 269.18/34.90 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', disjointsetsI1)). 269.18/34.90 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectER)). 269.18/34.90 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectSubset3)). 269.18/34.90 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectSubset2)). 269.18/34.90 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectEL)). 269.18/34.90 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectSubset5)). 269.18/34.90 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binunionRsub)). 269.18/34.90 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binunionE)). 269.18/34.90 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', bs114d)). 269.18/34.90 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectSubset1)). 269.18/34.90 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectRsub)). 269.18/34.90 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectLsub)). 269.18/34.90 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binintersectI)). 269.18/34.90 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binunionLsub)). 269.18/34.90 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', binunionIR)). 269.18/34.90 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', powersetsubset)). 269.18/34.90 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', powersetE1)). 269.18/34.90 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', powersetI1)). 269.18/34.90 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setextsub)). 269.18/34.90 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', subset2powerset)). 269.18/34.90 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setadjoinSub2)). 269.18/34.90 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setadjoinSub)). 269.18/34.90 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', subsetTrans)). 269.18/34.90 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', subsetRefl)). 269.18/34.90 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', notequalI2)). 269.18/34.90 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', notsubsetI)). 269.18/34.90 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', emptysetsubset)). 269.18/34.90 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', subsetI2)). 269.18/34.90 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', subsetI1)). 269.18/34.90 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', omega__Cong)). 269.18/34.90 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', powerset__Cong)). 269.18/34.90 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', emptyset__Cong)). 269.18/34.90 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', notdallE)). 269.18/34.90 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', notdexE)). 269.18/34.90 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', prop2setI)). 269.18/34.90 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', quantDeMorgan4)). 269.18/34.90 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', quantDeMorgan2)). 269.18/34.90 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', quantDeMorgan1)). 269.18/34.90 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', vacuousDall)). 269.18/34.90 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', upairsetIL)). 269.18/34.90 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', upairsetE)). 269.18/34.90 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', singletonsswitch)). 269.18/34.90 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', notinsingleton)). 269.18/34.90 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setunionE)). 269.18/34.90 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', powersetE)). 269.18/34.90 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', emptyInPowerset)). 269.18/34.90 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', emptyinPowerset)). 269.18/34.90 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', powersetI)). 269.18/34.90 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setadjoinE)). 269.18/34.90 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', emptyinunitempty)). 269.18/34.90 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setadjoinIL)). 269.18/34.90 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', emptysetimpfalse)). 269.18/34.90 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', prop2setE)). 269.18/34.90 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', foundationAx)). 269.18/34.90 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', omegaSAx)). 269.18/34.90 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', powersetAx)). 269.18/34.90 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', emptysetAx)). 269.18/34.90 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.QAQCxMG3Yr/E---3.1_5856.p', setextAx)). 269.18/34.90 thf(c_0_265, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 269.18/34.90 thf(c_0_266, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 269.18/34.90 thf(c_0_267, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 269.18/34.90 thf(c_0_268, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 269.18/34.90 thf(c_0_269, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 269.18/34.90 thf(c_0_270, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 269.18/34.90 thf(c_0_271, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 269.18/34.90 thf(c_0_272, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 269.18/34.90 thf(c_0_273, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 269.18/34.90 thf(c_0_274, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 269.18/34.90 thf(c_0_275, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 269.18/34.90 thf(c_0_276, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 269.18/34.90 thf(c_0_277, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 269.18/34.90 thf(c_0_278, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 269.18/34.90 thf(c_0_279, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 269.18/34.90 thf(c_0_280, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 269.18/34.90 thf(c_0_281, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 269.18/34.90 thf(c_0_282, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 269.18/34.90 thf(c_0_283, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 269.18/34.90 thf(c_0_284, plain, ((funcImageSingleton)<=>![X4:$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])). 269.18/34.90 thf(c_0_285, 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])). 269.18/34.90 thf(c_0_286, 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])). 269.18/34.90 thf(c_0_287, 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])). 269.18/34.90 thf(c_0_288, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 269.18/34.90 thf(c_0_289, plain, ((iffalseProp2)<=>![X4:$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])). 269.18/34.90 thf(c_0_290, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 269.18/34.90 thf(c_0_291, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 269.18/34.90 thf(c_0_292, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 269.18/34.90 thf(c_0_293, plain, ((beta2)<=>![X4:$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])). 269.18/34.90 thf(c_0_294, 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])). 269.18/34.90 thf(c_0_295, 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])). 269.18/34.90 thf(c_0_296, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 269.18/34.90 thf(c_0_297, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 269.18/34.90 thf(c_0_298, plain, ((lamProp)<=>![X4:$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])). 269.18/34.90 thf(c_0_299, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 269.18/34.90 thf(c_0_300, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 269.18/34.90 thf(c_0_301, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 269.18/34.90 thf(c_0_302, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 269.18/34.90 thf(c_0_303, plain, ((ex1I)<=>![X4:$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])). 269.18/34.90 thf(c_0_304, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 269.18/34.90 thf(c_0_305, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 269.18/34.90 thf(c_0_306, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 269.18/34.90 thf(c_0_307, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 269.18/34.90 thf(c_0_308, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 269.18/34.90 thf(c_0_309, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 269.18/34.90 thf(c_0_310, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 269.18/34.90 thf(c_0_311, 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])). 269.18/34.90 thf(c_0_312, 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])). 269.18/34.90 thf(c_0_313, 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])). 269.18/34.90 thf(c_0_314, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 269.18/34.90 thf(c_0_315, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 269.18/34.90 thf(c_0_316, plain, ((epred1_0)<=>![X1688:$i]:(?[X1689:$i]:((((![X1690:$i]:(((in @ X1690 @ X1689)=>![X1691:$i]:(((in @ X1691 @ X1690)=>(in @ X1691 @ X1688)))))&![X1692:$i, X1693:$i]:((((in @ X1692 @ X1688)&(in @ X1693 @ X1688))=>(![X1694:$i]:(((in @ X1694 @ X1689)=>((in @ X1692 @ X1694)<=>(in @ X1693 @ X1694))))=>((X1692)=(X1693))))))&![X1695:$i, X1696:$i]:((((in @ X1695 @ X1689)&(in @ X1696 @ X1689))=>(![X1697:$i]:(((in @ X1697 @ X1695)=>(in @ X1697 @ X1696)))|![X1698:$i]:(((in @ X1698 @ X1696)=>(in @ X1698 @ X1695)))))))&![X1699:$i]:(((![X1700:$i]:(((in @ X1700 @ X1699)=>(in @ X1700 @ X1688)))&?[X1701:$i]:((in @ X1701 @ X1699)))=>?[X1702:$i, X1703:$i]:(((((in @ X1702 @ X1689)&(in @ X1703 @ X1699))&~(?[X1704:$i]:(((in @ X1704 @ X1702)&(in @ X1704 @ X1699)))))&![X1705:$i]:(((in @ X1705 @ X1689)=>(![X1706:$i]:(((in @ X1706 @ X1705)=>(in @ X1706 @ X1702)))|(in @ X1703 @ X1705)))))))))))), introduced(definition)). 269.18/34.90 thf(c_0_317, negated_conjecture, ~((![X888:$i, X889:$i]:((![X890:$i]:(((in @ X890 @ X888)<=>(in @ X890 @ X889)))=>((X888)=(X889))))=>(![X891:$i]:(~(in @ X891 @ emptyset))=>(![X1719:$i, X1720:$i, X1721:$i]:(((in @ X1721 @ (setadjoin @ X1719 @ X1720))<=>(((X1721)=(X1719))|(in @ X1721 @ X1720))))=>(![X892:$i, X893:$i]:(((in @ X893 @ (powerset @ X892))<=>![X894:$i]:(((in @ X894 @ X893)=>(in @ X894 @ X892)))))=>(![X1716:$i, X1717:$i]:(((in @ X1717 @ (setunion @ X1716))<=>?[X1718:$i]:(((in @ X1717 @ X1718)&(in @ X1718 @ X1716)))))=>((in @ emptyset @ omega)=>(![X895:$i]:(((in @ X895 @ omega)=>(in @ (setadjoin @ X895 @ X895) @ omega)))=>(![X1713:$i]:((((in @ emptyset @ X1713)&![X1714:$i]:((((in @ X1714 @ omega)&(in @ X1714 @ X1713))=>(in @ (setadjoin @ X1714 @ X1714) @ X1713))))=>![X1715:$i]:(((in @ X1715 @ omega)=>(in @ X1715 @ X1713)))))=>(![X1707:$i > $i > $o, X1708:$i]:((![X1709:$i]:(((in @ X1709 @ X1708)=>(exu @ (X1707 @ X1709))))=>?[X1710:$i]:(![X1711:$i]:(((in @ X1711 @ X1710)<=>?[X1712:$i]:(((in @ X1712 @ X1708)&(X1707 @ X1712 @ X1711))))))))=>(![X896:$i]:((?[X897:$i]:((in @ X897 @ X896))=>?[X898:$i]:(((in @ X898 @ X896)&~(?[X899:$i]:(((in @ X899 @ X898)&(in @ X899 @ X896))))))))=>((epred1_0)=>(![X1687:$i > $o]:(((exu @ X1687)=>(X1687 @ (descr @ (^[Z0/* 17 */:$i]:(X1687 @ Z0))))))=>(![X1684:$i, X1685:$i > $o, X1686:$i]:(((in @ X1686 @ X1684)=>((X1685 @ X1686)=>(in @ X1686 @ (dsetconstr @ X1684 @ X1685)))))=>(![X900:$i, X901:$i > $o, X902:$i]:(((in @ X902 @ (dsetconstr @ X900 @ X901))=>(in @ X902 @ X900)))=>(![X903:$i, X904:$i > $o, X905:$i]:(((in @ X905 @ (dsetconstr @ X903 @ X904))=>(X904 @ X905)))=>(![X906:$i > $o]:(((exu @ X906)=>?[X907:$i]:(((X906 @ X907)&![X908:$i]:(((X906 @ X908)=>((X907)=(X908))))))))=>(![X909:$o, X910:$i]:(((in @ X910 @ (prop2set @ ((X909))))=>(X909)))=>(![X1682:$i]:(((in @ X1682 @ emptyset)=>![X1683:$o]:((X1683))))=>(![X911:$i]:(((in @ X911 @ emptyset)=>~($true)))=>(![X1681:$i]:(~(in @ X1681 @ emptyset))=>(![X1679:$i > $o]:(((exu @ X1679)=>?[X1680:$i]:((X1679 @ X1680))))=>(![X1675:$i, X1676:$i]:((![X1677:$i]:(((in @ X1677 @ X1675)=>(in @ X1677 @ X1676)))=>(![X1678:$i]:(((in @ X1678 @ X1676)=>(in @ X1678 @ X1675)))=>((X1675)=(X1676)))))=>(![X1673:$i]:((![X1674:$i]:(~(in @ X1674 @ X1673))=>((X1673)=(emptyset))))=>(![X1671:$i]:((![X1672:$i]:(~(in @ X1672 @ X1671))=>((X1671)=(emptyset))))=>(![X1668:$i, X1669:$i > $o, X1670:$i]:(((in @ X1670 @ X1668)=>((in @ X1670 @ (dsetconstr @ X1668 @ X1669))<=>(X1669 @ X1670))))=>(![X1666:$i]:(((nonempty @ X1666)=>?[X1667:$i]:((in @ X1667 @ X1666))))=>(![X1663:$i, X1664:$i > $o, X1665:$i]:(((in @ X1665 @ X1663)=>((X1664 @ X1665)=>(nonempty @ (dsetconstr @ X1663 @ X1664)))))=>(![X1661:$i]:((?[X1662:$i]:((in @ X1662 @ X1661))=>(nonempty @ X1661)))=>(![X912:$i, X913:$i]:((in @ X912 @ (setadjoin @ X912 @ X913)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1658:$i, X1659:$i, X1660:$i]:(((in @ X1660 @ X1659)=>(in @ X1660 @ (setadjoin @ X1658 @ X1659))))=>(![X914:$i, X915:$i, X916:$i]:(((in @ X916 @ (setadjoin @ X914 @ X915))=>![X917:$o]:(((((X916)=(X914))=>(X917))=>(((in @ X916 @ X915)=>(X917))=>(X917))))))=>(![X1655:$i, X1656:$i, X1657:$i]:(((in @ X1657 @ (setadjoin @ X1655 @ X1656))=>(((X1657)=(X1655))|(in @ X1657 @ X1656))))=>(![X1654:$i]:(((dsetconstr @ X1654 @ (^[Z0/* 1 */:$i]:($true)))=(X1654)))=>(![X918:$i, X919:$i]:((![X920:$i]:(((in @ X920 @ X919)=>(in @ X920 @ X918)))=>(in @ X919 @ (powerset @ X918))))=>(![X921:$i]:((in @ emptyset @ (powerset @ X921)))=>(![X922:$i]:((in @ emptyset @ (powerset @ X922)))=>(![X923:$i, X924:$i, X925:$i]:(((in @ X924 @ (powerset @ X923))=>((in @ X925 @ X924)=>(in @ X925 @ X923))))=>(![X1651:$i, X1652:$i, X1653:$i]:(((in @ X1652 @ X1653)=>((in @ X1653 @ X1651)=>(in @ X1652 @ (setunion @ X1651)))))=>(![X926:$i, X927:$i]:(((in @ X927 @ (setunion @ X926))=>![X928:$o]:((![X929:$i]:(((in @ X927 @ X929)=>((in @ X929 @ X926)=>(X928))))=>(X928)))))=>(![X1649:$i, X1650:$i]:(((in @ X1650 @ X1649)=>(in @ X1650 @ (powerset @ (setunion @ X1649)))))=>(![X1646:$i > $o]:(((exu @ X1646)=>?[X1647:$i]:(![X1648:$i]:(((X1646 @ X1648)<=>((X1648)=(X1647)))))))=>(![X1644:$i]:(((nonempty @ X1644)=>?[X1645:$i]:(((in @ X1645 @ X1644)&$true))))=>(![X1642:$i, X1643:$i]:(((in @ X1642 @ (setadjoin @ X1643 @ emptyset))=>((X1642)=(X1643))))=>(![X930:$i, X931:$i]:((((X930)!=(X931))=>~(in @ X931 @ (setadjoin @ X930 @ emptyset))))=>(![X1640:$i, X1641:$i]:((((X1640)=(X1641))=>(in @ X1640 @ (setadjoin @ X1641 @ emptyset))))=>(![X932:$i, X933:$i]:(((in @ X932 @ (setadjoin @ X933 @ emptyset))=>(in @ X933 @ (setadjoin @ X932 @ emptyset))))=>(![X934:$i, X935:$i, X936:$i]:(((in @ X936 @ (setadjoin @ X934 @ (setadjoin @ X935 @ emptyset)))=>(((X936)=(X934))|((X936)=(X935)))))=>(![X937:$i, X938:$i]:((in @ X937 @ (setadjoin @ X937 @ (setadjoin @ X938 @ emptyset))))=>(![X1638:$i, X1639:$i]:((in @ X1639 @ (setadjoin @ X1638 @ (setadjoin @ X1639 @ emptyset))))=>(![X939:$i, X940:$i > $o]:((?[X941:$i]:(((in @ X941 @ X939)&(X940 @ X941)))=>(((dsetconstr @ X939 @ X940)=(emptyset))=>~($true))))=>(![X942:$i > $o, X943:$i]:(((in @ X943 @ emptyset)=>(X942 @ X943)))=>(![X944:$i, X945:$i > $o]:((~(![X946:$i]:(((in @ X946 @ X944)=>(X945 @ X946))))=>?[X947:$i]:(((in @ X947 @ X944)&~((X945 @ X947))))))=>(![X948:$i, X949:$i > $o]:((![X950:$i]:(((in @ X950 @ X948)=>~((X949 @ X950))))=>~(?[X951:$i]:(((in @ X951 @ X948)&(X949 @ X951))))))=>(![X1634:$i, X1635:$i > $o]:((~(?[X1636:$i]:(((in @ X1636 @ X1634)&(X1635 @ X1636))))=>![X1637:$i]:(((in @ X1637 @ X1634)=>~((X1635 @ X1637))))))=>(![X952:$i, X953:$i > $o]:((?[X954:$i]:(((in @ X954 @ X952)&~((X953 @ X954))))=>~(![X955:$i]:(((in @ X955 @ X952)=>(X953 @ X955))))))=>(![X956:$o]:(((X956)=>(in @ emptyset @ (prop2set @ ((X956))))))=>((prop2set2propI)=>(![X957:$i, X958:$i > $o]:((~(?[X959:$i]:(((in @ X959 @ X957)&(X958 @ X959))))=>![X960:$i]:(((in @ X960 @ X957)=>~((X958 @ X960))))))=>(![X961:$i, X962:$i > $o]:((~(![X963:$i]:(((in @ X963 @ X961)=>(X962 @ X963))))=>?[X964:$i]:(((in @ X964 @ X961)&~((X962 @ X964))))))=>(![X1631:$i > $o]:((?[X1632:$i]:(((X1631 @ X1632)&![X1633:$i]:(((X1631 @ X1633)=>((X1632)=(X1633))))))=>(exu @ X1631)))=>(![X1627:$i > $o]:((?[X1628:$i]:((X1627 @ X1628))=>(![X1629:$i, X1630:$i]:(((X1627 @ X1629)=>((X1627 @ X1630)=>((X1629)=(X1630)))))=>(exu @ X1627))))=>(![X965:$i > $o]:((?[X966:$i]:(![X967:$i]:(((X965 @ X967)<=>((X967)=(X966)))))=>(exu @ X965)))=>(![X1623:$i, X1624:$i]:((((X1623)=(X1624))=>![X1625:$i, X1626:$i]:((((X1625)=(X1626))=>((in @ X1625 @ X1623)=>(in @ X1626 @ X1624))))))=>(![X1619:$i, X1620:$i]:((((X1619)=(X1620))=>![X1621:$i, X1622:$i]:((((X1621)=(X1622))=>((in @ X1621 @ X1619)<=>(in @ X1622 @ X1620))))))=>(![X968:$i > $o]:(((exu @ X968)=>![X969:$i, X970:$i]:(((X968 @ X969)=>((X968 @ X970)=>((X969)=(X970)))))))=>(![X971:$i > $o, X972:$i > $o]:((![X973:$i, X974:$i]:((((X973)=(X974))=>((X971 @ X973)<=>(X972 @ X974))))=>((exu @ X971)<=>(exu @ X972))))=>(((emptyset)=(emptyset))=>(![X1615:$i, X1616:$i]:((((X1615)=(X1616))=>![X1617:$i, X1618:$i]:((((X1617)=(X1618))=>((setadjoin @ X1615 @ X1617)=(setadjoin @ X1616 @ X1618))))))=>(![X975:$i, X976:$i]:((((X975)=(X976))=>((powerset @ X975)=(powerset @ X976))))=>(![X1613:$i, X1614:$i]:((((X1613)=(X1614))=>((setunion @ X1613)=(setunion @ X1614))))=>(((omega)=(omega))=>(![X977:$i > $o]:(((exu @ X977)=>![X978:$i, X979:$i]:(((X977 @ X978)=>((X977 @ X979)=>((X978)=(X979)))))))=>(![X980:$i > $o, X981:$i > $o]:((![X982:$i, X983:$i]:((((X982)=(X983))=>((X980 @ X982)<=>(X981 @ X983))))=>((exu @ X980)=>((exu @ X981)=>((descr @ X980)=(descr @ X981))))))=>(![X1607:$i, X1608:$i]:((((X1607)=(X1608))=>![X1609:$i > $o, X1610:$i > $o]:((![X1611:$i]:(((in @ X1611 @ X1607)=>![X1612:$i]:(((in @ X1612 @ X1608)=>(((X1611)=(X1612))=>((X1609 @ X1611)<=>(X1610 @ X1612)))))))=>((dsetconstr @ X1607 @ X1609)=(dsetconstr @ X1608 @ X1610))))))=>(![X984:$i, X985:$i]:((![X986:$i]:(((in @ X986 @ X984)=>(in @ X986 @ X985)))=>(subset @ X984 @ X985)))=>(![X1605:$i, X1606:$i]:((((X1605)=(X1606))=>(subset @ X1606 @ X1605)))=>(![X1603:$i, X1604:$i]:((((X1603)=(X1604))=>(subset @ X1603 @ X1604)))=>(![X987:$i, X988:$i]:((![X989:$i]:(((in @ X989 @ X987)=>(in @ X989 @ X988)))=>(subset @ X987 @ X988)))=>(![X990:$i]:((subset @ emptyset @ X990))=>(![X1600:$i, X1601:$i, X1602:$i]:(((subset @ X1600 @ X1601)=>((in @ X1602 @ X1600)=>(in @ X1602 @ X1601))))=>(![X1597:$i, X1598:$i, X1599:$i]:(((subset @ X1597 @ X1598)=>(~(in @ X1599 @ X1598)=>~(in @ X1599 @ X1597))))=>(![X991:$i, X992:$i, X993:$i]:(((in @ X993 @ X991)=>(~(in @ X993 @ X992)=>~(subset @ X991 @ X992))))=>(![X1595:$i, X1596:$i]:((~(subset @ X1595 @ X1596)=>((X1595)!=(X1596))))=>(![X994:$i, X995:$i, X996:$i]:(((in @ X996 @ X994)=>(~(in @ X996 @ X995)=>((X994)!=(X995)))))=>(![X997:$i]:((subset @ X997 @ X997))=>(![X998:$i, X999:$i, X1000:$i]:(((subset @ X998 @ X999)=>((subset @ X999 @ X1000)=>(subset @ X998 @ X1000))))=>(![X1001:$i, X1002:$i]:((subset @ X1002 @ (setadjoin @ X1001 @ X1002)))=>(![X1003:$i, X1004:$i, X1005:$i]:(((subset @ X1003 @ X1005)=>(subset @ X1003 @ (setadjoin @ X1004 @ X1005))))=>(![X1006:$i, X1007:$i]:(((subset @ X1006 @ X1007)=>(in @ X1006 @ (powerset @ X1007))))=>(![X1008:$i, X1009:$i]:(((subset @ X1008 @ X1009)=>((subset @ X1009 @ X1008)=>((X1008)=(X1009)))))=>(![X1594:$i]:(((subset @ X1594 @ emptyset)=>((X1594)=(emptyset))))=>(![X1010:$i, X1011:$i]:(((subset @ X1011 @ X1010)=>(in @ X1011 @ (powerset @ X1010))))=>(![X1012:$i, X1013:$i]:(((in @ X1013 @ (powerset @ X1012))=>(subset @ X1013 @ X1012)))=>(![X1593:$i]:((in @ X1593 @ (powerset @ X1593)))=>(![X1014:$i, X1015:$i]:(((subset @ X1014 @ X1015)=>(subset @ (powerset @ X1014) @ (powerset @ X1015))))=>(![X1591:$i, X1592:$i > $o]:((in @ (dsetconstr @ X1591 @ X1592) @ (powerset @ X1591)))=>(![X1016:$i, X1017:$i > $o]:((subset @ (dsetconstr @ X1016 @ X1017) @ X1016))=>(![X1588:$i, X1589:$i, X1590:$i]:(((in @ X1590 @ X1588)=>(in @ X1590 @ (binunion @ X1588 @ X1589))))=>(![X1586:$i, X1587:$i]:((in @ X1587 @ (setadjoin @ X1586 @ (setadjoin @ X1587 @ 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setminusER]), c_0_265]), setadjoinAx]), binunionIL]), setminusI]), c_0_266]), inPowerset]), setminusELneg]), subsetemptysetimpeq]), notequalI1]), subsetE2]), setminusILneg]), subsetE]), eqimpsubset1]), symdiffE]), eqimpsubset2]), c_0_267]), setunion__Cong]), symdiffI1]), setadjoin__Cong]), in__Cong]), symdiffI2]), inCongP]), c_0_268]), c_0_269]), quantDeMorgan3]), symdiffIneg1]), upairsetIR]), eqinunit]), secondinupair]), uniqinunit]), nonemptyImpWitness]), subPowSU]), kpairiskpair]), setunionI]), c_0_270]), kpairp]), setadjoinOr]), setadjoinIR]), nonemptyI1]), singletonsubset]), c_0_271]), nonemptyE1]), singletoninpowunion]), c_0_272]), noeltsimpempty]), emptyI]), upairinpowunion]), setext]), c_0_273]), cartprodpairin]), notinemptyset]), emptysetE]), c_0_274]), cartprodmempair1]), c_0_275]), wellorderingAx]), cartprodmempair]), c_0_276]), omegaIndAx]), omega0Ax]), setunionsingleton1]), setunionAx]), setminusSubset2]), setunionsingleton2]), singletonsuniq]), setukpairinjL1]), c_0_277]), theprop]), cartprodfstin]), setukpairinjL2]), iftrue]), iffalse]), setukpairinjR11]), setukpairinjR12]), setukpairinjR2]), setukpairinjR]), c_0_278]), ksndpairEq]), cartprodfstpairEq]), cartprodsndpairEq]), c_0_279]), c_0_280]), setminusERneg]), c_0_281]), c_0_282]), c_0_283]), c_0_284]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), brelnall1]), funcGraphProp1]), funcGraphProp3]), funcextLem]), funcGraphProp4]), funcext2]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), ifp]), binunionEcases]), upairset2IR]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), complementT_lem]), subsetTI]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT2]), doubleComplementI1]), doubleComplementE1]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInIntersectUnions]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), inComplementUnionImpNotIn1]), intersectInPowersetIntersectUnions]), inIntersectImpInUnion2]), contraSubsetComplement]), complementTnotintersectT]), doubleComplementEq]), doubleComplementSub2]), doubleComplementSub1]), contrasubsetT3]), contrasubsetT1]), contrasubsetT]), complementTE1]), complementTI1]), powersetTE1]), powersetTI1]), setextT]), setminusT_lem]), iftrueorfalse]), theeq]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), ap2apEq2]), ap2apEq1]), funcext]), eqbreln]), subbreln]), funcGraphProp2]), c_0_295]), brelnall2]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), c_0_300]), c_0_301]), cartprodpairsurjEq]), cartprodmempaircEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), upairequniteq]), setukpairinjR1]), setukpairinjL]), kfstpairEq]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), setunionsingleton]), setunionE2]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), upairsubunion]), upairset2E]), singletoninpowerset]), setukpairIR]), setukpairIL]), symdiffIneg2]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusEL]), binintersectSubset4]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectEL]), binintersectSubset5]), binunionRsub]), binunionE]), bs114d]), binintersectSubset1]), binintersectRsub]), binintersectLsub]), binintersectI]), binunionLsub]), binunionIR]), c_0_306]), powersetsubset]), powersetE1]), powersetI1]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notsubsetI]), emptysetsubset]), subsetI2]), subsetI1]), c_0_307]), c_0_308]), omega__Cong]), powerset__Cong]), emptyset__Cong]), c_0_309]), c_0_310]), c_0_311]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_312]), upairsetIL]), upairsetE]), singletonsswitch]), notinsingleton]), setunionE]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), setadjoinE]), emptyinunitempty]), setadjoinIL]), emptysetimpfalse]), prop2setE]), c_0_313]), c_0_314]), c_0_315]), foundationAx]), omegaSAx]), powersetAx]), emptysetAx]), setextAx])])]), c_0_316])). 269.18/34.90 thf(c_0_318, negated_conjecture, ![X1722:$i, X1723:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1735:$i, X1736:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1744:$i, X1745:$i > $i > $o, X1746:$i, X1749:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1756:$i, X1757:$i > $o, X1758:$i, X1759:$i > $o, X1760:$i, X1761:$i, X1762:$i > $o, X1763:$i, X1764:$i, X1765:$i > $o, X1766:$i, X1767:$i > $o, X1769:$i, X1770:$o, X1771:$i, X1772:$i, X1773:$o, X1774:$i, X1775:$i, X1776:$i > $o, X1778:$i, X1779:$i, X1782:$i, X1784:$i, X1786:$i, X1787:$i > $o, X1788:$i, X1789:$i, X1791:$i, X1792:$i > $o, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$o, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$o, X1824:$i, X1825:$i, X1826:$i > $o, X1828:$i, X1829:$i, X1830:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i > $o, X1849:$i, X1850:$i > $o, X1851:$i, X1852:$i, X1853:$i > $o, X1854:$i, X1856:$i, X1857:$i > $o, X1859:$i, X1860:$i, X1861:$i > $o, X1863:$i, X1864:$i, X1865:$i > $o, X1866:$i, X1868:$o, X1869:$i, X1870:$i > $o, X1872:$i, X1873:$i, X1874:$i > $o, X1875:$i, X1877:$i > $o, X1878:$i, X1880:$i > $o, X1881:$i, X1884:$i > $o, X1885:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i > $o, X1896:$i, X1897:$i, X1898:$i > $o, X1899:$i > $o, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i > $o, X1911:$i, X1912:$i, X1913:$i > $o, X1914:$i > $o, X1917:$i, X1918:$i, X1919:$i > $o, X1920:$i > $o, X1923:$i, X1924:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i > $o, X1971:$i, X1972:$i > $o, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$o, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$o, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i > $o, X2127:$i, X2128:$i, X2129:$i > $o, X2131:$i, X2132:$i > $o, X2133:$i, X2135:$i, X2136:$i > $o, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i > $i > $o, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i > $i > $o, X2217:$i, X2218:$i, X2219:$i > $i > $o, X2220:$i, X2221:$i, X2222:$i > $i > $o, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i > $i > $o, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i > $i > $o, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i > $i > $o, X2238:$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 > $i, X2266:$i, X2267:$i, X2268:$i > $i, X2270:$i, X2271:$i, X2272:$i > $i, X2274:$i, X2275:$i, X2276:$i, X2277:$i > $o, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i > $o, X2287:$i, X2288:$i, X2289:$i > $o, X2290:$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, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i > $i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i > $i, X2361:$i, X2362:$i, X2363:$i > $i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$o, X2371:$i, X2372:$i, X2373:$i, X2374:$o, X2375:$i, X2376:$i, X2377:$i, X2378:$o, X2379:$i, X2380:$i, X2381:$i, X2382:$o, X2383:$i, X2384:$i, X2385:$i, X2386:$o, X2387:$i, X2388:$i, X2389:$i, X2390:$o, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$o, X2397:$i, X2398:$i, X2399:$i, X2400:$o, X2401:$i, X2402:$i, X2403:$i, X2404:$o, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2425:$i, 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X2429)))&(((in @ (esk70_3 @ X2429 @ X2430 @ X2431) @ X2430)|(in @ X2430 @ (powerset @ X2431))|~(in @ X2431 @ (powerset @ X2429))|~(in @ X2430 @ (powerset @ X2429)))&(~(in @ (esk70_3 @ X2429 @ X2430 @ X2431) @ X2431)|(in @ X2430 @ (powerset @ X2431))|~(in @ X2431 @ (powerset @ X2429))|~(in @ X2430 @ (powerset @ X2429)))))&((~(in @ X2434 @ (powerset @ X2433))|(~(in @ X2435 @ (powerset @ X2433))|(~(in @ X2436 @ X2433)|(~(in @ X2434 @ (powerset @ X2435))|(~(in @ X2436 @ X2434)|(in @ X2436 @ X2435))))))&((~(in @ X2438 @ (powerset @ X2437))|(~(in @ X2439 @ X2437)|(~(in @ X2439 @ X2438)|~(in @ X2439 @ (setminus @ X2437 @ X2438)))))&((~(in @ X2441 @ (powerset @ X2440))|(~(in @ X2442 @ X2440)|((in @ X2442 @ (setminus @ X2440 @ X2441))|(in @ X2442 @ X2441))))&((~(in @ X2444 @ (powerset @ X2443))|(~(in @ X2445 @ (powerset @ X2443))|(~(in @ X2446 @ X2443)|((in @ X2446 @ X2444)|~(in @ X2446 @ (binintersect @ X2444 @ X2445))))))&((~(in @ X2448 @ (powerset @ X2447))|(~(in @ X2449 @ (powerset @ X2447))|(~(in @ X2450 @ X2447)|((in @ X2450 @ X2449)|~(in @ X2450 @ (binintersect @ X2448 @ X2449))))))&((~(in @ X2452 @ (powerset @ X2451))|(~(in @ X2453 @ (powerset @ X2451))|(~(in @ X2454 @ X2451)|(~(subset @ X2452 @ (setminus @ X2451 @ X2453))|(~(in @ X2454 @ X2453)|~(in @ X2454 @ X2452))))))&((~(in @ X2456 @ (powerset @ X2455))|(~(in @ X2457 @ (powerset @ X2455))|(~(in @ X2458 @ X2455)|(~(subset @ X2456 @ X2457)|((in @ X2458 @ X2457)|~(in @ X2458 @ X2456))))))&((~(in @ X2460 @ (powerset @ X2459))|(~(in @ X2461 @ (powerset @ X2459))|(~(subset @ X2460 @ X2461)|(subset @ (setminus @ X2459 @ X2461) @ (setminus @ X2459 @ X2460)))))&((~(in @ X2463 @ (powerset @ X2462))|(~(in @ X2464 @ (powerset @ X2462))|(~(subset @ (setminus @ X2462 @ X2464) @ (setminus @ X2462 @ X2463))|(subset @ X2463 @ X2464))))&((~(in @ X2466 @ (powerset @ X2465))|(~(in @ X2467 @ X2465)|(~(in @ X2467 @ X2466)|(in @ X2467 @ (setminus @ X2465 @ (setminus @ X2465 @ X2466))))))&((~(in @ X2469 @ (powerset @ X2468))|(~(in @ X2470 @ X2468)|(~(in @ X2470 @ (setminus @ X2468 @ (setminus @ X2468 @ X2469)))|(in @ X2470 @ X2469))))&((~(in @ X2472 @ (powerset @ X2471))|(subset @ X2472 @ (setminus @ X2471 @ (setminus @ X2471 @ X2472))))&((~(in @ X2474 @ (powerset @ X2473))|(subset @ (setminus @ X2473 @ (setminus @ X2473 @ X2474)) @ X2474))&((~(in @ X2476 @ (powerset @ X2475))|((X2476)=(setminus @ X2475 @ (setminus @ X2475 @ X2476))))&((~(in @ X2478 @ (powerset @ X2477))|(~(in @ X2479 @ (powerset @ X2477))|(~(in @ X2480 @ X2477)|(~(in @ X2480 @ (setminus @ X2477 @ X2478))|~(in @ X2480 @ (binintersect @ X2478 @ X2479))))))&((~(in @ X2482 @ (powerset @ X2481))|(~(in @ X2483 @ (powerset @ X2481))|(~(in @ X2484 @ X2481)|(~(in @ X2484 @ (setminus @ X2481 @ X2482))|(in @ X2484 @ (setminus @ X2481 @ (binintersect @ X2482 @ X2483)))))))&((~(in @ X2486 @ (powerset @ X2485))|(~(in @ X2487 @ (powerset @ X2485))|(subset @ (setminus @ X2485 @ X2486) @ (setminus @ X2485 @ (binintersect @ X2486 @ X2487)))))&((~(in @ X2489 @ (powerset @ X2488))|(~(in @ X2490 @ (powerset @ X2488))|(in @ (setminus @ X2488 @ X2489) @ (powerset @ (setminus @ X2488 @ (binintersect @ X2489 @ X2490))))))&((~(in @ X2492 @ (powerset @ X2491))|(~(in @ X2493 @ (powerset @ X2491))|(~(subset @ X2492 @ (setminus @ X2491 @ X2493))|(~(in @ X2494 @ X2491)|(~(in @ X2494 @ X2493)|(in @ X2494 @ (setminus @ X2491 @ X2492)))))))&((~(in @ X2496 @ (powerset @ X2495))|(~(in @ X2497 @ (powerset @ X2495))|(~(subset @ X2496 @ (setminus @ X2495 @ X2497))|(subset @ X2497 @ (setminus @ X2495 @ X2496)))))&((~(in @ X2499 @ (powerset @ X2498))|(~(in @ X2500 @ (powerset @ X2498))|(~(in @ X2501 @ X2498)|((in @ X2501 @ (binunion @ X2499 @ X2500))|~(in @ X2501 @ X2499)))))&((~(in @ X2503 @ (powerset @ X2502))|(~(in @ X2504 @ (powerset @ X2502))|(~(in @ X2505 @ X2502)|((in @ X2505 @ (binunion @ X2503 @ X2504))|~(in @ X2505 @ X2504)))))&((~(in @ X2507 @ (powerset @ X2506))|(~(in @ X2508 @ (powerset @ X2506))|(~(in @ X2509 @ (powerset @ X2506))|(~(in @ X2510 @ X2506)|(~(in @ X2510 @ (binintersect @ X2507 @ X2508))|(in @ X2510 @ (binunion @ X2507 @ X2509)))))))&((~(in @ X2512 @ (powerset @ X2511))|(~(in @ X2513 @ (powerset @ X2511))|(~(in @ X2514 @ (powerset @ X2511))|(~(in @ X2515 @ X2511)|(~(in @ X2515 @ (binintersect @ X2512 @ X2513))|(in @ X2515 @ (binunion @ X2513 @ X2514)))))))&((~(in @ X2517 @ (powerset @ X2516))|(~(in @ X2518 @ (powerset @ X2516))|(~(in @ X2519 @ (powerset @ X2516))|(~(in @ X2520 @ X2516)|(~(in @ X2520 @ (binintersect @ X2517 @ X2518))|(in @ X2520 @ (binintersect @ (binunion @ X2517 @ X2519) @ (binunion @ X2518 @ X2519))))))))&((~(in @ X2522 @ (powerset @ X2521))|(~(in @ X2523 @ (powerset @ X2521))|(~(in @ X2524 @ (powerset @ X2521))|(in @ (binintersect @ X2522 @ X2523) @ (powerset @ (binintersect @ (binunion @ X2522 @ X2524) @ (binunion @ X2523 @ X2524)))))))&((~(in @ X2526 @ (powerset @ X2525))|(~(in @ X2527 @ (powerset @ X2525))|(~(in @ X2528 @ X2525)|(~(in @ X2528 @ (setminus @ X2525 @ (binunion @ X2526 @ X2527)))|~(in @ X2528 @ X2526)))))&((~(in @ X2530 @ (powerset @ X2529))|(~(in @ X2531 @ (powerset @ X2529))|(~(in @ X2532 @ X2529)|(~(in @ X2532 @ (setminus @ X2529 @ (binunion @ X2530 @ X2531)))|(in @ X2532 @ (setminus @ X2529 @ X2530))))))&(((((in @ X2537 @ X2535)|(X2536)|(in @ X2537 @ X2534)|~(in @ X2537 @ (binunion @ X2534 @ X2535))|~(in @ X2537 @ X2533)|~(in @ X2535 @ (powerset @ X2533))|~(in @ X2534 @ (powerset @ X2533)))&(~(X2536)|(X2536)|(in @ X2537 @ X2534)|~(in @ X2537 @ (binunion @ X2534 @ X2535))|~(in @ X2537 @ X2533)|~(in @ X2535 @ (powerset @ X2533))|~(in @ X2534 @ (powerset @ X2533))))&(((in @ X2537 @ X2535)|(X2536)|~(X2536)|~(in @ X2537 @ (binunion @ X2534 @ X2535))|~(in @ X2537 @ X2533)|~(in @ X2535 @ (powerset @ X2533))|~(in @ X2534 @ (powerset @ X2533)))&(~(X2536)|(X2536)|~(X2536)|~(in @ X2537 @ (binunion @ X2534 @ X2535))|~(in @ X2537 @ X2533)|~(in @ X2535 @ (powerset @ X2533))|~(in @ X2534 @ (powerset @ X2533)))))&((~(in @ X2539 @ (powerset @ X2538))|(~(in @ X2540 @ (powerset @ X2538))|(~(in @ X2541 @ X2538)|((in @ X2541 @ X2539)|((in @ X2541 @ X2540)|~(in @ X2541 @ (binunion @ X2539 @ X2540)))))))&((~(in @ X2543 @ (powerset @ X2542))|(~(in @ X2544 @ (powerset @ X2542))|(~(in @ X2545 @ X2542)|(~(in @ X2545 @ (setminus @ X2542 @ (binunion @ X2543 @ X2544)))|(in @ X2545 @ (setminus @ X2542 @ X2543))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&~(in @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)) @ (powerset @ (setminus @ esk71_0 @ esk72_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_317])])])])])])])). 269.18/34.90 thf(c_0_319, negated_conjecture, ~((in @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)) @ (powerset @ (setminus @ esk71_0 @ esk72_0)))), inference(split_conjunct,[status(thm)],[c_0_318])). 269.18/34.90 thf(c_0_320, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_318])). 269.18/34.90 thf(c_0_321, negated_conjecture, ~((subset @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)) @ (setminus @ esk71_0 @ esk72_0))), inference(spm,[status(thm)],[c_0_319, c_0_320])). 269.18/34.90 thf(c_0_322, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ (setminus @ X3 @ X4) @ (setminus @ X3 @ X2))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((subset @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_318])). 269.18/34.90 thf(c_0_323, negated_conjecture, (in @ esk72_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_318])). 269.18/34.90 thf(c_0_324, negated_conjecture, ![X2:$i, X3:$i]:((subset @ X2 @ (binunion @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_318])). 269.18/34.90 thf(c_0_325, negated_conjecture, ~((in @ (binunion @ esk72_0 @ esk73_0) @ (powerset @ esk71_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_321, c_0_322]), c_0_323]), c_0_324])])). 269.18/34.90 thf(c_0_326, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ (binunion @ X2 @ X4) @ (powerset @ X3))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_318])). 269.18/34.90 thf(c_0_327, negated_conjecture, (in @ esk73_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_318])). 269.18/34.90 thf(c_0_328, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325, c_0_326]), c_0_327]), c_0_323])]), ['proof']). 269.18/34.90 # SZS output end CNFRefutation 269.18/34.90 # Parsed axioms : 573 269.18/34.90 # Removed by relevancy pruning/SinE : 308 269.18/34.90 # Initial clauses : 428 269.18/34.90 # Removed in clause preprocessing : 37 269.18/34.90 # Initial clauses in saturation : 391 269.18/34.90 # Processed clauses : 829 269.18/34.90 # ...of these trivial : 13 269.18/34.90 # ...subsumed : 117 269.18/34.90 # ...remaining for further processing : 699 269.18/34.90 # Other redundant clauses eliminated : 53 269.18/34.90 # Clauses deleted for lack of memory : 0 269.18/34.90 # Backward-subsumed : 1 269.18/34.90 # Backward-rewritten : 12 269.18/34.90 # Generated clauses : 5487 269.18/34.90 # ...of the previous two non-redundant : 5201 269.18/34.90 # ...aggressively subsumed : 0 269.18/34.90 # Contextual simplify-reflections : 8 269.18/34.90 # Paramodulations : 5401 269.18/34.90 # Factorizations : 2 269.18/34.90 # NegExts : 0 269.18/34.90 # Equation resolutions : 58 269.18/34.90 # Disequality decompositions : 0 269.18/34.90 # Total rewrite steps : 302 269.18/34.90 # ...of those cached : 205 269.18/34.90 # Propositional unsat checks : 0 269.18/34.90 # Propositional check models : 0 269.18/34.90 # Propositional check unsatisfiable : 0 269.18/34.90 # Propositional clauses : 0 269.18/34.90 # Propositional clauses after purity: 0 269.18/34.90 # Propositional unsat core size : 0 269.18/34.90 # Propositional preprocessing time : 0.000 269.18/34.90 # Propositional encoding time : 0.000 269.18/34.90 # Propositional solver time : 0.000 269.18/34.90 # Success case prop preproc time : 0.000 269.18/34.90 # Success case prop encoding time : 0.000 269.18/34.90 # Success case prop solver time : 0.000 269.18/34.90 # Current number of processed clauses : 331 269.18/34.90 # Positive orientable unit clauses : 58 269.18/34.90 # Positive unorientable unit clauses: 0 269.18/34.90 # Negative unit clauses : 14 269.18/34.90 # Non-unit-clauses : 259 269.18/34.90 # Current number of unprocessed clauses: 5067 269.18/34.90 # ...number of literals in the above : 17210 269.18/34.90 # Current number of archived formulas : 0 269.18/34.90 # Current number of archived clauses : 352 269.18/34.90 # Clause-clause subsumption calls (NU) : 37758 269.18/34.90 # Rec. Clause-clause subsumption calls : 19726 269.18/34.90 # Non-unit clause-clause subsumptions : 77 269.18/34.90 # Unit Clause-clause subsumption calls : 485 269.18/34.90 # Rewrite failures with RHS unbound : 0 269.18/34.90 # BW rewrite match attempts : 37 269.18/34.90 # BW rewrite match successes : 8 269.18/34.90 # Condensation attempts : 829 269.18/34.90 # Condensation successes : 8 269.18/34.90 # Termbank termtop insertions : 146731 269.18/34.90 # Search garbage collected termcells : 26934 269.18/34.90 269.18/34.90 # ------------------------------------------------- 269.18/34.90 # User time : 32.418 s 269.18/34.90 # System time : 0.994 s 269.18/34.90 # Total time : 33.412 s 269.18/34.90 # Maximum resident set size: 8728 pages 269.18/34.90 269.18/34.90 # ------------------------------------------------- 269.18/34.90 # User time : 32.440 s 269.18/34.90 # System time : 0.997 s 269.18/34.90 # Total time : 33.437 s 269.18/34.90 # Maximum resident set size: 2480 pages 269.18/34.90 % E---3.1 exiting 269.18/34.90 % E exiting 269.18/34.90 EOF